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      1 /* ----------------------------------------------------------------------
      2 * Copyright (C) 2010-2014 ARM Limited. All rights reserved.
      3 *
      4 * $Date:        12. March 2014
      5 * $Revision:    V1.4.4
      6 *
      7 * Project:      CMSIS DSP Library
      8 * Title:        arm_math.h
      9 *
     10 * Description:  Public header file for CMSIS DSP Library
     11 *
     12 * Target Processor: Cortex-M7/Cortex-M4/Cortex-M3/Cortex-M0
     13 *
     14 * Redistribution and use in source and binary forms, with or without
     15 * modification, are permitted provided that the following conditions
     16 * are met:
     17 *   - Redistributions of source code must retain the above copyright
     18 *     notice, this list of conditions and the following disclaimer.
     19 *   - Redistributions in binary form must reproduce the above copyright
     20 *     notice, this list of conditions and the following disclaimer in
     21 *     the documentation and/or other materials provided with the
     22 *     distribution.
     23 *   - Neither the name of ARM LIMITED nor the names of its contributors
     24 *     may be used to endorse or promote products derived from this
     25 *     software without specific prior written permission.
     26 *
     27 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
     28 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
     29 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
     30 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
     31 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
     32 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
     33 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
     34 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
     35 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     36 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
     37 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
     38 * POSSIBILITY OF SUCH DAMAGE.
     39  * -------------------------------------------------------------------- */
     40 
     41 /**
     42    \mainpage CMSIS DSP Software Library
     43    *
     44    * Introduction
     45    * ------------
     46    *
     47    * This user manual describes the CMSIS DSP software library,
     48    * a suite of common signal processing functions for use on Cortex-M processor based devices.
     49    *
     50    * The library is divided into a number of functions each covering a specific category:
     51    * - Basic math functions
     52    * - Fast math functions
     53    * - Complex math functions
     54    * - Filters
     55    * - Matrix functions
     56    * - Transforms
     57    * - Motor control functions
     58    * - Statistical functions
     59    * - Support functions
     60    * - Interpolation functions
     61    *
     62    * The library has separate functions for operating on 8-bit integers, 16-bit integers,
     63    * 32-bit integer and 32-bit floating-point values.
     64    *
     65    * Using the Library
     66    * ------------
     67    *
     68    * The library installer contains prebuilt versions of the libraries in the <code>Lib</code> folder.
     69    * - arm_cortexM4lf_math.lib (Little endian and Floating Point Unit on Cortex-M4)
     70    * - arm_cortexM4bf_math.lib (Big endian and Floating Point Unit on Cortex-M4)
     71    * - arm_cortexM4l_math.lib (Little endian on Cortex-M4)
     72    * - arm_cortexM4b_math.lib (Big endian on Cortex-M4)
     73    * - arm_cortexM3l_math.lib (Little endian on Cortex-M3)
     74    * - arm_cortexM3b_math.lib (Big endian on Cortex-M3)
     75    * - arm_cortexM0l_math.lib (Little endian on Cortex-M0)
     76    * - arm_cortexM0b_math.lib (Big endian on Cortex-M3)
     77    *
     78    * The library functions are declared in the public file <code>arm_math.h</code> which is placed in the <code>Include</code> folder.
     79    * Simply include this file and link the appropriate library in the application and begin calling the library functions. The Library supports single
     80    * public header file <code> arm_math.h</code> for Cortex-M4/M3/M0 with little endian and big endian. Same header file will be used for floating point unit(FPU) variants.
     81    * Define the appropriate pre processor MACRO ARM_MATH_CM4 or  ARM_MATH_CM3 or
     82    * ARM_MATH_CM0 or ARM_MATH_CM0PLUS depending on the target processor in the application.
     83    *
     84    * Examples
     85    * --------
     86    *
     87    * The library ships with a number of examples which demonstrate how to use the library functions.
     88    *
     89    * Toolchain Support
     90    * ------------
     91    *
     92    * The library has been developed and tested with MDK-ARM version 4.60.
     93    * The library is being tested in GCC and IAR toolchains and updates on this activity will be made available shortly.
     94    *
     95    * Building the Library
     96    * ------------
     97    *
     98    * The library installer contains a project file to re build libraries on MDK-ARM Tool chain in the <code>CMSIS\\DSP_Lib\\Source\\ARM</code> folder.
     99    * - arm_cortexM_math.uvproj
    100    *
    101    *
    102    * The libraries can be built by opening the arm_cortexM_math.uvproj project in MDK-ARM, selecting a specific target, and defining the optional pre processor MACROs detailed above.
    103    *
    104    * Pre-processor Macros
    105    * ------------
    106    *
    107    * Each library project have differant pre-processor macros.
    108    *
    109    * - UNALIGNED_SUPPORT_DISABLE:
    110    *
    111    * Define macro UNALIGNED_SUPPORT_DISABLE, If the silicon does not support unaligned memory access
    112    *
    113    * - ARM_MATH_BIG_ENDIAN:
    114    *
    115    * Define macro ARM_MATH_BIG_ENDIAN to build the library for big endian targets. By default library builds for little endian targets.
    116    *
    117    * - ARM_MATH_MATRIX_CHECK:
    118    *
    119    * Define macro ARM_MATH_MATRIX_CHECK for checking on the input and output sizes of matrices
    120    *
    121    * - ARM_MATH_ROUNDING:
    122    *
    123    * Define macro ARM_MATH_ROUNDING for rounding on support functions
    124    *
    125    * - ARM_MATH_CMx:
    126    *
    127    * Define macro ARM_MATH_CM4 for building the library on Cortex-M4 target, ARM_MATH_CM3 for building library on Cortex-M3 target
    128    * and ARM_MATH_CM0 for building library on cortex-M0 target, ARM_MATH_CM0PLUS for building library on cortex-M0+ target.
    129    *
    130    * - __FPU_PRESENT:
    131    *
    132    * Initialize macro __FPU_PRESENT = 1 when building on FPU supported Targets. Enable this macro for M4bf and M4lf libraries
    133    *
    134    * <hr>
    135    * CMSIS-DSP in ARM::CMSIS Pack
    136    * -----------------------------
    137    *
    138    * The following files relevant to CMSIS-DSP are present in the <b>ARM::CMSIS</b> Pack directories:
    139    * |File/Folder                   |Content                                                                 |
    140    * |------------------------------|------------------------------------------------------------------------|
    141    * |\b CMSIS\\Documentation\\DSP  | This documentation                                                     |
    142    * |\b CMSIS\\DSP_Lib             | Software license agreement (license.txt)                               |
    143    * |\b CMSIS\\DSP_Lib\\Examples   | Example projects demonstrating the usage of the library functions      |
    144    * |\b CMSIS\\DSP_Lib\\Source     | Source files for rebuilding the library                                |
    145    *
    146    * <hr>
    147    * Revision History of CMSIS-DSP
    148    * ------------
    149    * Please refer to \ref ChangeLog_pg.
    150    *
    151    * Copyright Notice
    152    * ------------
    153    *
    154    * Copyright (C) 2010-2014 ARM Limited. All rights reserved.
    155    */
    156 
    157 
    158 /**
    159  * @defgroup groupMath Basic Math Functions
    160  */
    161 
    162 /**
    163  * @defgroup groupFastMath Fast Math Functions
    164  * This set of functions provides a fast approximation to sine, cosine, and square root.
    165  * As compared to most of the other functions in the CMSIS math library, the fast math functions
    166  * operate on individual values and not arrays.
    167  * There are separate functions for Q15, Q31, and floating-point data.
    168  *
    169  */
    170 
    171 /**
    172  * @defgroup groupCmplxMath Complex Math Functions
    173  * This set of functions operates on complex data vectors.
    174  * The data in the complex arrays is stored in an interleaved fashion
    175  * (real, imag, real, imag, ...).
    176  * In the API functions, the number of samples in a complex array refers
    177  * to the number of complex values; the array contains twice this number of
    178  * real values.
    179  */
    180 
    181 /**
    182  * @defgroup groupFilters Filtering Functions
    183  */
    184 
    185 /**
    186  * @defgroup groupMatrix Matrix Functions
    187  *
    188  * This set of functions provides basic matrix math operations.
    189  * The functions operate on matrix data structures.  For example,
    190  * the type
    191  * definition for the floating-point matrix structure is shown
    192  * below:
    193  * <pre>
    194  *     typedef struct
    195  *     {
    196  *       uint16_t numRows;     // number of rows of the matrix.
    197  *       uint16_t numCols;     // number of columns of the matrix.
    198  *       float32_t *pData;     // points to the data of the matrix.
    199  *     } arm_matrix_instance_f32;
    200  * </pre>
    201  * There are similar definitions for Q15 and Q31 data types.
    202  *
    203  * The structure specifies the size of the matrix and then points to
    204  * an array of data.  The array is of size <code>numRows X numCols</code>
    205  * and the values are arranged in row order.  That is, the
    206  * matrix element (i, j) is stored at:
    207  * <pre>
    208  *     pData[i*numCols + j]
    209  * </pre>
    210  *
    211  * \par Init Functions
    212  * There is an associated initialization function for each type of matrix
    213  * data structure.
    214  * The initialization function sets the values of the internal structure fields.
    215  * Refer to the function <code>arm_mat_init_f32()</code>, <code>arm_mat_init_q31()</code>
    216  * and <code>arm_mat_init_q15()</code> for floating-point, Q31 and Q15 types,  respectively.
    217  *
    218  * \par
    219  * Use of the initialization function is optional. However, if initialization function is used
    220  * then the instance structure cannot be placed into a const data section.
    221  * To place the instance structure in a const data
    222  * section, manually initialize the data structure.  For example:
    223  * <pre>
    224  * <code>arm_matrix_instance_f32 S = {nRows, nColumns, pData};</code>
    225  * <code>arm_matrix_instance_q31 S = {nRows, nColumns, pData};</code>
    226  * <code>arm_matrix_instance_q15 S = {nRows, nColumns, pData};</code>
    227  * </pre>
    228  * where <code>nRows</code> specifies the number of rows, <code>nColumns</code>
    229  * specifies the number of columns, and <code>pData</code> points to the
    230  * data array.
    231  *
    232  * \par Size Checking
    233  * By default all of the matrix functions perform size checking on the input and
    234  * output matrices.  For example, the matrix addition function verifies that the
    235  * two input matrices and the output matrix all have the same number of rows and
    236  * columns.  If the size check fails the functions return:
    237  * <pre>
    238  *     ARM_MATH_SIZE_MISMATCH
    239  * </pre>
    240  * Otherwise the functions return
    241  * <pre>
    242  *     ARM_MATH_SUCCESS
    243  * </pre>
    244  * There is some overhead associated with this matrix size checking.
    245  * The matrix size checking is enabled via the \#define
    246  * <pre>
    247  *     ARM_MATH_MATRIX_CHECK
    248  * </pre>
    249  * within the library project settings.  By default this macro is defined
    250  * and size checking is enabled.  By changing the project settings and
    251  * undefining this macro size checking is eliminated and the functions
    252  * run a bit faster.  With size checking disabled the functions always
    253  * return <code>ARM_MATH_SUCCESS</code>.
    254  */
    255 
    256 /**
    257  * @defgroup groupTransforms Transform Functions
    258  */
    259 
    260 /**
    261  * @defgroup groupController Controller Functions
    262  */
    263 
    264 /**
    265  * @defgroup groupStats Statistics Functions
    266  */
    267 /**
    268  * @defgroup groupSupport Support Functions
    269  */
    270 
    271 /**
    272  * @defgroup groupInterpolation Interpolation Functions
    273  * These functions perform 1- and 2-dimensional interpolation of data.
    274  * Linear interpolation is used for 1-dimensional data and
    275  * bilinear interpolation is used for 2-dimensional data.
    276  */
    277 
    278 /**
    279  * @defgroup groupExamples Examples
    280  */
    281 #ifndef _ARM_MATH_H
    282 #define _ARM_MATH_H
    283 
    284 #define __CMSIS_GENERIC         /* disable NVIC and Systick functions */
    285 
    286 #if defined(ARM_MATH_CM7)
    287   #include "core_cm7.h"
    288 #elif defined (ARM_MATH_CM4)
    289   #include "core_cm4.h"
    290 #elif defined (ARM_MATH_CM3)
    291   #include "core_cm3.h"
    292 #elif defined (ARM_MATH_CM0)
    293   #include "core_cm0.h"
    294 #define ARM_MATH_CM0_FAMILY
    295   #elif defined (ARM_MATH_CM0PLUS)
    296 #include "core_cm0plus.h"
    297   #define ARM_MATH_CM0_FAMILY
    298 #else
    299   #error "Define according the used Cortex core ARM_MATH_CM7, ARM_MATH_CM4, ARM_MATH_CM3, ARM_MATH_CM0PLUS or ARM_MATH_CM0"
    300 #endif
    301 
    302 #undef  __CMSIS_GENERIC         /* enable NVIC and Systick functions */
    303 #include "string.h"
    304 #include "math.h"
    305 #ifdef  __cplusplus
    306 extern "C"
    307 {
    308 #endif
    309 
    310 
    311   /**
    312    * @brief Macros required for reciprocal calculation in Normalized LMS
    313    */
    314 
    315 #define DELTA_Q31    (0x100)
    316 #define DELTA_Q15    0x5
    317 #define INDEX_MASK   0x0000003F
    318 #ifndef PI
    319 #define PI           3.14159265358979f
    320 #endif
    321 
    322   /**
    323    * @brief Macros required for SINE and COSINE Fast math approximations
    324    */
    325 
    326 #define FAST_MATH_TABLE_SIZE  512
    327 #define FAST_MATH_Q31_SHIFT   (32 - 10)
    328 #define FAST_MATH_Q15_SHIFT   (16 - 10)
    329 #define CONTROLLER_Q31_SHIFT  (32 - 9)
    330 #define TABLE_SIZE  256
    331 #define TABLE_SPACING_Q31     0x400000
    332 #define TABLE_SPACING_Q15     0x80
    333 
    334   /**
    335    * @brief Macros required for SINE and COSINE Controller functions
    336    */
    337   /* 1.31(q31) Fixed value of 2/360 */
    338   /* -1 to +1 is divided into 360 values so total spacing is (2/360) */
    339 #define INPUT_SPACING      0xB60B61
    340 
    341   /**
    342    * @brief Macro for Unaligned Support
    343    */
    344 #ifndef UNALIGNED_SUPPORT_DISABLE
    345     #define ALIGN4
    346 #else
    347   #if defined  (__GNUC__)
    348     #define ALIGN4 __attribute__((aligned(4)))
    349   #else
    350     #define ALIGN4 __align(4)
    351   #endif
    352 #endif  /*  #ifndef UNALIGNED_SUPPORT_DISABLE  */
    353 
    354   /**
    355    * @brief Error status returned by some functions in the library.
    356    */
    357 
    358   typedef enum
    359   {
    360     ARM_MATH_SUCCESS = 0,                /**< No error */
    361     ARM_MATH_ARGUMENT_ERROR = -1,        /**< One or more arguments are incorrect */
    362     ARM_MATH_LENGTH_ERROR = -2,          /**< Length of data buffer is incorrect */
    363     ARM_MATH_SIZE_MISMATCH = -3,         /**< Size of matrices is not compatible with the operation. */
    364     ARM_MATH_NANINF = -4,                /**< Not-a-number (NaN) or infinity is generated */
    365     ARM_MATH_SINGULAR = -5,              /**< Generated by matrix inversion if the input matrix is singular and cannot be inverted. */
    366     ARM_MATH_TEST_FAILURE = -6           /**< Test Failed  */
    367   } arm_status;
    368 
    369   /**
    370    * @brief 8-bit fractional data type in 1.7 format.
    371    */
    372   typedef int8_t q7_t;
    373 
    374   /**
    375    * @brief 16-bit fractional data type in 1.15 format.
    376    */
    377   typedef int16_t q15_t;
    378 
    379   /**
    380    * @brief 32-bit fractional data type in 1.31 format.
    381    */
    382   typedef int32_t q31_t;
    383 
    384   /**
    385    * @brief 64-bit fractional data type in 1.63 format.
    386    */
    387   typedef int64_t q63_t;
    388 
    389   /**
    390    * @brief 32-bit floating-point type definition.
    391    */
    392   typedef float float32_t;
    393 
    394   /**
    395    * @brief 64-bit floating-point type definition.
    396    */
    397   typedef double float64_t;
    398 
    399   /**
    400    * @brief definition to read/write two 16 bit values.
    401    */
    402 #if defined __CC_ARM
    403 #define __SIMD32_TYPE int32_t __packed
    404 #define CMSIS_UNUSED __attribute__((unused))
    405 #elif defined __ICCARM__
    406 #define CMSIS_UNUSED
    407 #define __SIMD32_TYPE int32_t __packed
    408 #elif defined __GNUC__
    409 #define __SIMD32_TYPE int32_t
    410 #define CMSIS_UNUSED __attribute__((unused))
    411 #elif defined __CSMC__      /* Cosmic */
    412 #define CMSIS_UNUSED
    413 #define __SIMD32_TYPE int32_t
    414 #else
    415 #error Unknown compiler
    416 #endif
    417 
    418 #define __SIMD32(addr)  (*(__SIMD32_TYPE **) & (addr))
    419 #define __SIMD32_CONST(addr)  ((__SIMD32_TYPE *)(addr))
    420 
    421 #define _SIMD32_OFFSET(addr)  (*(__SIMD32_TYPE *)  (addr))
    422 
    423 #define __SIMD64(addr)  (*(int64_t **) & (addr))
    424 
    425 #if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY)
    426   /**
    427    * @brief definition to pack two 16 bit values.
    428    */
    429 #define __PKHBT(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0x0000FFFF) | \
    430                                          (((int32_t)(ARG2) << ARG3) & (int32_t)0xFFFF0000)  )
    431 #define __PKHTB(ARG1, ARG2, ARG3)      ( (((int32_t)(ARG1) <<  0) & (int32_t)0xFFFF0000) | \
    432                                          (((int32_t)(ARG2) >> ARG3) & (int32_t)0x0000FFFF)  )
    433 
    434 #endif
    435 
    436 
    437    /**
    438    * @brief definition to pack four 8 bit values.
    439    */
    440 #ifndef ARM_MATH_BIG_ENDIAN
    441 
    442 #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v0) <<  0) & (int32_t)0x000000FF) | \
    443                                 (((int32_t)(v1) <<  8) & (int32_t)0x0000FF00) | \
    444                                 (((int32_t)(v2) << 16) & (int32_t)0x00FF0000) | \
    445                                 (((int32_t)(v3) << 24) & (int32_t)0xFF000000)  )
    446 #else
    447 
    448 #define __PACKq7(v0,v1,v2,v3) ( (((int32_t)(v3) <<  0) & (int32_t)0x000000FF) | \
    449                                 (((int32_t)(v2) <<  8) & (int32_t)0x0000FF00) | \
    450                                 (((int32_t)(v1) << 16) & (int32_t)0x00FF0000) | \
    451                                 (((int32_t)(v0) << 24) & (int32_t)0xFF000000)  )
    452 
    453 #endif
    454 
    455 
    456   /**
    457    * @brief Clips Q63 to Q31 values.
    458    */
    459   static __INLINE q31_t clip_q63_to_q31(
    460   q63_t x)
    461   {
    462     return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
    463       ((0x7FFFFFFF ^ ((q31_t) (x >> 63)))) : (q31_t) x;
    464   }
    465 
    466   /**
    467    * @brief Clips Q63 to Q15 values.
    468    */
    469   static __INLINE q15_t clip_q63_to_q15(
    470   q63_t x)
    471   {
    472     return ((q31_t) (x >> 32) != ((q31_t) x >> 31)) ?
    473       ((0x7FFF ^ ((q15_t) (x >> 63)))) : (q15_t) (x >> 15);
    474   }
    475 
    476   /**
    477    * @brief Clips Q31 to Q7 values.
    478    */
    479   static __INLINE q7_t clip_q31_to_q7(
    480   q31_t x)
    481   {
    482     return ((q31_t) (x >> 24) != ((q31_t) x >> 23)) ?
    483       ((0x7F ^ ((q7_t) (x >> 31)))) : (q7_t) x;
    484   }
    485 
    486   /**
    487    * @brief Clips Q31 to Q15 values.
    488    */
    489   static __INLINE q15_t clip_q31_to_q15(
    490   q31_t x)
    491   {
    492     return ((q31_t) (x >> 16) != ((q31_t) x >> 15)) ?
    493       ((0x7FFF ^ ((q15_t) (x >> 31)))) : (q15_t) x;
    494   }
    495 
    496   /**
    497    * @brief Multiplies 32 X 64 and returns 32 bit result in 2.30 format.
    498    */
    499 
    500   static __INLINE q63_t mult32x64(
    501   q63_t x,
    502   q31_t y)
    503   {
    504     return ((((q63_t) (x & 0x00000000FFFFFFFF) * y) >> 32) +
    505             (((q63_t) (x >> 32) * y)));
    506   }
    507 
    508 
    509 #if defined (ARM_MATH_CM0_FAMILY) && defined ( __CC_ARM   )
    510 #define __CLZ __clz
    511 #endif
    512 
    513 #if defined (ARM_MATH_CM0_FAMILY) && ((defined (__ICCARM__)) ||(defined (__GNUC__)) || defined (__TASKING__) )
    514 
    515   static __INLINE uint32_t __CLZ(
    516   q31_t data);
    517 
    518 
    519   static __INLINE uint32_t __CLZ(
    520   q31_t data)
    521   {
    522     uint32_t count = 0;
    523     uint32_t mask = 0x80000000;
    524 
    525     while((data & mask) == 0)
    526     {
    527       count += 1u;
    528       mask = mask >> 1u;
    529     }
    530 
    531     return (count);
    532 
    533   }
    534 
    535 #endif
    536 
    537   /**
    538    * @brief Function to Calculates 1/in (reciprocal) value of Q31 Data type.
    539    */
    540 
    541   static __INLINE uint32_t arm_recip_q31(
    542   q31_t in,
    543   q31_t * dst,
    544   q31_t * pRecipTable)
    545   {
    546 
    547     uint32_t out, tempVal;
    548     uint32_t index, i;
    549     uint32_t signBits;
    550 
    551     if(in > 0)
    552     {
    553       signBits = __CLZ(in) - 1;
    554     }
    555     else
    556     {
    557       signBits = __CLZ(-in) - 1;
    558     }
    559 
    560     /* Convert input sample to 1.31 format */
    561     in = in << signBits;
    562 
    563     /* calculation of index for initial approximated Val */
    564     index = (uint32_t) (in >> 24u);
    565     index = (index & INDEX_MASK);
    566 
    567     /* 1.31 with exp 1 */
    568     out = pRecipTable[index];
    569 
    570     /* calculation of reciprocal value */
    571     /* running approximation for two iterations */
    572     for (i = 0u; i < 2u; i++)
    573     {
    574       tempVal = (q31_t) (((q63_t) in * out) >> 31u);
    575       tempVal = 0x7FFFFFFF - tempVal;
    576       /*      1.31 with exp 1 */
    577       //out = (q31_t) (((q63_t) out * tempVal) >> 30u);
    578       out = (q31_t) clip_q63_to_q31(((q63_t) out * tempVal) >> 30u);
    579     }
    580 
    581     /* write output */
    582     *dst = out;
    583 
    584     /* return num of signbits of out = 1/in value */
    585     return (signBits + 1u);
    586 
    587   }
    588 
    589   /**
    590    * @brief Function to Calculates 1/in (reciprocal) value of Q15 Data type.
    591    */
    592   static __INLINE uint32_t arm_recip_q15(
    593   q15_t in,
    594   q15_t * dst,
    595   q15_t * pRecipTable)
    596   {
    597 
    598     uint32_t out = 0, tempVal = 0;
    599     uint32_t index = 0, i = 0;
    600     uint32_t signBits = 0;
    601 
    602     if(in > 0)
    603     {
    604       signBits = __CLZ(in) - 17;
    605     }
    606     else
    607     {
    608       signBits = __CLZ(-in) - 17;
    609     }
    610 
    611     /* Convert input sample to 1.15 format */
    612     in = in << signBits;
    613 
    614     /* calculation of index for initial approximated Val */
    615     index = in >> 8;
    616     index = (index & INDEX_MASK);
    617 
    618     /*      1.15 with exp 1  */
    619     out = pRecipTable[index];
    620 
    621     /* calculation of reciprocal value */
    622     /* running approximation for two iterations */
    623     for (i = 0; i < 2; i++)
    624     {
    625       tempVal = (q15_t) (((q31_t) in * out) >> 15);
    626       tempVal = 0x7FFF - tempVal;
    627       /*      1.15 with exp 1 */
    628       out = (q15_t) (((q31_t) out * tempVal) >> 14);
    629     }
    630 
    631     /* write output */
    632     *dst = out;
    633 
    634     /* return num of signbits of out = 1/in value */
    635     return (signBits + 1);
    636 
    637   }
    638 
    639 
    640   /*
    641    * @brief C custom defined intrinisic function for only M0 processors
    642    */
    643 #if defined(ARM_MATH_CM0_FAMILY)
    644 
    645   static __INLINE q31_t __SSAT(
    646   q31_t x,
    647   uint32_t y)
    648   {
    649     int32_t posMax, negMin;
    650     uint32_t i;
    651 
    652     posMax = 1;
    653     for (i = 0; i < (y - 1); i++)
    654     {
    655       posMax = posMax * 2;
    656     }
    657 
    658     if(x > 0)
    659     {
    660       posMax = (posMax - 1);
    661 
    662       if(x > posMax)
    663       {
    664         x = posMax;
    665       }
    666     }
    667     else
    668     {
    669       negMin = -posMax;
    670 
    671       if(x < negMin)
    672       {
    673         x = negMin;
    674       }
    675     }
    676     return (x);
    677 
    678 
    679   }
    680 
    681 #endif /* end of ARM_MATH_CM0_FAMILY */
    682 
    683 
    684 
    685   /*
    686    * @brief C custom defined intrinsic function for M3 and M0 processors
    687    */
    688 #if defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY)
    689 
    690   /*
    691    * @brief C custom defined QADD8 for M3 and M0 processors
    692    */
    693   static __INLINE q31_t __QADD8(
    694   q31_t x,
    695   q31_t y)
    696   {
    697 
    698     q31_t sum;
    699     q7_t r, s, t, u;
    700 
    701     r = (q7_t) x;
    702     s = (q7_t) y;
    703 
    704     r = __SSAT((q31_t) (r + s), 8);
    705     s = __SSAT(((q31_t) (((x << 16) >> 24) + ((y << 16) >> 24))), 8);
    706     t = __SSAT(((q31_t) (((x << 8) >> 24) + ((y << 8) >> 24))), 8);
    707     u = __SSAT(((q31_t) ((x >> 24) + (y >> 24))), 8);
    708 
    709     sum =
    710       (((q31_t) u << 24) & 0xFF000000) | (((q31_t) t << 16) & 0x00FF0000) |
    711       (((q31_t) s << 8) & 0x0000FF00) | (r & 0x000000FF);
    712 
    713     return sum;
    714 
    715   }
    716 
    717   /*
    718    * @brief C custom defined QSUB8 for M3 and M0 processors
    719    */
    720   static __INLINE q31_t __QSUB8(
    721   q31_t x,
    722   q31_t y)
    723   {
    724 
    725     q31_t sum;
    726     q31_t r, s, t, u;
    727 
    728     r = (q7_t) x;
    729     s = (q7_t) y;
    730 
    731     r = __SSAT((r - s), 8);
    732     s = __SSAT(((q31_t) (((x << 16) >> 24) - ((y << 16) >> 24))), 8) << 8;
    733     t = __SSAT(((q31_t) (((x << 8) >> 24) - ((y << 8) >> 24))), 8) << 16;
    734     u = __SSAT(((q31_t) ((x >> 24) - (y >> 24))), 8) << 24;
    735 
    736     sum =
    737       (u & 0xFF000000) | (t & 0x00FF0000) | (s & 0x0000FF00) | (r &
    738                                                                 0x000000FF);
    739 
    740     return sum;
    741   }
    742 
    743   /*
    744    * @brief C custom defined QADD16 for M3 and M0 processors
    745    */
    746 
    747   /*
    748    * @brief C custom defined QADD16 for M3 and M0 processors
    749    */
    750   static __INLINE q31_t __QADD16(
    751   q31_t x,
    752   q31_t y)
    753   {
    754 
    755     q31_t sum;
    756     q31_t r, s;
    757 
    758     r = (q15_t) x;
    759     s = (q15_t) y;
    760 
    761     r = __SSAT(r + s, 16);
    762     s = __SSAT(((q31_t) ((x >> 16) + (y >> 16))), 16) << 16;
    763 
    764     sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
    765 
    766     return sum;
    767 
    768   }
    769 
    770   /*
    771    * @brief C custom defined SHADD16 for M3 and M0 processors
    772    */
    773   static __INLINE q31_t __SHADD16(
    774   q31_t x,
    775   q31_t y)
    776   {
    777 
    778     q31_t sum;
    779     q31_t r, s;
    780 
    781     r = (q15_t) x;
    782     s = (q15_t) y;
    783 
    784     r = ((r >> 1) + (s >> 1));
    785     s = ((q31_t) ((x >> 17) + (y >> 17))) << 16;
    786 
    787     sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
    788 
    789     return sum;
    790 
    791   }
    792 
    793   /*
    794    * @brief C custom defined QSUB16 for M3 and M0 processors
    795    */
    796   static __INLINE q31_t __QSUB16(
    797   q31_t x,
    798   q31_t y)
    799   {
    800 
    801     q31_t sum;
    802     q31_t r, s;
    803 
    804     r = (q15_t) x;
    805     s = (q15_t) y;
    806 
    807     r = __SSAT(r - s, 16);
    808     s = __SSAT(((q31_t) ((x >> 16) - (y >> 16))), 16) << 16;
    809 
    810     sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
    811 
    812     return sum;
    813   }
    814 
    815   /*
    816    * @brief C custom defined SHSUB16 for M3 and M0 processors
    817    */
    818   static __INLINE q31_t __SHSUB16(
    819   q31_t x,
    820   q31_t y)
    821   {
    822 
    823     q31_t diff;
    824     q31_t r, s;
    825 
    826     r = (q15_t) x;
    827     s = (q15_t) y;
    828 
    829     r = ((r >> 1) - (s >> 1));
    830     s = (((x >> 17) - (y >> 17)) << 16);
    831 
    832     diff = (s & 0xFFFF0000) | (r & 0x0000FFFF);
    833 
    834     return diff;
    835   }
    836 
    837   /*
    838    * @brief C custom defined QASX for M3 and M0 processors
    839    */
    840   static __INLINE q31_t __QASX(
    841   q31_t x,
    842   q31_t y)
    843   {
    844 
    845     q31_t sum = 0;
    846 
    847     sum =
    848       ((sum +
    849         clip_q31_to_q15((q31_t) ((q15_t) (x >> 16) + (q15_t) y))) << 16) +
    850       clip_q31_to_q15((q31_t) ((q15_t) x - (q15_t) (y >> 16)));
    851 
    852     return sum;
    853   }
    854 
    855   /*
    856    * @brief C custom defined SHASX for M3 and M0 processors
    857    */
    858   static __INLINE q31_t __SHASX(
    859   q31_t x,
    860   q31_t y)
    861   {
    862 
    863     q31_t sum;
    864     q31_t r, s;
    865 
    866     r = (q15_t) x;
    867     s = (q15_t) y;
    868 
    869     r = ((r >> 1) - (y >> 17));
    870     s = (((x >> 17) + (s >> 1)) << 16);
    871 
    872     sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
    873 
    874     return sum;
    875   }
    876 
    877 
    878   /*
    879    * @brief C custom defined QSAX for M3 and M0 processors
    880    */
    881   static __INLINE q31_t __QSAX(
    882   q31_t x,
    883   q31_t y)
    884   {
    885 
    886     q31_t sum = 0;
    887 
    888     sum =
    889       ((sum +
    890         clip_q31_to_q15((q31_t) ((q15_t) (x >> 16) - (q15_t) y))) << 16) +
    891       clip_q31_to_q15((q31_t) ((q15_t) x + (q15_t) (y >> 16)));
    892 
    893     return sum;
    894   }
    895 
    896   /*
    897    * @brief C custom defined SHSAX for M3 and M0 processors
    898    */
    899   static __INLINE q31_t __SHSAX(
    900   q31_t x,
    901   q31_t y)
    902   {
    903 
    904     q31_t sum;
    905     q31_t r, s;
    906 
    907     r = (q15_t) x;
    908     s = (q15_t) y;
    909 
    910     r = ((r >> 1) + (y >> 17));
    911     s = (((x >> 17) - (s >> 1)) << 16);
    912 
    913     sum = (s & 0xFFFF0000) | (r & 0x0000FFFF);
    914 
    915     return sum;
    916   }
    917 
    918   /*
    919    * @brief C custom defined SMUSDX for M3 and M0 processors
    920    */
    921   static __INLINE q31_t __SMUSDX(
    922   q31_t x,
    923   q31_t y)
    924   {
    925 
    926     return ((q31_t) (((q15_t) x * (q15_t) (y >> 16)) -
    927                      ((q15_t) (x >> 16) * (q15_t) y)));
    928   }
    929 
    930   /*
    931    * @brief C custom defined SMUADX for M3 and M0 processors
    932    */
    933   static __INLINE q31_t __SMUADX(
    934   q31_t x,
    935   q31_t y)
    936   {
    937 
    938     return ((q31_t) (((q15_t) x * (q15_t) (y >> 16)) +
    939                      ((q15_t) (x >> 16) * (q15_t) y)));
    940   }
    941 
    942   /*
    943    * @brief C custom defined QADD for M3 and M0 processors
    944    */
    945   static __INLINE q31_t __QADD(
    946   q31_t x,
    947   q31_t y)
    948   {
    949     return clip_q63_to_q31((q63_t) x + y);
    950   }
    951 
    952   /*
    953    * @brief C custom defined QSUB for M3 and M0 processors
    954    */
    955   static __INLINE q31_t __QSUB(
    956   q31_t x,
    957   q31_t y)
    958   {
    959     return clip_q63_to_q31((q63_t) x - y);
    960   }
    961 
    962   /*
    963    * @brief C custom defined SMLAD for M3 and M0 processors
    964    */
    965   static __INLINE q31_t __SMLAD(
    966   q31_t x,
    967   q31_t y,
    968   q31_t sum)
    969   {
    970 
    971     return (sum + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) +
    972             ((q15_t) x * (q15_t) y));
    973   }
    974 
    975   /*
    976    * @brief C custom defined SMLADX for M3 and M0 processors
    977    */
    978   static __INLINE q31_t __SMLADX(
    979   q31_t x,
    980   q31_t y,
    981   q31_t sum)
    982   {
    983 
    984     return (sum + ((q15_t) (x >> 16) * (q15_t) (y)) +
    985             ((q15_t) x * (q15_t) (y >> 16)));
    986   }
    987 
    988   /*
    989    * @brief C custom defined SMLSDX for M3 and M0 processors
    990    */
    991   static __INLINE q31_t __SMLSDX(
    992   q31_t x,
    993   q31_t y,
    994   q31_t sum)
    995   {
    996 
    997     return (sum - ((q15_t) (x >> 16) * (q15_t) (y)) +
    998             ((q15_t) x * (q15_t) (y >> 16)));
    999   }
   1000 
   1001   /*
   1002    * @brief C custom defined SMLALD for M3 and M0 processors
   1003    */
   1004   static __INLINE q63_t __SMLALD(
   1005   q31_t x,
   1006   q31_t y,
   1007   q63_t sum)
   1008   {
   1009 
   1010     return (sum + ((q15_t) (x >> 16) * (q15_t) (y >> 16)) +
   1011             ((q15_t) x * (q15_t) y));
   1012   }
   1013 
   1014   /*
   1015    * @brief C custom defined SMLALDX for M3 and M0 processors
   1016    */
   1017   static __INLINE q63_t __SMLALDX(
   1018   q31_t x,
   1019   q31_t y,
   1020   q63_t sum)
   1021   {
   1022 
   1023     return (sum + ((q15_t) (x >> 16) * (q15_t) y)) +
   1024       ((q15_t) x * (q15_t) (y >> 16));
   1025   }
   1026 
   1027   /*
   1028    * @brief C custom defined SMUAD for M3 and M0 processors
   1029    */
   1030   static __INLINE q31_t __SMUAD(
   1031   q31_t x,
   1032   q31_t y)
   1033   {
   1034 
   1035     return (((x >> 16) * (y >> 16)) +
   1036             (((x << 16) >> 16) * ((y << 16) >> 16)));
   1037   }
   1038 
   1039   /*
   1040    * @brief C custom defined SMUSD for M3 and M0 processors
   1041    */
   1042   static __INLINE q31_t __SMUSD(
   1043   q31_t x,
   1044   q31_t y)
   1045   {
   1046 
   1047     return (-((x >> 16) * (y >> 16)) +
   1048             (((x << 16) >> 16) * ((y << 16) >> 16)));
   1049   }
   1050 
   1051 
   1052   /*
   1053    * @brief C custom defined SXTB16 for M3 and M0 processors
   1054    */
   1055   static __INLINE q31_t __SXTB16(
   1056   q31_t x)
   1057   {
   1058 
   1059     return ((((x << 24) >> 24) & 0x0000FFFF) |
   1060             (((x << 8) >> 8) & 0xFFFF0000));
   1061   }
   1062 
   1063 
   1064 #endif /* defined (ARM_MATH_CM3) || defined (ARM_MATH_CM0_FAMILY) */
   1065 
   1066 
   1067   /**
   1068    * @brief Instance structure for the Q7 FIR filter.
   1069    */
   1070   typedef struct
   1071   {
   1072     uint16_t numTaps;        /**< number of filter coefficients in the filter. */
   1073     q7_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   1074     q7_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
   1075   } arm_fir_instance_q7;
   1076 
   1077   /**
   1078    * @brief Instance structure for the Q15 FIR filter.
   1079    */
   1080   typedef struct
   1081   {
   1082     uint16_t numTaps;         /**< number of filter coefficients in the filter. */
   1083     q15_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   1084     q15_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
   1085   } arm_fir_instance_q15;
   1086 
   1087   /**
   1088    * @brief Instance structure for the Q31 FIR filter.
   1089    */
   1090   typedef struct
   1091   {
   1092     uint16_t numTaps;         /**< number of filter coefficients in the filter. */
   1093     q31_t *pState;            /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   1094     q31_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps. */
   1095   } arm_fir_instance_q31;
   1096 
   1097   /**
   1098    * @brief Instance structure for the floating-point FIR filter.
   1099    */
   1100   typedef struct
   1101   {
   1102     uint16_t numTaps;     /**< number of filter coefficients in the filter. */
   1103     float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   1104     float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
   1105   } arm_fir_instance_f32;
   1106 
   1107 
   1108   /**
   1109    * @brief Processing function for the Q7 FIR filter.
   1110    * @param[in] *S points to an instance of the Q7 FIR filter structure.
   1111    * @param[in] *pSrc points to the block of input data.
   1112    * @param[out] *pDst points to the block of output data.
   1113    * @param[in] blockSize number of samples to process.
   1114    * @return none.
   1115    */
   1116   void arm_fir_q7(
   1117   const arm_fir_instance_q7 * S,
   1118   q7_t * pSrc,
   1119   q7_t * pDst,
   1120   uint32_t blockSize);
   1121 
   1122 
   1123   /**
   1124    * @brief  Initialization function for the Q7 FIR filter.
   1125    * @param[in,out] *S points to an instance of the Q7 FIR structure.
   1126    * @param[in] numTaps  Number of filter coefficients in the filter.
   1127    * @param[in] *pCoeffs points to the filter coefficients.
   1128    * @param[in] *pState points to the state buffer.
   1129    * @param[in] blockSize number of samples that are processed.
   1130    * @return none
   1131    */
   1132   void arm_fir_init_q7(
   1133   arm_fir_instance_q7 * S,
   1134   uint16_t numTaps,
   1135   q7_t * pCoeffs,
   1136   q7_t * pState,
   1137   uint32_t blockSize);
   1138 
   1139 
   1140   /**
   1141    * @brief Processing function for the Q15 FIR filter.
   1142    * @param[in] *S points to an instance of the Q15 FIR structure.
   1143    * @param[in] *pSrc points to the block of input data.
   1144    * @param[out] *pDst points to the block of output data.
   1145    * @param[in] blockSize number of samples to process.
   1146    * @return none.
   1147    */
   1148   void arm_fir_q15(
   1149   const arm_fir_instance_q15 * S,
   1150   q15_t * pSrc,
   1151   q15_t * pDst,
   1152   uint32_t blockSize);
   1153 
   1154   /**
   1155    * @brief Processing function for the fast Q15 FIR filter for Cortex-M3 and Cortex-M4.
   1156    * @param[in] *S points to an instance of the Q15 FIR filter structure.
   1157    * @param[in] *pSrc points to the block of input data.
   1158    * @param[out] *pDst points to the block of output data.
   1159    * @param[in] blockSize number of samples to process.
   1160    * @return none.
   1161    */
   1162   void arm_fir_fast_q15(
   1163   const arm_fir_instance_q15 * S,
   1164   q15_t * pSrc,
   1165   q15_t * pDst,
   1166   uint32_t blockSize);
   1167 
   1168   /**
   1169    * @brief  Initialization function for the Q15 FIR filter.
   1170    * @param[in,out] *S points to an instance of the Q15 FIR filter structure.
   1171    * @param[in] numTaps  Number of filter coefficients in the filter. Must be even and greater than or equal to 4.
   1172    * @param[in] *pCoeffs points to the filter coefficients.
   1173    * @param[in] *pState points to the state buffer.
   1174    * @param[in] blockSize number of samples that are processed at a time.
   1175    * @return The function returns ARM_MATH_SUCCESS if initialization was successful or ARM_MATH_ARGUMENT_ERROR if
   1176    * <code>numTaps</code> is not a supported value.
   1177    */
   1178 
   1179   arm_status arm_fir_init_q15(
   1180   arm_fir_instance_q15 * S,
   1181   uint16_t numTaps,
   1182   q15_t * pCoeffs,
   1183   q15_t * pState,
   1184   uint32_t blockSize);
   1185 
   1186   /**
   1187    * @brief Processing function for the Q31 FIR filter.
   1188    * @param[in] *S points to an instance of the Q31 FIR filter structure.
   1189    * @param[in] *pSrc points to the block of input data.
   1190    * @param[out] *pDst points to the block of output data.
   1191    * @param[in] blockSize number of samples to process.
   1192    * @return none.
   1193    */
   1194   void arm_fir_q31(
   1195   const arm_fir_instance_q31 * S,
   1196   q31_t * pSrc,
   1197   q31_t * pDst,
   1198   uint32_t blockSize);
   1199 
   1200   /**
   1201    * @brief Processing function for the fast Q31 FIR filter for Cortex-M3 and Cortex-M4.
   1202    * @param[in] *S points to an instance of the Q31 FIR structure.
   1203    * @param[in] *pSrc points to the block of input data.
   1204    * @param[out] *pDst points to the block of output data.
   1205    * @param[in] blockSize number of samples to process.
   1206    * @return none.
   1207    */
   1208   void arm_fir_fast_q31(
   1209   const arm_fir_instance_q31 * S,
   1210   q31_t * pSrc,
   1211   q31_t * pDst,
   1212   uint32_t blockSize);
   1213 
   1214   /**
   1215    * @brief  Initialization function for the Q31 FIR filter.
   1216    * @param[in,out] *S points to an instance of the Q31 FIR structure.
   1217    * @param[in]     numTaps  Number of filter coefficients in the filter.
   1218    * @param[in]     *pCoeffs points to the filter coefficients.
   1219    * @param[in]     *pState points to the state buffer.
   1220    * @param[in]     blockSize number of samples that are processed at a time.
   1221    * @return        none.
   1222    */
   1223   void arm_fir_init_q31(
   1224   arm_fir_instance_q31 * S,
   1225   uint16_t numTaps,
   1226   q31_t * pCoeffs,
   1227   q31_t * pState,
   1228   uint32_t blockSize);
   1229 
   1230   /**
   1231    * @brief Processing function for the floating-point FIR filter.
   1232    * @param[in] *S points to an instance of the floating-point FIR structure.
   1233    * @param[in] *pSrc points to the block of input data.
   1234    * @param[out] *pDst points to the block of output data.
   1235    * @param[in] blockSize number of samples to process.
   1236    * @return none.
   1237    */
   1238   void arm_fir_f32(
   1239   const arm_fir_instance_f32 * S,
   1240   float32_t * pSrc,
   1241   float32_t * pDst,
   1242   uint32_t blockSize);
   1243 
   1244   /**
   1245    * @brief  Initialization function for the floating-point FIR filter.
   1246    * @param[in,out] *S points to an instance of the floating-point FIR filter structure.
   1247    * @param[in]     numTaps  Number of filter coefficients in the filter.
   1248    * @param[in]     *pCoeffs points to the filter coefficients.
   1249    * @param[in]     *pState points to the state buffer.
   1250    * @param[in]     blockSize number of samples that are processed at a time.
   1251    * @return        none.
   1252    */
   1253   void arm_fir_init_f32(
   1254   arm_fir_instance_f32 * S,
   1255   uint16_t numTaps,
   1256   float32_t * pCoeffs,
   1257   float32_t * pState,
   1258   uint32_t blockSize);
   1259 
   1260 
   1261   /**
   1262    * @brief Instance structure for the Q15 Biquad cascade filter.
   1263    */
   1264   typedef struct
   1265   {
   1266     int8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
   1267     q15_t *pState;            /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
   1268     q15_t *pCoeffs;           /**< Points to the array of coefficients.  The array is of length 5*numStages. */
   1269     int8_t postShift;         /**< Additional shift, in bits, applied to each output sample. */
   1270 
   1271   } arm_biquad_casd_df1_inst_q15;
   1272 
   1273 
   1274   /**
   1275    * @brief Instance structure for the Q31 Biquad cascade filter.
   1276    */
   1277   typedef struct
   1278   {
   1279     uint32_t numStages;      /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
   1280     q31_t *pState;           /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
   1281     q31_t *pCoeffs;          /**< Points to the array of coefficients.  The array is of length 5*numStages. */
   1282     uint8_t postShift;       /**< Additional shift, in bits, applied to each output sample. */
   1283 
   1284   } arm_biquad_casd_df1_inst_q31;
   1285 
   1286   /**
   1287    * @brief Instance structure for the floating-point Biquad cascade filter.
   1288    */
   1289   typedef struct
   1290   {
   1291     uint32_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
   1292     float32_t *pState;          /**< Points to the array of state coefficients.  The array is of length 4*numStages. */
   1293     float32_t *pCoeffs;         /**< Points to the array of coefficients.  The array is of length 5*numStages. */
   1294 
   1295 
   1296   } arm_biquad_casd_df1_inst_f32;
   1297 
   1298 
   1299 
   1300   /**
   1301    * @brief Processing function for the Q15 Biquad cascade filter.
   1302    * @param[in]  *S points to an instance of the Q15 Biquad cascade structure.
   1303    * @param[in]  *pSrc points to the block of input data.
   1304    * @param[out] *pDst points to the block of output data.
   1305    * @param[in]  blockSize number of samples to process.
   1306    * @return     none.
   1307    */
   1308 
   1309   void arm_biquad_cascade_df1_q15(
   1310   const arm_biquad_casd_df1_inst_q15 * S,
   1311   q15_t * pSrc,
   1312   q15_t * pDst,
   1313   uint32_t blockSize);
   1314 
   1315   /**
   1316    * @brief  Initialization function for the Q15 Biquad cascade filter.
   1317    * @param[in,out] *S           points to an instance of the Q15 Biquad cascade structure.
   1318    * @param[in]     numStages    number of 2nd order stages in the filter.
   1319    * @param[in]     *pCoeffs     points to the filter coefficients.
   1320    * @param[in]     *pState      points to the state buffer.
   1321    * @param[in]     postShift    Shift to be applied to the output. Varies according to the coefficients format
   1322    * @return        none
   1323    */
   1324 
   1325   void arm_biquad_cascade_df1_init_q15(
   1326   arm_biquad_casd_df1_inst_q15 * S,
   1327   uint8_t numStages,
   1328   q15_t * pCoeffs,
   1329   q15_t * pState,
   1330   int8_t postShift);
   1331 
   1332 
   1333   /**
   1334    * @brief Fast but less precise processing function for the Q15 Biquad cascade filter for Cortex-M3 and Cortex-M4.
   1335    * @param[in]  *S points to an instance of the Q15 Biquad cascade structure.
   1336    * @param[in]  *pSrc points to the block of input data.
   1337    * @param[out] *pDst points to the block of output data.
   1338    * @param[in]  blockSize number of samples to process.
   1339    * @return     none.
   1340    */
   1341 
   1342   void arm_biquad_cascade_df1_fast_q15(
   1343   const arm_biquad_casd_df1_inst_q15 * S,
   1344   q15_t * pSrc,
   1345   q15_t * pDst,
   1346   uint32_t blockSize);
   1347 
   1348 
   1349   /**
   1350    * @brief Processing function for the Q31 Biquad cascade filter
   1351    * @param[in]  *S         points to an instance of the Q31 Biquad cascade structure.
   1352    * @param[in]  *pSrc      points to the block of input data.
   1353    * @param[out] *pDst      points to the block of output data.
   1354    * @param[in]  blockSize  number of samples to process.
   1355    * @return     none.
   1356    */
   1357 
   1358   void arm_biquad_cascade_df1_q31(
   1359   const arm_biquad_casd_df1_inst_q31 * S,
   1360   q31_t * pSrc,
   1361   q31_t * pDst,
   1362   uint32_t blockSize);
   1363 
   1364   /**
   1365    * @brief Fast but less precise processing function for the Q31 Biquad cascade filter for Cortex-M3 and Cortex-M4.
   1366    * @param[in]  *S         points to an instance of the Q31 Biquad cascade structure.
   1367    * @param[in]  *pSrc      points to the block of input data.
   1368    * @param[out] *pDst      points to the block of output data.
   1369    * @param[in]  blockSize  number of samples to process.
   1370    * @return     none.
   1371    */
   1372 
   1373   void arm_biquad_cascade_df1_fast_q31(
   1374   const arm_biquad_casd_df1_inst_q31 * S,
   1375   q31_t * pSrc,
   1376   q31_t * pDst,
   1377   uint32_t blockSize);
   1378 
   1379   /**
   1380    * @brief  Initialization function for the Q31 Biquad cascade filter.
   1381    * @param[in,out] *S           points to an instance of the Q31 Biquad cascade structure.
   1382    * @param[in]     numStages      number of 2nd order stages in the filter.
   1383    * @param[in]     *pCoeffs     points to the filter coefficients.
   1384    * @param[in]     *pState      points to the state buffer.
   1385    * @param[in]     postShift    Shift to be applied to the output. Varies according to the coefficients format
   1386    * @return        none
   1387    */
   1388 
   1389   void arm_biquad_cascade_df1_init_q31(
   1390   arm_biquad_casd_df1_inst_q31 * S,
   1391   uint8_t numStages,
   1392   q31_t * pCoeffs,
   1393   q31_t * pState,
   1394   int8_t postShift);
   1395 
   1396   /**
   1397    * @brief Processing function for the floating-point Biquad cascade filter.
   1398    * @param[in]  *S         points to an instance of the floating-point Biquad cascade structure.
   1399    * @param[in]  *pSrc      points to the block of input data.
   1400    * @param[out] *pDst      points to the block of output data.
   1401    * @param[in]  blockSize  number of samples to process.
   1402    * @return     none.
   1403    */
   1404 
   1405   void arm_biquad_cascade_df1_f32(
   1406   const arm_biquad_casd_df1_inst_f32 * S,
   1407   float32_t * pSrc,
   1408   float32_t * pDst,
   1409   uint32_t blockSize);
   1410 
   1411   /**
   1412    * @brief  Initialization function for the floating-point Biquad cascade filter.
   1413    * @param[in,out] *S           points to an instance of the floating-point Biquad cascade structure.
   1414    * @param[in]     numStages    number of 2nd order stages in the filter.
   1415    * @param[in]     *pCoeffs     points to the filter coefficients.
   1416    * @param[in]     *pState      points to the state buffer.
   1417    * @return        none
   1418    */
   1419 
   1420   void arm_biquad_cascade_df1_init_f32(
   1421   arm_biquad_casd_df1_inst_f32 * S,
   1422   uint8_t numStages,
   1423   float32_t * pCoeffs,
   1424   float32_t * pState);
   1425 
   1426 
   1427   /**
   1428    * @brief Instance structure for the floating-point matrix structure.
   1429    */
   1430 
   1431   typedef struct
   1432   {
   1433     uint16_t numRows;     /**< number of rows of the matrix.     */
   1434     uint16_t numCols;     /**< number of columns of the matrix.  */
   1435     float32_t *pData;     /**< points to the data of the matrix. */
   1436   } arm_matrix_instance_f32;
   1437 
   1438 
   1439   /**
   1440    * @brief Instance structure for the floating-point matrix structure.
   1441    */
   1442 
   1443   typedef struct
   1444   {
   1445     uint16_t numRows;     /**< number of rows of the matrix.     */
   1446     uint16_t numCols;     /**< number of columns of the matrix.  */
   1447     float64_t *pData;     /**< points to the data of the matrix. */
   1448   } arm_matrix_instance_f64;
   1449 
   1450   /**
   1451    * @brief Instance structure for the Q15 matrix structure.
   1452    */
   1453 
   1454   typedef struct
   1455   {
   1456     uint16_t numRows;     /**< number of rows of the matrix.     */
   1457     uint16_t numCols;     /**< number of columns of the matrix.  */
   1458     q15_t *pData;         /**< points to the data of the matrix. */
   1459 
   1460   } arm_matrix_instance_q15;
   1461 
   1462   /**
   1463    * @brief Instance structure for the Q31 matrix structure.
   1464    */
   1465 
   1466   typedef struct
   1467   {
   1468     uint16_t numRows;     /**< number of rows of the matrix.     */
   1469     uint16_t numCols;     /**< number of columns of the matrix.  */
   1470     q31_t *pData;         /**< points to the data of the matrix. */
   1471 
   1472   } arm_matrix_instance_q31;
   1473 
   1474 
   1475 
   1476   /**
   1477    * @brief Floating-point matrix addition.
   1478    * @param[in]       *pSrcA points to the first input matrix structure
   1479    * @param[in]       *pSrcB points to the second input matrix structure
   1480    * @param[out]      *pDst points to output matrix structure
   1481    * @return     The function returns either
   1482    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1483    */
   1484 
   1485   arm_status arm_mat_add_f32(
   1486   const arm_matrix_instance_f32 * pSrcA,
   1487   const arm_matrix_instance_f32 * pSrcB,
   1488   arm_matrix_instance_f32 * pDst);
   1489 
   1490   /**
   1491    * @brief Q15 matrix addition.
   1492    * @param[in]       *pSrcA points to the first input matrix structure
   1493    * @param[in]       *pSrcB points to the second input matrix structure
   1494    * @param[out]      *pDst points to output matrix structure
   1495    * @return     The function returns either
   1496    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1497    */
   1498 
   1499   arm_status arm_mat_add_q15(
   1500   const arm_matrix_instance_q15 * pSrcA,
   1501   const arm_matrix_instance_q15 * pSrcB,
   1502   arm_matrix_instance_q15 * pDst);
   1503 
   1504   /**
   1505    * @brief Q31 matrix addition.
   1506    * @param[in]       *pSrcA points to the first input matrix structure
   1507    * @param[in]       *pSrcB points to the second input matrix structure
   1508    * @param[out]      *pDst points to output matrix structure
   1509    * @return     The function returns either
   1510    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1511    */
   1512 
   1513   arm_status arm_mat_add_q31(
   1514   const arm_matrix_instance_q31 * pSrcA,
   1515   const arm_matrix_instance_q31 * pSrcB,
   1516   arm_matrix_instance_q31 * pDst);
   1517 
   1518   /**
   1519    * @brief Floating-point, complex, matrix multiplication.
   1520    * @param[in]       *pSrcA points to the first input matrix structure
   1521    * @param[in]       *pSrcB points to the second input matrix structure
   1522    * @param[out]      *pDst points to output matrix structure
   1523    * @return     The function returns either
   1524    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1525    */
   1526 
   1527   arm_status arm_mat_cmplx_mult_f32(
   1528   const arm_matrix_instance_f32 * pSrcA,
   1529   const arm_matrix_instance_f32 * pSrcB,
   1530   arm_matrix_instance_f32 * pDst);
   1531 
   1532   /**
   1533    * @brief Q15, complex,  matrix multiplication.
   1534    * @param[in]       *pSrcA points to the first input matrix structure
   1535    * @param[in]       *pSrcB points to the second input matrix structure
   1536    * @param[out]      *pDst points to output matrix structure
   1537    * @return     The function returns either
   1538    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1539    */
   1540 
   1541   arm_status arm_mat_cmplx_mult_q15(
   1542   const arm_matrix_instance_q15 * pSrcA,
   1543   const arm_matrix_instance_q15 * pSrcB,
   1544   arm_matrix_instance_q15 * pDst,
   1545   q15_t * pScratch);
   1546 
   1547   /**
   1548    * @brief Q31, complex, matrix multiplication.
   1549    * @param[in]       *pSrcA points to the first input matrix structure
   1550    * @param[in]       *pSrcB points to the second input matrix structure
   1551    * @param[out]      *pDst points to output matrix structure
   1552    * @return     The function returns either
   1553    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1554    */
   1555 
   1556   arm_status arm_mat_cmplx_mult_q31(
   1557   const arm_matrix_instance_q31 * pSrcA,
   1558   const arm_matrix_instance_q31 * pSrcB,
   1559   arm_matrix_instance_q31 * pDst);
   1560 
   1561 
   1562   /**
   1563    * @brief Floating-point matrix transpose.
   1564    * @param[in]  *pSrc points to the input matrix
   1565    * @param[out] *pDst points to the output matrix
   1566    * @return     The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
   1567    * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1568    */
   1569 
   1570   arm_status arm_mat_trans_f32(
   1571   const arm_matrix_instance_f32 * pSrc,
   1572   arm_matrix_instance_f32 * pDst);
   1573 
   1574 
   1575   /**
   1576    * @brief Q15 matrix transpose.
   1577    * @param[in]  *pSrc points to the input matrix
   1578    * @param[out] *pDst points to the output matrix
   1579    * @return     The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
   1580    * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1581    */
   1582 
   1583   arm_status arm_mat_trans_q15(
   1584   const arm_matrix_instance_q15 * pSrc,
   1585   arm_matrix_instance_q15 * pDst);
   1586 
   1587   /**
   1588    * @brief Q31 matrix transpose.
   1589    * @param[in]  *pSrc points to the input matrix
   1590    * @param[out] *pDst points to the output matrix
   1591    * @return     The function returns either  <code>ARM_MATH_SIZE_MISMATCH</code>
   1592    * or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1593    */
   1594 
   1595   arm_status arm_mat_trans_q31(
   1596   const arm_matrix_instance_q31 * pSrc,
   1597   arm_matrix_instance_q31 * pDst);
   1598 
   1599 
   1600   /**
   1601    * @brief Floating-point matrix multiplication
   1602    * @param[in]       *pSrcA points to the first input matrix structure
   1603    * @param[in]       *pSrcB points to the second input matrix structure
   1604    * @param[out]      *pDst points to output matrix structure
   1605    * @return     The function returns either
   1606    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1607    */
   1608 
   1609   arm_status arm_mat_mult_f32(
   1610   const arm_matrix_instance_f32 * pSrcA,
   1611   const arm_matrix_instance_f32 * pSrcB,
   1612   arm_matrix_instance_f32 * pDst);
   1613 
   1614   /**
   1615    * @brief Q15 matrix multiplication
   1616    * @param[in]       *pSrcA points to the first input matrix structure
   1617    * @param[in]       *pSrcB points to the second input matrix structure
   1618    * @param[out]      *pDst points to output matrix structure
   1619    * @param[in]       *pState points to the array for storing intermediate results
   1620    * @return     The function returns either
   1621    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1622    */
   1623 
   1624   arm_status arm_mat_mult_q15(
   1625   const arm_matrix_instance_q15 * pSrcA,
   1626   const arm_matrix_instance_q15 * pSrcB,
   1627   arm_matrix_instance_q15 * pDst,
   1628   q15_t * pState);
   1629 
   1630   /**
   1631    * @brief Q15 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
   1632    * @param[in]       *pSrcA  points to the first input matrix structure
   1633    * @param[in]       *pSrcB  points to the second input matrix structure
   1634    * @param[out]      *pDst   points to output matrix structure
   1635    * @param[in]       *pState points to the array for storing intermediate results
   1636    * @return     The function returns either
   1637    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1638    */
   1639 
   1640   arm_status arm_mat_mult_fast_q15(
   1641   const arm_matrix_instance_q15 * pSrcA,
   1642   const arm_matrix_instance_q15 * pSrcB,
   1643   arm_matrix_instance_q15 * pDst,
   1644   q15_t * pState);
   1645 
   1646   /**
   1647    * @brief Q31 matrix multiplication
   1648    * @param[in]       *pSrcA points to the first input matrix structure
   1649    * @param[in]       *pSrcB points to the second input matrix structure
   1650    * @param[out]      *pDst points to output matrix structure
   1651    * @return     The function returns either
   1652    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1653    */
   1654 
   1655   arm_status arm_mat_mult_q31(
   1656   const arm_matrix_instance_q31 * pSrcA,
   1657   const arm_matrix_instance_q31 * pSrcB,
   1658   arm_matrix_instance_q31 * pDst);
   1659 
   1660   /**
   1661    * @brief Q31 matrix multiplication (fast variant) for Cortex-M3 and Cortex-M4
   1662    * @param[in]       *pSrcA points to the first input matrix structure
   1663    * @param[in]       *pSrcB points to the second input matrix structure
   1664    * @param[out]      *pDst points to output matrix structure
   1665    * @return     The function returns either
   1666    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1667    */
   1668 
   1669   arm_status arm_mat_mult_fast_q31(
   1670   const arm_matrix_instance_q31 * pSrcA,
   1671   const arm_matrix_instance_q31 * pSrcB,
   1672   arm_matrix_instance_q31 * pDst);
   1673 
   1674 
   1675   /**
   1676    * @brief Floating-point matrix subtraction
   1677    * @param[in]       *pSrcA points to the first input matrix structure
   1678    * @param[in]       *pSrcB points to the second input matrix structure
   1679    * @param[out]      *pDst points to output matrix structure
   1680    * @return     The function returns either
   1681    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1682    */
   1683 
   1684   arm_status arm_mat_sub_f32(
   1685   const arm_matrix_instance_f32 * pSrcA,
   1686   const arm_matrix_instance_f32 * pSrcB,
   1687   arm_matrix_instance_f32 * pDst);
   1688 
   1689   /**
   1690    * @brief Q15 matrix subtraction
   1691    * @param[in]       *pSrcA points to the first input matrix structure
   1692    * @param[in]       *pSrcB points to the second input matrix structure
   1693    * @param[out]      *pDst points to output matrix structure
   1694    * @return     The function returns either
   1695    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1696    */
   1697 
   1698   arm_status arm_mat_sub_q15(
   1699   const arm_matrix_instance_q15 * pSrcA,
   1700   const arm_matrix_instance_q15 * pSrcB,
   1701   arm_matrix_instance_q15 * pDst);
   1702 
   1703   /**
   1704    * @brief Q31 matrix subtraction
   1705    * @param[in]       *pSrcA points to the first input matrix structure
   1706    * @param[in]       *pSrcB points to the second input matrix structure
   1707    * @param[out]      *pDst points to output matrix structure
   1708    * @return     The function returns either
   1709    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1710    */
   1711 
   1712   arm_status arm_mat_sub_q31(
   1713   const arm_matrix_instance_q31 * pSrcA,
   1714   const arm_matrix_instance_q31 * pSrcB,
   1715   arm_matrix_instance_q31 * pDst);
   1716 
   1717   /**
   1718    * @brief Floating-point matrix scaling.
   1719    * @param[in]  *pSrc points to the input matrix
   1720    * @param[in]  scale scale factor
   1721    * @param[out] *pDst points to the output matrix
   1722    * @return     The function returns either
   1723    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1724    */
   1725 
   1726   arm_status arm_mat_scale_f32(
   1727   const arm_matrix_instance_f32 * pSrc,
   1728   float32_t scale,
   1729   arm_matrix_instance_f32 * pDst);
   1730 
   1731   /**
   1732    * @brief Q15 matrix scaling.
   1733    * @param[in]       *pSrc points to input matrix
   1734    * @param[in]       scaleFract fractional portion of the scale factor
   1735    * @param[in]       shift number of bits to shift the result by
   1736    * @param[out]      *pDst points to output matrix
   1737    * @return     The function returns either
   1738    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1739    */
   1740 
   1741   arm_status arm_mat_scale_q15(
   1742   const arm_matrix_instance_q15 * pSrc,
   1743   q15_t scaleFract,
   1744   int32_t shift,
   1745   arm_matrix_instance_q15 * pDst);
   1746 
   1747   /**
   1748    * @brief Q31 matrix scaling.
   1749    * @param[in]       *pSrc points to input matrix
   1750    * @param[in]       scaleFract fractional portion of the scale factor
   1751    * @param[in]       shift number of bits to shift the result by
   1752    * @param[out]      *pDst points to output matrix structure
   1753    * @return     The function returns either
   1754    * <code>ARM_MATH_SIZE_MISMATCH</code> or <code>ARM_MATH_SUCCESS</code> based on the outcome of size checking.
   1755    */
   1756 
   1757   arm_status arm_mat_scale_q31(
   1758   const arm_matrix_instance_q31 * pSrc,
   1759   q31_t scaleFract,
   1760   int32_t shift,
   1761   arm_matrix_instance_q31 * pDst);
   1762 
   1763 
   1764   /**
   1765    * @brief  Q31 matrix initialization.
   1766    * @param[in,out] *S             points to an instance of the floating-point matrix structure.
   1767    * @param[in]     nRows          number of rows in the matrix.
   1768    * @param[in]     nColumns       number of columns in the matrix.
   1769    * @param[in]     *pData         points to the matrix data array.
   1770    * @return        none
   1771    */
   1772 
   1773   void arm_mat_init_q31(
   1774   arm_matrix_instance_q31 * S,
   1775   uint16_t nRows,
   1776   uint16_t nColumns,
   1777   q31_t * pData);
   1778 
   1779   /**
   1780    * @brief  Q15 matrix initialization.
   1781    * @param[in,out] *S             points to an instance of the floating-point matrix structure.
   1782    * @param[in]     nRows          number of rows in the matrix.
   1783    * @param[in]     nColumns       number of columns in the matrix.
   1784    * @param[in]     *pData         points to the matrix data array.
   1785    * @return        none
   1786    */
   1787 
   1788   void arm_mat_init_q15(
   1789   arm_matrix_instance_q15 * S,
   1790   uint16_t nRows,
   1791   uint16_t nColumns,
   1792   q15_t * pData);
   1793 
   1794   /**
   1795    * @brief  Floating-point matrix initialization.
   1796    * @param[in,out] *S             points to an instance of the floating-point matrix structure.
   1797    * @param[in]     nRows          number of rows in the matrix.
   1798    * @param[in]     nColumns       number of columns in the matrix.
   1799    * @param[in]     *pData         points to the matrix data array.
   1800    * @return        none
   1801    */
   1802 
   1803   void arm_mat_init_f32(
   1804   arm_matrix_instance_f32 * S,
   1805   uint16_t nRows,
   1806   uint16_t nColumns,
   1807   float32_t * pData);
   1808 
   1809 
   1810 
   1811   /**
   1812    * @brief Instance structure for the Q15 PID Control.
   1813    */
   1814   typedef struct
   1815   {
   1816     q15_t A0;    /**< The derived gain, A0 = Kp + Ki + Kd . */
   1817 #ifdef ARM_MATH_CM0_FAMILY
   1818     q15_t A1;
   1819     q15_t A2;
   1820 #else
   1821     q31_t A1;           /**< The derived gain A1 = -Kp - 2Kd | Kd.*/
   1822 #endif
   1823     q15_t state[3];       /**< The state array of length 3. */
   1824     q15_t Kp;           /**< The proportional gain. */
   1825     q15_t Ki;           /**< The integral gain. */
   1826     q15_t Kd;           /**< The derivative gain. */
   1827   } arm_pid_instance_q15;
   1828 
   1829   /**
   1830    * @brief Instance structure for the Q31 PID Control.
   1831    */
   1832   typedef struct
   1833   {
   1834     q31_t A0;            /**< The derived gain, A0 = Kp + Ki + Kd . */
   1835     q31_t A1;            /**< The derived gain, A1 = -Kp - 2Kd. */
   1836     q31_t A2;            /**< The derived gain, A2 = Kd . */
   1837     q31_t state[3];      /**< The state array of length 3. */
   1838     q31_t Kp;            /**< The proportional gain. */
   1839     q31_t Ki;            /**< The integral gain. */
   1840     q31_t Kd;            /**< The derivative gain. */
   1841 
   1842   } arm_pid_instance_q31;
   1843 
   1844   /**
   1845    * @brief Instance structure for the floating-point PID Control.
   1846    */
   1847   typedef struct
   1848   {
   1849     float32_t A0;          /**< The derived gain, A0 = Kp + Ki + Kd . */
   1850     float32_t A1;          /**< The derived gain, A1 = -Kp - 2Kd. */
   1851     float32_t A2;          /**< The derived gain, A2 = Kd . */
   1852     float32_t state[3];    /**< The state array of length 3. */
   1853     float32_t Kp;               /**< The proportional gain. */
   1854     float32_t Ki;               /**< The integral gain. */
   1855     float32_t Kd;               /**< The derivative gain. */
   1856   } arm_pid_instance_f32;
   1857 
   1858 
   1859 
   1860   /**
   1861    * @brief  Initialization function for the floating-point PID Control.
   1862    * @param[in,out] *S      points to an instance of the PID structure.
   1863    * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
   1864    * @return none.
   1865    */
   1866   void arm_pid_init_f32(
   1867   arm_pid_instance_f32 * S,
   1868   int32_t resetStateFlag);
   1869 
   1870   /**
   1871    * @brief  Reset function for the floating-point PID Control.
   1872    * @param[in,out] *S is an instance of the floating-point PID Control structure
   1873    * @return none
   1874    */
   1875   void arm_pid_reset_f32(
   1876   arm_pid_instance_f32 * S);
   1877 
   1878 
   1879   /**
   1880    * @brief  Initialization function for the Q31 PID Control.
   1881    * @param[in,out] *S points to an instance of the Q15 PID structure.
   1882    * @param[in]     resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
   1883    * @return none.
   1884    */
   1885   void arm_pid_init_q31(
   1886   arm_pid_instance_q31 * S,
   1887   int32_t resetStateFlag);
   1888 
   1889 
   1890   /**
   1891    * @brief  Reset function for the Q31 PID Control.
   1892    * @param[in,out] *S points to an instance of the Q31 PID Control structure
   1893    * @return none
   1894    */
   1895 
   1896   void arm_pid_reset_q31(
   1897   arm_pid_instance_q31 * S);
   1898 
   1899   /**
   1900    * @brief  Initialization function for the Q15 PID Control.
   1901    * @param[in,out] *S points to an instance of the Q15 PID structure.
   1902    * @param[in] resetStateFlag  flag to reset the state. 0 = no change in state 1 = reset the state.
   1903    * @return none.
   1904    */
   1905   void arm_pid_init_q15(
   1906   arm_pid_instance_q15 * S,
   1907   int32_t resetStateFlag);
   1908 
   1909   /**
   1910    * @brief  Reset function for the Q15 PID Control.
   1911    * @param[in,out] *S points to an instance of the q15 PID Control structure
   1912    * @return none
   1913    */
   1914   void arm_pid_reset_q15(
   1915   arm_pid_instance_q15 * S);
   1916 
   1917 
   1918   /**
   1919    * @brief Instance structure for the floating-point Linear Interpolate function.
   1920    */
   1921   typedef struct
   1922   {
   1923     uint32_t nValues;           /**< nValues */
   1924     float32_t x1;               /**< x1 */
   1925     float32_t xSpacing;         /**< xSpacing */
   1926     float32_t *pYData;          /**< pointer to the table of Y values */
   1927   } arm_linear_interp_instance_f32;
   1928 
   1929   /**
   1930    * @brief Instance structure for the floating-point bilinear interpolation function.
   1931    */
   1932 
   1933   typedef struct
   1934   {
   1935     uint16_t numRows;   /**< number of rows in the data table. */
   1936     uint16_t numCols;   /**< number of columns in the data table. */
   1937     float32_t *pData;   /**< points to the data table. */
   1938   } arm_bilinear_interp_instance_f32;
   1939 
   1940    /**
   1941    * @brief Instance structure for the Q31 bilinear interpolation function.
   1942    */
   1943 
   1944   typedef struct
   1945   {
   1946     uint16_t numRows;   /**< number of rows in the data table. */
   1947     uint16_t numCols;   /**< number of columns in the data table. */
   1948     q31_t *pData;       /**< points to the data table. */
   1949   } arm_bilinear_interp_instance_q31;
   1950 
   1951    /**
   1952    * @brief Instance structure for the Q15 bilinear interpolation function.
   1953    */
   1954 
   1955   typedef struct
   1956   {
   1957     uint16_t numRows;   /**< number of rows in the data table. */
   1958     uint16_t numCols;   /**< number of columns in the data table. */
   1959     q15_t *pData;       /**< points to the data table. */
   1960   } arm_bilinear_interp_instance_q15;
   1961 
   1962    /**
   1963    * @brief Instance structure for the Q15 bilinear interpolation function.
   1964    */
   1965 
   1966   typedef struct
   1967   {
   1968     uint16_t numRows;   /**< number of rows in the data table. */
   1969     uint16_t numCols;   /**< number of columns in the data table. */
   1970     q7_t *pData;                /**< points to the data table. */
   1971   } arm_bilinear_interp_instance_q7;
   1972 
   1973 
   1974   /**
   1975    * @brief Q7 vector multiplication.
   1976    * @param[in]       *pSrcA points to the first input vector
   1977    * @param[in]       *pSrcB points to the second input vector
   1978    * @param[out]      *pDst  points to the output vector
   1979    * @param[in]       blockSize number of samples in each vector
   1980    * @return none.
   1981    */
   1982 
   1983   void arm_mult_q7(
   1984   q7_t * pSrcA,
   1985   q7_t * pSrcB,
   1986   q7_t * pDst,
   1987   uint32_t blockSize);
   1988 
   1989   /**
   1990    * @brief Q15 vector multiplication.
   1991    * @param[in]       *pSrcA points to the first input vector
   1992    * @param[in]       *pSrcB points to the second input vector
   1993    * @param[out]      *pDst  points to the output vector
   1994    * @param[in]       blockSize number of samples in each vector
   1995    * @return none.
   1996    */
   1997 
   1998   void arm_mult_q15(
   1999   q15_t * pSrcA,
   2000   q15_t * pSrcB,
   2001   q15_t * pDst,
   2002   uint32_t blockSize);
   2003 
   2004   /**
   2005    * @brief Q31 vector multiplication.
   2006    * @param[in]       *pSrcA points to the first input vector
   2007    * @param[in]       *pSrcB points to the second input vector
   2008    * @param[out]      *pDst points to the output vector
   2009    * @param[in]       blockSize number of samples in each vector
   2010    * @return none.
   2011    */
   2012 
   2013   void arm_mult_q31(
   2014   q31_t * pSrcA,
   2015   q31_t * pSrcB,
   2016   q31_t * pDst,
   2017   uint32_t blockSize);
   2018 
   2019   /**
   2020    * @brief Floating-point vector multiplication.
   2021    * @param[in]       *pSrcA points to the first input vector
   2022    * @param[in]       *pSrcB points to the second input vector
   2023    * @param[out]      *pDst points to the output vector
   2024    * @param[in]       blockSize number of samples in each vector
   2025    * @return none.
   2026    */
   2027 
   2028   void arm_mult_f32(
   2029   float32_t * pSrcA,
   2030   float32_t * pSrcB,
   2031   float32_t * pDst,
   2032   uint32_t blockSize);
   2033 
   2034 
   2035 
   2036 
   2037 
   2038 
   2039   /**
   2040    * @brief Instance structure for the Q15 CFFT/CIFFT function.
   2041    */
   2042 
   2043   typedef struct
   2044   {
   2045     uint16_t fftLen;                 /**< length of the FFT. */
   2046     uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
   2047     uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
   2048     q15_t *pTwiddle;                     /**< points to the Sin twiddle factor table. */
   2049     uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
   2050     uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
   2051     uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
   2052   } arm_cfft_radix2_instance_q15;
   2053 
   2054 /* Deprecated */
   2055   arm_status arm_cfft_radix2_init_q15(
   2056   arm_cfft_radix2_instance_q15 * S,
   2057   uint16_t fftLen,
   2058   uint8_t ifftFlag,
   2059   uint8_t bitReverseFlag);
   2060 
   2061 /* Deprecated */
   2062   void arm_cfft_radix2_q15(
   2063   const arm_cfft_radix2_instance_q15 * S,
   2064   q15_t * pSrc);
   2065 
   2066 
   2067 
   2068   /**
   2069    * @brief Instance structure for the Q15 CFFT/CIFFT function.
   2070    */
   2071 
   2072   typedef struct
   2073   {
   2074     uint16_t fftLen;                 /**< length of the FFT. */
   2075     uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
   2076     uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
   2077     q15_t *pTwiddle;                 /**< points to the twiddle factor table. */
   2078     uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
   2079     uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
   2080     uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
   2081   } arm_cfft_radix4_instance_q15;
   2082 
   2083 /* Deprecated */
   2084   arm_status arm_cfft_radix4_init_q15(
   2085   arm_cfft_radix4_instance_q15 * S,
   2086   uint16_t fftLen,
   2087   uint8_t ifftFlag,
   2088   uint8_t bitReverseFlag);
   2089 
   2090 /* Deprecated */
   2091   void arm_cfft_radix4_q15(
   2092   const arm_cfft_radix4_instance_q15 * S,
   2093   q15_t * pSrc);
   2094 
   2095   /**
   2096    * @brief Instance structure for the Radix-2 Q31 CFFT/CIFFT function.
   2097    */
   2098 
   2099   typedef struct
   2100   {
   2101     uint16_t fftLen;                 /**< length of the FFT. */
   2102     uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
   2103     uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
   2104     q31_t *pTwiddle;                     /**< points to the Twiddle factor table. */
   2105     uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
   2106     uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
   2107     uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
   2108   } arm_cfft_radix2_instance_q31;
   2109 
   2110 /* Deprecated */
   2111   arm_status arm_cfft_radix2_init_q31(
   2112   arm_cfft_radix2_instance_q31 * S,
   2113   uint16_t fftLen,
   2114   uint8_t ifftFlag,
   2115   uint8_t bitReverseFlag);
   2116 
   2117 /* Deprecated */
   2118   void arm_cfft_radix2_q31(
   2119   const arm_cfft_radix2_instance_q31 * S,
   2120   q31_t * pSrc);
   2121 
   2122   /**
   2123    * @brief Instance structure for the Q31 CFFT/CIFFT function.
   2124    */
   2125 
   2126   typedef struct
   2127   {
   2128     uint16_t fftLen;                 /**< length of the FFT. */
   2129     uint8_t ifftFlag;                /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
   2130     uint8_t bitReverseFlag;          /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
   2131     q31_t *pTwiddle;                 /**< points to the twiddle factor table. */
   2132     uint16_t *pBitRevTable;          /**< points to the bit reversal table. */
   2133     uint16_t twidCoefModifier;       /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
   2134     uint16_t bitRevFactor;           /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
   2135   } arm_cfft_radix4_instance_q31;
   2136 
   2137 /* Deprecated */
   2138   void arm_cfft_radix4_q31(
   2139   const arm_cfft_radix4_instance_q31 * S,
   2140   q31_t * pSrc);
   2141 
   2142 /* Deprecated */
   2143   arm_status arm_cfft_radix4_init_q31(
   2144   arm_cfft_radix4_instance_q31 * S,
   2145   uint16_t fftLen,
   2146   uint8_t ifftFlag,
   2147   uint8_t bitReverseFlag);
   2148 
   2149   /**
   2150    * @brief Instance structure for the floating-point CFFT/CIFFT function.
   2151    */
   2152 
   2153   typedef struct
   2154   {
   2155     uint16_t fftLen;                   /**< length of the FFT. */
   2156     uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
   2157     uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
   2158     float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
   2159     uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
   2160     uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
   2161     uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
   2162     float32_t onebyfftLen;                 /**< value of 1/fftLen. */
   2163   } arm_cfft_radix2_instance_f32;
   2164 
   2165 /* Deprecated */
   2166   arm_status arm_cfft_radix2_init_f32(
   2167   arm_cfft_radix2_instance_f32 * S,
   2168   uint16_t fftLen,
   2169   uint8_t ifftFlag,
   2170   uint8_t bitReverseFlag);
   2171 
   2172 /* Deprecated */
   2173   void arm_cfft_radix2_f32(
   2174   const arm_cfft_radix2_instance_f32 * S,
   2175   float32_t * pSrc);
   2176 
   2177   /**
   2178    * @brief Instance structure for the floating-point CFFT/CIFFT function.
   2179    */
   2180 
   2181   typedef struct
   2182   {
   2183     uint16_t fftLen;                   /**< length of the FFT. */
   2184     uint8_t ifftFlag;                  /**< flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform. */
   2185     uint8_t bitReverseFlag;            /**< flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output. */
   2186     float32_t *pTwiddle;               /**< points to the Twiddle factor table. */
   2187     uint16_t *pBitRevTable;            /**< points to the bit reversal table. */
   2188     uint16_t twidCoefModifier;         /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
   2189     uint16_t bitRevFactor;             /**< bit reversal modifier that supports different size FFTs with the same bit reversal table. */
   2190     float32_t onebyfftLen;                 /**< value of 1/fftLen. */
   2191   } arm_cfft_radix4_instance_f32;
   2192 
   2193 /* Deprecated */
   2194   arm_status arm_cfft_radix4_init_f32(
   2195   arm_cfft_radix4_instance_f32 * S,
   2196   uint16_t fftLen,
   2197   uint8_t ifftFlag,
   2198   uint8_t bitReverseFlag);
   2199 
   2200 /* Deprecated */
   2201   void arm_cfft_radix4_f32(
   2202   const arm_cfft_radix4_instance_f32 * S,
   2203   float32_t * pSrc);
   2204 
   2205   /**
   2206    * @brief Instance structure for the fixed-point CFFT/CIFFT function.
   2207    */
   2208 
   2209   typedef struct
   2210   {
   2211     uint16_t fftLen;                   /**< length of the FFT. */
   2212     const q15_t *pTwiddle;             /**< points to the Twiddle factor table. */
   2213     const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
   2214     uint16_t bitRevLength;             /**< bit reversal table length. */
   2215   } arm_cfft_instance_q15;
   2216 
   2217   void arm_cfft_q15(
   2218   const arm_cfft_instance_q15 * S,
   2219   q15_t * p1,
   2220   uint8_t ifftFlag,
   2221   uint8_t bitReverseFlag);
   2222 
   2223   /**
   2224    * @brief Instance structure for the fixed-point CFFT/CIFFT function.
   2225    */
   2226 
   2227   typedef struct
   2228   {
   2229     uint16_t fftLen;                   /**< length of the FFT. */
   2230     const q31_t *pTwiddle;             /**< points to the Twiddle factor table. */
   2231     const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
   2232     uint16_t bitRevLength;             /**< bit reversal table length. */
   2233   } arm_cfft_instance_q31;
   2234 
   2235   void arm_cfft_q31(
   2236   const arm_cfft_instance_q31 * S,
   2237   q31_t * p1,
   2238   uint8_t ifftFlag,
   2239   uint8_t bitReverseFlag);
   2240 
   2241   /**
   2242    * @brief Instance structure for the floating-point CFFT/CIFFT function.
   2243    */
   2244 
   2245   typedef struct
   2246   {
   2247     uint16_t fftLen;                   /**< length of the FFT. */
   2248     const float32_t *pTwiddle;         /**< points to the Twiddle factor table. */
   2249     const uint16_t *pBitRevTable;      /**< points to the bit reversal table. */
   2250     uint16_t bitRevLength;             /**< bit reversal table length. */
   2251   } arm_cfft_instance_f32;
   2252 
   2253   void arm_cfft_f32(
   2254   const arm_cfft_instance_f32 * S,
   2255   float32_t * p1,
   2256   uint8_t ifftFlag,
   2257   uint8_t bitReverseFlag);
   2258 
   2259   /**
   2260    * @brief Instance structure for the Q15 RFFT/RIFFT function.
   2261    */
   2262 
   2263   typedef struct
   2264   {
   2265     uint32_t fftLenReal;                      /**< length of the real FFT. */
   2266     uint8_t ifftFlagR;                        /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
   2267     uint8_t bitReverseFlagR;                  /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
   2268     uint32_t twidCoefRModifier;               /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
   2269     q15_t *pTwiddleAReal;                     /**< points to the real twiddle factor table. */
   2270     q15_t *pTwiddleBReal;                     /**< points to the imag twiddle factor table. */
   2271     const arm_cfft_instance_q15 *pCfft;       /**< points to the complex FFT instance. */
   2272   } arm_rfft_instance_q15;
   2273 
   2274   arm_status arm_rfft_init_q15(
   2275   arm_rfft_instance_q15 * S,
   2276   uint32_t fftLenReal,
   2277   uint32_t ifftFlagR,
   2278   uint32_t bitReverseFlag);
   2279 
   2280   void arm_rfft_q15(
   2281   const arm_rfft_instance_q15 * S,
   2282   q15_t * pSrc,
   2283   q15_t * pDst);
   2284 
   2285   /**
   2286    * @brief Instance structure for the Q31 RFFT/RIFFT function.
   2287    */
   2288 
   2289   typedef struct
   2290   {
   2291     uint32_t fftLenReal;                        /**< length of the real FFT. */
   2292     uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
   2293     uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
   2294     uint32_t twidCoefRModifier;                 /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
   2295     q31_t *pTwiddleAReal;                       /**< points to the real twiddle factor table. */
   2296     q31_t *pTwiddleBReal;                       /**< points to the imag twiddle factor table. */
   2297     const arm_cfft_instance_q31 *pCfft;         /**< points to the complex FFT instance. */
   2298   } arm_rfft_instance_q31;
   2299 
   2300   arm_status arm_rfft_init_q31(
   2301   arm_rfft_instance_q31 * S,
   2302   uint32_t fftLenReal,
   2303   uint32_t ifftFlagR,
   2304   uint32_t bitReverseFlag);
   2305 
   2306   void arm_rfft_q31(
   2307   const arm_rfft_instance_q31 * S,
   2308   q31_t * pSrc,
   2309   q31_t * pDst);
   2310 
   2311   /**
   2312    * @brief Instance structure for the floating-point RFFT/RIFFT function.
   2313    */
   2314 
   2315   typedef struct
   2316   {
   2317     uint32_t fftLenReal;                        /**< length of the real FFT. */
   2318     uint16_t fftLenBy2;                         /**< length of the complex FFT. */
   2319     uint8_t ifftFlagR;                          /**< flag that selects forward (ifftFlagR=0) or inverse (ifftFlagR=1) transform. */
   2320     uint8_t bitReverseFlagR;                    /**< flag that enables (bitReverseFlagR=1) or disables (bitReverseFlagR=0) bit reversal of output. */
   2321     uint32_t twidCoefRModifier;                     /**< twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table. */
   2322     float32_t *pTwiddleAReal;                   /**< points to the real twiddle factor table. */
   2323     float32_t *pTwiddleBReal;                   /**< points to the imag twiddle factor table. */
   2324     arm_cfft_radix4_instance_f32 *pCfft;        /**< points to the complex FFT instance. */
   2325   } arm_rfft_instance_f32;
   2326 
   2327   arm_status arm_rfft_init_f32(
   2328   arm_rfft_instance_f32 * S,
   2329   arm_cfft_radix4_instance_f32 * S_CFFT,
   2330   uint32_t fftLenReal,
   2331   uint32_t ifftFlagR,
   2332   uint32_t bitReverseFlag);
   2333 
   2334   void arm_rfft_f32(
   2335   const arm_rfft_instance_f32 * S,
   2336   float32_t * pSrc,
   2337   float32_t * pDst);
   2338 
   2339   /**
   2340    * @brief Instance structure for the floating-point RFFT/RIFFT function.
   2341    */
   2342 
   2343   typedef struct
   2344   {
   2345     arm_cfft_instance_f32 Sint;      /**< Internal CFFT structure. */
   2346     uint16_t fftLenRFFT;                        /**< length of the real sequence */
   2347     float32_t * pTwiddleRFFT;                   /**< Twiddle factors real stage  */
   2348   } arm_rfft_fast_instance_f32 ;
   2349 
   2350   arm_status arm_rfft_fast_init_f32 (
   2351   arm_rfft_fast_instance_f32 * S,
   2352   uint16_t fftLen);
   2353 
   2354   void arm_rfft_fast_f32(
   2355   arm_rfft_fast_instance_f32 * S,
   2356   float32_t * p, float32_t * pOut,
   2357   uint8_t ifftFlag);
   2358 
   2359   /**
   2360    * @brief Instance structure for the floating-point DCT4/IDCT4 function.
   2361    */
   2362 
   2363   typedef struct
   2364   {
   2365     uint16_t N;                         /**< length of the DCT4. */
   2366     uint16_t Nby2;                      /**< half of the length of the DCT4. */
   2367     float32_t normalize;                /**< normalizing factor. */
   2368     float32_t *pTwiddle;                /**< points to the twiddle factor table. */
   2369     float32_t *pCosFactor;              /**< points to the cosFactor table. */
   2370     arm_rfft_instance_f32 *pRfft;        /**< points to the real FFT instance. */
   2371     arm_cfft_radix4_instance_f32 *pCfft; /**< points to the complex FFT instance. */
   2372   } arm_dct4_instance_f32;
   2373 
   2374   /**
   2375    * @brief  Initialization function for the floating-point DCT4/IDCT4.
   2376    * @param[in,out] *S         points to an instance of floating-point DCT4/IDCT4 structure.
   2377    * @param[in]     *S_RFFT    points to an instance of floating-point RFFT/RIFFT structure.
   2378    * @param[in]     *S_CFFT    points to an instance of floating-point CFFT/CIFFT structure.
   2379    * @param[in]     N          length of the DCT4.
   2380    * @param[in]     Nby2       half of the length of the DCT4.
   2381    * @param[in]     normalize  normalizing factor.
   2382    * @return        arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>fftLenReal</code> is not a supported transform length.
   2383    */
   2384 
   2385   arm_status arm_dct4_init_f32(
   2386   arm_dct4_instance_f32 * S,
   2387   arm_rfft_instance_f32 * S_RFFT,
   2388   arm_cfft_radix4_instance_f32 * S_CFFT,
   2389   uint16_t N,
   2390   uint16_t Nby2,
   2391   float32_t normalize);
   2392 
   2393   /**
   2394    * @brief Processing function for the floating-point DCT4/IDCT4.
   2395    * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure.
   2396    * @param[in]       *pState        points to state buffer.
   2397    * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
   2398    * @return none.
   2399    */
   2400 
   2401   void arm_dct4_f32(
   2402   const arm_dct4_instance_f32 * S,
   2403   float32_t * pState,
   2404   float32_t * pInlineBuffer);
   2405 
   2406   /**
   2407    * @brief Instance structure for the Q31 DCT4/IDCT4 function.
   2408    */
   2409 
   2410   typedef struct
   2411   {
   2412     uint16_t N;                         /**< length of the DCT4. */
   2413     uint16_t Nby2;                      /**< half of the length of the DCT4. */
   2414     q31_t normalize;                    /**< normalizing factor. */
   2415     q31_t *pTwiddle;                    /**< points to the twiddle factor table. */
   2416     q31_t *pCosFactor;                  /**< points to the cosFactor table. */
   2417     arm_rfft_instance_q31 *pRfft;        /**< points to the real FFT instance. */
   2418     arm_cfft_radix4_instance_q31 *pCfft; /**< points to the complex FFT instance. */
   2419   } arm_dct4_instance_q31;
   2420 
   2421   /**
   2422    * @brief  Initialization function for the Q31 DCT4/IDCT4.
   2423    * @param[in,out] *S         points to an instance of Q31 DCT4/IDCT4 structure.
   2424    * @param[in]     *S_RFFT    points to an instance of Q31 RFFT/RIFFT structure
   2425    * @param[in]     *S_CFFT    points to an instance of Q31 CFFT/CIFFT structure
   2426    * @param[in]     N          length of the DCT4.
   2427    * @param[in]     Nby2       half of the length of the DCT4.
   2428    * @param[in]     normalize  normalizing factor.
   2429    * @return        arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
   2430    */
   2431 
   2432   arm_status arm_dct4_init_q31(
   2433   arm_dct4_instance_q31 * S,
   2434   arm_rfft_instance_q31 * S_RFFT,
   2435   arm_cfft_radix4_instance_q31 * S_CFFT,
   2436   uint16_t N,
   2437   uint16_t Nby2,
   2438   q31_t normalize);
   2439 
   2440   /**
   2441    * @brief Processing function for the Q31 DCT4/IDCT4.
   2442    * @param[in]       *S             points to an instance of the Q31 DCT4 structure.
   2443    * @param[in]       *pState        points to state buffer.
   2444    * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
   2445    * @return none.
   2446    */
   2447 
   2448   void arm_dct4_q31(
   2449   const arm_dct4_instance_q31 * S,
   2450   q31_t * pState,
   2451   q31_t * pInlineBuffer);
   2452 
   2453   /**
   2454    * @brief Instance structure for the Q15 DCT4/IDCT4 function.
   2455    */
   2456 
   2457   typedef struct
   2458   {
   2459     uint16_t N;                         /**< length of the DCT4. */
   2460     uint16_t Nby2;                      /**< half of the length of the DCT4. */
   2461     q15_t normalize;                    /**< normalizing factor. */
   2462     q15_t *pTwiddle;                    /**< points to the twiddle factor table. */
   2463     q15_t *pCosFactor;                  /**< points to the cosFactor table. */
   2464     arm_rfft_instance_q15 *pRfft;        /**< points to the real FFT instance. */
   2465     arm_cfft_radix4_instance_q15 *pCfft; /**< points to the complex FFT instance. */
   2466   } arm_dct4_instance_q15;
   2467 
   2468   /**
   2469    * @brief  Initialization function for the Q15 DCT4/IDCT4.
   2470    * @param[in,out] *S         points to an instance of Q15 DCT4/IDCT4 structure.
   2471    * @param[in]     *S_RFFT    points to an instance of Q15 RFFT/RIFFT structure.
   2472    * @param[in]     *S_CFFT    points to an instance of Q15 CFFT/CIFFT structure.
   2473    * @param[in]     N          length of the DCT4.
   2474    * @param[in]     Nby2       half of the length of the DCT4.
   2475    * @param[in]     normalize  normalizing factor.
   2476    * @return        arm_status function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_ARGUMENT_ERROR if <code>N</code> is not a supported transform length.
   2477    */
   2478 
   2479   arm_status arm_dct4_init_q15(
   2480   arm_dct4_instance_q15 * S,
   2481   arm_rfft_instance_q15 * S_RFFT,
   2482   arm_cfft_radix4_instance_q15 * S_CFFT,
   2483   uint16_t N,
   2484   uint16_t Nby2,
   2485   q15_t normalize);
   2486 
   2487   /**
   2488    * @brief Processing function for the Q15 DCT4/IDCT4.
   2489    * @param[in]       *S             points to an instance of the Q15 DCT4 structure.
   2490    * @param[in]       *pState        points to state buffer.
   2491    * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer.
   2492    * @return none.
   2493    */
   2494 
   2495   void arm_dct4_q15(
   2496   const arm_dct4_instance_q15 * S,
   2497   q15_t * pState,
   2498   q15_t * pInlineBuffer);
   2499 
   2500   /**
   2501    * @brief Floating-point vector addition.
   2502    * @param[in]       *pSrcA points to the first input vector
   2503    * @param[in]       *pSrcB points to the second input vector
   2504    * @param[out]      *pDst points to the output vector
   2505    * @param[in]       blockSize number of samples in each vector
   2506    * @return none.
   2507    */
   2508 
   2509   void arm_add_f32(
   2510   float32_t * pSrcA,
   2511   float32_t * pSrcB,
   2512   float32_t * pDst,
   2513   uint32_t blockSize);
   2514 
   2515   /**
   2516    * @brief Q7 vector addition.
   2517    * @param[in]       *pSrcA points to the first input vector
   2518    * @param[in]       *pSrcB points to the second input vector
   2519    * @param[out]      *pDst points to the output vector
   2520    * @param[in]       blockSize number of samples in each vector
   2521    * @return none.
   2522    */
   2523 
   2524   void arm_add_q7(
   2525   q7_t * pSrcA,
   2526   q7_t * pSrcB,
   2527   q7_t * pDst,
   2528   uint32_t blockSize);
   2529 
   2530   /**
   2531    * @brief Q15 vector addition.
   2532    * @param[in]       *pSrcA points to the first input vector
   2533    * @param[in]       *pSrcB points to the second input vector
   2534    * @param[out]      *pDst points to the output vector
   2535    * @param[in]       blockSize number of samples in each vector
   2536    * @return none.
   2537    */
   2538 
   2539   void arm_add_q15(
   2540   q15_t * pSrcA,
   2541   q15_t * pSrcB,
   2542   q15_t * pDst,
   2543   uint32_t blockSize);
   2544 
   2545   /**
   2546    * @brief Q31 vector addition.
   2547    * @param[in]       *pSrcA points to the first input vector
   2548    * @param[in]       *pSrcB points to the second input vector
   2549    * @param[out]      *pDst points to the output vector
   2550    * @param[in]       blockSize number of samples in each vector
   2551    * @return none.
   2552    */
   2553 
   2554   void arm_add_q31(
   2555   q31_t * pSrcA,
   2556   q31_t * pSrcB,
   2557   q31_t * pDst,
   2558   uint32_t blockSize);
   2559 
   2560   /**
   2561    * @brief Floating-point vector subtraction.
   2562    * @param[in]       *pSrcA points to the first input vector
   2563    * @param[in]       *pSrcB points to the second input vector
   2564    * @param[out]      *pDst points to the output vector
   2565    * @param[in]       blockSize number of samples in each vector
   2566    * @return none.
   2567    */
   2568 
   2569   void arm_sub_f32(
   2570   float32_t * pSrcA,
   2571   float32_t * pSrcB,
   2572   float32_t * pDst,
   2573   uint32_t blockSize);
   2574 
   2575   /**
   2576    * @brief Q7 vector subtraction.
   2577    * @param[in]       *pSrcA points to the first input vector
   2578    * @param[in]       *pSrcB points to the second input vector
   2579    * @param[out]      *pDst points to the output vector
   2580    * @param[in]       blockSize number of samples in each vector
   2581    * @return none.
   2582    */
   2583 
   2584   void arm_sub_q7(
   2585   q7_t * pSrcA,
   2586   q7_t * pSrcB,
   2587   q7_t * pDst,
   2588   uint32_t blockSize);
   2589 
   2590   /**
   2591    * @brief Q15 vector subtraction.
   2592    * @param[in]       *pSrcA points to the first input vector
   2593    * @param[in]       *pSrcB points to the second input vector
   2594    * @param[out]      *pDst points to the output vector
   2595    * @param[in]       blockSize number of samples in each vector
   2596    * @return none.
   2597    */
   2598 
   2599   void arm_sub_q15(
   2600   q15_t * pSrcA,
   2601   q15_t * pSrcB,
   2602   q15_t * pDst,
   2603   uint32_t blockSize);
   2604 
   2605   /**
   2606    * @brief Q31 vector subtraction.
   2607    * @param[in]       *pSrcA points to the first input vector
   2608    * @param[in]       *pSrcB points to the second input vector
   2609    * @param[out]      *pDst points to the output vector
   2610    * @param[in]       blockSize number of samples in each vector
   2611    * @return none.
   2612    */
   2613 
   2614   void arm_sub_q31(
   2615   q31_t * pSrcA,
   2616   q31_t * pSrcB,
   2617   q31_t * pDst,
   2618   uint32_t blockSize);
   2619 
   2620   /**
   2621    * @brief Multiplies a floating-point vector by a scalar.
   2622    * @param[in]       *pSrc points to the input vector
   2623    * @param[in]       scale scale factor to be applied
   2624    * @param[out]      *pDst points to the output vector
   2625    * @param[in]       blockSize number of samples in the vector
   2626    * @return none.
   2627    */
   2628 
   2629   void arm_scale_f32(
   2630   float32_t * pSrc,
   2631   float32_t scale,
   2632   float32_t * pDst,
   2633   uint32_t blockSize);
   2634 
   2635   /**
   2636    * @brief Multiplies a Q7 vector by a scalar.
   2637    * @param[in]       *pSrc points to the input vector
   2638    * @param[in]       scaleFract fractional portion of the scale value
   2639    * @param[in]       shift number of bits to shift the result by
   2640    * @param[out]      *pDst points to the output vector
   2641    * @param[in]       blockSize number of samples in the vector
   2642    * @return none.
   2643    */
   2644 
   2645   void arm_scale_q7(
   2646   q7_t * pSrc,
   2647   q7_t scaleFract,
   2648   int8_t shift,
   2649   q7_t * pDst,
   2650   uint32_t blockSize);
   2651 
   2652   /**
   2653    * @brief Multiplies a Q15 vector by a scalar.
   2654    * @param[in]       *pSrc points to the input vector
   2655    * @param[in]       scaleFract fractional portion of the scale value
   2656    * @param[in]       shift number of bits to shift the result by
   2657    * @param[out]      *pDst points to the output vector
   2658    * @param[in]       blockSize number of samples in the vector
   2659    * @return none.
   2660    */
   2661 
   2662   void arm_scale_q15(
   2663   q15_t * pSrc,
   2664   q15_t scaleFract,
   2665   int8_t shift,
   2666   q15_t * pDst,
   2667   uint32_t blockSize);
   2668 
   2669   /**
   2670    * @brief Multiplies a Q31 vector by a scalar.
   2671    * @param[in]       *pSrc points to the input vector
   2672    * @param[in]       scaleFract fractional portion of the scale value
   2673    * @param[in]       shift number of bits to shift the result by
   2674    * @param[out]      *pDst points to the output vector
   2675    * @param[in]       blockSize number of samples in the vector
   2676    * @return none.
   2677    */
   2678 
   2679   void arm_scale_q31(
   2680   q31_t * pSrc,
   2681   q31_t scaleFract,
   2682   int8_t shift,
   2683   q31_t * pDst,
   2684   uint32_t blockSize);
   2685 
   2686   /**
   2687    * @brief Q7 vector absolute value.
   2688    * @param[in]       *pSrc points to the input buffer
   2689    * @param[out]      *pDst points to the output buffer
   2690    * @param[in]       blockSize number of samples in each vector
   2691    * @return none.
   2692    */
   2693 
   2694   void arm_abs_q7(
   2695   q7_t * pSrc,
   2696   q7_t * pDst,
   2697   uint32_t blockSize);
   2698 
   2699   /**
   2700    * @brief Floating-point vector absolute value.
   2701    * @param[in]       *pSrc points to the input buffer
   2702    * @param[out]      *pDst points to the output buffer
   2703    * @param[in]       blockSize number of samples in each vector
   2704    * @return none.
   2705    */
   2706 
   2707   void arm_abs_f32(
   2708   float32_t * pSrc,
   2709   float32_t * pDst,
   2710   uint32_t blockSize);
   2711 
   2712   /**
   2713    * @brief Q15 vector absolute value.
   2714    * @param[in]       *pSrc points to the input buffer
   2715    * @param[out]      *pDst points to the output buffer
   2716    * @param[in]       blockSize number of samples in each vector
   2717    * @return none.
   2718    */
   2719 
   2720   void arm_abs_q15(
   2721   q15_t * pSrc,
   2722   q15_t * pDst,
   2723   uint32_t blockSize);
   2724 
   2725   /**
   2726    * @brief Q31 vector absolute value.
   2727    * @param[in]       *pSrc points to the input buffer
   2728    * @param[out]      *pDst points to the output buffer
   2729    * @param[in]       blockSize number of samples in each vector
   2730    * @return none.
   2731    */
   2732 
   2733   void arm_abs_q31(
   2734   q31_t * pSrc,
   2735   q31_t * pDst,
   2736   uint32_t blockSize);
   2737 
   2738   /**
   2739    * @brief Dot product of floating-point vectors.
   2740    * @param[in]       *pSrcA points to the first input vector
   2741    * @param[in]       *pSrcB points to the second input vector
   2742    * @param[in]       blockSize number of samples in each vector
   2743    * @param[out]      *result output result returned here
   2744    * @return none.
   2745    */
   2746 
   2747   void arm_dot_prod_f32(
   2748   float32_t * pSrcA,
   2749   float32_t * pSrcB,
   2750   uint32_t blockSize,
   2751   float32_t * result);
   2752 
   2753   /**
   2754    * @brief Dot product of Q7 vectors.
   2755    * @param[in]       *pSrcA points to the first input vector
   2756    * @param[in]       *pSrcB points to the second input vector
   2757    * @param[in]       blockSize number of samples in each vector
   2758    * @param[out]      *result output result returned here
   2759    * @return none.
   2760    */
   2761 
   2762   void arm_dot_prod_q7(
   2763   q7_t * pSrcA,
   2764   q7_t * pSrcB,
   2765   uint32_t blockSize,
   2766   q31_t * result);
   2767 
   2768   /**
   2769    * @brief Dot product of Q15 vectors.
   2770    * @param[in]       *pSrcA points to the first input vector
   2771    * @param[in]       *pSrcB points to the second input vector
   2772    * @param[in]       blockSize number of samples in each vector
   2773    * @param[out]      *result output result returned here
   2774    * @return none.
   2775    */
   2776 
   2777   void arm_dot_prod_q15(
   2778   q15_t * pSrcA,
   2779   q15_t * pSrcB,
   2780   uint32_t blockSize,
   2781   q63_t * result);
   2782 
   2783   /**
   2784    * @brief Dot product of Q31 vectors.
   2785    * @param[in]       *pSrcA points to the first input vector
   2786    * @param[in]       *pSrcB points to the second input vector
   2787    * @param[in]       blockSize number of samples in each vector
   2788    * @param[out]      *result output result returned here
   2789    * @return none.
   2790    */
   2791 
   2792   void arm_dot_prod_q31(
   2793   q31_t * pSrcA,
   2794   q31_t * pSrcB,
   2795   uint32_t blockSize,
   2796   q63_t * result);
   2797 
   2798   /**
   2799    * @brief  Shifts the elements of a Q7 vector a specified number of bits.
   2800    * @param[in]  *pSrc points to the input vector
   2801    * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
   2802    * @param[out]  *pDst points to the output vector
   2803    * @param[in]  blockSize number of samples in the vector
   2804    * @return none.
   2805    */
   2806 
   2807   void arm_shift_q7(
   2808   q7_t * pSrc,
   2809   int8_t shiftBits,
   2810   q7_t * pDst,
   2811   uint32_t blockSize);
   2812 
   2813   /**
   2814    * @brief  Shifts the elements of a Q15 vector a specified number of bits.
   2815    * @param[in]  *pSrc points to the input vector
   2816    * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
   2817    * @param[out]  *pDst points to the output vector
   2818    * @param[in]  blockSize number of samples in the vector
   2819    * @return none.
   2820    */
   2821 
   2822   void arm_shift_q15(
   2823   q15_t * pSrc,
   2824   int8_t shiftBits,
   2825   q15_t * pDst,
   2826   uint32_t blockSize);
   2827 
   2828   /**
   2829    * @brief  Shifts the elements of a Q31 vector a specified number of bits.
   2830    * @param[in]  *pSrc points to the input vector
   2831    * @param[in]  shiftBits number of bits to shift.  A positive value shifts left; a negative value shifts right.
   2832    * @param[out]  *pDst points to the output vector
   2833    * @param[in]  blockSize number of samples in the vector
   2834    * @return none.
   2835    */
   2836 
   2837   void arm_shift_q31(
   2838   q31_t * pSrc,
   2839   int8_t shiftBits,
   2840   q31_t * pDst,
   2841   uint32_t blockSize);
   2842 
   2843   /**
   2844    * @brief  Adds a constant offset to a floating-point vector.
   2845    * @param[in]  *pSrc points to the input vector
   2846    * @param[in]  offset is the offset to be added
   2847    * @param[out]  *pDst points to the output vector
   2848    * @param[in]  blockSize number of samples in the vector
   2849    * @return none.
   2850    */
   2851 
   2852   void arm_offset_f32(
   2853   float32_t * pSrc,
   2854   float32_t offset,
   2855   float32_t * pDst,
   2856   uint32_t blockSize);
   2857 
   2858   /**
   2859    * @brief  Adds a constant offset to a Q7 vector.
   2860    * @param[in]  *pSrc points to the input vector
   2861    * @param[in]  offset is the offset to be added
   2862    * @param[out]  *pDst points to the output vector
   2863    * @param[in]  blockSize number of samples in the vector
   2864    * @return none.
   2865    */
   2866 
   2867   void arm_offset_q7(
   2868   q7_t * pSrc,
   2869   q7_t offset,
   2870   q7_t * pDst,
   2871   uint32_t blockSize);
   2872 
   2873   /**
   2874    * @brief  Adds a constant offset to a Q15 vector.
   2875    * @param[in]  *pSrc points to the input vector
   2876    * @param[in]  offset is the offset to be added
   2877    * @param[out]  *pDst points to the output vector
   2878    * @param[in]  blockSize number of samples in the vector
   2879    * @return none.
   2880    */
   2881 
   2882   void arm_offset_q15(
   2883   q15_t * pSrc,
   2884   q15_t offset,
   2885   q15_t * pDst,
   2886   uint32_t blockSize);
   2887 
   2888   /**
   2889    * @brief  Adds a constant offset to a Q31 vector.
   2890    * @param[in]  *pSrc points to the input vector
   2891    * @param[in]  offset is the offset to be added
   2892    * @param[out]  *pDst points to the output vector
   2893    * @param[in]  blockSize number of samples in the vector
   2894    * @return none.
   2895    */
   2896 
   2897   void arm_offset_q31(
   2898   q31_t * pSrc,
   2899   q31_t offset,
   2900   q31_t * pDst,
   2901   uint32_t blockSize);
   2902 
   2903   /**
   2904    * @brief  Negates the elements of a floating-point vector.
   2905    * @param[in]  *pSrc points to the input vector
   2906    * @param[out]  *pDst points to the output vector
   2907    * @param[in]  blockSize number of samples in the vector
   2908    * @return none.
   2909    */
   2910 
   2911   void arm_negate_f32(
   2912   float32_t * pSrc,
   2913   float32_t * pDst,
   2914   uint32_t blockSize);
   2915 
   2916   /**
   2917    * @brief  Negates the elements of a Q7 vector.
   2918    * @param[in]  *pSrc points to the input vector
   2919    * @param[out]  *pDst points to the output vector
   2920    * @param[in]  blockSize number of samples in the vector
   2921    * @return none.
   2922    */
   2923 
   2924   void arm_negate_q7(
   2925   q7_t * pSrc,
   2926   q7_t * pDst,
   2927   uint32_t blockSize);
   2928 
   2929   /**
   2930    * @brief  Negates the elements of a Q15 vector.
   2931    * @param[in]  *pSrc points to the input vector
   2932    * @param[out]  *pDst points to the output vector
   2933    * @param[in]  blockSize number of samples in the vector
   2934    * @return none.
   2935    */
   2936 
   2937   void arm_negate_q15(
   2938   q15_t * pSrc,
   2939   q15_t * pDst,
   2940   uint32_t blockSize);
   2941 
   2942   /**
   2943    * @brief  Negates the elements of a Q31 vector.
   2944    * @param[in]  *pSrc points to the input vector
   2945    * @param[out]  *pDst points to the output vector
   2946    * @param[in]  blockSize number of samples in the vector
   2947    * @return none.
   2948    */
   2949 
   2950   void arm_negate_q31(
   2951   q31_t * pSrc,
   2952   q31_t * pDst,
   2953   uint32_t blockSize);
   2954   /**
   2955    * @brief  Copies the elements of a floating-point vector.
   2956    * @param[in]  *pSrc input pointer
   2957    * @param[out]  *pDst output pointer
   2958    * @param[in]  blockSize number of samples to process
   2959    * @return none.
   2960    */
   2961   void arm_copy_f32(
   2962   float32_t * pSrc,
   2963   float32_t * pDst,
   2964   uint32_t blockSize);
   2965 
   2966   /**
   2967    * @brief  Copies the elements of a Q7 vector.
   2968    * @param[in]  *pSrc input pointer
   2969    * @param[out]  *pDst output pointer
   2970    * @param[in]  blockSize number of samples to process
   2971    * @return none.
   2972    */
   2973   void arm_copy_q7(
   2974   q7_t * pSrc,
   2975   q7_t * pDst,
   2976   uint32_t blockSize);
   2977 
   2978   /**
   2979    * @brief  Copies the elements of a Q15 vector.
   2980    * @param[in]  *pSrc input pointer
   2981    * @param[out]  *pDst output pointer
   2982    * @param[in]  blockSize number of samples to process
   2983    * @return none.
   2984    */
   2985   void arm_copy_q15(
   2986   q15_t * pSrc,
   2987   q15_t * pDst,
   2988   uint32_t blockSize);
   2989 
   2990   /**
   2991    * @brief  Copies the elements of a Q31 vector.
   2992    * @param[in]  *pSrc input pointer
   2993    * @param[out]  *pDst output pointer
   2994    * @param[in]  blockSize number of samples to process
   2995    * @return none.
   2996    */
   2997   void arm_copy_q31(
   2998   q31_t * pSrc,
   2999   q31_t * pDst,
   3000   uint32_t blockSize);
   3001   /**
   3002    * @brief  Fills a constant value into a floating-point vector.
   3003    * @param[in]  value input value to be filled
   3004    * @param[out]  *pDst output pointer
   3005    * @param[in]  blockSize number of samples to process
   3006    * @return none.
   3007    */
   3008   void arm_fill_f32(
   3009   float32_t value,
   3010   float32_t * pDst,
   3011   uint32_t blockSize);
   3012 
   3013   /**
   3014    * @brief  Fills a constant value into a Q7 vector.
   3015    * @param[in]  value input value to be filled
   3016    * @param[out]  *pDst output pointer
   3017    * @param[in]  blockSize number of samples to process
   3018    * @return none.
   3019    */
   3020   void arm_fill_q7(
   3021   q7_t value,
   3022   q7_t * pDst,
   3023   uint32_t blockSize);
   3024 
   3025   /**
   3026    * @brief  Fills a constant value into a Q15 vector.
   3027    * @param[in]  value input value to be filled
   3028    * @param[out]  *pDst output pointer
   3029    * @param[in]  blockSize number of samples to process
   3030    * @return none.
   3031    */
   3032   void arm_fill_q15(
   3033   q15_t value,
   3034   q15_t * pDst,
   3035   uint32_t blockSize);
   3036 
   3037   /**
   3038    * @brief  Fills a constant value into a Q31 vector.
   3039    * @param[in]  value input value to be filled
   3040    * @param[out]  *pDst output pointer
   3041    * @param[in]  blockSize number of samples to process
   3042    * @return none.
   3043    */
   3044   void arm_fill_q31(
   3045   q31_t value,
   3046   q31_t * pDst,
   3047   uint32_t blockSize);
   3048 
   3049 /**
   3050  * @brief Convolution of floating-point sequences.
   3051  * @param[in] *pSrcA points to the first input sequence.
   3052  * @param[in] srcALen length of the first input sequence.
   3053  * @param[in] *pSrcB points to the second input sequence.
   3054  * @param[in] srcBLen length of the second input sequence.
   3055  * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.
   3056  * @return none.
   3057  */
   3058 
   3059   void arm_conv_f32(
   3060   float32_t * pSrcA,
   3061   uint32_t srcALen,
   3062   float32_t * pSrcB,
   3063   uint32_t srcBLen,
   3064   float32_t * pDst);
   3065 
   3066 
   3067   /**
   3068    * @brief Convolution of Q15 sequences.
   3069    * @param[in] *pSrcA points to the first input sequence.
   3070    * @param[in] srcALen length of the first input sequence.
   3071    * @param[in] *pSrcB points to the second input sequence.
   3072    * @param[in] srcBLen length of the second input sequence.
   3073    * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   3074    * @param[in]  *pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   3075    * @param[in]  *pScratch2 points to scratch buffer of size min(srcALen, srcBLen).
   3076    * @return none.
   3077    */
   3078 
   3079 
   3080   void arm_conv_opt_q15(
   3081   q15_t * pSrcA,
   3082   uint32_t srcALen,
   3083   q15_t * pSrcB,
   3084   uint32_t srcBLen,
   3085   q15_t * pDst,
   3086   q15_t * pScratch1,
   3087   q15_t * pScratch2);
   3088 
   3089 
   3090 /**
   3091  * @brief Convolution of Q15 sequences.
   3092  * @param[in] *pSrcA points to the first input sequence.
   3093  * @param[in] srcALen length of the first input sequence.
   3094  * @param[in] *pSrcB points to the second input sequence.
   3095  * @param[in] srcBLen length of the second input sequence.
   3096  * @param[out] *pDst points to the location where the output result is written.  Length srcALen+srcBLen-1.
   3097  * @return none.
   3098  */
   3099 
   3100   void arm_conv_q15(
   3101   q15_t * pSrcA,
   3102   uint32_t srcALen,
   3103   q15_t * pSrcB,
   3104   uint32_t srcBLen,
   3105   q15_t * pDst);
   3106 
   3107   /**
   3108    * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
   3109    * @param[in] *pSrcA points to the first input sequence.
   3110    * @param[in] srcALen length of the first input sequence.
   3111    * @param[in] *pSrcB points to the second input sequence.
   3112    * @param[in] srcBLen length of the second input sequence.
   3113    * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   3114    * @return none.
   3115    */
   3116 
   3117   void arm_conv_fast_q15(
   3118   q15_t * pSrcA,
   3119   uint32_t srcALen,
   3120   q15_t * pSrcB,
   3121   uint32_t srcBLen,
   3122   q15_t * pDst);
   3123 
   3124   /**
   3125    * @brief Convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
   3126    * @param[in] *pSrcA points to the first input sequence.
   3127    * @param[in] srcALen length of the first input sequence.
   3128    * @param[in] *pSrcB points to the second input sequence.
   3129    * @param[in] srcBLen length of the second input sequence.
   3130    * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   3131    * @param[in]  *pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   3132    * @param[in]  *pScratch2 points to scratch buffer of size min(srcALen, srcBLen).
   3133    * @return none.
   3134    */
   3135 
   3136   void arm_conv_fast_opt_q15(
   3137   q15_t * pSrcA,
   3138   uint32_t srcALen,
   3139   q15_t * pSrcB,
   3140   uint32_t srcBLen,
   3141   q15_t * pDst,
   3142   q15_t * pScratch1,
   3143   q15_t * pScratch2);
   3144 
   3145 
   3146 
   3147   /**
   3148    * @brief Convolution of Q31 sequences.
   3149    * @param[in] *pSrcA points to the first input sequence.
   3150    * @param[in] srcALen length of the first input sequence.
   3151    * @param[in] *pSrcB points to the second input sequence.
   3152    * @param[in] srcBLen length of the second input sequence.
   3153    * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   3154    * @return none.
   3155    */
   3156 
   3157   void arm_conv_q31(
   3158   q31_t * pSrcA,
   3159   uint32_t srcALen,
   3160   q31_t * pSrcB,
   3161   uint32_t srcBLen,
   3162   q31_t * pDst);
   3163 
   3164   /**
   3165    * @brief Convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
   3166    * @param[in] *pSrcA points to the first input sequence.
   3167    * @param[in] srcALen length of the first input sequence.
   3168    * @param[in] *pSrcB points to the second input sequence.
   3169    * @param[in] srcBLen length of the second input sequence.
   3170    * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   3171    * @return none.
   3172    */
   3173 
   3174   void arm_conv_fast_q31(
   3175   q31_t * pSrcA,
   3176   uint32_t srcALen,
   3177   q31_t * pSrcB,
   3178   uint32_t srcBLen,
   3179   q31_t * pDst);
   3180 
   3181 
   3182     /**
   3183    * @brief Convolution of Q7 sequences.
   3184    * @param[in] *pSrcA points to the first input sequence.
   3185    * @param[in] srcALen length of the first input sequence.
   3186    * @param[in] *pSrcB points to the second input sequence.
   3187    * @param[in] srcBLen length of the second input sequence.
   3188    * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   3189    * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   3190    * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
   3191    * @return none.
   3192    */
   3193 
   3194   void arm_conv_opt_q7(
   3195   q7_t * pSrcA,
   3196   uint32_t srcALen,
   3197   q7_t * pSrcB,
   3198   uint32_t srcBLen,
   3199   q7_t * pDst,
   3200   q15_t * pScratch1,
   3201   q15_t * pScratch2);
   3202 
   3203 
   3204 
   3205   /**
   3206    * @brief Convolution of Q7 sequences.
   3207    * @param[in] *pSrcA points to the first input sequence.
   3208    * @param[in] srcALen length of the first input sequence.
   3209    * @param[in] *pSrcB points to the second input sequence.
   3210    * @param[in] srcBLen length of the second input sequence.
   3211    * @param[out] *pDst points to the block of output data  Length srcALen+srcBLen-1.
   3212    * @return none.
   3213    */
   3214 
   3215   void arm_conv_q7(
   3216   q7_t * pSrcA,
   3217   uint32_t srcALen,
   3218   q7_t * pSrcB,
   3219   uint32_t srcBLen,
   3220   q7_t * pDst);
   3221 
   3222 
   3223   /**
   3224    * @brief Partial convolution of floating-point sequences.
   3225    * @param[in]       *pSrcA points to the first input sequence.
   3226    * @param[in]       srcALen length of the first input sequence.
   3227    * @param[in]       *pSrcB points to the second input sequence.
   3228    * @param[in]       srcBLen length of the second input sequence.
   3229    * @param[out]      *pDst points to the block of output data
   3230    * @param[in]       firstIndex is the first output sample to start with.
   3231    * @param[in]       numPoints is the number of output points to be computed.
   3232    * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   3233    */
   3234 
   3235   arm_status arm_conv_partial_f32(
   3236   float32_t * pSrcA,
   3237   uint32_t srcALen,
   3238   float32_t * pSrcB,
   3239   uint32_t srcBLen,
   3240   float32_t * pDst,
   3241   uint32_t firstIndex,
   3242   uint32_t numPoints);
   3243 
   3244     /**
   3245    * @brief Partial convolution of Q15 sequences.
   3246    * @param[in]       *pSrcA points to the first input sequence.
   3247    * @param[in]       srcALen length of the first input sequence.
   3248    * @param[in]       *pSrcB points to the second input sequence.
   3249    * @param[in]       srcBLen length of the second input sequence.
   3250    * @param[out]      *pDst points to the block of output data
   3251    * @param[in]       firstIndex is the first output sample to start with.
   3252    * @param[in]       numPoints is the number of output points to be computed.
   3253    * @param[in]       * pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   3254    * @param[in]       * pScratch2 points to scratch buffer of size min(srcALen, srcBLen).
   3255    * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   3256    */
   3257 
   3258   arm_status arm_conv_partial_opt_q15(
   3259   q15_t * pSrcA,
   3260   uint32_t srcALen,
   3261   q15_t * pSrcB,
   3262   uint32_t srcBLen,
   3263   q15_t * pDst,
   3264   uint32_t firstIndex,
   3265   uint32_t numPoints,
   3266   q15_t * pScratch1,
   3267   q15_t * pScratch2);
   3268 
   3269 
   3270 /**
   3271    * @brief Partial convolution of Q15 sequences.
   3272    * @param[in]       *pSrcA points to the first input sequence.
   3273    * @param[in]       srcALen length of the first input sequence.
   3274    * @param[in]       *pSrcB points to the second input sequence.
   3275    * @param[in]       srcBLen length of the second input sequence.
   3276    * @param[out]      *pDst points to the block of output data
   3277    * @param[in]       firstIndex is the first output sample to start with.
   3278    * @param[in]       numPoints is the number of output points to be computed.
   3279    * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   3280    */
   3281 
   3282   arm_status arm_conv_partial_q15(
   3283   q15_t * pSrcA,
   3284   uint32_t srcALen,
   3285   q15_t * pSrcB,
   3286   uint32_t srcBLen,
   3287   q15_t * pDst,
   3288   uint32_t firstIndex,
   3289   uint32_t numPoints);
   3290 
   3291   /**
   3292    * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
   3293    * @param[in]       *pSrcA points to the first input sequence.
   3294    * @param[in]       srcALen length of the first input sequence.
   3295    * @param[in]       *pSrcB points to the second input sequence.
   3296    * @param[in]       srcBLen length of the second input sequence.
   3297    * @param[out]      *pDst points to the block of output data
   3298    * @param[in]       firstIndex is the first output sample to start with.
   3299    * @param[in]       numPoints is the number of output points to be computed.
   3300    * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   3301    */
   3302 
   3303   arm_status arm_conv_partial_fast_q15(
   3304   q15_t * pSrcA,
   3305   uint32_t srcALen,
   3306   q15_t * pSrcB,
   3307   uint32_t srcBLen,
   3308   q15_t * pDst,
   3309   uint32_t firstIndex,
   3310   uint32_t numPoints);
   3311 
   3312 
   3313   /**
   3314    * @brief Partial convolution of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4
   3315    * @param[in]       *pSrcA points to the first input sequence.
   3316    * @param[in]       srcALen length of the first input sequence.
   3317    * @param[in]       *pSrcB points to the second input sequence.
   3318    * @param[in]       srcBLen length of the second input sequence.
   3319    * @param[out]      *pDst points to the block of output data
   3320    * @param[in]       firstIndex is the first output sample to start with.
   3321    * @param[in]       numPoints is the number of output points to be computed.
   3322    * @param[in]       * pScratch1 points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   3323    * @param[in]       * pScratch2 points to scratch buffer of size min(srcALen, srcBLen).
   3324    * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   3325    */
   3326 
   3327   arm_status arm_conv_partial_fast_opt_q15(
   3328   q15_t * pSrcA,
   3329   uint32_t srcALen,
   3330   q15_t * pSrcB,
   3331   uint32_t srcBLen,
   3332   q15_t * pDst,
   3333   uint32_t firstIndex,
   3334   uint32_t numPoints,
   3335   q15_t * pScratch1,
   3336   q15_t * pScratch2);
   3337 
   3338 
   3339   /**
   3340    * @brief Partial convolution of Q31 sequences.
   3341    * @param[in]       *pSrcA points to the first input sequence.
   3342    * @param[in]       srcALen length of the first input sequence.
   3343    * @param[in]       *pSrcB points to the second input sequence.
   3344    * @param[in]       srcBLen length of the second input sequence.
   3345    * @param[out]      *pDst points to the block of output data
   3346    * @param[in]       firstIndex is the first output sample to start with.
   3347    * @param[in]       numPoints is the number of output points to be computed.
   3348    * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   3349    */
   3350 
   3351   arm_status arm_conv_partial_q31(
   3352   q31_t * pSrcA,
   3353   uint32_t srcALen,
   3354   q31_t * pSrcB,
   3355   uint32_t srcBLen,
   3356   q31_t * pDst,
   3357   uint32_t firstIndex,
   3358   uint32_t numPoints);
   3359 
   3360 
   3361   /**
   3362    * @brief Partial convolution of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
   3363    * @param[in]       *pSrcA points to the first input sequence.
   3364    * @param[in]       srcALen length of the first input sequence.
   3365    * @param[in]       *pSrcB points to the second input sequence.
   3366    * @param[in]       srcBLen length of the second input sequence.
   3367    * @param[out]      *pDst points to the block of output data
   3368    * @param[in]       firstIndex is the first output sample to start with.
   3369    * @param[in]       numPoints is the number of output points to be computed.
   3370    * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   3371    */
   3372 
   3373   arm_status arm_conv_partial_fast_q31(
   3374   q31_t * pSrcA,
   3375   uint32_t srcALen,
   3376   q31_t * pSrcB,
   3377   uint32_t srcBLen,
   3378   q31_t * pDst,
   3379   uint32_t firstIndex,
   3380   uint32_t numPoints);
   3381 
   3382 
   3383   /**
   3384    * @brief Partial convolution of Q7 sequences
   3385    * @param[in]       *pSrcA points to the first input sequence.
   3386    * @param[in]       srcALen length of the first input sequence.
   3387    * @param[in]       *pSrcB points to the second input sequence.
   3388    * @param[in]       srcBLen length of the second input sequence.
   3389    * @param[out]      *pDst points to the block of output data
   3390    * @param[in]       firstIndex is the first output sample to start with.
   3391    * @param[in]       numPoints is the number of output points to be computed.
   3392    * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   3393    * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
   3394    * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   3395    */
   3396 
   3397   arm_status arm_conv_partial_opt_q7(
   3398   q7_t * pSrcA,
   3399   uint32_t srcALen,
   3400   q7_t * pSrcB,
   3401   uint32_t srcBLen,
   3402   q7_t * pDst,
   3403   uint32_t firstIndex,
   3404   uint32_t numPoints,
   3405   q15_t * pScratch1,
   3406   q15_t * pScratch2);
   3407 
   3408 
   3409 /**
   3410    * @brief Partial convolution of Q7 sequences.
   3411    * @param[in]       *pSrcA points to the first input sequence.
   3412    * @param[in]       srcALen length of the first input sequence.
   3413    * @param[in]       *pSrcB points to the second input sequence.
   3414    * @param[in]       srcBLen length of the second input sequence.
   3415    * @param[out]      *pDst points to the block of output data
   3416    * @param[in]       firstIndex is the first output sample to start with.
   3417    * @param[in]       numPoints is the number of output points to be computed.
   3418    * @return  Returns either ARM_MATH_SUCCESS if the function completed correctly or ARM_MATH_ARGUMENT_ERROR if the requested subset is not in the range [0 srcALen+srcBLen-2].
   3419    */
   3420 
   3421   arm_status arm_conv_partial_q7(
   3422   q7_t * pSrcA,
   3423   uint32_t srcALen,
   3424   q7_t * pSrcB,
   3425   uint32_t srcBLen,
   3426   q7_t * pDst,
   3427   uint32_t firstIndex,
   3428   uint32_t numPoints);
   3429 
   3430 
   3431 
   3432   /**
   3433    * @brief Instance structure for the Q15 FIR decimator.
   3434    */
   3435 
   3436   typedef struct
   3437   {
   3438     uint8_t M;                      /**< decimation factor. */
   3439     uint16_t numTaps;               /**< number of coefficients in the filter. */
   3440     q15_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numTaps.*/
   3441     q15_t *pState;                   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   3442   } arm_fir_decimate_instance_q15;
   3443 
   3444   /**
   3445    * @brief Instance structure for the Q31 FIR decimator.
   3446    */
   3447 
   3448   typedef struct
   3449   {
   3450     uint8_t M;                  /**< decimation factor. */
   3451     uint16_t numTaps;           /**< number of coefficients in the filter. */
   3452     q31_t *pCoeffs;              /**< points to the coefficient array. The array is of length numTaps.*/
   3453     q31_t *pState;               /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   3454 
   3455   } arm_fir_decimate_instance_q31;
   3456 
   3457   /**
   3458    * @brief Instance structure for the floating-point FIR decimator.
   3459    */
   3460 
   3461   typedef struct
   3462   {
   3463     uint8_t M;                          /**< decimation factor. */
   3464     uint16_t numTaps;                   /**< number of coefficients in the filter. */
   3465     float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numTaps.*/
   3466     float32_t *pState;                   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   3467 
   3468   } arm_fir_decimate_instance_f32;
   3469 
   3470 
   3471 
   3472   /**
   3473    * @brief Processing function for the floating-point FIR decimator.
   3474    * @param[in] *S points to an instance of the floating-point FIR decimator structure.
   3475    * @param[in] *pSrc points to the block of input data.
   3476    * @param[out] *pDst points to the block of output data
   3477    * @param[in] blockSize number of input samples to process per call.
   3478    * @return none
   3479    */
   3480 
   3481   void arm_fir_decimate_f32(
   3482   const arm_fir_decimate_instance_f32 * S,
   3483   float32_t * pSrc,
   3484   float32_t * pDst,
   3485   uint32_t blockSize);
   3486 
   3487 
   3488   /**
   3489    * @brief  Initialization function for the floating-point FIR decimator.
   3490    * @param[in,out] *S points to an instance of the floating-point FIR decimator structure.
   3491    * @param[in] numTaps  number of coefficients in the filter.
   3492    * @param[in] M  decimation factor.
   3493    * @param[in] *pCoeffs points to the filter coefficients.
   3494    * @param[in] *pState points to the state buffer.
   3495    * @param[in] blockSize number of input samples to process per call.
   3496    * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   3497    * <code>blockSize</code> is not a multiple of <code>M</code>.
   3498    */
   3499 
   3500   arm_status arm_fir_decimate_init_f32(
   3501   arm_fir_decimate_instance_f32 * S,
   3502   uint16_t numTaps,
   3503   uint8_t M,
   3504   float32_t * pCoeffs,
   3505   float32_t * pState,
   3506   uint32_t blockSize);
   3507 
   3508   /**
   3509    * @brief Processing function for the Q15 FIR decimator.
   3510    * @param[in] *S points to an instance of the Q15 FIR decimator structure.
   3511    * @param[in] *pSrc points to the block of input data.
   3512    * @param[out] *pDst points to the block of output data
   3513    * @param[in] blockSize number of input samples to process per call.
   3514    * @return none
   3515    */
   3516 
   3517   void arm_fir_decimate_q15(
   3518   const arm_fir_decimate_instance_q15 * S,
   3519   q15_t * pSrc,
   3520   q15_t * pDst,
   3521   uint32_t blockSize);
   3522 
   3523   /**
   3524    * @brief Processing function for the Q15 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
   3525    * @param[in] *S points to an instance of the Q15 FIR decimator structure.
   3526    * @param[in] *pSrc points to the block of input data.
   3527    * @param[out] *pDst points to the block of output data
   3528    * @param[in] blockSize number of input samples to process per call.
   3529    * @return none
   3530    */
   3531 
   3532   void arm_fir_decimate_fast_q15(
   3533   const arm_fir_decimate_instance_q15 * S,
   3534   q15_t * pSrc,
   3535   q15_t * pDst,
   3536   uint32_t blockSize);
   3537 
   3538 
   3539 
   3540   /**
   3541    * @brief  Initialization function for the Q15 FIR decimator.
   3542    * @param[in,out] *S points to an instance of the Q15 FIR decimator structure.
   3543    * @param[in] numTaps  number of coefficients in the filter.
   3544    * @param[in] M  decimation factor.
   3545    * @param[in] *pCoeffs points to the filter coefficients.
   3546    * @param[in] *pState points to the state buffer.
   3547    * @param[in] blockSize number of input samples to process per call.
   3548    * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   3549    * <code>blockSize</code> is not a multiple of <code>M</code>.
   3550    */
   3551 
   3552   arm_status arm_fir_decimate_init_q15(
   3553   arm_fir_decimate_instance_q15 * S,
   3554   uint16_t numTaps,
   3555   uint8_t M,
   3556   q15_t * pCoeffs,
   3557   q15_t * pState,
   3558   uint32_t blockSize);
   3559 
   3560   /**
   3561    * @brief Processing function for the Q31 FIR decimator.
   3562    * @param[in] *S points to an instance of the Q31 FIR decimator structure.
   3563    * @param[in] *pSrc points to the block of input data.
   3564    * @param[out] *pDst points to the block of output data
   3565    * @param[in] blockSize number of input samples to process per call.
   3566    * @return none
   3567    */
   3568 
   3569   void arm_fir_decimate_q31(
   3570   const arm_fir_decimate_instance_q31 * S,
   3571   q31_t * pSrc,
   3572   q31_t * pDst,
   3573   uint32_t blockSize);
   3574 
   3575   /**
   3576    * @brief Processing function for the Q31 FIR decimator (fast variant) for Cortex-M3 and Cortex-M4.
   3577    * @param[in] *S points to an instance of the Q31 FIR decimator structure.
   3578    * @param[in] *pSrc points to the block of input data.
   3579    * @param[out] *pDst points to the block of output data
   3580    * @param[in] blockSize number of input samples to process per call.
   3581    * @return none
   3582    */
   3583 
   3584   void arm_fir_decimate_fast_q31(
   3585   arm_fir_decimate_instance_q31 * S,
   3586   q31_t * pSrc,
   3587   q31_t * pDst,
   3588   uint32_t blockSize);
   3589 
   3590 
   3591   /**
   3592    * @brief  Initialization function for the Q31 FIR decimator.
   3593    * @param[in,out] *S points to an instance of the Q31 FIR decimator structure.
   3594    * @param[in] numTaps  number of coefficients in the filter.
   3595    * @param[in] M  decimation factor.
   3596    * @param[in] *pCoeffs points to the filter coefficients.
   3597    * @param[in] *pState points to the state buffer.
   3598    * @param[in] blockSize number of input samples to process per call.
   3599    * @return    The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   3600    * <code>blockSize</code> is not a multiple of <code>M</code>.
   3601    */
   3602 
   3603   arm_status arm_fir_decimate_init_q31(
   3604   arm_fir_decimate_instance_q31 * S,
   3605   uint16_t numTaps,
   3606   uint8_t M,
   3607   q31_t * pCoeffs,
   3608   q31_t * pState,
   3609   uint32_t blockSize);
   3610 
   3611 
   3612 
   3613   /**
   3614    * @brief Instance structure for the Q15 FIR interpolator.
   3615    */
   3616 
   3617   typedef struct
   3618   {
   3619     uint8_t L;                      /**< upsample factor. */
   3620     uint16_t phaseLength;           /**< length of each polyphase filter component. */
   3621     q15_t *pCoeffs;                 /**< points to the coefficient array. The array is of length L*phaseLength. */
   3622     q15_t *pState;                  /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
   3623   } arm_fir_interpolate_instance_q15;
   3624 
   3625   /**
   3626    * @brief Instance structure for the Q31 FIR interpolator.
   3627    */
   3628 
   3629   typedef struct
   3630   {
   3631     uint8_t L;                      /**< upsample factor. */
   3632     uint16_t phaseLength;           /**< length of each polyphase filter component. */
   3633     q31_t *pCoeffs;                  /**< points to the coefficient array. The array is of length L*phaseLength. */
   3634     q31_t *pState;                   /**< points to the state variable array. The array is of length blockSize+phaseLength-1. */
   3635   } arm_fir_interpolate_instance_q31;
   3636 
   3637   /**
   3638    * @brief Instance structure for the floating-point FIR interpolator.
   3639    */
   3640 
   3641   typedef struct
   3642   {
   3643     uint8_t L;                     /**< upsample factor. */
   3644     uint16_t phaseLength;          /**< length of each polyphase filter component. */
   3645     float32_t *pCoeffs;             /**< points to the coefficient array. The array is of length L*phaseLength. */
   3646     float32_t *pState;              /**< points to the state variable array. The array is of length phaseLength+numTaps-1. */
   3647   } arm_fir_interpolate_instance_f32;
   3648 
   3649 
   3650   /**
   3651    * @brief Processing function for the Q15 FIR interpolator.
   3652    * @param[in] *S        points to an instance of the Q15 FIR interpolator structure.
   3653    * @param[in] *pSrc     points to the block of input data.
   3654    * @param[out] *pDst    points to the block of output data.
   3655    * @param[in] blockSize number of input samples to process per call.
   3656    * @return none.
   3657    */
   3658 
   3659   void arm_fir_interpolate_q15(
   3660   const arm_fir_interpolate_instance_q15 * S,
   3661   q15_t * pSrc,
   3662   q15_t * pDst,
   3663   uint32_t blockSize);
   3664 
   3665 
   3666   /**
   3667    * @brief  Initialization function for the Q15 FIR interpolator.
   3668    * @param[in,out] *S        points to an instance of the Q15 FIR interpolator structure.
   3669    * @param[in]     L         upsample factor.
   3670    * @param[in]     numTaps   number of filter coefficients in the filter.
   3671    * @param[in]     *pCoeffs  points to the filter coefficient buffer.
   3672    * @param[in]     *pState   points to the state buffer.
   3673    * @param[in]     blockSize number of input samples to process per call.
   3674    * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   3675    * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
   3676    */
   3677 
   3678   arm_status arm_fir_interpolate_init_q15(
   3679   arm_fir_interpolate_instance_q15 * S,
   3680   uint8_t L,
   3681   uint16_t numTaps,
   3682   q15_t * pCoeffs,
   3683   q15_t * pState,
   3684   uint32_t blockSize);
   3685 
   3686   /**
   3687    * @brief Processing function for the Q31 FIR interpolator.
   3688    * @param[in] *S        points to an instance of the Q15 FIR interpolator structure.
   3689    * @param[in] *pSrc     points to the block of input data.
   3690    * @param[out] *pDst    points to the block of output data.
   3691    * @param[in] blockSize number of input samples to process per call.
   3692    * @return none.
   3693    */
   3694 
   3695   void arm_fir_interpolate_q31(
   3696   const arm_fir_interpolate_instance_q31 * S,
   3697   q31_t * pSrc,
   3698   q31_t * pDst,
   3699   uint32_t blockSize);
   3700 
   3701   /**
   3702    * @brief  Initialization function for the Q31 FIR interpolator.
   3703    * @param[in,out] *S        points to an instance of the Q31 FIR interpolator structure.
   3704    * @param[in]     L         upsample factor.
   3705    * @param[in]     numTaps   number of filter coefficients in the filter.
   3706    * @param[in]     *pCoeffs  points to the filter coefficient buffer.
   3707    * @param[in]     *pState   points to the state buffer.
   3708    * @param[in]     blockSize number of input samples to process per call.
   3709    * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   3710    * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
   3711    */
   3712 
   3713   arm_status arm_fir_interpolate_init_q31(
   3714   arm_fir_interpolate_instance_q31 * S,
   3715   uint8_t L,
   3716   uint16_t numTaps,
   3717   q31_t * pCoeffs,
   3718   q31_t * pState,
   3719   uint32_t blockSize);
   3720 
   3721 
   3722   /**
   3723    * @brief Processing function for the floating-point FIR interpolator.
   3724    * @param[in] *S        points to an instance of the floating-point FIR interpolator structure.
   3725    * @param[in] *pSrc     points to the block of input data.
   3726    * @param[out] *pDst    points to the block of output data.
   3727    * @param[in] blockSize number of input samples to process per call.
   3728    * @return none.
   3729    */
   3730 
   3731   void arm_fir_interpolate_f32(
   3732   const arm_fir_interpolate_instance_f32 * S,
   3733   float32_t * pSrc,
   3734   float32_t * pDst,
   3735   uint32_t blockSize);
   3736 
   3737   /**
   3738    * @brief  Initialization function for the floating-point FIR interpolator.
   3739    * @param[in,out] *S        points to an instance of the floating-point FIR interpolator structure.
   3740    * @param[in]     L         upsample factor.
   3741    * @param[in]     numTaps   number of filter coefficients in the filter.
   3742    * @param[in]     *pCoeffs  points to the filter coefficient buffer.
   3743    * @param[in]     *pState   points to the state buffer.
   3744    * @param[in]     blockSize number of input samples to process per call.
   3745    * @return        The function returns ARM_MATH_SUCCESS if initialization is successful or ARM_MATH_LENGTH_ERROR if
   3746    * the filter length <code>numTaps</code> is not a multiple of the interpolation factor <code>L</code>.
   3747    */
   3748 
   3749   arm_status arm_fir_interpolate_init_f32(
   3750   arm_fir_interpolate_instance_f32 * S,
   3751   uint8_t L,
   3752   uint16_t numTaps,
   3753   float32_t * pCoeffs,
   3754   float32_t * pState,
   3755   uint32_t blockSize);
   3756 
   3757   /**
   3758    * @brief Instance structure for the high precision Q31 Biquad cascade filter.
   3759    */
   3760 
   3761   typedef struct
   3762   {
   3763     uint8_t numStages;       /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
   3764     q63_t *pState;           /**< points to the array of state coefficients.  The array is of length 4*numStages. */
   3765     q31_t *pCoeffs;          /**< points to the array of coefficients.  The array is of length 5*numStages. */
   3766     uint8_t postShift;       /**< additional shift, in bits, applied to each output sample. */
   3767 
   3768   } arm_biquad_cas_df1_32x64_ins_q31;
   3769 
   3770 
   3771   /**
   3772    * @param[in]  *S        points to an instance of the high precision Q31 Biquad cascade filter structure.
   3773    * @param[in]  *pSrc     points to the block of input data.
   3774    * @param[out] *pDst     points to the block of output data
   3775    * @param[in]  blockSize number of samples to process.
   3776    * @return none.
   3777    */
   3778 
   3779   void arm_biquad_cas_df1_32x64_q31(
   3780   const arm_biquad_cas_df1_32x64_ins_q31 * S,
   3781   q31_t * pSrc,
   3782   q31_t * pDst,
   3783   uint32_t blockSize);
   3784 
   3785 
   3786   /**
   3787    * @param[in,out] *S           points to an instance of the high precision Q31 Biquad cascade filter structure.
   3788    * @param[in]     numStages    number of 2nd order stages in the filter.
   3789    * @param[in]     *pCoeffs     points to the filter coefficients.
   3790    * @param[in]     *pState      points to the state buffer.
   3791    * @param[in]     postShift    shift to be applied to the output. Varies according to the coefficients format
   3792    * @return        none
   3793    */
   3794 
   3795   void arm_biquad_cas_df1_32x64_init_q31(
   3796   arm_biquad_cas_df1_32x64_ins_q31 * S,
   3797   uint8_t numStages,
   3798   q31_t * pCoeffs,
   3799   q63_t * pState,
   3800   uint8_t postShift);
   3801 
   3802 
   3803 
   3804   /**
   3805    * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
   3806    */
   3807 
   3808   typedef struct
   3809   {
   3810     uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
   3811     float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
   3812     float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
   3813   } arm_biquad_cascade_df2T_instance_f32;
   3814 
   3815 
   3816 
   3817   /**
   3818    * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
   3819    */
   3820 
   3821   typedef struct
   3822   {
   3823     uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
   3824     float32_t *pState;         /**< points to the array of state coefficients.  The array is of length 4*numStages. */
   3825     float32_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
   3826   } arm_biquad_cascade_stereo_df2T_instance_f32;
   3827 
   3828 
   3829 
   3830   /**
   3831    * @brief Instance structure for the floating-point transposed direct form II Biquad cascade filter.
   3832    */
   3833 
   3834   typedef struct
   3835   {
   3836     uint8_t numStages;         /**< number of 2nd order stages in the filter.  Overall order is 2*numStages. */
   3837     float64_t *pState;         /**< points to the array of state coefficients.  The array is of length 2*numStages. */
   3838     float64_t *pCoeffs;        /**< points to the array of coefficients.  The array is of length 5*numStages. */
   3839   } arm_biquad_cascade_df2T_instance_f64;
   3840 
   3841 
   3842   /**
   3843    * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
   3844    * @param[in]  *S        points to an instance of the filter data structure.
   3845    * @param[in]  *pSrc     points to the block of input data.
   3846    * @param[out] *pDst     points to the block of output data
   3847    * @param[in]  blockSize number of samples to process.
   3848    * @return none.
   3849    */
   3850 
   3851   void arm_biquad_cascade_df2T_f32(
   3852   const arm_biquad_cascade_df2T_instance_f32 * S,
   3853   float32_t * pSrc,
   3854   float32_t * pDst,
   3855   uint32_t blockSize);
   3856 
   3857 
   3858   /**
   3859    * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter. 2 channels
   3860    * @param[in]  *S        points to an instance of the filter data structure.
   3861    * @param[in]  *pSrc     points to the block of input data.
   3862    * @param[out] *pDst     points to the block of output data
   3863    * @param[in]  blockSize number of samples to process.
   3864    * @return none.
   3865    */
   3866 
   3867   void arm_biquad_cascade_stereo_df2T_f32(
   3868   const arm_biquad_cascade_stereo_df2T_instance_f32 * S,
   3869   float32_t * pSrc,
   3870   float32_t * pDst,
   3871   uint32_t blockSize);
   3872 
   3873   /**
   3874    * @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
   3875    * @param[in]  *S        points to an instance of the filter data structure.
   3876    * @param[in]  *pSrc     points to the block of input data.
   3877    * @param[out] *pDst     points to the block of output data
   3878    * @param[in]  blockSize number of samples to process.
   3879    * @return none.
   3880    */
   3881 
   3882   void arm_biquad_cascade_df2T_f64(
   3883   const arm_biquad_cascade_df2T_instance_f64 * S,
   3884   float64_t * pSrc,
   3885   float64_t * pDst,
   3886   uint32_t blockSize);
   3887 
   3888 
   3889   /**
   3890    * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
   3891    * @param[in,out] *S           points to an instance of the filter data structure.
   3892    * @param[in]     numStages    number of 2nd order stages in the filter.
   3893    * @param[in]     *pCoeffs     points to the filter coefficients.
   3894    * @param[in]     *pState      points to the state buffer.
   3895    * @return        none
   3896    */
   3897 
   3898   void arm_biquad_cascade_df2T_init_f32(
   3899   arm_biquad_cascade_df2T_instance_f32 * S,
   3900   uint8_t numStages,
   3901   float32_t * pCoeffs,
   3902   float32_t * pState);
   3903 
   3904 
   3905   /**
   3906    * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
   3907    * @param[in,out] *S           points to an instance of the filter data structure.
   3908    * @param[in]     numStages    number of 2nd order stages in the filter.
   3909    * @param[in]     *pCoeffs     points to the filter coefficients.
   3910    * @param[in]     *pState      points to the state buffer.
   3911    * @return        none
   3912    */
   3913 
   3914   void arm_biquad_cascade_stereo_df2T_init_f32(
   3915   arm_biquad_cascade_stereo_df2T_instance_f32 * S,
   3916   uint8_t numStages,
   3917   float32_t * pCoeffs,
   3918   float32_t * pState);
   3919 
   3920 
   3921   /**
   3922    * @brief  Initialization function for the floating-point transposed direct form II Biquad cascade filter.
   3923    * @param[in,out] *S           points to an instance of the filter data structure.
   3924    * @param[in]     numStages    number of 2nd order stages in the filter.
   3925    * @param[in]     *pCoeffs     points to the filter coefficients.
   3926    * @param[in]     *pState      points to the state buffer.
   3927    * @return        none
   3928    */
   3929 
   3930   void arm_biquad_cascade_df2T_init_f64(
   3931   arm_biquad_cascade_df2T_instance_f64 * S,
   3932   uint8_t numStages,
   3933   float64_t * pCoeffs,
   3934   float64_t * pState);
   3935 
   3936 
   3937 
   3938   /**
   3939    * @brief Instance structure for the Q15 FIR lattice filter.
   3940    */
   3941 
   3942   typedef struct
   3943   {
   3944     uint16_t numStages;                          /**< number of filter stages. */
   3945     q15_t *pState;                               /**< points to the state variable array. The array is of length numStages. */
   3946     q15_t *pCoeffs;                              /**< points to the coefficient array. The array is of length numStages. */
   3947   } arm_fir_lattice_instance_q15;
   3948 
   3949   /**
   3950    * @brief Instance structure for the Q31 FIR lattice filter.
   3951    */
   3952 
   3953   typedef struct
   3954   {
   3955     uint16_t numStages;                          /**< number of filter stages. */
   3956     q31_t *pState;                               /**< points to the state variable array. The array is of length numStages. */
   3957     q31_t *pCoeffs;                              /**< points to the coefficient array. The array is of length numStages. */
   3958   } arm_fir_lattice_instance_q31;
   3959 
   3960   /**
   3961    * @brief Instance structure for the floating-point FIR lattice filter.
   3962    */
   3963 
   3964   typedef struct
   3965   {
   3966     uint16_t numStages;                  /**< number of filter stages. */
   3967     float32_t *pState;                   /**< points to the state variable array. The array is of length numStages. */
   3968     float32_t *pCoeffs;                  /**< points to the coefficient array. The array is of length numStages. */
   3969   } arm_fir_lattice_instance_f32;
   3970 
   3971   /**
   3972    * @brief Initialization function for the Q15 FIR lattice filter.
   3973    * @param[in] *S points to an instance of the Q15 FIR lattice structure.
   3974    * @param[in] numStages  number of filter stages.
   3975    * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
   3976    * @param[in] *pState points to the state buffer.  The array is of length numStages.
   3977    * @return none.
   3978    */
   3979 
   3980   void arm_fir_lattice_init_q15(
   3981   arm_fir_lattice_instance_q15 * S,
   3982   uint16_t numStages,
   3983   q15_t * pCoeffs,
   3984   q15_t * pState);
   3985 
   3986 
   3987   /**
   3988    * @brief Processing function for the Q15 FIR lattice filter.
   3989    * @param[in] *S points to an instance of the Q15 FIR lattice structure.
   3990    * @param[in] *pSrc points to the block of input data.
   3991    * @param[out] *pDst points to the block of output data.
   3992    * @param[in] blockSize number of samples to process.
   3993    * @return none.
   3994    */
   3995   void arm_fir_lattice_q15(
   3996   const arm_fir_lattice_instance_q15 * S,
   3997   q15_t * pSrc,
   3998   q15_t * pDst,
   3999   uint32_t blockSize);
   4000 
   4001   /**
   4002    * @brief Initialization function for the Q31 FIR lattice filter.
   4003    * @param[in] *S points to an instance of the Q31 FIR lattice structure.
   4004    * @param[in] numStages  number of filter stages.
   4005    * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
   4006    * @param[in] *pState points to the state buffer.   The array is of length numStages.
   4007    * @return none.
   4008    */
   4009 
   4010   void arm_fir_lattice_init_q31(
   4011   arm_fir_lattice_instance_q31 * S,
   4012   uint16_t numStages,
   4013   q31_t * pCoeffs,
   4014   q31_t * pState);
   4015 
   4016 
   4017   /**
   4018    * @brief Processing function for the Q31 FIR lattice filter.
   4019    * @param[in]  *S        points to an instance of the Q31 FIR lattice structure.
   4020    * @param[in]  *pSrc     points to the block of input data.
   4021    * @param[out] *pDst     points to the block of output data
   4022    * @param[in]  blockSize number of samples to process.
   4023    * @return none.
   4024    */
   4025 
   4026   void arm_fir_lattice_q31(
   4027   const arm_fir_lattice_instance_q31 * S,
   4028   q31_t * pSrc,
   4029   q31_t * pDst,
   4030   uint32_t blockSize);
   4031 
   4032 /**
   4033  * @brief Initialization function for the floating-point FIR lattice filter.
   4034  * @param[in] *S points to an instance of the floating-point FIR lattice structure.
   4035  * @param[in] numStages  number of filter stages.
   4036  * @param[in] *pCoeffs points to the coefficient buffer.  The array is of length numStages.
   4037  * @param[in] *pState points to the state buffer.  The array is of length numStages.
   4038  * @return none.
   4039  */
   4040 
   4041   void arm_fir_lattice_init_f32(
   4042   arm_fir_lattice_instance_f32 * S,
   4043   uint16_t numStages,
   4044   float32_t * pCoeffs,
   4045   float32_t * pState);
   4046 
   4047   /**
   4048    * @brief Processing function for the floating-point FIR lattice filter.
   4049    * @param[in]  *S        points to an instance of the floating-point FIR lattice structure.
   4050    * @param[in]  *pSrc     points to the block of input data.
   4051    * @param[out] *pDst     points to the block of output data
   4052    * @param[in]  blockSize number of samples to process.
   4053    * @return none.
   4054    */
   4055 
   4056   void arm_fir_lattice_f32(
   4057   const arm_fir_lattice_instance_f32 * S,
   4058   float32_t * pSrc,
   4059   float32_t * pDst,
   4060   uint32_t blockSize);
   4061 
   4062   /**
   4063    * @brief Instance structure for the Q15 IIR lattice filter.
   4064    */
   4065   typedef struct
   4066   {
   4067     uint16_t numStages;                         /**< number of stages in the filter. */
   4068     q15_t *pState;                              /**< points to the state variable array. The array is of length numStages+blockSize. */
   4069     q15_t *pkCoeffs;                            /**< points to the reflection coefficient array. The array is of length numStages. */
   4070     q15_t *pvCoeffs;                            /**< points to the ladder coefficient array. The array is of length numStages+1. */
   4071   } arm_iir_lattice_instance_q15;
   4072 
   4073   /**
   4074    * @brief Instance structure for the Q31 IIR lattice filter.
   4075    */
   4076   typedef struct
   4077   {
   4078     uint16_t numStages;                         /**< number of stages in the filter. */
   4079     q31_t *pState;                              /**< points to the state variable array. The array is of length numStages+blockSize. */
   4080     q31_t *pkCoeffs;                            /**< points to the reflection coefficient array. The array is of length numStages. */
   4081     q31_t *pvCoeffs;                            /**< points to the ladder coefficient array. The array is of length numStages+1. */
   4082   } arm_iir_lattice_instance_q31;
   4083 
   4084   /**
   4085    * @brief Instance structure for the floating-point IIR lattice filter.
   4086    */
   4087   typedef struct
   4088   {
   4089     uint16_t numStages;                         /**< number of stages in the filter. */
   4090     float32_t *pState;                          /**< points to the state variable array. The array is of length numStages+blockSize. */
   4091     float32_t *pkCoeffs;                        /**< points to the reflection coefficient array. The array is of length numStages. */
   4092     float32_t *pvCoeffs;                        /**< points to the ladder coefficient array. The array is of length numStages+1. */
   4093   } arm_iir_lattice_instance_f32;
   4094 
   4095   /**
   4096    * @brief Processing function for the floating-point IIR lattice filter.
   4097    * @param[in] *S points to an instance of the floating-point IIR lattice structure.
   4098    * @param[in] *pSrc points to the block of input data.
   4099    * @param[out] *pDst points to the block of output data.
   4100    * @param[in] blockSize number of samples to process.
   4101    * @return none.
   4102    */
   4103 
   4104   void arm_iir_lattice_f32(
   4105   const arm_iir_lattice_instance_f32 * S,
   4106   float32_t * pSrc,
   4107   float32_t * pDst,
   4108   uint32_t blockSize);
   4109 
   4110   /**
   4111    * @brief Initialization function for the floating-point IIR lattice filter.
   4112    * @param[in] *S points to an instance of the floating-point IIR lattice structure.
   4113    * @param[in] numStages number of stages in the filter.
   4114    * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.
   4115    * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.
   4116    * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize-1.
   4117    * @param[in] blockSize number of samples to process.
   4118    * @return none.
   4119    */
   4120 
   4121   void arm_iir_lattice_init_f32(
   4122   arm_iir_lattice_instance_f32 * S,
   4123   uint16_t numStages,
   4124   float32_t * pkCoeffs,
   4125   float32_t * pvCoeffs,
   4126   float32_t * pState,
   4127   uint32_t blockSize);
   4128 
   4129 
   4130   /**
   4131    * @brief Processing function for the Q31 IIR lattice filter.
   4132    * @param[in] *S points to an instance of the Q31 IIR lattice structure.
   4133    * @param[in] *pSrc points to the block of input data.
   4134    * @param[out] *pDst points to the block of output data.
   4135    * @param[in] blockSize number of samples to process.
   4136    * @return none.
   4137    */
   4138 
   4139   void arm_iir_lattice_q31(
   4140   const arm_iir_lattice_instance_q31 * S,
   4141   q31_t * pSrc,
   4142   q31_t * pDst,
   4143   uint32_t blockSize);
   4144 
   4145 
   4146   /**
   4147    * @brief Initialization function for the Q31 IIR lattice filter.
   4148    * @param[in] *S points to an instance of the Q31 IIR lattice structure.
   4149    * @param[in] numStages number of stages in the filter.
   4150    * @param[in] *pkCoeffs points to the reflection coefficient buffer.  The array is of length numStages.
   4151    * @param[in] *pvCoeffs points to the ladder coefficient buffer.  The array is of length numStages+1.
   4152    * @param[in] *pState points to the state buffer.  The array is of length numStages+blockSize.
   4153    * @param[in] blockSize number of samples to process.
   4154    * @return none.
   4155    */
   4156 
   4157   void arm_iir_lattice_init_q31(
   4158   arm_iir_lattice_instance_q31 * S,
   4159   uint16_t numStages,
   4160   q31_t * pkCoeffs,
   4161   q31_t * pvCoeffs,
   4162   q31_t * pState,
   4163   uint32_t blockSize);
   4164 
   4165 
   4166   /**
   4167    * @brief Processing function for the Q15 IIR lattice filter.
   4168    * @param[in] *S points to an instance of the Q15 IIR lattice structure.
   4169    * @param[in] *pSrc points to the block of input data.
   4170    * @param[out] *pDst points to the block of output data.
   4171    * @param[in] blockSize number of samples to process.
   4172    * @return none.
   4173    */
   4174 
   4175   void arm_iir_lattice_q15(
   4176   const arm_iir_lattice_instance_q15 * S,
   4177   q15_t * pSrc,
   4178   q15_t * pDst,
   4179   uint32_t blockSize);
   4180 
   4181 
   4182 /**
   4183  * @brief Initialization function for the Q15 IIR lattice filter.
   4184  * @param[in] *S points to an instance of the fixed-point Q15 IIR lattice structure.
   4185  * @param[in] numStages  number of stages in the filter.
   4186  * @param[in] *pkCoeffs points to reflection coefficient buffer.  The array is of length numStages.
   4187  * @param[in] *pvCoeffs points to ladder coefficient buffer.  The array is of length numStages+1.
   4188  * @param[in] *pState points to state buffer.  The array is of length numStages+blockSize.
   4189  * @param[in] blockSize number of samples to process per call.
   4190  * @return none.
   4191  */
   4192 
   4193   void arm_iir_lattice_init_q15(
   4194   arm_iir_lattice_instance_q15 * S,
   4195   uint16_t numStages,
   4196   q15_t * pkCoeffs,
   4197   q15_t * pvCoeffs,
   4198   q15_t * pState,
   4199   uint32_t blockSize);
   4200 
   4201   /**
   4202    * @brief Instance structure for the floating-point LMS filter.
   4203    */
   4204 
   4205   typedef struct
   4206   {
   4207     uint16_t numTaps;    /**< number of coefficients in the filter. */
   4208     float32_t *pState;   /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   4209     float32_t *pCoeffs;  /**< points to the coefficient array. The array is of length numTaps. */
   4210     float32_t mu;        /**< step size that controls filter coefficient updates. */
   4211   } arm_lms_instance_f32;
   4212 
   4213   /**
   4214    * @brief Processing function for floating-point LMS filter.
   4215    * @param[in]  *S points to an instance of the floating-point LMS filter structure.
   4216    * @param[in]  *pSrc points to the block of input data.
   4217    * @param[in]  *pRef points to the block of reference data.
   4218    * @param[out] *pOut points to the block of output data.
   4219    * @param[out] *pErr points to the block of error data.
   4220    * @param[in]  blockSize number of samples to process.
   4221    * @return     none.
   4222    */
   4223 
   4224   void arm_lms_f32(
   4225   const arm_lms_instance_f32 * S,
   4226   float32_t * pSrc,
   4227   float32_t * pRef,
   4228   float32_t * pOut,
   4229   float32_t * pErr,
   4230   uint32_t blockSize);
   4231 
   4232   /**
   4233    * @brief Initialization function for floating-point LMS filter.
   4234    * @param[in] *S points to an instance of the floating-point LMS filter structure.
   4235    * @param[in] numTaps  number of filter coefficients.
   4236    * @param[in] *pCoeffs points to the coefficient buffer.
   4237    * @param[in] *pState points to state buffer.
   4238    * @param[in] mu step size that controls filter coefficient updates.
   4239    * @param[in] blockSize number of samples to process.
   4240    * @return none.
   4241    */
   4242 
   4243   void arm_lms_init_f32(
   4244   arm_lms_instance_f32 * S,
   4245   uint16_t numTaps,
   4246   float32_t * pCoeffs,
   4247   float32_t * pState,
   4248   float32_t mu,
   4249   uint32_t blockSize);
   4250 
   4251   /**
   4252    * @brief Instance structure for the Q15 LMS filter.
   4253    */
   4254 
   4255   typedef struct
   4256   {
   4257     uint16_t numTaps;    /**< number of coefficients in the filter. */
   4258     q15_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   4259     q15_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
   4260     q15_t mu;            /**< step size that controls filter coefficient updates. */
   4261     uint32_t postShift;  /**< bit shift applied to coefficients. */
   4262   } arm_lms_instance_q15;
   4263 
   4264 
   4265   /**
   4266    * @brief Initialization function for the Q15 LMS filter.
   4267    * @param[in] *S points to an instance of the Q15 LMS filter structure.
   4268    * @param[in] numTaps  number of filter coefficients.
   4269    * @param[in] *pCoeffs points to the coefficient buffer.
   4270    * @param[in] *pState points to the state buffer.
   4271    * @param[in] mu step size that controls filter coefficient updates.
   4272    * @param[in] blockSize number of samples to process.
   4273    * @param[in] postShift bit shift applied to coefficients.
   4274    * @return    none.
   4275    */
   4276 
   4277   void arm_lms_init_q15(
   4278   arm_lms_instance_q15 * S,
   4279   uint16_t numTaps,
   4280   q15_t * pCoeffs,
   4281   q15_t * pState,
   4282   q15_t mu,
   4283   uint32_t blockSize,
   4284   uint32_t postShift);
   4285 
   4286   /**
   4287    * @brief Processing function for Q15 LMS filter.
   4288    * @param[in] *S points to an instance of the Q15 LMS filter structure.
   4289    * @param[in] *pSrc points to the block of input data.
   4290    * @param[in] *pRef points to the block of reference data.
   4291    * @param[out] *pOut points to the block of output data.
   4292    * @param[out] *pErr points to the block of error data.
   4293    * @param[in] blockSize number of samples to process.
   4294    * @return none.
   4295    */
   4296 
   4297   void arm_lms_q15(
   4298   const arm_lms_instance_q15 * S,
   4299   q15_t * pSrc,
   4300   q15_t * pRef,
   4301   q15_t * pOut,
   4302   q15_t * pErr,
   4303   uint32_t blockSize);
   4304 
   4305 
   4306   /**
   4307    * @brief Instance structure for the Q31 LMS filter.
   4308    */
   4309 
   4310   typedef struct
   4311   {
   4312     uint16_t numTaps;    /**< number of coefficients in the filter. */
   4313     q31_t *pState;       /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   4314     q31_t *pCoeffs;      /**< points to the coefficient array. The array is of length numTaps. */
   4315     q31_t mu;            /**< step size that controls filter coefficient updates. */
   4316     uint32_t postShift;  /**< bit shift applied to coefficients. */
   4317 
   4318   } arm_lms_instance_q31;
   4319 
   4320   /**
   4321    * @brief Processing function for Q31 LMS filter.
   4322    * @param[in]  *S points to an instance of the Q15 LMS filter structure.
   4323    * @param[in]  *pSrc points to the block of input data.
   4324    * @param[in]  *pRef points to the block of reference data.
   4325    * @param[out] *pOut points to the block of output data.
   4326    * @param[out] *pErr points to the block of error data.
   4327    * @param[in]  blockSize number of samples to process.
   4328    * @return     none.
   4329    */
   4330 
   4331   void arm_lms_q31(
   4332   const arm_lms_instance_q31 * S,
   4333   q31_t * pSrc,
   4334   q31_t * pRef,
   4335   q31_t * pOut,
   4336   q31_t * pErr,
   4337   uint32_t blockSize);
   4338 
   4339   /**
   4340    * @brief Initialization function for Q31 LMS filter.
   4341    * @param[in] *S points to an instance of the Q31 LMS filter structure.
   4342    * @param[in] numTaps  number of filter coefficients.
   4343    * @param[in] *pCoeffs points to coefficient buffer.
   4344    * @param[in] *pState points to state buffer.
   4345    * @param[in] mu step size that controls filter coefficient updates.
   4346    * @param[in] blockSize number of samples to process.
   4347    * @param[in] postShift bit shift applied to coefficients.
   4348    * @return none.
   4349    */
   4350 
   4351   void arm_lms_init_q31(
   4352   arm_lms_instance_q31 * S,
   4353   uint16_t numTaps,
   4354   q31_t * pCoeffs,
   4355   q31_t * pState,
   4356   q31_t mu,
   4357   uint32_t blockSize,
   4358   uint32_t postShift);
   4359 
   4360   /**
   4361    * @brief Instance structure for the floating-point normalized LMS filter.
   4362    */
   4363 
   4364   typedef struct
   4365   {
   4366     uint16_t numTaps;     /**< number of coefficients in the filter. */
   4367     float32_t *pState;    /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   4368     float32_t *pCoeffs;   /**< points to the coefficient array. The array is of length numTaps. */
   4369     float32_t mu;        /**< step size that control filter coefficient updates. */
   4370     float32_t energy;    /**< saves previous frame energy. */
   4371     float32_t x0;        /**< saves previous input sample. */
   4372   } arm_lms_norm_instance_f32;
   4373 
   4374   /**
   4375    * @brief Processing function for floating-point normalized LMS filter.
   4376    * @param[in] *S points to an instance of the floating-point normalized LMS filter structure.
   4377    * @param[in] *pSrc points to the block of input data.
   4378    * @param[in] *pRef points to the block of reference data.
   4379    * @param[out] *pOut points to the block of output data.
   4380    * @param[out] *pErr points to the block of error data.
   4381    * @param[in] blockSize number of samples to process.
   4382    * @return none.
   4383    */
   4384 
   4385   void arm_lms_norm_f32(
   4386   arm_lms_norm_instance_f32 * S,
   4387   float32_t * pSrc,
   4388   float32_t * pRef,
   4389   float32_t * pOut,
   4390   float32_t * pErr,
   4391   uint32_t blockSize);
   4392 
   4393   /**
   4394    * @brief Initialization function for floating-point normalized LMS filter.
   4395    * @param[in] *S points to an instance of the floating-point LMS filter structure.
   4396    * @param[in] numTaps  number of filter coefficients.
   4397    * @param[in] *pCoeffs points to coefficient buffer.
   4398    * @param[in] *pState points to state buffer.
   4399    * @param[in] mu step size that controls filter coefficient updates.
   4400    * @param[in] blockSize number of samples to process.
   4401    * @return none.
   4402    */
   4403 
   4404   void arm_lms_norm_init_f32(
   4405   arm_lms_norm_instance_f32 * S,
   4406   uint16_t numTaps,
   4407   float32_t * pCoeffs,
   4408   float32_t * pState,
   4409   float32_t mu,
   4410   uint32_t blockSize);
   4411 
   4412 
   4413   /**
   4414    * @brief Instance structure for the Q31 normalized LMS filter.
   4415    */
   4416   typedef struct
   4417   {
   4418     uint16_t numTaps;     /**< number of coefficients in the filter. */
   4419     q31_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   4420     q31_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
   4421     q31_t mu;             /**< step size that controls filter coefficient updates. */
   4422     uint8_t postShift;    /**< bit shift applied to coefficients. */
   4423     q31_t *recipTable;    /**< points to the reciprocal initial value table. */
   4424     q31_t energy;         /**< saves previous frame energy. */
   4425     q31_t x0;             /**< saves previous input sample. */
   4426   } arm_lms_norm_instance_q31;
   4427 
   4428   /**
   4429    * @brief Processing function for Q31 normalized LMS filter.
   4430    * @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
   4431    * @param[in] *pSrc points to the block of input data.
   4432    * @param[in] *pRef points to the block of reference data.
   4433    * @param[out] *pOut points to the block of output data.
   4434    * @param[out] *pErr points to the block of error data.
   4435    * @param[in] blockSize number of samples to process.
   4436    * @return none.
   4437    */
   4438 
   4439   void arm_lms_norm_q31(
   4440   arm_lms_norm_instance_q31 * S,
   4441   q31_t * pSrc,
   4442   q31_t * pRef,
   4443   q31_t * pOut,
   4444   q31_t * pErr,
   4445   uint32_t blockSize);
   4446 
   4447   /**
   4448    * @brief Initialization function for Q31 normalized LMS filter.
   4449    * @param[in] *S points to an instance of the Q31 normalized LMS filter structure.
   4450    * @param[in] numTaps  number of filter coefficients.
   4451    * @param[in] *pCoeffs points to coefficient buffer.
   4452    * @param[in] *pState points to state buffer.
   4453    * @param[in] mu step size that controls filter coefficient updates.
   4454    * @param[in] blockSize number of samples to process.
   4455    * @param[in] postShift bit shift applied to coefficients.
   4456    * @return none.
   4457    */
   4458 
   4459   void arm_lms_norm_init_q31(
   4460   arm_lms_norm_instance_q31 * S,
   4461   uint16_t numTaps,
   4462   q31_t * pCoeffs,
   4463   q31_t * pState,
   4464   q31_t mu,
   4465   uint32_t blockSize,
   4466   uint8_t postShift);
   4467 
   4468   /**
   4469    * @brief Instance structure for the Q15 normalized LMS filter.
   4470    */
   4471 
   4472   typedef struct
   4473   {
   4474     uint16_t numTaps;    /**< Number of coefficients in the filter. */
   4475     q15_t *pState;        /**< points to the state variable array. The array is of length numTaps+blockSize-1. */
   4476     q15_t *pCoeffs;       /**< points to the coefficient array. The array is of length numTaps. */
   4477     q15_t mu;            /**< step size that controls filter coefficient updates. */
   4478     uint8_t postShift;   /**< bit shift applied to coefficients. */
   4479     q15_t *recipTable;   /**< Points to the reciprocal initial value table. */
   4480     q15_t energy;        /**< saves previous frame energy. */
   4481     q15_t x0;            /**< saves previous input sample. */
   4482   } arm_lms_norm_instance_q15;
   4483 
   4484   /**
   4485    * @brief Processing function for Q15 normalized LMS filter.
   4486    * @param[in] *S points to an instance of the Q15 normalized LMS filter structure.
   4487    * @param[in] *pSrc points to the block of input data.
   4488    * @param[in] *pRef points to the block of reference data.
   4489    * @param[out] *pOut points to the block of output data.
   4490    * @param[out] *pErr points to the block of error data.
   4491    * @param[in] blockSize number of samples to process.
   4492    * @return none.
   4493    */
   4494 
   4495   void arm_lms_norm_q15(
   4496   arm_lms_norm_instance_q15 * S,
   4497   q15_t * pSrc,
   4498   q15_t * pRef,
   4499   q15_t * pOut,
   4500   q15_t * pErr,
   4501   uint32_t blockSize);
   4502 
   4503 
   4504   /**
   4505    * @brief Initialization function for Q15 normalized LMS filter.
   4506    * @param[in] *S points to an instance of the Q15 normalized LMS filter structure.
   4507    * @param[in] numTaps  number of filter coefficients.
   4508    * @param[in] *pCoeffs points to coefficient buffer.
   4509    * @param[in] *pState points to state buffer.
   4510    * @param[in] mu step size that controls filter coefficient updates.
   4511    * @param[in] blockSize number of samples to process.
   4512    * @param[in] postShift bit shift applied to coefficients.
   4513    * @return none.
   4514    */
   4515 
   4516   void arm_lms_norm_init_q15(
   4517   arm_lms_norm_instance_q15 * S,
   4518   uint16_t numTaps,
   4519   q15_t * pCoeffs,
   4520   q15_t * pState,
   4521   q15_t mu,
   4522   uint32_t blockSize,
   4523   uint8_t postShift);
   4524 
   4525   /**
   4526    * @brief Correlation of floating-point sequences.
   4527    * @param[in] *pSrcA points to the first input sequence.
   4528    * @param[in] srcALen length of the first input sequence.
   4529    * @param[in] *pSrcB points to the second input sequence.
   4530    * @param[in] srcBLen length of the second input sequence.
   4531    * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   4532    * @return none.
   4533    */
   4534 
   4535   void arm_correlate_f32(
   4536   float32_t * pSrcA,
   4537   uint32_t srcALen,
   4538   float32_t * pSrcB,
   4539   uint32_t srcBLen,
   4540   float32_t * pDst);
   4541 
   4542 
   4543    /**
   4544    * @brief Correlation of Q15 sequences
   4545    * @param[in] *pSrcA points to the first input sequence.
   4546    * @param[in] srcALen length of the first input sequence.
   4547    * @param[in] *pSrcB points to the second input sequence.
   4548    * @param[in] srcBLen length of the second input sequence.
   4549    * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   4550    * @param[in]  *pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   4551    * @return none.
   4552    */
   4553   void arm_correlate_opt_q15(
   4554   q15_t * pSrcA,
   4555   uint32_t srcALen,
   4556   q15_t * pSrcB,
   4557   uint32_t srcBLen,
   4558   q15_t * pDst,
   4559   q15_t * pScratch);
   4560 
   4561 
   4562   /**
   4563    * @brief Correlation of Q15 sequences.
   4564    * @param[in] *pSrcA points to the first input sequence.
   4565    * @param[in] srcALen length of the first input sequence.
   4566    * @param[in] *pSrcB points to the second input sequence.
   4567    * @param[in] srcBLen length of the second input sequence.
   4568    * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   4569    * @return none.
   4570    */
   4571 
   4572   void arm_correlate_q15(
   4573   q15_t * pSrcA,
   4574   uint32_t srcALen,
   4575   q15_t * pSrcB,
   4576   uint32_t srcBLen,
   4577   q15_t * pDst);
   4578 
   4579   /**
   4580    * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
   4581    * @param[in] *pSrcA points to the first input sequence.
   4582    * @param[in] srcALen length of the first input sequence.
   4583    * @param[in] *pSrcB points to the second input sequence.
   4584    * @param[in] srcBLen length of the second input sequence.
   4585    * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   4586    * @return none.
   4587    */
   4588 
   4589   void arm_correlate_fast_q15(
   4590   q15_t * pSrcA,
   4591   uint32_t srcALen,
   4592   q15_t * pSrcB,
   4593   uint32_t srcBLen,
   4594   q15_t * pDst);
   4595 
   4596 
   4597 
   4598   /**
   4599    * @brief Correlation of Q15 sequences (fast version) for Cortex-M3 and Cortex-M4.
   4600    * @param[in] *pSrcA points to the first input sequence.
   4601    * @param[in] srcALen length of the first input sequence.
   4602    * @param[in] *pSrcB points to the second input sequence.
   4603    * @param[in] srcBLen length of the second input sequence.
   4604    * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   4605    * @param[in]  *pScratch points to scratch buffer of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   4606    * @return none.
   4607    */
   4608 
   4609   void arm_correlate_fast_opt_q15(
   4610   q15_t * pSrcA,
   4611   uint32_t srcALen,
   4612   q15_t * pSrcB,
   4613   uint32_t srcBLen,
   4614   q15_t * pDst,
   4615   q15_t * pScratch);
   4616 
   4617   /**
   4618    * @brief Correlation of Q31 sequences.
   4619    * @param[in] *pSrcA points to the first input sequence.
   4620    * @param[in] srcALen length of the first input sequence.
   4621    * @param[in] *pSrcB points to the second input sequence.
   4622    * @param[in] srcBLen length of the second input sequence.
   4623    * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   4624    * @return none.
   4625    */
   4626 
   4627   void arm_correlate_q31(
   4628   q31_t * pSrcA,
   4629   uint32_t srcALen,
   4630   q31_t * pSrcB,
   4631   uint32_t srcBLen,
   4632   q31_t * pDst);
   4633 
   4634   /**
   4635    * @brief Correlation of Q31 sequences (fast version) for Cortex-M3 and Cortex-M4
   4636    * @param[in] *pSrcA points to the first input sequence.
   4637    * @param[in] srcALen length of the first input sequence.
   4638    * @param[in] *pSrcB points to the second input sequence.
   4639    * @param[in] srcBLen length of the second input sequence.
   4640    * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   4641    * @return none.
   4642    */
   4643 
   4644   void arm_correlate_fast_q31(
   4645   q31_t * pSrcA,
   4646   uint32_t srcALen,
   4647   q31_t * pSrcB,
   4648   uint32_t srcBLen,
   4649   q31_t * pDst);
   4650 
   4651 
   4652 
   4653  /**
   4654    * @brief Correlation of Q7 sequences.
   4655    * @param[in] *pSrcA points to the first input sequence.
   4656    * @param[in] srcALen length of the first input sequence.
   4657    * @param[in] *pSrcB points to the second input sequence.
   4658    * @param[in] srcBLen length of the second input sequence.
   4659    * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   4660    * @param[in]  *pScratch1 points to scratch buffer(of type q15_t) of size max(srcALen, srcBLen) + 2*min(srcALen, srcBLen) - 2.
   4661    * @param[in]  *pScratch2 points to scratch buffer (of type q15_t) of size min(srcALen, srcBLen).
   4662    * @return none.
   4663    */
   4664 
   4665   void arm_correlate_opt_q7(
   4666   q7_t * pSrcA,
   4667   uint32_t srcALen,
   4668   q7_t * pSrcB,
   4669   uint32_t srcBLen,
   4670   q7_t * pDst,
   4671   q15_t * pScratch1,
   4672   q15_t * pScratch2);
   4673 
   4674 
   4675   /**
   4676    * @brief Correlation of Q7 sequences.
   4677    * @param[in] *pSrcA points to the first input sequence.
   4678    * @param[in] srcALen length of the first input sequence.
   4679    * @param[in] *pSrcB points to the second input sequence.
   4680    * @param[in] srcBLen length of the second input sequence.
   4681    * @param[out] *pDst points to the block of output data  Length 2 * max(srcALen, srcBLen) - 1.
   4682    * @return none.
   4683    */
   4684 
   4685   void arm_correlate_q7(
   4686   q7_t * pSrcA,
   4687   uint32_t srcALen,
   4688   q7_t * pSrcB,
   4689   uint32_t srcBLen,
   4690   q7_t * pDst);
   4691 
   4692 
   4693   /**
   4694    * @brief Instance structure for the floating-point sparse FIR filter.
   4695    */
   4696   typedef struct
   4697   {
   4698     uint16_t numTaps;             /**< number of coefficients in the filter. */
   4699     uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
   4700     float32_t *pState;            /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
   4701     float32_t *pCoeffs;           /**< points to the coefficient array. The array is of length numTaps.*/
   4702     uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
   4703     int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
   4704   } arm_fir_sparse_instance_f32;
   4705 
   4706   /**
   4707    * @brief Instance structure for the Q31 sparse FIR filter.
   4708    */
   4709 
   4710   typedef struct
   4711   {
   4712     uint16_t numTaps;             /**< number of coefficients in the filter. */
   4713     uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
   4714     q31_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
   4715     q31_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
   4716     uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
   4717     int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
   4718   } arm_fir_sparse_instance_q31;
   4719 
   4720   /**
   4721    * @brief Instance structure for the Q15 sparse FIR filter.
   4722    */
   4723 
   4724   typedef struct
   4725   {
   4726     uint16_t numTaps;             /**< number of coefficients in the filter. */
   4727     uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
   4728     q15_t *pState;                /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
   4729     q15_t *pCoeffs;               /**< points to the coefficient array. The array is of length numTaps.*/
   4730     uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
   4731     int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
   4732   } arm_fir_sparse_instance_q15;
   4733 
   4734   /**
   4735    * @brief Instance structure for the Q7 sparse FIR filter.
   4736    */
   4737 
   4738   typedef struct
   4739   {
   4740     uint16_t numTaps;             /**< number of coefficients in the filter. */
   4741     uint16_t stateIndex;          /**< state buffer index.  Points to the oldest sample in the state buffer. */
   4742     q7_t *pState;                 /**< points to the state buffer array. The array is of length maxDelay+blockSize-1. */
   4743     q7_t *pCoeffs;                /**< points to the coefficient array. The array is of length numTaps.*/
   4744     uint16_t maxDelay;            /**< maximum offset specified by the pTapDelay array. */
   4745     int32_t *pTapDelay;           /**< points to the array of delay values.  The array is of length numTaps. */
   4746   } arm_fir_sparse_instance_q7;
   4747 
   4748   /**
   4749    * @brief Processing function for the floating-point sparse FIR filter.
   4750    * @param[in]  *S          points to an instance of the floating-point sparse FIR structure.
   4751    * @param[in]  *pSrc       points to the block of input data.
   4752    * @param[out] *pDst       points to the block of output data
   4753    * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.
   4754    * @param[in]  blockSize   number of input samples to process per call.
   4755    * @return none.
   4756    */
   4757 
   4758   void arm_fir_sparse_f32(
   4759   arm_fir_sparse_instance_f32 * S,
   4760   float32_t * pSrc,
   4761   float32_t * pDst,
   4762   float32_t * pScratchIn,
   4763   uint32_t blockSize);
   4764 
   4765   /**
   4766    * @brief  Initialization function for the floating-point sparse FIR filter.
   4767    * @param[in,out] *S         points to an instance of the floating-point sparse FIR structure.
   4768    * @param[in]     numTaps    number of nonzero coefficients in the filter.
   4769    * @param[in]     *pCoeffs   points to the array of filter coefficients.
   4770    * @param[in]     *pState    points to the state buffer.
   4771    * @param[in]     *pTapDelay points to the array of offset times.
   4772    * @param[in]     maxDelay   maximum offset time supported.
   4773    * @param[in]     blockSize  number of samples that will be processed per block.
   4774    * @return none
   4775    */
   4776 
   4777   void arm_fir_sparse_init_f32(
   4778   arm_fir_sparse_instance_f32 * S,
   4779   uint16_t numTaps,
   4780   float32_t * pCoeffs,
   4781   float32_t * pState,
   4782   int32_t * pTapDelay,
   4783   uint16_t maxDelay,
   4784   uint32_t blockSize);
   4785 
   4786   /**
   4787    * @brief Processing function for the Q31 sparse FIR filter.
   4788    * @param[in]  *S          points to an instance of the Q31 sparse FIR structure.
   4789    * @param[in]  *pSrc       points to the block of input data.
   4790    * @param[out] *pDst       points to the block of output data
   4791    * @param[in]  *pScratchIn points to a temporary buffer of size blockSize.
   4792    * @param[in]  blockSize   number of input samples to process per call.
   4793    * @return none.
   4794    */
   4795 
   4796   void arm_fir_sparse_q31(
   4797   arm_fir_sparse_instance_q31 * S,
   4798   q31_t * pSrc,
   4799   q31_t * pDst,
   4800   q31_t * pScratchIn,
   4801   uint32_t blockSize);
   4802 
   4803   /**
   4804    * @brief  Initialization function for the Q31 sparse FIR filter.
   4805    * @param[in,out] *S         points to an instance of the Q31 sparse FIR structure.
   4806    * @param[in]     numTaps    number of nonzero coefficients in the filter.
   4807    * @param[in]     *pCoeffs   points to the array of filter coefficients.
   4808    * @param[in]     *pState    points to the state buffer.
   4809    * @param[in]     *pTapDelay points to the array of offset times.
   4810    * @param[in]     maxDelay   maximum offset time supported.
   4811    * @param[in]     blockSize  number of samples that will be processed per block.
   4812    * @return none
   4813    */
   4814 
   4815   void arm_fir_sparse_init_q31(
   4816   arm_fir_sparse_instance_q31 * S,
   4817   uint16_t numTaps,
   4818   q31_t * pCoeffs,
   4819   q31_t * pState,
   4820   int32_t * pTapDelay,
   4821   uint16_t maxDelay,
   4822   uint32_t blockSize);
   4823 
   4824   /**
   4825    * @brief Processing function for the Q15 sparse FIR filter.
   4826    * @param[in]  *S           points to an instance of the Q15 sparse FIR structure.
   4827    * @param[in]  *pSrc        points to the block of input data.
   4828    * @param[out] *pDst        points to the block of output data
   4829    * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.
   4830    * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.
   4831    * @param[in]  blockSize    number of input samples to process per call.
   4832    * @return none.
   4833    */
   4834 
   4835   void arm_fir_sparse_q15(
   4836   arm_fir_sparse_instance_q15 * S,
   4837   q15_t * pSrc,
   4838   q15_t * pDst,
   4839   q15_t * pScratchIn,
   4840   q31_t * pScratchOut,
   4841   uint32_t blockSize);
   4842 
   4843 
   4844   /**
   4845    * @brief  Initialization function for the Q15 sparse FIR filter.
   4846    * @param[in,out] *S         points to an instance of the Q15 sparse FIR structure.
   4847    * @param[in]     numTaps    number of nonzero coefficients in the filter.
   4848    * @param[in]     *pCoeffs   points to the array of filter coefficients.
   4849    * @param[in]     *pState    points to the state buffer.
   4850    * @param[in]     *pTapDelay points to the array of offset times.
   4851    * @param[in]     maxDelay   maximum offset time supported.
   4852    * @param[in]     blockSize  number of samples that will be processed per block.
   4853    * @return none
   4854    */
   4855 
   4856   void arm_fir_sparse_init_q15(
   4857   arm_fir_sparse_instance_q15 * S,
   4858   uint16_t numTaps,
   4859   q15_t * pCoeffs,
   4860   q15_t * pState,
   4861   int32_t * pTapDelay,
   4862   uint16_t maxDelay,
   4863   uint32_t blockSize);
   4864 
   4865   /**
   4866    * @brief Processing function for the Q7 sparse FIR filter.
   4867    * @param[in]  *S           points to an instance of the Q7 sparse FIR structure.
   4868    * @param[in]  *pSrc        points to the block of input data.
   4869    * @param[out] *pDst        points to the block of output data
   4870    * @param[in]  *pScratchIn  points to a temporary buffer of size blockSize.
   4871    * @param[in]  *pScratchOut points to a temporary buffer of size blockSize.
   4872    * @param[in]  blockSize    number of input samples to process per call.
   4873    * @return none.
   4874    */
   4875 
   4876   void arm_fir_sparse_q7(
   4877   arm_fir_sparse_instance_q7 * S,
   4878   q7_t * pSrc,
   4879   q7_t * pDst,
   4880   q7_t * pScratchIn,
   4881   q31_t * pScratchOut,
   4882   uint32_t blockSize);
   4883 
   4884   /**
   4885    * @brief  Initialization function for the Q7 sparse FIR filter.
   4886    * @param[in,out] *S         points to an instance of the Q7 sparse FIR structure.
   4887    * @param[in]     numTaps    number of nonzero coefficients in the filter.
   4888    * @param[in]     *pCoeffs   points to the array of filter coefficients.
   4889    * @param[in]     *pState    points to the state buffer.
   4890    * @param[in]     *pTapDelay points to the array of offset times.
   4891    * @param[in]     maxDelay   maximum offset time supported.
   4892    * @param[in]     blockSize  number of samples that will be processed per block.
   4893    * @return none
   4894    */
   4895 
   4896   void arm_fir_sparse_init_q7(
   4897   arm_fir_sparse_instance_q7 * S,
   4898   uint16_t numTaps,
   4899   q7_t * pCoeffs,
   4900   q7_t * pState,
   4901   int32_t * pTapDelay,
   4902   uint16_t maxDelay,
   4903   uint32_t blockSize);
   4904 
   4905 
   4906   /*
   4907    * @brief  Floating-point sin_cos function.
   4908    * @param[in]  theta    input value in degrees
   4909    * @param[out] *pSinVal points to the processed sine output.
   4910    * @param[out] *pCosVal points to the processed cos output.
   4911    * @return none.
   4912    */
   4913 
   4914   void arm_sin_cos_f32(
   4915   float32_t theta,
   4916   float32_t * pSinVal,
   4917   float32_t * pCcosVal);
   4918 
   4919   /*
   4920    * @brief  Q31 sin_cos function.
   4921    * @param[in]  theta    scaled input value in degrees
   4922    * @param[out] *pSinVal points to the processed sine output.
   4923    * @param[out] *pCosVal points to the processed cosine output.
   4924    * @return none.
   4925    */
   4926 
   4927   void arm_sin_cos_q31(
   4928   q31_t theta,
   4929   q31_t * pSinVal,
   4930   q31_t * pCosVal);
   4931 
   4932 
   4933   /**
   4934    * @brief  Floating-point complex conjugate.
   4935    * @param[in]  *pSrc points to the input vector
   4936    * @param[out]  *pDst points to the output vector
   4937    * @param[in]  numSamples number of complex samples in each vector
   4938    * @return none.
   4939    */
   4940 
   4941   void arm_cmplx_conj_f32(
   4942   float32_t * pSrc,
   4943   float32_t * pDst,
   4944   uint32_t numSamples);
   4945 
   4946   /**
   4947    * @brief  Q31 complex conjugate.
   4948    * @param[in]  *pSrc points to the input vector
   4949    * @param[out]  *pDst points to the output vector
   4950    * @param[in]  numSamples number of complex samples in each vector
   4951    * @return none.
   4952    */
   4953 
   4954   void arm_cmplx_conj_q31(
   4955   q31_t * pSrc,
   4956   q31_t * pDst,
   4957   uint32_t numSamples);
   4958 
   4959   /**
   4960    * @brief  Q15 complex conjugate.
   4961    * @param[in]  *pSrc points to the input vector
   4962    * @param[out]  *pDst points to the output vector
   4963    * @param[in]  numSamples number of complex samples in each vector
   4964    * @return none.
   4965    */
   4966 
   4967   void arm_cmplx_conj_q15(
   4968   q15_t * pSrc,
   4969   q15_t * pDst,
   4970   uint32_t numSamples);
   4971 
   4972 
   4973 
   4974   /**
   4975    * @brief  Floating-point complex magnitude squared
   4976    * @param[in]  *pSrc points to the complex input vector
   4977    * @param[out]  *pDst points to the real output vector
   4978    * @param[in]  numSamples number of complex samples in the input vector
   4979    * @return none.
   4980    */
   4981 
   4982   void arm_cmplx_mag_squared_f32(
   4983   float32_t * pSrc,
   4984   float32_t * pDst,
   4985   uint32_t numSamples);
   4986 
   4987   /**
   4988    * @brief  Q31 complex magnitude squared
   4989    * @param[in]  *pSrc points to the complex input vector
   4990    * @param[out]  *pDst points to the real output vector
   4991    * @param[in]  numSamples number of complex samples in the input vector
   4992    * @return none.
   4993    */
   4994 
   4995   void arm_cmplx_mag_squared_q31(
   4996   q31_t * pSrc,
   4997   q31_t * pDst,
   4998   uint32_t numSamples);
   4999 
   5000   /**
   5001    * @brief  Q15 complex magnitude squared
   5002    * @param[in]  *pSrc points to the complex input vector
   5003    * @param[out]  *pDst points to the real output vector
   5004    * @param[in]  numSamples number of complex samples in the input vector
   5005    * @return none.
   5006    */
   5007 
   5008   void arm_cmplx_mag_squared_q15(
   5009   q15_t * pSrc,
   5010   q15_t * pDst,
   5011   uint32_t numSamples);
   5012 
   5013 
   5014  /**
   5015    * @ingroup groupController
   5016    */
   5017 
   5018   /**
   5019    * @defgroup PID PID Motor Control
   5020    *
   5021    * A Proportional Integral Derivative (PID) controller is a generic feedback control
   5022    * loop mechanism widely used in industrial control systems.
   5023    * A PID controller is the most commonly used type of feedback controller.
   5024    *
   5025    * This set of functions implements (PID) controllers
   5026    * for Q15, Q31, and floating-point data types.  The functions operate on a single sample
   5027    * of data and each call to the function returns a single processed value.
   5028    * <code>S</code> points to an instance of the PID control data structure.  <code>in</code>
   5029    * is the input sample value. The functions return the output value.
   5030    *
   5031    * \par Algorithm:
   5032    * <pre>
   5033    *    y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]
   5034    *    A0 = Kp + Ki + Kd
   5035    *    A1 = (-Kp ) - (2 * Kd )
   5036    *    A2 = Kd  </pre>
   5037    *
   5038    * \par
   5039    * where \c Kp is proportional constant, \c Ki is Integral constant and \c Kd is Derivative constant
   5040    *
   5041    * \par
   5042    * \image html PID.gif "Proportional Integral Derivative Controller"
   5043    *
   5044    * \par
   5045    * The PID controller calculates an "error" value as the difference between
   5046    * the measured output and the reference input.
   5047    * The controller attempts to minimize the error by adjusting the process control inputs.
   5048    * The proportional value determines the reaction to the current error,
   5049    * the integral value determines the reaction based on the sum of recent errors,
   5050    * and the derivative value determines the reaction based on the rate at which the error has been changing.
   5051    *
   5052    * \par Instance Structure
   5053    * The Gains A0, A1, A2 and state variables for a PID controller are stored together in an instance data structure.
   5054    * A separate instance structure must be defined for each PID Controller.
   5055    * There are separate instance structure declarations for each of the 3 supported data types.
   5056    *
   5057    * \par Reset Functions
   5058    * There is also an associated reset function for each data type which clears the state array.
   5059    *
   5060    * \par Initialization Functions
   5061    * There is also an associated initialization function for each data type.
   5062    * The initialization function performs the following operations:
   5063    * - Initializes the Gains A0, A1, A2 from Kp,Ki, Kd gains.
   5064    * - Zeros out the values in the state buffer.
   5065    *
   5066    * \par
   5067    * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
   5068    *
   5069    * \par Fixed-Point Behavior
   5070    * Care must be taken when using the fixed-point versions of the PID Controller functions.
   5071    * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.
   5072    * Refer to the function specific documentation below for usage guidelines.
   5073    */
   5074 
   5075   /**
   5076    * @addtogroup PID
   5077    * @{
   5078    */
   5079 
   5080   /**
   5081    * @brief  Process function for the floating-point PID Control.
   5082    * @param[in,out] *S is an instance of the floating-point PID Control structure
   5083    * @param[in] in input sample to process
   5084    * @return out processed output sample.
   5085    */
   5086 
   5087 
   5088   static __INLINE float32_t arm_pid_f32(
   5089   arm_pid_instance_f32 * S,
   5090   float32_t in)
   5091   {
   5092     float32_t out;
   5093 
   5094     /* y[n] = y[n-1] + A0 * x[n] + A1 * x[n-1] + A2 * x[n-2]  */
   5095     out = (S->A0 * in) +
   5096       (S->A1 * S->state[0]) + (S->A2 * S->state[1]) + (S->state[2]);
   5097 
   5098     /* Update state */
   5099     S->state[1] = S->state[0];
   5100     S->state[0] = in;
   5101     S->state[2] = out;
   5102 
   5103     /* return to application */
   5104     return (out);
   5105 
   5106   }
   5107 
   5108   /**
   5109    * @brief  Process function for the Q31 PID Control.
   5110    * @param[in,out] *S points to an instance of the Q31 PID Control structure
   5111    * @param[in] in input sample to process
   5112    * @return out processed output sample.
   5113    *
   5114    * <b>Scaling and Overflow Behavior:</b>
   5115    * \par
   5116    * The function is implemented using an internal 64-bit accumulator.
   5117    * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
   5118    * Thus, if the accumulator result overflows it wraps around rather than clip.
   5119    * In order to avoid overflows completely the input signal must be scaled down by 2 bits as there are four additions.
   5120    * After all multiply-accumulates are performed, the 2.62 accumulator is truncated to 1.32 format and then saturated to 1.31 format.
   5121    */
   5122 
   5123   static __INLINE q31_t arm_pid_q31(
   5124   arm_pid_instance_q31 * S,
   5125   q31_t in)
   5126   {
   5127     q63_t acc;
   5128     q31_t out;
   5129 
   5130     /* acc = A0 * x[n]  */
   5131     acc = (q63_t) S->A0 * in;
   5132 
   5133     /* acc += A1 * x[n-1] */
   5134     acc += (q63_t) S->A1 * S->state[0];
   5135 
   5136     /* acc += A2 * x[n-2]  */
   5137     acc += (q63_t) S->A2 * S->state[1];
   5138 
   5139     /* convert output to 1.31 format to add y[n-1] */
   5140     out = (q31_t) (acc >> 31u);
   5141 
   5142     /* out += y[n-1] */
   5143     out += S->state[2];
   5144 
   5145     /* Update state */
   5146     S->state[1] = S->state[0];
   5147     S->state[0] = in;
   5148     S->state[2] = out;
   5149 
   5150     /* return to application */
   5151     return (out);
   5152 
   5153   }
   5154 
   5155   /**
   5156    * @brief  Process function for the Q15 PID Control.
   5157    * @param[in,out] *S points to an instance of the Q15 PID Control structure
   5158    * @param[in] in input sample to process
   5159    * @return out processed output sample.
   5160    *
   5161    * <b>Scaling and Overflow Behavior:</b>
   5162    * \par
   5163    * The function is implemented using a 64-bit internal accumulator.
   5164    * Both Gains and state variables are represented in 1.15 format and multiplications yield a 2.30 result.
   5165    * The 2.30 intermediate results are accumulated in a 64-bit accumulator in 34.30 format.
   5166    * There is no risk of internal overflow with this approach and the full precision of intermediate multiplications is preserved.
   5167    * After all additions have been performed, the accumulator is truncated to 34.15 format by discarding low 15 bits.
   5168    * Lastly, the accumulator is saturated to yield a result in 1.15 format.
   5169    */
   5170 
   5171   static __INLINE q15_t arm_pid_q15(
   5172   arm_pid_instance_q15 * S,
   5173   q15_t in)
   5174   {
   5175     q63_t acc;
   5176     q15_t out;
   5177 
   5178 #ifndef ARM_MATH_CM0_FAMILY
   5179     __SIMD32_TYPE *vstate;
   5180 
   5181     /* Implementation of PID controller */
   5182 
   5183     /* acc = A0 * x[n]  */
   5184     acc = (q31_t) __SMUAD(S->A0, in);
   5185 
   5186     /* acc += A1 * x[n-1] + A2 * x[n-2]  */
   5187     vstate = __SIMD32_CONST(S->state);
   5188     acc = __SMLALD(S->A1, (q31_t) *vstate, acc);
   5189 
   5190 #else
   5191     /* acc = A0 * x[n]  */
   5192     acc = ((q31_t) S->A0) * in;
   5193 
   5194     /* acc += A1 * x[n-1] + A2 * x[n-2]  */
   5195     acc += (q31_t) S->A1 * S->state[0];
   5196     acc += (q31_t) S->A2 * S->state[1];
   5197 
   5198 #endif
   5199 
   5200     /* acc += y[n-1] */
   5201     acc += (q31_t) S->state[2] << 15;
   5202 
   5203     /* saturate the output */
   5204     out = (q15_t) (__SSAT((acc >> 15), 16));
   5205 
   5206     /* Update state */
   5207     S->state[1] = S->state[0];
   5208     S->state[0] = in;
   5209     S->state[2] = out;
   5210 
   5211     /* return to application */
   5212     return (out);
   5213 
   5214   }
   5215 
   5216   /**
   5217    * @} end of PID group
   5218    */
   5219 
   5220 
   5221   /**
   5222    * @brief Floating-point matrix inverse.
   5223    * @param[in]  *src points to the instance of the input floating-point matrix structure.
   5224    * @param[out] *dst points to the instance of the output floating-point matrix structure.
   5225    * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
   5226    * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
   5227    */
   5228 
   5229   arm_status arm_mat_inverse_f32(
   5230   const arm_matrix_instance_f32 * src,
   5231   arm_matrix_instance_f32 * dst);
   5232 
   5233 
   5234   /**
   5235    * @brief Floating-point matrix inverse.
   5236    * @param[in]  *src points to the instance of the input floating-point matrix structure.
   5237    * @param[out] *dst points to the instance of the output floating-point matrix structure.
   5238    * @return The function returns ARM_MATH_SIZE_MISMATCH, if the dimensions do not match.
   5239    * If the input matrix is singular (does not have an inverse), then the algorithm terminates and returns error status ARM_MATH_SINGULAR.
   5240    */
   5241 
   5242   arm_status arm_mat_inverse_f64(
   5243   const arm_matrix_instance_f64 * src,
   5244   arm_matrix_instance_f64 * dst);
   5245 
   5246 
   5247 
   5248   /**
   5249    * @ingroup groupController
   5250    */
   5251 
   5252 
   5253   /**
   5254    * @defgroup clarke Vector Clarke Transform
   5255    * Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector.
   5256    * Generally the Clarke transform uses three-phase currents <code>Ia, Ib and Ic</code> to calculate currents
   5257    * in the two-phase orthogonal stator axis <code>Ialpha</code> and <code>Ibeta</code>.
   5258    * When <code>Ialpha</code> is superposed with <code>Ia</code> as shown in the figure below
   5259    * \image html clarke.gif Stator current space vector and its components in (a,b).
   5260    * and <code>Ia + Ib + Ic = 0</code>, in this condition <code>Ialpha</code> and <code>Ibeta</code>
   5261    * can be calculated using only <code>Ia</code> and <code>Ib</code>.
   5262    *
   5263    * The function operates on a single sample of data and each call to the function returns the processed output.
   5264    * The library provides separate functions for Q31 and floating-point data types.
   5265    * \par Algorithm
   5266    * \image html clarkeFormula.gif
   5267    * where <code>Ia</code> and <code>Ib</code> are the instantaneous stator phases and
   5268    * <code>pIalpha</code> and <code>pIbeta</code> are the two coordinates of time invariant vector.
   5269    * \par Fixed-Point Behavior
   5270    * Care must be taken when using the Q31 version of the Clarke transform.
   5271    * In particular, the overflow and saturation behavior of the accumulator used must be considered.
   5272    * Refer to the function specific documentation below for usage guidelines.
   5273    */
   5274 
   5275   /**
   5276    * @addtogroup clarke
   5277    * @{
   5278    */
   5279 
   5280   /**
   5281    *
   5282    * @brief  Floating-point Clarke transform
   5283    * @param[in]       Ia       input three-phase coordinate <code>a</code>
   5284    * @param[in]       Ib       input three-phase coordinate <code>b</code>
   5285    * @param[out]      *pIalpha points to output two-phase orthogonal vector axis alpha
   5286    * @param[out]      *pIbeta  points to output two-phase orthogonal vector axis beta
   5287    * @return none.
   5288    */
   5289 
   5290   static __INLINE void arm_clarke_f32(
   5291   float32_t Ia,
   5292   float32_t Ib,
   5293   float32_t * pIalpha,
   5294   float32_t * pIbeta)
   5295   {
   5296     /* Calculate pIalpha using the equation, pIalpha = Ia */
   5297     *pIalpha = Ia;
   5298 
   5299     /* Calculate pIbeta using the equation, pIbeta = (1/sqrt(3)) * Ia + (2/sqrt(3)) * Ib */
   5300     *pIbeta =
   5301       ((float32_t) 0.57735026919 * Ia + (float32_t) 1.15470053838 * Ib);
   5302 
   5303   }
   5304 
   5305   /**
   5306    * @brief  Clarke transform for Q31 version
   5307    * @param[in]       Ia       input three-phase coordinate <code>a</code>
   5308    * @param[in]       Ib       input three-phase coordinate <code>b</code>
   5309    * @param[out]      *pIalpha points to output two-phase orthogonal vector axis alpha
   5310    * @param[out]      *pIbeta  points to output two-phase orthogonal vector axis beta
   5311    * @return none.
   5312    *
   5313    * <b>Scaling and Overflow Behavior:</b>
   5314    * \par
   5315    * The function is implemented using an internal 32-bit accumulator.
   5316    * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
   5317    * There is saturation on the addition, hence there is no risk of overflow.
   5318    */
   5319 
   5320   static __INLINE void arm_clarke_q31(
   5321   q31_t Ia,
   5322   q31_t Ib,
   5323   q31_t * pIalpha,
   5324   q31_t * pIbeta)
   5325   {
   5326     q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
   5327 
   5328     /* Calculating pIalpha from Ia by equation pIalpha = Ia */
   5329     *pIalpha = Ia;
   5330 
   5331     /* Intermediate product is calculated by (1/(sqrt(3)) * Ia) */
   5332     product1 = (q31_t) (((q63_t) Ia * 0x24F34E8B) >> 30);
   5333 
   5334     /* Intermediate product is calculated by (2/sqrt(3) * Ib) */
   5335     product2 = (q31_t) (((q63_t) Ib * 0x49E69D16) >> 30);
   5336 
   5337     /* pIbeta is calculated by adding the intermediate products */
   5338     *pIbeta = __QADD(product1, product2);
   5339   }
   5340 
   5341   /**
   5342    * @} end of clarke group
   5343    */
   5344 
   5345   /**
   5346    * @brief  Converts the elements of the Q7 vector to Q31 vector.
   5347    * @param[in]  *pSrc     input pointer
   5348    * @param[out]  *pDst    output pointer
   5349    * @param[in]  blockSize number of samples to process
   5350    * @return none.
   5351    */
   5352   void arm_q7_to_q31(
   5353   q7_t * pSrc,
   5354   q31_t * pDst,
   5355   uint32_t blockSize);
   5356 
   5357 
   5358 
   5359 
   5360   /**
   5361    * @ingroup groupController
   5362    */
   5363 
   5364   /**
   5365    * @defgroup inv_clarke Vector Inverse Clarke Transform
   5366    * Inverse Clarke transform converts the two-coordinate time invariant vector into instantaneous stator phases.
   5367    *
   5368    * The function operates on a single sample of data and each call to the function returns the processed output.
   5369    * The library provides separate functions for Q31 and floating-point data types.
   5370    * \par Algorithm
   5371    * \image html clarkeInvFormula.gif
   5372    * where <code>pIa</code> and <code>pIb</code> are the instantaneous stator phases and
   5373    * <code>Ialpha</code> and <code>Ibeta</code> are the two coordinates of time invariant vector.
   5374    * \par Fixed-Point Behavior
   5375    * Care must be taken when using the Q31 version of the Clarke transform.
   5376    * In particular, the overflow and saturation behavior of the accumulator used must be considered.
   5377    * Refer to the function specific documentation below for usage guidelines.
   5378    */
   5379 
   5380   /**
   5381    * @addtogroup inv_clarke
   5382    * @{
   5383    */
   5384 
   5385    /**
   5386    * @brief  Floating-point Inverse Clarke transform
   5387    * @param[in]       Ialpha  input two-phase orthogonal vector axis alpha
   5388    * @param[in]       Ibeta   input two-phase orthogonal vector axis beta
   5389    * @param[out]      *pIa    points to output three-phase coordinate <code>a</code>
   5390    * @param[out]      *pIb    points to output three-phase coordinate <code>b</code>
   5391    * @return none.
   5392    */
   5393 
   5394 
   5395   static __INLINE void arm_inv_clarke_f32(
   5396   float32_t Ialpha,
   5397   float32_t Ibeta,
   5398   float32_t * pIa,
   5399   float32_t * pIb)
   5400   {
   5401     /* Calculating pIa from Ialpha by equation pIa = Ialpha */
   5402     *pIa = Ialpha;
   5403 
   5404     /* Calculating pIb from Ialpha and Ibeta by equation pIb = -(1/2) * Ialpha + (sqrt(3)/2) * Ibeta */
   5405     *pIb = -0.5 * Ialpha + (float32_t) 0.8660254039 *Ibeta;
   5406 
   5407   }
   5408 
   5409   /**
   5410    * @brief  Inverse Clarke transform for Q31 version
   5411    * @param[in]       Ialpha  input two-phase orthogonal vector axis alpha
   5412    * @param[in]       Ibeta   input two-phase orthogonal vector axis beta
   5413    * @param[out]      *pIa    points to output three-phase coordinate <code>a</code>
   5414    * @param[out]      *pIb    points to output three-phase coordinate <code>b</code>
   5415    * @return none.
   5416    *
   5417    * <b>Scaling and Overflow Behavior:</b>
   5418    * \par
   5419    * The function is implemented using an internal 32-bit accumulator.
   5420    * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
   5421    * There is saturation on the subtraction, hence there is no risk of overflow.
   5422    */
   5423 
   5424   static __INLINE void arm_inv_clarke_q31(
   5425   q31_t Ialpha,
   5426   q31_t Ibeta,
   5427   q31_t * pIa,
   5428   q31_t * pIb)
   5429   {
   5430     q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
   5431 
   5432     /* Calculating pIa from Ialpha by equation pIa = Ialpha */
   5433     *pIa = Ialpha;
   5434 
   5435     /* Intermediate product is calculated by (1/(2*sqrt(3)) * Ia) */
   5436     product1 = (q31_t) (((q63_t) (Ialpha) * (0x40000000)) >> 31);
   5437 
   5438     /* Intermediate product is calculated by (1/sqrt(3) * pIb) */
   5439     product2 = (q31_t) (((q63_t) (Ibeta) * (0x6ED9EBA1)) >> 31);
   5440 
   5441     /* pIb is calculated by subtracting the products */
   5442     *pIb = __QSUB(product2, product1);
   5443 
   5444   }
   5445 
   5446   /**
   5447    * @} end of inv_clarke group
   5448    */
   5449 
   5450   /**
   5451    * @brief  Converts the elements of the Q7 vector to Q15 vector.
   5452    * @param[in]  *pSrc     input pointer
   5453    * @param[out] *pDst     output pointer
   5454    * @param[in]  blockSize number of samples to process
   5455    * @return none.
   5456    */
   5457   void arm_q7_to_q15(
   5458   q7_t * pSrc,
   5459   q15_t * pDst,
   5460   uint32_t blockSize);
   5461 
   5462 
   5463 
   5464   /**
   5465    * @ingroup groupController
   5466    */
   5467 
   5468   /**
   5469    * @defgroup park Vector Park Transform
   5470    *
   5471    * Forward Park transform converts the input two-coordinate vector to flux and torque components.
   5472    * The Park transform can be used to realize the transformation of the <code>Ialpha</code> and the <code>Ibeta</code> currents
   5473    * from the stationary to the moving reference frame and control the spatial relationship between
   5474    * the stator vector current and rotor flux vector.
   5475    * If we consider the d axis aligned with the rotor flux, the diagram below shows the
   5476    * current vector and the relationship from the two reference frames:
   5477    * \image html park.gif "Stator current space vector and its component in (a,b) and in the d,q rotating reference frame"
   5478    *
   5479    * The function operates on a single sample of data and each call to the function returns the processed output.
   5480    * The library provides separate functions for Q31 and floating-point data types.
   5481    * \par Algorithm
   5482    * \image html parkFormula.gif
   5483    * where <code>Ialpha</code> and <code>Ibeta</code> are the stator vector components,
   5484    * <code>pId</code> and <code>pIq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
   5485    * cosine and sine values of theta (rotor flux position).
   5486    * \par Fixed-Point Behavior
   5487    * Care must be taken when using the Q31 version of the Park transform.
   5488    * In particular, the overflow and saturation behavior of the accumulator used must be considered.
   5489    * Refer to the function specific documentation below for usage guidelines.
   5490    */
   5491 
   5492   /**
   5493    * @addtogroup park
   5494    * @{
   5495    */
   5496 
   5497   /**
   5498    * @brief Floating-point Park transform
   5499    * @param[in]       Ialpha input two-phase vector coordinate alpha
   5500    * @param[in]       Ibeta  input two-phase vector coordinate beta
   5501    * @param[out]      *pId   points to output  rotor reference frame d
   5502    * @param[out]      *pIq   points to output  rotor reference frame q
   5503    * @param[in]       sinVal sine value of rotation angle theta
   5504    * @param[in]       cosVal cosine value of rotation angle theta
   5505    * @return none.
   5506    *
   5507    * The function implements the forward Park transform.
   5508    *
   5509    */
   5510 
   5511   static __INLINE void arm_park_f32(
   5512   float32_t Ialpha,
   5513   float32_t Ibeta,
   5514   float32_t * pId,
   5515   float32_t * pIq,
   5516   float32_t sinVal,
   5517   float32_t cosVal)
   5518   {
   5519     /* Calculate pId using the equation, pId = Ialpha * cosVal + Ibeta * sinVal */
   5520     *pId = Ialpha * cosVal + Ibeta * sinVal;
   5521 
   5522     /* Calculate pIq using the equation, pIq = - Ialpha * sinVal + Ibeta * cosVal */
   5523     *pIq = -Ialpha * sinVal + Ibeta * cosVal;
   5524 
   5525   }
   5526 
   5527   /**
   5528    * @brief  Park transform for Q31 version
   5529    * @param[in]       Ialpha input two-phase vector coordinate alpha
   5530    * @param[in]       Ibeta  input two-phase vector coordinate beta
   5531    * @param[out]      *pId   points to output rotor reference frame d
   5532    * @param[out]      *pIq   points to output rotor reference frame q
   5533    * @param[in]       sinVal sine value of rotation angle theta
   5534    * @param[in]       cosVal cosine value of rotation angle theta
   5535    * @return none.
   5536    *
   5537    * <b>Scaling and Overflow Behavior:</b>
   5538    * \par
   5539    * The function is implemented using an internal 32-bit accumulator.
   5540    * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
   5541    * There is saturation on the addition and subtraction, hence there is no risk of overflow.
   5542    */
   5543 
   5544 
   5545   static __INLINE void arm_park_q31(
   5546   q31_t Ialpha,
   5547   q31_t Ibeta,
   5548   q31_t * pId,
   5549   q31_t * pIq,
   5550   q31_t sinVal,
   5551   q31_t cosVal)
   5552   {
   5553     q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
   5554     q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
   5555 
   5556     /* Intermediate product is calculated by (Ialpha * cosVal) */
   5557     product1 = (q31_t) (((q63_t) (Ialpha) * (cosVal)) >> 31);
   5558 
   5559     /* Intermediate product is calculated by (Ibeta * sinVal) */
   5560     product2 = (q31_t) (((q63_t) (Ibeta) * (sinVal)) >> 31);
   5561 
   5562 
   5563     /* Intermediate product is calculated by (Ialpha * sinVal) */
   5564     product3 = (q31_t) (((q63_t) (Ialpha) * (sinVal)) >> 31);
   5565 
   5566     /* Intermediate product is calculated by (Ibeta * cosVal) */
   5567     product4 = (q31_t) (((q63_t) (Ibeta) * (cosVal)) >> 31);
   5568 
   5569     /* Calculate pId by adding the two intermediate products 1 and 2 */
   5570     *pId = __QADD(product1, product2);
   5571 
   5572     /* Calculate pIq by subtracting the two intermediate products 3 from 4 */
   5573     *pIq = __QSUB(product4, product3);
   5574   }
   5575 
   5576   /**
   5577    * @} end of park group
   5578    */
   5579 
   5580   /**
   5581    * @brief  Converts the elements of the Q7 vector to floating-point vector.
   5582    * @param[in]  *pSrc is input pointer
   5583    * @param[out]  *pDst is output pointer
   5584    * @param[in]  blockSize is the number of samples to process
   5585    * @return none.
   5586    */
   5587   void arm_q7_to_float(
   5588   q7_t * pSrc,
   5589   float32_t * pDst,
   5590   uint32_t blockSize);
   5591 
   5592 
   5593   /**
   5594    * @ingroup groupController
   5595    */
   5596 
   5597   /**
   5598    * @defgroup inv_park Vector Inverse Park transform
   5599    * Inverse Park transform converts the input flux and torque components to two-coordinate vector.
   5600    *
   5601    * The function operates on a single sample of data and each call to the function returns the processed output.
   5602    * The library provides separate functions for Q31 and floating-point data types.
   5603    * \par Algorithm
   5604    * \image html parkInvFormula.gif
   5605    * where <code>pIalpha</code> and <code>pIbeta</code> are the stator vector components,
   5606    * <code>Id</code> and <code>Iq</code> are rotor vector components and <code>cosVal</code> and <code>sinVal</code> are the
   5607    * cosine and sine values of theta (rotor flux position).
   5608    * \par Fixed-Point Behavior
   5609    * Care must be taken when using the Q31 version of the Park transform.
   5610    * In particular, the overflow and saturation behavior of the accumulator used must be considered.
   5611    * Refer to the function specific documentation below for usage guidelines.
   5612    */
   5613 
   5614   /**
   5615    * @addtogroup inv_park
   5616    * @{
   5617    */
   5618 
   5619    /**
   5620    * @brief  Floating-point Inverse Park transform
   5621    * @param[in]       Id        input coordinate of rotor reference frame d
   5622    * @param[in]       Iq        input coordinate of rotor reference frame q
   5623    * @param[out]      *pIalpha  points to output two-phase orthogonal vector axis alpha
   5624    * @param[out]      *pIbeta   points to output two-phase orthogonal vector axis beta
   5625    * @param[in]       sinVal    sine value of rotation angle theta
   5626    * @param[in]       cosVal    cosine value of rotation angle theta
   5627    * @return none.
   5628    */
   5629 
   5630   static __INLINE void arm_inv_park_f32(
   5631   float32_t Id,
   5632   float32_t Iq,
   5633   float32_t * pIalpha,
   5634   float32_t * pIbeta,
   5635   float32_t sinVal,
   5636   float32_t cosVal)
   5637   {
   5638     /* Calculate pIalpha using the equation, pIalpha = Id * cosVal - Iq * sinVal */
   5639     *pIalpha = Id * cosVal - Iq * sinVal;
   5640 
   5641     /* Calculate pIbeta using the equation, pIbeta = Id * sinVal + Iq * cosVal */
   5642     *pIbeta = Id * sinVal + Iq * cosVal;
   5643 
   5644   }
   5645 
   5646 
   5647   /**
   5648    * @brief  Inverse Park transform for Q31 version
   5649    * @param[in]       Id        input coordinate of rotor reference frame d
   5650    * @param[in]       Iq        input coordinate of rotor reference frame q
   5651    * @param[out]      *pIalpha  points to output two-phase orthogonal vector axis alpha
   5652    * @param[out]      *pIbeta   points to output two-phase orthogonal vector axis beta
   5653    * @param[in]       sinVal    sine value of rotation angle theta
   5654    * @param[in]       cosVal    cosine value of rotation angle theta
   5655    * @return none.
   5656    *
   5657    * <b>Scaling and Overflow Behavior:</b>
   5658    * \par
   5659    * The function is implemented using an internal 32-bit accumulator.
   5660    * The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format.
   5661    * There is saturation on the addition, hence there is no risk of overflow.
   5662    */
   5663 
   5664 
   5665   static __INLINE void arm_inv_park_q31(
   5666   q31_t Id,
   5667   q31_t Iq,
   5668   q31_t * pIalpha,
   5669   q31_t * pIbeta,
   5670   q31_t sinVal,
   5671   q31_t cosVal)
   5672   {
   5673     q31_t product1, product2;                    /* Temporary variables used to store intermediate results */
   5674     q31_t product3, product4;                    /* Temporary variables used to store intermediate results */
   5675 
   5676     /* Intermediate product is calculated by (Id * cosVal) */
   5677     product1 = (q31_t) (((q63_t) (Id) * (cosVal)) >> 31);
   5678 
   5679     /* Intermediate product is calculated by (Iq * sinVal) */
   5680     product2 = (q31_t) (((q63_t) (Iq) * (sinVal)) >> 31);
   5681 
   5682 
   5683     /* Intermediate product is calculated by (Id * sinVal) */
   5684     product3 = (q31_t) (((q63_t) (Id) * (sinVal)) >> 31);
   5685 
   5686     /* Intermediate product is calculated by (Iq * cosVal) */
   5687     product4 = (q31_t) (((q63_t) (Iq) * (cosVal)) >> 31);
   5688 
   5689     /* Calculate pIalpha by using the two intermediate products 1 and 2 */
   5690     *pIalpha = __QSUB(product1, product2);
   5691 
   5692     /* Calculate pIbeta by using the two intermediate products 3 and 4 */
   5693     *pIbeta = __QADD(product4, product3);
   5694 
   5695   }
   5696 
   5697   /**
   5698    * @} end of Inverse park group
   5699    */
   5700 
   5701 
   5702   /**
   5703    * @brief  Converts the elements of the Q31 vector to floating-point vector.
   5704    * @param[in]  *pSrc is input pointer
   5705    * @param[out]  *pDst is output pointer
   5706    * @param[in]  blockSize is the number of samples to process
   5707    * @return none.
   5708    */
   5709   void arm_q31_to_float(
   5710   q31_t * pSrc,
   5711   float32_t * pDst,
   5712   uint32_t blockSize);
   5713 
   5714   /**
   5715    * @ingroup groupInterpolation
   5716    */
   5717 
   5718   /**
   5719    * @defgroup LinearInterpolate Linear Interpolation
   5720    *
   5721    * Linear interpolation is a method of curve fitting using linear polynomials.
   5722    * Linear interpolation works by effectively drawing a straight line between two neighboring samples and returning the appropriate point along that line
   5723    *
   5724    * \par
   5725    * \image html LinearInterp.gif "Linear interpolation"
   5726    *
   5727    * \par
   5728    * A  Linear Interpolate function calculates an output value(y), for the input(x)
   5729    * using linear interpolation of the input values x0, x1( nearest input values) and the output values y0 and y1(nearest output values)
   5730    *
   5731    * \par Algorithm:
   5732    * <pre>
   5733    *       y = y0 + (x - x0) * ((y1 - y0)/(x1-x0))
   5734    *       where x0, x1 are nearest values of input x
   5735    *             y0, y1 are nearest values to output y
   5736    * </pre>
   5737    *
   5738    * \par
   5739    * This set of functions implements Linear interpolation process
   5740    * for Q7, Q15, Q31, and floating-point data types.  The functions operate on a single
   5741    * sample of data and each call to the function returns a single processed value.
   5742    * <code>S</code> points to an instance of the Linear Interpolate function data structure.
   5743    * <code>x</code> is the input sample value. The functions returns the output value.
   5744    *
   5745    * \par
   5746    * if x is outside of the table boundary, Linear interpolation returns first value of the table
   5747    * if x is below input range and returns last value of table if x is above range.
   5748    */
   5749 
   5750   /**
   5751    * @addtogroup LinearInterpolate
   5752    * @{
   5753    */
   5754 
   5755   /**
   5756    * @brief  Process function for the floating-point Linear Interpolation Function.
   5757    * @param[in,out] *S is an instance of the floating-point Linear Interpolation structure
   5758    * @param[in] x input sample to process
   5759    * @return y processed output sample.
   5760    *
   5761    */
   5762 
   5763   static __INLINE float32_t arm_linear_interp_f32(
   5764   arm_linear_interp_instance_f32 * S,
   5765   float32_t x)
   5766   {
   5767 
   5768     float32_t y;
   5769     float32_t x0, x1;                            /* Nearest input values */
   5770     float32_t y0, y1;                            /* Nearest output values */
   5771     float32_t xSpacing = S->xSpacing;            /* spacing between input values */
   5772     int32_t i;                                   /* Index variable */
   5773     float32_t *pYData = S->pYData;               /* pointer to output table */
   5774 
   5775     /* Calculation of index */
   5776     i = (int32_t) ((x - S->x1) / xSpacing);
   5777 
   5778     if(i < 0)
   5779     {
   5780       /* Iniatilize output for below specified range as least output value of table */
   5781       y = pYData[0];
   5782     }
   5783     else if((uint32_t)i >= S->nValues)
   5784     {
   5785       /* Iniatilize output for above specified range as last output value of table */
   5786       y = pYData[S->nValues - 1];
   5787     }
   5788     else
   5789     {
   5790       /* Calculation of nearest input values */
   5791       x0 = S->x1 + i * xSpacing;
   5792       x1 = S->x1 + (i + 1) * xSpacing;
   5793 
   5794       /* Read of nearest output values */
   5795       y0 = pYData[i];
   5796       y1 = pYData[i + 1];
   5797 
   5798       /* Calculation of output */
   5799       y = y0 + (x - x0) * ((y1 - y0) / (x1 - x0));
   5800 
   5801     }
   5802 
   5803     /* returns output value */
   5804     return (y);
   5805   }
   5806 
   5807    /**
   5808    *
   5809    * @brief  Process function for the Q31 Linear Interpolation Function.
   5810    * @param[in] *pYData  pointer to Q31 Linear Interpolation table
   5811    * @param[in] x input sample to process
   5812    * @param[in] nValues number of table values
   5813    * @return y processed output sample.
   5814    *
   5815    * \par
   5816    * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
   5817    * This function can support maximum of table size 2^12.
   5818    *
   5819    */
   5820 
   5821 
   5822   static __INLINE q31_t arm_linear_interp_q31(
   5823   q31_t * pYData,
   5824   q31_t x,
   5825   uint32_t nValues)
   5826   {
   5827     q31_t y;                                     /* output */
   5828     q31_t y0, y1;                                /* Nearest output values */
   5829     q31_t fract;                                 /* fractional part */
   5830     int32_t index;                               /* Index to read nearest output values */
   5831 
   5832     /* Input is in 12.20 format */
   5833     /* 12 bits for the table index */
   5834     /* Index value calculation */
   5835     index = ((x & 0xFFF00000) >> 20);
   5836 
   5837     if(index >= (int32_t)(nValues - 1))
   5838     {
   5839       return (pYData[nValues - 1]);
   5840     }
   5841     else if(index < 0)
   5842     {
   5843       return (pYData[0]);
   5844     }
   5845     else
   5846     {
   5847 
   5848       /* 20 bits for the fractional part */
   5849       /* shift left by 11 to keep fract in 1.31 format */
   5850       fract = (x & 0x000FFFFF) << 11;
   5851 
   5852       /* Read two nearest output values from the index in 1.31(q31) format */
   5853       y0 = pYData[index];
   5854       y1 = pYData[index + 1u];
   5855 
   5856       /* Calculation of y0 * (1-fract) and y is in 2.30 format */
   5857       y = ((q31_t) ((q63_t) y0 * (0x7FFFFFFF - fract) >> 32));
   5858 
   5859       /* Calculation of y0 * (1-fract) + y1 *fract and y is in 2.30 format */
   5860       y += ((q31_t) (((q63_t) y1 * fract) >> 32));
   5861 
   5862       /* Convert y to 1.31 format */
   5863       return (y << 1u);
   5864 
   5865     }
   5866 
   5867   }
   5868 
   5869   /**
   5870    *
   5871    * @brief  Process function for the Q15 Linear Interpolation Function.
   5872    * @param[in] *pYData  pointer to Q15 Linear Interpolation table
   5873    * @param[in] x input sample to process
   5874    * @param[in] nValues number of table values
   5875    * @return y processed output sample.
   5876    *
   5877    * \par
   5878    * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
   5879    * This function can support maximum of table size 2^12.
   5880    *
   5881    */
   5882 
   5883 
   5884   static __INLINE q15_t arm_linear_interp_q15(
   5885   q15_t * pYData,
   5886   q31_t x,
   5887   uint32_t nValues)
   5888   {
   5889     q63_t y;                                     /* output */
   5890     q15_t y0, y1;                                /* Nearest output values */
   5891     q31_t fract;                                 /* fractional part */
   5892     int32_t index;                               /* Index to read nearest output values */
   5893 
   5894     /* Input is in 12.20 format */
   5895     /* 12 bits for the table index */
   5896     /* Index value calculation */
   5897     index = ((x & 0xFFF00000) >> 20u);
   5898 
   5899     if(index >= (int32_t)(nValues - 1))
   5900     {
   5901       return (pYData[nValues - 1]);
   5902     }
   5903     else if(index < 0)
   5904     {
   5905       return (pYData[0]);
   5906     }
   5907     else
   5908     {
   5909       /* 20 bits for the fractional part */
   5910       /* fract is in 12.20 format */
   5911       fract = (x & 0x000FFFFF);
   5912 
   5913       /* Read two nearest output values from the index */
   5914       y0 = pYData[index];
   5915       y1 = pYData[index + 1u];
   5916 
   5917       /* Calculation of y0 * (1-fract) and y is in 13.35 format */
   5918       y = ((q63_t) y0 * (0xFFFFF - fract));
   5919 
   5920       /* Calculation of (y0 * (1-fract) + y1 * fract) and y is in 13.35 format */
   5921       y += ((q63_t) y1 * (fract));
   5922 
   5923       /* convert y to 1.15 format */
   5924       return (y >> 20);
   5925     }
   5926 
   5927 
   5928   }
   5929 
   5930   /**
   5931    *
   5932    * @brief  Process function for the Q7 Linear Interpolation Function.
   5933    * @param[in] *pYData  pointer to Q7 Linear Interpolation table
   5934    * @param[in] x input sample to process
   5935    * @param[in] nValues number of table values
   5936    * @return y processed output sample.
   5937    *
   5938    * \par
   5939    * Input sample <code>x</code> is in 12.20 format which contains 12 bits for table index and 20 bits for fractional part.
   5940    * This function can support maximum of table size 2^12.
   5941    */
   5942 
   5943 
   5944   static __INLINE q7_t arm_linear_interp_q7(
   5945   q7_t * pYData,
   5946   q31_t x,
   5947   uint32_t nValues)
   5948   {
   5949     q31_t y;                                     /* output */
   5950     q7_t y0, y1;                                 /* Nearest output values */
   5951     q31_t fract;                                 /* fractional part */
   5952     uint32_t index;                              /* Index to read nearest output values */
   5953 
   5954     /* Input is in 12.20 format */
   5955     /* 12 bits for the table index */
   5956     /* Index value calculation */
   5957     if (x < 0)
   5958     {
   5959       return (pYData[0]);
   5960     }
   5961     index = (x >> 20) & 0xfff;
   5962 
   5963 
   5964     if(index >= (nValues - 1))
   5965     {
   5966       return (pYData[nValues - 1]);
   5967     }
   5968     else
   5969     {
   5970 
   5971       /* 20 bits for the fractional part */
   5972       /* fract is in 12.20 format */
   5973       fract = (x & 0x000FFFFF);
   5974 
   5975       /* Read two nearest output values from the index and are in 1.7(q7) format */
   5976       y0 = pYData[index];
   5977       y1 = pYData[index + 1u];
   5978 
   5979       /* Calculation of y0 * (1-fract ) and y is in 13.27(q27) format */
   5980       y = ((y0 * (0xFFFFF - fract)));
   5981 
   5982       /* Calculation of y1 * fract + y0 * (1-fract) and y is in 13.27(q27) format */
   5983       y += (y1 * fract);
   5984 
   5985       /* convert y to 1.7(q7) format */
   5986       return (y >> 20u);
   5987 
   5988     }
   5989 
   5990   }
   5991   /**
   5992    * @} end of LinearInterpolate group
   5993    */
   5994 
   5995   /**
   5996    * @brief  Fast approximation to the trigonometric sine function for floating-point data.
   5997    * @param[in] x input value in radians.
   5998    * @return  sin(x).
   5999    */
   6000 
   6001   float32_t arm_sin_f32(
   6002   float32_t x);
   6003 
   6004   /**
   6005    * @brief  Fast approximation to the trigonometric sine function for Q31 data.
   6006    * @param[in] x Scaled input value in radians.
   6007    * @return  sin(x).
   6008    */
   6009 
   6010   q31_t arm_sin_q31(
   6011   q31_t x);
   6012 
   6013   /**
   6014    * @brief  Fast approximation to the trigonometric sine function for Q15 data.
   6015    * @param[in] x Scaled input value in radians.
   6016    * @return  sin(x).
   6017    */
   6018 
   6019   q15_t arm_sin_q15(
   6020   q15_t x);
   6021 
   6022   /**
   6023    * @brief  Fast approximation to the trigonometric cosine function for floating-point data.
   6024    * @param[in] x input value in radians.
   6025    * @return  cos(x).
   6026    */
   6027 
   6028   float32_t arm_cos_f32(
   6029   float32_t x);
   6030 
   6031   /**
   6032    * @brief Fast approximation to the trigonometric cosine function for Q31 data.
   6033    * @param[in] x Scaled input value in radians.
   6034    * @return  cos(x).
   6035    */
   6036 
   6037   q31_t arm_cos_q31(
   6038   q31_t x);
   6039 
   6040   /**
   6041    * @brief  Fast approximation to the trigonometric cosine function for Q15 data.
   6042    * @param[in] x Scaled input value in radians.
   6043    * @return  cos(x).
   6044    */
   6045 
   6046   q15_t arm_cos_q15(
   6047   q15_t x);
   6048 
   6049 
   6050   /**
   6051    * @ingroup groupFastMath
   6052    */
   6053 
   6054 
   6055   /**
   6056    * @defgroup SQRT Square Root
   6057    *
   6058    * Computes the square root of a number.
   6059    * There are separate functions for Q15, Q31, and floating-point data types.
   6060    * The square root function is computed using the Newton-Raphson algorithm.
   6061    * This is an iterative algorithm of the form:
   6062    * <pre>
   6063    *      x1 = x0 - f(x0)/f'(x0)
   6064    * </pre>
   6065    * where <code>x1</code> is the current estimate,
   6066    * <code>x0</code> is the previous estimate, and
   6067    * <code>f'(x0)</code> is the derivative of <code>f()</code> evaluated at <code>x0</code>.
   6068    * For the square root function, the algorithm reduces to:
   6069    * <pre>
   6070    *     x0 = in/2                         [initial guess]
   6071    *     x1 = 1/2 * ( x0 + in / x0)        [each iteration]
   6072    * </pre>
   6073    */
   6074 
   6075 
   6076   /**
   6077    * @addtogroup SQRT
   6078    * @{
   6079    */
   6080 
   6081   /**
   6082    * @brief  Floating-point square root function.
   6083    * @param[in]  in     input value.
   6084    * @param[out] *pOut  square root of input value.
   6085    * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
   6086    * <code>in</code> is negative value and returns zero output for negative values.
   6087    */
   6088 
   6089   static __INLINE arm_status arm_sqrt_f32(
   6090   float32_t in,
   6091   float32_t * pOut)
   6092   {
   6093     if(in > 0)
   6094     {
   6095 
   6096 //      #if __FPU_USED
   6097 #if (__FPU_USED == 1) && defined ( __CC_ARM   )
   6098       *pOut = __sqrtf(in);
   6099 #else
   6100       *pOut = sqrtf(in);
   6101 #endif
   6102 
   6103       return (ARM_MATH_SUCCESS);
   6104     }
   6105     else
   6106     {
   6107       *pOut = 0.0f;
   6108       return (ARM_MATH_ARGUMENT_ERROR);
   6109     }
   6110 
   6111   }
   6112 
   6113 
   6114   /**
   6115    * @brief Q31 square root function.
   6116    * @param[in]   in    input value.  The range of the input value is [0 +1) or 0x00000000 to 0x7FFFFFFF.
   6117    * @param[out]  *pOut square root of input value.
   6118    * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
   6119    * <code>in</code> is negative value and returns zero output for negative values.
   6120    */
   6121   arm_status arm_sqrt_q31(
   6122   q31_t in,
   6123   q31_t * pOut);
   6124 
   6125   /**
   6126    * @brief  Q15 square root function.
   6127    * @param[in]   in     input value.  The range of the input value is [0 +1) or 0x0000 to 0x7FFF.
   6128    * @param[out]  *pOut  square root of input value.
   6129    * @return The function returns ARM_MATH_SUCCESS if input value is positive value or ARM_MATH_ARGUMENT_ERROR if
   6130    * <code>in</code> is negative value and returns zero output for negative values.
   6131    */
   6132   arm_status arm_sqrt_q15(
   6133   q15_t in,
   6134   q15_t * pOut);
   6135 
   6136   /**
   6137    * @} end of SQRT group
   6138    */
   6139 
   6140 
   6141 
   6142 
   6143 
   6144 
   6145   /**
   6146    * @brief floating-point Circular write function.
   6147    */
   6148 
   6149   static __INLINE void arm_circularWrite_f32(
   6150   int32_t * circBuffer,
   6151   int32_t L,
   6152   uint16_t * writeOffset,
   6153   int32_t bufferInc,
   6154   const int32_t * src,
   6155   int32_t srcInc,
   6156   uint32_t blockSize)
   6157   {
   6158     uint32_t i = 0u;
   6159     int32_t wOffset;
   6160 
   6161     /* Copy the value of Index pointer that points
   6162      * to the current location where the input samples to be copied */
   6163     wOffset = *writeOffset;
   6164 
   6165     /* Loop over the blockSize */
   6166     i = blockSize;
   6167 
   6168     while(i > 0u)
   6169     {
   6170       /* copy the input sample to the circular buffer */
   6171       circBuffer[wOffset] = *src;
   6172 
   6173       /* Update the input pointer */
   6174       src += srcInc;
   6175 
   6176       /* Circularly update wOffset.  Watch out for positive and negative value */
   6177       wOffset += bufferInc;
   6178       if(wOffset >= L)
   6179         wOffset -= L;
   6180 
   6181       /* Decrement the loop counter */
   6182       i--;
   6183     }
   6184 
   6185     /* Update the index pointer */
   6186     *writeOffset = wOffset;
   6187   }
   6188 
   6189 
   6190 
   6191   /**
   6192    * @brief floating-point Circular Read function.
   6193    */
   6194   static __INLINE void arm_circularRead_f32(
   6195   int32_t * circBuffer,
   6196   int32_t L,
   6197   int32_t * readOffset,
   6198   int32_t bufferInc,
   6199   int32_t * dst,
   6200   int32_t * dst_base,
   6201   int32_t dst_length,
   6202   int32_t dstInc,
   6203   uint32_t blockSize)
   6204   {
   6205     uint32_t i = 0u;
   6206     int32_t rOffset, dst_end;
   6207 
   6208     /* Copy the value of Index pointer that points
   6209      * to the current location from where the input samples to be read */
   6210     rOffset = *readOffset;
   6211     dst_end = (int32_t) (dst_base + dst_length);
   6212 
   6213     /* Loop over the blockSize */
   6214     i = blockSize;
   6215 
   6216     while(i > 0u)
   6217     {
   6218       /* copy the sample from the circular buffer to the destination buffer */
   6219       *dst = circBuffer[rOffset];
   6220 
   6221       /* Update the input pointer */
   6222       dst += dstInc;
   6223 
   6224       if(dst == (int32_t *) dst_end)
   6225       {
   6226         dst = dst_base;
   6227       }
   6228 
   6229       /* Circularly update rOffset.  Watch out for positive and negative value  */
   6230       rOffset += bufferInc;
   6231 
   6232       if(rOffset >= L)
   6233       {
   6234         rOffset -= L;
   6235       }
   6236 
   6237       /* Decrement the loop counter */
   6238       i--;
   6239     }
   6240 
   6241     /* Update the index pointer */
   6242     *readOffset = rOffset;
   6243   }
   6244 
   6245   /**
   6246    * @brief Q15 Circular write function.
   6247    */
   6248 
   6249   static __INLINE void arm_circularWrite_q15(
   6250   q15_t * circBuffer,
   6251   int32_t L,
   6252   uint16_t * writeOffset,
   6253   int32_t bufferInc,
   6254   const q15_t * src,
   6255   int32_t srcInc,
   6256   uint32_t blockSize)
   6257   {
   6258     uint32_t i = 0u;
   6259     int32_t wOffset;
   6260 
   6261     /* Copy the value of Index pointer that points
   6262      * to the current location where the input samples to be copied */
   6263     wOffset = *writeOffset;
   6264 
   6265     /* Loop over the blockSize */
   6266     i = blockSize;
   6267 
   6268     while(i > 0u)
   6269     {
   6270       /* copy the input sample to the circular buffer */
   6271       circBuffer[wOffset] = *src;
   6272 
   6273       /* Update the input pointer */
   6274       src += srcInc;
   6275 
   6276       /* Circularly update wOffset.  Watch out for positive and negative value */
   6277       wOffset += bufferInc;
   6278       if(wOffset >= L)
   6279         wOffset -= L;
   6280 
   6281       /* Decrement the loop counter */
   6282       i--;
   6283     }
   6284 
   6285     /* Update the index pointer */
   6286     *writeOffset = wOffset;
   6287   }
   6288 
   6289 
   6290 
   6291   /**
   6292    * @brief Q15 Circular Read function.
   6293    */
   6294   static __INLINE void arm_circularRead_q15(
   6295   q15_t * circBuffer,
   6296   int32_t L,
   6297   int32_t * readOffset,
   6298   int32_t bufferInc,
   6299   q15_t * dst,
   6300   q15_t * dst_base,
   6301   int32_t dst_length,
   6302   int32_t dstInc,
   6303   uint32_t blockSize)
   6304   {
   6305     uint32_t i = 0;
   6306     int32_t rOffset, dst_end;
   6307 
   6308     /* Copy the value of Index pointer that points
   6309      * to the current location from where the input samples to be read */
   6310     rOffset = *readOffset;
   6311 
   6312     dst_end = (int32_t) (dst_base + dst_length);
   6313 
   6314     /* Loop over the blockSize */
   6315     i = blockSize;
   6316 
   6317     while(i > 0u)
   6318     {
   6319       /* copy the sample from the circular buffer to the destination buffer */
   6320       *dst = circBuffer[rOffset];
   6321 
   6322       /* Update the input pointer */
   6323       dst += dstInc;
   6324 
   6325       if(dst == (q15_t *) dst_end)
   6326       {
   6327         dst = dst_base;
   6328       }
   6329 
   6330       /* Circularly update wOffset.  Watch out for positive and negative value */
   6331       rOffset += bufferInc;
   6332 
   6333       if(rOffset >= L)
   6334       {
   6335         rOffset -= L;
   6336       }
   6337 
   6338       /* Decrement the loop counter */
   6339       i--;
   6340     }
   6341 
   6342     /* Update the index pointer */
   6343     *readOffset = rOffset;
   6344   }
   6345 
   6346 
   6347   /**
   6348    * @brief Q7 Circular write function.
   6349    */
   6350 
   6351   static __INLINE void arm_circularWrite_q7(
   6352   q7_t * circBuffer,
   6353   int32_t L,
   6354   uint16_t * writeOffset,
   6355   int32_t bufferInc,
   6356   const q7_t * src,
   6357   int32_t srcInc,
   6358   uint32_t blockSize)
   6359   {
   6360     uint32_t i = 0u;
   6361     int32_t wOffset;
   6362 
   6363     /* Copy the value of Index pointer that points
   6364      * to the current location where the input samples to be copied */
   6365     wOffset = *writeOffset;
   6366 
   6367     /* Loop over the blockSize */
   6368     i = blockSize;
   6369 
   6370     while(i > 0u)
   6371     {
   6372       /* copy the input sample to the circular buffer */
   6373       circBuffer[wOffset] = *src;
   6374 
   6375       /* Update the input pointer */
   6376       src += srcInc;
   6377 
   6378       /* Circularly update wOffset.  Watch out for positive and negative value */
   6379       wOffset += bufferInc;
   6380       if(wOffset >= L)
   6381         wOffset -= L;
   6382 
   6383       /* Decrement the loop counter */
   6384       i--;
   6385     }
   6386 
   6387     /* Update the index pointer */
   6388     *writeOffset = wOffset;
   6389   }
   6390 
   6391 
   6392 
   6393   /**
   6394    * @brief Q7 Circular Read function.
   6395    */
   6396   static __INLINE void arm_circularRead_q7(
   6397   q7_t * circBuffer,
   6398   int32_t L,
   6399   int32_t * readOffset,
   6400   int32_t bufferInc,
   6401   q7_t * dst,
   6402   q7_t * dst_base,
   6403   int32_t dst_length,
   6404   int32_t dstInc,
   6405   uint32_t blockSize)
   6406   {
   6407     uint32_t i = 0;
   6408     int32_t rOffset, dst_end;
   6409 
   6410     /* Copy the value of Index pointer that points
   6411      * to the current location from where the input samples to be read */
   6412     rOffset = *readOffset;
   6413 
   6414     dst_end = (int32_t) (dst_base + dst_length);
   6415 
   6416     /* Loop over the blockSize */
   6417     i = blockSize;
   6418 
   6419     while(i > 0u)
   6420     {
   6421       /* copy the sample from the circular buffer to the destination buffer */
   6422       *dst = circBuffer[rOffset];
   6423 
   6424       /* Update the input pointer */
   6425       dst += dstInc;
   6426 
   6427       if(dst == (q7_t *) dst_end)
   6428       {
   6429         dst = dst_base;
   6430       }
   6431 
   6432       /* Circularly update rOffset.  Watch out for positive and negative value */
   6433       rOffset += bufferInc;
   6434 
   6435       if(rOffset >= L)
   6436       {
   6437         rOffset -= L;
   6438       }
   6439 
   6440       /* Decrement the loop counter */
   6441       i--;
   6442     }
   6443 
   6444     /* Update the index pointer */
   6445     *readOffset = rOffset;
   6446   }
   6447 
   6448 
   6449   /**
   6450    * @brief  Sum of the squares of the elements of a Q31 vector.
   6451    * @param[in]  *pSrc is input pointer
   6452    * @param[in]  blockSize is the number of samples to process
   6453    * @param[out]  *pResult is output value.
   6454    * @return none.
   6455    */
   6456 
   6457   void arm_power_q31(
   6458   q31_t * pSrc,
   6459   uint32_t blockSize,
   6460   q63_t * pResult);
   6461 
   6462   /**
   6463    * @brief  Sum of the squares of the elements of a floating-point vector.
   6464    * @param[in]  *pSrc is input pointer
   6465    * @param[in]  blockSize is the number of samples to process
   6466    * @param[out]  *pResult is output value.
   6467    * @return none.
   6468    */
   6469 
   6470   void arm_power_f32(
   6471   float32_t * pSrc,
   6472   uint32_t blockSize,
   6473   float32_t * pResult);
   6474 
   6475   /**
   6476    * @brief  Sum of the squares of the elements of a Q15 vector.
   6477    * @param[in]  *pSrc is input pointer
   6478    * @param[in]  blockSize is the number of samples to process
   6479    * @param[out]  *pResult is output value.
   6480    * @return none.
   6481    */
   6482 
   6483   void arm_power_q15(
   6484   q15_t * pSrc,
   6485   uint32_t blockSize,
   6486   q63_t * pResult);
   6487 
   6488   /**
   6489    * @brief  Sum of the squares of the elements of a Q7 vector.
   6490    * @param[in]  *pSrc is input pointer
   6491    * @param[in]  blockSize is the number of samples to process
   6492    * @param[out]  *pResult is output value.
   6493    * @return none.
   6494    */
   6495 
   6496   void arm_power_q7(
   6497   q7_t * pSrc,
   6498   uint32_t blockSize,
   6499   q31_t * pResult);
   6500 
   6501   /**
   6502    * @brief  Mean value of a Q7 vector.
   6503    * @param[in]  *pSrc is input pointer
   6504    * @param[in]  blockSize is the number of samples to process
   6505    * @param[out]  *pResult is output value.
   6506    * @return none.
   6507    */
   6508 
   6509   void arm_mean_q7(
   6510   q7_t * pSrc,
   6511   uint32_t blockSize,
   6512   q7_t * pResult);
   6513 
   6514   /**
   6515    * @brief  Mean value of a Q15 vector.
   6516    * @param[in]  *pSrc is input pointer
   6517    * @param[in]  blockSize is the number of samples to process
   6518    * @param[out]  *pResult is output value.
   6519    * @return none.
   6520    */
   6521   void arm_mean_q15(
   6522   q15_t * pSrc,
   6523   uint32_t blockSize,
   6524   q15_t * pResult);
   6525 
   6526   /**
   6527    * @brief  Mean value of a Q31 vector.
   6528    * @param[in]  *pSrc is input pointer
   6529    * @param[in]  blockSize is the number of samples to process
   6530    * @param[out]  *pResult is output value.
   6531    * @return none.
   6532    */
   6533   void arm_mean_q31(
   6534   q31_t * pSrc,
   6535   uint32_t blockSize,
   6536   q31_t * pResult);
   6537 
   6538   /**
   6539    * @brief  Mean value of a floating-point vector.
   6540    * @param[in]  *pSrc is input pointer
   6541    * @param[in]  blockSize is the number of samples to process
   6542    * @param[out]  *pResult is output value.
   6543    * @return none.
   6544    */
   6545   void arm_mean_f32(
   6546   float32_t * pSrc,
   6547   uint32_t blockSize,
   6548   float32_t * pResult);
   6549 
   6550   /**
   6551    * @brief  Variance of the elements of a floating-point vector.
   6552    * @param[in]  *pSrc is input pointer
   6553    * @param[in]  blockSize is the number of samples to process
   6554    * @param[out]  *pResult is output value.
   6555    * @return none.
   6556    */
   6557 
   6558   void arm_var_f32(
   6559   float32_t * pSrc,
   6560   uint32_t blockSize,
   6561   float32_t * pResult);
   6562 
   6563   /**
   6564    * @brief  Variance of the elements of a Q31 vector.
   6565    * @param[in]  *pSrc is input pointer
   6566    * @param[in]  blockSize is the number of samples to process
   6567    * @param[out]  *pResult is output value.
   6568    * @return none.
   6569    */
   6570 
   6571   void arm_var_q31(
   6572   q31_t * pSrc,
   6573   uint32_t blockSize,
   6574   q31_t * pResult);
   6575 
   6576   /**
   6577    * @brief  Variance of the elements of a Q15 vector.
   6578    * @param[in]  *pSrc is input pointer
   6579    * @param[in]  blockSize is the number of samples to process
   6580    * @param[out]  *pResult is output value.
   6581    * @return none.
   6582    */
   6583 
   6584   void arm_var_q15(
   6585   q15_t * pSrc,
   6586   uint32_t blockSize,
   6587   q15_t * pResult);
   6588 
   6589   /**
   6590    * @brief  Root Mean Square of the elements of a floating-point vector.
   6591    * @param[in]  *pSrc is input pointer
   6592    * @param[in]  blockSize is the number of samples to process
   6593    * @param[out]  *pResult is output value.
   6594    * @return none.
   6595    */
   6596 
   6597   void arm_rms_f32(
   6598   float32_t * pSrc,
   6599   uint32_t blockSize,
   6600   float32_t * pResult);
   6601 
   6602   /**
   6603    * @brief  Root Mean Square of the elements of a Q31 vector.
   6604    * @param[in]  *pSrc is input pointer
   6605    * @param[in]  blockSize is the number of samples to process
   6606    * @param[out]  *pResult is output value.
   6607    * @return none.
   6608    */
   6609 
   6610   void arm_rms_q31(
   6611   q31_t * pSrc,
   6612   uint32_t blockSize,
   6613   q31_t * pResult);
   6614 
   6615   /**
   6616    * @brief  Root Mean Square of the elements of a Q15 vector.
   6617    * @param[in]  *pSrc is input pointer
   6618    * @param[in]  blockSize is the number of samples to process
   6619    * @param[out]  *pResult is output value.
   6620    * @return none.
   6621    */
   6622 
   6623   void arm_rms_q15(
   6624   q15_t * pSrc,
   6625   uint32_t blockSize,
   6626   q15_t * pResult);
   6627 
   6628   /**
   6629    * @brief  Standard deviation of the elements of a floating-point vector.
   6630    * @param[in]  *pSrc is input pointer
   6631    * @param[in]  blockSize is the number of samples to process
   6632    * @param[out]  *pResult is output value.
   6633    * @return none.
   6634    */
   6635 
   6636   void arm_std_f32(
   6637   float32_t * pSrc,
   6638   uint32_t blockSize,
   6639   float32_t * pResult);
   6640 
   6641   /**
   6642    * @brief  Standard deviation of the elements of a Q31 vector.
   6643    * @param[in]  *pSrc is input pointer
   6644    * @param[in]  blockSize is the number of samples to process
   6645    * @param[out]  *pResult is output value.
   6646    * @return none.
   6647    */
   6648 
   6649   void arm_std_q31(
   6650   q31_t * pSrc,
   6651   uint32_t blockSize,
   6652   q31_t * pResult);
   6653 
   6654   /**
   6655    * @brief  Standard deviation of the elements of a Q15 vector.
   6656    * @param[in]  *pSrc is input pointer
   6657    * @param[in]  blockSize is the number of samples to process
   6658    * @param[out]  *pResult is output value.
   6659    * @return none.
   6660    */
   6661 
   6662   void arm_std_q15(
   6663   q15_t * pSrc,
   6664   uint32_t blockSize,
   6665   q15_t * pResult);
   6666 
   6667   /**
   6668    * @brief  Floating-point complex magnitude
   6669    * @param[in]  *pSrc points to the complex input vector
   6670    * @param[out]  *pDst points to the real output vector
   6671    * @param[in]  numSamples number of complex samples in the input vector
   6672    * @return none.
   6673    */
   6674 
   6675   void arm_cmplx_mag_f32(
   6676   float32_t * pSrc,
   6677   float32_t * pDst,
   6678   uint32_t numSamples);
   6679 
   6680   /**
   6681    * @brief  Q31 complex magnitude
   6682    * @param[in]  *pSrc points to the complex input vector
   6683    * @param[out]  *pDst points to the real output vector
   6684    * @param[in]  numSamples number of complex samples in the input vector
   6685    * @return none.
   6686    */
   6687 
   6688   void arm_cmplx_mag_q31(
   6689   q31_t * pSrc,
   6690   q31_t * pDst,
   6691   uint32_t numSamples);
   6692 
   6693   /**
   6694    * @brief  Q15 complex magnitude
   6695    * @param[in]  *pSrc points to the complex input vector
   6696    * @param[out]  *pDst points to the real output vector
   6697    * @param[in]  numSamples number of complex samples in the input vector
   6698    * @return none.
   6699    */
   6700 
   6701   void arm_cmplx_mag_q15(
   6702   q15_t * pSrc,
   6703   q15_t * pDst,
   6704   uint32_t numSamples);
   6705 
   6706   /**
   6707    * @brief  Q15 complex dot product
   6708    * @param[in]  *pSrcA points to the first input vector
   6709    * @param[in]  *pSrcB points to the second input vector
   6710    * @param[in]  numSamples number of complex samples in each vector
   6711    * @param[out]  *realResult real part of the result returned here
   6712    * @param[out]  *imagResult imaginary part of the result returned here
   6713    * @return none.
   6714    */
   6715 
   6716   void arm_cmplx_dot_prod_q15(
   6717   q15_t * pSrcA,
   6718   q15_t * pSrcB,
   6719   uint32_t numSamples,
   6720   q31_t * realResult,
   6721   q31_t * imagResult);
   6722 
   6723   /**
   6724    * @brief  Q31 complex dot product
   6725    * @param[in]  *pSrcA points to the first input vector
   6726    * @param[in]  *pSrcB points to the second input vector
   6727    * @param[in]  numSamples number of complex samples in each vector
   6728    * @param[out]  *realResult real part of the result returned here
   6729    * @param[out]  *imagResult imaginary part of the result returned here
   6730    * @return none.
   6731    */
   6732 
   6733   void arm_cmplx_dot_prod_q31(
   6734   q31_t * pSrcA,
   6735   q31_t * pSrcB,
   6736   uint32_t numSamples,
   6737   q63_t * realResult,
   6738   q63_t * imagResult);
   6739 
   6740   /**
   6741    * @brief  Floating-point complex dot product
   6742    * @param[in]  *pSrcA points to the first input vector
   6743    * @param[in]  *pSrcB points to the second input vector
   6744    * @param[in]  numSamples number of complex samples in each vector
   6745    * @param[out]  *realResult real part of the result returned here
   6746    * @param[out]  *imagResult imaginary part of the result returned here
   6747    * @return none.
   6748    */
   6749 
   6750   void arm_cmplx_dot_prod_f32(
   6751   float32_t * pSrcA,
   6752   float32_t * pSrcB,
   6753   uint32_t numSamples,
   6754   float32_t * realResult,
   6755   float32_t * imagResult);
   6756 
   6757   /**
   6758    * @brief  Q15 complex-by-real multiplication
   6759    * @param[in]  *pSrcCmplx points to the complex input vector
   6760    * @param[in]  *pSrcReal points to the real input vector
   6761    * @param[out]  *pCmplxDst points to the complex output vector
   6762    * @param[in]  numSamples number of samples in each vector
   6763    * @return none.
   6764    */
   6765 
   6766   void arm_cmplx_mult_real_q15(
   6767   q15_t * pSrcCmplx,
   6768   q15_t * pSrcReal,
   6769   q15_t * pCmplxDst,
   6770   uint32_t numSamples);
   6771 
   6772   /**
   6773    * @brief  Q31 complex-by-real multiplication
   6774    * @param[in]  *pSrcCmplx points to the complex input vector
   6775    * @param[in]  *pSrcReal points to the real input vector
   6776    * @param[out]  *pCmplxDst points to the complex output vector
   6777    * @param[in]  numSamples number of samples in each vector
   6778    * @return none.
   6779    */
   6780 
   6781   void arm_cmplx_mult_real_q31(
   6782   q31_t * pSrcCmplx,
   6783   q31_t * pSrcReal,
   6784   q31_t * pCmplxDst,
   6785   uint32_t numSamples);
   6786 
   6787   /**
   6788    * @brief  Floating-point complex-by-real multiplication
   6789    * @param[in]  *pSrcCmplx points to the complex input vector
   6790    * @param[in]  *pSrcReal points to the real input vector
   6791    * @param[out]  *pCmplxDst points to the complex output vector
   6792    * @param[in]  numSamples number of samples in each vector
   6793    * @return none.
   6794    */
   6795 
   6796   void arm_cmplx_mult_real_f32(
   6797   float32_t * pSrcCmplx,
   6798   float32_t * pSrcReal,
   6799   float32_t * pCmplxDst,
   6800   uint32_t numSamples);
   6801 
   6802   /**
   6803    * @brief  Minimum value of a Q7 vector.
   6804    * @param[in]  *pSrc is input pointer
   6805    * @param[in]  blockSize is the number of samples to process
   6806    * @param[out]  *result is output pointer
   6807    * @param[in]  index is the array index of the minimum value in the input buffer.
   6808    * @return none.
   6809    */
   6810 
   6811   void arm_min_q7(
   6812   q7_t * pSrc,
   6813   uint32_t blockSize,
   6814   q7_t * result,
   6815   uint32_t * index);
   6816 
   6817   /**
   6818    * @brief  Minimum value of a Q15 vector.
   6819    * @param[in]  *pSrc is input pointer
   6820    * @param[in]  blockSize is the number of samples to process
   6821    * @param[out]  *pResult is output pointer
   6822    * @param[in]  *pIndex is the array index of the minimum value in the input buffer.
   6823    * @return none.
   6824    */
   6825 
   6826   void arm_min_q15(
   6827   q15_t * pSrc,
   6828   uint32_t blockSize,
   6829   q15_t * pResult,
   6830   uint32_t * pIndex);
   6831 
   6832   /**
   6833    * @brief  Minimum value of a Q31 vector.
   6834    * @param[in]  *pSrc is input pointer
   6835    * @param[in]  blockSize is the number of samples to process
   6836    * @param[out]  *pResult is output pointer
   6837    * @param[out]  *pIndex is the array index of the minimum value in the input buffer.
   6838    * @return none.
   6839    */
   6840   void arm_min_q31(
   6841   q31_t * pSrc,
   6842   uint32_t blockSize,
   6843   q31_t * pResult,
   6844   uint32_t * pIndex);
   6845 
   6846   /**
   6847    * @brief  Minimum value of a floating-point vector.
   6848    * @param[in]  *pSrc is input pointer
   6849    * @param[in]  blockSize is the number of samples to process
   6850    * @param[out]  *pResult is output pointer
   6851    * @param[out]  *pIndex is the array index of the minimum value in the input buffer.
   6852    * @return none.
   6853    */
   6854 
   6855   void arm_min_f32(
   6856   float32_t * pSrc,
   6857   uint32_t blockSize,
   6858   float32_t * pResult,
   6859   uint32_t * pIndex);
   6860 
   6861 /**
   6862  * @brief Maximum value of a Q7 vector.
   6863  * @param[in]       *pSrc points to the input buffer
   6864  * @param[in]       blockSize length of the input vector
   6865  * @param[out]      *pResult maximum value returned here
   6866  * @param[out]      *pIndex index of maximum value returned here
   6867  * @return none.
   6868  */
   6869 
   6870   void arm_max_q7(
   6871   q7_t * pSrc,
   6872   uint32_t blockSize,
   6873   q7_t * pResult,
   6874   uint32_t * pIndex);
   6875 
   6876 /**
   6877  * @brief Maximum value of a Q15 vector.
   6878  * @param[in]       *pSrc points to the input buffer
   6879  * @param[in]       blockSize length of the input vector
   6880  * @param[out]      *pResult maximum value returned here
   6881  * @param[out]      *pIndex index of maximum value returned here
   6882  * @return none.
   6883  */
   6884 
   6885   void arm_max_q15(
   6886   q15_t * pSrc,
   6887   uint32_t blockSize,
   6888   q15_t * pResult,
   6889   uint32_t * pIndex);
   6890 
   6891 /**
   6892  * @brief Maximum value of a Q31 vector.
   6893  * @param[in]       *pSrc points to the input buffer
   6894  * @param[in]       blockSize length of the input vector
   6895  * @param[out]      *pResult maximum value returned here
   6896  * @param[out]      *pIndex index of maximum value returned here
   6897  * @return none.
   6898  */
   6899 
   6900   void arm_max_q31(
   6901   q31_t * pSrc,
   6902   uint32_t blockSize,
   6903   q31_t * pResult,
   6904   uint32_t * pIndex);
   6905 
   6906 /**
   6907  * @brief Maximum value of a floating-point vector.
   6908  * @param[in]       *pSrc points to the input buffer
   6909  * @param[in]       blockSize length of the input vector
   6910  * @param[out]      *pResult maximum value returned here
   6911  * @param[out]      *pIndex index of maximum value returned here
   6912  * @return none.
   6913  */
   6914 
   6915   void arm_max_f32(
   6916   float32_t * pSrc,
   6917   uint32_t blockSize,
   6918   float32_t * pResult,
   6919   uint32_t * pIndex);
   6920 
   6921   /**
   6922    * @brief  Q15 complex-by-complex multiplication
   6923    * @param[in]  *pSrcA points to the first input vector
   6924    * @param[in]  *pSrcB points to the second input vector
   6925    * @param[out]  *pDst  points to the output vector
   6926    * @param[in]  numSamples number of complex samples in each vector
   6927    * @return none.
   6928    */
   6929 
   6930   void arm_cmplx_mult_cmplx_q15(
   6931   q15_t * pSrcA,
   6932   q15_t * pSrcB,
   6933   q15_t * pDst,
   6934   uint32_t numSamples);
   6935 
   6936   /**
   6937    * @brief  Q31 complex-by-complex multiplication
   6938    * @param[in]  *pSrcA points to the first input vector
   6939    * @param[in]  *pSrcB points to the second input vector
   6940    * @param[out]  *pDst  points to the output vector
   6941    * @param[in]  numSamples number of complex samples in each vector
   6942    * @return none.
   6943    */
   6944 
   6945   void arm_cmplx_mult_cmplx_q31(
   6946   q31_t * pSrcA,
   6947   q31_t * pSrcB,
   6948   q31_t * pDst,
   6949   uint32_t numSamples);
   6950 
   6951   /**
   6952    * @brief  Floating-point complex-by-complex multiplication
   6953    * @param[in]  *pSrcA points to the first input vector
   6954    * @param[in]  *pSrcB points to the second input vector
   6955    * @param[out]  *pDst  points to the output vector
   6956    * @param[in]  numSamples number of complex samples in each vector
   6957    * @return none.
   6958    */
   6959 
   6960   void arm_cmplx_mult_cmplx_f32(
   6961   float32_t * pSrcA,
   6962   float32_t * pSrcB,
   6963   float32_t * pDst,
   6964   uint32_t numSamples);
   6965 
   6966   /**
   6967    * @brief Converts the elements of the floating-point vector to Q31 vector.
   6968    * @param[in]       *pSrc points to the floating-point input vector
   6969    * @param[out]      *pDst points to the Q31 output vector
   6970    * @param[in]       blockSize length of the input vector
   6971    * @return none.
   6972    */
   6973   void arm_float_to_q31(
   6974   float32_t * pSrc,
   6975   q31_t * pDst,
   6976   uint32_t blockSize);
   6977 
   6978   /**
   6979    * @brief Converts the elements of the floating-point vector to Q15 vector.
   6980    * @param[in]       *pSrc points to the floating-point input vector
   6981    * @param[out]      *pDst points to the Q15 output vector
   6982    * @param[in]       blockSize length of the input vector
   6983    * @return          none
   6984    */
   6985   void arm_float_to_q15(
   6986   float32_t * pSrc,
   6987   q15_t * pDst,
   6988   uint32_t blockSize);
   6989 
   6990   /**
   6991    * @brief Converts the elements of the floating-point vector to Q7 vector.
   6992    * @param[in]       *pSrc points to the floating-point input vector
   6993    * @param[out]      *pDst points to the Q7 output vector
   6994    * @param[in]       blockSize length of the input vector
   6995    * @return          none
   6996    */
   6997   void arm_float_to_q7(
   6998   float32_t * pSrc,
   6999   q7_t * pDst,
   7000   uint32_t blockSize);
   7001 
   7002 
   7003   /**
   7004    * @brief  Converts the elements of the Q31 vector to Q15 vector.
   7005    * @param[in]  *pSrc is input pointer
   7006    * @param[out]  *pDst is output pointer
   7007    * @param[in]  blockSize is the number of samples to process
   7008    * @return none.
   7009    */
   7010   void arm_q31_to_q15(
   7011   q31_t * pSrc,
   7012   q15_t * pDst,
   7013   uint32_t blockSize);
   7014 
   7015   /**
   7016    * @brief  Converts the elements of the Q31 vector to Q7 vector.
   7017    * @param[in]  *pSrc is input pointer
   7018    * @param[out]  *pDst is output pointer
   7019    * @param[in]  blockSize is the number of samples to process
   7020    * @return none.
   7021    */
   7022   void arm_q31_to_q7(
   7023   q31_t * pSrc,
   7024   q7_t * pDst,
   7025   uint32_t blockSize);
   7026 
   7027   /**
   7028    * @brief  Converts the elements of the Q15 vector to floating-point vector.
   7029    * @param[in]  *pSrc is input pointer
   7030    * @param[out]  *pDst is output pointer
   7031    * @param[in]  blockSize is the number of samples to process
   7032    * @return none.
   7033    */
   7034   void arm_q15_to_float(
   7035   q15_t * pSrc,
   7036   float32_t * pDst,
   7037   uint32_t blockSize);
   7038 
   7039 
   7040   /**
   7041    * @brief  Converts the elements of the Q15 vector to Q31 vector.
   7042    * @param[in]  *pSrc is input pointer
   7043    * @param[out]  *pDst is output pointer
   7044    * @param[in]  blockSize is the number of samples to process
   7045    * @return none.
   7046    */
   7047   void arm_q15_to_q31(
   7048   q15_t * pSrc,
   7049   q31_t * pDst,
   7050   uint32_t blockSize);
   7051 
   7052 
   7053   /**
   7054    * @brief  Converts the elements of the Q15 vector to Q7 vector.
   7055    * @param[in]  *pSrc is input pointer
   7056    * @param[out]  *pDst is output pointer
   7057    * @param[in]  blockSize is the number of samples to process
   7058    * @return none.
   7059    */
   7060   void arm_q15_to_q7(
   7061   q15_t * pSrc,
   7062   q7_t * pDst,
   7063   uint32_t blockSize);
   7064 
   7065 
   7066   /**
   7067    * @ingroup groupInterpolation
   7068    */
   7069 
   7070   /**
   7071    * @defgroup BilinearInterpolate Bilinear Interpolation
   7072    *
   7073    * Bilinear interpolation is an extension of linear interpolation applied to a two dimensional grid.
   7074    * The underlying function <code>f(x, y)</code> is sampled on a regular grid and the interpolation process
   7075    * determines values between the grid points.
   7076    * Bilinear interpolation is equivalent to two step linear interpolation, first in the x-dimension and then in the y-dimension.
   7077    * Bilinear interpolation is often used in image processing to rescale images.
   7078    * The CMSIS DSP library provides bilinear interpolation functions for Q7, Q15, Q31, and floating-point data types.
   7079    *
   7080    * <b>Algorithm</b>
   7081    * \par
   7082    * The instance structure used by the bilinear interpolation functions describes a two dimensional data table.
   7083    * For floating-point, the instance structure is defined as:
   7084    * <pre>
   7085    *   typedef struct
   7086    *   {
   7087    *     uint16_t numRows;
   7088    *     uint16_t numCols;
   7089    *     float32_t *pData;
   7090    * } arm_bilinear_interp_instance_f32;
   7091    * </pre>
   7092    *
   7093    * \par
   7094    * where <code>numRows</code> specifies the number of rows in the table;
   7095    * <code>numCols</code> specifies the number of columns in the table;
   7096    * and <code>pData</code> points to an array of size <code>numRows*numCols</code> values.
   7097    * The data table <code>pTable</code> is organized in row order and the supplied data values fall on integer indexes.
   7098    * That is, table element (x,y) is located at <code>pTable[x + y*numCols]</code> where x and y are integers.
   7099    *
   7100    * \par
   7101    * Let <code>(x, y)</code> specify the desired interpolation point.  Then define:
   7102    * <pre>
   7103    *     XF = floor(x)
   7104    *     YF = floor(y)
   7105    * </pre>
   7106    * \par
   7107    * The interpolated output point is computed as:
   7108    * <pre>
   7109    *  f(x, y) = f(XF, YF) * (1-(x-XF)) * (1-(y-YF))
   7110    *           + f(XF+1, YF) * (x-XF)*(1-(y-YF))
   7111    *           + f(XF, YF+1) * (1-(x-XF))*(y-YF)
   7112    *           + f(XF+1, YF+1) * (x-XF)*(y-YF)
   7113    * </pre>
   7114    * Note that the coordinates (x, y) contain integer and fractional components.
   7115    * The integer components specify which portion of the table to use while the
   7116    * fractional components control the interpolation processor.
   7117    *
   7118    * \par
   7119    * if (x,y) are outside of the table boundary, Bilinear interpolation returns zero output.
   7120    */
   7121 
   7122   /**
   7123    * @addtogroup BilinearInterpolate
   7124    * @{
   7125    */
   7126 
   7127   /**
   7128   *
   7129   * @brief  Floating-point bilinear interpolation.
   7130   * @param[in,out] *S points to an instance of the interpolation structure.
   7131   * @param[in] X interpolation coordinate.
   7132   * @param[in] Y interpolation coordinate.
   7133   * @return out interpolated value.
   7134   */
   7135 
   7136 
   7137   static __INLINE float32_t arm_bilinear_interp_f32(
   7138   const arm_bilinear_interp_instance_f32 * S,
   7139   float32_t X,
   7140   float32_t Y)
   7141   {
   7142     float32_t out;
   7143     float32_t f00, f01, f10, f11;
   7144     float32_t *pData = S->pData;
   7145     int32_t xIndex, yIndex, index;
   7146     float32_t xdiff, ydiff;
   7147     float32_t b1, b2, b3, b4;
   7148 
   7149     xIndex = (int32_t) X;
   7150     yIndex = (int32_t) Y;
   7151 
   7152     /* Care taken for table outside boundary */
   7153     /* Returns zero output when values are outside table boundary */
   7154     if(xIndex < 0 || xIndex > (S->numRows - 1) || yIndex < 0
   7155        || yIndex > (S->numCols - 1))
   7156     {
   7157       return (0);
   7158     }
   7159 
   7160     /* Calculation of index for two nearest points in X-direction */
   7161     index = (xIndex - 1) + (yIndex - 1) * S->numCols;
   7162 
   7163 
   7164     /* Read two nearest points in X-direction */
   7165     f00 = pData[index];
   7166     f01 = pData[index + 1];
   7167 
   7168     /* Calculation of index for two nearest points in Y-direction */
   7169     index = (xIndex - 1) + (yIndex) * S->numCols;
   7170 
   7171 
   7172     /* Read two nearest points in Y-direction */
   7173     f10 = pData[index];
   7174     f11 = pData[index + 1];
   7175 
   7176     /* Calculation of intermediate values */
   7177     b1 = f00;
   7178     b2 = f01 - f00;
   7179     b3 = f10 - f00;
   7180     b4 = f00 - f01 - f10 + f11;
   7181 
   7182     /* Calculation of fractional part in X */
   7183     xdiff = X - xIndex;
   7184 
   7185     /* Calculation of fractional part in Y */
   7186     ydiff = Y - yIndex;
   7187 
   7188     /* Calculation of bi-linear interpolated output */
   7189     out = b1 + b2 * xdiff + b3 * ydiff + b4 * xdiff * ydiff;
   7190 
   7191     /* return to application */
   7192     return (out);
   7193 
   7194   }
   7195 
   7196   /**
   7197   *
   7198   * @brief  Q31 bilinear interpolation.
   7199   * @param[in,out] *S points to an instance of the interpolation structure.
   7200   * @param[in] X interpolation coordinate in 12.20 format.
   7201   * @param[in] Y interpolation coordinate in 12.20 format.
   7202   * @return out interpolated value.
   7203   */
   7204 
   7205   static __INLINE q31_t arm_bilinear_interp_q31(
   7206   arm_bilinear_interp_instance_q31 * S,
   7207   q31_t X,
   7208   q31_t Y)
   7209   {
   7210     q31_t out;                                   /* Temporary output */
   7211     q31_t acc = 0;                               /* output */
   7212     q31_t xfract, yfract;                        /* X, Y fractional parts */
   7213     q31_t x1, x2, y1, y2;                        /* Nearest output values */
   7214     int32_t rI, cI;                              /* Row and column indices */
   7215     q31_t *pYData = S->pData;                    /* pointer to output table values */
   7216     uint32_t nCols = S->numCols;                 /* num of rows */
   7217 
   7218 
   7219     /* Input is in 12.20 format */
   7220     /* 12 bits for the table index */
   7221     /* Index value calculation */
   7222     rI = ((X & 0xFFF00000) >> 20u);
   7223 
   7224     /* Input is in 12.20 format */
   7225     /* 12 bits for the table index */
   7226     /* Index value calculation */
   7227     cI = ((Y & 0xFFF00000) >> 20u);
   7228 
   7229     /* Care taken for table outside boundary */
   7230     /* Returns zero output when values are outside table boundary */
   7231     if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
   7232     {
   7233       return (0);
   7234     }
   7235 
   7236     /* 20 bits for the fractional part */
   7237     /* shift left xfract by 11 to keep 1.31 format */
   7238     xfract = (X & 0x000FFFFF) << 11u;
   7239 
   7240     /* Read two nearest output values from the index */
   7241     x1 = pYData[(rI) + nCols * (cI)];
   7242     x2 = pYData[(rI) + nCols * (cI) + 1u];
   7243 
   7244     /* 20 bits for the fractional part */
   7245     /* shift left yfract by 11 to keep 1.31 format */
   7246     yfract = (Y & 0x000FFFFF) << 11u;
   7247 
   7248     /* Read two nearest output values from the index */
   7249     y1 = pYData[(rI) + nCols * (cI + 1)];
   7250     y2 = pYData[(rI) + nCols * (cI + 1) + 1u];
   7251 
   7252     /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 3.29(q29) format */
   7253     out = ((q31_t) (((q63_t) x1 * (0x7FFFFFFF - xfract)) >> 32));
   7254     acc = ((q31_t) (((q63_t) out * (0x7FFFFFFF - yfract)) >> 32));
   7255 
   7256     /* x2 * (xfract) * (1-yfract)  in 3.29(q29) and adding to acc */
   7257     out = ((q31_t) ((q63_t) x2 * (0x7FFFFFFF - yfract) >> 32));
   7258     acc += ((q31_t) ((q63_t) out * (xfract) >> 32));
   7259 
   7260     /* y1 * (1 - xfract) * (yfract)  in 3.29(q29) and adding to acc */
   7261     out = ((q31_t) ((q63_t) y1 * (0x7FFFFFFF - xfract) >> 32));
   7262     acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
   7263 
   7264     /* y2 * (xfract) * (yfract)  in 3.29(q29) and adding to acc */
   7265     out = ((q31_t) ((q63_t) y2 * (xfract) >> 32));
   7266     acc += ((q31_t) ((q63_t) out * (yfract) >> 32));
   7267 
   7268     /* Convert acc to 1.31(q31) format */
   7269     return (acc << 2u);
   7270 
   7271   }
   7272 
   7273   /**
   7274   * @brief  Q15 bilinear interpolation.
   7275   * @param[in,out] *S points to an instance of the interpolation structure.
   7276   * @param[in] X interpolation coordinate in 12.20 format.
   7277   * @param[in] Y interpolation coordinate in 12.20 format.
   7278   * @return out interpolated value.
   7279   */
   7280 
   7281   static __INLINE q15_t arm_bilinear_interp_q15(
   7282   arm_bilinear_interp_instance_q15 * S,
   7283   q31_t X,
   7284   q31_t Y)
   7285   {
   7286     q63_t acc = 0;                               /* output */
   7287     q31_t out;                                   /* Temporary output */
   7288     q15_t x1, x2, y1, y2;                        /* Nearest output values */
   7289     q31_t xfract, yfract;                        /* X, Y fractional parts */
   7290     int32_t rI, cI;                              /* Row and column indices */
   7291     q15_t *pYData = S->pData;                    /* pointer to output table values */
   7292     uint32_t nCols = S->numCols;                 /* num of rows */
   7293 
   7294     /* Input is in 12.20 format */
   7295     /* 12 bits for the table index */
   7296     /* Index value calculation */
   7297     rI = ((X & 0xFFF00000) >> 20);
   7298 
   7299     /* Input is in 12.20 format */
   7300     /* 12 bits for the table index */
   7301     /* Index value calculation */
   7302     cI = ((Y & 0xFFF00000) >> 20);
   7303 
   7304     /* Care taken for table outside boundary */
   7305     /* Returns zero output when values are outside table boundary */
   7306     if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
   7307     {
   7308       return (0);
   7309     }
   7310 
   7311     /* 20 bits for the fractional part */
   7312     /* xfract should be in 12.20 format */
   7313     xfract = (X & 0x000FFFFF);
   7314 
   7315     /* Read two nearest output values from the index */
   7316     x1 = pYData[(rI) + nCols * (cI)];
   7317     x2 = pYData[(rI) + nCols * (cI) + 1u];
   7318 
   7319 
   7320     /* 20 bits for the fractional part */
   7321     /* yfract should be in 12.20 format */
   7322     yfract = (Y & 0x000FFFFF);
   7323 
   7324     /* Read two nearest output values from the index */
   7325     y1 = pYData[(rI) + nCols * (cI + 1)];
   7326     y2 = pYData[(rI) + nCols * (cI + 1) + 1u];
   7327 
   7328     /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 13.51 format */
   7329 
   7330     /* x1 is in 1.15(q15), xfract in 12.20 format and out is in 13.35 format */
   7331     /* convert 13.35 to 13.31 by right shifting  and out is in 1.31 */
   7332     out = (q31_t) (((q63_t) x1 * (0xFFFFF - xfract)) >> 4u);
   7333     acc = ((q63_t) out * (0xFFFFF - yfract));
   7334 
   7335     /* x2 * (xfract) * (1-yfract)  in 1.51 and adding to acc */
   7336     out = (q31_t) (((q63_t) x2 * (0xFFFFF - yfract)) >> 4u);
   7337     acc += ((q63_t) out * (xfract));
   7338 
   7339     /* y1 * (1 - xfract) * (yfract)  in 1.51 and adding to acc */
   7340     out = (q31_t) (((q63_t) y1 * (0xFFFFF - xfract)) >> 4u);
   7341     acc += ((q63_t) out * (yfract));
   7342 
   7343     /* y2 * (xfract) * (yfract)  in 1.51 and adding to acc */
   7344     out = (q31_t) (((q63_t) y2 * (xfract)) >> 4u);
   7345     acc += ((q63_t) out * (yfract));
   7346 
   7347     /* acc is in 13.51 format and down shift acc by 36 times */
   7348     /* Convert out to 1.15 format */
   7349     return (acc >> 36);
   7350 
   7351   }
   7352 
   7353   /**
   7354   * @brief  Q7 bilinear interpolation.
   7355   * @param[in,out] *S points to an instance of the interpolation structure.
   7356   * @param[in] X interpolation coordinate in 12.20 format.
   7357   * @param[in] Y interpolation coordinate in 12.20 format.
   7358   * @return out interpolated value.
   7359   */
   7360 
   7361   static __INLINE q7_t arm_bilinear_interp_q7(
   7362   arm_bilinear_interp_instance_q7 * S,
   7363   q31_t X,
   7364   q31_t Y)
   7365   {
   7366     q63_t acc = 0;                               /* output */
   7367     q31_t out;                                   /* Temporary output */
   7368     q31_t xfract, yfract;                        /* X, Y fractional parts */
   7369     q7_t x1, x2, y1, y2;                         /* Nearest output values */
   7370     int32_t rI, cI;                              /* Row and column indices */
   7371     q7_t *pYData = S->pData;                     /* pointer to output table values */
   7372     uint32_t nCols = S->numCols;                 /* num of rows */
   7373 
   7374     /* Input is in 12.20 format */
   7375     /* 12 bits for the table index */
   7376     /* Index value calculation */
   7377     rI = ((X & 0xFFF00000) >> 20);
   7378 
   7379     /* Input is in 12.20 format */
   7380     /* 12 bits for the table index */
   7381     /* Index value calculation */
   7382     cI = ((Y & 0xFFF00000) >> 20);
   7383 
   7384     /* Care taken for table outside boundary */
   7385     /* Returns zero output when values are outside table boundary */
   7386     if(rI < 0 || rI > (S->numRows - 1) || cI < 0 || cI > (S->numCols - 1))
   7387     {
   7388       return (0);
   7389     }
   7390 
   7391     /* 20 bits for the fractional part */
   7392     /* xfract should be in 12.20 format */
   7393     xfract = (X & 0x000FFFFF);
   7394 
   7395     /* Read two nearest output values from the index */
   7396     x1 = pYData[(rI) + nCols * (cI)];
   7397     x2 = pYData[(rI) + nCols * (cI) + 1u];
   7398 
   7399 
   7400     /* 20 bits for the fractional part */
   7401     /* yfract should be in 12.20 format */
   7402     yfract = (Y & 0x000FFFFF);
   7403 
   7404     /* Read two nearest output values from the index */
   7405     y1 = pYData[(rI) + nCols * (cI + 1)];
   7406     y2 = pYData[(rI) + nCols * (cI + 1) + 1u];
   7407 
   7408     /* Calculation of x1 * (1-xfract ) * (1-yfract) and acc is in 16.47 format */
   7409     out = ((x1 * (0xFFFFF - xfract)));
   7410     acc = (((q63_t) out * (0xFFFFF - yfract)));
   7411 
   7412     /* x2 * (xfract) * (1-yfract)  in 2.22 and adding to acc */
   7413     out = ((x2 * (0xFFFFF - yfract)));
   7414     acc += (((q63_t) out * (xfract)));
   7415 
   7416     /* y1 * (1 - xfract) * (yfract)  in 2.22 and adding to acc */
   7417     out = ((y1 * (0xFFFFF - xfract)));
   7418     acc += (((q63_t) out * (yfract)));
   7419 
   7420     /* y2 * (xfract) * (yfract)  in 2.22 and adding to acc */
   7421     out = ((y2 * (yfract)));
   7422     acc += (((q63_t) out * (xfract)));
   7423 
   7424     /* acc in 16.47 format and down shift by 40 to convert to 1.7 format */
   7425     return (acc >> 40);
   7426 
   7427   }
   7428 
   7429   /**
   7430    * @} end of BilinearInterpolate group
   7431    */
   7432 
   7433 
   7434 //SMMLAR
   7435 #define multAcc_32x32_keep32_R(a, x, y) \
   7436     a = (q31_t) (((((q63_t) a) << 32) + ((q63_t) x * y) + 0x80000000LL ) >> 32)
   7437 
   7438 //SMMLSR
   7439 #define multSub_32x32_keep32_R(a, x, y) \
   7440     a = (q31_t) (((((q63_t) a) << 32) - ((q63_t) x * y) + 0x80000000LL ) >> 32)
   7441 
   7442 //SMMULR
   7443 #define mult_32x32_keep32_R(a, x, y) \
   7444     a = (q31_t) (((q63_t) x * y + 0x80000000LL ) >> 32)
   7445 
   7446 //SMMLA
   7447 #define multAcc_32x32_keep32(a, x, y) \
   7448     a += (q31_t) (((q63_t) x * y) >> 32)
   7449 
   7450 //SMMLS
   7451 #define multSub_32x32_keep32(a, x, y) \
   7452     a -= (q31_t) (((q63_t) x * y) >> 32)
   7453 
   7454 //SMMUL
   7455 #define mult_32x32_keep32(a, x, y) \
   7456     a = (q31_t) (((q63_t) x * y ) >> 32)
   7457 
   7458 
   7459 #if defined ( __CC_ARM ) //Keil
   7460 
   7461 //Enter low optimization region - place directly above function definition
   7462     #ifdef ARM_MATH_CM4
   7463       #define LOW_OPTIMIZATION_ENTER \
   7464          _Pragma ("push")         \
   7465          _Pragma ("O1")
   7466     #else
   7467       #define LOW_OPTIMIZATION_ENTER
   7468     #endif
   7469 
   7470 //Exit low optimization region - place directly after end of function definition
   7471     #ifdef ARM_MATH_CM4
   7472       #define LOW_OPTIMIZATION_EXIT \
   7473          _Pragma ("pop")
   7474     #else
   7475       #define LOW_OPTIMIZATION_EXIT
   7476     #endif
   7477 
   7478 //Enter low optimization region - place directly above function definition
   7479   #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
   7480 
   7481 //Exit low optimization region - place directly after end of function definition
   7482   #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
   7483 
   7484 #elif defined(__ICCARM__) //IAR
   7485 
   7486 //Enter low optimization region - place directly above function definition
   7487     #ifdef ARM_MATH_CM4
   7488       #define LOW_OPTIMIZATION_ENTER \
   7489          _Pragma ("optimize=low")
   7490     #else
   7491       #define LOW_OPTIMIZATION_ENTER
   7492     #endif
   7493 
   7494 //Exit low optimization region - place directly after end of function definition
   7495   #define LOW_OPTIMIZATION_EXIT
   7496 
   7497 //Enter low optimization region - place directly above function definition
   7498     #ifdef ARM_MATH_CM4
   7499       #define IAR_ONLY_LOW_OPTIMIZATION_ENTER \
   7500          _Pragma ("optimize=low")
   7501     #else
   7502       #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
   7503     #endif
   7504 
   7505 //Exit low optimization region - place directly after end of function definition
   7506   #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
   7507 
   7508 #elif defined(__GNUC__)
   7509 
   7510   #define LOW_OPTIMIZATION_ENTER __attribute__(( optimize("-O1") ))
   7511 
   7512   #define LOW_OPTIMIZATION_EXIT
   7513 
   7514   #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
   7515 
   7516   #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
   7517 
   7518 #elif defined(__CSMC__)    // Cosmic
   7519 
   7520 #define LOW_OPTIMIZATION_ENTER
   7521 #define LOW_OPTIMIZATION_EXIT
   7522 #define IAR_ONLY_LOW_OPTIMIZATION_ENTER
   7523 #define IAR_ONLY_LOW_OPTIMIZATION_EXIT
   7524 
   7525 #endif
   7526 
   7527 
   7528 #ifdef  __cplusplus
   7529 }
   7530 #endif
   7531 
   7532 
   7533 #endif /* _ARM_MATH_H */
   7534 
   7535 /**
   7536  *
   7537  * End of file.
   7538  */
   7539