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_sin_f32.c 9 * 10 * Description: Fast sine calculation for floating-point values. 11 * Fast cosine calculation for floating-point values. 12 * 13 * 14 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 15 * 16 * Redistribution and use in source and binary forms, with or without 17 * modification, are permitted provided that the following conditions 18 * are met: 19 * - Redistributions of source code must retain the above copyright 20 * notice, this list of conditions and the following disclaimer. 21 * - Redistributions in binary form must reproduce the above copyright 22 * notice, this list of conditions and the following disclaimer in 23 * the documentation and/or other materials provided with the 24 * distribution. 25 * - Neither the name of ARM LIMITED nor the names of its contributors 26 * may be used to endorse or promote products derived from this 27 * software without specific prior written permission. 28 * 29 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 30 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 31 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 32 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 33 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, 34 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, 35 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 36 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER 37 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 38 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN 39 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 40 * POSSIBILITY OF SUCH DAMAGE. 41 * -------------------------------------------------------------------- */ 42 43 #include <stdint.h> 44 #include <nanohub_math.h> 45 46 #define FAST_MATH_TABLE_SIZE 512 47 typedef float float32_t; 48 49 /** 50 * \par 51 * Example code for the generation of the floating-point sine table: 52 * <pre> 53 * tableSize = 512; 54 * for(n = 0; n < (tableSize + 1); n++) 55 * { 56 * sinTable[n]=sin(2*pi*n/tableSize); 57 * }</pre> 58 * \par 59 * where pi value is 3.14159265358979 60 */ 61 62 static const float32_t sinTable_f32[FAST_MATH_TABLE_SIZE + 1] = { 63 0.00000000f, 0.01227154f, 0.02454123f, 0.03680722f, 0.04906767f, 0.06132074f, 64 0.07356456f, 0.08579731f, 0.09801714f, 0.11022221f, 0.12241068f, 0.13458071f, 65 0.14673047f, 0.15885814f, 0.17096189f, 0.18303989f, 0.19509032f, 0.20711138f, 66 0.21910124f, 0.23105811f, 0.24298018f, 0.25486566f, 0.26671276f, 0.27851969f, 67 0.29028468f, 0.30200595f, 0.31368174f, 0.32531029f, 0.33688985f, 0.34841868f, 68 0.35989504f, 0.37131719f, 0.38268343f, 0.39399204f, 0.40524131f, 0.41642956f, 69 0.42755509f, 0.43861624f, 0.44961133f, 0.46053871f, 0.47139674f, 0.48218377f, 70 0.49289819f, 0.50353838f, 0.51410274f, 0.52458968f, 0.53499762f, 0.54532499f, 71 0.55557023f, 0.56573181f, 0.57580819f, 0.58579786f, 0.59569930f, 0.60551104f, 72 0.61523159f, 0.62485949f, 0.63439328f, 0.64383154f, 0.65317284f, 0.66241578f, 73 0.67155895f, 0.68060100f, 0.68954054f, 0.69837625f, 0.70710678f, 0.71573083f, 74 0.72424708f, 0.73265427f, 0.74095113f, 0.74913639f, 0.75720885f, 0.76516727f, 75 0.77301045f, 0.78073723f, 0.78834643f, 0.79583690f, 0.80320753f, 0.81045720f, 76 0.81758481f, 0.82458930f, 0.83146961f, 0.83822471f, 0.84485357f, 0.85135519f, 77 0.85772861f, 0.86397286f, 0.87008699f, 0.87607009f, 0.88192126f, 0.88763962f, 78 0.89322430f, 0.89867447f, 0.90398929f, 0.90916798f, 0.91420976f, 0.91911385f, 79 0.92387953f, 0.92850608f, 0.93299280f, 0.93733901f, 0.94154407f, 0.94560733f, 80 0.94952818f, 0.95330604f, 0.95694034f, 0.96043052f, 0.96377607f, 0.96697647f, 81 0.97003125f, 0.97293995f, 0.97570213f, 0.97831737f, 0.98078528f, 0.98310549f, 82 0.98527764f, 0.98730142f, 0.98917651f, 0.99090264f, 0.99247953f, 0.99390697f, 83 0.99518473f, 0.99631261f, 0.99729046f, 0.99811811f, 0.99879546f, 0.99932238f, 84 0.99969882f, 0.99992470f, 1.00000000f, 0.99992470f, 0.99969882f, 0.99932238f, 85 0.99879546f, 0.99811811f, 0.99729046f, 0.99631261f, 0.99518473f, 0.99390697f, 86 0.99247953f, 0.99090264f, 0.98917651f, 0.98730142f, 0.98527764f, 0.98310549f, 87 0.98078528f, 0.97831737f, 0.97570213f, 0.97293995f, 0.97003125f, 0.96697647f, 88 0.96377607f, 0.96043052f, 0.95694034f, 0.95330604f, 0.94952818f, 0.94560733f, 89 0.94154407f, 0.93733901f, 0.93299280f, 0.92850608f, 0.92387953f, 0.91911385f, 90 0.91420976f, 0.90916798f, 0.90398929f, 0.89867447f, 0.89322430f, 0.88763962f, 91 0.88192126f, 0.87607009f, 0.87008699f, 0.86397286f, 0.85772861f, 0.85135519f, 92 0.84485357f, 0.83822471f, 0.83146961f, 0.82458930f, 0.81758481f, 0.81045720f, 93 0.80320753f, 0.79583690f, 0.78834643f, 0.78073723f, 0.77301045f, 0.76516727f, 94 0.75720885f, 0.74913639f, 0.74095113f, 0.73265427f, 0.72424708f, 0.71573083f, 95 0.70710678f, 0.69837625f, 0.68954054f, 0.68060100f, 0.67155895f, 0.66241578f, 96 0.65317284f, 0.64383154f, 0.63439328f, 0.62485949f, 0.61523159f, 0.60551104f, 97 0.59569930f, 0.58579786f, 0.57580819f, 0.56573181f, 0.55557023f, 0.54532499f, 98 0.53499762f, 0.52458968f, 0.51410274f, 0.50353838f, 0.49289819f, 0.48218377f, 99 0.47139674f, 0.46053871f, 0.44961133f, 0.43861624f, 0.42755509f, 0.41642956f, 100 0.40524131f, 0.39399204f, 0.38268343f, 0.37131719f, 0.35989504f, 0.34841868f, 101 0.33688985f, 0.32531029f, 0.31368174f, 0.30200595f, 0.29028468f, 0.27851969f, 102 0.26671276f, 0.25486566f, 0.24298018f, 0.23105811f, 0.21910124f, 0.20711138f, 103 0.19509032f, 0.18303989f, 0.17096189f, 0.15885814f, 0.14673047f, 0.13458071f, 104 0.12241068f, 0.11022221f, 0.09801714f, 0.08579731f, 0.07356456f, 0.06132074f, 105 0.04906767f, 0.03680722f, 0.02454123f, 0.01227154f, 0.00000000f, -0.01227154f, 106 -0.02454123f, -0.03680722f, -0.04906767f, -0.06132074f, -0.07356456f, 107 -0.08579731f, -0.09801714f, -0.11022221f, -0.12241068f, -0.13458071f, 108 -0.14673047f, -0.15885814f, -0.17096189f, -0.18303989f, -0.19509032f, 109 -0.20711138f, -0.21910124f, -0.23105811f, -0.24298018f, -0.25486566f, 110 -0.26671276f, -0.27851969f, -0.29028468f, -0.30200595f, -0.31368174f, 111 -0.32531029f, -0.33688985f, -0.34841868f, -0.35989504f, -0.37131719f, 112 -0.38268343f, -0.39399204f, -0.40524131f, -0.41642956f, -0.42755509f, 113 -0.43861624f, -0.44961133f, -0.46053871f, -0.47139674f, -0.48218377f, 114 -0.49289819f, -0.50353838f, -0.51410274f, -0.52458968f, -0.53499762f, 115 -0.54532499f, -0.55557023f, -0.56573181f, -0.57580819f, -0.58579786f, 116 -0.59569930f, -0.60551104f, -0.61523159f, -0.62485949f, -0.63439328f, 117 -0.64383154f, -0.65317284f, -0.66241578f, -0.67155895f, -0.68060100f, 118 -0.68954054f, -0.69837625f, -0.70710678f, -0.71573083f, -0.72424708f, 119 -0.73265427f, -0.74095113f, -0.74913639f, -0.75720885f, -0.76516727f, 120 -0.77301045f, -0.78073723f, -0.78834643f, -0.79583690f, -0.80320753f, 121 -0.81045720f, -0.81758481f, -0.82458930f, -0.83146961f, -0.83822471f, 122 -0.84485357f, -0.85135519f, -0.85772861f, -0.86397286f, -0.87008699f, 123 -0.87607009f, -0.88192126f, -0.88763962f, -0.89322430f, -0.89867447f, 124 -0.90398929f, -0.90916798f, -0.91420976f, -0.91911385f, -0.92387953f, 125 -0.92850608f, -0.93299280f, -0.93733901f, -0.94154407f, -0.94560733f, 126 -0.94952818f, -0.95330604f, -0.95694034f, -0.96043052f, -0.96377607f, 127 -0.96697647f, -0.97003125f, -0.97293995f, -0.97570213f, -0.97831737f, 128 -0.98078528f, -0.98310549f, -0.98527764f, -0.98730142f, -0.98917651f, 129 -0.99090264f, -0.99247953f, -0.99390697f, -0.99518473f, -0.99631261f, 130 -0.99729046f, -0.99811811f, -0.99879546f, -0.99932238f, -0.99969882f, 131 -0.99992470f, -1.00000000f, -0.99992470f, -0.99969882f, -0.99932238f, 132 -0.99879546f, -0.99811811f, -0.99729046f, -0.99631261f, -0.99518473f, 133 -0.99390697f, -0.99247953f, -0.99090264f, -0.98917651f, -0.98730142f, 134 -0.98527764f, -0.98310549f, -0.98078528f, -0.97831737f, -0.97570213f, 135 -0.97293995f, -0.97003125f, -0.96697647f, -0.96377607f, -0.96043052f, 136 -0.95694034f, -0.95330604f, -0.94952818f, -0.94560733f, -0.94154407f, 137 -0.93733901f, -0.93299280f, -0.92850608f, -0.92387953f, -0.91911385f, 138 -0.91420976f, -0.90916798f, -0.90398929f, -0.89867447f, -0.89322430f, 139 -0.88763962f, -0.88192126f, -0.87607009f, -0.87008699f, -0.86397286f, 140 -0.85772861f, -0.85135519f, -0.84485357f, -0.83822471f, -0.83146961f, 141 -0.82458930f, -0.81758481f, -0.81045720f, -0.80320753f, -0.79583690f, 142 -0.78834643f, -0.78073723f, -0.77301045f, -0.76516727f, -0.75720885f, 143 -0.74913639f, -0.74095113f, -0.73265427f, -0.72424708f, -0.71573083f, 144 -0.70710678f, -0.69837625f, -0.68954054f, -0.68060100f, -0.67155895f, 145 -0.66241578f, -0.65317284f, -0.64383154f, -0.63439328f, -0.62485949f, 146 -0.61523159f, -0.60551104f, -0.59569930f, -0.58579786f, -0.57580819f, 147 -0.56573181f, -0.55557023f, -0.54532499f, -0.53499762f, -0.52458968f, 148 -0.51410274f, -0.50353838f, -0.49289819f, -0.48218377f, -0.47139674f, 149 -0.46053871f, -0.44961133f, -0.43861624f, -0.42755509f, -0.41642956f, 150 -0.40524131f, -0.39399204f, -0.38268343f, -0.37131719f, -0.35989504f, 151 -0.34841868f, -0.33688985f, -0.32531029f, -0.31368174f, -0.30200595f, 152 -0.29028468f, -0.27851969f, -0.26671276f, -0.25486566f, -0.24298018f, 153 -0.23105811f, -0.21910124f, -0.20711138f, -0.19509032f, -0.18303989f, 154 -0.17096189f, -0.15885814f, -0.14673047f, -0.13458071f, -0.12241068f, 155 -0.11022221f, -0.09801714f, -0.08579731f, -0.07356456f, -0.06132074f, 156 -0.04906767f, -0.03680722f, -0.02454123f, -0.01227154f, -0.00000000f 157 }; 158 159 /** 160 * @ingroup groupFastMath 161 */ 162 163 /** 164 * @defgroup sin Sine 165 * 166 * Computes the trigonometric sine function using a combination of table lookup 167 * and cubic interpolation. There are separate functions for 168 * Q15, Q31, and floating-point data types. 169 * The input to the floating-point version is in radians while the 170 * fixed-point Q15 and Q31 have a scaled input with the range 171 * [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a 172 * value of 2*pi wraps around to 0. 173 * 174 * The implementation is based on table lookup using 256 values together with cubic interpolation. 175 * The steps used are: 176 * -# Calculation of the nearest integer table index 177 * -# Fetch the four table values a, b, c, and d 178 * -# Compute the fractional portion (fract) of the table index. 179 * -# Calculation of wa, wb, wc, wd 180 * -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code> 181 * 182 * where 183 * <pre> 184 * a=Table[index-1]; 185 * b=Table[index+0]; 186 * c=Table[index+1]; 187 * d=Table[index+2]; 188 * </pre> 189 * and 190 * <pre> 191 * wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract; 192 * wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1; 193 * wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract; 194 * wd=(1/6)*fract.^3 - (1/6)*fract; 195 * </pre> 196 */ 197 198 /** 199 * @addtogroup sin 200 * @{ 201 */ 202 203 /** 204 * @brief Fast approximation to the trigonometric sine function for floating-point data. 205 * @param[in] x input value in radians. 206 * @return sin(x). 207 */ 208 209 float32_t arm_sin_f32( 210 float32_t x) 211 { 212 float32_t sinVal, fract, in; /* Temporary variables for input, output */ 213 uint16_t index; /* Index variable */ 214 float32_t a, b; /* Two nearest output values */ 215 int32_t n; 216 float32_t findex; 217 218 /* input x is in radians */ 219 /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi */ 220 in = x * 0.159154943092f; 221 222 /* Calculation of floor value of input */ 223 n = (int32_t) in; 224 225 /* Make negative values towards -infinity */ 226 if(x < 0.0f) 227 { 228 n--; 229 } 230 231 /* Map input value to [0 1] */ 232 in = in - (float32_t) n; 233 234 /* Calculation of index of the table */ 235 findex = (float32_t) FAST_MATH_TABLE_SIZE * in; 236 index = ((uint16_t)findex) & 0x1ff; 237 238 /* fractional value calculation */ 239 fract = findex - (float32_t) index; 240 241 /* Read two nearest values of input value from the sin table */ 242 a = sinTable_f32[index]; 243 b = sinTable_f32[index+1]; 244 245 /* Linear interpolation process */ 246 sinVal = (1.0f-fract)*a + fract*b; 247 248 /* Return the output value */ 249 return (sinVal); 250 } 251 252 /** 253 * @defgroup cos Cosine 254 * 255 * Computes the trigonometric cosine function using a combination of table lookup 256 * and cubic interpolation. There are separate functions for 257 * Q15, Q31, and floating-point data types. 258 * The input to the floating-point version is in radians while the 259 * fixed-point Q15 and Q31 have a scaled input with the range 260 * [0 +0.9999] mapping to [0 2*pi). The fixed-point range is chosen so that a 261 * value of 2*pi wraps around to 0. 262 * 263 * The implementation is based on table lookup using 256 values together with cubic interpolation. 264 * The steps used are: 265 * -# Calculation of the nearest integer table index 266 * -# Fetch the four table values a, b, c, and d 267 * -# Compute the fractional portion (fract) of the table index. 268 * -# Calculation of wa, wb, wc, wd 269 * -# The final result equals <code>a*wa + b*wb + c*wc + d*wd</code> 270 * 271 * where 272 * <pre> 273 * a=Table[index-1]; 274 * b=Table[index+0]; 275 * c=Table[index+1]; 276 * d=Table[index+2]; 277 * </pre> 278 * and 279 * <pre> 280 * wa=-(1/6)*fract.^3 + (1/2)*fract.^2 - (1/3)*fract; 281 * wb=(1/2)*fract.^3 - fract.^2 - (1/2)*fract + 1; 282 * wc=-(1/2)*fract.^3+(1/2)*fract.^2+fract; 283 * wd=(1/6)*fract.^3 - (1/6)*fract; 284 * </pre> 285 */ 286 287 /** 288 * @addtogroup cos 289 * @{ 290 */ 291 292 /** 293 * @brief Fast approximation to the trigonometric cosine function for floating-point data. 294 * @param[in] x input value in radians. 295 * @return cos(x). 296 */ 297 298 float32_t arm_cos_f32( 299 float32_t x) 300 { 301 float32_t cosVal, fract, in; /* Temporary variables for input, output */ 302 uint16_t index; /* Index variable */ 303 float32_t a, b; /* Two nearest output values */ 304 int32_t n; 305 float32_t findex; 306 307 /* input x is in radians */ 308 /* Scale the input to [0 1] range from [0 2*PI] , divide input by 2*pi, add 0.25 (pi/2) to read sine table */ 309 in = x * 0.159154943092f + 0.25f; 310 311 /* Calculation of floor value of input */ 312 n = (int32_t) in; 313 314 /* Make negative values towards -infinity */ 315 if(in < 0.0f) 316 { 317 n--; 318 } 319 320 /* Map input value to [0 1] */ 321 in = in - (float32_t) n; 322 323 /* Calculation of index of the table */ 324 findex = (float32_t) FAST_MATH_TABLE_SIZE * in; 325 index = ((uint16_t)findex) & 0x1ff; 326 327 /* fractional value calculation */ 328 fract = findex - (float32_t) index; 329 330 /* Read two nearest values of input value from the cos table */ 331 a = sinTable_f32[index]; 332 b = sinTable_f32[index+1]; 333 334 /* Linear interpolation process */ 335 cosVal = (1.0f-fract)*a + fract*b; 336 337 /* Return the output value */ 338 return (cosVal); 339 } 340 341 /** 342 * @} end of cos group 343 */ 344
