1 /* Copyright (c) 2002-2008 Jean-Marc Valin 2 Copyright (c) 2007-2008 CSIRO 3 Copyright (c) 2007-2009 Xiph.Org Foundation 4 Written by Jean-Marc Valin */ 5 /** 6 @file mathops.h 7 @brief Various math functions 8 */ 9 /* 10 Redistribution and use in source and binary forms, with or without 11 modification, are permitted provided that the following conditions 12 are met: 13 14 - Redistributions of source code must retain the above copyright 15 notice, this list of conditions and the following disclaimer. 16 17 - Redistributions in binary form must reproduce the above copyright 18 notice, this list of conditions and the following disclaimer in the 19 documentation and/or other materials provided with the distribution. 20 21 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 22 ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 23 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 24 A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER 25 OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 26 EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 27 PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 28 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF 29 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING 30 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 31 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 32 */ 33 34 #ifndef MATHOPS_H 35 #define MATHOPS_H 36 37 #include "arch.h" 38 #include "entcode.h" 39 #include "os_support.h" 40 41 /* Multiplies two 16-bit fractional values. Bit-exactness of this macro is important */ 42 #define FRAC_MUL16(a,b) ((16384+((opus_int32)(opus_int16)(a)*(opus_int16)(b)))>>15) 43 44 unsigned isqrt32(opus_uint32 _val); 45 46 #ifndef FIXED_POINT 47 48 #define PI 3.141592653f 49 #define celt_sqrt(x) ((float)sqrt(x)) 50 #define celt_rsqrt(x) (1.f/celt_sqrt(x)) 51 #define celt_rsqrt_norm(x) (celt_rsqrt(x)) 52 #define celt_cos_norm(x) ((float)cos((.5f*PI)*(x))) 53 #define celt_rcp(x) (1.f/(x)) 54 #define celt_div(a,b) ((a)/(b)) 55 #define frac_div32(a,b) ((float)(a)/(b)) 56 57 #ifdef FLOAT_APPROX 58 59 /* Note: This assumes radix-2 floating point with the exponent at bits 23..30 and an offset of 127 60 denorm, +/- inf and NaN are *not* handled */ 61 62 /** Base-2 log approximation (log2(x)). */ 63 static inline float celt_log2(float x) 64 { 65 int integer; 66 float frac; 67 union { 68 float f; 69 opus_uint32 i; 70 } in; 71 in.f = x; 72 integer = (in.i>>23)-127; 73 in.i -= integer<<23; 74 frac = in.f - 1.5f; 75 frac = -0.41445418f + frac*(0.95909232f 76 + frac*(-0.33951290f + frac*0.16541097f)); 77 return 1+integer+frac; 78 } 79 80 /** Base-2 exponential approximation (2^x). */ 81 static inline float celt_exp2(float x) 82 { 83 int integer; 84 float frac; 85 union { 86 float f; 87 opus_uint32 i; 88 } res; 89 integer = floor(x); 90 if (integer < -50) 91 return 0; 92 frac = x-integer; 93 /* K0 = 1, K1 = log(2), K2 = 3-4*log(2), K3 = 3*log(2) - 2 */ 94 res.f = 0.99992522f + frac * (0.69583354f 95 + frac * (0.22606716f + 0.078024523f*frac)); 96 res.i = (res.i + (integer<<23)) & 0x7fffffff; 97 return res.f; 98 } 99 100 #else 101 #define celt_log2(x) ((float)(1.442695040888963387*log(x))) 102 #define celt_exp2(x) ((float)exp(0.6931471805599453094*(x))) 103 #endif 104 105 #endif 106 107 #ifdef FIXED_POINT 108 109 #include "os_support.h" 110 111 #ifndef OVERRIDE_CELT_ILOG2 112 /** Integer log in base2. Undefined for zero and negative numbers */ 113 static inline opus_int16 celt_ilog2(opus_int32 x) 114 { 115 celt_assert2(x>0, "celt_ilog2() only defined for strictly positive numbers"); 116 return EC_ILOG(x)-1; 117 } 118 #endif 119 120 #ifndef OVERRIDE_CELT_MAXABS16 121 static inline opus_val16 celt_maxabs16(opus_val16 *x, int len) 122 { 123 int i; 124 opus_val16 maxval = 0; 125 for (i=0;i<len;i++) 126 maxval = MAX16(maxval, ABS16(x[i])); 127 return maxval; 128 } 129 #endif 130 131 #ifndef OVERRIDE_CELT_MAXABS32 132 static inline opus_val32 celt_maxabs32(opus_val32 *x, int len) 133 { 134 int i; 135 opus_val32 maxval = 0; 136 for (i=0;i<len;i++) 137 maxval = MAX32(maxval, ABS32(x[i])); 138 return maxval; 139 } 140 #endif 141 142 /** Integer log in base2. Defined for zero, but not for negative numbers */ 143 static inline opus_int16 celt_zlog2(opus_val32 x) 144 { 145 return x <= 0 ? 0 : celt_ilog2(x); 146 } 147 148 opus_val16 celt_rsqrt_norm(opus_val32 x); 149 150 opus_val32 celt_sqrt(opus_val32 x); 151 152 opus_val16 celt_cos_norm(opus_val32 x); 153 154 static inline opus_val16 celt_log2(opus_val32 x) 155 { 156 int i; 157 opus_val16 n, frac; 158 /* -0.41509302963303146, 0.9609890551383969, -0.31836011537636605, 159 0.15530808010959576, -0.08556153059057618 */ 160 static const opus_val16 C[5] = {-6801+(1<<(13-DB_SHIFT)), 15746, -5217, 2545, -1401}; 161 if (x==0) 162 return -32767; 163 i = celt_ilog2(x); 164 n = VSHR32(x,i-15)-32768-16384; 165 frac = ADD16(C[0], MULT16_16_Q15(n, ADD16(C[1], MULT16_16_Q15(n, ADD16(C[2], MULT16_16_Q15(n, ADD16(C[3], MULT16_16_Q15(n, C[4])))))))); 166 return SHL16(i-13,DB_SHIFT)+SHR16(frac,14-DB_SHIFT); 167 } 168 169 /* 170 K0 = 1 171 K1 = log(2) 172 K2 = 3-4*log(2) 173 K3 = 3*log(2) - 2 174 */ 175 #define D0 16383 176 #define D1 22804 177 #define D2 14819 178 #define D3 10204 179 /** Base-2 exponential approximation (2^x). (Q10 input, Q16 output) */ 180 static inline opus_val32 celt_exp2(opus_val16 x) 181 { 182 int integer; 183 opus_val16 frac; 184 integer = SHR16(x,10); 185 if (integer>14) 186 return 0x7f000000; 187 else if (integer < -15) 188 return 0; 189 frac = SHL16(x-SHL16(integer,10),4); 190 frac = ADD16(D0, MULT16_16_Q15(frac, ADD16(D1, MULT16_16_Q15(frac, ADD16(D2 , MULT16_16_Q15(D3,frac)))))); 191 return VSHR32(EXTEND32(frac), -integer-2); 192 } 193 194 opus_val32 celt_rcp(opus_val32 x); 195 196 #define celt_div(a,b) MULT32_32_Q31((opus_val32)(a),celt_rcp(b)) 197 198 opus_val32 frac_div32(opus_val32 a, opus_val32 b); 199 200 #define M1 32767 201 #define M2 -21 202 #define M3 -11943 203 #define M4 4936 204 205 /* Atan approximation using a 4th order polynomial. Input is in Q15 format 206 and normalized by pi/4. Output is in Q15 format */ 207 static inline opus_val16 celt_atan01(opus_val16 x) 208 { 209 return MULT16_16_P15(x, ADD32(M1, MULT16_16_P15(x, ADD32(M2, MULT16_16_P15(x, ADD32(M3, MULT16_16_P15(M4, x))))))); 210 } 211 212 #undef M1 213 #undef M2 214 #undef M3 215 #undef M4 216 217 /* atan2() approximation valid for positive input values */ 218 static inline opus_val16 celt_atan2p(opus_val16 y, opus_val16 x) 219 { 220 if (y < x) 221 { 222 opus_val32 arg; 223 arg = celt_div(SHL32(EXTEND32(y),15),x); 224 if (arg >= 32767) 225 arg = 32767; 226 return SHR16(celt_atan01(EXTRACT16(arg)),1); 227 } else { 228 opus_val32 arg; 229 arg = celt_div(SHL32(EXTEND32(x),15),y); 230 if (arg >= 32767) 231 arg = 32767; 232 return 25736-SHR16(celt_atan01(EXTRACT16(arg)),1); 233 } 234 } 235 236 #endif /* FIXED_POINT */ 237 #endif /* MATHOPS_H */ 238
