OLD | NEW |
(Empty) | |
| 1 /* Copyright (C) 2002 Jean-Marc Valin */ |
| 2 /** |
| 3 @file math_approx.h |
| 4 @brief Various math approximation functions for Speex |
| 5 */ |
| 6 /* |
| 7 Redistribution and use in source and binary forms, with or without |
| 8 modification, are permitted provided that the following conditions |
| 9 are met: |
| 10 |
| 11 - Redistributions of source code must retain the above copyright |
| 12 notice, this list of conditions and the following disclaimer. |
| 13 |
| 14 - Redistributions in binary form must reproduce the above copyright |
| 15 notice, this list of conditions and the following disclaimer in the |
| 16 documentation and/or other materials provided with the distribution. |
| 17 |
| 18 - Neither the name of the Xiph.org Foundation nor the names of its |
| 19 contributors may be used to endorse or promote products derived from |
| 20 this software without specific prior written permission. |
| 21 |
| 22 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| 23 ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| 24 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| 25 A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR |
| 26 CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
| 27 EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
| 28 PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
| 29 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF |
| 30 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING |
| 31 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| 32 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| 33 */ |
| 34 |
| 35 #ifndef MATH_APPROX_H |
| 36 #define MATH_APPROX_H |
| 37 |
| 38 #include "arch.h" |
| 39 |
| 40 #ifndef FIXED_POINT |
| 41 |
| 42 #define spx_sqrt sqrt |
| 43 #define spx_acos acos |
| 44 #define spx_exp exp |
| 45 #define spx_cos_norm(x) (cos((.5f*M_PI)*(x))) |
| 46 #define spx_atan atan |
| 47 |
| 48 /** Generate a pseudo-random number */ |
| 49 static inline spx_word16_t speex_rand(spx_word16_t std, spx_int32_t *seed) |
| 50 { |
| 51 const unsigned int jflone = 0x3f800000; |
| 52 const unsigned int jflmsk = 0x007fffff; |
| 53 union {int i; float f;} ran; |
| 54 *seed = 1664525 * *seed + 1013904223; |
| 55 ran.i = jflone | (jflmsk & *seed); |
| 56 ran.f -= 1.5; |
| 57 return 3.4642*std*ran.f; |
| 58 } |
| 59 |
| 60 |
| 61 #endif |
| 62 |
| 63 |
| 64 static inline spx_int16_t spx_ilog2(spx_uint32_t x) |
| 65 { |
| 66 int r=0; |
| 67 if (x>=(spx_int32_t)65536) |
| 68 { |
| 69 x >>= 16; |
| 70 r += 16; |
| 71 } |
| 72 if (x>=256) |
| 73 { |
| 74 x >>= 8; |
| 75 r += 8; |
| 76 } |
| 77 if (x>=16) |
| 78 { |
| 79 x >>= 4; |
| 80 r += 4; |
| 81 } |
| 82 if (x>=4) |
| 83 { |
| 84 x >>= 2; |
| 85 r += 2; |
| 86 } |
| 87 if (x>=2) |
| 88 { |
| 89 r += 1; |
| 90 } |
| 91 return r; |
| 92 } |
| 93 |
| 94 static inline spx_int16_t spx_ilog4(spx_uint32_t x) |
| 95 { |
| 96 int r=0; |
| 97 if (x>=(spx_int32_t)65536) |
| 98 { |
| 99 x >>= 16; |
| 100 r += 8; |
| 101 } |
| 102 if (x>=256) |
| 103 { |
| 104 x >>= 8; |
| 105 r += 4; |
| 106 } |
| 107 if (x>=16) |
| 108 { |
| 109 x >>= 4; |
| 110 r += 2; |
| 111 } |
| 112 if (x>=4) |
| 113 { |
| 114 r += 1; |
| 115 } |
| 116 return r; |
| 117 } |
| 118 |
| 119 #ifdef FIXED_POINT |
| 120 |
| 121 /** Generate a pseudo-random number */ |
| 122 static inline spx_word16_t speex_rand(spx_word16_t std, spx_int32_t *seed) |
| 123 { |
| 124 spx_word32_t res; |
| 125 *seed = 1664525 * *seed + 1013904223; |
| 126 res = MULT16_16(EXTRACT16(SHR32(*seed,16)),std); |
| 127 return EXTRACT16(PSHR32(SUB32(res, SHR32(res, 3)),14)); |
| 128 } |
| 129 |
| 130 /* sqrt(x) ~= 0.22178 + 1.29227*x - 0.77070*x^2 + 0.25723*x^3 (for .25 < x < 1)
*/ |
| 131 /*#define C0 3634 |
| 132 #define C1 21173 |
| 133 #define C2 -12627 |
| 134 #define C3 4215*/ |
| 135 |
| 136 /* sqrt(x) ~= 0.22178 + 1.29227*x - 0.77070*x^2 + 0.25659*x^3 (for .25 < x < 1)
*/ |
| 137 #define C0 3634 |
| 138 #define C1 21173 |
| 139 #define C2 -12627 |
| 140 #define C3 4204 |
| 141 |
| 142 static inline spx_word16_t spx_sqrt(spx_word32_t x) |
| 143 { |
| 144 int k; |
| 145 spx_word32_t rt; |
| 146 k = spx_ilog4(x)-6; |
| 147 x = VSHR32(x, (k<<1)); |
| 148 rt = ADD16(C0, MULT16_16_Q14(x, ADD16(C1, MULT16_16_Q14(x, ADD16(C2, MULT16_1
6_Q14(x, (C3))))))); |
| 149 rt = VSHR32(rt,7-k); |
| 150 return rt; |
| 151 } |
| 152 |
| 153 /* log(x) ~= -2.18151 + 4.20592*x - 2.88938*x^2 + 0.86535*x^3 (for .5 < x < 1) *
/ |
| 154 |
| 155 |
| 156 #define A1 16469 |
| 157 #define A2 2242 |
| 158 #define A3 1486 |
| 159 |
| 160 static inline spx_word16_t spx_acos(spx_word16_t x) |
| 161 { |
| 162 int s=0; |
| 163 spx_word16_t ret; |
| 164 spx_word16_t sq; |
| 165 if (x<0) |
| 166 { |
| 167 s=1; |
| 168 x = NEG16(x); |
| 169 } |
| 170 x = SUB16(16384,x); |
| 171 |
| 172 x = x >> 1; |
| 173 sq = MULT16_16_Q13(x, ADD16(A1, MULT16_16_Q13(x, ADD16(A2, MULT16_16_Q13(x, (
A3)))))); |
| 174 ret = spx_sqrt(SHL32(EXTEND32(sq),13)); |
| 175 |
| 176 /*ret = spx_sqrt(67108864*(-1.6129e-04 + 2.0104e+00*f + 2.7373e-01*f*f + 1.81
36e-01*f*f*f));*/ |
| 177 if (s) |
| 178 ret = SUB16(25736,ret); |
| 179 return ret; |
| 180 } |
| 181 |
| 182 |
| 183 #define K1 8192 |
| 184 #define K2 -4096 |
| 185 #define K3 340 |
| 186 #define K4 -10 |
| 187 |
| 188 static inline spx_word16_t spx_cos(spx_word16_t x) |
| 189 { |
| 190 spx_word16_t x2; |
| 191 |
| 192 if (x<12868) |
| 193 { |
| 194 x2 = MULT16_16_P13(x,x); |
| 195 return ADD32(K1, MULT16_16_P13(x2, ADD32(K2, MULT16_16_P13(x2, ADD32(K3, M
ULT16_16_P13(K4, x2)))))); |
| 196 } else { |
| 197 x = SUB16(25736,x); |
| 198 x2 = MULT16_16_P13(x,x); |
| 199 return SUB32(-K1, MULT16_16_P13(x2, ADD32(K2, MULT16_16_P13(x2, ADD32(K3,
MULT16_16_P13(K4, x2)))))); |
| 200 } |
| 201 } |
| 202 |
| 203 #define L1 32767 |
| 204 #define L2 -7651 |
| 205 #define L3 8277 |
| 206 #define L4 -626 |
| 207 |
| 208 static inline spx_word16_t _spx_cos_pi_2(spx_word16_t x) |
| 209 { |
| 210 spx_word16_t x2; |
| 211 |
| 212 x2 = MULT16_16_P15(x,x); |
| 213 return ADD16(1,MIN16(32766,ADD32(SUB16(L1,x2), MULT16_16_P15(x2, ADD32(L2, MU
LT16_16_P15(x2, ADD32(L3, MULT16_16_P15(L4, x2)))))))); |
| 214 } |
| 215 |
| 216 static inline spx_word16_t spx_cos_norm(spx_word32_t x) |
| 217 { |
| 218 x = x&0x0001ffff; |
| 219 if (x>SHL32(EXTEND32(1), 16)) |
| 220 x = SUB32(SHL32(EXTEND32(1), 17),x); |
| 221 if (x&0x00007fff) |
| 222 { |
| 223 if (x<SHL32(EXTEND32(1), 15)) |
| 224 { |
| 225 return _spx_cos_pi_2(EXTRACT16(x)); |
| 226 } else { |
| 227 return NEG32(_spx_cos_pi_2(EXTRACT16(65536-x))); |
| 228 } |
| 229 } else { |
| 230 if (x&0x0000ffff) |
| 231 return 0; |
| 232 else if (x&0x0001ffff) |
| 233 return -32767; |
| 234 else |
| 235 return 32767; |
| 236 } |
| 237 } |
| 238 |
| 239 /* |
| 240 K0 = 1 |
| 241 K1 = log(2) |
| 242 K2 = 3-4*log(2) |
| 243 K3 = 3*log(2) - 2 |
| 244 */ |
| 245 #define D0 16384 |
| 246 #define D1 11356 |
| 247 #define D2 3726 |
| 248 #define D3 1301 |
| 249 /* Input in Q11 format, output in Q16 */ |
| 250 static inline spx_word32_t spx_exp2(spx_word16_t x) |
| 251 { |
| 252 int integer; |
| 253 spx_word16_t frac; |
| 254 integer = SHR16(x,11); |
| 255 if (integer>14) |
| 256 return 0x7fffffff; |
| 257 else if (integer < -15) |
| 258 return 0; |
| 259 frac = SHL16(x-SHL16(integer,11),3); |
| 260 frac = ADD16(D0, MULT16_16_Q14(frac, ADD16(D1, MULT16_16_Q14(frac, ADD16(D2 ,
MULT16_16_Q14(D3,frac)))))); |
| 261 return VSHR32(EXTEND32(frac), -integer-2); |
| 262 } |
| 263 |
| 264 /* Input in Q11 format, output in Q16 */ |
| 265 static inline spx_word32_t spx_exp(spx_word16_t x) |
| 266 { |
| 267 if (x>21290) |
| 268 return 0x7fffffff; |
| 269 else if (x<-21290) |
| 270 return 0; |
| 271 else |
| 272 return spx_exp2(MULT16_16_P14(23637,x)); |
| 273 } |
| 274 #define M1 32767 |
| 275 #define M2 -21 |
| 276 #define M3 -11943 |
| 277 #define M4 4936 |
| 278 |
| 279 static inline spx_word16_t spx_atan01(spx_word16_t x) |
| 280 { |
| 281 return MULT16_16_P15(x, ADD32(M1, MULT16_16_P15(x, ADD32(M2, MULT16_16_P15(x,
ADD32(M3, MULT16_16_P15(M4, x))))))); |
| 282 } |
| 283 |
| 284 #undef M1 |
| 285 #undef M2 |
| 286 #undef M3 |
| 287 #undef M4 |
| 288 |
| 289 /* Input in Q15, output in Q14 */ |
| 290 static inline spx_word16_t spx_atan(spx_word32_t x) |
| 291 { |
| 292 if (x <= 32767) |
| 293 { |
| 294 return SHR16(spx_atan01(x),1); |
| 295 } else { |
| 296 int e = spx_ilog2(x); |
| 297 if (e>=29) |
| 298 return 25736; |
| 299 x = DIV32_16(SHL32(EXTEND32(32767),29-e), EXTRACT16(SHR32(x, e-14))); |
| 300 return SUB16(25736, SHR16(spx_atan01(x),1)); |
| 301 } |
| 302 } |
| 303 #else |
| 304 |
| 305 #ifndef M_PI |
| 306 #define M_PI 3.14159265358979323846 /* pi */ |
| 307 #endif |
| 308 |
| 309 #define C1 0.9999932946f |
| 310 #define C2 -0.4999124376f |
| 311 #define C3 0.0414877472f |
| 312 #define C4 -0.0012712095f |
| 313 |
| 314 |
| 315 #define SPX_PI_2 1.5707963268 |
| 316 static inline spx_word16_t spx_cos(spx_word16_t x) |
| 317 { |
| 318 if (x<SPX_PI_2) |
| 319 { |
| 320 x *= x; |
| 321 return C1 + x*(C2+x*(C3+C4*x)); |
| 322 } else { |
| 323 x = M_PI-x; |
| 324 x *= x; |
| 325 return NEG16(C1 + x*(C2+x*(C3+C4*x))); |
| 326 } |
| 327 } |
| 328 |
| 329 #endif |
| 330 |
| 331 |
| 332 #endif |
OLD | NEW |