media/libopus/celt/mathops.h

   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 #define PI 3.141592653f
  42
  43 /* Multiplies two 16-bit fractional values. Bit-exactness of this macro is important */
  44 #define FRAC_MUL16(a,b) ((16384+((opus_int32)(opus_int16)(a)*(opus_int16)(b)))>>15)
  45
  46 unsigned isqrt32(opus_uint32 _val);
  47
  48 /* CELT doesn't need it for fixed-point, by analysis.c does. */
  49 #if !defined(FIXED_POINT) || defined(ANALYSIS_C)
  50 #define cA 0.43157974f
  51 #define cB 0.67848403f
  52 #define cC 0.08595542f
  53 #define cE ((float)PI/2)
  54 static OPUS_INLINE float fast_atan2f(float y, float x) {
  55    float x2, y2;
  56    x2 = x*x;
  57    y2 = y*y;
  58    /* For very small values, we don't care about the answer, so
  59       we can just return 0. */
  60    if (x2 + y2 < 1e-18f)
  61    {
  62       return 0;
  63    }
  64    if(x2<y2){
  65       float den = (y2 + cB*x2) * (y2 + cC*x2);
  66       return -x*y*(y2 + cA*x2) / den + (y<0 ? -cE : cE);
  67    }else{
  68       float den = (x2 + cB*y2) * (x2 + cC*y2);
  69       return  x*y*(x2 + cA*y2) / den + (y<0 ? -cE : cE) - (x*y<0 ? -cE : cE);
  70    }
  71 }
  72 #undef cA
  73 #undef cB
  74 #undef cC
  75 #undef cE
  76 #endif
  77
  78
  79 #ifndef OVERRIDE_CELT_MAXABS16
  80 static OPUS_INLINE opus_val32 celt_maxabs16(const opus_val16 *x, int len)
  81 {
  82    int i;
  83    opus_val16 maxval = 0;
  84    opus_val16 minval = 0;
  85    for (i=0;i<len;i++)
  86    {
  87       maxval = MAX16(maxval, x[i]);
  88       minval = MIN16(minval, x[i]);
  89    }
  90    return MAX32(EXTEND32(maxval),-EXTEND32(minval));
  91 }
  92 #endif
  93
  94 #ifndef OVERRIDE_CELT_MAXABS32
  95 #ifdef FIXED_POINT
  96 static OPUS_INLINE opus_val32 celt_maxabs32(const opus_val32 *x, int len)
  97 {
  98    int i;
  99    opus_val32 maxval = 0;
 100    opus_val32 minval = 0;
 101    for (i=0;i<len;i++)
 102    {
 103       maxval = MAX32(maxval, x[i]);
 104       minval = MIN32(minval, x[i]);
 105    }
 106    return MAX32(maxval, -minval);
 107 }
 108 #else
 109 #define celt_maxabs32(x,len) celt_maxabs16(x,len)
 110 #endif
 111 #endif
 112
 113
 114 #ifndef FIXED_POINT
 115
 116 #define celt_sqrt(x) ((float)sqrt(x))
 117 #define celt_rsqrt(x) (1.f/celt_sqrt(x))
 118 #define celt_rsqrt_norm(x) (celt_rsqrt(x))
 119 #define celt_cos_norm(x) ((float)cos((.5f*PI)*(x)))
 120 #define celt_rcp(x) (1.f/(x))
 121 #define celt_div(a,b) ((a)/(b))
 122 #define frac_div32(a,b) ((float)(a)/(b))
 123
 124 #ifdef FLOAT_APPROX
 125
 126 /* Note: This assumes radix-2 floating point with the exponent at bits 23..30 and an offset of 127
 127          denorm, +/- inf and NaN are *not* handled */
 128
 129 /** Base-2 log approximation (log2(x)). */
 130 static OPUS_INLINE float celt_log2(float x)
 131 {
 132    int integer;
 133    float frac;
 134    union {
 135       float f;
 136       opus_uint32 i;
 137    } in;
 138    in.f = x;
 139    integer = (in.i>>23)-127;
 140    in.i -= (opus_uint32)integer<<23;
 141    frac = in.f - 1.5f;
 142    frac = -0.41445418f + frac*(0.95909232f
 143           + frac*(-0.33951290f + frac*0.16541097f));
 144    return 1+integer+frac;
 145 }
 146
 147 /** Base-2 exponential approximation (2^x). */
 148 static OPUS_INLINE float celt_exp2(float x)
 149 {
 150    int integer;
 151    float frac;
 152    union {
 153       float f;
 154       opus_uint32 i;
 155    } res;
 156    integer = (int)floor(x);
 157    if (integer < -50)
 158       return 0;
 159    frac = x-integer;
 160    /* K0 = 1, K1 = log(2), K2 = 3-4*log(2), K3 = 3*log(2) - 2 */
 161    res.f = 0.99992522f + frac * (0.69583354f
 162            + frac * (0.22606716f + 0.078024523f*frac));
 163    res.i = (res.i + ((opus_uint32)integer<<23)) & 0x7fffffff;
 164    return res.f;
 165 }
 166
 167 #else
 168 #define celt_log2(x) ((float)(1.442695040888963387*log(x)))
 169 #define celt_exp2(x) ((float)exp(0.6931471805599453094*(x)))
 170 #endif
 171
 172 #endif
 173
 174 #ifdef FIXED_POINT
 175
 176 #include "os_support.h"
 177
 178 #ifndef OVERRIDE_CELT_ILOG2
 179 /** Integer log in base2. Undefined for zero and negative numbers */
 180 static OPUS_INLINE opus_int16 celt_ilog2(opus_int32 x)
 181 {
 182    celt_sig_assert(x>0);
 183    return EC_ILOG(x)-1;
 184 }
 185 #endif
 186
 187
 188 /** Integer log in base2. Defined for zero, but not for negative numbers */
 189 static OPUS_INLINE opus_int16 celt_zlog2(opus_val32 x)
 190 {
 191    return x <= 0 ? 0 : celt_ilog2(x);
 192 }
 193
 194 opus_val16 celt_rsqrt_norm(opus_val32 x);
 195
 196 opus_val32 celt_sqrt(opus_val32 x);
 197
 198 opus_val16 celt_cos_norm(opus_val32 x);
 199
 200 /** Base-2 logarithm approximation (log2(x)). (Q14 input, Q10 output) */
 201 static OPUS_INLINE opus_val16 celt_log2(opus_val32 x)
 202 {
 203    int i;
 204    opus_val16 n, frac;
 205    /* -0.41509302963303146, 0.9609890551383969, -0.31836011537636605,
 206        0.15530808010959576, -0.08556153059057618 */
 207    static const opus_val16 C[5] = {-6801+(1<<(13-DB_SHIFT)), 15746, -5217, 2545, -1401};
 208    if (x==0)
 209       return -32767;
 210    i = celt_ilog2(x);
 211    n = VSHR32(x,i-15)-32768-16384;
 212    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]))))))));
 213    return SHL16(i-13,DB_SHIFT)+SHR16(frac,14-DB_SHIFT);
 214 }
 215
 216 /*
 217  K0 = 1
 218  K1 = log(2)
 219  K2 = 3-4*log(2)
 220  K3 = 3*log(2) - 2
 221 */
 222 #define D0 16383
 223 #define D1 22804
 224 #define D2 14819
 225 #define D3 10204
 226
 227 static OPUS_INLINE opus_val32 celt_exp2_frac(opus_val16 x)
 228 {
 229    opus_val16 frac;
 230    frac = SHL16(x, 4);
 231    return ADD16(D0, MULT16_16_Q15(frac, ADD16(D1, MULT16_16_Q15(frac, ADD16(D2 , MULT16_16_Q15(D3,frac))))));
 232 }
 233 /** Base-2 exponential approximation (2^x). (Q10 input, Q16 output) */
 234 static OPUS_INLINE opus_val32 celt_exp2(opus_val16 x)
 235 {
 236    int integer;
 237    opus_val16 frac;
 238    integer = SHR16(x,10);
 239    if (integer>14)
 240       return 0x7f000000;
 241    else if (integer < -15)
 242       return 0;
 243    frac = celt_exp2_frac(x-SHL16(integer,10));
 244    return VSHR32(EXTEND32(frac), -integer-2);
 245 }
 246
 247 opus_val32 celt_rcp(opus_val32 x);
 248
 249 #define celt_div(a,b) MULT32_32_Q31((opus_val32)(a),celt_rcp(b))
 250
 251 opus_val32 frac_div32(opus_val32 a, opus_val32 b);
 252
 253 #define M1 32767
 254 #define M2 -21
 255 #define M3 -11943
 256 #define M4 4936
 257
 258 /* Atan approximation using a 4th order polynomial. Input is in Q15 format
 259    and normalized by pi/4. Output is in Q15 format */
 260 static OPUS_INLINE opus_val16 celt_atan01(opus_val16 x)
 261 {
 262    return MULT16_16_P15(x, ADD32(M1, MULT16_16_P15(x, ADD32(M2, MULT16_16_P15(x, ADD32(M3, MULT16_16_P15(M4, x)))))));
 263 }
 264
 265 #undef M1
 266 #undef M2
 267 #undef M3
 268 #undef M4
 269
 270 /* atan2() approximation valid for positive input values */
 271 static OPUS_INLINE opus_val16 celt_atan2p(opus_val16 y, opus_val16 x)
 272 {
 273    if (y < x)
 274    {
 275       opus_val32 arg;
 276       arg = celt_div(SHL32(EXTEND32(y),15),x);
 277       if (arg >= 32767)
 278          arg = 32767;
 279       return SHR16(celt_atan01(EXTRACT16(arg)),1);
 280    } else {
 281       opus_val32 arg;
 282       arg = celt_div(SHL32(EXTEND32(x),15),y);
 283       if (arg >= 32767)
 284          arg = 32767;
 285       return 25736-SHR16(celt_atan01(EXTRACT16(arg)),1);
 286    }
 287 }
 288
 289 #endif /* FIXED_POINT */
 290 #endif /* MATHOPS_H */