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 /* 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 OVERRIDE_CELT_MAXABS16
  47 static OPUS_INLINE opus_val32 celt_maxabs16(const opus_val16 *x, int len)
  48 {
  49    int i;
  50    opus_val16 maxval = 0;
  51    opus_val16 minval = 0;
  52    for (i=0;i<len;i++)
  53    {
  54       maxval = MAX16(maxval, x[i]);
  55       minval = MIN16(minval, x[i]);
  56    }
  57    return MAX32(EXTEND32(maxval),-EXTEND32(minval));
  58 }
  59 #endif
  60
  61 #ifndef OVERRIDE_CELT_MAXABS32
  62 #ifdef FIXED_POINT
  63 static OPUS_INLINE opus_val32 celt_maxabs32(const opus_val32 *x, int len)
  64 {
  65    int i;
  66    opus_val32 maxval = 0;
  67    opus_val32 minval = 0;
  68    for (i=0;i<len;i++)
  69    {
  70       maxval = MAX32(maxval, x[i]);
  71       minval = MIN32(minval, x[i]);
  72    }
  73    return MAX32(maxval, -minval);
  74 }
  75 #else
  76 #define celt_maxabs32(x,len) celt_maxabs16(x,len)
  77 #endif
  78 #endif
  79
  80
  81 #ifndef FIXED_POINT
  82
  83 #define PI 3.141592653f
  84 #define celt_sqrt(x) ((float)sqrt(x))
  85 #define celt_rsqrt(x) (1.f/celt_sqrt(x))
  86 #define celt_rsqrt_norm(x) (celt_rsqrt(x))
  87 #define celt_cos_norm(x) ((float)cos((.5f*PI)*(x)))
  88 #define celt_rcp(x) (1.f/(x))
  89 #define celt_div(a,b) ((a)/(b))
  90 #define frac_div32(a,b) ((float)(a)/(b))
  91
  92 #ifdef FLOAT_APPROX
  93
  94 /* Note: This assumes radix-2 floating point with the exponent at bits 23..30 and an offset of 127
  95          denorm, +/- inf and NaN are *not* handled */
  96
  97 /** Base-2 log approximation (log2(x)). */
  98 static OPUS_INLINE float celt_log2(float x)
  99 {
 100    int integer;
 101    float frac;
 102    union {
 103       float f;
 104       opus_uint32 i;
 105    } in;
 106    in.f = x;
 107    integer = (in.i>>23)-127;
 108    in.i -= integer<<23;
 109    frac = in.f - 1.5f;
 110    frac = -0.41445418f + frac*(0.95909232f
 111           + frac*(-0.33951290f + frac*0.16541097f));
 112    return 1+integer+frac;
 113 }
 114
 115 /** Base-2 exponential approximation (2^x). */
 116 static OPUS_INLINE float celt_exp2(float x)
 117 {
 118    int integer;
 119    float frac;
 120    union {
 121       float f;
 122       opus_uint32 i;
 123    } res;
 124    integer = floor(x);
 125    if (integer < -50)
 126       return 0;
 127    frac = x-integer;
 128    /* K0 = 1, K1 = log(2), K2 = 3-4*log(2), K3 = 3*log(2) - 2 */
 129    res.f = 0.99992522f + frac * (0.69583354f
 130            + frac * (0.22606716f + 0.078024523f*frac));
 131    res.i = (res.i + (integer<<23)) & 0x7fffffff;
 132    return res.f;
 133 }
 134
 135 #else
 136 #define celt_log2(x) ((float)(1.442695040888963387*log(x)))
 137 #define celt_exp2(x) ((float)exp(0.6931471805599453094*(x)))
 138 #endif
 139
 140 #endif
 141
 142 #ifdef FIXED_POINT
 143
 144 #include "os_support.h"
 145
 146 #ifndef OVERRIDE_CELT_ILOG2
 147 /** Integer log in base2. Undefined for zero and negative numbers */
 148 static OPUS_INLINE opus_int16 celt_ilog2(opus_int32 x)
 149 {
 150    celt_assert2(x>0, "celt_ilog2() only defined for strictly positive numbers");
 151    return EC_ILOG(x)-1;
 152 }
 153 #endif
 154
 155
 156 /** Integer log in base2. Defined for zero, but not for negative numbers */
 157 static OPUS_INLINE opus_int16 celt_zlog2(opus_val32 x)
 158 {
 159    return x <= 0 ? 0 : celt_ilog2(x);
 160 }
 161
 162 opus_val16 celt_rsqrt_norm(opus_val32 x);
 163
 164 opus_val32 celt_sqrt(opus_val32 x);
 165
 166 opus_val16 celt_cos_norm(opus_val32 x);
 167
 168 /** Base-2 logarithm approximation (log2(x)). (Q14 input, Q10 output) */
 169 static OPUS_INLINE opus_val16 celt_log2(opus_val32 x)
 170 {
 171    int i;
 172    opus_val16 n, frac;
 173    /* -0.41509302963303146, 0.9609890551383969, -0.31836011537636605,
 174        0.15530808010959576, -0.08556153059057618 */
 175    static const opus_val16 C[5] = {-6801+(1<<(13-DB_SHIFT)), 15746, -5217, 2545, -1401};
 176    if (x==0)
 177       return -32767;
 178    i = celt_ilog2(x);
 179    n = VSHR32(x,i-15)-32768-16384;
 180    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]))))))));
 181    return SHL16(i-13,DB_SHIFT)+SHR16(frac,14-DB_SHIFT);
 182 }
 183
 184 /*
 185  K0 = 1
 186  K1 = log(2)
 187  K2 = 3-4*log(2)
 188  K3 = 3*log(2) - 2
 189 */
 190 #define D0 16383
 191 #define D1 22804
 192 #define D2 14819
 193 #define D3 10204
 194
 195 static OPUS_INLINE opus_val32 celt_exp2_frac(opus_val16 x)
 196 {
 197    opus_val16 frac;
 198    frac = SHL16(x, 4);
 199    return ADD16(D0, MULT16_16_Q15(frac, ADD16(D1, MULT16_16_Q15(frac, ADD16(D2 , MULT16_16_Q15(D3,frac))))));
 200 }
 201 /** Base-2 exponential approximation (2^x). (Q10 input, Q16 output) */
 202 static OPUS_INLINE opus_val32 celt_exp2(opus_val16 x)
 203 {
 204    int integer;
 205    opus_val16 frac;
 206    integer = SHR16(x,10);
 207    if (integer>14)
 208       return 0x7f000000;
 209    else if (integer < -15)
 210       return 0;
 211    frac = celt_exp2_frac(x-SHL16(integer,10));
 212    return VSHR32(EXTEND32(frac), -integer-2);
 213 }
 214
 215 opus_val32 celt_rcp(opus_val32 x);
 216
 217 #define celt_div(a,b) MULT32_32_Q31((opus_val32)(a),celt_rcp(b))
 218
 219 opus_val32 frac_div32(opus_val32 a, opus_val32 b);
 220
 221 #define M1 32767
 222 #define M2 -21
 223 #define M3 -11943
 224 #define M4 4936
 225
 226 /* Atan approximation using a 4th order polynomial. Input is in Q15 format
 227    and normalized by pi/4. Output is in Q15 format */
 228 static OPUS_INLINE opus_val16 celt_atan01(opus_val16 x)
 229 {
 230    return MULT16_16_P15(x, ADD32(M1, MULT16_16_P15(x, ADD32(M2, MULT16_16_P15(x, ADD32(M3, MULT16_16_P15(M4, x)))))));
 231 }
 232
 233 #undef M1
 234 #undef M2
 235 #undef M3
 236 #undef M4
 237
 238 /* atan2() approximation valid for positive input values */
 239 static OPUS_INLINE opus_val16 celt_atan2p(opus_val16 y, opus_val16 x)
 240 {
 241    if (y < x)
 242    {
 243       opus_val32 arg;
 244       arg = celt_div(SHL32(EXTEND32(y),15),x);
 245       if (arg >= 32767)
 246          arg = 32767;
 247       return SHR16(celt_atan01(EXTRACT16(arg)),1);
 248    } else {
 249       opus_val32 arg;
 250       arg = celt_div(SHL32(EXTEND32(x),15),y);
 251       if (arg >= 32767)
 252          arg = 32767;
 253       return 25736-SHR16(celt_atan01(EXTRACT16(arg)),1);
 254    }
 255 }
 256
 257 #endif /* FIXED_POINT */
 258 #endif /* MATHOPS_H */