media/libopus/celt/mathops.c

   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 #ifdef HAVE_CONFIG_H
  35 #include "config.h"
  36 #endif
  37
  38 #include "mathops.h"
  39
  40 /*Compute floor(sqrt(_val)) with exact arithmetic.
  41   _val must be greater than 0.
  42   This has been tested on all possible 32-bit inputs greater than 0.*/
  43 unsigned isqrt32(opus_uint32 _val){
  44   unsigned b;
  45   unsigned g;
  46   int      bshift;
  47   /*Uses the second method from
  48      http://www.azillionmonkeys.com/qed/sqroot.html
  49     The main idea is to search for the largest binary digit b such that
  50      (g+b)*(g+b) <= _val, and add it to the solution g.*/
  51   g=0;
  52   bshift=(EC_ILOG(_val)-1)>>1;
  53   b=1U<<bshift;
  54   do{
  55     opus_uint32 t;
  56     t=(((opus_uint32)g<<1)+b)<<bshift;
  57     if(t<=_val){
  58       g+=b;
  59       _val-=t;
  60     }
  61     b>>=1;
  62     bshift--;
  63   }
  64   while(bshift>=0);
  65   return g;
  66 }
  67
  68 #ifdef FIXED_POINT
  69
  70 opus_val32 frac_div32(opus_val32 a, opus_val32 b)
  71 {
  72    opus_val16 rcp;
  73    opus_val32 result, rem;
  74    int shift = celt_ilog2(b)-29;
  75    a = VSHR32(a,shift);
  76    b = VSHR32(b,shift);
  77    /* 16-bit reciprocal */
  78    rcp = ROUND16(celt_rcp(ROUND16(b,16)),3);
  79    result = MULT16_32_Q15(rcp, a);
  80    rem = PSHR32(a,2)-MULT32_32_Q31(result, b);
  81    result = ADD32(result, SHL32(MULT16_32_Q15(rcp, rem),2));
  82    if (result >= 536870912)       /*  2^29 */
  83       return 2147483647;          /*  2^31 - 1 */
  84    else if (result <= -536870912) /* -2^29 */
  85       return -2147483647;         /* -2^31 */
  86    else
  87       return SHL32(result, 2);
  88 }
  89
  90 /** Reciprocal sqrt approximation in the range [0.25,1) (Q16 in, Q14 out) */
  91 opus_val16 celt_rsqrt_norm(opus_val32 x)
  92 {
  93    opus_val16 n;
  94    opus_val16 r;
  95    opus_val16 r2;
  96    opus_val16 y;
  97    /* Range of n is [-16384,32767] ([-0.5,1) in Q15). */
  98    n = x-32768;
  99    /* Get a rough initial guess for the root.
 100       The optimal minimax quadratic approximation (using relative error) is
 101        r = 1.437799046117536+n*(-0.823394375837328+n*0.4096419668459485).
 102       Coefficients here, and the final result r, are Q14.*/
 103    r = ADD16(23557, MULT16_16_Q15(n, ADD16(-13490, MULT16_16_Q15(n, 6713))));
 104    /* We want y = x*r*r-1 in Q15, but x is 32-bit Q16 and r is Q14.
 105       We can compute the result from n and r using Q15 multiplies with some
 106        adjustment, carefully done to avoid overflow.
 107       Range of y is [-1564,1594]. */
 108    r2 = MULT16_16_Q15(r, r);
 109    y = SHL16(SUB16(ADD16(MULT16_16_Q15(r2, n), r2), 16384), 1);
 110    /* Apply a 2nd-order Householder iteration: r += r*y*(y*0.375-0.5).
 111       This yields the Q14 reciprocal square root of the Q16 x, with a maximum
 112        relative error of 1.04956E-4, a (relative) RMSE of 2.80979E-5, and a
 113        peak absolute error of 2.26591/16384. */
 114    return ADD16(r, MULT16_16_Q15(r, MULT16_16_Q15(y,
 115               SUB16(MULT16_16_Q15(y, 12288), 16384))));
 116 }
 117
 118 /** Sqrt approximation (QX input, QX/2 output) */
 119 opus_val32 celt_sqrt(opus_val32 x)
 120 {
 121    int k;
 122    opus_val16 n;
 123    opus_val32 rt;
 124    static const opus_val16 C[5] = {23175, 11561, -3011, 1699, -664};
 125    if (x==0)
 126       return 0;
 127    else if (x>=1073741824)
 128       return 32767;
 129    k = (celt_ilog2(x)>>1)-7;
 130    x = VSHR32(x, 2*k);
 131    n = x-32768;
 132    rt = ADD16(C[0], MULT16_16_Q15(n, ADD16(C[1], MULT16_16_Q15(n, ADD16(C[2],
 133               MULT16_16_Q15(n, ADD16(C[3], MULT16_16_Q15(n, (C[4])))))))));
 134    rt = VSHR32(rt,7-k);
 135    return rt;
 136 }
 137
 138 #define L1 32767
 139 #define L2 -7651
 140 #define L3 8277
 141 #define L4 -626
 142
 143 static OPUS_INLINE opus_val16 _celt_cos_pi_2(opus_val16 x)
 144 {
 145    opus_val16 x2;
 146
 147    x2 = MULT16_16_P15(x,x);
 148    return ADD16(1,MIN16(32766,ADD32(SUB16(L1,x2), MULT16_16_P15(x2, ADD32(L2, MULT16_16_P15(x2, ADD32(L3, MULT16_16_P15(L4, x2
 149                                                                                 ))))))));
 150 }
 151
 152 #undef L1
 153 #undef L2
 154 #undef L3
 155 #undef L4
 156
 157 opus_val16 celt_cos_norm(opus_val32 x)
 158 {
 159    x = x&0x0001ffff;
 160    if (x>SHL32(EXTEND32(1), 16))
 161       x = SUB32(SHL32(EXTEND32(1), 17),x);
 162    if (x&0x00007fff)
 163    {
 164       if (x<SHL32(EXTEND32(1), 15))
 165       {
 166          return _celt_cos_pi_2(EXTRACT16(x));
 167       } else {
 168          return NEG16(_celt_cos_pi_2(EXTRACT16(65536-x)));
 169       }
 170    } else {
 171       if (x&0x0000ffff)
 172          return 0;
 173       else if (x&0x0001ffff)
 174          return -32767;
 175       else
 176          return 32767;
 177    }
 178 }
 179
 180 /** Reciprocal approximation (Q15 input, Q16 output) */
 181 opus_val32 celt_rcp(opus_val32 x)
 182 {
 183    int i;
 184    opus_val16 n;
 185    opus_val16 r;
 186    celt_sig_assert(x>0);
 187    i = celt_ilog2(x);
 188    /* n is Q15 with range [0,1). */
 189    n = VSHR32(x,i-15)-32768;
 190    /* Start with a linear approximation:
 191       r = 1.8823529411764706-0.9411764705882353*n.
 192       The coefficients and the result are Q14 in the range [15420,30840].*/
 193    r = ADD16(30840, MULT16_16_Q15(-15420, n));
 194    /* Perform two Newton iterations:
 195       r -= r*((r*n)-1.Q15)
 196          = r*((r*n)+(r-1.Q15)). */
 197    r = SUB16(r, MULT16_16_Q15(r,
 198              ADD16(MULT16_16_Q15(r, n), ADD16(r, -32768))));
 199    /* We subtract an extra 1 in the second iteration to avoid overflow; it also
 200        neatly compensates for truncation error in the rest of the process. */
 201    r = SUB16(r, ADD16(1, MULT16_16_Q15(r,
 202              ADD16(MULT16_16_Q15(r, n), ADD16(r, -32768)))));
 203    /* r is now the Q15 solution to 2/(n+1), with a maximum relative error
 204        of 7.05346E-5, a (relative) RMSE of 2.14418E-5, and a peak absolute
 205        error of 1.24665/32768. */
 206    return VSHR32(EXTEND32(r),i-16);
 207 }
 208
 209 #endif