290 lines
7.7 KiB
C
290 lines
7.7 KiB
C
/* Copyright (c) 2002-2008 Jean-Marc Valin
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Copyright (c) 2007-2008 CSIRO
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Copyright (c) 2007-2009 Xiph.Org Foundation
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Written by Jean-Marc Valin */
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/**
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@file mathops.h
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@brief Various math functions
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*/
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/*
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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- Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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- Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
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OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#ifndef MATHOPS_H
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#define MATHOPS_H
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#include "arch.h"
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#include "entcode.h"
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#include "os_support.h"
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#define PI 3.141592653f
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/* Multiplies two 16-bit fractional values. Bit-exactness of this macro is important */
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#define FRAC_MUL16(a,b) ((16384+((opus_int32)(opus_int16)(a)*(opus_int16)(b)))>>15)
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unsigned isqrt32(opus_uint32 _val);
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/* CELT doesn't need it for fixed-point, by analysis.c does. */
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#if !defined(FIXED_POINT) || defined(ANALYSIS_C)
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#define cA 0.43157974f
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#define cB 0.67848403f
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#define cC 0.08595542f
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#define cE ((float)PI/2)
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static OPUS_INLINE float fast_atan2f(float y, float x) {
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float x2, y2;
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x2 = x*x;
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y2 = y*y;
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/* For very small values, we don't care about the answer, so
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we can just return 0. */
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if (x2 + y2 < 1e-18f)
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{
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return 0;
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}
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if(x2<y2){
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float den = (y2 + cB*x2) * (y2 + cC*x2);
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return -x*y*(y2 + cA*x2) / den + (y<0 ? -cE : cE);
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}else{
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float den = (x2 + cB*y2) * (x2 + cC*y2);
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return x*y*(x2 + cA*y2) / den + (y<0 ? -cE : cE) - (x*y<0 ? -cE : cE);
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}
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}
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#undef cA
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#undef cB
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#undef cC
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#undef cE
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#endif
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#ifndef OVERRIDE_CELT_MAXABS16
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static OPUS_INLINE opus_val32 celt_maxabs16(const opus_val16 *x, int len)
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{
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int i;
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opus_val16 maxval = 0;
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opus_val16 minval = 0;
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for (i=0;i<len;i++)
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{
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maxval = MAX16(maxval, x[i]);
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minval = MIN16(minval, x[i]);
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}
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return MAX32(EXTEND32(maxval),-EXTEND32(minval));
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}
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#endif
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#ifndef OVERRIDE_CELT_MAXABS32
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#ifdef FIXED_POINT
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static OPUS_INLINE opus_val32 celt_maxabs32(const opus_val32 *x, int len)
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{
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int i;
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opus_val32 maxval = 0;
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opus_val32 minval = 0;
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for (i=0;i<len;i++)
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{
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maxval = MAX32(maxval, x[i]);
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minval = MIN32(minval, x[i]);
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}
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return MAX32(maxval, -minval);
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}
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#else
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#define celt_maxabs32(x,len) celt_maxabs16(x,len)
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#endif
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#endif
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#ifndef FIXED_POINT
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#define celt_sqrt(x) ((float)sqrt(x))
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#define celt_rsqrt(x) (1.f/celt_sqrt(x))
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#define celt_rsqrt_norm(x) (celt_rsqrt(x))
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#define celt_cos_norm(x) ((float)cos((.5f*PI)*(x)))
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#define celt_rcp(x) (1.f/(x))
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#define celt_div(a,b) ((a)/(b))
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#define frac_div32(a,b) ((float)(a)/(b))
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#ifdef FLOAT_APPROX
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/* Note: This assumes radix-2 floating point with the exponent at bits 23..30 and an offset of 127
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denorm, +/- inf and NaN are *not* handled */
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/** Base-2 log approximation (log2(x)). */
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static OPUS_INLINE float celt_log2(float x)
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{
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int integer;
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float frac;
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union {
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float f;
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opus_uint32 i;
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} in;
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in.f = x;
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integer = (in.i>>23)-127;
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in.i -= integer<<23;
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frac = in.f - 1.5f;
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frac = -0.41445418f + frac*(0.95909232f
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+ frac*(-0.33951290f + frac*0.16541097f));
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return 1+integer+frac;
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}
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/** Base-2 exponential approximation (2^x). */
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static OPUS_INLINE float celt_exp2(float x)
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{
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int integer;
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float frac;
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union {
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float f;
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opus_uint32 i;
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} res;
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integer = floor(x);
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if (integer < -50)
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return 0;
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frac = x-integer;
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/* K0 = 1, K1 = log(2), K2 = 3-4*log(2), K3 = 3*log(2) - 2 */
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res.f = 0.99992522f + frac * (0.69583354f
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+ frac * (0.22606716f + 0.078024523f*frac));
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res.i = (res.i + (integer<<23)) & 0x7fffffff;
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return res.f;
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}
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#else
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#define celt_log2(x) ((float)(1.442695040888963387*log(x)))
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#define celt_exp2(x) ((float)exp(0.6931471805599453094*(x)))
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#endif
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#endif
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#ifdef FIXED_POINT
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#include "os_support.h"
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#ifndef OVERRIDE_CELT_ILOG2
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/** Integer log in base2. Undefined for zero and negative numbers */
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static OPUS_INLINE opus_int16 celt_ilog2(opus_int32 x)
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{
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celt_sig_assert(x>0);
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return EC_ILOG(x)-1;
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}
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#endif
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/** Integer log in base2. Defined for zero, but not for negative numbers */
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static OPUS_INLINE opus_int16 celt_zlog2(opus_val32 x)
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{
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return x <= 0 ? 0 : celt_ilog2(x);
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}
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opus_val16 celt_rsqrt_norm(opus_val32 x);
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opus_val32 celt_sqrt(opus_val32 x);
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opus_val16 celt_cos_norm(opus_val32 x);
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/** Base-2 logarithm approximation (log2(x)). (Q14 input, Q10 output) */
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static OPUS_INLINE opus_val16 celt_log2(opus_val32 x)
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{
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int i;
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opus_val16 n, frac;
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/* -0.41509302963303146, 0.9609890551383969, -0.31836011537636605,
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0.15530808010959576, -0.08556153059057618 */
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static const opus_val16 C[5] = {-6801+(1<<(13-DB_SHIFT)), 15746, -5217, 2545, -1401};
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if (x==0)
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return -32767;
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i = celt_ilog2(x);
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n = VSHR32(x,i-15)-32768-16384;
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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]))))))));
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return SHL16(i-13,DB_SHIFT)+SHR16(frac,14-DB_SHIFT);
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}
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/*
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K0 = 1
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K1 = log(2)
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K2 = 3-4*log(2)
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K3 = 3*log(2) - 2
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*/
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#define D0 16383
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#define D1 22804
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#define D2 14819
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#define D3 10204
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static OPUS_INLINE opus_val32 celt_exp2_frac(opus_val16 x)
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{
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opus_val16 frac;
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frac = SHL16(x, 4);
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return ADD16(D0, MULT16_16_Q15(frac, ADD16(D1, MULT16_16_Q15(frac, ADD16(D2 , MULT16_16_Q15(D3,frac))))));
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}
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/** Base-2 exponential approximation (2^x). (Q10 input, Q16 output) */
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static OPUS_INLINE opus_val32 celt_exp2(opus_val16 x)
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{
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int integer;
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opus_val16 frac;
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integer = SHR16(x,10);
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if (integer>14)
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return 0x7f000000;
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else if (integer < -15)
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return 0;
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frac = celt_exp2_frac(x-SHL16(integer,10));
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return VSHR32(EXTEND32(frac), -integer-2);
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}
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opus_val32 celt_rcp(opus_val32 x);
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#define celt_div(a,b) MULT32_32_Q31((opus_val32)(a),celt_rcp(b))
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opus_val32 frac_div32(opus_val32 a, opus_val32 b);
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#define M1 32767
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#define M2 -21
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#define M3 -11943
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#define M4 4936
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/* Atan approximation using a 4th order polynomial. Input is in Q15 format
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and normalized by pi/4. Output is in Q15 format */
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static OPUS_INLINE opus_val16 celt_atan01(opus_val16 x)
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{
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return MULT16_16_P15(x, ADD32(M1, MULT16_16_P15(x, ADD32(M2, MULT16_16_P15(x, ADD32(M3, MULT16_16_P15(M4, x)))))));
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}
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#undef M1
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#undef M2
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#undef M3
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#undef M4
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/* atan2() approximation valid for positive input values */
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static OPUS_INLINE opus_val16 celt_atan2p(opus_val16 y, opus_val16 x)
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{
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if (y < x)
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{
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opus_val32 arg;
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arg = celt_div(SHL32(EXTEND32(y),15),x);
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if (arg >= 32767)
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arg = 32767;
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return SHR16(celt_atan01(EXTRACT16(arg)),1);
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} else {
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opus_val32 arg;
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arg = celt_div(SHL32(EXTEND32(x),15),y);
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if (arg >= 32767)
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arg = 32767;
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return 25736-SHR16(celt_atan01(EXTRACT16(arg)),1);
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}
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}
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#endif /* FIXED_POINT */
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#endif /* MATHOPS_H */
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