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333 lines
7.4 KiB
C
333 lines
7.4 KiB
C
/* Copyright (C) 2002 Jean-Marc Valin */
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/**
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@file math_approx.h
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@brief Various math approximation functions for Speex
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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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- Neither the name of the Xiph.org Foundation nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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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 FOUNDATION OR
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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 MATH_APPROX_H
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#define MATH_APPROX_H
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#include "arch.h"
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#ifndef FIXED_POINT
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#define spx_sqrt sqrt
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#define spx_acos acos
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#define spx_exp exp
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#define spx_cos_norm(x) (cos((.5f*M_PI)*(x)))
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#define spx_atan atan
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/** Generate a pseudo-random number */
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static inline spx_word16_t speex_rand(spx_word16_t std, spx_int32_t *seed)
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{
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const unsigned int jflone = 0x3f800000;
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const unsigned int jflmsk = 0x007fffff;
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union {int i; float f;} ran;
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*seed = 1664525 * *seed + 1013904223;
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ran.i = jflone | (jflmsk & *seed);
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ran.f -= 1.5;
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return 3.4642*std*ran.f;
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}
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#endif
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static inline spx_int16_t spx_ilog2(spx_uint32_t x)
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{
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int r=0;
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if (x>=(spx_int32_t)65536)
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{
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x >>= 16;
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r += 16;
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}
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if (x>=256)
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{
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x >>= 8;
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r += 8;
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}
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if (x>=16)
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{
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x >>= 4;
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r += 4;
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}
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if (x>=4)
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{
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x >>= 2;
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r += 2;
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}
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if (x>=2)
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{
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r += 1;
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}
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return r;
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}
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static inline spx_int16_t spx_ilog4(spx_uint32_t x)
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{
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int r=0;
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if (x>=(spx_int32_t)65536)
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{
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x >>= 16;
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r += 8;
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}
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if (x>=256)
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{
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x >>= 8;
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r += 4;
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}
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if (x>=16)
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{
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x >>= 4;
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r += 2;
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}
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if (x>=4)
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{
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r += 1;
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}
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return r;
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}
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#ifdef FIXED_POINT
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/** Generate a pseudo-random number */
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static inline spx_word16_t speex_rand(spx_word16_t std, spx_int32_t *seed)
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{
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spx_word32_t res;
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*seed = 1664525 * *seed + 1013904223;
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res = MULT16_16(EXTRACT16(SHR32(*seed,16)),std);
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return EXTRACT16(PSHR32(SUB32(res, SHR32(res, 3)),14));
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}
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/* sqrt(x) ~= 0.22178 + 1.29227*x - 0.77070*x^2 + 0.25723*x^3 (for .25 < x < 1) */
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/*#define C0 3634
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#define C1 21173
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#define C2 -12627
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#define C3 4215*/
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/* sqrt(x) ~= 0.22178 + 1.29227*x - 0.77070*x^2 + 0.25659*x^3 (for .25 < x < 1) */
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#define C0 3634
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#define C1 21173
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#define C2 -12627
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#define C3 4204
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static inline spx_word16_t spx_sqrt(spx_word32_t x)
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{
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int k;
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spx_word32_t rt;
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k = spx_ilog4(x)-6;
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x = VSHR32(x, (k<<1));
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rt = ADD16(C0, MULT16_16_Q14(x, ADD16(C1, MULT16_16_Q14(x, ADD16(C2, MULT16_16_Q14(x, (C3)))))));
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rt = VSHR32(rt,7-k);
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return rt;
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}
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/* log(x) ~= -2.18151 + 4.20592*x - 2.88938*x^2 + 0.86535*x^3 (for .5 < x < 1) */
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#define A1 16469
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#define A2 2242
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#define A3 1486
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static inline spx_word16_t spx_acos(spx_word16_t x)
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{
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int s=0;
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spx_word16_t ret;
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spx_word16_t sq;
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if (x<0)
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{
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s=1;
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x = NEG16(x);
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}
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x = SUB16(16384,x);
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x = x >> 1;
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sq = MULT16_16_Q13(x, ADD16(A1, MULT16_16_Q13(x, ADD16(A2, MULT16_16_Q13(x, (A3))))));
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ret = spx_sqrt(SHL32(EXTEND32(sq),13));
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/*ret = spx_sqrt(67108864*(-1.6129e-04 + 2.0104e+00*f + 2.7373e-01*f*f + 1.8136e-01*f*f*f));*/
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if (s)
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ret = SUB16(25736,ret);
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return ret;
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}
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#define K1 8192
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#define K2 -4096
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#define K3 340
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#define K4 -10
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static inline spx_word16_t spx_cos(spx_word16_t x)
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{
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spx_word16_t x2;
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if (x<12868)
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{
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x2 = MULT16_16_P13(x,x);
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return ADD32(K1, MULT16_16_P13(x2, ADD32(K2, MULT16_16_P13(x2, ADD32(K3, MULT16_16_P13(K4, x2))))));
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} else {
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x = SUB16(25736,x);
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x2 = MULT16_16_P13(x,x);
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return SUB32(-K1, MULT16_16_P13(x2, ADD32(K2, MULT16_16_P13(x2, ADD32(K3, MULT16_16_P13(K4, x2))))));
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}
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}
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#define L1 32767
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#define L2 -7651
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#define L3 8277
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#define L4 -626
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static inline spx_word16_t _spx_cos_pi_2(spx_word16_t x)
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{
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spx_word16_t x2;
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x2 = MULT16_16_P15(x,x);
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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))))))));
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}
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static inline spx_word16_t spx_cos_norm(spx_word32_t x)
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{
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x = x&0x0001ffff;
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if (x>SHL32(EXTEND32(1), 16))
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x = SUB32(SHL32(EXTEND32(1), 17),x);
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if (x&0x00007fff)
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{
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if (x<SHL32(EXTEND32(1), 15))
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{
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return _spx_cos_pi_2(EXTRACT16(x));
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} else {
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return NEG32(_spx_cos_pi_2(EXTRACT16(65536-x)));
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}
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} else {
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if (x&0x0000ffff)
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return 0;
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else if (x&0x0001ffff)
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return -32767;
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else
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return 32767;
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}
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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 16384
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#define D1 11356
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#define D2 3726
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#define D3 1301
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/* Input in Q11 format, output in Q16 */
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static inline spx_word32_t spx_exp2(spx_word16_t x)
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{
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int integer;
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spx_word16_t frac;
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integer = SHR16(x,11);
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if (integer>14)
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return 0x7fffffff;
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else if (integer < -15)
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return 0;
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frac = SHL16(x-SHL16(integer,11),3);
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frac = ADD16(D0, MULT16_16_Q14(frac, ADD16(D1, MULT16_16_Q14(frac, ADD16(D2 , MULT16_16_Q14(D3,frac))))));
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return VSHR32(EXTEND32(frac), -integer-2);
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}
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/* Input in Q11 format, output in Q16 */
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static inline spx_word32_t spx_exp(spx_word16_t x)
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{
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if (x>21290)
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return 0x7fffffff;
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else if (x<-21290)
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return 0;
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else
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return spx_exp2(MULT16_16_P14(23637,x));
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}
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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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static inline spx_word16_t spx_atan01(spx_word16_t 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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/* Input in Q15, output in Q14 */
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static inline spx_word16_t spx_atan(spx_word32_t x)
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{
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if (x <= 32767)
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{
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return SHR16(spx_atan01(x),1);
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} else {
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int e = spx_ilog2(x);
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if (e>=29)
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return 25736;
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x = DIV32_16(SHL32(EXTEND32(32767),29-e), EXTRACT16(SHR32(x, e-14)));
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return SUB16(25736, SHR16(spx_atan01(x),1));
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}
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}
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#else
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#ifndef M_PI
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#define M_PI 3.14159265358979323846 /* pi */
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#endif
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#define C1 0.9999932946f
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#define C2 -0.4999124376f
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#define C3 0.0414877472f
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#define C4 -0.0012712095f
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#define SPX_PI_2 1.5707963268
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static inline spx_word16_t spx_cos(spx_word16_t x)
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{
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if (x<SPX_PI_2)
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{
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x *= x;
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return C1 + x*(C2+x*(C3+C4*x));
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} else {
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x = M_PI-x;
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x *= x;
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return NEG16(C1 + x*(C2+x*(C3+C4*x)));
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}
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}
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#endif
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#endif
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