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-/* Copyright (C) 2002 Jean-Marc Valin */
-/**
- @file math_approx.h
- @brief Various math approximation functions for Speex
-*/
-/*
- Redistribution and use in source and binary forms, with or without
- modification, are permitted provided that the following conditions
- are met:
-
- - Redistributions of source code must retain the above copyright
- notice, this list of conditions and the following disclaimer.
-
- - Redistributions in binary form must reproduce the above copyright
- notice, this list of conditions and the following disclaimer in the
- documentation and/or other materials provided with the distribution.
-
- - Neither the name of the Xiph.org Foundation nor the names of its
- contributors may be used to endorse or promote products derived from
- this software without specific prior written permission.
-
- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
- ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
- LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
- A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR
- CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
- EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
- PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
- PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
- LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
- NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
- SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-*/
-
-#ifndef MATH_APPROX_H
-#define MATH_APPROX_H
-
-#include "arch.h"
-
-#ifndef FIXED_POINT
-
-#define spx_sqrt sqrt
-#define spx_acos acos
-#define spx_exp exp
-#define spx_cos_norm(x) (cos((.5f*M_PI)*(x)))
-#define spx_atan atan
-
-/** Generate a pseudo-random number */
-static inline spx_word16_t speex_rand(spx_word16_t std, spx_int32_t *seed)
-{
- const unsigned int jflone = 0x3f800000;
- const unsigned int jflmsk = 0x007fffff;
- union {int i; float f;} ran;
- *seed = 1664525 * *seed + 1013904223;
- ran.i = jflone | (jflmsk & *seed);
- ran.f -= 1.5;
- return 3.4642*std*ran.f;
-}
-
-
-#endif
-
-
-static inline spx_int16_t spx_ilog2(spx_uint32_t x)
-{
- int r=0;
- if (x>=(spx_int32_t)65536)
- {
- x >>= 16;
- r += 16;
- }
- if (x>=256)
- {
- x >>= 8;
- r += 8;
- }
- if (x>=16)
- {
- x >>= 4;
- r += 4;
- }
- if (x>=4)
- {
- x >>= 2;
- r += 2;
- }
- if (x>=2)
- {
- r += 1;
- }
- return r;
-}
-
-static inline spx_int16_t spx_ilog4(spx_uint32_t x)
-{
- int r=0;
- if (x>=(spx_int32_t)65536)
- {
- x >>= 16;
- r += 8;
- }
- if (x>=256)
- {
- x >>= 8;
- r += 4;
- }
- if (x>=16)
- {
- x >>= 4;
- r += 2;
- }
- if (x>=4)
- {
- r += 1;
- }
- return r;
-}
-
-#ifdef FIXED_POINT
-
-/** Generate a pseudo-random number */
-static inline spx_word16_t speex_rand(spx_word16_t std, spx_int32_t *seed)
-{
- spx_word32_t res;
- *seed = 1664525 * *seed + 1013904223;
- res = MULT16_16(EXTRACT16(SHR32(*seed,16)),std);
- return EXTRACT16(PSHR32(SUB32(res, SHR32(res, 3)),14));
-}
-
-/* sqrt(x) ~= 0.22178 + 1.29227*x - 0.77070*x^2 + 0.25723*x^3 (for .25 < x < 1) */
-/*#define C0 3634
-#define C1 21173
-#define C2 -12627
-#define C3 4215*/
-
-/* sqrt(x) ~= 0.22178 + 1.29227*x - 0.77070*x^2 + 0.25659*x^3 (for .25 < x < 1) */
-#define C0 3634
-#define C1 21173
-#define C2 -12627
-#define C3 4204
-
-static inline spx_word16_t spx_sqrt(spx_word32_t x)
-{
- int k;
- spx_word32_t rt;
- k = spx_ilog4(x)-6;
- x = VSHR32(x, (k<<1));
- rt = ADD16(C0, MULT16_16_Q14(x, ADD16(C1, MULT16_16_Q14(x, ADD16(C2, MULT16_16_Q14(x, (C3)))))));
- rt = VSHR32(rt,7-k);
- return rt;
-}
-
-/* log(x) ~= -2.18151 + 4.20592*x - 2.88938*x^2 + 0.86535*x^3 (for .5 < x < 1) */
-
-
-#define A1 16469
-#define A2 2242
-#define A3 1486
-
-static inline spx_word16_t spx_acos(spx_word16_t x)
-{
- int s=0;
- spx_word16_t ret;
- spx_word16_t sq;
- if (x<0)
- {
- s=1;
- x = NEG16(x);
- }
- x = SUB16(16384,x);
-
- x = x >> 1;
- sq = MULT16_16_Q13(x, ADD16(A1, MULT16_16_Q13(x, ADD16(A2, MULT16_16_Q13(x, (A3))))));
- ret = spx_sqrt(SHL32(EXTEND32(sq),13));
-
- /*ret = spx_sqrt(67108864*(-1.6129e-04 + 2.0104e+00*f + 2.7373e-01*f*f + 1.8136e-01*f*f*f));*/
- if (s)
- ret = SUB16(25736,ret);
- return ret;
-}
-
-
-#define K1 8192
-#define K2 -4096
-#define K3 340
-#define K4 -10
-
-static inline spx_word16_t spx_cos(spx_word16_t x)
-{
- spx_word16_t x2;
-
- if (x<12868)
- {
- x2 = MULT16_16_P13(x,x);
- return ADD32(K1, MULT16_16_P13(x2, ADD32(K2, MULT16_16_P13(x2, ADD32(K3, MULT16_16_P13(K4, x2))))));
- } else {
- x = SUB16(25736,x);
- x2 = MULT16_16_P13(x,x);
- return SUB32(-K1, MULT16_16_P13(x2, ADD32(K2, MULT16_16_P13(x2, ADD32(K3, MULT16_16_P13(K4, x2))))));
- }
-}
-
-#define L1 32767
-#define L2 -7651
-#define L3 8277
-#define L4 -626
-
-static inline spx_word16_t _spx_cos_pi_2(spx_word16_t x)
-{
- spx_word16_t x2;
-
- x2 = MULT16_16_P15(x,x);
- 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))))))));
-}
-
-static inline spx_word16_t spx_cos_norm(spx_word32_t x)
-{
- x = x&0x0001ffff;
- if (x>SHL32(EXTEND32(1), 16))
- x = SUB32(SHL32(EXTEND32(1), 17),x);
- if (x&0x00007fff)
- {
- if (x<SHL32(EXTEND32(1), 15))
- {
- return _spx_cos_pi_2(EXTRACT16(x));
- } else {
- return NEG32(_spx_cos_pi_2(EXTRACT16(65536-x)));
- }
- } else {
- if (x&0x0000ffff)
- return 0;
- else if (x&0x0001ffff)
- return -32767;
- else
- return 32767;
- }
-}
-
-/*
- K0 = 1
- K1 = log(2)
- K2 = 3-4*log(2)
- K3 = 3*log(2) - 2
-*/
-#define D0 16384
-#define D1 11356
-#define D2 3726
-#define D3 1301
-/* Input in Q11 format, output in Q16 */
-static inline spx_word32_t spx_exp2(spx_word16_t x)
-{
- int integer;
- spx_word16_t frac;
- integer = SHR16(x,11);
- if (integer>14)
- return 0x7fffffff;
- else if (integer < -15)
- return 0;
- frac = SHL16(x-SHL16(integer,11),3);
- frac = ADD16(D0, MULT16_16_Q14(frac, ADD16(D1, MULT16_16_Q14(frac, ADD16(D2 , MULT16_16_Q14(D3,frac))))));
- return VSHR32(EXTEND32(frac), -integer-2);
-}
-
-/* Input in Q11 format, output in Q16 */
-static inline spx_word32_t spx_exp(spx_word16_t x)
-{
- if (x>21290)
- return 0x7fffffff;
- else if (x<-21290)
- return 0;
- else
- return spx_exp2(MULT16_16_P14(23637,x));
-}
-#define M1 32767
-#define M2 -21
-#define M3 -11943
-#define M4 4936
-
-static inline spx_word16_t spx_atan01(spx_word16_t x)
-{
- return MULT16_16_P15(x, ADD32(M1, MULT16_16_P15(x, ADD32(M2, MULT16_16_P15(x, ADD32(M3, MULT16_16_P15(M4, x)))))));
-}
-
-#undef M1
-#undef M2
-#undef M3
-#undef M4
-
-/* Input in Q15, output in Q14 */
-static inline spx_word16_t spx_atan(spx_word32_t x)
-{
- if (x <= 32767)
- {
- return SHR16(spx_atan01(x),1);
- } else {
- int e = spx_ilog2(x);
- if (e>=29)
- return 25736;
- x = DIV32_16(SHL32(EXTEND32(32767),29-e), EXTRACT16(SHR32(x, e-14)));
- return SUB16(25736, SHR16(spx_atan01(x),1));
- }
-}
-#else
-
-#ifndef M_PI
-#define M_PI 3.14159265358979323846 /* pi */
-#endif
-
-#define C1 0.9999932946f
-#define C2 -0.4999124376f
-#define C3 0.0414877472f
-#define C4 -0.0012712095f
-
-
-#define SPX_PI_2 1.5707963268
-static inline spx_word16_t spx_cos(spx_word16_t x)
-{
- if (x<SPX_PI_2)
- {
- x *= x;
- return C1 + x*(C2+x*(C3+C4*x));
- } else {
- x = M_PI-x;
- x *= x;
- return NEG16(C1 + x*(C2+x*(C3+C4*x)));
- }
-}
-
-#endif
-
-
-#endif