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/* Copyright (C) 2002 Jean-Marc Valin
File: math_approx.c
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.
*/
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include "math_approx.h"
#include "misc.h"
#ifdef FIXED_POINT
/* 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
spx_word16_t spx_sqrt(spx_word32_t x)
{
int k=0;
spx_word32_t rt;
if (x==0)
return 0;
#if 1
if (x>16777216)
{
x>>=10;
k+=5;
}
if (x>1048576)
{
x>>=6;
k+=3;
}
if (x>262144)
{
x>>=4;
k+=2;
}
if (x>32768)
{
x>>=2;
k+=1;
}
if (x>16384)
{
x>>=2;
k+=1;
}
#else
while (x>16384)
{
x>>=2;
k++;
}
#endif
while (x<4096)
{
x<<=2;
k--;
}
rt = ADD16(C0, MULT16_16_Q14(x, ADD16(C1, MULT16_16_Q14(x, ADD16(C2, MULT16_16_Q14(x, (C3)))))));
if (k>0)
rt <<= k;
else
rt >>= -k;
rt >>=7;
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
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
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))))));
}
}
#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
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
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