97623c5e97
git-svn-id: svn://svn.rockbox.org/rockbox/trunk@12248 a1c6a512-1295-4272-9138-f99709370657
444 lines
12 KiB
C
444 lines
12 KiB
C
/* Copyright (C) 2002 Jean-Marc Valin
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File: math_approx.c
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Various math approximation functions for Speex
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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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#ifdef HAVE_CONFIG_H
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#include "config.h"
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#endif
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#include "math_approx.h"
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#include "misc.h"
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#ifdef FIXED_POINT
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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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spx_word16_t spx_sqrt(spx_word32_t x)
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{
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int k=0;
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spx_word32_t rt;
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if (x<=0)
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return 0;
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#if 1
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if (x>=16777216)
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{
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x>>=10;
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k+=5;
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}
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if (x>=1048576)
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{
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x>>=6;
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k+=3;
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}
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if (x>=262144)
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{
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x>>=4;
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k+=2;
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}
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if (x>=32768)
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{
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x>>=2;
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k+=1;
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}
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if (x>=16384)
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{
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x>>=2;
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k+=1;
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}
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#else
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while (x>=16384)
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{
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x>>=2;
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k++;
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}
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#endif
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while (x<4096)
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{
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x<<=2;
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k--;
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}
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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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if (rt > 16383)
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rt = 16383;
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if (k>0)
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rt <<= k;
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else
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rt >>= -k;
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rt >>=7;
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return rt;
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}
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static int intSqrt(int x) {
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int xn;
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static int sqrt_table[256] = {
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0, 16, 22, 27, 32, 35, 39, 42, 45, 48, 50, 53, 55, 57,
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59, 61, 64, 65, 67, 69, 71, 73, 75, 76, 78, 80, 81, 83,
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84, 86, 87, 89, 90, 91, 93, 94, 96, 97, 98, 99, 101, 102,
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103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118,
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119, 120, 121, 122, 123, 124, 125, 126, 128, 128, 129, 130, 131, 132,
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133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 144, 145,
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146, 147, 148, 149, 150, 150, 151, 152, 153, 154, 155, 155, 156, 157,
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158, 159, 160, 160, 161, 162, 163, 163, 164, 165, 166, 167, 167, 168,
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169, 170, 170, 171, 172, 173, 173, 174, 175, 176, 176, 177, 178, 178,
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179, 180, 181, 181, 182, 183, 183, 184, 185, 185, 186, 187, 187, 188,
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189, 189, 190, 191, 192, 192, 193, 193, 194, 195, 195, 196, 197, 197,
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198, 199, 199, 200, 201, 201, 202, 203, 203, 204, 204, 205, 206, 206,
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207, 208, 208, 209, 209, 210, 211, 211, 212, 212, 213, 214, 214, 215,
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215, 216, 217, 217, 218, 218, 219, 219, 220, 221, 221, 222, 222, 223,
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224, 224, 225, 225, 226, 226, 227, 227, 228, 229, 229, 230, 230, 231,
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231, 232, 232, 233, 234, 234, 235, 235, 236, 236, 237, 237, 238, 238,
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239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 245, 246,
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246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253,
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253, 254, 254, 255
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};
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if (x >= 0x10000) {
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if (x >= 0x1000000) {
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if (x >= 0x10000000) {
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if (x >= 0x40000000) {
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xn = sqrt_table[x >> 24] << 8;
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} else {
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xn = sqrt_table[x >> 22] << 7;
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}
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} else {
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if (x >= 0x4000000) {
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xn = sqrt_table[x >> 20] << 6;
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} else {
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xn = sqrt_table[x >> 18] << 5;
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}
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}
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xn = (xn + 1 + (x / xn)) >> 1;
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xn = (xn + 1 + (x / xn)) >> 1;
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return ((xn * xn) > x) ? --xn : xn;
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} else {
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if (x >= 0x100000) {
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if (x >= 0x400000) {
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xn = sqrt_table[x >> 16] << 4;
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} else {
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xn = sqrt_table[x >> 14] << 3;
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}
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} else {
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if (x >= 0x40000) {
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xn = sqrt_table[x >> 12] << 2;
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} else {
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xn = sqrt_table[x >> 10] << 1;
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}
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}
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xn = (xn + 1 + (x / xn)) >> 1;
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return ((xn * xn) > x) ? --xn : xn;
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}
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} else {
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if (x >= 0x100) {
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if (x >= 0x1000) {
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if (x >= 0x4000) {
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xn = (sqrt_table[x >> 8]) + 1;
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} else {
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xn = (sqrt_table[x >> 6] >> 1) + 1;
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}
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} else {
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if (x >= 0x400) {
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xn = (sqrt_table[x >> 4] >> 2) + 1;
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} else {
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xn = (sqrt_table[x >> 2] >> 3) + 1;
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}
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}
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return ((xn * xn) > x) ? --xn : xn;
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} else {
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if (x >= 0) {
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return sqrt_table[x] >> 4;
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}
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}
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}
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return -1;
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}
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float spx_sqrtf(float arg)
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{
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if(arg==0.0)
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return 0.0;
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else if(arg==1.0)
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return 1.0;
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else if(arg==2.0)
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return 1.414;
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else if(arg==3.27)
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return 1.8083;
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//printf("Sqrt:%f:%f:%f\n",arg,(((float)intSqrt((int)(arg*10000)))/100)+0.0055,(float)spx_sqrt((spx_word32_t)arg));
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//return ((float)fastSqrt((int)(arg*2500)))/50;
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//LOGF("Sqrt:%d:%d\n",arg,(intSqrt((int)(arg*2500)))/50);
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return (((float)intSqrt((int)(arg*10000)))/100)+0.0055;//(float)spx_sqrt((spx_word32_t)arg);
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//return 1;
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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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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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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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#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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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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inline float spx_floor(float x){
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return ((float)(((int)x)));
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}
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#define FP_BITS (14)
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#define FP_MASK ((1 << FP_BITS) - 1)
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#define FP_ONE (1 << FP_BITS)
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#define FP_TWO (2 << FP_BITS)
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#define FP_HALF (1 << (FP_BITS - 1))
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#define FP_LN2 ( 45426 >> (16 - FP_BITS))
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#define FP_LN2_INV ( 94548 >> (16 - FP_BITS))
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#define FP_EXP_ZERO ( 10922 >> (16 - FP_BITS))
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#define FP_EXP_ONE ( -182 >> (16 - FP_BITS))
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#define FP_EXP_TWO ( 4 >> (16 - FP_BITS))
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// #define FP_INF (0x7fffffff)
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// #define FP_LN10 (150902 >> (16 - FP_BITS))
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#define FP_MAX_DIGITS (4)
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#define FP_MAX_DIGITS_INT (10000)
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// #define FP_FAST_MUL_DIV
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// #ifdef FP_FAST_MUL_DIV
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/* These macros can easily overflow, but they are good enough for our uses,
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* and saves some code.
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*/
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#define fp_mul(x, y) (((x) * (y)) >> FP_BITS)
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#define fp_div(x, y) (((x) << FP_BITS) / (y))
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#ifndef abs
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#define abs(x) (((x)<0)?((x)*-1):(x))
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#endif
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float spx_sqrt2(float xf) {
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long x=(xf*(2.0*FP_BITS));
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int i=0, s = (x + FP_ONE) >> 1;
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for (; i < 8; i++) {
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s = (s + fp_div(x, s)) >> 1;
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}
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return s/((float)(2*FP_BITS));
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}
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static int exp_s16p16(int x)
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{
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int t;
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int y = 0x00010000;
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if (x < 0) x += 0xb1721, y >>= 16;
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t = x - 0x58b91; if (t >= 0) x = t, y <<= 8;
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t = x - 0x2c5c8; if (t >= 0) x = t, y <<= 4;
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t = x - 0x162e4; if (t >= 0) x = t, y <<= 2;
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t = x - 0x0b172; if (t >= 0) x = t, y <<= 1;
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t = x - 0x067cd; if (t >= 0) x = t, y += y >> 1;
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t = x - 0x03920; if (t >= 0) x = t, y += y >> 2;
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t = x - 0x01e27; if (t >= 0) x = t, y += y >> 3;
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t = x - 0x00f85; if (t >= 0) x = t, y += y >> 4;
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t = x - 0x007e1; if (t >= 0) x = t, y += y >> 5;
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t = x - 0x003f8; if (t >= 0) x = t, y += y >> 6;
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t = x - 0x001fe; if (t >= 0) x = t, y += y >> 7;
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y += ((y >> 8) * x) >> 8;
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return y;
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}
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float spx_expB(float xf) {
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return exp_s16p16(xf*32)/32;
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}
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float spx_expC(float xf){
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long x=xf*(2*FP_BITS);
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/*
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static long fp_exp(long x)
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{*/
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long k;
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long z;
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long R;
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long xp;
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if (x == 0)
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{
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return FP_ONE;
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}
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k = (fp_mul(abs(x), FP_LN2_INV) + FP_HALF) & ~FP_MASK;
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if (x < 0)
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{
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k = -k;
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}
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x -= fp_mul(k, FP_LN2);
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z = fp_mul(x, x);
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R = FP_TWO + fp_mul(z, FP_EXP_ZERO + fp_mul(z, FP_EXP_ONE
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+ fp_mul(z, FP_EXP_TWO)));
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xp = FP_ONE + fp_div(fp_mul(FP_TWO, x), R - x);
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if (k < 0)
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{
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k = FP_ONE >> (-k >> FP_BITS);
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}
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else
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{
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k = FP_ONE << (k >> FP_BITS);
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}
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return fp_mul(k, xp)/(2*FP_BITS);
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}
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/*To generate (ruby code): (0...33).each { |idx| puts Math.exp((idx-10) / 8.0).to_s + "," } */
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const float exp_lookup_int[33]={0.28650479686019,0.32465246735835,0.367879441171442,0.416862019678508,0.472366552741015,0.53526142851899,0.606530659712633,0.687289278790972,0.778800783071405,0.882496902584595,1.0,1.13314845306683,1.28402541668774,1.4549914146182,1.64872127070013,1.86824595743222,2.11700001661267,2.3988752939671,2.71828182845905,3.08021684891803,3.49034295746184,3.95507672292058,4.48168907033806,5.07841903718008,5.75460267600573,6.52081912033011,7.38905609893065,8.37289748812726,9.48773583635853,10.7510131860764,12.1824939607035,13.8045741860671,15.6426318841882};
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/*To generate (ruby code): (0...32).each { |idx| puts Math.exp((idx-16.0) / 4.0).to_s+","} */
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static const float exp_table[32]={0.0183156388887342,0.0235177458560091,0.0301973834223185,0.038774207831722,0.0497870683678639,0.0639278612067076,0.0820849986238988,0.105399224561864,0.135335283236613,0.173773943450445,0.22313016014843,0.28650479686019,0.367879441171442,0.472366552741015,0.606530659712633,0.778800783071405,1.0,1.28402541668774,1.64872127070013,2.11700001661267,2.71828182845905,3.49034295746184,4.48168907033806,5.75460267600573,7.38905609893065,9.48773583635853,12.1824939607035,15.6426318841882,20.0855369231877,25.7903399171931,33.1154519586923,42.5210820000628};
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/**Returns exp(x) Range x=-4-+4 {x.0,x.25,x.5,x.75} */
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float spx_exp(float xf){
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float flt=spx_floor(xf);
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if(-4<xf&&4>xf&&(abs(xf-flt)==0.0||abs(xf-flt)==0.25||abs(xf-flt)==0.5||abs(xf-flt)==0.75||abs(xf-flt)==1.0)){
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#ifdef SIMULATOR
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/* printf("NtbSexp:%f,%d,%f:%f,%f,%f:%d,%d:%d\n",
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exp_sqrt_table[(int)((xf+4.0)*4.0)],
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(int)((xf-4.0)*4.0),
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(xf-4.0)*4.0,
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xf,
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flt,
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xf-flt,
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-4<xf,
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4>xf,
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abs(xf-flt)
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);*/
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#endif
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return exp_table[(int)((xf+4.0)*4.0)];
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} else if (-4<xf&&4>xf){
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#ifdef SIMULATOR
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/* printf("NtbLexp:%f,%f,%f:%d,%d:%d\n",xf,flt,xf-flt,-4<xf,4>xf,abs(xf-flt)); */
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#endif
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return exp_table[(int)((xf+4.0)*4.0)];
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}
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#ifdef SIMULATOR
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/* printf("NTBLexp:%f,%f,%f:%d,%d:%d\n",xf,flt,xf-flt,-4<xf,4>xf,abs(xf-flt)); */
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#endif
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return spx_expB(xf);
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//return exp(xf);
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}
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//Placeholders (not fixed point, only used when encoding):
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float pow(float a,float b){
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return 0;
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}
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float log(float l){
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return 0;
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}
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float fabs(float a){
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return 0;
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}
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float sin(float a){
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return 0;
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}
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