Fixed-point implementation of ff_cos, ff_log2, ff_exp2.

Also implemented routine for calculating sum(a[i] * a[i-offset]>>shift)

Originally committed as revision 12974 to svn://svn.ffmpeg.org/ffmpeg/trunk

libavcodec/acelp_math.c

+/*
+ * Various fixed-point math operations
+ *
+ * Copyright (c) 2008 Vladimir Voroshilov
+ *
+ * This file is part of FFmpeg.
+ *
+ * FFmpeg is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * FFmpeg is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with FFmpeg; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
+ */
+
+#include <inttypes.h>
+#include <limits.h>
+#include <assert.h>
+
+#include "avcodec.h"
+#include "acelp_math.h"
+
+#ifdef G729_BITEXACT
+/**
+ * Cosine table: base_cos[i] = (1<<15) * cos(i*PI/64)
+ */
+static const int16_t base_cos[64] =
+{
+  32767,  32729,  32610,  32413,  32138,  31786,  31357,  30853,
+  30274,  29622,  28899,  28106,  27246,  26320,  25330,  24279,
+  23170,  22006,  20788,  19520,  18205,  16846,  15447,  14010,
+  12540,  11039,   9512,   7962,   6393,   4808,   3212,   1608,
+      0,  -1608,  -3212,  -4808,  -6393,  -7962,  -9512, -11039,
+ -12540, -14010, -15447, -16846, -18205, -19520, -20788, -22006,
+ -23170, -24279, -25330, -26320, -27246, -28106, -28899, -29622,
+ -30274, -30853, -31357, -31786, -32138, -32413, -32610, -32729
+};
+
+/**
+ * Slope used to compute cos(x)
+ *
+ * cos(ind*64+offset) = base_cos[ind]+offset*slope_cos[ind]
+ * values multiplied by 1<<19
+ */
+static const int16_t slope_cos[64] =
+{
+   -632,  -1893,  -3150,  -4399,  -5638,  -6863,  -8072,  -9261,
+ -10428, -11570, -12684, -13767, -14817, -15832, -16808, -17744,
+ -18637, -19486, -20287, -21039, -21741, -22390, -22986, -23526,
+ -24009, -24435, -24801, -25108, -25354, -25540, -25664, -25726,
+ -25726, -25664, -25540, -25354, -25108, -24801, -24435, -24009,
+ -23526, -22986, -22390, -21741, -21039, -20287, -19486, -18637,
+ -17744, -16808, -15832, -14817, -13767, -12684, -11570, -10428,
+  -9261,  -8072,  -6863,  -5638,  -4399,  -3150,  -1893,   -632
+};
+
+/**
+ * Table used to compute exp2(x)
+ *
+ * tab_exp2[i] = (1<<14) * exp2(i/32) = 2^(i/32) i=0..32
+ */
+static const uint16_t tab_exp2[33] =
+{
+  16384, 16743, 17109, 17484, 17867, 18258, 18658, 19066, 19484, 19911,
+  20347, 20792, 21247, 21713, 22188, 22674, 23170, 23678, 24196, 24726,
+  25268, 25821, 26386, 26964, 27554, 28158, 28774, 29405, 30048, 30706,
+  31379, 32066, 32767
+};
+
+int16_t ff_cos(uint16_t arg)
+{
+    uint8_t offset= arg;
+    uint8_t ind = arg >> 8;
+
+    assert(arg < 0x4000);
+
+    return FFMAX(base_cos[ind] + ((slope_cos[ind] * offset) >> 12), -0x8000);
+}
+
+int ff_exp2(uint16_t power)
+{
+    uint16_t frac_x0;
+    uint16_t frac_dx;
+    int result;
+
+    assert(power <= 0x7fff);
+
+    frac_x0 = power >> 10;
+    frac_dx = (power & 0x03ff) << 5;
+
+    result = tab_exp2[frac_x0] << 15;
+    result += frac_dx * (tab_exp2[frac_x0+1] - tab_exp2[frac_x0]);
+
+    return result >> 10;
+}
+
+#else // G729_BITEXACT
+
+/**
+ * Cosine table: base_cos[i] = (1<<15) * cos(i*PI/64)
+ */
+static const int16_t tab_cos[65] =
+{
+  32767,  32738,  32617,  32421,  32145,  31793,  31364,  30860,
+  30280,  29629,  28905,  28113,  27252,  26326,  25336,  24285,
+  23176,  22011,  20793,  19525,  18210,  16851,  15451,  14014,
+  12543,  11043,   9515,   7965,   6395,   4810,   3214,   1609,
+      1,  -1607,  -3211,  -4808,  -6393,  -7962,  -9513, -11040,
+ -12541, -14012, -15449, -16848, -18207, -19523, -20791, -22009,
+ -23174, -24283, -25334, -26324, -27250, -28111, -28904, -29627,
+ -30279, -30858, -31363, -31792, -32144, -32419, -32616, -32736, -32768,
+};
+
+static const uint16_t exp2a[]=
+{
+     0,  1435,  2901,  4400,  5931,  7496,  9096, 10730,
+ 12400, 14106, 15850, 17632, 19454, 21315, 23216, 25160,
+ 27146, 29175, 31249, 33368, 35534, 37747, 40009, 42320,
+ 44682, 47095, 49562, 52082, 54657, 57289, 59979, 62727,
+};
+
+static const uint16_t exp2b[]=
+{
+     3,   712,  1424,  2134,  2845,  3557,  4270,  4982,
+  5696,  6409,  7124,  7839,  8554,  9270,  9986, 10704,
+ 11421, 12138, 12857, 13576, 14295, 15014, 15734, 16455,
+ 17176, 17898, 18620, 19343, 20066, 20790, 21514, 22238,
+};
+
+int16_t ff_cos(uint16_t arg)
+{
+    uint8_t offset= arg;
+    uint8_t ind = arg >> 8;
+
+    assert(arg <= 0x3fff);
+
+    return tab_cos[ind] + (offset * (tab_cos[ind+1] - tab_cos[ind]) >> 8);
+}
+
+int ff_exp2(uint16_t power)
+{
+    unsigned int result= exp2a[power>>10] + 0x10000;
+
+    assert(arg <= 0x7fff);
+
+    result= (result<<3) + ((result*exp2b[(power>>5)&31])>>17);
+    return result + ((result*(power&31)*89)>>22);
+}
+
+#endif // else G729_BITEXACT
+
+/**
+ * Table used to compute log2(x)
+ *
+ * tab_log2[i] = (1<<15) * log2(1 + i/32), i=0..32
+ */
+static const uint16_t tab_log2[33] =
+{
+#ifdef G729_BITEXACT
+      0,   1455,   2866,   4236,   5568,   6863,   8124,   9352,
+  10549,  11716,  12855,  13967,  15054,  16117,  17156,  18172,
+  19167,  20142,  21097,  22033,  22951,  23852,  24735,  25603,
+  26455,  27291,  28113,  28922,  29716,  30497,  31266,  32023,  32767,
+#else
+      4,   1459,   2870,   4240,   5572,   6867,   8127,   9355,
+  10552,  11719,  12858,  13971,  15057,  16120,  17158,  18175,
+  19170,  20145,  21100,  22036,  22954,  23854,  24738,  25605,
+  26457,  27294,  28116,  28924,  29719,  30500,  31269,  32025,  32769,
+#endif
+};
+
+int ff_log2(uint32_t value)
+{
+    uint8_t  power_int;
+    uint8_t  frac_x0;
+    uint16_t frac_dx;
+
+    // Stripping zeros from beginning
+    power_int = av_log2(value);
+    value <<= (31 - power_int);
+
+    // b31 is always non-zero now
+    frac_x0 = (value & 0x7c000000) >> 26; // b26-b31 and [32..63] -> [0..31]
+    frac_dx = (value & 0x03fff800) >> 11;
+
+    value = tab_log2[frac_x0];
+    value += (frac_dx * (tab_log2[frac_x0+1] - tab_log2[frac_x0])) >> 15;
+
+    return (power_int << 15) + value;
+}

libavcodec/acelp_math.h

+/*
+ * Various fixed-point math operations
+ *
+ * Copyright (c) 2008 Vladimir Voroshilov
+ *
+ * This file is part of FFmpeg.
+ *
+ * FFmpeg is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * FFmpeg is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with FFmpeg; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
+ */
+
+#ifndef FFMPEG_ACELP_MATH_H
+#define FFMPEG_ACELP_MATH_H
+
+/**
+ * \brief fixed-point implementation of cosine in [0; PI) domain
+ * \param arg fixed-point cosine argument, 0 <= arg < 0x4000
+ *
+ * \return value of (1<<15) * cos(arg * PI / (1<<14)), -0x8000 <= result <= 0x7fff
+ */
+int16_t ff_cos(uint16_t arg);
+
+/**
+ * \brief fixed-point implementation of exp2(x) in [0; 1] domain
+ * \param power argument to exp2, 0 <= power <= 0x7fff
+ *
+ * \return value of (1<<20) * exp2(power / (1<<15))
+ *         0x8000c <= result <= 0xfffea
+ */
+int ff_exp2(uint16_t power);
+
+/**
+ * \brief Calculates log2(x)
+ * \param value function argument, 0 < value <= 7fff ffff
+ *
+ * \return value of (1<<15) * log2(value)
+ */
+int ff_log2(uint32_t value);
+
+/**
+ * \brief Calculates sum of array elements multiplications
+ * \param speech array with input data
+ * \param length number elements to proceed
+ * \param offset offset for calculation sum of s[i]*s[i+offset]
+ * \param shift right shift by this value will be done before multiplication
+ *
+ * \return sum of multiplications
+ *
+ * \note array must be at least length+offset long!
+ */
+static int sum_of_squares(const int16_t* speech, int length, int offset, int shift)
+{
+    const int16_t* speech_end;
+    int sum = 0;
+
+    for(speech_end=speech+length; speech<speech_end; speech++)
+       sum += (speech[0] * speech[offset]) >> shift;
+
+    return sum;
+}
+
+#endif // FFMPEG_ACELP_MATH_H