/* ** FFT and FHT routines ** Copyright 1988, 1993; Ron Mayer ** Copyright (c) 1999-2000 Takehiro Tominaga ** ** fht(fz,n); ** Does a hartley transform of "n" points in the array "fz". ** ** NOTE: This routine uses at least 2 patented algorithms, and may be ** under the restrictions of a bunch of different organizations. ** Although I wrote it completely myself; it is kind of a derivative ** of a routine I once authored and released under the GPL, so it ** may fall under the free software foundation's restrictions; ** it was worked on as a Stanford Univ project, so they claim ** some rights to it; it was further optimized at work here, so ** I think this company claims parts of it. The patents are ** held by R. Bracewell (the FHT algorithm) and O. Buneman (the ** trig generator), both at Stanford Univ. ** If it were up to me, I'd say go do whatever you want with it; ** but it would be polite to give credit to the following people ** if you use this anywhere: ** Euler - probable inventor of the fourier transform. ** Gauss - probable inventor of the FFT. ** Hartley - probable inventor of the hartley transform. ** Buneman - for a really cool trig generator ** Mayer(me) - for authoring this particular version and ** including all the optimizations in one package. ** Thanks, ** Ron Mayer; mayer@acuson.com ** and added some optimization by ** Mather - idea of using lookup table ** Takehiro - some dirty hack for speed up */ /* $Id: fft.c,v 1.39 2017/09/06 15:07:29 robert Exp $ */ #ifdef HAVE_CONFIG_H # include #endif #include "lame.h" #include "machine.h" #include "encoder.h" #include "util.h" #include "fft.h" #include "vector/lame_intrin.h" #define TRI_SIZE (5-1) /* 1024 = 4**5 */ /* fft.c */ static const FLOAT costab[TRI_SIZE * 2] = { 9.238795325112867e-01, 3.826834323650898e-01, 9.951847266721969e-01, 9.801714032956060e-02, 9.996988186962042e-01, 2.454122852291229e-02, 9.999811752826011e-01, 6.135884649154475e-03 }; static void fht(FLOAT * fz, int n) { const FLOAT *tri = costab; int k4; FLOAT *fi, *gi; FLOAT const *fn; n <<= 1; /* to get BLKSIZE, because of 3DNow! ASM routine */ fn = fz + n; k4 = 4; do { FLOAT s1, c1; int i, k1, k2, k3, kx; kx = k4 >> 1; k1 = k4; k2 = k4 << 1; k3 = k2 + k1; k4 = k2 << 1; fi = fz; gi = fi + kx; do { FLOAT f0, f1, f2, f3; f1 = fi[0] - fi[k1]; f0 = fi[0] + fi[k1]; f3 = fi[k2] - fi[k3]; f2 = fi[k2] + fi[k3]; fi[k2] = f0 - f2; fi[0] = f0 + f2; fi[k3] = f1 - f3; fi[k1] = f1 + f3; f1 = gi[0] - gi[k1]; f0 = gi[0] + gi[k1]; f3 = SQRT2 * gi[k3]; f2 = SQRT2 * gi[k2]; gi[k2] = f0 - f2; gi[0] = f0 + f2; gi[k3] = f1 - f3; gi[k1] = f1 + f3; gi += k4; fi += k4; } while (fi < fn); c1 = tri[0]; s1 = tri[1]; for (i = 1; i < kx; i++) { FLOAT c2, s2; c2 = 1 - (2 * s1) * s1; s2 = (2 * s1) * c1; fi = fz + i; gi = fz + k1 - i; do { FLOAT a, b, g0, f0, f1, g1, f2, g2, f3, g3; b = s2 * fi[k1] - c2 * gi[k1]; a = c2 * fi[k1] + s2 * gi[k1]; f1 = fi[0] - a; f0 = fi[0] + a; g1 = gi[0] - b; g0 = gi[0] + b; b = s2 * fi[k3] - c2 * gi[k3]; a = c2 * fi[k3] + s2 * gi[k3]; f3 = fi[k2] - a; f2 = fi[k2] + a; g3 = gi[k2] - b; g2 = gi[k2] + b; b = s1 * f2 - c1 * g3; a = c1 * f2 + s1 * g3; fi[k2] = f0 - a; fi[0] = f0 + a; gi[k3] = g1 - b; gi[k1] = g1 + b; b = c1 * g2 - s1 * f3; a = s1 * g2 + c1 * f3; gi[k2] = g0 - a; gi[0] = g0 + a; fi[k3] = f1 - b; fi[k1] = f1 + b; gi += k4; fi += k4; } while (fi < fn); c2 = c1; c1 = c2 * tri[0] - s1 * tri[1]; s1 = c2 * tri[1] + s1 * tri[0]; } tri += 2; } while (k4 < n); } static const unsigned char rv_tbl[] = { 0x00, 0x80, 0x40, 0xc0, 0x20, 0xa0, 0x60, 0xe0, 0x10, 0x90, 0x50, 0xd0, 0x30, 0xb0, 0x70, 0xf0, 0x08, 0x88, 0x48, 0xc8, 0x28, 0xa8, 0x68, 0xe8, 0x18, 0x98, 0x58, 0xd8, 0x38, 0xb8, 0x78, 0xf8, 0x04, 0x84, 0x44, 0xc4, 0x24, 0xa4, 0x64, 0xe4, 0x14, 0x94, 0x54, 0xd4, 0x34, 0xb4, 0x74, 0xf4, 0x0c, 0x8c, 0x4c, 0xcc, 0x2c, 0xac, 0x6c, 0xec, 0x1c, 0x9c, 0x5c, 0xdc, 0x3c, 0xbc, 0x7c, 0xfc, 0x02, 0x82, 0x42, 0xc2, 0x22, 0xa2, 0x62, 0xe2, 0x12, 0x92, 0x52, 0xd2, 0x32, 0xb2, 0x72, 0xf2, 0x0a, 0x8a, 0x4a, 0xca, 0x2a, 0xaa, 0x6a, 0xea, 0x1a, 0x9a, 0x5a, 0xda, 0x3a, 0xba, 0x7a, 0xfa, 0x06, 0x86, 0x46, 0xc6, 0x26, 0xa6, 0x66, 0xe6, 0x16, 0x96, 0x56, 0xd6, 0x36, 0xb6, 0x76, 0xf6, 0x0e, 0x8e, 0x4e, 0xce, 0x2e, 0xae, 0x6e, 0xee, 0x1e, 0x9e, 0x5e, 0xde, 0x3e, 0xbe, 0x7e, 0xfe }; #define ch01(index) (buffer[chn][index]) #define ml00(f) (window[i ] * f(i)) #define ml10(f) (window[i + 0x200] * f(i + 0x200)) #define ml20(f) (window[i + 0x100] * f(i + 0x100)) #define ml30(f) (window[i + 0x300] * f(i + 0x300)) #define ml01(f) (window[i + 0x001] * f(i + 0x001)) #define ml11(f) (window[i + 0x201] * f(i + 0x201)) #define ml21(f) (window[i + 0x101] * f(i + 0x101)) #define ml31(f) (window[i + 0x301] * f(i + 0x301)) #define ms00(f) (window_s[i ] * f(i + k)) #define ms10(f) (window_s[0x7f - i] * f(i + k + 0x80)) #define ms20(f) (window_s[i + 0x40] * f(i + k + 0x40)) #define ms30(f) (window_s[0x3f - i] * f(i + k + 0xc0)) #define ms01(f) (window_s[i + 0x01] * f(i + k + 0x01)) #define ms11(f) (window_s[0x7e - i] * f(i + k + 0x81)) #define ms21(f) (window_s[i + 0x41] * f(i + k + 0x41)) #define ms31(f) (window_s[0x3e - i] * f(i + k + 0xc1)) void fft_short(lame_internal_flags const *const gfc, FLOAT x_real[3][BLKSIZE_s], int chn, const sample_t *const buffer[2]) { int i; int j; int b; #define window_s gfc->cd_psy->window_s #define window gfc->cd_psy->window for (b = 0; b < 3; b++) { FLOAT *x = &x_real[b][BLKSIZE_s / 2]; short const k = (576 / 3) * (b + 1); j = BLKSIZE_s / 8 - 1; do { FLOAT f0, f1, f2, f3, w; i = rv_tbl[j << 2]; f0 = ms00(ch01); w = ms10(ch01); f1 = f0 - w; f0 = f0 + w; f2 = ms20(ch01); w = ms30(ch01); f3 = f2 - w; f2 = f2 + w; x -= 4; x[0] = f0 + f2; x[2] = f0 - f2; x[1] = f1 + f3; x[3] = f1 - f3; f0 = ms01(ch01); w = ms11(ch01); f1 = f0 - w; f0 = f0 + w; f2 = ms21(ch01); w = ms31(ch01); f3 = f2 - w; f2 = f2 + w; x[BLKSIZE_s / 2 + 0] = f0 + f2; x[BLKSIZE_s / 2 + 2] = f0 - f2; x[BLKSIZE_s / 2 + 1] = f1 + f3; x[BLKSIZE_s / 2 + 3] = f1 - f3; } while (--j >= 0); #undef window #undef window_s gfc->fft_fht(x, BLKSIZE_s / 2); /* BLKSIZE_s/2 because of 3DNow! ASM routine */ } } void fft_long(lame_internal_flags const *const gfc, FLOAT x[BLKSIZE], int chn, const sample_t *const buffer[2]) { int i; int jj = BLKSIZE / 8 - 1; x += BLKSIZE / 2; #define window_s gfc->cd_psy->window_s #define window gfc->cd_psy->window do { FLOAT f0, f1, f2, f3, w; i = rv_tbl[jj]; f0 = ml00(ch01); w = ml10(ch01); f1 = f0 - w; f0 = f0 + w; f2 = ml20(ch01); w = ml30(ch01); f3 = f2 - w; f2 = f2 + w; x -= 4; x[0] = f0 + f2; x[2] = f0 - f2; x[1] = f1 + f3; x[3] = f1 - f3; f0 = ml01(ch01); w = ml11(ch01); f1 = f0 - w; f0 = f0 + w; f2 = ml21(ch01); w = ml31(ch01); f3 = f2 - w; f2 = f2 + w; x[BLKSIZE / 2 + 0] = f0 + f2; x[BLKSIZE / 2 + 2] = f0 - f2; x[BLKSIZE / 2 + 1] = f1 + f3; x[BLKSIZE / 2 + 3] = f1 - f3; } while (--jj >= 0); #undef window #undef window_s gfc->fft_fht(x, BLKSIZE / 2); /* BLKSIZE/2 because of 3DNow! ASM routine */ } #ifdef HAVE_NASM extern void fht_3DN(FLOAT * fz, int n); extern void fht_SSE(FLOAT * fz, int n); #endif void init_fft(lame_internal_flags * const gfc) { int i; /* The type of window used here will make no real difference, but */ /* in the interest of merging nspsytune stuff - switch to blackman window */ for (i = 0; i < BLKSIZE; i++) /* blackman window */ gfc->cd_psy->window[i] = 0.42 - 0.5 * cos(2 * PI * (i + .5) / BLKSIZE) + 0.08 * cos(4 * PI * (i + .5) / BLKSIZE); for (i = 0; i < BLKSIZE_s / 2; i++) gfc->cd_psy->window_s[i] = 0.5 * (1.0 - cos(2.0 * PI * (i + 0.5) / BLKSIZE_s)); gfc->fft_fht = fht; #ifdef HAVE_NASM if (gfc->CPU_features.AMD_3DNow) { gfc->fft_fht = fht_3DN; } else if (gfc->CPU_features.SSE) { gfc->fft_fht = fht_SSE; } else { gfc->fft_fht = fht; } #else #ifdef HAVE_XMMINTRIN_H #ifdef MIN_ARCH_SSE gfc->fft_fht = fht_SSE2; #endif #endif #endif }