/* ***** BEGIN LICENSE BLOCK ***** * Source last modified: $Id: fft.c,v 1.1 2005/02/26 01:47:34 jrecker Exp $ * * Portions Copyright (c) 1995-2005 RealNetworks, Inc. All Rights Reserved. * * The contents of this file, and the files included with this file, * are subject to the current version of the RealNetworks Public * Source License (the "RPSL") available at * http://www.helixcommunity.org/content/rpsl unless you have licensed * the file under the current version of the RealNetworks Community * Source License (the "RCSL") available at * http://www.helixcommunity.org/content/rcsl, in which case the RCSL * will apply. You may also obtain the license terms directly from * RealNetworks. You may not use this file except in compliance with * the RPSL or, if you have a valid RCSL with RealNetworks applicable * to this file, the RCSL. Please see the applicable RPSL or RCSL for * the rights, obligations and limitations governing use of the * contents of the file. * * This file is part of the Helix DNA Technology. RealNetworks is the * developer of the Original Code and owns the copyrights in the * portions it created. * * This file, and the files included with this file, is distributed * and made available on an 'AS IS' basis, WITHOUT WARRANTY OF ANY * KIND, EITHER EXPRESS OR IMPLIED, AND REALNETWORKS HEREBY DISCLAIMS * ALL SUCH WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, QUIET * ENJOYMENT OR NON-INFRINGEMENT. * * Technology Compatibility Kit Test Suite(s) Location: * http://www.helixcommunity.org/content/tck * * Contributor(s): * * ***** END LICENSE BLOCK ***** */ /************************************************************************************** * Fixed-point HE-AAC decoder * Jon Recker (jrecker@real.com), Ken Cooke (kenc@real.com) * February 2005 * * fft.c - Ken's optimized radix-4 DIT FFT, optional radix-8 first pass for odd log2(N) **************************************************************************************/ #include "coder.h" #include "assembly.h" #define NUM_FFT_SIZES 2 static const int nfftTab[NUM_FFT_SIZES] PROGMEM ={64, 512}; static const int nfftlog2Tab[NUM_FFT_SIZES] PROGMEM = {6, 9}; #define SQRT1_2 0x5a82799a /* sqrt(1/2) in Q31 */ #define swapcplx(p0,p1) \ t = p0; t1 = *(&(p0)+1); p0 = p1; *(&(p0)+1) = *(&(p1)+1); p1 = t; *(&(p1)+1) = t1 /************************************************************************************** * Function: BitReverse * * Description: Ken's fast in-place bit reverse, using super-small table * * Inputs: buffer of samples * table index (for transform size) * * Outputs: bit-reversed samples in same buffer * * Return: none **************************************************************************************/ /*__attribute__ ((section (".data"))) */ static void BitReverse(int *inout, int tabidx) { int *part0, *part1; int a,b, t,t1; const unsigned char* tab = bitrevtab + bitrevtabOffset[tabidx]; int nbits = nfftlog2Tab[tabidx]; part0 = inout; part1 = inout + (1 << nbits); while ((a = pgm_read_byte(tab++)) != 0) { b = pgm_read_byte(tab++); swapcplx(part0[4*a+0], part0[4*b+0]); /* 0xxx0 <-> 0yyy0 */ swapcplx(part0[4*a+2], part1[4*b+0]); /* 0xxx1 <-> 1yyy0 */ swapcplx(part1[4*a+0], part0[4*b+2]); /* 1xxx0 <-> 0yyy1 */ swapcplx(part1[4*a+2], part1[4*b+2]); /* 1xxx1 <-> 1yyy1 */ } do { swapcplx(part0[4*a+2], part1[4*a+0]); /* 0xxx1 <-> 1xxx0 */ } while ((a = pgm_read_byte(tab++)) != 0); } /************************************************************************************** * Function: R4FirstPass * * Description: radix-4 trivial pass for decimation-in-time FFT * * Inputs: buffer of (bit-reversed) samples * number of R4 butterflies per group (i.e. nfft / 4) * * Outputs: processed samples in same buffer * * Return: none * * Notes: assumes 2 guard bits, gains no integer bits, * guard bits out = guard bits in - 2 **************************************************************************************/ /* __attribute__ ((section (".data"))) */ static void R4FirstPass(int *x, int bg) { int ar, ai, br, bi, cr, ci, dr, di; for (; bg != 0; bg--) { ar = x[0] + x[2]; br = x[0] - x[2]; ai = x[1] + x[3]; bi = x[1] - x[3]; cr = x[4] + x[6]; dr = x[4] - x[6]; ci = x[5] + x[7]; di = x[5] - x[7]; /* max per-sample gain = 4.0 (adding 4 inputs together) */ x[0] = ar + cr; x[4] = ar - cr; x[1] = ai + ci; x[5] = ai - ci; x[2] = br + di; x[6] = br - di; x[3] = bi - dr; x[7] = bi + dr; x += 8; } } /************************************************************************************** * Function: R8FirstPass * * Description: radix-8 trivial pass for decimation-in-time FFT * * Inputs: buffer of (bit-reversed) samples * number of R8 butterflies per group (i.e. nfft / 8) * * Outputs: processed samples in same buffer * * Return: none * * Notes: assumes 3 guard bits, gains 1 integer bit * guard bits out = guard bits in - 3 (if inputs are full scale) * or guard bits in - 2 (if inputs bounded to +/- sqrt(2)/2) * see scaling comments in code **************************************************************************************/ /* __attribute__ ((section (".data"))) */ static void R8FirstPass(int *x, int bg) { int ar, ai, br, bi, cr, ci, dr, di; int sr, si, tr, ti, ur, ui, vr, vi; int wr, wi, xr, xi, yr, yi, zr, zi; for (; bg != 0; bg--) { ar = x[0] + x[2]; br = x[0] - x[2]; ai = x[1] + x[3]; bi = x[1] - x[3]; cr = x[4] + x[6]; dr = x[4] - x[6]; ci = x[5] + x[7]; di = x[5] - x[7]; sr = ar + cr; ur = ar - cr; si = ai + ci; ui = ai - ci; tr = br - di; vr = br + di; ti = bi + dr; vi = bi - dr; ar = x[ 8] + x[10]; br = x[ 8] - x[10]; ai = x[ 9] + x[11]; bi = x[ 9] - x[11]; cr = x[12] + x[14]; dr = x[12] - x[14]; ci = x[13] + x[15]; di = x[13] - x[15]; /* max gain of wr/wi/yr/yi vs input = 2 * (sum of 4 samples >> 1) */ wr = (ar + cr) >> 1; yr = (ar - cr) >> 1; wi = (ai + ci) >> 1; yi = (ai - ci) >> 1; /* max gain of output vs input = 4 * (sum of 4 samples >> 1 + sum of 4 samples >> 1) */ x[ 0] = (sr >> 1) + wr; x[ 8] = (sr >> 1) - wr; x[ 1] = (si >> 1) + wi; x[ 9] = (si >> 1) - wi; x[ 4] = (ur >> 1) + yi; x[12] = (ur >> 1) - yi; x[ 5] = (ui >> 1) - yr; x[13] = (ui >> 1) + yr; ar = br - di; cr = br + di; ai = bi + dr; ci = bi - dr; /* max gain of xr/xi/zr/zi vs input = 4*sqrt(2)/2 = 2*sqrt(2) * (sum of 8 samples, multiply by sqrt(2)/2, implicit >> 1 from Q31) */ xr = MULSHIFT32(SQRT1_2, ar - ai); xi = MULSHIFT32(SQRT1_2, ar + ai); zr = MULSHIFT32(SQRT1_2, cr - ci); zi = MULSHIFT32(SQRT1_2, cr + ci); /* max gain of output vs input = (2 + 2*sqrt(2) ~= 4.83) * (sum of 4 samples >> 1, plus xr/xi/zr/zi with gain of 2*sqrt(2)) * in absolute terms, we have max gain of appx 9.656 (4 + 0.707*8) * but we also gain 1 int bit (from MULSHIFT32 or from explicit >> 1) */ x[ 6] = (tr >> 1) - xr; x[14] = (tr >> 1) + xr; x[ 7] = (ti >> 1) - xi; x[15] = (ti >> 1) + xi; x[ 2] = (vr >> 1) + zi; x[10] = (vr >> 1) - zi; x[ 3] = (vi >> 1) - zr; x[11] = (vi >> 1) + zr; x += 16; } } /************************************************************************************** * Function: R4Core * * Description: radix-4 pass for decimation-in-time FFT * * Inputs: buffer of samples * number of R4 butterflies per group * number of R4 groups per pass * pointer to twiddle factors tables * * Outputs: processed samples in same buffer * * Return: none * * Notes: gain 2 integer bits per pass (see scaling comments in code) * min 1 GB in * gbOut = gbIn - 1 (short block) or gbIn - 2 (long block) * uses 3-mul, 3-add butterflies instead of 4-mul, 2-add **************************************************************************************/ /* __attribute__ ((section (".data"))) */ static void R4Core(int *x, int bg, int gp, int *wtab) { int ar, ai, br, bi, cr, ci, dr, di, tr, ti; int wd, ws, wi; int i, j, step; int *xptr, *wptr; for (; bg != 0; gp <<= 2, bg >>= 2) { step = 2*gp; xptr = x; /* max per-sample gain, per group < 1 + 3*sqrt(2) ~= 5.25 if inputs x are full-scale * do 3 groups for long block, 2 groups for short block (gain 2 int bits per group) * * very conservative scaling: * group 1: max gain = 5.25, int bits gained = 2, gb used = 1 (2^3 = 8) * group 2: max gain = 5.25^2 = 27.6, int bits gained = 4, gb used = 1 (2^5 = 32) * group 3: max gain = 5.25^3 = 144.7, int bits gained = 6, gb used = 2 (2^8 = 256) */ for (i = bg; i != 0; i--) { wptr = wtab; for (j = gp; j != 0; j--) { ar = xptr[0]; ai = xptr[1]; xptr += step; /* gain 2 int bits for br/bi, cr/ci, dr/di (MULSHIFT32 by Q30) * gain 1 net GB */ ws = wptr[0]; wi = wptr[1]; br = xptr[0]; bi = xptr[1]; wd = ws + 2*wi; tr = MULSHIFT32(wi, br + bi); br = MULSHIFT32(wd, br) - tr; /* cos*br + sin*bi */ bi = MULSHIFT32(ws, bi) + tr; /* cos*bi - sin*br */ xptr += step; ws = wptr[2]; wi = wptr[3]; cr = xptr[0]; ci = xptr[1]; wd = ws + 2*wi; tr = MULSHIFT32(wi, cr + ci); cr = MULSHIFT32(wd, cr) - tr; ci = MULSHIFT32(ws, ci) + tr; xptr += step; ws = wptr[4]; wi = wptr[5]; dr = xptr[0]; di = xptr[1]; wd = ws + 2*wi; tr = MULSHIFT32(wi, dr + di); dr = MULSHIFT32(wd, dr) - tr; di = MULSHIFT32(ws, di) + tr; wptr += 6; tr = ar; ti = ai; ar = (tr >> 2) - br; ai = (ti >> 2) - bi; br = (tr >> 2) + br; bi = (ti >> 2) + bi; tr = cr; ti = ci; cr = tr + dr; ci = di - ti; dr = tr - dr; di = di + ti; xptr[0] = ar + ci; xptr[1] = ai + dr; xptr -= step; xptr[0] = br - cr; xptr[1] = bi - di; xptr -= step; xptr[0] = ar - ci; xptr[1] = ai - dr; xptr -= step; xptr[0] = br + cr; xptr[1] = bi + di; xptr += 2; } xptr += 3*step; } wtab += 3*step; } } /************************************************************************************** * Function: R4FFT * * Description: Ken's very fast in-place radix-4 decimation-in-time FFT * * Inputs: table index (for transform size) * buffer of samples (non bit-reversed) * * Outputs: processed samples in same buffer * * Return: none * * Notes: assumes 5 guard bits in for nfft <= 512 * gbOut = gbIn - 4 (assuming input is from PreMultiply) * gains log2(nfft) - 2 int bits total * so gain 7 int bits (LONG), 4 int bits (SHORT) **************************************************************************************/ void R4FFT(int tabidx, int *x) { int order = nfftlog2Tab[tabidx]; int nfft = nfftTab[tabidx]; /* decimation in time */ BitReverse(x, tabidx); if (order & 0x1) { /* long block: order = 9, nfft = 512 */ R8FirstPass(x, nfft >> 3); /* gain 1 int bit, lose 2 GB */ R4Core(x, nfft >> 5, 8, (int *)twidTabOdd); /* gain 6 int bits, lose 2 GB */ } else { /* short block: order = 6, nfft = 64 */ R4FirstPass(x, nfft >> 2); /* gain 0 int bits, lose 2 GB */ R4Core(x, nfft >> 4, 4, (int *)twidTabEven); /* gain 4 int bits, lose 1 GB */ } }