/* Public domain FFT implementation in C by John Green */ #include <stdint.h>#include <stdlib.h>#include <math.h>#include "base.h" #ifndef M_PI#define M_PI 3.14159265358979323846#endif #define LOG2(n) (log(n) / log(2)) #define POW2(m) ((uint32_t) 1 << (m)) /* integer power of 2 for m<32 */ /* fft's with M bigger than this bust primary cache */#undef MCACHE#define MCACHE (11 - (sizeof(SPFLOAT) / 8)) /* some math constants to 40 decimal places */#define MYPI 3.141592653589793238462643383279502884197 /* pi */#define MYROOT2 1.414213562373095048801688724209698078569 /* sqrt(2) */#define MYCOSPID8 0.9238795325112867561281831893967882868224 /* cos(pi/8) */#define MYSINPID8 0.3826834323650897717284599840303988667613 /* sin(pi/8) */ /****************************************************** routines to initialize tables used by fft routines ******************************************************/ static void fftCosInit(int M, SPFLOAT *Utbl){ /* Compute Utbl, the cosine table for ffts */ /* of size (pow(2,M)/4 +1) */ /* INPUTS */ /* M = log2 of fft size */ /* OUTPUTS */ /* *Utbl = cosine table */ unsigned int fftN = POW2(M); unsigned int i1; Utbl[0] = 1.0; for (i1 = 1; i1 < fftN/4; i1++) Utbl[i1] = cos((2.0 * M_PI * (SPFLOAT)i1) / (SPFLOAT)fftN); Utbl[fftN/4] = 0.0;} void fftBRInit(int M, int16_t *BRLow){ /* Compute BRLow, the bit reversed table for ffts */ /* of size pow(2,M/2 -1) */ /* INPUTS */ /* M = log2 of fft size */ /* OUTPUTS */ /* *BRLow = bit reversed counter table */ int Mroot_1 = M / 2 - 1; int Nroot_1 = POW2(Mroot_1); int i1; int bitsum; int bitmask; int bit; for (i1 = 0; i1 < Nroot_1; i1++) { bitsum = 0; bitmask = 1; for (bit = 1; bit <= Mroot_1; bitmask <<= 1, bit++) if (i1 & bitmask) bitsum = bitsum + (Nroot_1 >> bit); BRLow[i1] = bitsum; }} /****************** parts of ffts1 ******************/ static void bitrevR2(SPFLOAT *ioptr, int M, int16_t *BRLow){ /*** bit reverse and first radix 2 stage of forward or inverse fft ***/ SPFLOAT f0r; SPFLOAT f0i; SPFLOAT f1r; SPFLOAT f1i; SPFLOAT f2r; SPFLOAT f2i; SPFLOAT f3r; SPFLOAT f3i; SPFLOAT f4r; SPFLOAT f4i; SPFLOAT f5r; SPFLOAT f5i; SPFLOAT f6r; SPFLOAT f6i; SPFLOAT f7r; SPFLOAT f7i; SPFLOAT t0r; SPFLOAT t0i; SPFLOAT t1r; SPFLOAT t1i; SPFLOAT *p0r; SPFLOAT *p1r; SPFLOAT *IOP; SPFLOAT *iolimit; int Colstart; int iCol; unsigned int posA; unsigned int posAi; unsigned int posB; unsigned int posBi; const unsigned int Nrems2 = POW2((M + 3) / 2); const unsigned int Nroot_1_ColInc = POW2(M) - Nrems2; const unsigned int Nroot_1 = POW2(M / 2 - 1) - 1; const unsigned int ColstartShift = (M + 1) / 2 + 1; posA = POW2(M); /* 1/2 of POW2(M) complexes */ posAi = posA + 1; posB = posA + 2; posBi = posB + 1; iolimit = ioptr + Nrems2; for (; ioptr < iolimit; ioptr += POW2(M / 2 + 1)) { for (Colstart = Nroot_1; Colstart >= 0; Colstart--) { iCol = Nroot_1; p0r = ioptr + Nroot_1_ColInc + BRLow[Colstart] * 4; IOP = ioptr + (Colstart << ColstartShift); p1r = IOP + BRLow[iCol] * 4; f0r = *(p0r); f0i = *(p0r + 1); f1r = *(p0r + posA); f1i = *(p0r + posAi); for (; iCol > Colstart;) { f2r = *(p0r + 2); f2i = *(p0r + (2 + 1)); f3r = *(p0r + posB); f3i = *(p0r + posBi); f4r = *(p1r); f4i = *(p1r + 1); f5r = *(p1r + posA); f5i = *(p1r + posAi); f6r = *(p1r + 2); f6i = *(p1r + (2 + 1)); f7r = *(p1r + posB); f7i = *(p1r + posBi); t0r = f0r + f1r; t0i = f0i + f1i; f1r = f0r - f1r; f1i = f0i - f1i; t1r = f2r + f3r; t1i = f2i + f3i; f3r = f2r - f3r; f3i = f2i - f3i; f0r = f4r + f5r; f0i = f4i + f5i; f5r = f4r - f5r; f5i = f4i - f5i; f2r = f6r + f7r; f2i = f6i + f7i; f7r = f6r - f7r; f7i = f6i - f7i; *(p1r) = t0r; *(p1r + 1) = t0i; *(p1r + 2) = f1r; *(p1r + (2 + 1)) = f1i; *(p1r + posA) = t1r; *(p1r + posAi) = t1i; *(p1r + posB) = f3r; *(p1r + posBi) = f3i; *(p0r) = f0r; *(p0r + 1) = f0i; *(p0r + 2) = f5r; *(p0r + (2 + 1)) = f5i; *(p0r + posA) = f2r; *(p0r + posAi) = f2i; *(p0r + posB) = f7r; *(p0r + posBi) = f7i; p0r -= Nrems2; f0r = *(p0r); f0i = *(p0r + 1); f1r = *(p0r + posA); f1i = *(p0r + posAi); iCol -= 1; p1r = IOP + BRLow[iCol] * 4; } f2r = *(p0r + 2); f2i = *(p0r + (2 + 1)); f3r = *(p0r + posB); f3i = *(p0r + posBi); t0r = f0r + f1r; t0i = f0i + f1i; f1r = f0r - f1r; f1i = f0i - f1i; t1r = f2r + f3r; t1i = f2i + f3i; f3r = f2r - f3r; f3i = f2i - f3i; *(p0r) = t0r; *(p0r + 1) = t0i; *(p0r + 2) = f1r; *(p0r + (2 + 1)) = f1i; *(p0r + posA) = t1r; *(p0r + posAi) = t1i; *(p0r + posB) = f3r; *(p0r + posBi) = f3i; } }} static void fft2pt(SPFLOAT *ioptr){ /*** RADIX 2 fft ***/ SPFLOAT f0r, f0i, f1r, f1i; SPFLOAT t0r, t0i; /* bit reversed load */ f0r = ioptr[0]; f0i = ioptr[1]; f1r = ioptr[2]; f1i = ioptr[3]; /* Butterflys */ /* f0 - - t0 f1 - 1 - f1 */ t0r = f0r + f1r; t0i = f0i + f1i; f1r = f0r - f1r; f1i = f0i - f1i; /* store result */ ioptr[0] = t0r; ioptr[1] = t0i; ioptr[2] = f1r; ioptr[3] = f1i;} static void fft4pt(SPFLOAT *ioptr){ /*** RADIX 4 fft ***/ SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i; SPFLOAT t0r, t0i, t1r, t1i; /* bit reversed load */ f0r = ioptr[0]; f0i = ioptr[1]; f1r = ioptr[4]; f1i = ioptr[5]; f2r = ioptr[2]; f2i = ioptr[3]; f3r = ioptr[6]; f3i = ioptr[7]; /* Butterflys */ /* f0 - - t0 - - f0 f1 - 1 - f1 - - f1 f2 - - f2 - 1 - f2 f3 - 1 - t1 - -i - f3 */ t0r = f0r + f1r; t0i = f0i + f1i; f1r = f0r - f1r; f1i = f0i - f1i; t1r = f2r - f3r; t1i = f2i - f3i; f2r = f2r + f3r; f2i = f2i + f3i; f0r = t0r + f2r; f0i = t0i + f2i; f2r = t0r - f2r; f2i = t0i - f2i; f3r = f1r - t1i; f3i = f1i + t1r; f1r = f1r + t1i; f1i = f1i - t1r; /* store result */ ioptr[0] = f0r; ioptr[1] = f0i; ioptr[2] = f1r; ioptr[3] = f1i; ioptr[4] = f2r; ioptr[5] = f2i; ioptr[6] = f3r; ioptr[7] = f3i;} static void fft8pt(SPFLOAT *ioptr){ /*** RADIX 8 fft ***/ SPFLOAT w0r = (SPFLOAT)(1.0 / MYROOT2); /* cos(pi/4) */ SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i; SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i; SPFLOAT t0r, t0i, t1r, t1i; const SPFLOAT Two = 2.0; /* bit reversed load */ f0r = ioptr[0]; f0i = ioptr[1]; f1r = ioptr[8]; f1i = ioptr[9]; f2r = ioptr[4]; f2i = ioptr[5]; f3r = ioptr[12]; f3i = ioptr[13]; f4r = ioptr[2]; f4i = ioptr[3]; f5r = ioptr[10]; f5i = ioptr[11]; f6r = ioptr[6]; f6i = ioptr[7]; f7r = ioptr[14]; f7i = ioptr[15]; /* Butterflys */ /* f0 - - t0 - - f0 - - f0 f1 - 1 - f1 - - f1 - - f1 f2 - - f2 - 1 - f2 - - f2 f3 - 1 - t1 - -i - f3 - - f3 f4 - - t0 - - f4 - 1 - t0 f5 - 1 - f5 - - f5 - w3 - f4 f6 - - f6 - 1 - f6 - -i - t1 f7 - 1 - t1 - -i - f7 - iw3- f6 */ t0r = f0r + f1r; t0i = f0i + f1i; f1r = f0r - f1r; f1i = f0i - f1i; t1r = f2r - f3r; t1i = f2i - f3i; f2r = f2r + f3r; f2i = f2i + f3i; f0r = t0r + f2r; f0i = t0i + f2i; f2r = t0r - f2r; f2i = t0i - f2i; f3r = f1r - t1i; f3i = f1i + t1r; f1r = f1r + t1i; f1i = f1i - t1r; t0r = f4r + f5r; t0i = f4i + f5i; f5r = f4r - f5r; f5i = f4i - f5i; t1r = f6r - f7r; t1i = f6i - f7i; f6r = f6r + f7r; f6i = f6i + f7i; f4r = t0r + f6r; f4i = t0i + f6i; f6r = t0r - f6r; f6i = t0i - f6i; f7r = f5r - t1i; f7i = f5i + t1r; f5r = f5r + t1i; f5i = f5i - t1r; t0r = f0r - f4r; t0i = f0i - f4i; f0r = f0r + f4r; f0i = f0i + f4i; t1r = f2r - f6i; t1i = f2i + f6r; f2r = f2r + f6i; f2i = f2i - f6r; f4r = f1r - f5r * w0r - f5i * w0r; f4i = f1i + f5r * w0r - f5i * w0r; f1r = f1r * Two - f4r; f1i = f1i * Two - f4i; f6r = f3r + f7r * w0r - f7i * w0r; f6i = f3i + f7r * w0r + f7i * w0r; f3r = f3r * Two - f6r; f3i = f3i * Two - f6i; /* store result */ ioptr[0] = f0r; ioptr[1] = f0i; ioptr[2] = f1r; ioptr[3] = f1i; ioptr[4] = f2r; ioptr[5] = f2i; ioptr[6] = f3r; ioptr[7] = f3i; ioptr[8] = t0r; ioptr[9] = t0i; ioptr[10] = f4r; ioptr[11] = f4i; ioptr[12] = t1r; ioptr[13] = t1i; ioptr[14] = f6r; ioptr[15] = f6i;} static void bfR2(SPFLOAT *ioptr, int M, int NDiffU){ /*** 2nd radix 2 stage ***/ unsigned int pos; unsigned int posi; unsigned int pinc; unsigned int pnext; unsigned int NSameU; unsigned int SameUCnt; SPFLOAT *pstrt; SPFLOAT *p0r, *p1r, *p2r, *p3r; SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i; SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i; pinc = NDiffU * 2; /* 2 floats per complex */ pnext = pinc * 4; pos = 2; posi = pos + 1; NSameU = POW2(M) / 4 / NDiffU; /* 4 Us at a time */ pstrt = ioptr; p0r = pstrt; p1r = pstrt + pinc; p2r = p1r + pinc; p3r = p2r + pinc; /* Butterflys */ /* f0 - - f4 f1 - 1 - f5 f2 - - f6 f3 - 1 - f7 */ /* Butterflys */ /* f0 - - f4 f1 - 1 - f5 f2 - - f6 f3 - 1 - f7 */ for (SameUCnt = NSameU; SameUCnt > 0; SameUCnt--) { f0r = *p0r; f1r = *p1r; f0i = *(p0r + 1); f1i = *(p1r + 1); f2r = *p2r; f3r = *p3r; f2i = *(p2r + 1); f3i = *(p3r + 1); f4r = f0r + f1r; f4i = f0i + f1i; f5r = f0r - f1r; f5i = f0i - f1i; f6r = f2r + f3r; f6i = f2i + f3i; f7r = f2r - f3r; f7i = f2i - f3i; *p0r = f4r; *(p0r + 1) = f4i; *p1r = f5r; *(p1r + 1) = f5i; *p2r = f6r; *(p2r + 1) = f6i; *p3r = f7r; *(p3r + 1) = f7i; f0r = *(p0r + pos); f1i = *(p1r + posi); f0i = *(p0r + posi); f1r = *(p1r + pos); f2r = *(p2r + pos); f3i = *(p3r + posi); f2i = *(p2r + posi); f3r = *(p3r + pos); f4r = f0r + f1i; f4i = f0i - f1r; f5r = f0r - f1i; f5i = f0i + f1r; Lines 1–500 of 3083. 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/* Public domain FFT implementation in C by John Green */ #include <stdint.h> #include <stdlib.h> #include <math.h> #include "base.h" #ifndef M_PI #define M_PI 3.14159265358979323846 #endif #define LOG2(n) (log(n) / log(2)) #define POW2(m) ((uint32_t) 1 << (m)) /* integer power of 2 for m<32 */ /* fft's with M bigger than this bust primary cache */ #undef MCACHE #define MCACHE (11 - (sizeof(SPFLOAT) / 8)) /* some math constants to 40 decimal places */ #define MYPI 3.141592653589793238462643383279502884197 /* pi */ #define MYROOT2 1.414213562373095048801688724209698078569 /* sqrt(2) */ #define MYCOSPID8 0.9238795325112867561281831893967882868224 /* cos(pi/8) */ #define MYSINPID8 0.3826834323650897717284599840303988667613 /* sin(pi/8) */ /***************************************************** * routines to initialize tables used by fft routines * *****************************************************/ static void fftCosInit(int M, SPFLOAT *Utbl) { /* Compute Utbl, the cosine table for ffts */ /* of size (pow(2,M)/4 +1) */ /* INPUTS */ /* M = log2 of fft size */ /* OUTPUTS */ /* *Utbl = cosine table */ unsigned int fftN = POW2(M); unsigned int i1; Utbl[0] = 1.0; for (i1 = 1; i1 < fftN/4; i1++) Utbl[i1] = cos((2.0 * M_PI * (SPFLOAT)i1) / (SPFLOAT)fftN); Utbl[fftN/4] = 0.0; } void fftBRInit(int M, int16_t *BRLow) { /* Compute BRLow, the bit reversed table for ffts */ /* of size pow(2,M/2 -1) */ /* INPUTS */ /* M = log2 of fft size */ /* OUTPUTS */ /* *BRLow = bit reversed counter table */ int Mroot_1 = M / 2 - 1; int Nroot_1 = POW2(Mroot_1); int i1; int bitsum; int bitmask; int bit; for (i1 = 0; i1 < Nroot_1; i1++) { bitsum = 0; bitmask = 1; for (bit = 1; bit <= Mroot_1; bitmask <<= 1, bit++) if (i1 & bitmask) bitsum = bitsum + (Nroot_1 >> bit); BRLow[i1] = bitsum; } } /***************** * parts of ffts1 * *****************/ static void bitrevR2(SPFLOAT *ioptr, int M, int16_t *BRLow) { /*** bit reverse and first radix 2 stage of forward or inverse fft ***/ SPFLOAT f0r; SPFLOAT f0i; SPFLOAT f1r; SPFLOAT f1i; SPFLOAT f2r; SPFLOAT f2i; SPFLOAT f3r; SPFLOAT f3i; SPFLOAT f4r; SPFLOAT f4i; SPFLOAT f5r; SPFLOAT f5i; SPFLOAT f6r; SPFLOAT f6i; SPFLOAT f7r; SPFLOAT f7i; SPFLOAT t0r; SPFLOAT t0i; SPFLOAT t1r; SPFLOAT t1i; SPFLOAT *p0r; SPFLOAT *p1r; SPFLOAT *IOP; SPFLOAT *iolimit; int Colstart; int iCol; unsigned int posA; unsigned int posAi; unsigned int posB; unsigned int posBi; const unsigned int Nrems2 = POW2((M + 3) / 2); const unsigned int Nroot_1_ColInc = POW2(M) - Nrems2; const unsigned int Nroot_1 = POW2(M / 2 - 1) - 1; const unsigned int ColstartShift = (M + 1) / 2 + 1; posA = POW2(M); /* 1/2 of POW2(M) complexes */ posAi = posA + 1; posB = posA + 2; posBi = posB + 1; iolimit = ioptr + Nrems2; for (; ioptr < iolimit; ioptr += POW2(M / 2 + 1)) { for (Colstart = Nroot_1; Colstart >= 0; Colstart--) { iCol = Nroot_1; p0r = ioptr + Nroot_1_ColInc + BRLow[Colstart] * 4; IOP = ioptr + (Colstart << ColstartShift); p1r = IOP + BRLow[iCol] * 4; f0r = *(p0r); f0i = *(p0r + 1); f1r = *(p0r + posA); f1i = *(p0r + posAi); for (; iCol > Colstart;) { f2r = *(p0r + 2); f2i = *(p0r + (2 + 1)); f3r = *(p0r + posB); f3i = *(p0r + posBi); f4r = *(p1r); f4i = *(p1r + 1); f5r = *(p1r + posA); f5i = *(p1r + posAi); f6r = *(p1r + 2); f6i = *(p1r + (2 + 1)); f7r = *(p1r + posB); f7i = *(p1r + posBi); t0r = f0r + f1r; t0i = f0i + f1i; f1r = f0r - f1r; f1i = f0i - f1i; t1r = f2r + f3r; t1i = f2i + f3i; f3r = f2r - f3r; f3i = f2i - f3i; f0r = f4r + f5r; f0i = f4i + f5i; f5r = f4r - f5r; f5i = f4i - f5i; f2r = f6r + f7r; f2i = f6i + f7i; f7r = f6r - f7r; f7i = f6i - f7i; *(p1r) = t0r; *(p1r + 1) = t0i; *(p1r + 2) = f1r; *(p1r + (2 + 1)) = f1i; *(p1r + posA) = t1r; *(p1r + posAi) = t1i; *(p1r + posB) = f3r; *(p1r + posBi) = f3i; *(p0r) = f0r; *(p0r + 1) = f0i; *(p0r + 2) = f5r; *(p0r + (2 + 1)) = f5i; *(p0r + posA) = f2r; *(p0r + posAi) = f2i; *(p0r + posB) = f7r; *(p0r + posBi) = f7i; p0r -= Nrems2; f0r = *(p0r); f0i = *(p0r + 1); f1r = *(p0r + posA); f1i = *(p0r + posAi); iCol -= 1; p1r = IOP + BRLow[iCol] * 4; } f2r = *(p0r + 2); f2i = *(p0r + (2 + 1)); f3r = *(p0r + posB); f3i = *(p0r + posBi); t0r = f0r + f1r; t0i = f0i + f1i; f1r = f0r - f1r; f1i = f0i - f1i; t1r = f2r + f3r; t1i = f2i + f3i; f3r = f2r - f3r; f3i = f2i - f3i; *(p0r) = t0r; *(p0r + 1) = t0i; *(p0r + 2) = f1r; *(p0r + (2 + 1)) = f1i; *(p0r + posA) = t1r; *(p0r + posAi) = t1i; *(p0r + posB) = f3r; *(p0r + posBi) = f3i; } } } static void fft2pt(SPFLOAT *ioptr) { /*** RADIX 2 fft ***/ SPFLOAT f0r, f0i, f1r, f1i; SPFLOAT t0r, t0i; /* bit reversed load */ f0r = ioptr[0]; f0i = ioptr[1]; f1r = ioptr[2]; f1i = ioptr[3]; /* Butterflys */ /* f0 - - t0 f1 - 1 - f1 */ t0r = f0r + f1r; t0i = f0i + f1i; f1r = f0r - f1r; f1i = f0i - f1i; /* store result */ ioptr[0] = t0r; ioptr[1] = t0i; ioptr[2] = f1r; ioptr[3] = f1i; } static void fft4pt(SPFLOAT *ioptr) { /*** RADIX 4 fft ***/ SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i; SPFLOAT t0r, t0i, t1r, t1i; /* bit reversed load */ f0r = ioptr[0]; f0i = ioptr[1]; f1r = ioptr[4]; f1i = ioptr[5]; f2r = ioptr[2]; f2i = ioptr[3]; f3r = ioptr[6]; f3i = ioptr[7]; /* Butterflys */ /* f0 - - t0 - - f0 f1 - 1 - f1 - - f1 f2 - - f2 - 1 - f2 f3 - 1 - t1 - -i - f3 */ t0r = f0r + f1r; t0i = f0i + f1i; f1r = f0r - f1r; f1i = f0i - f1i; t1r = f2r - f3r; t1i = f2i - f3i; f2r = f2r + f3r; f2i = f2i + f3i; f0r = t0r + f2r; f0i = t0i + f2i; f2r = t0r - f2r; f2i = t0i - f2i; f3r = f1r - t1i; f3i = f1i + t1r; f1r = f1r + t1i; f1i = f1i - t1r; /* store result */ ioptr[0] = f0r; ioptr[1] = f0i; ioptr[2] = f1r; ioptr[3] = f1i; ioptr[4] = f2r; ioptr[5] = f2i; ioptr[6] = f3r; ioptr[7] = f3i; } static void fft8pt(SPFLOAT *ioptr) { /*** RADIX 8 fft ***/ SPFLOAT w0r = (SPFLOAT)(1.0 / MYROOT2); /* cos(pi/4) */ SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i; SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i; SPFLOAT t0r, t0i, t1r, t1i; const SPFLOAT Two = 2.0; /* bit reversed load */ f0r = ioptr[0]; f0i = ioptr[1]; f1r = ioptr[8]; f1i = ioptr[9]; f2r = ioptr[4]; f2i = ioptr[5]; f3r = ioptr[12]; f3i = ioptr[13]; f4r = ioptr[2]; f4i = ioptr[3]; f5r = ioptr[10]; f5i = ioptr[11]; f6r = ioptr[6]; f6i = ioptr[7]; f7r = ioptr[14]; f7i = ioptr[15]; /* Butterflys */ /* f0 - - t0 - - f0 - - f0 f1 - 1 - f1 - - f1 - - f1 f2 - - f2 - 1 - f2 - - f2 f3 - 1 - t1 - -i - f3 - - f3 f4 - - t0 - - f4 - 1 - t0 f5 - 1 - f5 - - f5 - w3 - f4 f6 - - f6 - 1 - f6 - -i - t1 f7 - 1 - t1 - -i - f7 - iw3- f6 */ t0r = f0r + f1r; t0i = f0i + f1i; f1r = f0r - f1r; f1i = f0i - f1i; t1r = f2r - f3r; t1i = f2i - f3i; f2r = f2r + f3r; f2i = f2i + f3i; f0r = t0r + f2r; f0i = t0i + f2i; f2r = t0r - f2r; f2i = t0i - f2i; f3r = f1r - t1i; f3i = f1i + t1r; f1r = f1r + t1i; f1i = f1i - t1r; t0r = f4r + f5r; t0i = f4i + f5i; f5r = f4r - f5r; f5i = f4i - f5i; t1r = f6r - f7r; t1i = f6i - f7i; f6r = f6r + f7r; f6i = f6i + f7i; f4r = t0r + f6r; f4i = t0i + f6i; f6r = t0r - f6r; f6i = t0i - f6i; f7r = f5r - t1i; f7i = f5i + t1r; f5r = f5r + t1i; f5i = f5i - t1r; t0r = f0r - f4r; t0i = f0i - f4i; f0r = f0r + f4r; f0i = f0i + f4i; t1r = f2r - f6i; t1i = f2i + f6r; f2r = f2r + f6i; f2i = f2i - f6r; f4r = f1r - f5r * w0r - f5i * w0r; f4i = f1i + f5r * w0r - f5i * w0r; f1r = f1r * Two - f4r; f1i = f1i * Two - f4i; f6r = f3r + f7r * w0r - f7i * w0r; f6i = f3i + f7r * w0r + f7i * w0r; f3r = f3r * Two - f6r; f3i = f3i * Two - f6i; /* store result */ ioptr[0] = f0r; ioptr[1] = f0i; ioptr[2] = f1r; ioptr[3] = f1i; ioptr[4] = f2r; ioptr[5] = f2i; ioptr[6] = f3r; ioptr[7] = f3i; ioptr[8] = t0r; ioptr[9] = t0i; ioptr[10] = f4r; ioptr[11] = f4i; ioptr[12] = t1r; ioptr[13] = t1i; ioptr[14] = f6r; ioptr[15] = f6i; } static void bfR2(SPFLOAT *ioptr, int M, int NDiffU) { /*** 2nd radix 2 stage ***/ unsigned int pos; unsigned int posi; unsigned int pinc; unsigned int pnext; unsigned int NSameU; unsigned int SameUCnt; SPFLOAT *pstrt; SPFLOAT *p0r, *p1r, *p2r, *p3r; SPFLOAT f0r, f0i, f1r, f1i, f2r, f2i, f3r, f3i; SPFLOAT f4r, f4i, f5r, f5i, f6r, f6i, f7r, f7i; pinc = NDiffU * 2; /* 2 floats per complex */ pnext = pinc * 4; pos = 2; posi = pos + 1; NSameU = POW2(M) / 4 / NDiffU; /* 4 Us at a time */ pstrt = ioptr; p0r = pstrt; p1r = pstrt + pinc; p2r = p1r + pinc; p3r = p2r + pinc; /* Butterflys */ /* f0 - - f4 f1 - 1 - f5 f2 - - f6 f3 - 1 - f7 */ /* Butterflys */ /* f0 - - f4 f1 - 1 - f5 f2 - - f6 f3 - 1 - f7 */ for (SameUCnt = NSameU; SameUCnt > 0; SameUCnt--) { f0r = *p0r; f1r = *p1r; f0i = *(p0r + 1); f1i = *(p1r + 1); f2r = *p2r; f3r = *p3r; f2i = *(p2r + 1); f3i = *(p3r + 1); f4r = f0r + f1r; f4i = f0i + f1i; f5r = f0r - f1r; f5i = f0i - f1i; f6r = f2r + f3r; f6i = f2i + f3i; f7r = f2r - f3r; f7i = f2i - f3i; *p0r = f4r; *(p0r + 1) = f4i; *p1r = f5r; *(p1r + 1) = f5i; *p2r = f6r; *(p2r + 1) = f6i; *p3r = f7r; *(p3r + 1) = f7i; f0r = *(p0r + pos); f1i = *(p1r + posi); f0i = *(p0r + posi); f1r = *(p1r + pos); f2r = *(p2r + pos); f3i = *(p3r + posi); f2i = *(p2r + posi); f3r = *(p3r + pos); f4r = f0r + f1i; f4i = f0i - f1r; f5r = f0r - f1i; f5i = f0i + f1r;