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Diffstat (limited to 'sc4pd/source/fftlib.c')
| -rw-r--r-- | sc4pd/source/fftlib.c | 3306 |
1 files changed, 3306 insertions, 0 deletions
diff --git a/sc4pd/source/fftlib.c b/sc4pd/source/fftlib.c new file mode 100644 index 0000000..4bbdcb1 --- /dev/null +++ b/sc4pd/source/fftlib.c @@ -0,0 +1,3306 @@ +/* FFT library */ +/* Library of in-place fast fourier transforms */ +/* Forward and inverse complex transforms */ +/* and real forward transform */ +/* Optimized for RISC processors with many registers */ +/* Version 1.1 John Green NUWC New London CT January 96 */ +/* Version 1.1 renamed as fftlib from fftbig */ +/* Version 1.1 removed (float *)((char *) ptr) optimization */ +/* Version 1.0 John Green NUWC New London CT December 95 */ +/* (John Green) green_jt@vsdec.nl.nuwc.navy.mil */ +/* green_jt@vsdec.nl.nuwc.navy.mil */ + +#include <math.h> +#include "fftlib.h" + +#define MAXMROOT 9 /* 2^(MAXMROOT-1) = # of elements in BRcnt */ + +/* Bit reversed counter */ +static const unsigned char BRcnt[256] = { + 0, 128, 64, 192, 32, 160, 96, 224, 16, 144, 80, 208, + 48, 176, 112, 240, 8, 136, 72, 200, 40, 168, 104, 232, + 24, 152, 88, 216, 56, 184, 120, 248, 4, 132, 68, 196, + 36, 164, 100, 228, 20, 148, 84, 212, 52, 180, 116, 244, + 12, 140, 76, 204, 44, 172, 108, 236, 28, 156, 92, 220, + 60, 188, 124, 252, 2, 130, 66, 194, 34, 162, 98, 226, + 18, 146, 82, 210, 50, 178, 114, 242, 10, 138, 74, 202, + 42, 170, 106, 234, 26, 154, 90, 218, 58, 186, 122, 250, + 6, 134, 70, 198, 38, 166, 102, 230, 22, 150, 86, 214, + 54, 182, 118, 246, 14, 142, 78, 206, 46, 174, 110, 238, + 30, 158, 94, 222, 62, 190, 126, 254, 1, 129, 65, 193, + 33, 161, 97, 225, 17, 145, 81, 209, 49, 177, 113, 241, + 9, 137, 73, 201, 41, 169, 105, 233, 25, 153, 89, 217, + 57, 185, 121, 249, 5, 133, 69, 197, 37, 165, 101, 229, + 21, 149, 85, 213, 53, 181, 117, 245, 13, 141, 77, 205, + 45, 173, 109, 237, 29, 157, 93, 221, 61, 189, 125, 253, + 3, 131, 67, 195, 35, 163, 99, 227, 19, 147, 83, 211, + 51, 179, 115, 243, 11, 139, 75, 203, 43, 171, 107, 235, + 27, 155, 91, 219, 59, 187, 123, 251, 7, 135, 71, 199, + 39, 167, 103, 231, 23, 151, 87, 215, 55, 183, 119, 247, + 15, 143, 79, 207, 47, 175, 111, 239, 31, 159, 95, 223, + 63, 191, 127, 255 }; + +/* Table of powers of 2 */ +static const long Ntbl[21] = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, + 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576}; + +long FFTInit(long *fftMptr, long fftN, float *Utbl){ +/* Compute cosine table and check size for complex ffts */ +/* INPUTS */ +/* fftN = size of fft */ +/* OUTPUTS */ +/* *fftMptr = log2 of fft size */ +/* *Utbl = cosine table with fftN/4 + 1 entries (angles = 0 to pi/2 inclusive) */ +/* RETURNS */ +/* 1 if fftN is invalid, 0 otherwise */ +long i1, ErrVal; +ErrVal = 0; +*fftMptr = (long)(log(fftN)/log(2.0) + 0.5); +if ((*fftMptr >= 3) & (*fftMptr <= 19) & (int)(pow(2,*fftMptr)+.5) == fftN) + for (i1 = 0; i1 <= fftN/4; i1++) + Utbl[i1] = cos( ( 3.1415926535897932384626433832795 * 2.0 * i1 ) / fftN ); +else + ErrVal = 1; +return ErrVal; +} + +long rFFTInit(long *fftMptr, long fftN, float *Utbl){ +/* Compute cosine table and check size for a real input fft */ +/* INPUTS */ +/* fftN = size of fft */ +/* OUTPUTS */ +/* *fftMptr = log2 of fft size */ +/* *Utbl = cosine table with fftN/4 + 1 entries (angles = 0 to pi/2 inclusive) */ +/* RETURNS */ +/* 1 if fftN is invalid, 0 otherwise */ +long i1, ErrVal; +ErrVal = 0; +*fftMptr = (long)(log(fftN)/log(2.0) + 0.5); +if ((*fftMptr >= 4) & (*fftMptr <= 20) & (int)(pow(2,*fftMptr)+.5) == fftN) + + for (i1 = 0; i1 <= fftN/4; i1++) + Utbl[i1] = cos( ( 3.1415926535897932384626433832795 * 2.0 * i1 ) / fftN ); +else + ErrVal = 1; +return ErrVal; +} + +void ffts(float *ioptr, long M, long Rows, float *Utbl){ +/* Compute in-place complex fft on the rows of the input array */ +/* INPUTS */ +/* M = log2 of fft size */ +/* *ioptr = input data array */ +/* *Utbl = cosine table */ +/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */ +/* OUTPUTS */ +/* *ioptr = output data array */ + +long Flyinc; +long FlyOffsetA; +long FlyOffsetAIm; +long FlyOffsetB; +long FlyOffsetBIm; +long NsameU1; +long NsameU2; +long NsameU4; +long diffUcnt; +long LoopCnt; + +float scale; +float fly0r; +float fly0i; +float fly1r; +float fly1i; +float fly2r; +float fly2i; +float fly3r; +float fly3i; +float fly4r; +float fly4i; +float fly5r; +float fly5i; +float fly6r; +float fly6i; +float fly7r; +float fly7i; +float U0r; +float U0i; +float U1r; +float U1i; +float U2r; +float U2i; +float U3r; +float U3i; +float t0r; +float t0i; +float t1r; +float t1i; + +float *fly0P; +float *fly1P; +float *fly2P; +float *fly3P; + +float *U0rP; +float *U0iP; +float *U1rP; +float *U1iP; +float *U2rP; +float *U2iP; +float *IOP; +long U3offset; + +long stage; +long NdiffU; +long LoopN; + +const long BRshift = MAXMROOT - (M>>1); +const long Nrems2 = Ntbl[M-(M>>1)+1]; +const long Nroot_1_ColInc = (Ntbl[M-1]-Ntbl[M-(M>>1)])*2; + +scale = 2.0; +for (;Rows>0;Rows--){ + +FlyOffsetA = Ntbl[M] * (2/2); +FlyOffsetAIm = FlyOffsetA + 1; +FlyOffsetB = FlyOffsetA + 2; +FlyOffsetBIm = FlyOffsetB + 1; + +/* BitrevR2 ** bit reverse and first radix 2 stage ******/ + +for (stage = 0; stage < Ntbl[M-(M>>1)]*2; stage += Ntbl[M>>1]*2){ + for (LoopN = (Ntbl[(M>>1)-1]-1); LoopN >= 0; LoopN--){ + LoopCnt = (Ntbl[(M>>1)-1]-1); + fly0P = ioptr+ Nroot_1_ColInc + ((int)BRcnt[LoopN] >> BRshift)*(2*2) + stage; + IOP = ioptr + (LoopN<<(M+1)/2) * 2 + stage; + fly1P = IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2); + fly0r = *(fly0P); + fly0i = *(fly0P+1); + fly1r = *(fly0P+FlyOffsetA); + fly1i = *(fly0P+FlyOffsetAIm); + for (; LoopCnt > LoopN;){ + fly2r = *(fly0P+2); + fly2i = *(fly0P+(2+1)); + fly3r = *(fly0P+FlyOffsetB); + fly3i = *(fly0P+FlyOffsetBIm); + fly4r = *(fly1P); + fly4i = *(fly1P+1); + fly5r = *(fly1P+FlyOffsetA); + fly5i = *(fly1P+FlyOffsetAIm); + fly6r = *(fly1P+2); + fly6i = *(fly1P+(2+1)); + fly7r = *(fly1P+FlyOffsetB); + fly7i = *(fly1P+FlyOffsetBIm); + + t0r = fly0r + fly1r; + t0i = fly0i + fly1i; + fly1r = fly0r - fly1r; + fly1i = fly0i - fly1i; + t1r = fly2r + fly3r; + t1i = fly2i + fly3i; + fly3r = fly2r - fly3r; + fly3i = fly2i - fly3i; + fly0r = fly4r + fly5r; + fly0i = fly4i + fly5i; + fly5r = fly4r - fly5r; + fly5i = fly4i - fly5i; + fly2r = fly6r + fly7r; + fly2i = fly6i + fly7i; + fly7r = fly6r - fly7r; + fly7i = fly6i - fly7i; + + *(fly1P) = t0r; + *(fly1P+1) = t0i; + *(fly1P+2) = fly1r; + *(fly1P+(2+1)) = fly1i; + *(fly1P+FlyOffsetA) = t1r; + *(fly1P+FlyOffsetAIm) = t1i; + *(fly1P+FlyOffsetB) = fly3r; + *(fly1P+FlyOffsetBIm) = fly3i; + *(fly0P) = fly0r; + *(fly0P+1) = fly0i; + *(fly0P+2) = fly5r; + *(fly0P+(2+1)) = fly5i; + *(fly0P+FlyOffsetA) = fly2r; + *(fly0P+FlyOffsetAIm) = fly2i; + *(fly0P+FlyOffsetB) = fly7r; + *(fly0P+FlyOffsetBIm) = fly7i; + + fly0P -= Nrems2; + fly0r = *(fly0P); + fly0i = *(fly0P+1); + fly1r = *(fly0P+FlyOffsetA); + fly1i = *(fly0P+FlyOffsetAIm); + LoopCnt -= 1; + fly1P = (IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2)); + }; + fly2r = *(fly0P+2); + fly2i = *(fly0P+(2+1)); + fly3r = *(fly0P+FlyOffsetB); + fly3i = *(fly0P+FlyOffsetBIm); + + t0r = fly0r + fly1r; + t0i = fly0i + fly1i; + fly1r = fly0r - fly1r; + fly1i = fly0i - fly1i; + t1r = fly2r + fly3r; + t1i = fly2i + fly3i; + fly3r = fly2r - fly3r; + fly3i = fly2i - fly3i; + + *(fly0P) = t0r; + *(fly0P+1) = t0i; + *(fly0P+2) = fly1r; + *(fly0P+(2+1)) = fly1i; + *(fly0P+FlyOffsetA) = t1r; + *(fly0P+FlyOffsetAIm) = t1i; + *(fly0P+FlyOffsetB) = fly3r; + *(fly0P+FlyOffsetBIm) = fly3i; + + }; +}; + + + +/**** FFTC **************/ + +NdiffU = 2; +Flyinc = (NdiffU); + +NsameU4 = Ntbl[M]/4; +LoopN = Ntbl[M-3]; + +stage = ((M-1)/3); +if ( (M-1-(stage * 3)) != 0 ){ + FlyOffsetA = Flyinc << 2; + FlyOffsetB = FlyOffsetA << 1; + FlyOffsetAIm = FlyOffsetA + 1; + FlyOffsetBIm = FlyOffsetB + 1; + if ( (M-1-(stage * 3)) == 1 ){ + /* 1 radix 2 stage */ + + IOP = ioptr; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + /* Butterflys */ + /* + t0 - - t0 + t1 - - t1 + f2 - 1- f5 + f1 - -i- f7 + f4 - - f4 + f0 - - f0 + f6 - 1- f2 + f3 - -i- f1 + */ + + for (LoopCnt = LoopN; LoopCnt > 0 ; LoopCnt--){ + t0r = *(fly0P); + t0i = *(fly0P + 1); + t1r = *(fly1P); + t1i = *(fly1P + 1); + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly1r = *(fly3P); + fly1i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly0r = *(fly1P + FlyOffsetA); + fly0i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly3r = *(fly3P + FlyOffsetA); + fly3i = *(fly3P + FlyOffsetAIm); + + fly5r = t0r - fly2r; + fly5i = t0i - fly2i; + t0r = t0r + fly2r; + t0i = t0i + fly2i; + + fly7r = t1r - fly1i; + fly7i = t1i + fly1r; + t1r = t1r + fly1i; + t1i = t1i - fly1r; + + fly2r = fly4r - fly6r; + fly2i = fly4i - fly6i; + fly4r = fly4r + fly6r; + fly4i = fly4i + fly6i; + + fly1r = fly0r - fly3i; + fly1i = fly0i + fly3r; + fly0r = fly0r + fly3i; + fly0i = fly0i - fly3r; + + *(fly2P) = fly5r; + *(fly2P + 1) = fly5i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + *(fly0P + FlyOffsetA) = fly4r; + *(fly0P + FlyOffsetAIm) = fly4i; + *(fly3P + FlyOffsetA) = fly1r; + *(fly3P + FlyOffsetAIm) = fly1i; + *(fly1P + FlyOffsetA) = fly0r; + *(fly1P + FlyOffsetAIm) = fly0i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + }; + + NsameU4 >>= 1; + LoopN >>= 1; + NdiffU <<= 1; + Flyinc = Flyinc << 1; + } + else{ + /* 1 radix 4 stage */ + IOP = ioptr; + + U3r = 0.7071067811865475244008443621; /* sqrt(0.5); */ + U3i = U3r; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + /* Butterflys */ + /* + t0 - - t0 - - t0 + t1 - - t1 - - t1 + f2 - 1- f5 - - f5 + f1 - -i- f7 - - f7 + f4 - - f4 - 1- f6 + f0 - - f0 -U3 - f3 + f6 - 1- f2 - -i- f4 + f3 - -i- f1 -U3a- f2 + */ + + for (LoopCnt = LoopN; LoopCnt > 0 ; LoopCnt--){ + t0r = *(fly0P); + t0i = *(fly0P + 1); + t1r = *(fly1P); + t1i = *(fly1P + 1); + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly1r = *(fly3P); + fly1i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly0r = *(fly1P + FlyOffsetA); + fly0i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly3r = *(fly3P + FlyOffsetA); + fly3i = *(fly3P + FlyOffsetAIm); + + fly5r = t0r - fly2r; + fly5i = t0i - fly2i; + t0r = t0r + fly2r; + t0i = t0i + fly2i; + + fly7r = t1r - fly1i; + fly7i = t1i + fly1r; + t1r = t1r + fly1i; + t1i = t1i - fly1r; + + fly2r = fly4r - fly6r; + fly2i = fly4i - fly6i; + fly4r = fly4r + fly6r; + fly4i = fly4i + fly6i; + + fly1r = fly0r - fly3i; + fly1i = fly0i + fly3r; + fly0r = fly0r + fly3i; + fly0i = fly0i - fly3r; + + + fly6r = t0r - fly4r; + fly6i = t0i - fly4i; + t0r = t0r + fly4r; + t0i = t0i + fly4i; + + fly3r = fly5r - fly2i; + fly3i = fly5i + fly2r; + fly5r = fly5r + fly2i; + fly5i = fly5i - fly2r; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r - U3i * fly0i; + fly4i = t1i + U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly2r = fly7r + U3i * fly1r; + fly2r = fly2r - U3r * fly1i; + fly2i = fly7i + U3r * fly1r; + fly2i = fly2i + U3i * fly1i; + fly7r = scale * fly7r - fly2r; + fly7i = scale * fly7i - fly2i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly2P + FlyOffsetA) = fly3r; + *(fly2P + FlyOffsetAIm) = fly3i; + *(fly2P) = fly5r; + *(fly2P + 1) = fly5i; + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + *(fly3P + FlyOffsetA) = fly2r; + *(fly3P + FlyOffsetAIm) = fly2i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + + }; + + NsameU4 >>= 2; + LoopN >>= 2; + NdiffU <<= 2; + Flyinc = Flyinc << 2; + }; +}; + +NsameU2 = NsameU4 >> 1; +NsameU1 = NsameU2 >> 1; +Flyinc <<= 1; +FlyOffsetA = Flyinc << 2; +FlyOffsetB = FlyOffsetA << 1; +FlyOffsetAIm = FlyOffsetA + 1; +FlyOffsetBIm = FlyOffsetB + 1; +LoopN >>= 1; +/* ****** RADIX 8 Stages */ +for (stage = stage<<1; stage > 0 ; stage--){ + + /* an fft stage is done in two parts to ease use of the single quadrant cos table */ + +/* fftcalc1(iobuf, Utbl, N, NdiffU, LoopN); */ + if(!(stage&1)){ + U0rP = &Utbl[0]; + U0iP = &Utbl[Ntbl[M-2]]; + U1rP = U0rP; + U1iP = U0iP; + U2rP = U0rP; + U2iP = U0iP; + U3offset = (Ntbl[M]) / 8; + + IOP = ioptr; + + U0r = *U0rP, + U0i = *U0iP; + U1r = *U1rP, + U1i = *U1iP; + U2r = *U2rP, + U2i = *U2iP; + U3r = *( U2rP + U3offset); + U3i = *( U2iP - U3offset); + } + + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + for (diffUcnt = (NdiffU)>>1; diffUcnt != 0; diffUcnt--){ + + /* Butterflys */ + /* + f0 - - t0 - - t0 - - t0 + f1 -U0 - t1 - - t1 - - t1 + f2 - - f2 -U1 - f5 - - f3 + f3 -U0 - f1 -U1a- f7 - - f7 + f4 - - f4 - - f4 -U2 - f6 + f5 -U0 - f0 - - f0 -U3 - f4 + f6 - - f6 -U1 - f2 -U2a- f2 + f7 -U0 - f3 -U1a- f1 -U3a- f5 + */ + + fly0r = *(IOP); + fly0i = *(IOP+1); + fly1r = *(fly1P); + fly1i = *(fly1P+1); + + for (LoopCnt = LoopN-1; LoopCnt > 0 ; LoopCnt--){ + + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly3r = *(fly3P); + fly3i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly5r = *(fly1P + FlyOffsetA); + fly5i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly7r = *(fly3P + FlyOffsetA); + fly7i = *(fly3P + FlyOffsetAIm); + + t1r = fly0r - U0r * fly1r; + t1r = t1r - U0i * fly1i; + t1i = fly0i + U0i * fly1r; + t1i = t1i - U0r * fly1i; + t0r = scale * fly0r - t1r; + t0i = scale * fly0i - t1i; + + fly1r = fly2r - U0r * fly3r; + fly1r = fly1r - U0i * fly3i; + fly1i = fly2i + U0i * fly3r; + fly1i = fly1i - U0r * fly3i; + fly2r = scale * fly2r - fly1r; + fly2i = scale * fly2i - fly1i; + + fly0r = fly4r - U0r * fly5r; + fly0r = fly0r - U0i * fly5i; + fly0i = fly4i + U0i * fly5r; + fly0i = fly0i - U0r * fly5i; + fly4r = scale * fly4r - fly0r; + fly4i = scale * fly4i - fly0i; + + fly3r = fly6r - U0r * fly7r; + fly3r = fly3r - U0i * fly7i; + fly3i = fly6i + U0i * fly7r; + fly3i = fly3i - U0r * fly7i; + fly6r = scale * fly6r - fly3r; + fly6i = scale * fly6i - fly3i; + + + fly5r = t0r - U1r * fly2r; + fly5r = fly5r - U1i * fly2i; + fly5i = t0i + U1i * fly2r; + fly5i = fly5i - U1r * fly2i; + t0r = scale * t0r - fly5r; + t0i = scale * t0i - fly5i; + + fly7r = t1r + U1i * fly1r; + fly7r = fly7r - U1r * fly1i; + fly7i = t1i + U1r * fly1r; + fly7i = fly7i + U1i * fly1i; + t1r = scale * t1r - fly7r; + t1i = scale * t1i - fly7i; + + fly2r = fly4r - U1r * fly6r; + fly2r = fly2r - U1i * fly6i; + fly2i = fly4i + U1i * fly6r; + fly2i = fly2i - U1r * fly6i; + fly4r = scale * fly4r - fly2r; + fly4i = scale * fly4i - fly2i; + + fly1r = fly0r + U1i * fly3r; + fly1r = fly1r - U1r * fly3i; + fly1i = fly0i + U1r * fly3r; + fly1i = fly1i + U1i * fly3i; + fly0r = scale * fly0r - fly1r; + fly0i = scale * fly0i - fly1i; + + fly6r = t0r - U2r * fly4r; + fly6r = fly6r - U2i * fly4i; + fly6i = t0i + U2i * fly4r; + fly6i = fly6i - U2r * fly4i; + t0r = scale * t0r - fly6r; + t0i = scale * t0i - fly6i; + + fly3r = fly5r - U2i * fly2r; + fly3r = fly3r + U2r * fly2i; + fly3i = fly5i - U2r * fly2r; + fly3i = fly3i - U2i * fly2i; + fly2r = scale * fly5r - fly3r; + fly2i = scale * fly5i - fly3i; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r - U3i * fly0i; + fly4i = t1i + U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly5r = fly7r + U3i * fly1r; + fly5r = fly5r - U3r * fly1i; + fly5i = fly7i + U3r * fly1r; + fly5i = fly5i + U3i * fly1i; + fly7r = scale * fly7r - fly5r; + fly7i = scale * fly7i - fly5i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly2P) = fly3r; + *(fly2P + 1) = fly3i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + + fly0r = *(fly0P + FlyOffsetB); + fly0i = *(fly0P + FlyOffsetBIm); + + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + + fly1r = *(fly1P + FlyOffsetB); + fly1i = *(fly1P + FlyOffsetBIm); + + *(fly3P + FlyOffsetA) = fly5r; + *(fly3P + FlyOffsetAIm) = fly5i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + }; + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly3r = *(fly3P); + fly3i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly5r = *(fly1P + FlyOffsetA); + fly5i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly7r = *(fly3P + FlyOffsetA); + fly7i = *(fly3P + FlyOffsetAIm); + + t1r = fly0r - U0r * fly1r; + t1r = t1r - U0i * fly1i; + t1i = fly0i + U0i * fly1r; + t1i = t1i - U0r * fly1i; + t0r = scale * fly0r - t1r; + t0i = scale * fly0i - t1i; + + fly1r = fly2r - U0r * fly3r; + fly1r = fly1r - U0i * fly3i; + fly1i = fly2i + U0i * fly3r; + fly1i = fly1i - U0r * fly3i; + fly2r = scale * fly2r - fly1r; + fly2i = scale * fly2i - fly1i; + + fly0r = fly4r - U0r * fly5r; + fly0r = fly0r - U0i * fly5i; + fly0i = fly4i + U0i * fly5r; + fly0i = fly0i - U0r * fly5i; + fly4r = scale * fly4r - fly0r; + fly4i = scale * fly4i - fly0i; + + fly3r = fly6r - U0r * fly7r; + fly3r = fly3r - U0i * fly7i; + fly3i = fly6i + U0i * fly7r; + fly3i = fly3i - U0r * fly7i; + fly6r = scale * fly6r - fly3r; + fly6i = scale * fly6i - fly3i; + + fly5r = t0r - U1r * fly2r; + fly5r = fly5r - U1i * fly2i; + fly5i = t0i + U1i * fly2r; + fly5i = fly5i - U1r * fly2i; + t0r = scale * t0r - fly5r; + t0i = scale * t0i - fly5i; + + fly7r = t1r + U1i * fly1r; + fly7r = fly7r - U1r * fly1i; + fly7i = t1i + U1r * fly1r; + fly7i = fly7i + U1i * fly1i; + t1r = scale * t1r - fly7r; + t1i = scale * t1i - fly7i; + + fly2r = fly4r - U1r * fly6r; + fly2r = fly2r - U1i * fly6i; + fly2i = fly4i + U1i * fly6r; + fly2i = fly2i - U1r * fly6i; + fly4r = scale * fly4r - fly2r; + fly4i = scale * fly4i - fly2i; + + fly1r = fly0r + U1i * fly3r; + fly1r = fly1r - U1r * fly3i; + fly1i = fly0i + U1r * fly3r; + fly1i = fly1i + U1i * fly3i; + fly0r = scale * fly0r - fly1r; + fly0i = scale * fly0i - fly1i; + + U0i = *(U0iP = (U0iP - NsameU4)); + U0r = *(U0rP = (U0rP + NsameU4)); + U1r = *(U1rP = (U1rP + NsameU2)); + U1i = *(U1iP = (U1iP - NsameU2)); + if(stage&1) + U0r = -U0r; + + fly6r = t0r - U2r * fly4r; + fly6r = fly6r - U2i * fly4i; + fly6i = t0i + U2i * fly4r; + fly6i = fly6i - U2r * fly4i; + t0r = scale * t0r - fly6r; + t0i = scale * t0i - fly6i; + + fly3r = fly5r - U2i * fly2r; + fly3r = fly3r + U2r * fly2i; + fly3i = fly5i - U2r * fly2r; + fly3i = fly3i - U2i * fly2i; + fly2r = scale * fly5r - fly3r; + fly2i = scale * fly5i - fly3i; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r - U3i * fly0i; + fly4i = t1i + U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly5r = fly7r + U3i * fly1r; + fly5r = fly5r - U3r * fly1i; + fly5i = fly7i + U3r * fly1r; + fly5i = fly5i + U3i * fly1i; + fly7r = scale * fly7r - fly5r; + fly7i = scale * fly7i - fly5i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + + U2r = *(U2rP = (U2rP + NsameU1)); + U2i = *(U2iP = (U2iP - NsameU1)); + + *(fly2P) = fly3r; + *(fly2P + 1) = fly3i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + + U3r = *( U2rP + U3offset); + U3i = *( U2iP - U3offset); + + *(fly3P + FlyOffsetA) = fly5r; + *(fly3P + FlyOffsetAIm) = fly5i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + IOP = IOP + 2; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + }; + NsameU4 = -NsameU4; + + if(stage&1){ + LoopN >>= 3; + NsameU1 >>= 3; + NsameU2 >>= 3; + NsameU4 >>= 3; + NdiffU <<= 3; + Flyinc <<= 3; + FlyOffsetA <<= 3; + FlyOffsetB <<= 3; + FlyOffsetAIm = FlyOffsetA + 1; + FlyOffsetBIm = FlyOffsetB + 1; + } +} +ioptr += 2*Ntbl[M]; +} +} + +void iffts(float *ioptr, long M, long Rows, float *Utbl){ +/* Compute in-place inverse complex fft on the rows of the input array */ +/* INPUTS */ +/* M = log2 of fft size */ +/* *ioptr = input data array */ +/* *Utbl = cosine table */ +/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */ +/* OUTPUTS */ +/* *ioptr = output data array */ + +long Flyinc; +long FlyOffsetA; +long FlyOffsetAIm; +long FlyOffsetB; +long FlyOffsetBIm; +long NsameU1; +long NsameU2; +long NsameU4; +long diffUcnt; +long LoopCnt; + +float scale; +float fly0r; +float fly0i; +float fly1r; +float fly1i; +float fly2r; +float fly2i; +float fly3r; +float fly3i; +float fly4r; +float fly4i; +float fly5r; +float fly5i; +float fly6r; +float fly6i; +float fly7r; +float fly7i; +float U0r; +float U0i; +float U1r; +float U1i; +float U2r; +float U2i; +float U3r; +float U3i; +float t0r; +float t0i; +float t1r; +float t1i; + +float *fly0P; +float *fly1P; +float *fly2P; +float *fly3P; +float *U0rP; +float *U0iP; +float *U1rP; +float *U1iP; +float *U2rP; +float *U2iP; +float *IOP; +long U3offset; + +long stage; +long NdiffU; +long LoopN; + +const long BRshift = MAXMROOT - (M>>1); +const long Nrems2 = Ntbl[M-(M>>1)+1]; +const long Nroot_1_ColInc = (Ntbl[M-1]-Ntbl[M-(M>>1)])*2; + +for (;Rows>0;Rows--){ + +FlyOffsetA = Ntbl[M] * 2/2; +FlyOffsetAIm = FlyOffsetA + 1; +FlyOffsetB = FlyOffsetA + 2; +FlyOffsetBIm = FlyOffsetB + 1; + +/* BitrevR2 ** bit reverse and first radix 2 stage ******/ + +scale = 1./Ntbl[M]; +for (stage = 0; stage < Ntbl[M-(M>>1)]*2; stage += Ntbl[M>>1]*2){ + for (LoopN = (Ntbl[(M>>1)-1]-1); LoopN >= 0; LoopN--){ + LoopCnt = (Ntbl[(M>>1)-1]-1); + fly0P = ioptr + Nroot_1_ColInc + ((int)BRcnt[LoopN] >> BRshift)*(2*2) + stage; + IOP = ioptr + (LoopN<<(M+1)/2) * 2 + stage; + fly1P = IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2); + fly0r = *(fly0P); + fly0i = *(fly0P+1); + fly1r = *(fly0P+FlyOffsetA); + fly1i = *(fly0P+FlyOffsetAIm); + for (; LoopCnt > LoopN;){ + fly2r = *(fly0P+2); + fly2i = *(fly0P+(2+1)); + fly3r = *(fly0P+FlyOffsetB); + fly3i = *(fly0P+FlyOffsetBIm); + fly4r = *(fly1P); + fly4i = *(fly1P+1); + fly5r = *(fly1P+FlyOffsetA); + fly5i = *(fly1P+FlyOffsetAIm); + fly6r = *(fly1P+2); + fly6i = *(fly1P+(2+1)); + fly7r = *(fly1P+FlyOffsetB); + fly7i = *(fly1P+FlyOffsetBIm); + + t0r = fly0r + fly1r; + t0i = fly0i + fly1i; + fly1r = fly0r - fly1r; + fly1i = fly0i - fly1i; + t1r = fly2r + fly3r; + t1i = fly2i + fly3i; + fly3r = fly2r - fly3r; + fly3i = fly2i - fly3i; + fly0r = fly4r + fly5r; + fly0i = fly4i + fly5i; + fly5r = fly4r - fly5r; + fly5i = fly4i - fly5i; + fly2r = fly6r + fly7r; + fly2i = fly6i + fly7i; + fly7r = fly6r - fly7r; + fly7i = fly6i - fly7i; + + *(fly1P) = scale*t0r; + *(fly1P+1) = scale*t0i; + *(fly1P+2) = scale*fly1r; + *(fly1P+(2+1)) = scale*fly1i; + *(fly1P+FlyOffsetA) = scale*t1r; + *(fly1P+FlyOffsetAIm) = scale*t1i; + *(fly1P+FlyOffsetB) = scale*fly3r; + *(fly1P+FlyOffsetBIm) = scale*fly3i; + *(fly0P) = scale*fly0r; + *(fly0P+1) = scale*fly0i; + *(fly0P+2) = scale*fly5r; + *(fly0P+(2+1)) = scale*fly5i; + *(fly0P+FlyOffsetA) = scale*fly2r; + *(fly0P+FlyOffsetAIm) = scale*fly2i; + *(fly0P+FlyOffsetB) = scale*fly7r; + *(fly0P+FlyOffsetBIm) = scale*fly7i; + + fly0P -= Nrems2; + fly0r = *(fly0P); + fly0i = *(fly0P+1); + fly1r = *(fly0P+FlyOffsetA); + fly1i = *(fly0P+FlyOffsetAIm); + LoopCnt -= 1; + fly1P = (IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2)); + }; + fly2r = *(fly0P+2); + fly2i = *(fly0P+(2+1)); + fly3r = *(fly0P+FlyOffsetB); + fly3i = *(fly0P+FlyOffsetBIm); + + t0r = fly0r + fly1r; + t0i = fly0i + fly1i; + fly1r = fly0r - fly1r; + fly1i = fly0i - fly1i; + t1r = fly2r + fly3r; + t1i = fly2i + fly3i; + fly3r = fly2r - fly3r; + fly3i = fly2i - fly3i; + + *(fly0P) = scale*t0r; + *(fly0P+1) = scale*t0i; + *(fly0P+2) = scale*fly1r; + *(fly0P+(2+1)) = scale*fly1i; + *(fly0P+FlyOffsetA) = scale*t1r; + *(fly0P+FlyOffsetAIm) = scale*t1i; + *(fly0P+FlyOffsetB) = scale*fly3r; + *(fly0P+FlyOffsetBIm) = scale*fly3i; + + }; +}; + +/**** FFTC **************/ + +scale = 2.0; + +NdiffU = 2; +Flyinc = (NdiffU); + +NsameU4 = Ntbl[M]/4; +LoopN = Ntbl[M-3]; + +stage = ((M-1)/3); +if ( (M-1-(stage * 3)) != 0 ){ + FlyOffsetA = Flyinc << 2; + FlyOffsetB = FlyOffsetA << 1; + FlyOffsetAIm = FlyOffsetA + 1; + FlyOffsetBIm = FlyOffsetB + 1; + if ( (M-1-(stage * 3)) == 1 ){ + /* 1 radix 2 stage */ + + IOP = ioptr; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + /* Butterflys */ + /* + t0 - - t0 + t1 - - t1 + f2 - 1- f5 + f1 - -i- f7 + f4 - - f4 + f0 - - f0 + f6 - 1- f2 + f3 - -i- f1 + */ + + for (LoopCnt = LoopN; LoopCnt > 0 ; LoopCnt--){ + t0r = *(fly0P); + t0i = *(fly0P + 1); + t1r = *(fly1P); + t1i = *(fly1P + 1); + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly1r = *(fly3P); + fly1i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly0r = *(fly1P + FlyOffsetA); + fly0i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly3r = *(fly3P + FlyOffsetA); + fly3i = *(fly3P + FlyOffsetAIm); + + fly5r = t0r - fly2r; + fly5i = t0i - fly2i; + t0r = t0r + fly2r; + t0i = t0i + fly2i; + + fly7r = t1r + fly1i; + fly7i = t1i - fly1r; + t1r = t1r - fly1i; + t1i = t1i + fly1r; + + fly2r = fly4r - fly6r; + fly2i = fly4i - fly6i; + fly4r = fly4r + fly6r; + fly4i = fly4i + fly6i; + + fly1r = fly0r + fly3i; + fly1i = fly0i - fly3r; + fly0r = fly0r - fly3i; + fly0i = fly0i + fly3r; + + *(fly2P) = fly5r; + *(fly2P + 1) = fly5i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + *(fly0P + FlyOffsetA) = fly4r; + *(fly0P + FlyOffsetAIm) = fly4i; + *(fly3P + FlyOffsetA) = fly1r; + *(fly3P + FlyOffsetAIm) = fly1i; + *(fly1P + FlyOffsetA) = fly0r; + *(fly1P + FlyOffsetAIm) = fly0i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + }; + + NsameU4 >>= 1; + LoopN >>= 1; + NdiffU <<= 1; + Flyinc = Flyinc << 1; + } + else{ + /* 1 radix 4 stage */ + IOP = ioptr; + + U3r = 0.7071067811865475244008443621; /* sqrt(0.5); */ + U3i = U3r; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + /* Butterflys */ + /* + t0 - - t0 - - t0 + t1 - - t1 - - t1 + f2 - 1- f5 - - f5 + f1 - -i- f7 - - f7 + f4 - - f4 - 1- f6 + f0 - - f0 -U3 - f3 + f6 - 1- f2 - -i- f4 + f3 - -i- f1 -U3a- f2 + */ + + for (LoopCnt = LoopN; LoopCnt > 0 ; LoopCnt--){ + t0r = *(fly0P); + t0i = *(fly0P + 1); + t1r = *(fly1P); + t1i = *(fly1P + 1); + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly1r = *(fly3P); + fly1i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly0r = *(fly1P + FlyOffsetA); + fly0i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly3r = *(fly3P + FlyOffsetA); + fly3i = *(fly3P + FlyOffsetAIm); + + fly5r = t0r - fly2r; + fly5i = t0i - fly2i; + t0r = t0r + fly2r; + t0i = t0i + fly2i; + + fly7r = t1r + fly1i; + fly7i = t1i - fly1r; + t1r = t1r - fly1i; + t1i = t1i + fly1r; + + fly2r = fly4r - fly6r; + fly2i = fly4i - fly6i; + fly4r = fly4r + fly6r; + fly4i = fly4i + fly6i; + + fly1r = fly0r + fly3i; + fly1i = fly0i - fly3r; + fly0r = fly0r - fly3i; + fly0i = fly0i + fly3r; + + fly6r = t0r - fly4r; + fly6i = t0i - fly4i; + t0r = t0r + fly4r; + t0i = t0i + fly4i; + + fly3r = fly5r + fly2i; + fly3i = fly5i - fly2r; + fly5r = fly5r - fly2i; + fly5i = fly5i + fly2r; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r + U3i * fly0i; + fly4i = t1i - U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly2r = fly7r + U3i * fly1r; + fly2r = fly2r + U3r * fly1i; + fly2i = fly7i - U3r * fly1r; + fly2i = fly2i + U3i * fly1i; + fly7r = scale * fly7r - fly2r; + fly7i = scale * fly7i - fly2i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly2P + FlyOffsetA) = fly3r; + *(fly2P + FlyOffsetAIm) = fly3i; + *(fly2P) = fly5r; + *(fly2P + 1) = fly5i; + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + *(fly3P + FlyOffsetA) = fly2r; + *(fly3P + FlyOffsetAIm) = fly2i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + + }; + + NsameU4 >>= 2; + LoopN >>= 2; + NdiffU <<= 2; + Flyinc = Flyinc << 2; + }; +}; + +NsameU2 = NsameU4 >> 1; +NsameU1 = NsameU2 >> 1; +Flyinc <<= 1; +FlyOffsetA = Flyinc << 2; +FlyOffsetB = FlyOffsetA << 1; +FlyOffsetAIm = FlyOffsetA + 1; +FlyOffsetBIm = FlyOffsetB + 1; +LoopN >>= 1; + +/* ****** RADIX 8 Stages */ +for (stage = stage<<1; stage > 0 ; stage--){ + + /* an fft stage is done in two parts to ease use of the single quadrant cos table */ + +/* fftcalc1(iobuf, Utbl, N, NdiffU, LoopN); */ + if(!(stage&1)){ + U0rP = &Utbl[0]; + U0iP = &Utbl[Ntbl[M-2]]; + U1rP = U0rP; + U1iP = U0iP; + U2rP = U0rP; + U2iP = U0iP; + U3offset = (Ntbl[M]) / 8; + + IOP = ioptr; + + U0r = *U0rP, + U0i = *U0iP; + U1r = *U1rP, + U1i = *U1iP; + U2r = *U2rP, + U2i = *U2iP; + U3r = *( U2rP + U3offset); + U3i = *( U2iP - U3offset); + } + + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + for (diffUcnt = (NdiffU)>>1; diffUcnt > 0; diffUcnt--){ + + /* Butterflys */ + /* + f0 - - t0 - - t0 - - t0 + f1 -U0 - t1 - - t1 - - t1 + f2 - - f2 -U1 - f5 - - f3 + f3 -U0 - f1 -U1a- f7 - - f7 + f4 - - f4 - - f4 -U2 - f6 + f5 -U0 - f0 - - f0 -U3 - f4 + f6 - - f6 -U1 - f2 -U2a- f2 + f7 -U0 - f3 -U1a- f1 -U3a- f5 + */ + + fly0r = *(IOP); + fly0i = *(IOP+1); + fly1r = *(fly1P); + fly1i = *(fly1P+1); + + for (LoopCnt = LoopN-1; LoopCnt > 0 ; LoopCnt--){ + + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly3r = *(fly3P); + fly3i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly5r = *(fly1P + FlyOffsetA); + fly5i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly7r = *(fly3P + FlyOffsetA); + fly7i = *(fly3P + FlyOffsetAIm); + + t1r = fly0r - U0r * fly1r; + t1r = t1r + U0i * fly1i; + t1i = fly0i - U0i * fly1r; + t1i = t1i - U0r * fly1i; + t0r = scale * fly0r - t1r; + t0i = scale * fly0i - t1i; + + fly1r = fly2r - U0r * fly3r; + fly1r = fly1r + U0i * fly3i; + fly1i = fly2i - U0i * fly3r; + fly1i = fly1i - U0r * fly3i; + fly2r = scale * fly2r - fly1r; + fly2i = scale * fly2i - fly1i; + + fly0r = fly4r - U0r * fly5r; + fly0r = fly0r + U0i * fly5i; + fly0i = fly4i - U0i * fly5r; + fly0i = fly0i - U0r * fly5i; + fly4r = scale * fly4r - fly0r; + fly4i = scale * fly4i - fly0i; + + fly3r = fly6r - U0r * fly7r; + fly3r = fly3r + U0i * fly7i; + fly3i = fly6i - U0i * fly7r; + fly3i = fly3i - U0r * fly7i; + fly6r = scale * fly6r - fly3r; + fly6i = scale * fly6i - fly3i; + + + fly5r = t0r - U1r * fly2r; + fly5r = fly5r + U1i * fly2i; + fly5i = t0i - U1i * fly2r; + fly5i = fly5i - U1r * fly2i; + t0r = scale * t0r - fly5r; + t0i = scale * t0i - fly5i; + + fly7r = t1r + U1i * fly1r; + fly7r = fly7r + U1r * fly1i; + fly7i = t1i - U1r * fly1r; + fly7i = fly7i + U1i * fly1i; + t1r = scale * t1r - fly7r; + t1i = scale * t1i - fly7i; + + fly2r = fly4r - U1r * fly6r; + fly2r = fly2r + U1i * fly6i; + fly2i = fly4i - U1i * fly6r; + fly2i = fly2i - U1r * fly6i; + fly4r = scale * fly4r - fly2r; + fly4i = scale * fly4i - fly2i; + + fly1r = fly0r + U1i * fly3r; + fly1r = fly1r + U1r * fly3i; + fly1i = fly0i - U1r * fly3r; + fly1i = fly1i + U1i * fly3i; + fly0r = scale * fly0r - fly1r; + fly0i = scale * fly0i - fly1i; + + fly6r = t0r - U2r * fly4r; + fly6r = fly6r + U2i * fly4i; + fly6i = t0i - U2i * fly4r; + fly6i = fly6i - U2r * fly4i; + t0r = scale * t0r - fly6r; + t0i = scale * t0i - fly6i; + + fly3r = fly5r - U2i * fly2r; + fly3r = fly3r - U2r * fly2i; + fly3i = fly5i + U2r * fly2r; + fly3i = fly3i - U2i * fly2i; + fly2r = scale * fly5r - fly3r; + fly2i = scale * fly5i - fly3i; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r + U3i * fly0i; + fly4i = t1i - U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly5r = fly7r + U3i * fly1r; + fly5r = fly5r + U3r * fly1i; + fly5i = fly7i - U3r * fly1r; + fly5i = fly5i + U3i * fly1i; + fly7r = scale * fly7r - fly5r; + fly7i = scale * fly7i - fly5i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly2P) = fly3r; + *(fly2P + 1) = fly3i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + + fly0r = *(fly0P + FlyOffsetB); + fly0i = *(fly0P + FlyOffsetBIm); + + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + + fly1r = *(fly1P + FlyOffsetB); + fly1i = *(fly1P + FlyOffsetBIm); + + *(fly3P + FlyOffsetA) = fly5r; + *(fly3P + FlyOffsetAIm) = fly5i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + + }; + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly3r = *(fly3P); + fly3i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly5r = *(fly1P + FlyOffsetA); + fly5i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly7r = *(fly3P + FlyOffsetA); + fly7i = *(fly3P + FlyOffsetAIm); + + t1r = fly0r - U0r * fly1r; + t1r = t1r + U0i * fly1i; + t1i = fly0i - U0i * fly1r; + t1i = t1i - U0r * fly1i; + t0r = scale * fly0r - t1r; + t0i = scale * fly0i - t1i; + + fly1r = fly2r - U0r * fly3r; + fly1r = fly1r + U0i * fly3i; + fly1i = fly2i - U0i * fly3r; + fly1i = fly1i - U0r * fly3i; + fly2r = scale * fly2r - fly1r; + fly2i = scale * fly2i - fly1i; + + fly0r = fly4r - U0r * fly5r; + fly0r = fly0r + U0i * fly5i; + fly0i = fly4i - U0i * fly5r; + fly0i = fly0i - U0r * fly5i; + fly4r = scale * fly4r - fly0r; + fly4i = scale * fly4i - fly0i; + + fly3r = fly6r - U0r * fly7r; + fly3r = fly3r + U0i * fly7i; + fly3i = fly6i - U0i * fly7r; + fly3i = fly3i - U0r * fly7i; + fly6r = scale * fly6r - fly3r; + fly6i = scale * fly6i - fly3i; + + fly5r = t0r - U1r * fly2r; + fly5r = fly5r + U1i * fly2i; + fly5i = t0i - U1i * fly2r; + fly5i = fly5i - U1r * fly2i; + t0r = scale * t0r - fly5r; + t0i = scale * t0i - fly5i; + + fly7r = t1r + U1i * fly1r; + fly7r = fly7r + U1r * fly1i; + fly7i = t1i - U1r * fly1r; + fly7i = fly7i + U1i * fly1i; + t1r = scale * t1r - fly7r; + t1i = scale * t1i - fly7i; + + fly2r = fly4r - U1r * fly6r; + fly2r = fly2r + U1i * fly6i; + fly2i = fly4i - U1i * fly6r; + fly2i = fly2i - U1r * fly6i; + fly4r = scale * fly4r - fly2r; + fly4i = scale * fly4i - fly2i; + + fly1r = fly0r + U1i * fly3r; + fly1r = fly1r + U1r * fly3i; + fly1i = fly0i - U1r * fly3r; + fly1i = fly1i + U1i * fly3i; + fly0r = scale * fly0r - fly1r; + fly0i = scale * fly0i - fly1i; + + U0i = *(U0iP = (U0iP - NsameU4)); + U0r = *(U0rP = (U0rP + NsameU4)); + U1r = *(U1rP = (U1rP + NsameU2)); + U1i = *(U1iP = (U1iP - NsameU2)); + if(stage&1) + U0r = - U0r; + + fly6r = t0r - U2r * fly4r; + fly6r = fly6r + U2i * fly4i; + fly6i = t0i - U2i * fly4r; + fly6i = fly6i - U2r * fly4i; + t0r = scale * t0r - fly6r; + t0i = scale * t0i - fly6i; + + fly3r = fly5r - U2i * fly2r; + fly3r = fly3r - U2r * fly2i; + fly3i = fly5i + U2r * fly2r; + fly3i = fly3i - U2i * fly2i; + fly2r = scale * fly5r - fly3r; + fly2i = scale * fly5i - fly3i; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r + U3i * fly0i; + fly4i = t1i - U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly5r = fly7r + U3i * fly1r; + fly5r = fly5r + U3r * fly1i; + fly5i = fly7i - U3r * fly1r; + fly5i = fly5i + U3i * fly1i; + fly7r = scale * fly7r - fly5r; + fly7i = scale * fly7i - fly5i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + + U2r = *(U2rP = (U2rP + NsameU1)); + U2i = *(U2iP = (U2iP - NsameU1)); + + *(fly2P) = fly3r; + *(fly2P + 1) = fly3i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + + U3r = *( U2rP + U3offset); + U3i = *( U2iP - U3offset); + + *(fly3P + FlyOffsetA) = fly5r; + *(fly3P + FlyOffsetAIm) = fly5i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + IOP = IOP + 2; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + }; + NsameU4 = -NsameU4; + + if(stage&1){ + LoopN >>= 3; + NsameU1 >>= 3; + NsameU2 >>= 3; + NsameU4 >>= 3; + NdiffU <<= 3; + Flyinc = Flyinc << 3; + FlyOffsetA <<= 3; + FlyOffsetB <<= 3; + FlyOffsetAIm = FlyOffsetA + 1; + FlyOffsetBIm = FlyOffsetB + 1; + } +} +ioptr += 2*Ntbl[M]; +} +} + +/* rffts */ +/* compute multiple real input FFTs on 'Rows' consecutively stored arrays */ +/* ioptr = pointer to the data in and out */ +/* M = log2 of fft size */ +/* Rows = number of FFTs to compute */ +/* Utbl = Pointer to cosine table */ + +void rffts(float *ioptr, long M, long Rows, float *Utbl){ +/* Compute in-place real fft on the rows of the input array */ +/* INPUTS */ +/* M = log2 of fft size */ +/* *ioptr = real input data array */ +/* *Utbl = cosine table */ +/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */ +/* OUTPUTS */ +/* *ioptr = output data array in the following order */ +/* Re(x[0]), Re(x[N/2]), Re(x[1]), Im(x[1]), Re(x[2]), Im(x[2]), ... Re(x[N/2-1]), Im(x[N/2-1]). */ + +long Flyinc; +long FlyOffsetA; +long FlyOffsetAIm; +long FlyOffsetB; +long FlyOffsetBIm; +long NsameU1; +long NsameU2; +long NsameU4; +long diffUcnt; +long LoopCnt; +float scale; +float fly0r; +float fly0i; +float fly1r; +float fly1i; +float fly2r; +float fly2i; +float fly3r; +float fly3i; +float fly4r; +float fly4i; +float fly5r; +float fly5i; +float fly6r; +float fly6i; +float fly7r; +float fly7i; +float U0r; +float U0i; +float U1r; +float U1i; +float U2r; +float U2i; +float U3r; +float U3i; +float t0r; +float t0i; +float t1r; +float t1i; + +float *fly0P; +float *fly1P; +float *fly2P; +float *fly3P; + +float *U0rP; +float *U0iP; +float *U1rP; +float *U1iP; +float *U2rP; +float *U2iP; +float *IOP; +long U3offset; + +long stage; +long NdiffU; +long LoopN; + +const long BRshift = MAXMROOT - ((M-1)>>1); /* for RFFT */ +const long Nrems2 = Ntbl[(M-1)-((M-1)>>1)+1]; /* for RFFT */ +const long Nroot_1_ColInc = (Ntbl[(M-1)-1]-Ntbl[(M-1)-((M-1)>>1)])*2; /* for RFFT */ + +for (;Rows>0;Rows--){ + +M=M-1; /* for RFFT */ + +FlyOffsetA = Ntbl[M] * 2/2; +FlyOffsetAIm = FlyOffsetA + 1; +FlyOffsetB = FlyOffsetA + 2; +FlyOffsetBIm = FlyOffsetB + 1; + +/* BitrevR2 ** bit reverse shuffle and first radix 2 stage ******/ + +scale = 0.5; +for (stage = 0; stage < Ntbl[M-(M>>1)]*2; stage += Ntbl[M>>1]*2){ + for (LoopN = (Ntbl[(M>>1)-1]-1); LoopN >= 0; LoopN--){ + LoopCnt = (Ntbl[(M>>1)-1]-1); + fly0P = ioptr + Nroot_1_ColInc + ((int)BRcnt[LoopN] >> BRshift)*(2*2) + stage; + IOP = ioptr + (LoopN<<(M+1)/2) * 2 + stage; + fly1P = IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2); + fly0r = *fly0P; + fly0i = *(fly0P+1); + fly1r = *(fly0P+FlyOffsetA); + fly1i = *(fly0P+FlyOffsetAIm); + for (; LoopCnt > LoopN;){ + fly2r = *(fly0P+2); + fly2i = *(fly0P+(2+1)); + fly3r = *(fly0P+FlyOffsetB); + fly3i = *(fly0P+FlyOffsetBIm); + fly4r = *fly1P; + fly4i = *(fly1P+1); + fly5r = *(fly1P+FlyOffsetA); + fly5i = *(fly1P+FlyOffsetAIm); + fly6r = *(fly1P+2); + fly6i = *(fly1P+(2+1)); + fly7r = *(fly1P+FlyOffsetB); + fly7i = *(fly1P+FlyOffsetBIm); + + t0r = fly0r + fly1r; + t0i = fly0i + fly1i; + fly1r = fly0r - fly1r; + fly1i = fly0i - fly1i; + t1r = fly2r + fly3r; + t1i = fly2i + fly3i; + fly3r = fly2r - fly3r; + fly3i = fly2i - fly3i; + fly0r = fly4r + fly5r; + fly0i = fly4i + fly5i; + fly5r = fly4r - fly5r; + fly5i = fly4i - fly5i; + fly2r = fly6r + fly7r; + fly2i = fly6i + fly7i; + fly7r = fly6r - fly7r; + fly7i = fly6i - fly7i; + + *fly1P = scale*t0r; + *(fly1P+1) = scale*t0i; + *(fly1P+2) = scale*fly1r; + *(fly1P+(2+1)) = scale*fly1i; + *(fly1P+FlyOffsetA) = scale*t1r; + *(fly1P+FlyOffsetAIm) = scale*t1i; + *(fly1P+FlyOffsetB) = scale*fly3r; + *(fly1P+FlyOffsetBIm) = scale*fly3i; + *fly0P = scale*fly0r; + *(fly0P+1) = scale*fly0i; + *(fly0P+2) = scale*fly5r; + *(fly0P+(2+1)) = scale*fly5i; + *(fly0P+FlyOffsetA) = scale*fly2r; + *(fly0P+FlyOffsetAIm) = scale*fly2i; + *(fly0P+FlyOffsetB) = scale*fly7r; + *(fly0P+FlyOffsetBIm) = scale*fly7i; + + fly0P -= Nrems2; + fly0r = *fly0P; + fly0i = *(fly0P+1); + fly1r = *(fly0P+FlyOffsetA); + fly1i = *(fly0P+FlyOffsetAIm); + LoopCnt -= 1; + fly1P = (IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2)); + }; + fly2r = *(fly0P+2); + fly2i = *(fly0P+(2+1)); + fly3r = *(fly0P+FlyOffsetB); + fly3i = *(fly0P+FlyOffsetBIm); + + t0r = fly0r + fly1r; + t0i = fly0i + fly1i; + fly1r = fly0r - fly1r; + fly1i = fly0i - fly1i; + t1r = fly2r + fly3r; + t1i = fly2i + fly3i; + fly3r = fly2r - fly3r; + fly3i = fly2i - fly3i; + + *fly0P = scale*t0r; + *(fly0P+1) = scale*t0i; + *(fly0P+2) = scale*fly1r; + *(fly0P+(2+1)) = scale*fly1i; + *(fly0P+FlyOffsetA) = scale*t1r; + *(fly0P+FlyOffsetAIm) = scale*t1i; + *(fly0P+FlyOffsetB) = scale*fly3r; + *(fly0P+FlyOffsetBIm) = scale*fly3i; + + }; +}; + + + +/**** FFTC **************/ + +scale = 2.0; + +NdiffU = 2; +Flyinc = (NdiffU); + +NsameU4 = Ntbl[M+1]/4; /* for RFFT */ +LoopN = Ntbl[M-3]; + +stage = ((M-1)/3); +if ( (M-1-(stage * 3)) != 0 ){ + FlyOffsetA = Flyinc << 2; + FlyOffsetB = FlyOffsetA << 1; + FlyOffsetAIm = FlyOffsetA + 1; + FlyOffsetBIm = FlyOffsetB + 1; + if ( (M-1-(stage * 3)) == 1 ){ + /* 1 radix 2 stage */ + + IOP = ioptr; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + /* Butterflys */ + /* + t0 - - t0 + t1 - - t1 + f2 - 1- f5 + f1 - -i- f7 + f4 - - f4 + f0 - - f0 + f6 - 1- f2 + f3 - -i- f1 + */ + + for (LoopCnt = LoopN; LoopCnt > 0 ; LoopCnt--){ + t0r = *(fly0P); + t0i = *(fly0P + 1); + t1r = *(fly1P); + t1i = *(fly1P + 1); + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly1r = *(fly3P); + fly1i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly0r = *(fly1P + FlyOffsetA); + fly0i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly3r = *(fly3P + FlyOffsetA); + fly3i = *(fly3P + FlyOffsetAIm); + + fly5r = t0r - fly2r; + fly5i = t0i - fly2i; + t0r = t0r + fly2r; + t0i = t0i + fly2i; + + fly7r = t1r - fly1i; + fly7i = t1i + fly1r; + t1r = t1r + fly1i; + t1i = t1i - fly1r; + + fly2r = fly4r - fly6r; + fly2i = fly4i - fly6i; + fly4r = fly4r + fly6r; + fly4i = fly4i + fly6i; + + fly1r = fly0r - fly3i; + fly1i = fly0i + fly3r; + fly0r = fly0r + fly3i; + fly0i = fly0i - fly3r; + + *(fly2P) = fly5r; + *(fly2P + 1) = fly5i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + *(fly0P + FlyOffsetA) = fly4r; + *(fly0P + FlyOffsetAIm) = fly4i; + *(fly3P + FlyOffsetA) = fly1r; + *(fly3P + FlyOffsetAIm) = fly1i; + *(fly1P + FlyOffsetA) = fly0r; + *(fly1P + FlyOffsetAIm) = fly0i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + }; + + NsameU4 >>= 1; + LoopN >>= 1; + NdiffU <<= 1; + Flyinc = Flyinc << 1; + } + else{ + /* 1 radix 4 stage */ + IOP = ioptr; + + U3r = 0.7071067811865475244008443621; /* sqrt(0.5); */ + U3i = U3r; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + /* Butterflys */ + /* + t0 - - t0 - - t0 + t1 - - t1 - - t1 + f2 - 1- f5 - - f5 + f1 - -i- f7 - - f7 + f4 - - f4 - 1- f6 + f0 - - f0 -U3 - f3 + f6 - 1- f2 - -i- f4 + f3 - -i- f1 -U3a- f2 + */ + + for (LoopCnt = LoopN; LoopCnt > 0 ; LoopCnt--){ + t0r = *(fly0P); + t0i = *(fly0P + 1); + t1r = *(fly1P); + t1i = *(fly1P + 1); + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly1r = *(fly3P); + fly1i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly0r = *(fly1P + FlyOffsetA); + fly0i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly3r = *(fly3P + FlyOffsetA); + fly3i = *(fly3P + FlyOffsetAIm); + + fly5r = t0r - fly2r; + fly5i = t0i - fly2i; + t0r = t0r + fly2r; + t0i = t0i + fly2i; + + fly7r = t1r - fly1i; + fly7i = t1i + fly1r; + t1r = t1r + fly1i; + t1i = t1i - fly1r; + + fly2r = fly4r - fly6r; + fly2i = fly4i - fly6i; + fly4r = fly4r + fly6r; + fly4i = fly4i + fly6i; + + fly1r = fly0r - fly3i; + fly1i = fly0i + fly3r; + fly0r = fly0r + fly3i; + fly0i = fly0i - fly3r; + + fly6r = t0r - fly4r; + fly6i = t0i - fly4i; + t0r = t0r + fly4r; + t0i = t0i + fly4i; + + fly3r = fly5r - fly2i; + fly3i = fly5i + fly2r; + fly5r = fly5r + fly2i; + fly5i = fly5i - fly2r; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r - U3i * fly0i; + fly4i = t1i + U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly2r = fly7r + U3i * fly1r; + fly2r = fly2r - U3r * fly1i; + fly2i = fly7i + U3r * fly1r; + fly2i = fly2i + U3i * fly1i; + fly7r = scale * fly7r - fly2r; + fly7i = scale * fly7i - fly2i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly2P + FlyOffsetA) = fly3r; + *(fly2P + FlyOffsetAIm) = fly3i; + *(fly2P) = fly5r; + *(fly2P + 1) = fly5i; + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + *(fly3P + FlyOffsetA) = fly2r; + *(fly3P + FlyOffsetAIm) = fly2i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + + }; + + NsameU4 >>= 2; + LoopN >>= 2; + NdiffU <<= 2; + Flyinc = Flyinc << 2; + }; +}; + +NsameU2 = NsameU4 >> 1; +NsameU1 = NsameU2 >> 1; +Flyinc <<= 1; +FlyOffsetA = Flyinc << 2; +FlyOffsetB = FlyOffsetA << 1; +FlyOffsetAIm = FlyOffsetA + 1; +FlyOffsetBIm = FlyOffsetB + 1; +LoopN >>= 1; + +/* ****** RADIX 8 Stages */ +for (stage = stage<<1; stage > 0 ; stage--){ + + /* an fft stage is done in two parts to ease use of the single quadrant cos table */ + +/* fftcalc1(iobuf, Utbl, N, NdiffU, LoopN); */ + if(!(stage&1)){ + U0rP = &Utbl[0]; + U0iP = &Utbl[Ntbl[M-1]]; /* for RFFT */ + U1rP = U0rP; + U1iP = U0iP; + U2rP = U0rP; + U2iP = U0iP; + U3offset = (Ntbl[M+1]) / 8; /* for RFFT */ + + IOP = ioptr; + + U0r = *U0rP, + U0i = *U0iP; + U1r = *U1rP, + U1i = *U1iP; + U2r = *U2rP, + U2i = *U2iP; + U3r = *( U2rP + U3offset); + U3i = *( U2iP - U3offset); + } + + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + for (diffUcnt = (NdiffU)>>1; diffUcnt > 0; diffUcnt--){ + + /* Butterflys */ + /* + f0 - - t0 - - t0 - - t0 + f1 -U0 - t1 - - t1 - - t1 + f2 - - f2 -U1 - f5 - - f3 + f3 -U0 - f1 -U1a- f7 - - f7 + f4 - - f4 - - f4 -U2 - f6 + f5 -U0 - f0 - - f0 -U3 - f4 + f6 - - f6 -U1 - f2 -U2a- f2 + f7 -U0 - f3 -U1a- f1 -U3a- f5 + */ + + fly0r = *(IOP); + fly0i = *(IOP+1); + fly1r = *(fly1P); + fly1i = *(fly1P+1); + + for (LoopCnt = LoopN-1; LoopCnt > 0 ; LoopCnt--){ + + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly3r = *(fly3P); + fly3i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly5r = *(fly1P + FlyOffsetA); + fly5i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly7r = *(fly3P + FlyOffsetA); + fly7i = *(fly3P + FlyOffsetAIm); + + t1r = fly0r - U0r * fly1r; + t1r = t1r - U0i * fly1i; + t1i = fly0i + U0i * fly1r; + t1i = t1i - U0r * fly1i; + t0r = scale * fly0r - t1r; + t0i = scale * fly0i - t1i; + + fly1r = fly2r - U0r * fly3r; + fly1r = fly1r - U0i * fly3i; + fly1i = fly2i + U0i * fly3r; + fly1i = fly1i - U0r * fly3i; + fly2r = scale * fly2r - fly1r; + fly2i = scale * fly2i - fly1i; + + fly0r = fly4r - U0r * fly5r; + fly0r = fly0r - U0i * fly5i; + fly0i = fly4i + U0i * fly5r; + fly0i = fly0i - U0r * fly5i; + fly4r = scale * fly4r - fly0r; + fly4i = scale * fly4i - fly0i; + + fly3r = fly6r - U0r * fly7r; + fly3r = fly3r - U0i * fly7i; + fly3i = fly6i + U0i * fly7r; + fly3i = fly3i - U0r * fly7i; + fly6r = scale * fly6r - fly3r; + fly6i = scale * fly6i - fly3i; + + + fly5r = t0r - U1r * fly2r; + fly5r = fly5r - U1i * fly2i; + fly5i = t0i + U1i * fly2r; + fly5i = fly5i - U1r * fly2i; + t0r = scale * t0r - fly5r; + t0i = scale * t0i - fly5i; + + fly7r = t1r + U1i * fly1r; + fly7r = fly7r - U1r * fly1i; + fly7i = t1i + U1r * fly1r; + fly7i = fly7i + U1i * fly1i; + t1r = scale * t1r - fly7r; + t1i = scale * t1i - fly7i; + + fly2r = fly4r - U1r * fly6r; + fly2r = fly2r - U1i * fly6i; + fly2i = fly4i + U1i * fly6r; + fly2i = fly2i - U1r * fly6i; + fly4r = scale * fly4r - fly2r; + fly4i = scale * fly4i - fly2i; + + fly1r = fly0r + U1i * fly3r; + fly1r = fly1r - U1r * fly3i; + fly1i = fly0i + U1r * fly3r; + fly1i = fly1i + U1i * fly3i; + fly0r = scale * fly0r - fly1r; + fly0i = scale * fly0i - fly1i; + + fly6r = t0r - U2r * fly4r; + fly6r = fly6r - U2i * fly4i; + fly6i = t0i + U2i * fly4r; + fly6i = fly6i - U2r * fly4i; + t0r = scale * t0r - fly6r; + t0i = scale * t0i - fly6i; + + fly3r = fly5r - U2i * fly2r; + fly3r = fly3r + U2r * fly2i; + fly3i = fly5i - U2r * fly2r; + fly3i = fly3i - U2i * fly2i; + fly2r = scale * fly5r - fly3r; + fly2i = scale * fly5i - fly3i; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r - U3i * fly0i; + fly4i = t1i + U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly5r = fly7r + U3i * fly1r; + fly5r = fly5r - U3r * fly1i; + fly5i = fly7i + U3r * fly1r; + fly5i = fly5i + U3i * fly1i; + fly7r = scale * fly7r - fly5r; + fly7i = scale * fly7i - fly5i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly2P) = fly3r; + *(fly2P + 1) = fly3i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + + fly0r = *(fly0P + FlyOffsetB); + fly0i = *(fly0P + FlyOffsetBIm); + + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + + fly1r = *(fly1P + FlyOffsetB); + fly1i = *(fly1P + FlyOffsetBIm); + + *(fly3P + FlyOffsetA) = fly5r; + *(fly3P + FlyOffsetAIm) = fly5i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + }; + + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly3r = *(fly3P); + fly3i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly5r = *(fly1P + FlyOffsetA); + fly5i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly7r = *(fly3P + FlyOffsetA); + fly7i = *(fly3P + FlyOffsetAIm); + + t1r = fly0r - U0r * fly1r; + t1r = t1r - U0i * fly1i; + t1i = fly0i + U0i * fly1r; + t1i = t1i - U0r * fly1i; + t0r = scale * fly0r - t1r; + t0i = scale * fly0i - t1i; + + fly1r = fly2r - U0r * fly3r; + fly1r = fly1r - U0i * fly3i; + fly1i = fly2i + U0i * fly3r; + fly1i = fly1i - U0r * fly3i; + fly2r = scale * fly2r - fly1r; + fly2i = scale * fly2i - fly1i; + + fly0r = fly4r - U0r * fly5r; + fly0r = fly0r - U0i * fly5i; + fly0i = fly4i + U0i * fly5r; + fly0i = fly0i - U0r * fly5i; + fly4r = scale * fly4r - fly0r; + fly4i = scale * fly4i - fly0i; + + fly3r = fly6r - U0r * fly7r; + fly3r = fly3r - U0i * fly7i; + fly3i = fly6i + U0i * fly7r; + fly3i = fly3i - U0r * fly7i; + fly6r = scale * fly6r - fly3r; + fly6i = scale * fly6i - fly3i; + + + fly5r = t0r - U1r * fly2r; + fly5r = fly5r - U1i * fly2i; + fly5i = t0i + U1i * fly2r; + fly5i = fly5i - U1r * fly2i; + t0r = scale * t0r - fly5r; + t0i = scale * t0i - fly5i; + + fly7r = t1r + U1i * fly1r; + fly7r = fly7r - U1r * fly1i; + fly7i = t1i + U1r * fly1r; + fly7i = fly7i + U1i * fly1i; + t1r = scale * t1r - fly7r; + t1i = scale * t1i - fly7i; + + fly2r = fly4r - U1r * fly6r; + fly2r = fly2r - U1i * fly6i; + fly2i = fly4i + U1i * fly6r; + fly2i = fly2i - U1r * fly6i; + fly4r = scale * fly4r - fly2r; + fly4i = scale * fly4i - fly2i; + + fly1r = fly0r + U1i * fly3r; + fly1r = fly1r - U1r * fly3i; + fly1i = fly0i + U1r * fly3r; + fly1i = fly1i + U1i * fly3i; + fly0r = scale * fly0r - fly1r; + fly0i = scale * fly0i - fly1i; + + U0i = *(U0iP = (U0iP - NsameU4)); + U0r = *(U0rP = (U0rP + NsameU4)); + U1r = *(U1rP = (U1rP + NsameU2)); + U1i = *(U1iP = (U1iP - NsameU2)); + if(stage&1) + U0r = -U0r; + + fly6r = t0r - U2r * fly4r; + fly6r = fly6r - U2i * fly4i; + fly6i = t0i + U2i * fly4r; + fly6i = fly6i - U2r * fly4i; + t0r = scale * t0r - fly6r; + t0i = scale * t0i - fly6i; + + fly3r = fly5r - U2i * fly2r; + fly3r = fly3r + U2r * fly2i; + fly3i = fly5i - U2r * fly2r; + fly3i = fly3i - U2i * fly2i; + fly2r = scale * fly5r - fly3r; + fly2i = scale * fly5i - fly3i; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r - U3i * fly0i; + fly4i = t1i + U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly5r = fly7r + U3i * fly1r; + fly5r = fly5r - U3r * fly1i; + fly5i = fly7i + U3r * fly1r; + fly5i = fly5i + U3i * fly1i; + fly7r = scale * fly7r - fly5r; + fly7i = scale * fly7i - fly5i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + + U2r = *(U2rP = (U2rP + NsameU1)); + U2i = *(U2iP = (U2iP - NsameU1)); + + *(fly2P) = fly3r; + *(fly2P + 1) = fly3i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + + U3r = *( U2rP + U3offset); + U3i = *( U2iP - U3offset); + + *(fly3P + FlyOffsetA) = fly5r; + *(fly3P + FlyOffsetAIm) = fly5i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + IOP = IOP + 2; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + }; + NsameU4 = -NsameU4; + + if(stage&1){ + LoopN >>= 3; + NsameU1 >>= 3; + NsameU2 >>= 3; + NsameU4 >>= 3; + NdiffU <<= 3; + Flyinc = Flyinc << 3; + FlyOffsetA <<= 3; + FlyOffsetB <<= 3; + FlyOffsetAIm = FlyOffsetA + 1; + FlyOffsetBIm = FlyOffsetB + 1; + } +} + +/* Finish RFFT */ +M=M+1; + +FlyOffsetA = Ntbl[M] * 2/4; +FlyOffsetAIm = Ntbl[M] * 2/4 + 1; + +IOP = ioptr; + +fly0P = (IOP + Ntbl[M]*2/4); +fly1P = (IOP + Ntbl[M]*2/8); + +U0rP = &Utbl[Ntbl[M-3]]; + +U0r = *U0rP, + +fly0r = *(IOP); +fly0i = *(IOP + 1); +fly1r = *(fly0P); +fly1i = *(fly0P + 1); +fly2r = *(fly1P); +fly2i = *(fly1P + 1); +fly3r = *(fly1P + FlyOffsetA); +fly3i = *(fly1P + FlyOffsetAIm); + + t0r = scale * fly0r + scale * fly0i; /* compute Re(x[0]) */ + t0i = scale * fly0r - scale * fly0i; /* compute Re(x[N/2]) */ + t1r = scale * fly1r; + t1i = -scale * fly1i; + + fly0r = fly2r + fly3r; + fly0i = fly2i - fly3i; + fly1r = fly2i + fly3i; + fly1i = fly3r - fly2r; + + fly2r = fly0r + U0r * fly1r; + fly2r = fly2r + U0r * fly1i; + fly2i = fly0i - U0r * fly1r; + fly2i = fly2i + U0r * fly1i; + fly3r = scale * fly0r - fly2r; + fly3i = fly2i - scale * fly0i; + +*(IOP) = t0r; +*(IOP + 1) = t0i; +*(fly0P) = t1r; +*(fly0P + 1) = t1i; +*(fly1P) = fly2r; +*(fly1P + 1) = fly2i; +*(fly1P + FlyOffsetA) = fly3r; +*(fly1P + FlyOffsetAIm) = fly3i; + +U0rP = &Utbl[1]; +U0iP = &Utbl[Ntbl[M-2]-1]; + +U0r = *U0rP, +U0i = *U0iP; + +fly0P = (IOP + 2); +fly1P = (IOP + (Ntbl[M-2]-1)*2); + + /* Butterflys */ + /* + f0 - t0 - - f2 + f1 - t1 -U0 - f3 + f2 - f0 - - t0 + f3 - f1 -U0a- t1 + */ + +for (diffUcnt = Ntbl[M-3]-1; diffUcnt > 0 ; diffUcnt--){ + + fly0r = *(fly0P); + fly0i = *(fly0P + 1); + fly1r = *(fly1P + FlyOffsetA); + fly1i = *(fly1P + FlyOffsetAIm); + fly2r = *(fly1P); + fly2i = *(fly1P + 1); + fly3r = *(fly0P + FlyOffsetA); + fly3i = *(fly0P + FlyOffsetAIm); + + t0r = fly0r + fly1r; + t0i = fly0i - fly1i; + t1r = fly0i + fly1i; + t1i = fly1r - fly0r; + + fly0r = fly2r + fly3r; + fly0i = fly2i - fly3i; + fly1r = fly2i + fly3i; + fly1i = fly3r - fly2r; + + fly2r = t0r + U0r * t1r; + fly2r = fly2r + U0i * t1i; + fly2i = t0i - U0i * t1r; + fly2i = fly2i + U0r * t1i; + fly3r = scale * t0r - fly2r; + fly3i = fly2i - scale * t0i; + + t0r = fly0r + U0i * fly1r; + t0r = t0r + U0r * fly1i; + t0i = fly0i - U0r * fly1r; + t0i = t0i + U0i * fly1i; + t1r = scale * fly0r - t0r; + t1i = t0i - scale * fly0i; + + *(fly0P) = fly2r; + *(fly0P + 1) = fly2i; + *(fly1P + FlyOffsetA) = fly3r; + *(fly1P + FlyOffsetAIm) = fly3i; + + U0r = *(U0rP = (U0rP + 1)); + U0i = *(U0iP = (U0iP - 1)); + + *(fly1P) = t0r; + *(fly1P + 1) = t0i; + *(fly0P + FlyOffsetA) = t1r; + *(fly0P + FlyOffsetAIm) = t1i; + + fly0P += 2; + fly1P -= 2; +}; + +ioptr += Ntbl[M]; +} +} + +void riffts(float *ioptr, long M, long Rows, float *Utbl){ +/* Compute in-place real ifft on the rows of the input array */ +/* INPUTS */ +/* M = log2 of fft size */ +/* *ioptr = input data array in the following order */ +/* Re(x[0]), Re(x[N/2]), Re(x[1]), Im(x[1]), Re(x[2]), Im(x[2]), ... Re(x[N/2-1]), Im(x[N/2-1]). */ +/* *Utbl = cosine table */ +/* Rows = number of rows in ioptr array (use Rows of 1 if ioptr is a 1 dimensional array) */ +/* OUTPUTS */ +/* *ioptr = real output data array */ + +long Flyinc; +long FlyOffsetA; +long FlyOffsetAIm; +long FlyOffsetB; +long FlyOffsetBIm; +long NsameU1; +long NsameU2; +long NsameU4; +long diffUcnt; +long LoopCnt; +float scale; +float fly0r; +float fly0i; +float fly1r; +float fly1i; +float fly2r; +float fly2i; +float fly3r; +float fly3i; +float fly4r; +float fly4i; +float fly5r; +float fly5i; +float fly6r; +float fly6i; +float fly7r; +float fly7i; +float U0r; +float U0i; +float U1r; +float U1i; +float U2r; +float U2i; +float U3r; +float U3i; +float t0r; +float t0i; +float t1r; +float t1i; + +float *fly0P; +float *fly1P; +float *fly2P; +float *fly3P; + +float *U0rP; +float *U0iP; +float *U1rP; +float *U1iP; +float *U2rP; +float *U2iP; +float *IOP; +long U3offset; + +long stage; +long NdiffU; +long LoopN; + +const long BRshift = MAXMROOT - ((M-1)>>1); /* for RIFFT */ +const long Nrems2 = Ntbl[(M-1)-((M-1)>>1)+1]; /* for RIFFT */ +const long Nroot_1_ColInc = (Ntbl[(M-1)-1]-Ntbl[(M-1)-((M-1)>>1)])*2; /* for RIFFT */ + +for (;Rows>0;Rows--){ + +/* Start RIFFT */ + +FlyOffsetA = Ntbl[M] * 2/4; +FlyOffsetAIm = Ntbl[M] * 2/4 + 1; + +IOP = ioptr; + +fly0P = (IOP + Ntbl[M]*2/4); +fly1P = (IOP + Ntbl[M]*2/8); + +U0rP = &Utbl[Ntbl[M-3]]; + +U0r = *U0rP, + +fly0r = *(IOP); +fly0i = *(IOP + 1); +fly1r = *(fly0P); +fly1i = *(fly0P + 1); +fly2r = *(fly1P); +fly2i = *(fly1P + 1); +fly3r = *(fly1P + FlyOffsetA); +fly3i = *(fly1P + FlyOffsetAIm); + + t0r = fly0r + fly0i; + t0i = fly0r - fly0i; + t1r = fly1r + fly1r; + t1i = -fly1i - fly1i; + + fly0r = fly2r + fly3r; + fly0i = fly2i - fly3i; + fly1r = fly2r - fly3r; + fly1i = fly2i + fly3i; + + fly3r = fly1r * U0r; + fly3r = fly3r - U0r * fly1i; + fly3i = fly1r * U0r; + fly3i = fly3i + U0r * fly1i; + + fly2r = fly0r - fly3i; + fly2i = fly0i + fly3r; + fly1r = fly0r + fly3i; + fly1i = -fly0i + fly3r; + +*(IOP) = t0r; +*(IOP + 1) = t0i; +*(fly0P) = t1r; +*(fly0P + 1) = t1i; +*(fly1P) = fly2r; +*(fly1P + 1) = fly2i; +*(fly1P + FlyOffsetA) = fly1r; +*(fly1P + FlyOffsetAIm) = fly1i; + +U0rP = &Utbl[1]; +U0iP = &Utbl[Ntbl[M-2]-1]; + +U0r = *U0rP, +U0i = *U0iP; + +fly0P = (IOP + 2); +fly1P = (IOP + (Ntbl[M-2]-1)*2); + + /* Butterflys */ + /* + f0 - t0 - f2 + f1 -t1 -U0- f3 - f1 + f2 - f0 - t0 + f3 -f1 -U0a t1 - f3 + */ + +for (diffUcnt = Ntbl[M-3]-1; diffUcnt > 0 ; diffUcnt--){ + + fly0r = *(fly0P); + fly0i = *(fly0P + 1); + fly1r = *(fly1P + FlyOffsetA); + fly1i = *(fly1P + FlyOffsetAIm); + fly2r = *(fly1P); + fly2i = *(fly1P + 1); + fly3r = *(fly0P + FlyOffsetA); + fly3i = *(fly0P + FlyOffsetAIm); + + t0r = fly0r + fly1r; + t0i = fly0i - fly1i; + t1r = fly0r - fly1r; + t1i = fly0i + fly1i; + + fly0r = fly2r + fly3r; + fly0i = fly2i - fly3i; + fly1r = fly2r - fly3r; + fly1i = fly2i + fly3i; + + + fly3r = t1r * U0r; + fly3r = fly3r - U0i * t1i; + fly3i = t1r * U0i; + fly3i = fly3i + U0r * t1i; + + t1r = fly1r * U0i; + t1r = t1r - U0r * fly1i; + t1i = fly1r * U0r; + t1i = t1i + U0i * fly1i; + + + fly2r = t0r - fly3i; + fly2i = t0i + fly3r; + fly1r = t0r + fly3i; + fly1i = -t0i + fly3r; + + t0r = fly0r - t1i; + t0i = fly0i + t1r; + fly3r = fly0r + t1i; + fly3i = -fly0i + t1r; + + + *(fly0P) = fly2r; + *(fly0P + 1) = fly2i; + *(fly1P + FlyOffsetA) = fly1r; + *(fly1P + FlyOffsetAIm) = fly1i; + + U0r = *(U0rP = (U0rP + 1)); + U0i = *(U0iP = (U0iP - 1)); + + *(fly1P) = t0r; + *(fly1P + 1) = t0i; + *(fly0P + FlyOffsetA) = fly3r; + *(fly0P + FlyOffsetAIm) = fly3i; + + fly0P += 2; + fly1P -= 2; +}; + +M=M-1; /* for RIFFT */ + +FlyOffsetA = Ntbl[M] * 2/2; +FlyOffsetAIm = FlyOffsetA + 1; +FlyOffsetB = FlyOffsetA + 2; +FlyOffsetBIm = FlyOffsetB + 1; + +/* BitrevR2 ** bit reverse shuffle and first radix 2 stage ******/ + +scale = 1./Ntbl[M+1]; +for (stage = 0; stage < Ntbl[M-(M>>1)]*2; stage += Ntbl[M>>1]*2){ + for (LoopN = (Ntbl[(M>>1)-1]-1); LoopN >= 0; LoopN--){ + LoopCnt = (Ntbl[(M>>1)-1]-1); + fly0P = ioptr + Nroot_1_ColInc + ((int)BRcnt[LoopN] >> BRshift)*(2*2) + stage; + IOP = ioptr + (LoopN<<(M+1)/2) * 2 + stage; + fly1P = IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2); + fly0r = *(fly0P); + fly0i = *(fly0P+1); + fly1r = *(fly0P+FlyOffsetA); + fly1i = *(fly0P+FlyOffsetAIm); + for (; LoopCnt > LoopN;){ + fly2r = *(fly0P+2); + fly2i = *(fly0P+(2+1)); + fly3r = *(fly0P+FlyOffsetB); + fly3i = *(fly0P+FlyOffsetBIm); + fly4r = *(fly1P); + fly4i = *(fly1P+1); + fly5r = *(fly1P+FlyOffsetA); + fly5i = *(fly1P+FlyOffsetAIm); + fly6r = *(fly1P+2); + fly6i = *(fly1P+(2+1)); + fly7r = *(fly1P+FlyOffsetB); + fly7i = *(fly1P+FlyOffsetBIm); + + t0r = fly0r + fly1r; + t0i = fly0i + fly1i; + fly1r = fly0r - fly1r; + fly1i = fly0i - fly1i; + t1r = fly2r + fly3r; + t1i = fly2i + fly3i; + fly3r = fly2r - fly3r; + fly3i = fly2i - fly3i; + fly0r = fly4r + fly5r; + fly0i = fly4i + fly5i; + fly5r = fly4r - fly5r; + fly5i = fly4i - fly5i; + fly2r = fly6r + fly7r; + fly2i = fly6i + fly7i; + fly7r = fly6r - fly7r; + fly7i = fly6i - fly7i; + + *(fly1P) = scale*t0r; + *(fly1P+1) = scale*t0i; + *(fly1P+2) = scale*fly1r; + *(fly1P+(2+1)) = scale*fly1i; + *(fly1P+FlyOffsetA) = scale*t1r; + *(fly1P+FlyOffsetAIm) = scale*t1i; + *(fly1P+FlyOffsetB) = scale*fly3r; + *(fly1P+FlyOffsetBIm) = scale*fly3i; + *(fly0P) = scale*fly0r; + *(fly0P+1) = scale*fly0i; + *(fly0P+2) = scale*fly5r; + *(fly0P+(2+1)) = scale*fly5i; + *(fly0P+FlyOffsetA) = scale*fly2r; + *(fly0P+FlyOffsetAIm) = scale*fly2i; + *(fly0P+FlyOffsetB) = scale*fly7r; + *(fly0P+FlyOffsetBIm) = scale*fly7i; + + fly0P -= Nrems2; + fly0r = *(fly0P); + fly0i = *(fly0P+1); + fly1r = *(fly0P+FlyOffsetA); + fly1i = *(fly0P+FlyOffsetAIm); + LoopCnt -= 1; + fly1P = (IOP + ((int)BRcnt[LoopCnt] >> BRshift)*(2*2)); + }; + fly2r = *(fly0P+2); + fly2i = *(fly0P+(2+1)); + fly3r = *(fly0P+FlyOffsetB); + fly3i = *(fly0P+FlyOffsetBIm); + + t0r = fly0r + fly1r; + t0i = fly0i + fly1i; + fly1r = fly0r - fly1r; + fly1i = fly0i - fly1i; + t1r = fly2r + fly3r; + t1i = fly2i + fly3i; + fly3r = fly2r - fly3r; + fly3i = fly2i - fly3i; + + *(fly0P) = scale*t0r; + *(fly0P+1) = scale*t0i; + *(fly0P+2) = scale*fly1r; + *(fly0P+(2+1)) = scale*fly1i; + *(fly0P+FlyOffsetA) = scale*t1r; + *(fly0P+FlyOffsetAIm) = scale*t1i; + *(fly0P+FlyOffsetB) = scale*fly3r; + *(fly0P+FlyOffsetBIm) = scale*fly3i; + + }; +}; + +/**** FFTC **************/ + +scale = 2.0; + +NdiffU = 2; +Flyinc = (NdiffU); + +NsameU4 = Ntbl[M+1]/4; /* for RIFFT */ +LoopN = Ntbl[M-3]; + +stage = ((M-1)/3); +if ( (M-1-(stage * 3)) != 0 ){ + FlyOffsetA = Flyinc << 2; + FlyOffsetB = FlyOffsetA << 1; + FlyOffsetAIm = FlyOffsetA + 1; + FlyOffsetBIm = FlyOffsetB + 1; + if ( (M-1-(stage * 3)) == 1 ){ + /* 1 radix 2 stage */ + + IOP = ioptr; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + /* Butterflys */ + /* + t0 - - t0 + t1 - - t1 + f2 - 1- f5 + f1 - -i- f7 + f4 - - f4 + f0 - - f0 + f6 - 1- f2 + f3 - -i- f1 + */ + + for (LoopCnt = LoopN; LoopCnt > 0 ; LoopCnt--){ + t0r = *(fly0P); + t0i = *(fly0P + 1); + t1r = *(fly1P); + t1i = *(fly1P + 1); + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly1r = *(fly3P); + fly1i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly0r = *(fly1P + FlyOffsetA); + fly0i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly3r = *(fly3P + FlyOffsetA); + fly3i = *(fly3P + FlyOffsetAIm); + + fly5r = t0r - fly2r; + fly5i = t0i - fly2i; + t0r = t0r + fly2r; + t0i = t0i + fly2i; + + fly7r = t1r + fly1i; + fly7i = t1i - fly1r; + t1r = t1r - fly1i; + t1i = t1i + fly1r; + + fly2r = fly4r - fly6r; + fly2i = fly4i - fly6i; + fly4r = fly4r + fly6r; + fly4i = fly4i + fly6i; + + fly1r = fly0r + fly3i; + fly1i = fly0i - fly3r; + fly0r = fly0r - fly3i; + fly0i = fly0i + fly3r; + + *(fly2P) = fly5r; + *(fly2P + 1) = fly5i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + *(fly0P + FlyOffsetA) = fly4r; + *(fly0P + FlyOffsetAIm) = fly4i; + *(fly3P + FlyOffsetA) = fly1r; + *(fly3P + FlyOffsetAIm) = fly1i; + *(fly1P + FlyOffsetA) = fly0r; + *(fly1P + FlyOffsetAIm) = fly0i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + }; + + NsameU4 >>= 1; + LoopN >>= 1; + NdiffU <<= 1; + Flyinc = Flyinc << 1; + } + else{ + /* 1 radix 4 stage */ + IOP = ioptr; + + U3r = 0.7071067811865475244008443621; /* sqrt(0.5); */ + U3i = U3r; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + /* Butterflys */ + /* + t0 - - t0 - - t0 + t1 - - t1 - - t1 + f2 - 1- f5 - - f5 + f1 - -i- f7 - - f7 + f4 - - f4 - 1- f6 + f0 - - f0 -U3 - f3 + f6 - 1- f2 - -i- f4 + f3 - -i- f1 -U3a- f2 + */ + + for (LoopCnt = LoopN; LoopCnt > 0 ; LoopCnt--){ + t0r = *(fly0P); + t0i = *(fly0P + 1); + t1r = *(fly1P); + t1i = *(fly1P + 1); + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly1r = *(fly3P); + fly1i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly0r = *(fly1P + FlyOffsetA); + fly0i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly3r = *(fly3P + FlyOffsetA); + fly3i = *(fly3P + FlyOffsetAIm); + + fly5r = t0r - fly2r; + fly5i = t0i - fly2i; + t0r = t0r + fly2r; + t0i = t0i + fly2i; + + fly7r = t1r + fly1i; + fly7i = t1i - fly1r; + t1r = t1r - fly1i; + t1i = t1i + fly1r; + + fly2r = fly4r - fly6r; + fly2i = fly4i - fly6i; + fly4r = fly4r + fly6r; + fly4i = fly4i + fly6i; + + fly1r = fly0r + fly3i; + fly1i = fly0i - fly3r; + fly0r = fly0r - fly3i; + fly0i = fly0i + fly3r; + + fly6r = t0r - fly4r; + fly6i = t0i - fly4i; + t0r = t0r + fly4r; + t0i = t0i + fly4i; + + fly3r = fly5r + fly2i; + fly3i = fly5i - fly2r; + fly5r = fly5r - fly2i; + fly5i = fly5i + fly2r; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r + U3i * fly0i; + fly4i = t1i - U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly2r = fly7r + U3i * fly1r; + fly2r = fly2r + U3r * fly1i; + fly2i = fly7i - U3r * fly1r; + fly2i = fly2i + U3i * fly1i; + fly7r = scale * fly7r - fly2r; + fly7i = scale * fly7i - fly2i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly2P + FlyOffsetA) = fly3r; + *(fly2P + FlyOffsetAIm) = fly3i; + *(fly2P) = fly5r; + *(fly2P + 1) = fly5i; + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + *(fly3P + FlyOffsetA) = fly2r; + *(fly3P + FlyOffsetAIm) = fly2i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + + }; + + NsameU4 >>= 2; + LoopN >>= 2; + NdiffU <<= 2; + Flyinc = Flyinc << 2; + }; +}; + +NsameU2 = NsameU4 >> 1; +NsameU1 = NsameU2 >> 1; +Flyinc <<= 1; +FlyOffsetA = Flyinc << 2; +FlyOffsetB = FlyOffsetA << 1; +FlyOffsetAIm = FlyOffsetA + 1; +FlyOffsetBIm = FlyOffsetB + 1; +LoopN >>= 1; + +/* ****** RADIX 8 Stages */ +for (stage = stage<<1; stage > 0 ; stage--){ + + /* an fft stage is done in two parts to ease use of the single quadrant cos table */ + +/* fftcalc1(iobuf, Utbl, N, NdiffU, LoopN); */ + if(!(stage&1)){ + U0rP = &Utbl[0]; + U0iP = &Utbl[Ntbl[M-1]]; /* for RIFFT */ + U1rP = U0rP; + U1iP = U0iP; + U2rP = U0rP; + U2iP = U0iP; + U3offset = (Ntbl[M+1]) / 8; /* for RIFFT */ + + IOP = ioptr; + + U0r = *U0rP, + U0i = *U0iP; + U1r = *U1rP, + U1i = *U1iP; + U2r = *U2rP, + U2i = *U2iP; + U3r = *( U2rP + U3offset); + U3i = *( U2iP - U3offset); + } + + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + + for (diffUcnt = (NdiffU)>>1; diffUcnt > 0; diffUcnt--){ + + /* Butterflys */ + /* + f0 - - t0 - - t0 - - t0 + f1 -U0 - t1 - - t1 - - t1 + f2 - - f2 -U1 - f5 - - f3 + f3 -U0 - f1 -U1a- f7 - - f7 + f4 - - f4 - - f4 -U2 - f6 + f5 -U0 - f0 - - f0 -U3 - f4 + f6 - - f6 -U1 - f2 -U2a- f2 + f7 -U0 - f3 -U1a- f1 -U3a- f5 + */ + + fly0r = *(IOP); + fly0i = *(IOP+1); + fly1r = *(fly1P); + fly1i = *(fly1P+1); + + for (LoopCnt = LoopN-1; LoopCnt > 0 ; LoopCnt--){ + + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly3r = *(fly3P); + fly3i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly5r = *(fly1P + FlyOffsetA); + fly5i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly7r = *(fly3P + FlyOffsetA); + fly7i = *(fly3P + FlyOffsetAIm); + + t1r = fly0r - U0r * fly1r; + t1r = t1r + U0i * fly1i; + t1i = fly0i - U0i * fly1r; + t1i = t1i - U0r * fly1i; + t0r = scale * fly0r - t1r; + t0i = scale * fly0i - t1i; + + fly1r = fly2r - U0r * fly3r; + fly1r = fly1r + U0i * fly3i; + fly1i = fly2i - U0i * fly3r; + fly1i = fly1i - U0r * fly3i; + fly2r = scale * fly2r - fly1r; + fly2i = scale * fly2i - fly1i; + + fly0r = fly4r - U0r * fly5r; + fly0r = fly0r + U0i * fly5i; + fly0i = fly4i - U0i * fly5r; + fly0i = fly0i - U0r * fly5i; + fly4r = scale * fly4r - fly0r; + fly4i = scale * fly4i - fly0i; + + fly3r = fly6r - U0r * fly7r; + fly3r = fly3r + U0i * fly7i; + fly3i = fly6i - U0i * fly7r; + fly3i = fly3i - U0r * fly7i; + fly6r = scale * fly6r - fly3r; + fly6i = scale * fly6i - fly3i; + + + fly5r = t0r - U1r * fly2r; + fly5r = fly5r + U1i * fly2i; + fly5i = t0i - U1i * fly2r; + fly5i = fly5i - U1r * fly2i; + t0r = scale * t0r - fly5r; + t0i = scale * t0i - fly5i; + + fly7r = t1r + U1i * fly1r; + fly7r = fly7r + U1r * fly1i; + fly7i = t1i - U1r * fly1r; + fly7i = fly7i + U1i * fly1i; + t1r = scale * t1r - fly7r; + t1i = scale * t1i - fly7i; + + fly2r = fly4r - U1r * fly6r; + fly2r = fly2r + U1i * fly6i; + fly2i = fly4i - U1i * fly6r; + fly2i = fly2i - U1r * fly6i; + fly4r = scale * fly4r - fly2r; + fly4i = scale * fly4i - fly2i; + + fly1r = fly0r + U1i * fly3r; + fly1r = fly1r + U1r * fly3i; + fly1i = fly0i - U1r * fly3r; + fly1i = fly1i + U1i * fly3i; + fly0r = scale * fly0r - fly1r; + fly0i = scale * fly0i - fly1i; + + fly6r = t0r - U2r * fly4r; + fly6r = fly6r + U2i * fly4i; + fly6i = t0i - U2i * fly4r; + fly6i = fly6i - U2r * fly4i; + t0r = scale * t0r - fly6r; + t0i = scale * t0i - fly6i; + + fly3r = fly5r - U2i * fly2r; + fly3r = fly3r - U2r * fly2i; + fly3i = fly5i + U2r * fly2r; + fly3i = fly3i - U2i * fly2i; + fly2r = scale * fly5r - fly3r; + fly2i = scale * fly5i - fly3i; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r + U3i * fly0i; + fly4i = t1i - U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly5r = fly7r + U3i * fly1r; + fly5r = fly5r + U3r * fly1i; + fly5i = fly7i - U3r * fly1r; + fly5i = fly5i + U3i * fly1i; + fly7r = scale * fly7r - fly5r; + fly7i = scale * fly7i - fly5i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + *(fly2P) = fly3r; + *(fly2P + 1) = fly3i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + + fly0r = *(fly0P + FlyOffsetB); + fly0i = *(fly0P + FlyOffsetBIm); + + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + + fly1r = *(fly1P + FlyOffsetB); + fly1i = *(fly1P + FlyOffsetBIm); + + *(fly3P + FlyOffsetA) = fly5r; + *(fly3P + FlyOffsetAIm) = fly5i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + fly0P = (fly0P + FlyOffsetB); + fly1P = (fly1P + FlyOffsetB); + fly2P = (fly2P + FlyOffsetB); + fly3P = (fly3P + FlyOffsetB); + + }; + fly2r = *(fly2P); + fly2i = *(fly2P + 1); + fly3r = *(fly3P); + fly3i = *(fly3P + 1); + fly4r = *(fly0P + FlyOffsetA); + fly4i = *(fly0P + FlyOffsetAIm); + fly5r = *(fly1P + FlyOffsetA); + fly5i = *(fly1P + FlyOffsetAIm); + fly6r = *(fly2P + FlyOffsetA); + fly6i = *(fly2P + FlyOffsetAIm); + fly7r = *(fly3P + FlyOffsetA); + fly7i = *(fly3P + FlyOffsetAIm); + + t1r = fly0r - U0r * fly1r; + t1r = t1r + U0i * fly1i; + t1i = fly0i - U0i * fly1r; + t1i = t1i - U0r * fly1i; + t0r = scale * fly0r - t1r; + t0i = scale * fly0i - t1i; + + fly1r = fly2r - U0r * fly3r; + fly1r = fly1r + U0i * fly3i; + fly1i = fly2i - U0i * fly3r; + fly1i = fly1i - U0r * fly3i; + fly2r = scale * fly2r - fly1r; + fly2i = scale * fly2i - fly1i; + + fly0r = fly4r - U0r * fly5r; + fly0r = fly0r + U0i * fly5i; + fly0i = fly4i - U0i * fly5r; + fly0i = fly0i - U0r * fly5i; + fly4r = scale * fly4r - fly0r; + fly4i = scale * fly4i - fly0i; + + fly3r = fly6r - U0r * fly7r; + fly3r = fly3r + U0i * fly7i; + fly3i = fly6i - U0i * fly7r; + fly3i = fly3i - U0r * fly7i; + fly6r = scale * fly6r - fly3r; + fly6i = scale * fly6i - fly3i; + + fly5r = t0r - U1r * fly2r; + fly5r = fly5r + U1i * fly2i; + fly5i = t0i - U1i * fly2r; + fly5i = fly5i - U1r * fly2i; + t0r = scale * t0r - fly5r; + t0i = scale * t0i - fly5i; + + fly7r = t1r + U1i * fly1r; + fly7r = fly7r + U1r * fly1i; + fly7i = t1i - U1r * fly1r; + fly7i = fly7i + U1i * fly1i; + t1r = scale * t1r - fly7r; + t1i = scale * t1i - fly7i; + + fly2r = fly4r - U1r * fly6r; + fly2r = fly2r + U1i * fly6i; + fly2i = fly4i - U1i * fly6r; + fly2i = fly2i - U1r * fly6i; + fly4r = scale * fly4r - fly2r; + fly4i = scale * fly4i - fly2i; + + fly1r = fly0r + U1i * fly3r; + fly1r = fly1r + U1r * fly3i; + fly1i = fly0i - U1r * fly3r; + fly1i = fly1i + U1i * fly3i; + fly0r = scale * fly0r - fly1r; + fly0i = scale * fly0i - fly1i; + + U0i = *(U0iP = (U0iP - NsameU4)); + U0r = *(U0rP = (U0rP + NsameU4)); + U1r = *(U1rP = (U1rP + NsameU2)); + U1i = *(U1iP = (U1iP - NsameU2)); + if(stage&1) + U0r = - U0r; + + fly6r = t0r - U2r * fly4r; + fly6r = fly6r + U2i * fly4i; + fly6i = t0i - U2i * fly4r; + fly6i = fly6i - U2r * fly4i; + t0r = scale * t0r - fly6r; + t0i = scale * t0i - fly6i; + + fly3r = fly5r - U2i * fly2r; + fly3r = fly3r - U2r * fly2i; + fly3i = fly5i + U2r * fly2r; + fly3i = fly3i - U2i * fly2i; + fly2r = scale * fly5r - fly3r; + fly2i = scale * fly5i - fly3i; + + fly4r = t1r - U3r * fly0r; + fly4r = fly4r + U3i * fly0i; + fly4i = t1i - U3i * fly0r; + fly4i = fly4i - U3r * fly0i; + t1r = scale * t1r - fly4r; + t1i = scale * t1i - fly4i; + + fly5r = fly7r + U3i * fly1r; + fly5r = fly5r + U3r * fly1i; + fly5i = fly7i - U3r * fly1r; + fly5i = fly5i + U3i * fly1i; + fly7r = scale * fly7r - fly5r; + fly7i = scale * fly7i - fly5i; + + *(fly0P + FlyOffsetA) = fly6r; + *(fly0P + FlyOffsetAIm) = fly6i; + *(fly0P) = t0r; + *(fly0P + 1) = t0i; + + U2r = *(U2rP = (U2rP + NsameU1)); + U2i = *(U2iP = (U2iP - NsameU1)); + + *(fly2P) = fly3r; + *(fly2P + 1) = fly3i; + *(fly2P + FlyOffsetA) = fly2r; + *(fly2P + FlyOffsetAIm) = fly2i; + *(fly1P + FlyOffsetA) = fly4r; + *(fly1P + FlyOffsetAIm) = fly4i; + *(fly1P) = t1r; + *(fly1P + 1) = t1i; + + U3r = *( U2rP + U3offset); + U3i = *( U2iP - U3offset); + + *(fly3P + FlyOffsetA) = fly5r; + *(fly3P + FlyOffsetAIm) = fly5i; + *(fly3P) = fly7r; + *(fly3P + 1) = fly7i; + + IOP = IOP + 2; + fly0P = IOP; + fly1P = (IOP+Flyinc); + fly2P = (fly1P+Flyinc); + fly3P = (fly2P+Flyinc); + }; + NsameU4 = -NsameU4; + + if(stage&1){ + LoopN >>= 3; + NsameU1 >>= 3; + NsameU2 >>= 3; + NsameU4 >>= 3; + NdiffU <<= 3; + Flyinc = Flyinc << 3; + FlyOffsetA <<= 3; + FlyOffsetB <<= 3; + FlyOffsetAIm = FlyOffsetA + 1; + FlyOffsetBIm = FlyOffsetB + 1; + } +} +M=M+1; /* for RIFFT */ + +ioptr += Ntbl[M]; +} +} |