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hippo_fft.s
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;APS00000000000000000000000000000000000000000000000000000000000000000000000000000000
;; /* fix_fft.c - Fixed-point Fast Fourier Transform */
;; /*
;; fix_fft() perform FFT or inverse FFT
;; window() applies a Hanning window to the (time) input
;; fix_loud() calculates the loudness of the signal, for
;; each freq point. Result is an integer array,
;; units are dB (values will be negative).
;; iscale() scale an integer value by (numer/denom).
;; fix_mpy() perform fixed-point multiplication.
;; Sinewave[1024] sinewave normalized to 32767 (= 1.0).
;; Loudampl[100] Amplitudes for lopudnesses from 0 to -99 dB.
;; Low_pass Low-pass filter, cutoff at sample_freq / 4.
;; All data are fixed-point short integers, in which
;; -32768 to +32768 represent -1.0 to +1.0. Integer arithmetic
;; is used for speed, instead of the more natural floating-point.
;; For the forward FFT (time -> freq), fixed scaling is
;; performed to prevent arithmetic overflow, and to map a 0dB
;; sine/cosine wave (i.e. amplitude = 32767) to two -6dB freq
;; coefficients; the one in the lower half is reported as 0dB
;; by fix_loud(). The return value is always 0.
;; For the inverse FFT (freq -> time), fixed scaling cannot be
;; done, as two 0dB coefficients would sum to a peak amplitude of
;; 64K, overflowing the 32k range of the fixed-point integers.
;; Thus, the fix_fft() routine performs variable scaling, and
;; returns a value which is the number of bits LEFT by which
;; the output must be shifted to get the actual amplitude
;; (i.e. if fix_fft() returns 3, each value of fr[] and fi[]
;; must be multiplied by 8 (2**3) for proper scaling.
;; Clearly, this cannot be done within the fixed-point short
;; integers. In practice, if the result is to be used as a
;; filter, the scale_shift can usually be ignored, as the
;; result will be approximately correctly normalized as is.
;; TURBO C, any memory model; uses inline assembly for speed
;; and for carefully-scaled arithmetic.
;; Written by: Tom Roberts 11/8/89
;; Made portable: Malcolm Slaney 12/15/94 [email protected]
;; Timing on a Macintosh PowerBook 180.... (using Symantec C6.0)
;; fix_fft (1024 points) 8 ticks
;; fft (1024 points - Using SANE) 112 Ticks
;; fft (1024 points - Using FPU) 11
;; */
;; /* FIX_MPY() - fixed-point multiplication macro.
;; This macro is a statement, not an expression (uses asm).
;; BEWARE: make sure _DX is not clobbered by evaluating (A) or DEST.
;; args are all of type fixed.
;; Scaling ensures that 32767*32767 = 32767. */
;; #define dosFIX_MPY(DEST,A,B) { \
;; _DX = (B); \
;; _AX = (A); \
;; asm imul dx; \
;; asm add ax,ax; \
;; asm adc dx,dx; \
;; DEST = _DX; }
;; #define FIX_MPY(DEST,A,B) DEST = ((long)(A) * (long)(B))>>15
;; #define N_WAVE 1024 /* dimension of Sinewave[] */
N_WAVE = 1024
;; #define LOG2_N_WAVE 10 /* log2(N_WAVE) */
LOG2_N_WAVE = 10
;; #define N_LOUD 100 /* dimension of Loudampl[] */
N_LOUD = 100
;; #ifndef fixed
;; #define fixed short
;; #endif
;; extern fixed Sinewave[N_WAVE]; /* placed at end of this file for clarity */
;; extern fixed Loudampl[N_LOUD];
;; int db_from_ampl(fixed re, fixed im);
;; fixed fix_mpy(fixed a, fixed b);
;; /*
;; fix_fft() - perform fast Fourier transform.
;; if n>0 FFT is done, if n<0 inverse FFT is done
;; fr[n],fi[n] are real,imaginary arrays, INPUT AND RESULT.
;; size of data = 2**m
;; set inverse to 0=dft, 1=idft
;; */
FFT_TEST = 0
* Enables different way to handle fixed points,
* faster but breaks the test. Though it should still be
* accurate.
FFT_ALTERNATE_ASR = 1
ifne FFT_TEST
FFT_SIZE = 4
else
FFT_SIZE = 7
endif
FFT_LENGTH = 1<<FFT_SIZE
FFT_LOOPS = 0
; disable multitasking for more accuracy
ifne FFT_TEST
incdir "include:"
include "exec/exec_lib.i"
test
move.l 4.w,a6
jsr _LVOForbid(a6)
jsr _LVODisable(a6)
bsr convert_sine
bsr.w .waitVBlank
bsr testFFT
bsr testFFT
bsr testFFT
move.l $dff004,d6
and.l #$1ff00,d6
lsr.l #8,d6
* FS-UAE A500 kick13+68000:
* - 165
* - 163: sine conversion ASRs removed
* - 162: use SP for vars, a5 for another sine pointer
* - 160: use all table indexes multiplied by two
* - 139: do asr #15 to the sum instead of components before
* this breaks the unit test but probably
* because it is just more accurate.
* - 125: replace asr #15 with add,swap
* - 123: use the now free d5 as .m(sp)
move.l 4.w,a6
jsr _LVOEnable(a6)
jsr _LVOPermit(a6)
rts
.waitVBlank
.v1 btst #0,$dff005
beq.b .v1
.v2 btst #0,$dff005
bne.b .v2
rts
testFFT
lea .test_real_in(pc),a0
lea fr(pc),a1
moveq #FFT_LENGTH-1,d0
.c move (a0)+,(a1)+
dbf d0,.c
lea fr(pc),a0
;bsr windowFFT
lea fr(pc),a0
lea fi(pc),a1
bsr.w sampleFFT
moveq #-1,d7
moveq #FFT_LENGTH-1,d0
lea .test_real_out(pc),a0
lea fr(pc),a1
.ch1 cmpm.w (a0)+,(a1)+
bne.b .error
dbf d0,.ch1
moveq #FFT_LENGTH-1,d0
lea .test_img_out(pc),a0
lea fi(pc),a1
.ch2 cmpm.w (a0)+,(a1)+
bne.b .error
dbf d0,.ch2
;; passed
moveq #0,d7
; lea fr(pc),a0
; lea fi(pc),a1
; bsr loudFFT
; rts
; lea fr(pc),a0
; lea fi(pc),a1
; move.l d7,-(sp)
; bsr.w calcFFTPower
; move.l (sp)+,d7
.error
movem.l cloop1,d0-d4
rts
.test_real_in
dc.w 1000,923,707,382,0,-382,-707,-923,-1000,-923,-707,-382,0,382,707,923
.test_real_out
dc.w -2,498,0,0,0,1,1,0,0,0,0,0,0,-1,-1,498
.test_img_out
dc.w 0,-3,-1,-2,0,-1,-1,-2,0,1,1,0,0,1,1,2
temp dc.l 0
cloop1 dc.l 0
cloop2 dc.l 0
cloop3 dc.l 0
cloop4 dc.l 0
cloop5 dc.l 0
maxSqr dc.l 0
temp2 dc.l 0
endif ; FFT_TEST
if 0
prepareSquareTable
lea squareTable,a0
move #$ffff,d1
moveq #0,d0
.l
move d0,d2
muls d2,d2
move.l d2,(a0)+
addq #1,d0
cmp d0,d1
bne.b .l
rts
endif
;in
; a0 = result array reals
; a1 = result array imaginary
;out
; a0 = result (overwritten input array)
; REM ;;;;;;;;;;;;;,
;calcFFTPower
; ; Calculate for the 1st half, 2nd half is mirror of the 1st and
; ; not used in drawing.
; moveq #FFT_LENGTH/2-1,d7
; move.l #$ffff,d6
;; lea squareTable,a2
;.l
; move (a0),d0
; move (a1)+,d1
; muls d0,d0
; muls d1,d1
; add.l d1,d0
;
;
;; cmp.l maxSqr(pc),d0
;; blo.b .s
;; move.l d0,maxSqr
;; move (a0),temp
;; move -2(a1),temp2
;;.s
; ; See which square root to use
; cmp.l d6,d0
; bls.b .16
;
; bsr.b isqrt32
;
; move d1,(a0)+
; dbf d7,.l
; rts
;.16
; bsr.b isqrt16
; move d1,(a0)+
; dbf d7,.l
; rts
;
;
; incdir
; include "isqrt16.s"
; EREM ;;;;;;;;;;;;;;;;;
ifne FFT_TEST
fi ds.w FFT_LENGTH
fr ds.w FFT_LENGTH
fpow ds.w FFT_LENGTH
endif
ifne FFT_TEST
convert_sine
lea Sinewave(pc),a3
move #N_WAVE-1,d0
.loop
asr (a3)+
dbf d0,.loop
rts
endif
; in
; a0 = 16-bit signed sampledata (real array)
; a1 = imaginary array, to be overwritten
; a2 = sinewave
; out
; a0 = result array, real (overwritten input)
; a1 = result array, imaginary
sampleFFT
; clear first half of the imaginary array
move.l a1,a3
moveq #FFT_LENGTH/2/4-1,d0
moveq #0,d6
.c
move.l d6,(a3)+
move.l d6,(a3)+
move.l d6,(a3)+
move.l d6,(a3)+
dbf d0,.c
fix_fft
rsreset
.m rs.w 1
.k rs.w 1
.i rs.w 1
.l rs.w 1
.istep rs.w 1
.varsSizeof rs.b 0
movem.l a4/a5/a6,-(sp)
lea -.varsSizeof(sp),sp
;lea .vars(pc),a5
; m, data size 1<<7 = 128
move #FFT_SIZE,.m(sp)
ifne FFT_TEST
lea Sinewave(pc),a2
endif
; Cosine
lea N_WAVE/4*2(a2),a5
;; int fix_fft(fixed fr[], fixed fi[], int m, int inverse)
;; {
;; int mr,nn,i,j,l,k,istep, n, scale, shift;
;; fixed qr,qi,tr,ti,wr,wi,t;
;; n = 1<<m;
.n = FFT_LENGTH
;; if(n > N_WAVE)
;; return -1;
;; mr = 0;
; clr.w .mr(sp)
;; nn = n - 1;
.nn = .n-1
;; /* decimation in time - re-order data */
;; for(m=1; m<=nn; ++m) {
moveq #.nn-1,d7 ; loop counter
moveq #.nn,d3 ; loop comparison
; Cleared earlier:
; moveq #0,d6 ; mr
moveq #1,d5 ; m
move #.n,d4 ; preloaded constant
lea (.n*2).w,a6 ; loop condition constant for loop5 preloaded
;; ------------------------------------------------------------------
; top level loop
.loop1
; loop 1 run 127 times when FFT_LENGTH = 128
ifne FFT_LOOPS
addq.l #1,cloop1
endif
;; l = n;
move d4,d0 ; d4 = .n
;; ------------------------------------------------------------------
.loop2
; loop 2 run 247 times when FFT_LENGTH = 128
ifne FFT_LOOPS
addq.l #1,cloop2
endif
;; do {
;; l >>= 1;
lsr.w #1,d0
;; } while(mr+l > nn);
move.w d6,d2
add.w d0,d2
cmp.w d3,d2
bhi.b .loop2
;; ------------------------------------------------------------------
;move.w d0,.l(sp)
;; mr = (mr & (l-1)) + l;
; d6 = mr
move.w d0,d1
subq.w #1,d1 ; l-1
and.w d6,d1 ; d6 = mr
add.w d0,d1
move.w d1,d6
;; if(mr <= m) continue;
cmp.w d5,d1 ; d5 = m
bls.b .continue
add d1,d1 ; mr index
move.w d5,d2 ; m index
add d2,d2
;; tr = fr[m];
; d0 = tr/ti
move (a0,d2.w),d0
;; fr[m] = fr[mr];
move (a0,d1.w),(a0,d2.w)
;; fr[mr] = tr;
move d0,(a0,d1.w)
;; ti = fi[m];
move (a1,d2.w),d0
;; fi[m] = fi[mr];
move (a1,d1.w),(a1,d2.w)
;; fi[mr] = ti;
move d0,(a1,d1.w)
;; ------------------------------------------------------------------
; loop condition and increment
.continue
addq #1,d5 ; d5 = m
dbf d7,.loop1
;; }
;; l = 1;
move.w #1*2,.l(sp) * index
;; k = LOG2_N_WAVE-1;
move.w #LOG2_N_WAVE-1,.k(sp)
ifeq FFT_ALTERNATE_ASR
moveq #15,d5 ; shift for multiplications for loop 5
endif
;; ------------------------------------------------------------------
; top level loop
.loop3
; loop 3 run 7 times when FFT_LENGTH = 128
ifne FFT_LOOPS
addq.l #1,cloop3
endif
;; while(l < n) {
;; /* it may not be obvious, but the shift will be performed
;; on each data point exactly once, during this pass. */
;; istep = l << 1;
move.w .l(sp),d0 * index
add.w d0,d0
move.w d0,.istep(sp) * index
;; for(m=0; m<l; ++m) {
; clr.w .m(sp)
ifne FFT_ALTERNATE_ASR
moveq #0,d5
else
clr.w (sp)
endif
;; ------------------------------------------------------------------
.loop4
ifne FFT_LOOPS
addq.l #1,cloop4
endif
; loop 4 run 127 times when FFT_LENGTH = 128
;; j = m << k;
; move.w .m(sp),d0
; move.w (sp),d0
; move.w .k(sp),d1
ifne FFT_ALTERNATE_ASR
move d5,d0
move d5,d6
move .k(sp),d1
lsl d1,d0
else
movem.w (sp),d0/d1 ; load both .m an .k, stored sequentially
move d0,d6 * index .m
lsl d1,d0
endif
;; wi = -Sinewave[j];
;; wi >>= 1;
;add.w d0,d0
move.w (a2,d0.w),d1
neg.w d1
; asr.w #1,d1
move d1,a4
; a4 = wi
;; wr = Sinewave[j+N_WAVE/4];
;; wr >>= 1;
; add.w #N_WAVE/4*2,d0
; move.w (a2,d0.w),d1
; asr.w #1,d1
; move d1,a3
move (a5,d0.w),a3
; a3 = wr
;; ------------------------------------------------------------------
;; for(i=m; i<n; i+=istep) {
;move.w .m(sp),d6 ; i
;move.w (sp),d6 ; i - load a few lins above already
move .l(sp),d7 ; j
add d6,d7
; add d6,d6 ; i table index
; add d7,d7 ; j table index
; loop increment
; use double as d6 and d7 are word table indices
move .istep(sp),d0 * index
; add d0,d0
; loop condition is in a6
.loop5
ifne FFT_LOOPS
addq.l #1,cloop5
endif
;speed 162 to 160 when removed moveq #15,d5 from inside the loop
; loop 5 run 448 times when FFT_LENGTH = 128
;; j = i + l;
; step one at loop end
;; tr = fix_mpy(wr,fr[j])-fix_mpy(wi,fi[j]);
move (a0,d7),d3 ; fr(j)
move (a1,d7),d4 ; fi(j)
move.w a3,d1 ; fr(j)*wr
muls.w d3,d1
ifeq FFT_ALTERNATE_ASR
asr.l d5,d1
endif
move.w a4,d2 ; fi(j)*wi
muls.w d4,d2
ifeq FFT_ALTERNATE_ASR
asr.l d5,d2
endif
sub.l d2,d1
ifne FFT_ALTERNATE_ASR
; Tricky asr #15
; Calculations use 16-bit words with fixed point at bit 15.
; Multiplying these will yield a value where the fixed point is at 30,
; with one sign bit and one value bit. Doing an add.l d1,d1 could cause
; an overflow but in practice it seems to work fine. Much faster
; than asr.l #15.
add.l d1,d1
swap d1
endif
; d1 = tr
;; qr = fr[i];
;; qr >>= 1;
move.w (a0,d6.w),d2
asr.w #1,d2
; d2 = qr
;; Use of d5 or not:
if 0
;; fr[j] = qr - tr
move d2,d5
sub d1,d5
move d5,(a0,d7.w)
;; fr[i] = qr + tr
add.w d1,d2
move d2,(a0,d6.w)
else
;; fr[j] = qr - tr
sub d1,d2
move d2,(a0,d7.w)
;; fr[i] = qr + tr
add.w d1,d2
add.w d1,d2
move d2,(a0,d6.w)
endif
;; ti = fix_mpy(wr,fi[j])+fix_mpy(wi,fr[j]);
move.w a3,d1 ; fi(j)*wr
muls.w d4,d1
ifeq FFT_ALTERNATE_ASR
asr.l d5,d1
endif
move.w a4,d2 ; fr(j)*wi
muls.w d3,d2
ifeq FFT_ALTERNATE_ASR
asr.l d5,d2
endif
add.l d2,d1
ifne FFT_ALTERNATE_ASR
; Tricky asr #15
add.l d1,d1
swap d1
endif
; d1 = ti
;; qi = fi[i];
;; qi >>= 1;
move.w (a1,d6.w),d2
asr.w #1,d2
; d2 = qi
;; Use of d5 or not:
if 0
;; fi[j] = qi - ti
move d2,d5
sub d1,d5
move d5,(a1,d7.w)
;; fi[i] = qi + ti
add d1,d2
move d2,(a1,d6.w)
else
;; fi[j] = qi - ti
sub d1,d2
move d2,(a1,d7.w)
;; fi[i] = qi + ti
add d1,d2
add d1,d2
move d2,(a1,d6.w)
endif
;; }
; for loop: for(i=m; i<n; i+=istep)
; add istep twice as d6 and d7 are word table indices
; d0 = 2*istep
add d0,d6 ; i+=istep
add d0,d7 ; j+=istep
; a6 = 2*.n
cmp.w a6,d6
blo.b .loop5
;; }
ifne .m
fail .m referred without index, so it must be zero
endif
;for loop: for(m=0; m<l; ++m)
ifne FFT_ALTERNATE_ASR
addq #1*2,d5
cmp .l(sp),d5
blo.b .loop4
else
addq #1*2,(sp)
;move.w .m(sp),d0
move.w (sp),d0
cmp.w .l(sp),d0
blo.b .loop4
endif
;; --k;
subq.w #1,.k(sp)
;; l = istep;
move.w .istep(sp),.l(sp)
;; }
; loop condition: while(l < n)
; move.w .l(sp),d0
; cmp.w #.n,d0
cmp.w #.n*2,.l(sp)
blo.w .loop3
;; return scale;
;; }
; DONE
lea .varsSizeof(sp),sp
movem.l (sp)+,a4/a5/a6
rts
;; /* window() - apply a Hanning window */
;; void window(fixed fr[], int n)
; in:
; a0 = input data
; a2 = sinewave
windowFFT
;; {
;; int i,j,k;
;; j = N_WAVE/n;
; sinewave index step
move #N_WAVE/FFT_LENGTH*2,d7
;; n >>= 1;
; loop end condition
moveq #FFT_LENGTH/2-1,d6
;; for(i=0,k=N_WAVE/4; i<n; ++i,k+=j)
;; FIX_MPY(fr[i],fr[i],16384-(Sinewave[k]>>1));
;i=0
;k=N_WAVE/4
;index to sinewave
;lea Sinewave+N_WAVE/4*2(pc),a1
lea N_WAVE/4*2(a2),a1
moveq #15,d3 ; muls shift
move #16384,d2
.for1
; 16384-(Sinewave(k)>>1)
move (a1),d4
;asr #1,d4 * sinetable prescaled earlier
move d2,d5
sub d4,d5
; fr(i)
muls (a0),d5
asr.l d3,d5
move d5,(a0)+
; ++i
;addq #1,d0
; k+=j
;add d7,d1
add d7,a1
;i<n
dbf d6,.for1
;; n <<= 1;
; loop end condition
; add d6,d6
moveq #FFT_LENGTH/2-1,d6
;; for(k-=j; i<n; ++i,k-=j)
;; FIX_MPY(fr[i],fr[i],16384-(Sinewave[k]>>1));
;; }
; k-=j
;sub d7,d1
sub d7,a1
.for2
; 16384-(Sinewave(k)>>1)
move (a1),d4
;asr #1,d4 * sinetable prescaled earlier
move d2,d5
sub d4,d5
muls (a0),d5
asr.l d3,d5
move d5,(a0)+
;++i
;addq #1,d0
;k-=j
;sub d7,d1
sub d7,a1
;i<n
dbf d6,.for2
rts
;; /* fix_loud() - compute loudness of freq-spectrum components.
;; n should be ntot/2, where ntot was passed to fix_fft();
;; 6 dB is added to account for the omitted alias components.
;; scale_shift should be the result of fix_fft(), if the time-series
;; was obtained from an inverse FFT, 0 otherwise.
;; loud[] is the loudness, in dB wrt 32767; will be +10 to -N_LOUD.
;; */
;; void fix_loud(fixed loud[], fixed fr[], fixed fi[], int n, int scale_shift)
;; {
;; int i, max;
;; max = 0;
;; if(scale_shift > 0)
;; max = 10;
;; scale_shift = (scale_shift+1) * 6;
;; for(i=0; i<n; ++i) {
;; loud[i] = db_from_ampl(fr[i],fi[i]) + scale_shift;
;; if(loud[i] > max)
;; loud[i] = max;
;; }
;; }
;in
; a0 = result array reals
; a1 = result array imaginary
;out
; a0 = result (overwritten input array)
; rem ;;;;;;;;;
;loudFFT
; lea Loudampl(pc),a2
; lea Loudampl2(pc),a3
;
; tst.l (a3)
; bne.b .1
;
; move (a2)+,d0
; muls d0,d0
; move.l d0,(a3)+
;
; moveq #N_LOUD-1-1,d7
;.l1
; move (a2)+,d0
; muls d0,d0
; move.l d0,(a3)
; add.l -4(a3),d0
; lsr.l #1,d0
; move.l d0,-4(a3)
; addq.l #4,a3
; dbf d7,.l1
;.1
;
;nok
; moveq #FFT_LENGTH/2-1,d7
;.l2
; move (a0)+,d0
; muls d0,d0
; move (a1)+,d1
; muls d1,d1
; add.l d1,d0
;
; lea Loudampl2(pc),a2
; moveq #0,d6
; moveq #N_LOUD,d5
;.l3
; cmp.l (a2)+,d0
; bhi.b .break
;
; addq #1,d6
; ;cmp #N_LOUD,d6
; cmp d5,d6
; bne.b .l3
;
;.break
; * d6 = dB level
; ;neg d6
; ;addq #6,d6
; ;bmi.b .2
; ;moveq #0,d6
;.2
;
; subq #6,d6
; bpl.b .3
; moveq #0,d6
;.3
; move d6,-2(a0)
;
; dbf d7,.l2
;
;
; rts
; EREM ;;;;;;;;;;;;;;;
;; /* db_from_ampl() - find loudness (in dB) from
;; the complex amplitude.
;; */
;; int db_from_ampl(fixed re, fixed im)
;; {
;; static long loud2[N_LOUD] = {0};
;; long v;
;; int i;
;; if(loud2[0] == 0) {
;; loud2[0] = (long)Loudampl[0] * (long)Loudampl[0];
;; for(i=1; i<N_LOUD; ++i) {
;; v = (long)Loudampl[i] * (long)Loudampl[i];
;; loud2[i] = v;
;; loud2[i-1] = (loud2[i-1]+v) / 2;
;; }
;; }
;; v = (long)re * (long)re + (long)im * (long)im;
;; for(i=0; i<N_LOUD; ++i)
;; if(loud2[i] <= v)
;; break;
;; return (-i);
;; }
;; /*
;; fix_mpy() - fixed-point multiplication
;; */
;; fixed fix_mpy(fixed a, fixed b)
;; {
;; FIX_MPY(a,a,b);
;; return a;
;; }
;; /*
;; iscale() - scale an integer value by (numer/denom)
;; */
;; int iscale(int value, int numer, int denom)
;; {
;; #ifdef DOS
;; asm mov ax,value
;; asm imul WORD PTR numer
;; asm idiv WORD PTR denom
;; return _AX;
;; #else
;; return (long) value * (long)numer/(long)denom;
;; #endif
;; }
;; /*
;; fix_dot() - dot product of two fixed arrays
;; */
;; fixed fix_dot(fixed *hpa, fixed *pb, int n)
;; {
;; fixed *pa;
;; long sum;
;; register fixed a,b;
;; unsigned int seg,off;
;; /* seg = FP_SEG(hpa);
;; off = FP_OFF(hpa);
;; seg += off>>4;
;; off &= 0x000F;
;; pa = MK_FP(seg,off);
;; */
;; sum = 0L;
;; while(n--) {
;; a = *pa++;
;; b = *pb++;