kolibrios/programs/other/fft/FHT4i.inc
Artem Jerdev (art_zh) 6641043d17 fast Hartley transform presented
git-svn-id: svn://kolibrios.org@2210 a494cfbc-eb01-0410-851d-a64ba20cac60
2011-09-18 21:08:53 +00:00

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16 KiB
PHP

; Fast Hartley Transform routine
; Copyright (C) 1999, 2004, 2010
; Artem Jerdev artem@jerdev.co.uk
;
; free KolibriOS version - not to be ported to other OSes
; ==========================================================
; global constants
align 8
_r dq 1.41421356237309504880169 ; = sqrt(2)
_r2 dq 0.70710678118654752440084 ; = sqrt(2)/2
_c1 dq 0.92387953251128675612818 ; = cos(pi/8)
_s1 dq 0.38268343236508977172846 ; = sin(pi/8)
;=================================================================
; parameter1:
; -- reg dl (bits[3:0]) = Power_of_4
; returns:
; -- reg edx = _CosTable address (4k-aligned)
; assumes: _SinTable = _CosTable + (N/2)*8
; user heap has to be initialized
; destroys:
; -- eax, ebx, ecx
;; ==========================
align 4
CreateSinCosTable:
xor eax, eax
inc eax
mov cl, dl
and cl, 15
shl eax, cl
shl eax, cl
mov ecx, eax ; now ecx = N
shl ecx, 3
mov ebx, 12
mov eax, 68
int 0x40 ; getmem(N*sizeof(double))
mov edx, eax ; edx = _CosTable
shr ecx, 1
mov ebx, eax
add ebx, ecx ; ebx = _SinTable
shr ecx, 3
push ecx ; [esp] = ecx = N/2
xor eax, eax
fldpi
fidiv dword[esp] ; st : dx = 2*pi/N
pop ecx
fldz ; st : 0, dx
.loop:
fld st0 ; st : x, x, dx
FSINCOS ; st : cos, sin, x, dx
fstp qword [edx+eax*8] ; st : sin, x, dx
fstp qword [ebx+eax*8] ; st : x, dx
fadd st0, st1 ; st : x+dx, dx
inc eax
cmp eax, ecx
jne .loop
fstp st0 ; st : dx
fstp st0 ; st : <empty>
ret
;=================================================================
; parameter1:
; -- reg edx = _CosTable address
; destroys:
; -- eax, ebx, ecx
;; ==========================
align 4
DestroySinCosTable:
mov ecx, edx
mov ebx, 13
mov eax, 68
int 0x40 ; free(SinCosTable)
ret
;=================================================================
; parameter1:
; -- reg dl (bits[3:0]) = Power_of_4
; -- reg edx && (-16) = 4k-aligned data array address
; returns:
; -- edx = Power_of_4
; -- ecx = N
; destroys:
; -- eax, ebx, ecx, edx, esi
;; ==========================
align 4
BitInvert:
mov esi, edx
and esi, 0xFFFFFFF0
and edx, 0x0F
push edx
mov cl, dl
xor eax, eax
inc eax
shl eax, cl
shl eax, cl
push eax
xor ecx, ecx ; index term
.newterm:
inc ecx
cmp ecx, [esp] ; N
jge .done
xor eax, eax
mov edx, ecx
xor bl, bl
.do_invert:
inc bl
cmp bl, byte[esp+4] ; Power_of_4
jg .switch
mov bh, dl
and bh, 3
shl eax, 2
or al, bh
shr edx, 2
jmp .do_invert
.switch:
cmp eax, ecx
jle .newterm
fld qword [esi+eax*8]
fld qword [esi+ecx*8]
fstp qword [esi+eax*8]
fstp qword [esi+ecx*8]
jmp .newterm
.done:
pop ecx
pop edx
ret
;=================================================================
;=================================================================
; stdcall parameters:
; -- [esp+4] = N
; -- [esp+8] = 4k-aligned data array address
; returns:
; -- nothing
; destroys:
; -- ebx, esi
;; ==========================
align 4
step1:
mov ebx, [esp+8]
mov esi, [esp+4]
shl esi, 3
add esi, ebx
.loop:
fld qword[ebx]
fld qword[ebx+8]
fld st1
fsub st0, st1 ; st : t2, f[i+1], f[i]
fxch st1 ; st : f[i+1], t2, f[i]
faddp st2, st0 ; st : t2, t1
fld qword[ebx+16]
fld qword[ebx+24]
fld st1 ; st : f[i+2], f[i+3], f[i+2], t2, t1
fadd st0, st1 ; st : t3, f[i+3], f[i+2], t2, t1
fxch st2 ; st : f[i+2], f[i+3], t3, t2, t1
fsub st0, st1 ; st : t4, f[i+3], t3, t2, t1
fstp st1 ; st : t4, t3, t2, t1
fld st2 ; st : t2, t4, t3, t2, t1
fadd st0, st1 ; st : t2+t4, t4, t3, t2, t1
fstp qword[ebx+16] ; st : t4, t3, t2, t1
fsubp st2, st0 ; st : t3, t2-t4, t1
fld st2 ; st : t1, t3, t2-t4, t1
fadd st0, st1 ; st : t1+t3, t3, t2-t4, t1
fstp qword[ebx] ; st : t3, t2-t4, t1
fsubp st2, st0 ; st : t2-t4, t1-t3
fstp qword[ebx+24] ; st : t1-t3
fstp qword[ebx+8] ; st : <empty>
add ebx, 32
cmp ebx, esi
jnz .loop
ret
; local stack definitions
;===========================================================================
_t0 equ dword [esp]
_t1 equ dword[esp+4]
_t2 equ dword[esp+8]
_t3 equ dword[esp+12]
_t4 equ dword[esp+16]
_t5 equ dword[esp+20]
_t6 equ dword[esp+24]
_t7 equ dword[esp+28]
_t8 equ dword[esp+32]
_t9 equ dword[esp+36]
_l1 equ dword[esp+40]
_l2 equ dword[esp+44]
_l3 equ dword[esp+48]
_l4 equ dword[esp+52]
_l5 equ dword[esp+56]
_l6 equ dword[esp+60]
_l7 equ dword[esp+64]
_l8 equ dword[esp+68]
_l9 equ dword[esp+72]
_l0 equ dword[esp+76]
_d1 equ dword[esp+80]
_d2 equ dword[esp+84]
_d3 equ dword[esp+88]
_d4 equ dword[esp+92]
_d5 equ dword[esp+96]
_d6 equ dword[esp+100]
_j5 equ dword[esp+104]
_jj equ dword[esp+108]
_end_of_array equ dword[esp+112]
_step equ word [esp+116]
;=================================================================
; cdecl parameters:
; -- [ebp+8] = N
; -- [ebp+12] = 4k-aligned data array address
; returns:
; -- nothing
; destroys:
; -- eax, ebx
; locals:
; -- 10 stack-located dwords (_t0 ... _t9)
;; ==========================
align 4
step2:
push ebp
mov ebp, esp
sub esp, 40
mov ebx, [ebp+12]
mov eax, [ebp+ 8]
shl eax, 3
add eax, ebx
.loop_i:
; -- quad subelements +0, +4, +8 and +12 (simpliest operations)
fld qword[ebx]
fld qword[ebx+8*4]
fld st0
fadd st0, st2 ; st : t1, f_4, f_0
fxch st1
fsubp st2, st0 ; st : t1, t2
fld qword[ebx+8*8]
fld qword[ebx+8*12]
fld st0
fadd st0, st2 ; st : t3, f_12, t1, t2
fxch st1
fsubp st2, st0 ; st : t3, t4, t1, t2
; ------
fld st2 ; st : t1, t3, t4, t1, t2
fadd st0, st1
fstp qword[ebx] ; st : t3, t4, t1, t2
fsub st0, st2 ; st : t3-t1, t4, t1, t2
fchs ; st : t1-t3, t4, t1, t2
fstp qword[ebx+8*4] ; st : t4, t1, t2
fst st1 ; st : t4, t4, t2
fadd st0, st2 ; st : t2+t4, t4, t2
fstp qword[ebx+8*8] ; st : t4, t2
fsubp st1, st0 ; st : t2-t4
fstp qword[ebx+8*12] ; st : <empty>
; -- even subelements +2, +6, +10 and +14 (2 multiplications needed)
fld qword[ebx+8*2]
fld qword[ebx+8*6]
fld [_r]
fmul st1, st0 ; st : r, t2, t1
fld qword[ebx+8*10]
fxch st1 ; st : r, t3, t2, t1
fmul qword[ebx+8*14] ; st : t4, t3, t2, t1
; ------
fld st3 ; st : t1, t4, t3, t2, t1
fadd st0, st3 ;
fadd st0, st2 ;
fst qword[ebx+8*2] ; store f[i+8] = t1+t2+t3
fsub st0, st3 ;
fsub st0, st3 ;
fstp qword[ebx+8*10] ; store f[i+10]= t1-t2+t3
fld st3 ; st : t1, t4, t3, t2, t1
fsub st0, st2 ;
fsub st0, st1 ;
fst qword[ebx+8*14] ; store f[i+14]= t1-t3-t4
fadd st0, st1 ;
faddp st1, st0 ; st : t1-t3+t4, t3, t2, t1
fstp qword[ebx+8*6] ; store f[i+6]
fstp st0 ; st : t2, t1
fstp st0 ; st : t1
fstp st0 ; st : <empty>
; -- odd subelements
fld qword[ebx+8*9]
fld qword[ebx+8*11]
fld st1
fsub st0, st1
fxch st1
faddp st2, st0 ; st : (f[l3]-f[l7]), (f[l3]+f[l7])
fld [_r2]
fmul st2, st0
fmulp st1, st0 ; st : t9, t6
fld qword[ebx+8*3]
fld st0
fadd st0, st2 ; st : t1, f[l5], t9, t6
fstp _t1
fsub st0, st1
fstp _t2
fstp _t9 ; (t9 never used)
fstp _t6 ; st : <empty>
fld [_c1]
fld [_s1]
fld qword[ebx+8*5]
fld qword[ebx+8*7]
fld st3 ; st: c1, f[l6], f[l2], s1, c1
fmul st0, st2 ; st: f_2*c, f_6, f_2, s, c
fld st1 ; st: f_6, f_2*c, f_6, f_2, s, c
fmul st0, st4 ; st: f_6*s, f_2*c, f_6, f_2, s, c
faddp st1, st0 ; st: t5, f_6, f_2, s, c
fstp _t5 ; st: f_6, f_2, s, c
fld st3 ; st: c, f_6, f_2, s, c
fmul st0, st1
fld st3
fmul st0, st3 ; st: f_2*s, f_6*c, f_6, f_2, s, c
fsubp st1, st0 ; st: t8, f_6, f_2, s, c
fstp _t8 ; st: f_6, f_2, s, c
fstp st0 ; st: f_2, s, c
fstp st0 ; st: s, c
fld qword[ebx+8*13]
fld qword[ebx+8*15]
fld st3 ; st: c1, f[l8], f[l4], s1, c1
fmul st0, st1
fld st3
fmul st0, st3 ; st: f_4*s, f_8*c, f_8, f_4, s, c
faddp st1, st0 ; st: t7, f_8, f_4, s, c
fld _t5 ; st: t5, t7, f_8, f_4, s, c
fsub st0, st1 ; st: t4, t7, f_8, f_4, s, c
fstp _t4
fstp _t7 ; st: f_8, f_4, s, c
fld st3 ; st: c, f_8, f_4, s, c
fmul st0, st2
fld st3
fmul st0, st2 ; st: f_8*s, f_4*c, f_8, f_4, s, c
fsubp st1, st0 ; st:-t0, f_8, f_4, s, c
fchs
fld _t8
fchs ; st:-t8, t0, f_8, f_4, s, c
fsub st0, st1 ; st: t3, t0, f_8, f_4, s, c
fstp _t3
fstp _t0 ; st: f_8, f_4, s, c
fstp st0 ; st: f_4, s, c
fstp st0 ; st: s, c
fstp st0 ; st: c
fstp st0 ; st: <empty>
fld _t1
fld _t4
fld st1
fsub st0, st1
fstp qword[ebx+8*11] ; f[l7] = t1-t4
faddp st1, st0
fstp qword[ebx+8*3] ; f[l5] = t1+t4
fld _t2
fld _t3
fld st1
fsub st0, st1
fstp qword[ebx+8*15] ; f[l8]
faddp st1, st0
fstp qword[ebx+8*7] ; f[l6]
fld _t6
fld qword[ebx+8]
fld st1
fsub st0, st1
fxch st1
faddp st2, st0 ; st : t2, t1
fld _t8
fsub _t0
fld _t5
fadd _t7 ; st : t4, t3, t2, t1
fld st3
fsub st0, st1
fstp qword[ebx+8*9] ; f[l3] = t1-t4
fadd st0, st3
fstp qword[ebx+8] ; f[l1] = t1+t4
fld st1 ; st : t2, t3, t2, t1
fsub st0, st1 ; f[l4] = t2-t3
fstp qword[ebx+8*13] ; st : t3, t2, t1
faddp st1, st0 ; st : t2+t3, t1
fstp qword[ebx+8*5] ; f[l2] = t2+t3
fstp st0 ; st : <empty>
add ebx, 16*8
cmp ebx, eax
jb .loop_i
mov esp, ebp
pop ebp
ret
;=================================================================
; cdecl parameters:
; -- [ebp+8] = N
; -- [ebp+12] = p
; -- [ebp+16] = 4k-aligned data array address
; -- [ebp+20] = 4k-aligned SinCosTable address
; returns:
; -- nothing
; destroys:
; -- all GPRegs
; locals:
; -- 120 stack-located dwords (_t0 ... _t9, _l0..._step)
;; ==========================
align 4
step3:
push ebp
mov ebp, esp
sub esp, 120
; 283 : {
; 293 : for (l=3; l<=p; l++)
mov cx, 0x0200
.newstep:
inc ch
cmp ch, byte[ebp+12]
jg .done
mov _step, cx
; 294 : {
; 295 : d1 = 1 << (l + l - 3);
mov cl, ch
add cl, cl
sub cl, 3
mov edx, 1
shl edx, cl
mov _d1, edx
; 296 : d2 = d1 << 1;
shl edx, 1
mov _d2, edx
mov eax, edx
; 297 : d3 = d2 << 1;
shl edx, 1
mov _d3, edx
; 298 : d4 = d2 + d3;
add eax, edx
mov _d4, eax
; 299 : d5 = d3 << 1;
shl edx, 1
mov _d5, edx
shl edx, 3
mov _d6, edx ; d6 = d5*8 to simplify index operations
; 339 : j5 = N / d5; ; moved out of internal loop
mov cl, [ebp+12]
sub cl, ch
add cl, cl
mov edx, 1
shl edx, cl
mov _j5, edx
; 300 :
; 301 : for (j=0; j<N; j+=d5)
mov ebx, [ebp+16]
mov esi, [ebp+8]
shl esi, 3
add esi, ebx
mov _end_of_array, esi
.next_j:
; {
; t1 = f[j] + f[j+d2];
mov eax, _d2
fld qword[ebx]
fld qword[ebx+eax*8]
fld st1
fadd st0, st1
fstp _t1
; t2 = f[j] - f[j+d2];
fsubp st1, st0
fstp _t2
; t3 = f[j+d3] + f[j+d4];
mov edi, _d3
fld qword[ebx+edi*8]
mov edx, _d4
fld qword[ebx+edx*8]
fld st1
fsub st0, st1 ; st : t4, f4, f3
fxch st1 ; st : f4, t4, f3
; t4 = f[j+d3] - f[j+d4];
faddp st2, st0 ; st : t4, t3
; f[j+d4] = t2 - t4;
; f[j+d3] = t2 + t4;
fld _t2
fld st0
fsub st0, st2 ; st : f4, t2, t4, t3
fstp qword[ebx+edx*8] ; st : t2, t4, t3
fadd st0, st1 ; st : f3, t4, t3
fstp qword[ebx+edi*8] ; st : t4, t3
; f[j+d2] = t1 - t3;
; f[j] = t1 + t3;
fld _t1
fst st1
fsub st0, st2 ; st : f2, t1, t3
fstp qword[ebx+eax*8] ; st : t1, t3
fadd st0, st1 ; st : f0, t3
fstp qword[ebx] ; st : t3
fstp st0
; jj = j + d1; / ??
mov edi, _d1
shl edi, 3 ; = d1*8
mov edx, edi
mov eax, edi
add eax, eax ; eax = d2*8
shl edx, 2 ; = d3*8
add edi, ebx ; now [edi] points to f[jj]
add edx, edi ; and [edx] points to f[jj+d3]
; t1 = f[jj];
fld qword [edi] ; st : t1
; t3 = f[jj+d3];
fld qword [edx] ; st : t3, t1
; t2 = f[jj+d2] * r;
fld qword [edi+eax]
fld [_r]
fmul st1, st0 ; st : r, t2, t3, t1
; t4 = f[jj+d4] * r
fmul qword [edx+eax] ; st : t4, t2, t3, t1
; f[jj] = t1 + t2 + t3;
fld st3 ; st : t1, t4, t2, t3, t1
fadd st0, st3
fadd st0, st2
fstp qword [edi]
; f[jj+d2] = t1 - t3 + t4;
fld st3
fsub st0, st3 ; st : (t1-t3), t4, t2, t3, t1
fld st0
fadd st0, st2 ; st : f2, (t1-t3), t4, t2, t3, t1
fstp qword [edi+eax]
; f[jj+d4] = t1 - t3 - t4;
fsub st0, st1 ; st : f4, t4, t2, t3, t1
fstp qword [edx+eax]
; f[jj+d3] = t1 - t2 + t3;
fstp st0 ; st : t2, t3, t1
fsubp st1, st0 ; st : (t3-t2), t1
faddp st1, st0 ; st : f3
fstp qword [edx]
; for (k=1; k<d1; k++)
xor ecx, ecx ; ecx = k
mov _jj, ecx
.next_k:
inc ecx
cmp ecx, _d1
jge .done_k
; {
mov eax, _d2 ; the sector increment
; l1 = j + k;
mov edx, ecx
mov _l1, edx ; [ebx+edx*8] --> f[j+k]
; l2 = l1 + d2;
add edx, eax
mov _l2, edx
; l3 = l1 + d3;
add edx, eax
mov _l3, edx
; l4 = l1 + d4;
add edx, eax
mov _l4, edx
; l5 = j + d2 - k;
mov edx, eax
sub edx, ecx
mov _l5, edx
; l6 = l5 + d2;
add edx, eax
mov _l6, edx
; l7 = l5 + d3;
add edx, eax
mov _l7, edx
; l8 = l5 + d4;
add edx, eax
mov _l8, edx
; 340 : j5 *= k; // add-substituted multiplication
mov eax, _jj
add eax, _j5
mov _jj, eax
; c1 = C[jj];
; s1 = S[jj];
mov edi, [ebp+20]
fld qword[edi+eax*8]
mov esi, [ebp+8]
shl esi, 2
add esi, edi
fld qword[esi+eax*8] ; st : s1, c1
; t5 = f[l2] * c1 + f[l6] * s1;
; t8 = f[l6] * c1 - f[l2] * s1;
mov edx, _l6
fld qword[ebx+edx*8]
mov edx, _l2
fld st0
fmul st0, st2
fxch st1
fmul st0, st3
fld qword[ebx+edx*8] ; st : f[l2], f[l6]*c, f[l6]*s, s, c
fmul st4, st0
fmulp st3, st0 ; st : f[l6]*c, f[l6]*s, f[l2]*s, f[l2]*c
fsub st0, st2 ; st : t8, f[l6]*s, f[l2]*s, f[l2]*c
fstp _t8
faddp st2, st0 ; st : f[l2]*s, t5
fstp st0 ; st : t5
fstp _t5 ; st : <empty>
; c2 = C[2*jj];
; s2 = S[2*jj];
shl eax, 1
fld qword[edi+eax*8]
fld qword[esi+eax*8] ; st : s2, c2
; t6 = f[l3] * c2 + f[l7] * s2;
; t9 = f[l7] * c2 - f[l3] * s2;
mov edx, _l7
fld qword[ebx+edx*8]
mov edx, _l3
fld st0
fmul st0, st2
fxch st1
fmul st0, st3
fld qword[ebx+edx*8] ; st : f[l3], f[l7]*c, f[l7]*s, s, c
fmul st4, st0
fmulp st3, st0 ; st : f[l7]*c, f[l7]*s, f[l3]*s, f[l3]*c
fsub st0, st2 ; st : t9, f[l7]*s, f[l3]*s, f[l3]*c
fstp _t9
faddp st2, st0 ; st : f[l2]*s, t6
fstp st0 ; st : t6
fstp _t6 ; st : <empty>
; c3 = C[3*jj];
; s3 = S[3*jj];
add eax, _jj
fld qword[edi+eax*8]
fld qword[esi+eax*8] ; st : s3, c3
; t7 = f[l4] * c3 + f[l8] * s3;
; t0 = f[l8] * c3 - f[l4] * s3;
mov edx, _l8
fld qword[ebx+edx*8]
mov edx, _l4
fld st0
fmul st0, st2
fxch st1
fmul st0, st3
fld qword[ebx+edx*8] ; st : f[l4], f[l8]*c, f[l8]*s, s, c
fmul st4, st0
fmulp st3, st0 ; st : f[l8]*c, f[l8]*s, f[l4]*s, f[l4]*c
fsub st0, st2 ; st : t9, f[l8]*s, f[l4]*s, f[l4]*c
fstp _t0
faddp st2, st0 ; st : f[l2]*s, t7
fstp st0 ; st : t7
fstp _t7 ; st : <empty>
; t1 = f[l5] - t9;
; t2 = f[l5] + t9;
mov eax, _l5
fld qword [ebx+eax*8]
fld _t9
fld st0
fadd st0, st2
fstp _t2
fsubp st1, st0
fstp _t1
; t3 = - t8 - t0;
fld _t8
fadd _t0
fchs
fstp _t3
; t4 = t5 - t7;
fld _t5
fsub _t7
fstp _t4
; f[l5] = t1 + t4;
fld _t1
fld _t4
fld st0
fadd st0, st2
fstp qword [ebx+eax*8]
; f[l7] = t1 - t4;
mov eax, _l7
fsubp st1, st0
fstp qword [ebx+eax*8]
; f[l6] = t2 + t3;
mov eax, _l6
fld _t2
fld _t3
fld st0
fadd st0, st2
fstp qword [ebx+eax*8]
; f[l8] = t2 - t3;
mov eax, _l8
fsubp st1, st0
fstp qword [ebx+eax*8]
; t1 = f[l1] + t6;
mov eax, _l1
fld qword [ebx+eax*8]
fld _t6
fld st0
fadd st0, st2
fstp _t1
; t2 = f[l1] - t6;
fsubp st1, st0
fstp _t2
; t3 = t8 - t0;
fld _t8
fsub _t0
fstp _t3
; t4 = t5 + t7;
fld _t5
fadd _t7
fstp _t4
; f[l1] = t1 + t4;
mov eax, _l1
fld _t1
fld _t4
fld st0
fadd st0, st2
fstp qword [ebx+eax*8]
; f[l3] = t1 - t4;
mov eax, _l3
fsubp st1, st0
fstp qword [ebx+eax*8]
; f[l2] = t2 + t3;
mov eax, _l2
fld _t2
fld _t3
fld st0
fadd st0, st2
fstp qword [ebx+eax*8]
; f[l4] = t2 - t3;
mov eax, _l4
fsubp st1, st0
fstp qword [ebx+eax*8]
; 374 : }
jmp .next_k
.done_k:
; 375 : }
add ebx, _d6 ; d6 = d5*8
cmp ebx, _end_of_array
jb .next_j
; 376 : }
mov cx, _step
jmp .newstep
.done:
mov esp, ebp
pop ebp
; 377 : }
ret
;=========== Step3 ends here ===========
; =================================================================
;=================================================================
; parameters:
; -- [ebp+8] = N
; -- [ebp+12] = p
; -- [ebp+16] = 4k-aligned data array address
; -- [ebp+20] = 4k-aligned SinCosTable address
; returns:
; -- nothing
; destroys:
; -- all GPRegs
;; ==========================
align 4
FHT_4:
push ebp
mov ebp, esp
mov edx, [ebp+16]
add edx, [ebp+12]
call BitInvert
push dword[ebp+16]
push dword[ebp+8]
call step1
call step2
pop edx ; N
pop ecx ; a
push dword[ebp+20] ; t
push ecx
push dword[ebp+12] ; p
push edx ; N
call step3
mov esp, ebp
pop ebp
ret