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|
; COMPLEX NUMBER ARITHMETICS
; Mateusz Malczak
; NASM version
; http://www.malczak.info
; SFFE libs
; http://segfaultlabs.com/projects/sffe
global _sffecabs,_sffecarg,_sffecargs,_sffecargc
global _sffecinv
global _sffecexp,_sffecln,_sffeclog2,_sffeclog
global _sffecsin,_sffeccos,_sffecsincos,_sffectan,_sffeccot
global _sffecsinh,_sffeccosh,_sffectanh,_sffeccoth
global _sffeccpow, _sffecpowd, _sffecpowi, _sffecpowc
global _sffecsqrt, _sffecrtni
%ifndef DELPHI
; section .text use32 class=CODE ;class=CODE - needed for Borlands Compiler
; section CODE use32
; ".text" is more portable than "CODE use32":
section .text
%endif
;; internal use
%ifdef DELPHI
[section expfunc_text use32]
%endif
_sffecexpfnc: ; exponent of real argument
fldl2e
fmulp st1
fld st0
frndint
fsub to st1
fld1
fscale
fstp st1
fxch st1
f2xm1
fld1
faddp st1
fmulp st1
ret
;; globals
%ifdef DELPHI
[section cabs_text use32]
%endif
_sffecabs:
push ebp
mov ebp, esp
fld qword [ebp+08h]
fmul qword [ebp+08h]
fld qword [ebp+10h]
fmul qword [ebp+10h]
faddp st1
fsqrt
leave
ret
%ifdef DELPHI
[section carg_text use32]
%endif
_sffecarg:
push ebp
mov ebp, esp
fld qword [ebp+08h]
fld qword [ebp+10h]
fpatan
wait
leave
ret
%ifdef DELPHI
[section cargs_text use32]
%endif
_sffecargs:
push ebp
mov ebp, esp
fld qword [ebp+10h]
fld qword [ebp+08h]
fmul qword [ebp+08h]
fld qword [ebp+10h]
fmul qword [ebp+10h]
faddp st1
fsqrt
fdivp st1
wait
leave
ret
%ifdef DELPHI
[section cargc_text use32]
%endif
_sffecargc:
push ebp
mov ebp, esp
fld qword [ebp+08h]
fld qword [ebp+08h]
fmul qword [ebp+08h]
fld qword [ebp+10h]
fmul qword [ebp+10h]
faddp st1
fsqrt
fdivp st1
wait
leave
ret
%ifdef DELPHI
[section cinv_text use32]
%endif
_sffecinv:
push ebp
mov ebp, esp
mov edx, [ebp+08h]
fld qword [ebp+0ch]
fld qword [ebp+14h]
fld st0
fmul to st0
fld st2
fmul to st0
faddp st1
fdiv to st1
fdiv to st2
fstp st0
fchs
fstp qword [edx+08h]
fstp qword [edx]
wait
leave
ret
%ifdef DELPHI
[section cexp_text use32]
%endif
_sffecexp:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
fld qword [ebp+0ch]
call _sffecexpfnc
fld qword [ebp+14h]
fsincos
fld st2
fmulp st1
fstp qword [eax]
fmulp st1
fstp qword [eax+08h]
wait
leave
ret
%ifdef DELPHI
[section cln_text use32]
%endif
_sffecln:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
;theta
fld qword [ebp+14h]
fld qword [ebp+0ch]
fpatan
;z module
fld qword [ebp+0ch]
fmul qword [ebp+0ch]
fld qword [ebp+14h]
fmul qword [ebp+14h]
faddp st1
fsqrt
;ln||z||
fld1
fxch st1
fyl2x
fldl2e
fdivp st1
fstp qword [eax]
fstp qword [eax+08h]
wait
leave
ret
%ifdef DELPHI
[section clog2_text use32]
%endif
_sffeclog2:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
fld1
;z module
fld qword [ebp+0ch]
fmul qword [ebp+0ch]
fld qword [ebp+14h]
fmul qword [ebp+14h]
faddp st1
fsqrt
fyl2x
;theta
fld qword [ebp+14h]
fld qword [ebp+0ch]
fpatan
fldln2
fdivp st1
fstp qword [eax+08h]
fstp qword [eax]
wait
leave
ret
%ifdef DELPHI
[section clog_text use32]
%endif
_sffeclog:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
;ln(base)
fld1
fild word [ebp+1ch]
fyl2x
fldl2e
fdivp st1
;z module
fld qword [ebp+0ch]
fmul qword [ebp+0ch]
fld qword [ebp+14h]
fmul qword [ebp+14h]
faddp st1
fsqrt
;ln||z||
fld1
fxch st1
fyl2x
fldl2e
fdivp st1
fdiv st1
;theta
fld qword [ebp+14h]
fld qword [ebp+0ch]
fpatan
fdiv st2
fstp qword [eax+08h]
fstp qword [eax]
fstp st0
wait
leave
ret
%ifdef DELPHI
[section csin_text use32]
%endif
_sffecsin:
push ebp
mov ebp, esp
mov eax, [ebp+08h]
fld1
fld1
faddp st1
fld qword [ebp+14h]
call _sffecexpfnc
fld1
fdiv st1
fld st1;-
fld st1;- optimize
faddp st1;-
fdiv st3
fxch st2
fxch st1
fsubp st1
fdiv st2
fld qword [ebp+0ch]
fsincos
fxch st3
fmulp st1
fstp qword [eax]
fmulp st1
fstp qword [eax+08h]
fstp st0
fwait
leave
ret
%ifdef DELPHI
[section ccos_text use32]
%endif
_sffeccos:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
fld1
fld1
faddp st1
fld qword [ebp+14h]
call _sffecexpfnc
fld1
fdiv st1
fld st1
fld st1
faddp st1
fdiv st3
fxch st2
fxch st1
fsubp st1
fdiv st2
fld qword [ebp+0ch]
fsincos
fxch st2
fmulp st1
fchs
fstp qword [eax+08h]
fmulp st1
fstp qword [eax]
fstp st0
fwait
leave
ret
%ifdef DELPHI
[section ctan_text use32]
%endif
_sffectan:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
;sinh(2b) cosh(2b)
fld1
fld1
faddp st1
fld qword [ebp+14h]
fadd qword [ebp+14h]
call _sffecexpfnc
fld1
fdiv st1
fld st1
fld st1
faddp st1
fdiv st3
fxch st2
fxch st1
fsubp st1
fdivrp st2 ;fdivrp st(2),st(0)
;sin(2b) cos(2b)
fld qword [ebp+0ch]
fadd qword [ebp+0ch]
fsincos
faddp st2
;check if zero
fdiv st1
fstp qword [eax]
fdivp st1
fstp qword [eax+08h]
fwait
leave
ret
%ifdef DELPHI
[section ccot_text use32]
%endif
_sffeccot:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
;sinh(2b) cosh(2b)
fld1
fld1
faddp st1
fld qword [ebp+14h]
fadd qword [ebp+14h]
call _sffecexpfnc
fld1
fdiv st1
fld st1
fld st1
fsubp st1
fdiv st3
fxch st2
fxch st1
faddp st1
fdivrp st2 ;fdivrp st(2),st(0)
;sin(2b) cos(2b)
fld qword [ebp+0ch]
fld st0
faddp st1
fsincos
fsubp st3
;check if zero
fdiv st2
fstp qword [eax]
fdiv st1
fchs
fstp qword [eax+08h]
fstp st0
fwait
leave
ret
%ifdef DELPHI
[section csinh_text use32]
%endif
_sffecsinh:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
fld1
fld1
faddp st1
fld qword [ebp+0Ch]
call _sffecexpfnc
fld1
fdiv st1
fld st1
fld st1
faddp st1
fdiv st3
fxch st2
fxch st1
fsubp st1
fdivrp st2 ;jak w tan i cot
fld qword [ebp+14h]
fsincos
fxch st2
fmulp st1
fstp qword [eax+08h]
fmulp st1
fstp qword [eax]
fwait
leave
ret
%ifdef DELPHI
[section ccosh_text use32]
%endif
_sffeccosh:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
fld qword [ebp+0ch]
call _sffecexpfnc
fld st0
fld1
fxch st1
fdivp st1
fld st1
fld st1
faddp st1
fld1
fld1
faddp st1
fdivp st1
fxch st2
fxch st1
fsubp st1
fld1
fld1
faddp st1
fdivp st1
fld qword [ebp+14h]
fsincos
fxch st2
fmulp st1
fstp qword [eax+08h]
fmulp st1
fstp qword [eax]
fwait
leave
ret
%ifdef DELPHI
[section ctanh_text use32]
%endif
_sffectanh:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
;sinh(2a) cosh(2a)
fld1
fld1
faddp st1
fld qword [ebp+0ch]
fadd qword [ebp+0ch]
call _sffecexpfnc
fld1
fdiv st1
fld st1
fld st1
fsubp st1
fdiv st3
fxch st2
fxch st1
faddp st1
fdivrp st2 ;jak wczesniej
;sin(2b) cos(2b)
fld qword [ebp+14h]
fadd qword [ebp+14h]
fsincos
faddp st3
;check if zero
fdiv st2
fstp qword [eax+08h]
fxch st1
fdivp st1
fstp qword [eax]
fwait
leave
ret
%ifdef DELPHI
[section ccoth_text use32]
%endif
_sffeccoth:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
;sinh(2b) cosh(2b)
fld1
fld1
faddp st1
fld qword [ebp+0ch]
fadd qword [ebp+0ch]
call _sffecexpfnc
fld1
fdiv st1
fld st1
fld st1
fsubp st1
fdiv st3
fxch st2
fxch st1
faddp st1
fdivrp st2 ;jak wczesniej
;sin(2b) cos(2b)
fld qword [ebp+14h]
fadd qword [ebp+14h]
fsincos
fsubp st3
;check if zero
fdiv st2
fchs
fstp qword [eax+08h]
fxch st1
fdivp st1
fstp qword [eax]
fwait
leave
ret
;***************** COMPLEX TO COMPLEX POWER
%ifdef DELPHI
[section ccpow_text use32]
%endif
_sffeccpow:
;TODO: wyeliminowac xch po wystepujace po obliczeniu theta
push ebp
mov ebp,esp
fld1
;z module
fld qword [ebp+0ch]
fmul qword [ebp+0ch]
fld qword [ebp+14h]
fmul qword [ebp+14h]
faddp st1
fsqrt
ftst
fstsw ax
test ah, 1000000b
jnz MZ
mov eax, [ebp+08h]
;ln||z||*/
fyl2x
fldl2e
fdivp st1
;theta*/
fld qword [ebp+14h]
fld qword [ebp+0ch]
fpatan
fld st1 ;ln||z||
fmul qword [ebp+1ch]
fld st1 ;theta
fmul qword [ebp+24h]
fsubp st1 ; st0-st1
fxch st2 ; w st2 mam teraz a = z2.re * lnz - z2.im * theta w st0 jest ln||z||
fmul qword [ebp+24h]
fxch st1
fmul qword [ebp+1ch]
faddp st1
fxch st1
call _sffecexpfnc
fxch st1
fsincos
fld st2
fmulp st1
fstp qword [eax]
fmulp st1
fstp qword [eax+08h]
jmp END
MZ:
mov eax, [ebp+08h]
fstp qword [eax+08h]
fldz
fstp qword [eax]
fstp st0
END:
s fwait
leave
ret
;***************** COMPLEX TO REAL POWER
%ifdef DELPHI
[section cpowd_text use32]
%endif
_sffecpowd:
push ebp
mov ebp,esp
; fld1
;z module
fld qword [ebp+0ch]
fmul qword [ebp+0ch]
fld qword [ebp+14h]
fmul qword [ebp+14h]
faddp st1
fsqrt
ftst
fstsw ax
test ah, 1000000b
jnz MZ2
mov eax, [ebp+08h]
fld1
;theta
fld qword [ebp+14h]
fld qword [ebp+0ch]
fpatan
fmul qword [ebp+1ch]
fxch st2
;ln||z||
fyl2x
fldl2e
fdivp st1
fmul qword [ebp+1ch]
call _sffecexpfnc
fxch st1
fsincos
fld st2
fmulp st1
fstp qword [eax]
fmulp st1
fstp qword [eax+08h]
jmp END2
MZ2:
mov eax, [ebp+08h]
fstp qword [eax+08h]
fldz
fstp qword [eax]
END2:
fwait
leave
ret
;***************** COMPLEX TO INT POWER
%ifdef DELPHI
[section cpowi_text use32]
%endif
_sffecpowi:
push ebp
mov ebp,esp
;z module
fild dword [ebp+1ch] ;st(0)=n
fld qword [ebp+0ch]
fmul qword [ebp+0ch]
fld qword [ebp+14h]
fmul qword [ebp+14h]
faddp st1
fsqrt
ftst
fstsw ax
test ah, 1000000b
jnz MZ5
mov eax, [ebp+08h]
;||z||^n
fld1
fxch st1
fyl2x
fmulp st1
fld st0
frndint
fsub to st1
fld1
fscale
fstp st1
fxch st1
f2xm1
fld1
faddp st1
fmulp st1
;theta
fld qword [ebp+14h]
fld qword [ebp+0ch]
fpatan
fild dword [ebp+1ch]
fmulp st1
fsincos
fld st2
fmulp st1
fstp qword [eax]
fmulp st1
fstp qword [eax+08h]
jmp END53
MZ5:
mov eax, [ebp+08h]
fstp qword [eax+08h]
fldz
fstp qword [eax]
fstp st0
END53:
fwait
leave
ret
;***************** INT/DOUBLE TO COMPLEX POWER
%ifdef DELPHI
[section cpowc_text use32]
%endif
_sffecpowc:
push ebp
mov ebp,esp
fld qword [ebp+0ch]
ftst
fstsw ax
test ah, 1000000b
jnz MZ3
mov eax, [ebp+08h]
;n^a
fld qword [ebp+14h]
fxch st1
fabs
fld1
fxch st1
fyl2x
fmulp st1
fld st0
frndint
fsub to st1
fld1
fscale
fstp st1
fxch st1
f2xm1
fld1
faddp st1
fmulp st1
;ln||n||
fld qword [ebp+0ch]
fabs
fld1
fxch st1
fyl2x
fldl2e
fdivp st1
fld qword [ebp+1ch]
fmulp st1
fsincos
fld st2
fmulp st1
fstp qword [eax]
fmulp st1
fstp qword [eax+08h]
jmp END3
MZ3:
mov eax, [ebp+08h]
fstp qword [eax+08h]
fldz
fstp qword [eax]
END3:
fwait
leave
ret
;***************** SQRT
%ifdef DELPHI
[section csqrt_text use32]
%endif
_sffecsqrt:
push ebp
mov ebp,esp
push ebx
mov ebx, [ebp+08h]
;z module
fld qword [ebp+0ch]
fmul qword [ebp+0ch]
fld qword [ebp+14h]
fmul qword [ebp+14h]
faddp st1
fsqrt
fld st0 ;duplicate |z|
;real
fadd qword [ebp+0ch]
fld1
fld1
faddp st1
fdivp st1
fsqrt
fstp qword [ebx]
fwait
;imag
fsub qword [ebp+0ch]
fld1
fld1
faddp st1
fdivp st1
fsqrt
;imag sign check
push eax
fld qword [ebp+14h]
ftst
fstp st0
fstsw ax
test ah, 1b
jz IMAGPOS
fchs
IMAGPOS:
pop eax
fwait
fstp qword [ebx+08h]
pop ebx
leave
ret
;***************** Nth ORDER ROOT
%ifdef DELPHI
[section crtni_text use32]
%endif
_sffecrtni:
push ebp
mov ebp,esp
;z module
fld qword [ebp+0ch]
fmul qword [ebp+0ch]
fld qword [ebp+14h]
fmul qword [ebp+14h]
faddp st1
fsqrt
ftst
fstsw ax
test ah, 1000000b
jnz MZ4
mov eax, [ebp+08h]
;n-th root if ||z||
fld1
fild word [ebp+1ch]
fdivp st1 ;st0=1/n
fxch st1 ;st0=||z|| st1=1/n
fyl2x ;log2(||z||/n)
fld st0 ;duplikuj st0
frndint
fsub to st1 ;st0=int( log2(||z||/n) ) st1=frac( log2(||z||/n) )
fld1 ;st0=1
fscale ;st0=2^int( log2(||z||/n) ) st1=frac( log2(||z||/n) )
fstp st1
fxch st1
f2xm1 ;st1=2^frac( log2(||z||/n) )-1
fld1
faddp st1
fmulp st1 ;sqrt(||z||)
;theta
fld qword [ebp+14h]
fld qword [ebp+0ch]
fpatan ;st0=theta st1=sqrN(||z||)
;theta_i
fldpi
fldpi
faddp st1 ;st0=2Pi st1=theta st2=sqrN(||z||)
fimul word [ebp+20h]
faddp st1 ;st1=theta+i2Pi
fidiv word [ebp+1ch] ;st0=theta_i
;re/im
fsincos
fld st2
fmulp st1
fstp qword [eax]
fmulp st1
fstp qword [eax+08h]
jmp END4
MZ4:
fldz
fstp qword [eax]
fstp qword [eax+08h]
END4:
leave
ret
%ifndef DELPHI
_sffecfunc:
push ebp
mov ebp,esp
mov eax, [ebp+08h]
leave
ret
%endif
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