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BIGNUMA.ASM
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Assembly Source File
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1995-02-03
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88KB
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2,476 lines
; bignuma.asm - asm routines for bignumbers
; far pointer version
; Wesley Loewer's Big Numbers. (C) 1994, Wesley B. Loewer
; IMPORTANT!!! The following routines assume that all the bignumber arrays
; were allocated from the same far segment. This allows the routines to
; switch the DS register to that segment and treat everything then as a
; near pointer. If that array is not in this segment, then copy it into
; an array that is.
; See BIGNUMC.C for further documentation.
.MODEL medium, c
ifdef ??version ; for TASM
ideal
TYPEDEF bn_t far ptr byte
masm
masm51
quirks
; invoke w/ one arg
invoke macro a,b
call a, b
endm
; invoke with 2 args
invoke2 macro a,b,c
call a, b, c
endm
extern equ extrn
else
bn_t TYPEDEF far ptr byte ; far pointer to bignumber array
endif
.DATA
extern cpu:word
extern bnlength:word, rlength:word;
.CODE
.8086
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = 0
clear_bn PROC USES di, r:bn_t
les di, r ; load pointer in es:di for stos
mov cx, bnlength
cmp cpu, 386 ; check cpu
je short use_32_bit ; use faster 32 bit code if possible
sub ax, ax ; clear ax
shr cx, 1 ; 1 byte = 1/2 word
rep stosw ; clear r, word at a time
jmp bottom
use_32_bit:
.386
sub eax, eax ; clear eax
shr cx, 2 ; 1 byte = 1/4 word
rep stosd ; clear r, dword at a time
bottom:
.8086
mov dx, es ; return r in dx:ax
mov ax, word ptr r
ret
clear_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = max positive value
max_bn PROC USES di, r:bn_t
les di, r ; load pointer in es:di for stos
mov cx, bnlength
cmp cpu, 386 ; check cpu
je short use_32_bit ; use faster 32 bit code if possible
mov ax, 0FFFFh ; set ax to max value
shr cx, 1 ; 1 byte = 1/2 word
rep stosw ; max out r, word at a time
jmp bottom
use_32_bit:
.386
mov eax, 0FFFFFFFFh ; set eax to max value
shr cx, 2 ; 1 byte = 1/4 word
rep stosd ; max out r, dword at a time
bottom:
.8086
; when the above stos is finished, di points to the byte past the end
dec di ; find sign bit in msb
mov byte ptr es:[di], 7Fh ; turn off the sign bit
mov dx, es ; return r in dx:ax
mov ax, word ptr r
ret
max_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = n
copy_bn PROC USES di si, r:bn_t, n:bn_t
les di, r ; load pointer in es:di for movs
mov ax, ds ; save ds for later
mov cx, bnlength
cmp cpu, 386 ; check cpu
je short use_32_bit ; use faster 32 bit code if possible
lds si, n ; load pointer in ds:si for movs
shr cx, 1 ; 1 byte = 1/2 word
rep movsw ; copy word at a time
jmp bottom
use_32_bit:
.386
lds si, n ; load pointer in ds:si for movs
shr cx, 2 ; 1 byte = 1/4 word
rep movsd ; copy dword at a time
bottom:
.8086
mov ds, ax ; restore ds
mov dx, es ; return r in dx:ax
mov ax, word ptr r
ret
copy_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; n1 != n2 ?
; RETURNS: if n1 == n2 returns 0
; if n1 > n2 returns a positive (steps left to go when mismatch occured)
; if n1 < n2 returns a negative (steps left to go when mismatch occured)
cmp_bn PROC USES di, n1:bn_t, n2:bn_t
mov cx, bnlength
push ds ; save DS
mov di, word ptr n2
lds bx, n1 ; load pointers
add bx, cx ; point to end of bignumbers
add di, cx ; where the msb is
cmp cpu, 386 ; check cpu
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
mov dx, cx ; keep a copy of cx
top_loop_16:
sub bx, 2 ; decrement to previous word
sub di, 2
mov ax, [bx] ; load n1
cmp ax, [di] ; compare to n2
jne bottom ; don't match
loop top_loop_16
jmp match
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 dword
mov dx, cx ; keep a copy of cx
top_loop_32:
sub bx, 4 ; decrement to previous dword
sub di, 4
mov eax, [bx] ; load n1
cmp eax, [di] ; compare to n2
jne bottom ; don't match
loop top_loop_32
jmp match
bottom:
.8086
; flags are still set from last cmp
; if cx == dx, then most significant part didn't match, use signed comparison
; else the decimals didn't match, use unsigned comparison
lahf ; load results of last cmp
cmp cx, dx ; did they differ on very first cmp
jne not_first_step ; no
sahf ; yes
jg n1_bigger ; signed comparison
jmp n2_bigger
not_first_step:
sahf
ja n1_bigger ; unsigned comparison
n2_bigger:
neg cx ; make it negative
n1_bigger: ; leave it positive
match: ; leave it zero
mov ax, cx
pop ds ; restore DS
ret
cmp_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r < 0 ?
; returns 1 if negative, 0 if positive or zero
is_bn_neg PROC n:bn_t
; for a one-pass routine like this, don't bother with ds
les bx, n ; find sign bit
add bx, bnlength
dec bx ; here it is
mov al, es:[bx] ; got it
and al, 80h ; check the sign bit
rol al, 1 ; rotate sign big to bit 0
sub ah, ah ; clear upper ax
ret
is_bn_neg ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; n != 0 ?
; RETURNS: if n != 0 returns 1
; else returns 0
is_bn_not_zero PROC n:bn_t
mov cx, bnlength
mov ax, ds ; save DS
lds bx, n ; load pointers with DS
cmp cpu, 386 ; check cpu
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
top_loop_16:
cmp word ptr [bx], 0 ; compare to n to 0
jnz bottom ; not zero
add bx, 2 ; increment to next word
loop top_loop_16
jmp bottom
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 dword
top_loop_32:
cmp dword ptr [bx], 0 ; compare to n to 0
jnz bottom ; not zero
add bx, 4 ; increment to next dword
loop top_loop_32
jmp bottom
bottom:
.8086
mov ds, ax ; restore DS
; if cx is zero, then n was zero
mov ax, cx
ret
is_bn_not_zero ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = n1 + n2
add_bn PROC USES di si, r:bn_t, n1:bn_t, n2:bn_t
mov cx, bnlength
push ds ; save ds
mov di, word ptr n1 ; load pointers ds:di
mov si, word ptr n2 ; ds:si
lds bx, r ; ds:bx
cmp cpu, 386 ; check cpu
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
clc ; clear carry flag
top_loop_16:
mov ax, [di] ; n1
adc ax, [si] ; n1+n2
mov [bx], ax ; r = n1+n2
; inc does not change carry flag
inc di ; add di, 2
inc di
inc si ; add si, 2
inc si
inc bx ; add bx, 2
inc bx
loop top_loop_16
jmp short bottom
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 double word
clc ; clear carry flag
top_loop_32:
mov eax, [di] ; n1
adc eax, [si] ; n1+n2
mov [bx], eax ; r = n1+n2
lahf ; save carry flag
add di, 4 ; increment by double word size
add si, 4
add bx, 4
sahf ; restore carry flag
loop top_loop_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
pop ds ; restore ds
mov ax, word ptr r
ret
add_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r += n
add_a_bn PROC USES di, r:bn_t, n:bn_t
mov cx, bnlength
push ds
mov di, word ptr n ; load pointers ds:di
lds bx, r ; ds:bx
cmp cpu, 386 ; check cpu
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
clc ; clear carry flag
top_loop_16:
mov ax, [di] ; n
adc [bx], ax ; r += n
; inc does not change carry flag
inc di ; add di, 2
inc di
inc bx ; add di, 2
inc bx
loop top_loop_16
jmp short bottom
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 double word
clc ; clear carry flag
top_loop_32:
mov eax, [di] ; n
adc [bx], eax ; r += n
lahf ; save carry flag
add di, 4 ; increment by double word size
add bx, 4
sahf ; restore carry flag
loop top_loop_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
pop ds ; restore ds
mov ax, word ptr r
ret
add_a_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = n1 - n2
sub_bn PROC USES di si, r:bn_t, n1:bn_t, n2:bn_t
mov cx, bnlength
push ds
mov di, word ptr n1 ; load pointers ds:di
mov si, word ptr n2 ; ds:si
lds bx, r ; ds:bx
cmp cpu, 386 ; check cpu
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
clc ; clear carry flag
top_loop_16:
mov ax, [di] ; n1
sbb ax, [si] ; n1-n2
mov [bx], ax ; r = n1-n2
; inc does not change carry flag
inc di ; add di, 2
inc di
inc si ; add si, 2
inc si
inc bx ; add bx, 2
inc bx
loop top_loop_16
jmp short bottom
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 double word
clc ; clear carry flag
top_loop_32:
mov eax, [di] ; n1
sbb eax, [si] ; n1-n2
mov [bx], eax ; r = n1-n2
lahf ; save carry flag
add di, 4 ; increment by double word size
add si, 4
add bx, 4
sahf ; restore carry flag
loop top_loop_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
pop ds ; restore ds
mov ax, word ptr r
ret
sub_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r -= n
sub_a_bn PROC USES di, r:bn_t, n:bn_t
mov cx, bnlength
push ds
mov di, word ptr n ; load pointers ds:di
lds bx, r ; ds:bx
cmp cpu, 386 ; check cpu
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
clc ; clear carry flag
top_loop_16:
mov ax, [di] ; n
sbb [bx], ax ; r -= n
; inc does not change carry flag
inc di ; add di, 2
inc di
inc bx ; add di, 2
inc bx
loop top_loop_16
jmp short bottom
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 double word
clc ; clear carry flag
top_loop_32:
mov eax, [di] ; n
sbb [bx], eax ; r -= n
lahf ; save carry flag
add di, 4 ; increment by double word size
add bx, 4
sahf ; restore carry flag
loop top_loop_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
pop ds ; restore ds
mov ax, word ptr r
ret
sub_a_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = -n
neg_bn PROC USES di, r:bn_t, n:bn_t
mov cx, bnlength
push ds
mov di, word ptr n ; load pointers ds:di
lds bx, r ; ds:bx
cmp cpu, 386
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
top_loop_16:
mov ax, [di]
neg ax
mov [bx], ax
jc short no_more_carry_16 ; notice the "reverse" logic here
add di, 2 ; increment by word size
add bx, 2
loop top_loop_16
jmp short bottom
no_more_carry_16:
add di, 2
add bx, 2
loop top_loop_no_more_carry_16 ; jump down
jmp short bottom
top_loop_no_more_carry_16:
mov ax, [di]
not ax
mov [bx], ax
add di, 2
add bx, 2
loop top_loop_no_more_carry_16
jmp short bottom
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 dword
top_loop_32:
mov eax, [di]
neg eax
mov [bx], eax
jc short no_more_carry_32 ; notice the "reverse" logic here
add di, 4 ; increment by double word size
add bx, 4
loop top_loop_32
jmp short bottom
no_more_carry_32:
add di, 4 ; increment by double word size
add bx, 4
loop top_loop_no_more_carry_32 ; jump down
jmp short bottom
top_loop_no_more_carry_32:
mov eax, [di]
not eax
mov [bx], eax
add di, 4 ; increment by double word size
add bx, 4
loop top_loop_no_more_carry_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
pop ds ; restore ds
mov ax, word ptr r
ret
neg_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r *= -1
neg_a_bn PROC r:bn_t
mov cx, bnlength
push ds
lds bx, r ; ds:bx
cmp cpu, 386
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
top_loop_16:
neg word ptr [bx]
jc short no_more_carry_16 ; notice the "reverse" logic here
add bx, 2
loop top_loop_16
jmp short bottom
no_more_carry_16:
add bx, 2
loop top_loop_no_more_carry_16 ; jump down
jmp short bottom
top_loop_no_more_carry_16:
not word ptr [bx]
add bx, 2
loop top_loop_no_more_carry_16
jmp short bottom
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 dword
top_loop_32:
neg dword ptr [bx]
jc short no_more_carry_32 ; notice the "reverse" logic here
add bx, 4
loop top_loop_32
jmp short bottom
no_more_carry_32:
add bx, 4
loop top_loop_no_more_carry_32 ; jump down
jmp short bottom
top_loop_no_more_carry_32:
not dword ptr [bx]
add bx, 4
loop top_loop_no_more_carry_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
pop ds ; restore ds
mov ax, word ptr r
ret
neg_a_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = 2*n
double_bn PROC USES di, r:bn_t, n:bn_t
mov cx, bnlength
push ds
mov di, word ptr n ; load pointers ds:di
lds bx, r ; ds:bx
cmp cpu, 386
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
clc
top_loop_16:
mov ax, [di]
rcl ax, 1 ; rotate with carry left
mov [bx], ax
; inc does not change carry flag
inc di ; add di, 2
inc di
inc bx ; add bx, 2
inc bx
loop top_loop_16
jmp short bottom
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 dword
clc ; clear carry flag
top_loop_32:
mov eax, [di]
rcl eax, 1 ; rotate with carry left
mov [bx], eax
lahf ; save carry flag
add di, 4 ; increment by double word size
add bx, 4
sahf ; restore carry flag
loop top_loop_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
pop ds ; restore ds
mov ax, word ptr r
ret
double_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r *= 2
double_a_bn PROC r:bn_t
mov cx, bnlength
push ds
lds bx, r ; ds:bx
cmp cpu, 386
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
clc
top_loop_16:
rcl word ptr [bx], 1 ; rotate with carry left
; inc does not change carry flag
inc bx ; add bx, 2
inc bx
loop top_loop_16
jmp short bottom
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 dword
clc ; clear carry flag
top_loop_32:
rcl dword ptr [bx], 1 ; rotate with carry left
lahf ; save carry flag
add bx, 4
sahf ; restore carry flag
loop top_loop_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
pop ds ; restore ds
mov ax, word ptr r
ret
double_a_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = n/2
half_bn PROC USES di, r:bn_t, n:bn_t
mov cx, bnlength
push ds
mov di, word ptr n ; load pointers ds:di
lds bx, r ; ds:bx
add di, cx ; start with msb
add bx, cx
cmp cpu, 386
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
; handle the first step with sar, the rest with rcr
sub di, 2
sub bx, 2
mov ax, [di]
sar ax, 1 ; shift arithmetic right
mov [bx], ax
loop top_loop_16
jmp short bottom
top_loop_16:
; inc does not change carry flag
dec di ; sub di, 2
dec di
dec bx ; sub bx, 2
dec bx
mov ax, [di]
rcr ax, 1 ; rotate with carry right
mov [bx], ax
loop top_loop_16
jmp short bottom
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 dword
sub di, 4 ; decrement by double word size
sub bx, 4
mov eax, [di]
sar eax, 1 ; shift arithmetic right
mov [bx], eax
loop top_loop_32
jmp short bottom
top_loop_32:
lahf ; save carry flag
sub di, 4 ; decrement by double word size
sub bx, 4
sahf ; restore carry flag
mov eax, [di]
rcr eax, 1 ; rotate with carry right
mov [bx], eax
loop top_loop_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
pop ds ; restore ds
mov ax, word ptr r
ret
half_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r /= 2
half_a_bn PROC r:bn_t
mov cx, bnlength
push ds
lds bx, r ; ds:bx
add bx, cx
cmp cpu, 386
je short use_32_bit ; use faster 32 bit code if possible
shr cx, 1 ; byte = 1/2 word
; handle the first step with sar, the rest with rcr
sub bx, 2
sar word ptr [bx], 1 ; shift arithmetic right
loop top_loop_16
jmp short bottom
top_loop_16:
; inc does not change carry flag
dec bx ; sub bx, 2
dec bx
rcr word ptr [bx], 1 ; rotate with carry right
loop top_loop_16
jmp short bottom
use_32_bit:
.386
shr cx, 2 ; byte = 1/4 dword
sub bx, 4 ; decrement by double word size
sar dword ptr [bx], 1 ; shift arithmetic right
loop top_loop_32
jmp short bottom
top_loop_32:
lahf ; save carry flag
sub di, 4 ; decrement by double word size
sub bx, 4
sahf ; restore carry flag
rcr dword ptr [bx], 1 ; rotate with carry right
loop top_loop_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
pop ds ; restore ds
mov ax, word ptr r
ret
half_a_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = n1 * n2
; Note: r will be a double wide result, 2*bnlength
; n1 and n2 can be the same pointer
; SIDE-EFFECTS: n1 and n2 are changed to their absolute values
;
unsafe_full_mult_bn PROC USES di si, r:bn_t, n1:bn_t, n2:bn_t
LOCAL sign1:byte, sign2:byte, samevar:byte, \
i:word, j:word, steps:word, doublesteps:word, carry_steps:word, \
n1p: ptr byte, n2p: ptr byte
; This routine uses near variables and far pointers together in the
; inner-most loops. Therefore, there is little to gain by setting DS
; to the far segment. Instead, set ES to the far segment and use segment
; overrides where necessary.
; By forcing the bignumber to be positive and keeping track of the sign
; bits separately, quite a few multiplies are saved.
; set the ES register
les bx, n1 ; check for sign bits
add bx, bnlength
dec bx
mov al, es:[bx]
and al, 80h ; check the sign bit
mov sign1, al
jz already_pos1
invoke neg_a_bn, n1
already_pos1:
; Test to see if n1 and n2 are the same variable. It would be better to
; use square_bn(), but it could happen.
mov samevar, 1 ; assume they are the same
mov bx, word ptr n2
cmp bx, word ptr n1 ; are they the same?
je already_pos2 ; if so, it has already been negated
mov samevar, 0 ; they weren't the same after all
add bx, bnlength
dec bx
mov al, es:[bx]
and al, 80h ; check the sign bit
mov sign2, al
jz already_pos2
invoke neg_a_bn, n2
already_pos2:
; in the following loops, the following pointers are used
; n1p, n2p = points to the part of n1, n2 being used
; di = points to part of doublebignumber used in outer loop
; si = points to part of doublebignumber used in inner loop
; bx = points to part of doublebignumber for carry flag loop
cmp cpu, 386 ; check cpu
je use_32_bit ; use faster 32 bit code if possible
mov ax, word ptr n1 ; load pointers
mov n1p, ax
mov dx, bnlength ; set outer loop counter
shr dx, 1 ; byte = 1/2 word
mov steps, dx ; save in steps
mov i, dx
shl dx, 1 ; double steps
sub ax, ax ; clear ax
mov cx, dx ; size of doublebignumber (r) in words
mov di, word ptr r ; es already set
rep stosw ; initialize r to 0
sub dx, 2 ; only 2*s-2 steps are really needed
mov doublesteps, dx
mov carry_steps, dx
mov di, word ptr r
mov si, di ; both si and di are used here
top_outer_loop_16:
mov ax, word ptr n2 ; set n2p pointer
mov n2p, ax
mov ax, steps ; set inner loop counter
mov j, ax
top_inner_loop_16:
mov bx, n1p
mov ax, es:[bx]
mov bx, n2p
mul word ptr es:[bx]
mov bx, si
add es:[bx], ax ; add low word
inc bx ; increase by size of word
inc bx
adc es:[bx], dx ; add high word
jnc no_more_carry_16 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_16
add bx, 2 ; move pointer to next word
; loop until no more carry or until end of double big number
top_carry_loop_16:
add word ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_16
add bx, 2 ; increase by size of word
loop top_carry_loop_16
no_more_carry_16:
add n2p, 2 ; increase by word size
add si, 2
dec carry_steps ; use one less step
dec j
ja top_inner_loop_16
add n1p, 2 ; increase by word size
add di, 2
mov si, di ; start with si=di
dec doublesteps ; reduce the carry steps needed
mov ax, doublesteps
mov carry_steps, ax
dec i
ja top_outer_loop_16
; result is now r, a double wide bignumber
jmp bottom
use_32_bit:
.386
mov ax, word ptr n1 ; load pointers
mov n1p, ax
mov dx, bnlength ; set outer loop counter
shr dx, 2 ; byte = 1/4 dword
mov steps, dx ; save in steps
mov i, dx
shl dx, 1 ; double steps
sub eax, eax ; clear eax
mov cx, dx ; size of doublebignumber in dwords
mov di, word ptr r ; es already set
rep stosd ; initialize r to 0
sub dx, 2 ; only 2*s-2 steps are really needed
mov doublesteps, dx
mov carry_steps, dx
mov di, word ptr r
mov si, di ; both si and di are used here
top_outer_loop_32:
mov ax, word ptr n2 ; set n2p pointer
mov n2p, ax
mov ax, steps ; set inner loop counter
mov j, ax
top_inner_loop_32:
mov bx, n1p
mov eax, es:[bx]
mov bx, n2p
mul dword ptr es:[bx]
mov bx, si
add es:[bx], eax ; add low dword
lahf ; save carry flag
add bx, 4 ; increase by size of dword
sahf ; restor carry flag
adc es:[bx], edx ; add high dword
jnc no_more_carry_32 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_32
add bx, 4 ; move pointer to next dword
; loop until no more carry or until end of double big number
top_carry_loop_32:
add dword ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_32
add bx, 4 ; increase by size of dword
loop top_carry_loop_32
no_more_carry_32:
add n2p, 4 ; increase by dword size
add si, 4
dec carry_steps ; use one less step
dec j
ja top_inner_loop_32
add n1p, 4 ; increase by dword size
add di, 4
mov si, di ; start with si=di
dec doublesteps ; reduce the carry steps needed
mov ax, doublesteps
mov carry_steps, ax
dec i
ja top_outer_loop_32
; result is now r, a double wide bignumber
bottom:
.8086
cmp samevar, 1 ; were the variable the same ones?
je pos_answer ; if yes, then jump
mov al, sign1 ; is result + or - ?
cmp al, sign2 ; sign(n1) == sign(n2) ?
je pos_answer ; yes
push bnlength ; save bnlength
shl bnlength, 1 ; temporarily double bnlength
; for double wide bignumber
invoke neg_a_bn, r ; does not affect ES
pop bnlength ; restore bnlength
pos_answer:
mov dx, es ; return r in dx:ax
mov ax, word ptr r
ret
unsafe_full_mult_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = n1 * n2 calculating only the top rlength bytes
; Note: r will be of length rlength
; 2*bnlength <= rlength < bnlength
; n1 and n2 can be the same pointer
; SIDE-EFFECTS: n1 and n2 are changed to their absolute values
;
unsafe_mult_bn PROC USES di si, r:bn_t, n1:bn_t, n2:bn_t
LOCAL sign1:byte, sign2:byte, samevar:byte, \
i:word, j:word, steps:word, doublesteps:word, \
carry_steps:word, skips:word, \
n1p: ptr byte, n2p: ptr byte
; By forcing the bignumber to be positive and keeping track of the sign
; bits separately, quite a few multiplies are saved.
; set the ES register here
les bx, n1 ; check for sign bits
add bx, bnlength
dec bx
mov al, es:[bx]
and al, 80h ; check the sign bit
mov sign1, al
jz already_pos1
invoke neg_a_bn, n1
already_pos1:
; Test to see if n1 and n2 are the same variable. It would be better to
; use square_bn(), but it could happen.
mov samevar, 1 ; assume they are the same
mov bx, word ptr n2
cmp bx, word ptr n1 ; are they the same?
je already_pos2 ; if so, it has already been negated
mov samevar, 0 ; they weren't the same after all
add bx, bnlength
dec bx
mov al, es:[bx]
and al, 80h ; check the sign bit
mov sign2, al
jz already_pos2
invoke neg_a_bn, n2
already_pos2:
mov ax, word ptr n1 ; load pointers
mov n1p, ax
mov ax, bnlength
shl ax, 1 ; 2*bnlength
sub ax, rlength ; 2*bnlength-rlength
add word ptr n2, ax ; n2 = n2+2*bnlength-rlength
; in the following loops, the following pointers are used
; n1p, n2p = points to the part of n1, n2 being used
; di = points to part of doublebignumber used in outer loop
; si = points to part of doublebignumber used in inner loop
; bx = points to part of doublebignumber for carry flag loop
cmp cpu, 386 ; check cpu
je use_32_bit ; use faster 32 bit code if possible
sub ax, ax ; clear ax
mov cx, rlength ; size of r in bytes
shr cx, 1 ; byte = 1/2 word
mov di, word ptr r ; es already set
rep stosw ; initialize r to 0
mov ax, rlength ; set steps for first loop
sub ax, bnlength
shr ax, 1 ; byte = 1/2 word
mov steps, ax ; save in steps
mov ax, bnlength
shr ax, 1 ; byte = 1/2 word
mov i, ax
sub ax, steps
mov skips, ax ; how long to skip over pointer shifts
mov ax, rlength ; set steps for first loop
shr ax, 1 ; byte = 1/2 word
sub ax, 2 ; only rlength/2-2 steps are really needed
mov doublesteps, ax
mov carry_steps, ax
mov di, word ptr r ; this is r
mov si, di ; both si and di are used here
top_outer_loop_16:
mov ax, word ptr n2 ; set n2p pointer
mov n2p, ax
mov ax, steps ; set inner loop counter
mov j, ax
top_inner_loop_16:
mov bx, n1p
mov ax, es:[bx]
mov bx, n2p
mul word ptr es:[bx]
mov bx, si
add es:[bx], ax ; add low word
inc bx ; increase by size of word
inc bx
adc es:[bx], dx ; add high word
jnc no_more_carry_16 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_16
add bx, 2 ; move pointer to next word
; loop until no more carry or until end of double big number
top_carry_loop_16:
add word ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_16
add bx, 2 ; increase by size of word
loop top_carry_loop_16
no_more_carry_16:
add n2p, 2 ; increase by word size
add si, 2
dec carry_steps ; use one less step
dec j
ja top_inner_loop_16
add n1p, 2 ; increase by word size
cmp skips, 0
je type2_shifts_16
sub word ptr n2, 2 ; shift n2 back a word
inc steps ; one more step this time
; leave di and doublesteps where they are
dec skips ; keep track of how many times we've done this
jmp shifts_bottom_16
type2_shifts_16:
add di, 2 ; shift di forward a word
dec doublesteps ; reduce the carry steps needed
shifts_bottom_16:
mov si, di ; start with si=di
mov ax, doublesteps
mov carry_steps, ax
dec i
ja top_outer_loop_16
; result is in r
jmp bottom
use_32_bit:
.386
sub eax, eax ; clear eax
mov cx, rlength ; size of r in bytes
shr cx, 2 ; byte = 1/4 dword
mov di, word ptr r ; es already set
rep stosd ; initialize r to 0
mov ax, rlength ; set steps for first loop
sub ax, bnlength
shr ax, 2 ; byte = 1/4 dword
mov steps, ax ; save in steps
mov ax, bnlength
shr ax, 2 ; byte = 1/4 dword
mov i, ax
sub ax, steps
mov skips, ax ; how long to skip over pointer shifts
mov ax, rlength ; set steps for first loop
shr ax, 2 ; byte = 1/4 dword
sub ax, 2 ; only rlength/4-2 steps are really needed
mov doublesteps, ax
mov carry_steps, ax
mov di, word ptr r ; this is r
mov si, di ; both si and di are used here
top_outer_loop_32:
mov ax, word ptr n2 ; set n2p pointer
mov n2p, ax
mov ax, steps ; set inner loop counter
mov j, ax
top_inner_loop_32:
mov bx, n1p
mov eax, es:[bx]
mov bx, n2p
mul dword ptr es:[bx]
mov bx, si
add es:[bx], eax ; add low dword
lahf ; save carry flag
add bx, 4 ; increase by size of dword
sahf ; restor carry flag
adc es:[bx], edx ; add high dword
jnc no_more_carry_32 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_32
add bx, 4 ; move pointer to next dword
; loop until no more carry or until end of r
top_carry_loop_32:
add dword ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_32
add bx, 4 ; increase by size of dword
loop top_carry_loop_32
no_more_carry_32:
add n2p, 4 ; increase by dword size
add si, 4
dec carry_steps ; use one less step
dec j
ja top_inner_loop_32
add n1p, 4 ; increase by dword size
cmp skips, 0
je type2_shifts_32
sub word ptr n2, 4 ; shift n2 back a dword
inc steps ; one more step this time
; leave di and doublesteps where they are
dec skips ; keep track of how many times we've done this
jmp shifts_bottom_32
type2_shifts_32:
add di, 4 ; shift di forward a dword
dec doublesteps ; reduce the carry steps needed
shifts_bottom_32:
mov si, di ; start with si=di
mov ax, doublesteps
mov carry_steps, ax
dec i
ja top_outer_loop_32
; result is in r
bottom:
.8086
cmp samevar, 1 ; were the variable the same ones?
je pos_answer ; if yes, then jump
mov al, sign1 ; is result + or - ?
cmp al, sign2 ; sign(n1) == sign(n2) ?
je pos_answer ; yes
push bnlength ; save bnlength
mov ax, rlength
mov bnlength, ax ; set bnlength = rlength
invoke neg_a_bn, r ; does not affect ES
pop bnlength ; restore bnlength
pos_answer:
mov dx, es ; return r in dx:ax
mov ax, word ptr r
ret
unsafe_mult_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = n^2
; because of the symetry involved, n^2 is much faster than n*n
; for a bignumber of length l
; n*n takes l^2 multiplications
; n^2 takes (l^2+l)/2 multiplications
; which is about 1/2 n*n as l gets large
; uses the fact that (a+b+c+...)^2 = (a^2+b^2+c^2+...)+2(ab+ac+bc+...)
;
; Note: r will be a double wide result, 2*bnlength
; SIDE-EFFECTS: n is changed to its absolute value
;
unsafe_full_square_bn PROC USES di si, r:bn_t, n:bn_t
LOCAL i:word, j:word, steps:word, doublesteps:word, carry_steps:word, \
rp1: ptr byte, rp2: ptr byte
; This routine uses near variables and far pointers together in the
; inner-most loops. Therefore, there is little to gain by setting DS
; to the far segment. Instead, set ES to the far segment and use segment
; overrides where necessary.
; By forcing the bignumber to be positive and keeping track of the sign
; bits separately, quite a few multiplies are saved.
; load ES here
les bx, n ; check for sign bit
add bx, bnlength
dec bx
mov al, es:[bx]
and al, 80h ; check the sign bit
jz already_pos
invoke neg_a_bn, n
already_pos:
; in the following loops, the following pointers are used
; n1p(di), n2p(si) = points to the parts of n being used
; rp1 = points to part of doublebignumber used in outer loop
; rp2 = points to part of doublebignumber used in inner loop
; bx = points to part of doublebignumber for carry flag loop
mov cx, bnlength ; size of doublebignumber in words
cmp cpu, 386 ; check cpu
je use_32_bit ; use faster 32 bit code if possible
sub ax, ax ; clear ax
; 2{twice the size}*bnlength/2{bytes per word}
mov di, word ptr r ; es already set
rep stosw ; initialize r to 0
mov dx, bnlength ; set outer loop counter
shr dx, 1 ; byte = 1/2 word
dec dx ; don't need to do last one
mov i, dx ; loop counter
mov steps, dx ; save in steps
shl dx, 1 ; double steps
sub dx, 1 ; only 2*s-1 steps are really needed
mov doublesteps, dx
mov carry_steps, dx
mov ax, word ptr r
add ax, 2 ; start with second word
mov rp1, ax
mov rp2, ax ; start with rp2=rp1
mov di, word ptr n ; load n1p pointer
cmp i, 0 ; if bignumberlength is 2
je skip_middle_terms_16
top_outer_loop_16:
mov si, di ; set n2p pointer
add si, 2 ; to 1 word beyond n1p(di)
mov ax, steps ; set inner loop counter
mov j, ax
top_inner_loop_16:
mov ax, es:[di]
mul word ptr es:[si]
mov bx, rp2
add es:[bx], ax ; add low word
inc bx ; increase by size of word
inc bx
adc es:[bx], dx ; add high word
jnc no_more_carry_16 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_16
add bx, 2 ; move pointer to next word
; loop until no more carry or until end of double big number
top_carry_loop_16:
add word ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_16
add bx, 2 ; increase by size of word
loop top_carry_loop_16
no_more_carry_16:
add si, 2 ; increase by word size
add rp2, 2
dec carry_steps ; use one less step
dec j
ja top_inner_loop_16
add di, 2 ; increase by word size
add rp1, 4 ; increase by 2*word size
mov ax, rp1
mov rp2, ax ; start with rp2=rp1
sub doublesteps,2 ; reduce the carry steps needed
mov ax, doublesteps
mov carry_steps, ax
dec steps ; use one less step
dec i
ja top_outer_loop_16
; All the middle terms have been multiplied. Now double it.
push bnlength
shl bnlength, 1 ; r is a double wide bignumber
invoke double_a_bn, r
pop bnlength
skip_middle_terms_16:
; Now go back and add in the squared terms.
; In the following loops, the following pointers are used
; n1p(di) = points to the parts of n being used
; rp1(si) = points to part of doublebignumber used in outer loop
; bx = points to part of doublebignumber for carry flag loop
mov di, word ptr n ; load n1p pointer
mov dx, bnlength ; set outer loop counter
shr dx, 1 ; 1 bytes = 1/2 word
mov i, dx ; loop counter
shl dx, 1 ; double steps
sub dx, 2 ; only 2*s-2 steps are really needed
mov doublesteps, dx
mov carry_steps, dx
mov si, word ptr r ; set rp1
top_outer_loop_squares_16:
mov ax, es:[di]
mul ax ; square it
mov bx, si
add es:[bx], ax ; add low word
inc bx ; increase by size of word
inc bx
adc es:[bx], dx ; add high word
jnc no_more_carry_squares_16 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_squares_16
add bx, 2 ; move pointer to next word
; loop until no more carry or until end of double big number
top_carry_loop_squares_16:
add word ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_squares_16
add bx, 2 ; increase by size of word
loop top_carry_loop_squares_16
no_more_carry_squares_16:
add di, 2 ; increase by word size
add si, 4 ; increase by 2*word size
sub doublesteps,2 ; reduce the carry steps needed
mov ax, doublesteps
mov carry_steps, ax
dec i
ja top_outer_loop_squares_16
; result is in r, a double wide bignumber
jmp bottom
use_32_bit:
.386
sub eax, eax ; clear eax
; 2{twice the size}*bnlength/4{bytes per word}
shr cx, 1 ; size of doublebignumber in dwords
mov di, word ptr r ; es already set
rep stosd ; initialize r to 0
mov dx, bnlength ; set outer loop counter
shr dx, 2 ; byte = 1/4 dword
dec dx ; don't need to do last one
mov i, dx ; loop counter
mov steps, dx ; save in steps
shl dx, 1 ; double steps
sub dx, 1 ; only 2*s-1 steps are really needed
mov doublesteps, dx
mov carry_steps, dx
mov ax, word ptr r
add ax, 4 ; start with second dword
mov rp1, ax
mov rp2, ax ; start with rp2=rp1
mov di, word ptr n ; load n1p pointer
cmp i, 0 ; if bignumberlength is 4
je skip_middle_terms_32
top_outer_loop_32:
mov si, di ; set n2p pointer
add si, 4 ; to 1 dword beyond n1p(di)
mov ax, steps ; set inner loop counter
mov j, ax
top_inner_loop_32:
mov eax, es:[di]
mul dword ptr es:[si]
mov bx, rp2
add es:[bx], eax ; add low dword
lahf
add bx, 4 ; increase by size of dword
sahf
adc es:[bx], edx ; add high dword
jnc no_more_carry_32 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_32
add bx, 4 ; move pointer to next dword
; loop until no more carry or until end of double big number
top_carry_loop_32:
add dword ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_32
add bx, 4 ; increase by size of dword
loop top_carry_loop_32
no_more_carry_32:
add si, 4 ; increase by dword size
add rp2, 4
dec carry_steps ; use one less step
dec j
ja top_inner_loop_32
add di, 4 ; increase by dword size
add rp1, 8 ; increase by 2*dword size
mov ax, rp1
mov rp2, ax ; start with rp2=rp1
sub doublesteps,2 ; reduce the carry steps needed
mov ax, doublesteps
mov carry_steps, ax
dec steps ; use one less step
dec i
ja top_outer_loop_32
; All the middle terms have been multiplied. Now double it.
push bnlength
shl bnlength, 1 ; r is a double wide bignumber
invoke double_a_bn, r
pop bnlength
skip_middle_terms_32:
; Now go back and add in the squared terms.
; In the following loops, the following pointers are used
; n1p(di) = points to the parts of n being used
; rp1(si) = points to part of doublebignumber used in outer loop
; bx = points to part of doublebignumber for carry flag loop
mov di, word ptr n ; load n1p pointer
mov dx, bnlength ; set outer loop counter
shr dx, 2 ; 1 bytes = 1/4 dword
mov i, dx ; loop counter
shl dx, 1 ; double steps
sub dx, 2 ; only 2*s-2 steps are really needed
mov doublesteps, dx
mov carry_steps, dx
mov si, word ptr r ; set rp1
top_outer_loop_squares_32:
mov eax, es:[di]
mul eax ; square it
mov bx, si
add es:[bx], eax ; add low dword
lahf
add bx, 4 ; increase by size of dword
sahf
adc es:[bx], edx ; add high dword
jnc no_more_carry_squares_32 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_squares_32
add bx, 4 ; move pointer to next dword
; loop until no more carry or until end of double big number
top_carry_loop_squares_32:
add dword ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_squares_32
add bx, 4 ; increase by size of dword
loop top_carry_loop_squares_32
no_more_carry_squares_32:
add di, 4 ; increase by dword size
add si, 8 ; increase by 2*dword size
sub doublesteps,2 ; reduce the carry steps needed
mov ax, doublesteps
mov carry_steps, ax
dec i
ja top_outer_loop_squares_32
; result is in r, a double wide bignumber
bottom:
.8086
; since it is a square, the result has to already be positive
mov dx, es ; return r in dx:ax
mov ax, word ptr r
ret
unsafe_full_square_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = n^2
; because of the symetry involved, n^2 is much faster than n*n
; for a bignumber of length l
; n*n takes l^2 multiplications
; n^2 takes (l^2+l)/2 multiplications
; which is about 1/2 n*n as l gets large
; uses the fact that (a+b+c+...)^2 = (a^2+b^2+c^2+...)+2(ab+ac+bc+...)
;
; Note: r will be of length rlength
; 2*bnlength >= rlength > bnlength
; SIDE-EFFECTS: n is changed to its absolute value
;
unsafe_square_bn PROC USES di si, r:bn_t, n:bn_t
LOCAL i:word, j:word, steps:word, doublesteps:word, carry_steps:word, \
skips:word, rodd:word, \
n3p: ptr byte, \
rp1: ptr byte, rp2: ptr byte
; This whole procedure would be a great deal simpler if we could assume that
; rlength < 2*bnlength (that is, not =). Therefore, we will take the
; easy way out and call full_square_bn() if it is.
mov ax, rlength
shr ax, 1 ; 1/2 * rlength
cmp ax, bnlength ; 1/2 * rlength == bnlength?
jne not_full_square
ifndef ??version
invoke unsafe_full_square_bn, r, n
else
invoke2 unsafe_full_square_bn, r, n
endif
; dx:ax is still loaded with return value
jmp quit_proc ; we're outa here
not_full_square:
; This routine uses near variables and far pointers together in the
; inner-most loops. Therefore, there is little to gain by setting DS
; to the far segment. Instead, set ES to the far segment and use segment
; overrides where necessary.
; By forcing the bignumber to be positive and keeping track of the sign
; bits separately, quite a few multiplies are saved.
; set ES here
les bx, n ; check for sign bit
add bx, bnlength
dec bx
mov al, es:[bx]
and al, 80h ; check the sign bit
jz already_pos
invoke neg_a_bn, n
already_pos:
; in the following loops, the following pointers are used
; n1p(di), n2p(si) = points to the parts of n being used
; rp1 = points to part of doublebignumber used in outer loop
; rp2 = points to part of doublebignumber used in inner loop
; bx = points to part of doublebignumber for carry flag loop
cmp cpu, 386 ; check cpu
je use_32_bit ; use faster 32 bit code if possible
sub ax, ax ; clear ax
mov cx, rlength ; size of rlength in bytes
shr cx, 1 ; byte = 1/2 word
mov di, word ptr r ; es already set
rep stosw ; initialize r to 0
; determine whether r is on an odd or even word in the number
; (even if rlength==2*bnlength, dec r alternates odd/even)
mov ax, bnlength
shl ax, 1 ; double wide width
sub ax, rlength ; 2*bnlength-rlength
shr ax, 1 ; 1 byte = 1/2 word
and ax, 0001h ; check the odd sign bit
mov rodd, ax
mov ax, bnlength ; set outer loop counter
shr ax, 1 ; byte = 1/2 word
dec ax ; don't need to do last one
mov i, ax ; loop counter
mov ax, rlength ; set steps for first loop
sub ax, bnlength
shr ax, 1 ; byte = 1/2 word
mov steps, ax ; save in steps
mov dx, bnlength
shr dx, 1 ; bnlength/2
add ax, dx ; steps+bnlength/2
sub ax, 2 ; steps+bnlength/2-2
mov doublesteps, ax
mov carry_steps, ax
mov ax, i
sub ax, steps
shr ax, 1 ; for both words and dwords
mov skips, ax ; how long to skip over pointer shifts
mov ax, word ptr r
mov rp1, ax
mov rp2, ax ; start with rp2=rp1
mov di, word ptr n ; load n1p pointer
mov si, di
mov ax, bnlength
shr ax, 1 ; 1 byte = 1/2 word
sub ax, steps
shl ax, 1 ; 1 byte = 1/2 word
add si, ax ; n2p = n1p + 2*(bnlength/2 - steps)
mov n3p, si ; save for later use
cmp i, 0 ; if bignumberlength is 2
je skip_middle_terms_16
top_outer_loop_16:
mov ax, steps ; set inner loop counter
mov j, ax
top_inner_loop_16:
mov ax, es:[di]
mul word ptr es:[si]
mov bx, rp2
add es:[bx], ax ; add low word
inc bx ; increase by size of word
inc bx
adc es:[bx], dx ; add high word
jnc no_more_carry_16 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_16
add bx, 2 ; move pointer to next word
; loop until no more carry or until end of double big number
top_carry_loop_16:
add word ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_16
add bx, 2 ; increase by size of word
loop top_carry_loop_16
no_more_carry_16:
add si, 2 ; increase by word size
add rp2, 2
dec carry_steps ; use one less step
dec j
ja top_inner_loop_16
add di, 2 ; increase by word size
mov ax, rodd ; whether r is on an odd or even word
cmp skips, 0
jle type2_shifts_16
sub n3p, 2 ; point to previous word
mov si, n3p
inc steps ; one more step this time
; leave rp1 and doublesteps where they are
dec skips
jmp shifts_bottom_16
type2_shifts_16: ; only gets executed once
jl type3_shifts_16
sub steps, ax ; steps -= (0 or 1)
inc ax ; ax = 1 or 2 now
sub doublesteps, ax ; decrease double steps by 1 or 2
shl ax, 1 ; 1 byte = 1/2 word
add rp1, ax ; add 1 or 2 words
mov si, di
add si, 2 ; si = di + word
dec skips ; make skips negative
jmp shifts_bottom_16
type3_shifts_16:
dec steps
sub doublesteps, 2
add rp1, 4 ; + two words
mov si, di
add si, 2 ; si = di + word
shifts_bottom_16:
mov ax, rp1
mov rp2, ax ; start with rp2=rp1
mov ax, doublesteps
mov carry_steps, ax
dec i
ja top_outer_loop_16
; All the middle terms have been multiplied. Now double it.
push bnlength ; save bnlength
mov ax, rlength
mov bnlength, ax ; r is of length rlength
invoke double_a_bn, r
pop bnlength
skip_middle_terms_16:
; Now go back and add in the squared terms.
; In the following loops, the following pointers are used
; n1p(di) = points to the parts of n being used
; rp1(si) = points to part of doublebignumber used in outer loop
; bx = points to part of doublebignumber for carry flag loop
; be careful, the next dozen or so lines are confusing!
; determine whether r is on an odd or even word in the number
mov ax, bnlength
shl ax, 1 ; double wide width
sub ax, rlength ; 2*bnlength-rlength
mov dx, ax ; save this for a moment
and ax, 0002h ; check the odd sign bit
mov si, word ptr r
add si, ax ; depending on odd or even byte
shr dx, 1 ; assumes word size
inc dx
and dx, 0FFFEh ; ~2+1, turn off last bit, mult of 2
mov di, word ptr n
add di, dx
mov ax, bnlength
sub ax, dx
shr ax, 1 ; 1 byte = 1/2 word
mov i, ax
shl ax, 1 ; double steps
sub ax, 2 ; only 2*s-2 steps are really needed
mov doublesteps, ax
mov carry_steps, ax
top_outer_loop_squares_16:
mov ax, es:[di]
mul ax ; square it
mov bx, si
add es:[bx], ax ; add low word
inc bx ; increase by size of word
inc bx
adc es:[bx], dx ; add high word
jnc no_more_carry_squares_16 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_squares_16
add bx, 2 ; move pointer to next word
; loop until no more carry or until end of double big number
top_carry_loop_squares_16:
add word ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_squares_16
add bx, 2 ; increase by size of word
loop top_carry_loop_squares_16
no_more_carry_squares_16:
add di, 2 ; increase by word size
add si, 4 ; increase by 2*word size
sub doublesteps,2 ; reduce the carry steps needed
mov ax, doublesteps
mov carry_steps, ax
dec i
ja top_outer_loop_squares_16
; result is in r
jmp bottom
use_32_bit:
.386
sub eax, eax ; clear eax
mov cx, rlength ; size of rlength in bytes
shr cx, 2 ; byte = 1/4 dword
mov di, word ptr r ; es already set
rep stosd ; initialize r to 0
; determine whether r is on an odd or even dword in the number
; (even if rlength==2*bnlength, dec r alternates odd/even)
mov ax, bnlength
shl ax, 1 ; double wide width
sub ax, rlength ; 2*bnlength-rlength
shr ax, 2 ; 1 byte = 1/4 dword
and ax, 0001h ; check the odd sign bit
mov rodd, ax
mov ax, bnlength ; set outer loop counter
shr ax, 2 ; byte = 1/4 dword
dec ax ; don't need to do last one
mov i, ax ; loop counter
mov ax, rlength ; set steps for first loop
sub ax, bnlength
shr ax, 2 ; byte = 1/4 dword
mov steps, ax ; save in steps
mov dx, bnlength
shr dx, 2 ; bnlength/4
add ax, dx ; steps+bnlength/4
sub ax, 2 ; steps+bnlength/4-2
mov doublesteps, ax
mov carry_steps, ax
mov ax, i
sub ax, steps
shr ax, 1 ; for both words and dwords
mov skips, ax ; how long to skip over pointer shifts
mov ax, word ptr r
mov rp1, ax
mov rp2, ax ; start with rp2=rp1
mov di, word ptr n ; load n1p pointer
mov si, di
mov ax, bnlength
shr ax, 2 ; 1 byte = 1/4 dword
sub ax, steps
shl ax, 2 ; 1 byte = 1/4 dword
add si, ax ; n2p = n1p + bnlength/4 - steps
mov n3p, si ; save for later use
cmp i, 0 ; if bignumberlength is 2
je skip_middle_terms_32
top_outer_loop_32:
mov ax, steps ; set inner loop counter
mov j, ax
top_inner_loop_32:
mov eax, es:[di]
mul dword ptr es:[si]
mov bx, rp2
add es:[bx], eax ; add low dword
lahf ; save carry flag
add bx, 4 ; increase by size of dword
sahf ; restore carry flag
adc es:[bx], edx ; add high dword
jnc no_more_carry_32 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_32
add bx, 4 ; move pointer to next dword
; loop until no more carry or until end of double big number
top_carry_loop_32:
add dword ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_32
add bx, 4 ; increase by size of dword
loop top_carry_loop_32
no_more_carry_32:
add si, 4 ; increase by dword size
add rp2, 4
dec carry_steps ; use one less step
dec j
ja top_inner_loop_32
add di, 4 ; increase by dword size
mov ax, rodd ; whether r is on an odd or even dword
cmp skips, 0
jle type2_shifts_32
sub n3p, 4 ; point to previous dword
mov si, n3p
inc steps ; one more step this time
; leave rp1 and doublesteps where they are
dec skips
jmp shifts_bottom_32
type2_shifts_32: ; only gets executed once
jl type3_shifts_32
sub steps, ax ; steps -= (0 or 1)
inc ax ; ax = 1 or 2 now
sub doublesteps, ax ; decrease double steps by 1 or 2
shl ax, 2 ; 1 byte = 1/4 dword
add rp1, ax ; add 1 or 2 dwords
mov si, di
add si, 4 ; si = di + dword
dec skips ; make skips negative
jmp shifts_bottom_32
type3_shifts_32:
dec steps
sub doublesteps, 2
add rp1, 8 ; + two dwords
mov si, di
add si, 4 ; si = di + dword
shifts_bottom_32:
mov ax, rp1
mov rp2, ax ; start with rp2=rp1
mov ax, doublesteps
mov carry_steps, ax
dec i
ja top_outer_loop_32
; All the middle terms have been multiplied. Now double it.
push bnlength ; save bnlength
mov ax, rlength
mov bnlength, ax ; r is of length rlength
invoke double_a_bn, r
pop bnlength
skip_middle_terms_32:
; Now go back and add in the squared terms.
; In the following loops, the following pointers are used
; n1p(di) = points to the parts of n being used
; rp1(si) = points to part of doublebignumber used in outer loop
; bx = points to part of doublebignumber for carry flag loop
; be careful, the next dozen or so lines are confusing!
; determine whether r is on an odd or even word in the number
mov ax, bnlength
shl ax, 1 ; double wide width
sub ax, rlength ; 2*bnlength-rlength
mov dx, ax ; save this for a moment
and ax, 0004h ; check the odd sign bit
mov si, word ptr r
add si, ax ; depending on odd or even byte
shr dx, 2 ; assumes dword size
inc dx
and dx, 0FFFEh ; ~2+1, turn off last bit, mult of 2
shl dx, 1
mov di, word ptr n
add di, dx
mov ax, bnlength
sub ax, dx
shr ax, 2 ; 1 byte = 1/4 dword
mov i, ax
shl ax, 1 ; double steps
sub ax, 2 ; only 2*s-2 steps are really needed
mov doublesteps, ax
mov carry_steps, ax
top_outer_loop_squares_32:
mov eax, es:[di]
mul eax ; square it
mov bx, si
add es:[bx], eax ; add low dword
lahf ; save carry flag
add bx, 4 ; increase by size of dword
sahf ; restore carry flag
adc es:[bx], edx ; add high dword
jnc no_more_carry_squares_32 ; carry loop not necessary
mov cx, carry_steps ; how many till end of double big number
jcxz no_more_carry_squares_32
add bx, 4 ; move pointer to next dword
; loop until no more carry or until end of double big number
top_carry_loop_squares_32:
add dword ptr es:[bx], 1 ; use add, not inc
jnc no_more_carry_squares_32
add bx, 4 ; increase by size of dword
loop top_carry_loop_squares_32
no_more_carry_squares_32:
add di, 4 ; increase by dword size
add si, 8 ; increase by 2*dword size
sub doublesteps,2 ; reduce the carry steps needed
mov ax, doublesteps
mov carry_steps, ax
dec i
ja top_outer_loop_squares_32
; result is in r
bottom:
.8086
; since it is a square, the result has to already be positive
mov dx, es ; return r in dx:ax
mov ax, word ptr r
quit_proc:
ret
unsafe_square_bn ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = n * u where u is an unsigned integer
mult_bn_int PROC USES di si, r:bn_t, n:bn_t, u:word
LOCAL lu:dword ; long unsigned integer in 32 bit math
mov cx, bnlength ; set outer loop counter
mov ax, ds ; mov DS to ES for one segment override
mov es, ax
mov si, word ptr n ; load pointers ds:si
lds di, r ; ds:di
cmp cpu, 386 ; check cpu
je use_32_bit ; use faster 32 bit code if possible
; no need to clear r
shr cx, 1 ; byte = 1/2 word
sub bx, bx ; use bx for temp holding carried word
top_loop_16:
mov ax, [si] ; load next word from n
mul es:u ; n * u
add ax, bx ; add last carried upper word
adc dx, 0 ; inc the carried word if carry flag set
mov bx, dx ; save high word in bx
mov [di], ax ; save low word
add di, 2 ; next word in r
add si, 2 ; next word in n
loop top_loop_16
jmp bottom
use_32_bit:
.386
; no need to clear r
shr cx, 2 ; byte = 1/4 dword
sub ebx, ebx ; use ebx for temp holding carried dword
sub eax, eax ; clear upper eax
mov ax, es:u ; convert u (unsigned int)
mov es:lu, eax ; to lu (long unsigned int)
top_loop_32:
mov eax, [si] ; load next dword from n
mul es:lu ; n * lu
add eax, ebx ; add last carried upper dword
adc edx, 0 ; inc the carried dword if carry flag set
mov ebx, edx ; save high dword in ebx
mov [di], eax ; save low dword
add di, 4 ; next dword in r
add si, 4 ; next dword in n
loop top_loop_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
mov ax, es ; restore ds
mov ds, ax
mov ax, word ptr r
ret
mult_bn_int ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r *= u where u is an unsigned integer
mult_a_bn_int PROC USES di si, r:bn_t, u:word
mov cx, bnlength ; set outer loop counter
mov ax, ds ; save ds
mov es, ax
mov si, u ; save u in ds:si
lds di, r ; load pointer ds:di
cmp cpu, 386 ; check cpu
je use_32_bit ; use faster 32 bit code if possible
; no need to clear r
shr cx, 1 ; byte = 1/2 word
sub bx, bx ; use bx for temp holding carried word
top_loop_16:
mov ax, [di] ; load next word from r
mul si ; r * u
add ax, bx ; add last carried upper word
adc dx, 0 ; inc the carried word if carry flag set
mov bx, dx ; save high word in bx
mov [di], ax ; save low word
add di, 2 ; next word in r
loop top_loop_16
jmp bottom
use_32_bit:
.386
; no need to clear r
shr cx, 2 ; byte = 1/4 dword
sub ebx, ebx ; use ebx for temp holding carried dword
sub esi, esi ; clear upper esi
top_loop_32:
mov eax, [di] ; load next dword from r
mul esi ; r * u
add eax, ebx ; add last carried upper dword
adc edx, 0 ; inc the carried dword if carry flag set
mov ebx, edx ; save high dword in ebx
mov [di], eax ; save low dword
add di, 4 ; next dword in r
loop top_loop_32
bottom:
.8086
mov dx, ds ; return r in dx:ax
mov ax, es ; restore ds
mov ds, ax
mov ax, word ptr r
ret
mult_a_bn_int ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r = n / u where u is an unsigned integer
unsafe_div_bn_int PROC USES di si, r:bn_t, n:bn_t, u:word
LOCAL sign:byte
les bx, n ; check for sign bits
add bx, bnlength
dec bx
mov al, es:[bx]
and al, 80h ; check the sign bit
mov sign, al
jz already_pos
invoke neg_a_bn, n
already_pos:
mov cx, bnlength ; set outer loop counter
mov ax, ds ; use es for default ds
mov es, ax
; past most significant portion of the number
mov si, word ptr n ; load pointers ds:si
add si, cx
lds di, r ; ds:di
add di, cx
cmp cpu, 386 ; check cpu
je use_32_bit ; use faster 32 bit code if possible
; no need to clear r here, values get mov'ed, not add'ed
shr cx, 1 ; byte = 1/2 word
mov bx, es:u
; need to start with most significant portion of the number
sub si, 2 ; most sig word
sub di, 2 ; most sig word
sub dx, dx ; clear dx register
; for first time through loop
top_loop_16:
mov ax, [si] ; load next word from n
div bx
mov [di], ax ; store low word
; leave remainder in dx
sub si, 2 ; next word in n
sub di, 2 ; next word in r
loop top_loop_16
jmp bottom
use_32_bit:
.386
; no need to clear r here, values get mov'ed, not add'ed
shr cx, 2 ; byte = 1/4 dword
sub ebx, ebx ; clear upper word or ebx
mov bx, es:u
; need to start with most significant portion of the number
sub si, 4 ; most sig dword
sub di, 4 ; most sig dword
sub edx, edx ; clear edx register
; for first time through loop
top_loop_32:
mov eax, [si] ; load next dword from n
div ebx
mov [di], eax ; store low dword
; leave remainder in edx
sub si, 4 ; next dword in n
sub di, 4 ; next dword in r
loop top_loop_32
bottom:
.8086
mov ax, es ; swap es & ds
mov bx, ds
mov ds, ax
mov es, bx
cmp sign, 0 ; is result + or - ?
je pos_answer ; yes
invoke neg_a_bn, r ; does not affect ES
pos_answer:
mov dx, es ; return r in dx:ax
mov ax, word ptr r ;
ret
unsafe_div_bn_int ENDP
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; r /= u where u is an unsigned integer
div_a_bn_int PROC USES di, r:bn_t, u:word
LOCAL sign:byte
les bx, r ; check for sign bits
add bx, bnlength
dec bx
mov al, es:[bx]
and al, 80h ; check the sign bit
mov sign, al
jz already_pos
invoke neg_a_bn, r
already_pos:
mov cx, bnlength ; set outer loop counter
mov ax, ds ; save ds in es
mov es, ax
lds di, r ; load pointer r in ds:di
add di, cx
cmp cpu, 386 ; check cpu
je use_32_bit ; use faster 32 bit code if possible
; no need to clear r here, values get mov'ed, not add'ed
shr cx, 1 ; byte = 1/2 word
mov bx, es:u
; need to start with most significant portion of the number
sub di, 2 ; most sig word
sub dx, dx ; clear dx register
; for first time through loop
top_loop_16:
mov ax, [di] ; load next word from r
div bx
mov [di], ax ; store low word
; leave remainder in dx
sub di, 2 ; next word in r
loop top_loop_16
jmp bottom
use_32_bit:
.386
; no need to clear r here, values get mov'ed, not add'ed
shr cx, 2 ; byte = 1/4 dword
sub ebx, ebx ; clear upper word or ebx
mov bx, es:u
; need to start with most significant portion of the number
sub di, 4 ; most sig dword
sub edx, edx ; clear edx register
; for first time through loop
top_loop_32:
mov eax, [di] ; load next dword from r
div ebx
mov [di], eax ; store low dword
; leave remainder in edx
sub di, 4 ; next dword in r
loop top_loop_32
bottom:
.8086
mov ax, es ; swap es & ds
mov bx, ds
mov ds, ax
mov es, bx
cmp sign, 0 ; is result + or - ?
je pos_answer ; yes
invoke neg_a_bn, r ; does not affect ES
pos_answer:
mov dx, es ; return r in dx:ax
mov ax, word ptr r ;
ret
div_a_bn_int ENDP
END
