; }
;
; Using EDIV would be very easy, if it didn't do signed calculations.
-; Therefore, som extra things have to happen around it. The way to
-; handle that is to shift all operands right one step (basically dividing
-; them by 2) and handle the different cases depending on what the lowest
-; bit of each operand was.
+; It doesn't accept a signed dividend, but accepts a signed divisor.
+; So, shifting down the dividend right one bit makes it positive, and
+; just makes us lose the lowest bit, which can be used afterwards as
+; an addition to the remainder. All that needs to be done at the end
+; is a little bit of fiddling; shifting both quotient and remainder
+; one step to the left, and deal with the situation when the remainder
+; ends up being larger than the divisor.
;
-; To start with, let's define the following:
+; We end up doing something like this:
;
-; a' = l & 1
-; a2 = <h,l> >> 1 # UNSIGNED shift!
-; b' = d & 1
-; b2 = d >> 1 # UNSIGNED shift!
+; l' = l & 1
+; [h,l] = [h,l] >> 1
+; [q,r] = floor([h,l] / d)
+; if (q < 0) q = -q # Because EDIV thought d was negative
;
-; Now, use EDIV to calculate a quotient and a remainder:
+; Now, we need to adjust back by multiplying quotient and remainder with 2,
+; and add the bit that dropped out when dividing by 2:
;
-; q'' = a2/b2
-; r'' = a2 - q''*b2
+; r' = r & 0x80000000
+; q = q << 1
+; r = (r << 1) + a'
;
-; If b' is 0, the quotient is already correct, we just need to adjust the
-; remainder:
+; And now, the final adjustment if the remainder happens to get larger than
+; the divisor:
;
-; if (b' == 0)
+; if (r')
; {
-; r = 2*r'' + a'
-; q = q''
+; r = r - d
+; q = q + 1
; }
-;
-; If b' is 1, we need to do other adjustements. The first thought is the
-; following (note that r' will not always have the right value, but an
-; adjustement follows further down):
-;
-; if (b' == 1)
-; {
-; q' = q''
-; r' = a - q'*b
-;
-; However, one can note the folowing relationship:
-;
-; r'' = a2 - q''*b2
-; => 2*r'' = 2*a2 - 2*q''*b2
-; = { a = 2*a2 + a', b = 2*b2 + b' = 2*b2 + 1,
-; q' = q'' }
-; = a - a' - q'*(b - 1)
-; = a - q'*b - a' + q'
-; = r' - a' + q'
-; => r' = 2*r'' - q' + a'
-;
-; This enables us to use r'' instead of discarding and calculating another
-; modulo:
-;
-; if (b' == 1)
+; while (r > d)
; {
-; q' = q''
-; r' = (r'' << 1) - q' + a'
-;
-; Now, all we have to do is adjust r', because it might be < 0:
-;
-; while (r' < 0)
-; {
-; r' = r' + b
-; q' = q' - 1
-; }
+; r = r - d
+; q = q + 1
; }
;
-; return q'
+; return q
h=4 ;(AP) h by value (input)
l=8 ;(AP) l by value (input)
d=12 ;(AP) d by value (input)
-;aprim=r5
-;a2=r6
-;a20=r6
-;a21=r7
-;bprim=r8
-;b2=r9
-;qprim=r10 ; initially used as q''
-;rprim=r11 ; initially used as r''
+;lprim=r5
+;rprim=r6
.psect code,nowrt
-.entry bn_div_words,^m<r2,r3,r4,r5,r6,r7,r8,r9,r10,r11>
+.entry bn_div_words,^m<r2,r3,r4,r5,r6>
movl l(ap),r2
movl h(ap),r3
movl d(ap),r4
movl #0,r5
- movl #0,r8
- movl #0,r0
-; movl #0,r1
+ movl #0,r6
- rotl #-1,r2,r6 ; a20 = l >> 1 (almost)
- rotl #-1,r3,r7 ; a21 = h >> 1 (almost)
- rotl #-1,r4,r9 ; b2 = d >> 1 (almost)
+ rotl #-1,r2,r2 ; l = l >> 1 (almost)
+ rotl #-1,r3,r3 ; h = h >> 1 (almost)
- tstl r6
+ tstl r2
bgeq 1$
- xorl2 #^X80000000,r6 ; fixup a20 so highest bit is 0
- incl r5 ; a' = 1
+ xorl2 #^X80000000,r2 ; fixup l so highest bit is 0
+ incl r5 ; l' = 1
1$:
- tstl r7
+ tstl r3
bgeq 2$
- xorl2 #^X80000000,r6 ; fixup a20 so highest bit is 1,
- ; since that's what was lowest in a21
- xorl2 #^X80000000,r7 ; fixup a21 so highest bit is 1
+ xorl2 #^X80000000,r2 ; fixup l so highest bit is 1,
+ ; since that's what was lowest in h
+ xorl2 #^X80000000,r3 ; fixup h so highest bit is 0
2$:
- tstl r9
+ tstl r4
beql 666$ ; Uh-oh, the divisor is 0...
- bgtr 3$
- xorl2 #^X80000000,r9 ; fixup b2 so highest bit is 0
- incl r8 ; b' = 1
+
+ ediv r4,r2,r2,r3 ; Do the actual division
+
+ tstl r2
+ bgeq 3$
+ mnegl r2,r2 ; if q < 0, negate it
3$:
- tstl r9
- bneq 4$ ; if b2 is 0, we know that b' is 1
tstl r3
- bneq 666$ ; if higher half isn't 0, we overflow
- movl r2,r10 ; otherwise, we have our result
- brb 42$ ; This is a success, really.
+ bgeq 4$
+ incl r6 ; since the high bit in r is set, set rprim
4$:
- ediv r9,r6,r10,r11
+ ashl #1,r2,r2
+ ashl #1,r3,r3
+ addl r5,r3
- tstl r8
- bneq 5$ ; If b' != 0, go to the other part
-; addl3 r11,r11,r1
-; addl2 r5,r1
- brb 42$
+ tstl r6
+ beql 5$
+ subl r4,r3
+ incl r2
5$:
- ashl #1,r11,r11
- subl2 r10,r11
- addl2 r5,r11
- bgeq 7$
-6$:
- decl r10
- addl2 r4,r11
- blss 6$
-7$:
-; movl r11,r1
+ cmpl r3,r4
+ blequ 42$
+ subl r4,r3
+ incl r2
+ brb 5$
42$:
- movl r10,r0
+; movl r3,r1
+ movl r2,r0
666$:
ret
\f
projects / openssl / commitdiff