; }
;
; Using EDIV would be very easy, if it didn't do signed calculations.
-; 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.
+; Any time, any of the input numbers are signed, there are problems,
+; usually with integer overflow, at which point it returns useless
+; data (the quotient gets the value of l, and the remainder becomes 0).
;
-; We end up doing something like this:
+; If it was just for the dividend, it would be very easy, just divide
+; it by 2 (unsigned), do the division, multiply the resulting quotient
+; and remainder by 2, add the bit that was dropped when dividing by 2
+; to the remainder, and do some adjustment so the remainder doesn't
+; end up larger than the divisor. This method works as long as the
+; divisor is positive, so we'll keep that (with a small adjustment)
+; as the main method.
+; For some cases when the divisor is negative (from EDIV's point of
+; view, i.e. when the highest bit is set), dividing the dividend by
+; 2 isn't enough, it needs to be divided by 4. Furthermore, the
+; divisor needs to be divided by 2 (unsigned) as well, to avoid more
+; problems with the sign. In this case, the divisor is so large,
+; from an unsigned point of view, that the dropped lowest bit is
+; insignificant for the operation, and therefore doesn't need
+; bothering with. The remainder might end up incorrect, bit that's
+; adjusted at the end of the routine anyway.
;
-; 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
+; So, the simplest way to handle this is always to divide the dividend
+; by 4, and to divide the divisor by 2 if it's highest bit is set.
+; After EDIV has been used, the quotient gets multiplied by 4 if the
+; original divisor was positive, otherwise 2. The remainder, oddly
+; enough, is *always* multiplied by 4.
;
-; Now, we need to adjust back by multiplying quotient and remainder with 2,
-; and add the bit that dropped out when dividing by 2:
+; The routine ends with comparing the resulting remainder with the
+; original divisor and if the remainder is larger, subtract the
+; original divisor from it, and increase the quotient by 1. This is
+; done until the remainder is smaller than the divisor.
;
-; r' = r & 0x80000000
-; q = q << 1
-; r = (r << 1) + a'
+; The complete algorithm looks like this:
;
-; And now, the final adjustment if the remainder happens to get larger than
-; the divisor:
+; d' = d
+; l' = l & 3
+; [h,l] = [h,l] >> 2
+; [q,r] = floor([h,l] / d) # This is the EDIV operation
+; if (q < 0) q = -q # I doubt this is necessary any more
;
-; if (r')
-; {
-; r = r - d
-; q = q + 1
-; }
-; while (r >= d)
+; r' = r >> 30
+; if (d' > 0) q = q << 1
+; q = q << 1
+; r = (r << 2) + l'
+;
+; while ([r',r] >= d)
; {
-; r = r - d
+; [r',r] = [r',r] - d
; q = q + 1
; }
;
;lprim=r5
;rprim=r6
+;dprim=r7
.psect code,nowrt
-.entry bn_div_words,^m<r2,r3,r4,r5,r6>
+.entry bn_div_words,^m<r2,r3,r4,r5,r6,r7>
movl l(ap),r2
movl h(ap),r3
movl d(ap),r4
- movl #0,r5
- movl #0,r6
+ bicl3 #^XFFFFFFFC,r2,r5 ; l' = l & 3
+ bicl3 #^X00000003,r2,r2
- rotl #-1,r2,r2 ; l = l >> 1 (almost)
- rotl #-1,r3,r3 ; h = h >> 1 (almost)
+ bicl3 #^XFFFFFFFC,r3,r6
+ bicl3 #^X00000003,r3,r3
+
+ addl r6,r2
+ rotl #-2,r2,r2 ; l = l >> 2
+ rotl #-2,r3,r3 ; h = h >> 2
+
+ movl #0,r6
+ movl r4,r7 ; d' = d
- tstl r2
- bgeq 1$
- xorl2 #^X80000000,r2 ; fixup l so highest bit is 0
- incl r5 ; l' = 1
-1$:
- tstl r3
- bgeq 2$
- 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$:
tstl r4
beql 666$ ; Uh-oh, the divisor is 0...
-
+ bgtr 1$
+ rotl #-1,r4,r4 ; If d is negative, shift it right.
+ bicl2 #^X80000000,r4 ; Since d is then a large number, the
+ ; lowest bit is insignificant
+ ; (contradict that, and I'll fix the problem!)
+1$:
ediv r4,r2,r2,r3 ; Do the actual division
tstl r2
bgeq 3$
mnegl r2,r2 ; if q < 0, negate it
-3$:
- tstl r3
- bgeq 4$
- incl r6 ; since the high bit in r is set, set r'
-4$:
+3$:
+ tstl r7
+ blss 4$
ashl #1,r2,r2 ; q = q << 1
- ashl #1,r3,r3 ; r = r << 1
- addl r5,r3 ; r = r + a'
+4$:
+ ashl #1,r2,r2 ; q = q << 1
+ rotl #2,r3,r3 ; r = r << 2
+ bicl3 #^XFFFFFFFC,r3,r6 ; r' gets the high bits from r
+ bicl3 #^X00000003,r3,r3
+ addl r5,r3 ; r = r + l'
- tstl r6
- beql 5$ ; if r'
- subl r4,r3 ; r = r - d
- incl r2 ; q = q + 1
5$:
- cmpl r3,r4
- blssu 42$ ; while r >= d
- subl r4,r3 ; r = r - d
+ tstl r6
+ bneq 6$
+ cmpl r3,r7
+ blssu 42$ ; while [r',r] >= d'
+6$:
+ subl r7,r3 ; r = r - d
+ sbwc #0,r6
incl r2 ; q = q + 1
brb 5$
42$:
; movl r3,r1
movl r2,r0
+ ret
666$:
+ movl #^XFFFFFFFF,r0
ret
\f
.title vax_bn_add_words unsigned add of two arrays
projects / openssl / commitdiff