siiky
2023/04/08
2023/04/08
en
I was working yesterday on sbn and accidentally fixed digit subtraction (and consequently sbn subtraction).
Definitions needed to understand these excerpts: `sbn_digit` is `uint32_t`; `sbn_double_digit` is `uint64_t`; `sbn_double_digit_lower_half` is a macro that takes the 32 least-significant bits of a `sbn_double_digit`.
Here's the old (wrong) version:
static sbn_digit _sbn_sub_digits (sbn_digit _a, sbn_digit _b, sbn_digit * _carry)
{
sbn_double_digit carry = *_carry;
sbn_double_digit a = _a;
sbn_double_digit b = _b; b += carry;
return (a >= b) ?
(*_carry = 0), sbn_double_digit_lower_half(a - b):
(*_carry = 1), sbn_double_digit_lower_half(b - a);
}
Here's the new (fixed) version:
static sbn_digit _sbn_sub_digits (sbn_digit _a, sbn_digit _b, sbn_digit * _carry)
{
sbn_double_digit carry = *_carry;
sbn_double_digit a = _a;
sbn_double_digit b = _b; b += carry;
sbn_double_digit r = (a >= b) ?
((*_carry = 0), (a - b)):
((*_carry = 1), (b - a));
return sbn_double_digit_lower_half(r);
}
What's the difference? Why does one work correctly but the other doesn't? I have no clue... Obviously I expected both to be the same.
It didn't occur to me but a friend suggested taking a look at the assembly -- good idea! For some reason `gcc -S` generated a huge file like this:
// ... .LASF151: .string "_sbn_sub_digits" // ... .long .LASF151 .byte 0x5 .value 0x186 .byte 0x12 .long 0x9e .long 0x1216 .uleb128 0x1 .string "_a" .byte 0x5 .value 0x186 .byte 0x2d .long 0x9e .uleb128 0x1 .string "_b" .byte 0x5 .value 0x186 .byte 0x3b .long 0x9e .uleb128 0x2 // ...
No clue what this is either... So I turned to `objdump`, which was more helpful.
Here's the old (wrong) version:
0000000000401834 <_sbn_sub_digits>: 401834: 8b 02 mov (%rdx),%eax 401836: 89 ff mov %edi,%edi 401838: 89 f6 mov %esi,%esi 40183a: 48 01 f0 add %rsi,%rax 40183d: 48 39 c7 cmp %rax,%rdi 401840: 72 09 jb 40184b <_sbn_sub_digits+0x17> 401842: c7 02 00 00 00 00 movl $0x0,(%rdx) 401848: 29 f8 sub %edi,%eax 40184a: c3 ret 40184b: c7 02 01 00 00 00 movl $0x1,(%rdx) 401851: eb f5 jmp 401848 <_sbn_sub_digits+0x14>
Here's the new (fixed) version:
0000000000401834 <_sbn_sub_digits>: 401834: 8b 0a mov (%rdx),%ecx 401836: 89 ff mov %edi,%edi 401838: 89 f6 mov %esi,%esi 40183a: 48 01 f1 add %rsi,%rcx 40183d: 48 39 cf cmp %rcx,%rdi 401840: 72 0d jb 40184f <_sbn_sub_digits+0x1b> 401842: c7 02 00 00 00 00 movl $0x0,(%rdx) 401848: 48 89 f8 mov %rdi,%rax 40184b: 48 29 c8 sub %rcx,%rax 40184e: c3 ret 40184f: c7 02 01 00 00 00 movl $0x1,(%rdx) 401855: 48 89 c8 mov %rcx,%rax 401858: 48 29 f8 sub %rdi,%rax 40185b: c3 ret
My ASM-fu was never very good but by now it's non-existent. One thing I noticed though is that on the wrong version it's using edi/eax (the 32bit registers right?), while the fixed version is using the rdi/rcx/rax (the 64bit registers right?). Is that it? But why? I can't even remember what's the arguments order: `sub X,Y` is `X-Y` or `Y-X`? `mov X,Y` is `X<-Y` or `X->Y`?