improve double and refactoring

[ashWhiteHat]

Abstract

Hi there.
I improve the double method with bit shift and commonalize the field operation.

What I did

• test add and double method
• replace double arithmetic with bit shift

I would appreciate it if you could confirm.
Thank you!

[therealyingtong]

LGTM! This reduces code duplication between the Fp and Fq implementations.

[str4d]

I want to take the first commit from this branch but not (yet) the second. I don't really want to maintain a second macro-based field implementation (the other being the proc-macro-based ff_derive). We should think about how we want to make the field impls more maintainable going forward, whether that be this declarative macro, ff_derive, something based on crypto-bigint, or another approach. But that should be separated from the doubling improvement.

[str4d]

I've opened #49 for discussing code de-duplication approaches. In the meantime, I will open another PR with the first commit from this branch, so we can get it reviewed.

[str4d]

Per #50 (comment), the manual bitshift-based doubling does not appear to be more efficient than the self.add(self) doubling.

[ashWhiteHat]

Hi @str4d
Thank you for the review.

I think we can speed up if we implement as following.
https://github.com/zero-network/zero/blob/master/primitive/crypto/src/arithmetic/limbs/bits_256/normal.rs#L29

fn dbc do 1 right shift, and return high and low.
It can optimize double and square as well.
https://github.com/zero-network/zero/blob/master/primitive/crypto/src/arithmetic/limbs/bits_256/normal.rs#L64

I am going to implement these if you think it's good idea.

[ashWhiteHat]

double Before

➜  pasta_curves git:(main) rustc +stable --version                                                      
rustc 1.66.1 (90743e729 2023-01-10)
➜  pasta_curves git:(main) cargo +stable asm --lib "<pasta_curves::fields::fp::Fp as ff::Field>::double"
<pasta_curves::fields::fp::Fp as ff::Field>::double:
 push    rbp
 mov     rbp, rsp
 push    rbx
 mov     rax, qword, ptr, [rsi]
 mov     r11, qword, ptr, [rsi, +, 8]
 lea     r10, [rax, +, rax]
 mov     r9, qword, ptr, [rsi, +, 16]
 mov     rsi, qword, ptr, [rsi, +, 24]
 xor     edx, edx
 movabs  r8, 7409212017489215487
 add     r8, r10
 adc     rdx, -1
 shrd    rax, r11, 63
 sar     rdx, 63
 add     rax, rdx
 adc     rdx, 0
 movabs  r10, -2469829653914515739
 add     r10, rax
 adc     rdx, -1
 shrd    r11, r9, 63
 sar     rdx, 63
 add     r11, rdx
 adc     rdx, 0
 shld    rsi, r9, 1
 sar     rdx, 63
 add     rsi, rdx
 adc     rdx, 0
 movabs  r9, -4611686018427387904
 add     r9, rsi
 adc     rdx, -1
 movabs  rsi, -7409212017489215487
 and     rsi, rdx
 movabs  rcx, 2469829653914515739
 and     rcx, rdx
 movabs  rbx, 4611686018427387904
 and     rbx, rdx
 add     rsi, r8
 adc     rcx, r10
 adc     r11, 0
 mov     rax, rdi
 adc     rbx, r9
 mov     qword, ptr, [rdi], rsi
 mov     qword, ptr, [rdi, +, 8], rcx
 mov     qword, ptr, [rdi, +, 16], r11
 mov     qword, ptr, [rdi, +, 24], rbx
 pop     rbx
 pop     rbp
 ret

double After

➜  pasta_curves git:(feat/improve-double-and-refactoring) rustc +stable --version
rustc 1.66.1 (90743e729 2023-01-10)
➜  pasta_curves git:(feat/improve-double-and-refactoring) cargo +stable asm --lib "<pasta_curves::fields::fp::Fp as ff::Field>::double"
<pasta_curves::fields::fp::Fp as ff::Field>::double:
 push    rbp
 mov     rbp, rsp
 mov     rax, qword, ptr, [rsi]
 mov     r9, qword, ptr, [rsi, +, 8]
 mov     rcx, r9
 shld    rcx, rax, 1
 add     rax, rax
 mov     rdx, qword, ptr, [rsi, +, 16]
 shrd    r9, rdx, 63
 mov     rsi, qword, ptr, [rsi, +, 24]
 shld    rsi, rdx, 1
 xor     edx, edx
 movabs  r8, 7409212017489215487
 add     r8, rax
 adc     rdx, -1
 sar     rdx, 63
 add     rcx, rdx
 adc     rdx, 0
 movabs  rax, -2469829653914515739
 add     rax, rcx
 adc     rdx, -1
 sar     rdx, 63
 add     r9, rdx
 adc     rdx, 0
 sar     rdx, 63
 add     rsi, rdx
 adc     rdx, 0
 movabs  r10, -4611686018427387904
 add     r10, rsi
 adc     rdx, -1
 movabs  r11, -7409212017489215487
 and     r11, rdx
 movabs  rcx, 2469829653914515739
 and     rcx, rdx
 movabs  rsi, 4611686018427387904
 and     rsi, rdx
 add     r11, r8
 adc     rcx, rax
 adc     r9, 0
 mov     rax, rdi
 adc     rsi, r10
 mov     qword, ptr, [rdi], r11
 mov     qword, ptr, [rdi, +, 8], rcx
 mov     qword, ptr, [rdi, +, 16], r9
 mov     qword, ptr, [rdi, +, 24], rsi
 pop     rbp
 ret

_	Before	After
push	2	1
mov	10	11
add	7	8
adc	9	9
xor	1	1
movabs	6	6
shrd	2	1
shld	1	2
lea	1	0
sar	3	3
and	3	3
pop	2	1
ret	1	1
SUM	48	47

soooo slightly improved 😅
It seems near to refactoring.