ftu/blst/asm/ct_is_square_mod_384-x86_64.pl

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2022-09-09 06:47:49 +00:00
#!/usr/bin/env perl
#
# Copyright Supranational LLC
# Licensed under the Apache License, Version 2.0, see LICENSE for details.
# SPDX-License-Identifier: Apache-2.0
#
# Both constant-time and fast quadratic residue test as suggested in
# https://eprint.iacr.org/2020/972. Performance is >5x better than
# modulus-specific Legendre symbol addition chain...
#
# bool ct_is_square_mod_384(const vec384 inp, const vec384 mod);
#
$python_ref.=<<'___';
def ct_is_square_mod_384(inp, mod):
a = inp
b = mod
L = 0 # only least significant bit, adding 1 makes up for sign change
k = 30
w = 32
mask = (1 << w) - 1
for i in range(0, 768 // k - 1):
# __ab_approximation_30
n = max(a.bit_length(), b.bit_length())
if n < 64:
a_, b_ = a, b
else:
a_ = (a & mask) | ((a >> (n-w)) << w)
b_ = (b & mask) | ((b >> (n-w)) << w)
# __inner_loop_30
f0, g0, f1, g1 = 1, 0, 0, 1
for j in range(0, k):
if a_ & 1:
if a_ < b_:
a_, b_, f0, g0, f1, g1 = b_, a_, f1, g1, f0, g0
L += (a_ & b_) >> 1 # |a| and |b| are both odd, second bits
# tell the whole story
a_, f0, g0 = a_-b_, f0-f1, g0-g1
a_, f1, g1 = a_ >> 1, f1 << 1, g1 << 1
L += (b_ + 2) >> 2 # if |b|%8 is 3 or 5 [out of 1,3,5,7]
# __smulq_384_n_shift_by_30
a, b = (a*f0 + b*g0) >> k, (a*f1 + b*g1) >> k
if b < 0:
b = -b
if a < 0:
a = -a
L += (b % 4) >> 1 # |b| is always odd, the second bit
# tells the whole story
if True:
for j in range(0, 768 % k + k):
if a & 1:
if a < b:
a, b = b, a
L += (a & b) >> 1 # |a| and |b| are both odd, second bits
# tell the whole story
a = a-b
a = a >> 1
L += (b + 2) >> 2 # if |b|%8 is 3 or 5 [out of 1,3,5,7]
return (L & 1) ^ 1
___
$flavour = shift;
$output = shift;
if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
$win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
die "can't locate x86_64-xlate.pl";
open STDOUT,"| \"$^X\" \"$xlate\" $flavour \"$output\""
or die "can't call $xlate: $!";
my ($out_ptr, $in_ptr) = ("%rdi", "%rsi");
my ($f0, $g0, $f1, $g1) = ("%rax", "%rbx", "%rdx","%rcx");
my @acc=map("%r$_",(8..15));
my $L = "%rbp";
$frame = 8*3+2*256;
$code.=<<___;
.text
.globl ct_is_square_mod_384
.type ct_is_square_mod_384,\@function,2,"unwind"
.align 32
ct_is_square_mod_384:
.cfi_startproc
push %rbp
.cfi_push %rbp
push %rbx
.cfi_push %rbx
push %r12
.cfi_push %r12
push %r13
.cfi_push %r13
push %r14
.cfi_push %r14
push %r15
.cfi_push %r15
sub \$$frame, %rsp
.cfi_adjust_cfa_offset $frame
.cfi_end_prologue
lea 8*3+255(%rsp), %rax # find closest 256-byte-aligned spot
and \$-256, %rax # in the frame...
mov 8*0(%rdi), @acc[0] # load input
mov 8*1(%rdi), @acc[1]
mov 8*2(%rdi), @acc[2]
mov 8*3(%rdi), @acc[3]
mov 8*4(%rdi), @acc[4]
mov 8*5(%rdi), @acc[5]
mov 8*0(%rsi), @acc[6] # load modulus
mov 8*1(%rsi), @acc[7]
mov 8*2(%rsi), %rbx
mov 8*3(%rsi), %rcx
mov 8*4(%rsi), %rdx
mov 8*5(%rsi), %rdi
mov %rax, $in_ptr # pointer to source |a|b|
mov @acc[0], 8*0(%rax) # copy input to |a|
mov @acc[1], 8*1(%rax)
mov @acc[2], 8*2(%rax)
mov @acc[3], 8*3(%rax)
mov @acc[4], 8*4(%rax)
mov @acc[5], 8*5(%rax)
mov @acc[6], 8*6(%rax) # copy modulus to |b|
mov @acc[7], 8*7(%rax)
mov %rbx, 8*8(%rax)
mov %rcx, 8*9(%rax)
mov %rdx, 8*10(%rax)
mov %rdi, 8*11(%rax)
xor $L, $L # initialize the Legendre symbol
mov \$24, %ecx # 24 is 768/30-1
jmp .Loop_is_square
.align 32
.Loop_is_square:
mov %ecx, 8*2(%rsp) # offload loop counter
call __ab_approximation_30
mov $f0, 8*0(%rsp) # offload |f0| and |g0|
mov $g0, 8*1(%rsp)
mov \$128+8*6, $out_ptr
xor $in_ptr, $out_ptr # pointer to destination |b|
call __smulq_384_n_shift_by_30
mov 8*0(%rsp), $f1 # pop |f0| and |g0|
mov 8*1(%rsp), $g1
lea -8*6($out_ptr),$out_ptr # pointer to destination |a|
call __smulq_384_n_shift_by_30
mov 8*2(%rsp), %ecx # re-load loop counter
xor \$128, $in_ptr # flip-flop pointer to source |a|b|
and 8*6($out_ptr), @acc[6] # if |a| was negative, adjust |L|
shr \$1, @acc[6]
add @acc[6], $L
sub \$1, %ecx
jnz .Loop_is_square
################################# last iteration
#call __ab_approximation_30 # |a| and |b| are exact, just load
#mov 8*0($in_ptr), @acc[0] # |a_|
mov 8*6($in_ptr), @acc[1] # |b_|
call __inner_loop_48 # 48 is 768%30+30
mov \$1, %rax
and $L, %rax
xor \$1, %rax # return value
lea $frame(%rsp), %r8 # size optimization
mov 8*0(%r8),%r15
.cfi_restore %r15
mov 8*1(%r8),%r14
.cfi_restore %r14
mov 8*2(%r8),%r13
.cfi_restore %r13
mov 8*3(%r8),%r12
.cfi_restore %r12
mov 8*4(%r8),%rbx
.cfi_restore %rbx
mov 8*5(%r8),%rbp
.cfi_restore %rbp
lea 8*6(%r8),%rsp
.cfi_adjust_cfa_offset -$frame-8*6
.cfi_epilogue
ret
.cfi_endproc
.size ct_is_square_mod_384,.-ct_is_square_mod_384
.type __smulq_384_n_shift_by_30,\@abi-omnipotent
.align 32
__smulq_384_n_shift_by_30:
___
for($j=0; $j<2; $j++) {
$code.=<<___;
mov 8*0($in_ptr), @acc[0] # load |a| (or |b|)
mov 8*1($in_ptr), @acc[1]
mov 8*2($in_ptr), @acc[2]
mov 8*3($in_ptr), @acc[3]
mov 8*4($in_ptr), @acc[4]
mov 8*5($in_ptr), @acc[5]
mov %rdx, %rbx # |f1| (or |g1|)
sar \$63, %rdx # |f1|'s sign as mask (or |g1|'s)
xor %rax, %rax
sub %rdx, %rax # |f1|'s sign as bit (or |g1|'s)
xor %rdx, %rbx # conditionally negate |f1| (or |g1|)
add %rax, %rbx
xor %rdx, @acc[0] # conditionally negate |a| (or |b|)
xor %rdx, @acc[1]
xor %rdx, @acc[2]
xor %rdx, @acc[3]
xor %rdx, @acc[4]
xor %rdx, @acc[5]
add @acc[0], %rax
adc \$0, @acc[1]
adc \$0, @acc[2]
adc \$0, @acc[3]
adc \$0, @acc[4]
adc \$0, @acc[5]
mov %rdx, @acc[6+$j]
and %rbx, @acc[6+$j]
mulq %rbx # |a|*|f1| (or |b|*|g1|)
mov %rax, @acc[0]
mov @acc[1], %rax
mov %rdx, @acc[1]
___
for($i=1; $i<5; $i++) {
$code.=<<___;
mulq %rbx
add %rax, @acc[$i]
mov @acc[$i+1], %rax
adc \$0, %rdx
mov %rdx, @acc[$i+1]
___
}
$code.=<<___;
neg @acc[6+$j]
mulq %rbx
add %rax, @acc[5]
adc %rdx, @acc[6+$j]
___
$code.=<<___ if ($j==0);
lea 8*6($in_ptr), $in_ptr # pointer to |b|
mov $g1, %rdx
mov @acc[0], 8*0($out_ptr)
mov @acc[1], 8*1($out_ptr)
mov @acc[2], 8*2($out_ptr)
mov @acc[3], 8*3($out_ptr)
mov @acc[4], 8*4($out_ptr)
mov @acc[5], 8*5($out_ptr)
___
}
$code.=<<___;
lea -8*6($in_ptr), $in_ptr # restore original in_ptr
add 8*0($out_ptr), @acc[0]
adc 8*1($out_ptr), @acc[1]
adc 8*2($out_ptr), @acc[2]
adc 8*3($out_ptr), @acc[3]
adc 8*4($out_ptr), @acc[4]
adc 8*5($out_ptr), @acc[5]
adc @acc[7], @acc[6]
shrd \$30, @acc[1], @acc[0]
shrd \$30, @acc[2], @acc[1]
shrd \$30, @acc[3], @acc[2]
shrd \$30, @acc[4], @acc[3]
shrd \$30, @acc[5], @acc[4]
shrd \$30, @acc[6], @acc[5]
sar \$63, @acc[6] # sign as mask
xor %rbx, %rbx
sub @acc[6], %rbx # sign as bit
xor @acc[6], @acc[0] # conditionally negate the result
xor @acc[6], @acc[1]
xor @acc[6], @acc[2]
xor @acc[6], @acc[3]
xor @acc[6], @acc[4]
xor @acc[6], @acc[5]
add %rbx, @acc[0]
adc \$0, @acc[1]
adc \$0, @acc[2]
adc \$0, @acc[3]
adc \$0, @acc[4]
adc \$0, @acc[5]
mov @acc[0], 8*0($out_ptr)
mov @acc[1], 8*1($out_ptr)
mov @acc[2], 8*2($out_ptr)
mov @acc[3], 8*3($out_ptr)
mov @acc[4], 8*4($out_ptr)
mov @acc[5], 8*5($out_ptr)
ret
.size __smulq_384_n_shift_by_30,.-__smulq_384_n_shift_by_30
___
{
my ($a_, $b_) = @acc[0..1];
my ($t0, $t1, $t2, $t3, $t4, $t5) = map("%r$_",(10..15));
my ($fg0, $fg1, $bias) = ($g0, $g1, $t5);
my $cnt = "%edi";
{
my @a = @acc[0..5];
my @b = (@a[1..3], $t4, $t5, $g0);
$code.=<<___;
.type __ab_approximation_30,\@abi-omnipotent
.align 32
__ab_approximation_30:
mov 8*11($in_ptr), @b[5] # load |b| in reverse order
mov 8*10($in_ptr), @b[4]
mov 8*9($in_ptr), @b[3]
mov @a[5], %rax
or @b[5], %rax # check top-most limbs, ...
cmovz @a[4], @a[5]
cmovz @b[4], @b[5]
cmovz @a[3], @a[4]
mov 8*8($in_ptr), @b[2]
cmovz @b[3], @b[4]
mov @a[5], %rax
or @b[5], %rax # ... ones before top-most, ...
cmovz @a[4], @a[5]
cmovz @b[4], @b[5]
cmovz @a[2], @a[4]
mov 8*7($in_ptr), @b[1]
cmovz @b[2], @b[4]
mov @a[5], %rax
or @b[5], %rax # ... and ones before that ...
cmovz @a[4], @a[5]
cmovz @b[4], @b[5]
cmovz @a[1], @a[4]
mov 8*6($in_ptr), @b[0]
cmovz @b[1], @b[4]
mov @a[5], %rax
or @b[5], %rax # ... and ones before that ...
cmovz @a[4], @a[5]
cmovz @b[4], @b[5]
cmovz @a[0], @a[4]
cmovz @b[0], @b[4]
mov @a[5], %rax
or @b[5], %rax
bsr %rax, %rcx
lea 1(%rcx), %rcx
cmovz @a[0], @a[5]
cmovz @b[0], @b[5]
cmovz %rax, %rcx
neg %rcx
#and \$63, %rcx # debugging artefact
shldq %cl, @a[4], @a[5] # align second limb to the left
shldq %cl, @b[4], @b[5]
mov \$0xFFFFFFFF00000000, %rax
mov @a[0]d, ${a_}d
mov @b[0]d, ${b_}d
and %rax, @a[5]
and %rax, @b[5]
or @a[5], ${a_}
or @b[5], ${b_}
jmp __inner_loop_30
ret
.size __ab_approximation_30,.-__ab_approximation_30
___
}
$code.=<<___;
.type __inner_loop_30,\@abi-omnipotent
.align 32
__inner_loop_30: ################# by Thomas Pornin
mov \$0x7FFFFFFF80000000, $fg0 # |f0|=1, |g0|=0
mov \$0x800000007FFFFFFF, $fg1 # |f1|=0, |g1|=1
lea -1($fg0), $bias # 0x7FFFFFFF7FFFFFFF
mov \$30, $cnt
.Loop_30:
mov $a_, %rax
and $b_, %rax
shr \$1, %rax # (a_ & b_) >> 1
cmp $b_, $a_ # if |a_|<|b_|, swap the variables
mov $a_, $t0
mov $b_, $t1
lea (%rax,$L), %rax # pre-"negate" |L|
mov $fg0, $t2
mov $fg1, $t3
mov $L, $t4
cmovb $b_, $a_
cmovb $t0, $b_
cmovb $fg1, $fg0
cmovb $t2, $fg1
cmovb %rax, $L
sub $b_, $a_ # |a_|-|b_|
sub $fg1, $fg0 # |f0|-|f1|, |g0|-|g1|
add $bias, $fg0
test \$1, $t0 # if |a_| was even, roll back
cmovz $t0, $a_
cmovz $t1, $b_
cmovz $t2, $fg0
cmovz $t3, $fg1
cmovz $t4, $L
lea 2($b_), %rax
shr \$1, $a_ # |a_|>>=1
shr \$2, %rax
add $fg1, $fg1 # |f1|<<=1, |g1|<<=1
lea (%rax,$L), $L # "negate" |L| if |b|%8 is 3 or 5
sub $bias, $fg1
sub \$1, $cnt
jnz .Loop_30
shr \$32, $bias
mov %ebx, %eax # $fg0 -> $f0
shr \$32, $g0
mov %ecx, %edx # $fg1 -> $f1
shr \$32, $g1
sub $bias, $f0 # remove the bias
sub $bias, $g0
sub $bias, $f1
sub $bias, $g1
ret
.size __inner_loop_30,.-__inner_loop_30
.type __inner_loop_48,\@abi-omnipotent
.align 32
__inner_loop_48:
mov \$48, $cnt # 48 is 768%30+30
.Loop_48:
mov $a_, %rax
and $b_, %rax
shr \$1, %rax # (a_ & b_) >> 1
cmp $b_, $a_ # if |a_|<|b_|, swap the variables
mov $a_, $t0
mov $b_, $t1
lea (%rax,$L), %rax
mov $L, $t2
cmovb $b_, $a_
cmovb $t0, $b_
cmovb %rax, $L
sub $b_, $a_ # |a_|-|b_|
test \$1, $t0 # if |a_| was even, roll back
cmovz $t0, $a_
cmovz $t1, $b_
cmovz $t2, $L
lea 2($b_), %rax
shr \$1, $a_ # |a_|>>=1
shr \$2, %rax
add %rax, $L # "negate" |L| if |b|%8 is 3 or 5
sub \$1, $cnt
jnz .Loop_48
ret
.size __inner_loop_48,.-__inner_loop_48
___
}
print $code;
close STDOUT;