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ftu/blst/asm/ctx_inverse_mod_384-x86_64.pl
John Doe 943c07066e initial stuff
2022-09-09 02:47:49 -04:00

996 lines
24 KiB
Raku
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#!/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 Euclidean inversion as suggested in
# https://eprint.iacr.org/2020/972. Performance is >4x better than
# modulus-specific FLT addition chain...
#
# void ct_inverse_mod_383(vec768 ret, const vec384 inp, const vec384 mod);
#
$python_ref.=<<'___';
def ct_inverse_mod_383(inp, mod):
a, u = inp, 1
b, v = mod, 0
k = 31
mask = (1 << k) - 1
for i in range(0, 766 // k):
# __ab_approximation_31
n = max(a.bit_length(), b.bit_length())
if n < 64:
a_, b_ = a, b
else:
a_ = (a & mask) | ((a >> (n-k-2)) << k)
b_ = (b & mask) | ((b >> (n-k-2)) << k)
# __inner_loop_31
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
a_, f0, g0 = a_-b_, f0-f1, g0-g1
a_, f1, g1 = a_ >> 1, f1 << 1, g1 << 1
# __smulx_383_n_shift_by_31
a, b = (a*f0 + b*g0) >> k, (a*f1 + b*g1) >> k
if a < 0:
a, f0, g0 = -a, -f0, -g0
if b < 0:
b, f1, g1 = -b, -f1, -g1
# __smulx_767x63
u, v = u*f0 + v*g0, u*f1 + v*g1
if 766 % k:
f0, g0, f1, g1 = 1, 0, 0, 1
for j in range(0, 766 % k):
if a & 1:
if a < b:
a, b, f0, g0, f1, g1 = b, a, f1, g1, f0, g0
a, f0, g0 = a-b, f0-f1, g0-g1
a, f1, g1 = a >> 1, f1 << 1, g1 << 1
v = u*f1 + v*g1
if v < 0:
v += mod << (768 - mod.bit_length()) # left aligned
return v & (2**768 - 1) # to be reduced % mod
___
$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, $n_ptr, $nx_ptr) = ("%rdi", "%rsi", "%rdx", "%rcx");
my @acc=(map("%r$_",(8..15)), "%rbx", "%rbp", $in_ptr, $out_ptr);
my ($f0, $g0, $f1, $g1) = ("%rdx","%rcx","%r12","%r13");
my $cnt = "%edi";
$frame = 8*11+2*512;
$code.=<<___;
.text
.globl ctx_inverse_mod_383
.type ctx_inverse_mod_383,\@function,4,"unwind"
.align 32
ctx_inverse_mod_383:
.cfi_startproc
push %rbp
.cfi_push %rbp
push %rbx
.cfi_push %rbx
push %r12
.cfi_push %r12
push %r13
.cfi_push %r13
push %r14
.cfi_push %r14
push %r15
.cfi_push %r15
sub \$$frame, %rsp
.cfi_adjust_cfa_offset $frame
.cfi_end_prologue
lea 8*11+511(%rsp), %rax # find closest 512-byte-aligned spot
and \$-512, %rax # in the frame...
mov $out_ptr, 8*4(%rsp)
mov $nx_ptr, 8*5(%rsp)
mov 8*0($in_ptr), @acc[0] # load input
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($in_ptr), @acc[5]
mov 8*0($n_ptr), @acc[6] # load modulus
mov 8*1($n_ptr), @acc[7]
mov 8*2($n_ptr), @acc[8]
mov 8*3($n_ptr), @acc[9]
mov 8*4($n_ptr), @acc[10]
mov 8*5($n_ptr), @acc[11]
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 @acc[8], 8*8(%rax)
mov @acc[9], 8*9(%rax)
mov @acc[10], 8*10(%rax)
mov %rax, $in_ptr
mov @acc[11], 8*11(%rax)
################################# first iteration
mov \$31, $cnt
call __ab_approximation_31
#mov $f0, 8*7(%rsp)
#mov $g0, 8*8(%rsp)
mov $f1, 8*9(%rsp)
mov $g1, 8*10(%rsp)
mov \$256, $out_ptr
xor $in_ptr, $out_ptr # pointer to destination |a|b|u|v|
call __smulx_383_n_shift_by_31
#mov $f0, 8*7(%rsp) # corrected |f0|
#mov $g0, 8*8(%rsp) # corrected |g0|
mov $f0, 8*12($out_ptr) # initialize |u| with |f0|
mov 8*9(%rsp), $f0 # |f1|
mov 8*10(%rsp), $g0 # |g1|
lea 8*6($out_ptr), $out_ptr # pointer to destination |b|
call __smulx_383_n_shift_by_31
#mov $f0, 8*9(%rsp) # corrected |f1|
#mov $g0, 8*10(%rsp) # corrected |g1|
mov $f0, 8*12($out_ptr) # initialize |v| with |f1|
################################# second iteration
xor \$256, $in_ptr # flip-flop pointer to source |a|b|u|v|
mov \$31, $cnt
call __ab_approximation_31
#mov $f0, 8*7(%rsp)
#mov $g0, 8*8(%rsp)
mov $f1, 8*9(%rsp)
mov $g1, 8*10(%rsp)
mov \$256, $out_ptr
xor $in_ptr, $out_ptr # pointer to destination |a|b|u|v|
call __smulx_383_n_shift_by_31
mov $f0, 8*7(%rsp) # corrected |f0|
mov $g0, 8*8(%rsp) # corrected |g0|
mov 8*9(%rsp), $f0 # |f1|
mov 8*10(%rsp), $g0 # |g1|
lea 8*6($out_ptr), $out_ptr # pointer to destination |b|
call __smulx_383_n_shift_by_31
#mov $f0, 8*9(%rsp) # corrected |f1|
#mov $g0, 8*10(%rsp) # corrected |g1|
mov 8*12($in_ptr), %rax # |u|
mov 8*18($in_ptr), @acc[3] # |v|
mov $f0, %rbx
mov %rax, @acc[2]
imulq 8*7(%rsp) # |u|*|f0|
mov %rax, @acc[0]
mov @acc[3], %rax
mov %rdx, @acc[1]
imulq 8*8(%rsp) # |v|*|g0|
add %rax, @acc[0]
adc %rdx, @acc[1]
mov @acc[0], 8*6($out_ptr) # destination |u|
mov @acc[1], 8*7($out_ptr)
sar \$63, @acc[1] # sign extension
mov @acc[1], 8*8($out_ptr)
mov @acc[1], 8*9($out_ptr)
mov @acc[1], 8*10($out_ptr)
mov @acc[1], 8*11($out_ptr)
lea 8*12($in_ptr), $in_ptr # make in_ptr "rewindable" with xor
mov @acc[2], %rax
imulq %rbx # |u|*|f1|
mov %rax, @acc[0]
mov @acc[3], %rax
mov %rdx, @acc[1]
imulq %rcx # |v|*|g1|
add %rax, @acc[0]
adc %rdx, @acc[1]
mov @acc[0], 8*12($out_ptr) # destination |v|
mov @acc[1], 8*13($out_ptr)
sar \$63, @acc[1] # sign extension
mov @acc[1], 8*14($out_ptr)
mov @acc[1], 8*15($out_ptr)
mov @acc[1], 8*16($out_ptr)
mov @acc[1], 8*17($out_ptr)
___
for($i=2; $i<23; $i++) {
my $smul_n_shift = $i<19 ? "__smulx_383_n_shift_by_31"
: "__smulx_191_n_shift_by_31";
my $smul_767x63 = $i>11 ? "__smulx_767x63"
: "__smulx_383x63";
$code.=<<___;
xor \$256+8*12, $in_ptr # flip-flop pointer to source |a|b|u|v|
mov \$31, $cnt
call __ab_approximation_31
#mov $f0, 8*7(%rsp)
#mov $g0, 8*8(%rsp)
mov $f1, 8*9(%rsp)
mov $g1, 8*10(%rsp)
mov \$256, $out_ptr
xor $in_ptr, $out_ptr # pointer to destination |a|b|u|v|
call $smul_n_shift
mov $f0, 8*7(%rsp) # corrected |f0|
mov $g0, 8*8(%rsp) # corrected |g0|
mov 8*9(%rsp), $f0 # |f1|
mov 8*10(%rsp), $g0 # |g1|
lea 8*6($out_ptr), $out_ptr # pointer to destination |b|
call $smul_n_shift
mov $f0, 8*9(%rsp) # corrected |f1|
mov $g0, 8*10(%rsp) # corrected |g1|
mov 8*7(%rsp), $f0 # |f0|
mov 8*8(%rsp), $g0 # |g0|
lea 8*12($in_ptr), $in_ptr # pointer to source |u|v|
lea 8*6($out_ptr), $out_ptr # pointer to destination |u|
call __smulx_383x63
mov 8*9(%rsp), $f0 # |f1|
mov 8*10(%rsp), $g0 # |g1|
lea 8*6($out_ptr),$out_ptr # pointer to destination |v|
call $smul_767x63
___
$code.=<<___ if ($i==11);
sar \$63, @acc[5] # sign extension
mov @acc[5], 8*6($out_ptr)
mov @acc[5], 8*7($out_ptr)
mov @acc[5], 8*8($out_ptr)
mov @acc[5], 8*9($out_ptr)
mov @acc[5], 8*10($out_ptr)
mov @acc[5], 8*11($out_ptr)
___
}
$code.=<<___;
################################# two[!] last iterations in one go
xor \$256+8*12, $in_ptr # flip-flop pointer to source |a|b|u|v|
mov \$53, $cnt # 31 + 766 % 31
#call __ab_approximation_31 # |a| and |b| are exact, just load
mov 8*0($in_ptr), @acc[0] # |a_lo|
#xor @acc[1], @acc[1] # |a_hi|
mov 8*6($in_ptr), @acc[2] # |b_lo|
#xor @acc[3], @acc[3] # |b_hi|
call __inner_loop_62
#mov $f0, 8*7(%rsp)
#mov $g0, 8*8(%rsp)
#mov $f1, 8*9(%rsp)
#mov $g1, 8*10(%rsp)
#mov 8*7(%rsp), $f0 # |f0|
#mov 8*8(%rsp), $g0 # |g0|
lea 8*12($in_ptr), $in_ptr # pointer to source |u|v|
#lea 8*6($out_ptr), $out_ptr # pointer to destination |u|
#call __smulx_383x63
#mov 8*9(%rsp), $f0 # |f1|
#mov 8*10(%rsp), $g0 # |g1|
mov $f1, $f0
mov $g1, $g0
mov 8*4(%rsp), $out_ptr # original out_ptr
call __smulx_767x63
mov 8*5(%rsp), $in_ptr # original n_ptr
mov %rax, %rdx # top limb of the result
sar \$63, %rax # result's sign as mask
mov %rax, @acc[0] # mask |modulus|
mov %rax, @acc[1]
mov %rax, @acc[2]
and 8*0($in_ptr), @acc[0]
and 8*1($in_ptr), @acc[1]
mov %rax, @acc[3]
and 8*2($in_ptr), @acc[2]
and 8*3($in_ptr), @acc[3]
mov %rax, @acc[4]
and 8*4($in_ptr), @acc[4]
and 8*5($in_ptr), %rax
add @acc[0], @acc[6] # conditionally add |modulus|<<384
adc @acc[1], @acc[7]
adc @acc[2], @acc[8]
adc @acc[3], @acc[9]
adc @acc[4], %rcx
adc %rax, %rdx
mov @acc[6], 8*6($out_ptr) # store absolute value
mov @acc[7], 8*7($out_ptr)
mov @acc[8], 8*8($out_ptr)
mov @acc[9], 8*9($out_ptr)
mov %rcx, 8*10($out_ptr)
mov %rdx, 8*11($out_ptr)
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 ctx_inverse_mod_383,.-ctx_inverse_mod_383
___
########################################################################
# Signed |u|*|f?|+|v|*|g?| subroutines. "NNN" in "NNNx63" suffix refers
# to the maximum bit-length of the *result*, and "63" - to the maximum
# bit-length of the |f?| and |g?| single-limb multiplicands. However!
# The latter should not be taken literally, as they are always chosen so
# that "bad things" don't happen. For example, there comes a point when
# |v| grows beyond 383 bits, while |u| remains 383 bits wide. Yet, we
# always call __smul_383x63 to perform |u|*|f0|+|v|*|g0| step. This is
# because past that point |f0| is always 1 and |g0| is always 0. And,
# since |u| never grows beyond 383 bits, __smul_767x63 doesn't have to
# perform full-width |u|*|f1| multiplication, half-width one with sign
# extension is sufficient...
{
my ($out_ptr, $in_ptr, $f0, $g0) = ("%rdi", "%rsi", "%rdx", "%rcx");
my @acc = map("%r$_",(8..15),"bx","bp","cx","di");
my $fx = @acc[9];
$code.=<<___;
.type __smulx_767x63,\@abi-omnipotent
.align 32
__smulx_767x63:
mov 8*0($in_ptr), @acc[0] # load |u|
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 $f0, %rax
sar \$63, %rax # |f0|'s sign as mask
xor $fx, $fx # overrides in_ptr
sub %rax, $fx # |f0|'s sign as bit
mov $out_ptr, 8*1(%rsp)
mov $in_ptr, 8*2(%rsp)
lea 8*6($in_ptr), $in_ptr # pointer to |v|
xor %rax, $f0 # conditionally negate |f0|
add $fx, $f0
xor %rax, @acc[0] # conditionally negate |u|
xor %rax, @acc[1]
xor %rax, @acc[2]
xor %rax, @acc[3]
xor %rax, @acc[4]
xor @acc[5], %rax
add $fx, @acc[0]
adc \$0, @acc[1]
adc \$0, @acc[2]
adc \$0, @acc[3]
adc \$0, @acc[4]
adc \$0, %rax
mulx @acc[0], @acc[0], $fx # |u|*|f0|
mulx @acc[1], @acc[1], @acc[5]
add $fx, @acc[1]
___
for(my ($a,$b) = ($fx, @acc[5]), $i=2; $i<5; $i++) {
$code.=<<___;
mulx @acc[$i], @acc[$i], $a
adc $b, @acc[$i]
___
($a, $b) = ($b, $a);
}
$code.=<<___;
adc \$0, $fx
imulq %rdx
add $fx, %rax
adc \$0, %rdx
mov @acc[0], 8*0($out_ptr) # offload |u|*|f0|
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 %rax, 8*5($out_ptr)
mov %rdx, 8*6($out_ptr)
sar \$63, %rdx # sign extension
mov %rdx, 8*7($out_ptr)
___
{
my $fx=$in_ptr;
$code.=<<___;
mov $g0, $f0 # load |g0|
mov $g0, %rax
mov 8*0($in_ptr), @acc[0] # load |v|
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($in_ptr), @acc[5]
mov 8*6($in_ptr), @acc[6]
mov 8*7($in_ptr), @acc[7]
mov 8*8($in_ptr), @acc[8]
mov 8*9($in_ptr), @acc[9]
mov 8*10($in_ptr), @acc[10]
mov 8*11($in_ptr), @acc[11]
sar \$63, %rax # |g0|'s sign as mask
xor $fx, $fx # overrides in_ptr
sub %rax, $fx # |g0|'s sign as bit
xor %rax, $f0 # conditionally negate |g0|
add $fx, $f0
xor %rax, @acc[0] # conditionally negate |v|
xor %rax, @acc[1]
xor %rax, @acc[2]
xor %rax, @acc[3]
xor %rax, @acc[4]
xor %rax, @acc[5]
xor %rax, @acc[6]
xor %rax, @acc[7]
xor %rax, @acc[8]
xor %rax, @acc[9]
xor %rax, @acc[10]
xor %rax, @acc[11]
add $fx, @acc[0]
adc \$0, @acc[1]
adc \$0, @acc[2]
adc \$0, @acc[3]
adc \$0, @acc[4]
adc \$0, @acc[5]
adc \$0, @acc[6]
adc \$0, @acc[7]
adc \$0, @acc[8]
adc \$0, @acc[9]
adc \$0, @acc[10]
adc \$0, @acc[11]
mulx @acc[0], @acc[0], %rax # |v|*|g0|
mulx @acc[1], @acc[1], $fx
add %rax, @acc[1]
___
for(my ($a,$b) = ("%rax", $fx), $i=2; $i<11; $i++) {
$code.=<<___;
mulx @acc[$i], @acc[$i], $a
adc $b, @acc[$i]
___
($a, $b) = ($b, $a);
}
$code.=<<___;
mulx @acc[11], @acc[11], $fx
mov 8*1(%rsp), %rdx # out_ptr
mov 8*2(%rsp), $in_ptr # restore original in_ptr
adc @acc[11], %rax
add 8*0(%rdx), @acc[0] # accumulate |u|*|f0|
adc 8*1(%rdx), @acc[1]
adc 8*2(%rdx), @acc[2]
adc 8*3(%rdx), @acc[3]
adc 8*4(%rdx), @acc[4]
adc 8*5(%rdx), @acc[5]
adc 8*6(%rdx), @acc[6]
mov 8*7(%rdx), @acc[11] # sign extension
adc @acc[11], @acc[7]
adc @acc[11], @acc[8]
adc @acc[11], @acc[9]
adc @acc[11], @acc[10]
adc @acc[11], %rax
mov %rdx, $out_ptr # restore original out_ptr
mov @acc[0], 8*0(%rdx)
mov @acc[1], 8*1(%rdx)
mov @acc[2], 8*2(%rdx)
mov @acc[3], 8*3(%rdx)
mov @acc[4], 8*4(%rdx)
mov @acc[5], 8*5(%rdx)
mov @acc[6], 8*6(%rdx)
mov @acc[7], 8*7(%rdx)
mov @acc[8], 8*8(%rdx)
mov @acc[9], 8*9(%rdx)
mov @acc[10], 8*10(%rdx)
mov %rax, 8*11(%rdx)
ret
.size __smulx_767x63,.-__smulx_767x63
___
}
$code.=<<___;
.type __smulx_383x63,\@abi-omnipotent
.align 32
__smulx_383x63:
___
for($j=0; $j<2; $j++) {
my $k = 8*6*$j;
$code.=<<___;
mov $k+8*0($in_ptr), @acc[0] # load |u| (or |v|)
mov $k+8*1($in_ptr), @acc[1]
mov $k+8*2($in_ptr), @acc[2]
mov $k+8*3($in_ptr), @acc[3]
mov $k+8*4($in_ptr), @acc[4]
mov $k+8*5($in_ptr), @acc[5]
mov $f0, $fx
sar \$63, $fx # |f0|'s sign as mask (or |g0|'s)
xor %rax, %rax
sub $fx, %rax # |f0|'s sign as bit (or |g0|'s)
xor $fx, $f0 # conditionally negate |f0|
add %rax, $f0
xor $fx, @acc[0] # conditionally negate |u| (or |v|)
xor $fx, @acc[1]
xor $fx, @acc[2]
xor $fx, @acc[3]
xor $fx, @acc[4]
xor $fx, @acc[5]
add %rax, @acc[0]
adc \$0, @acc[1]
adc \$0, @acc[2]
adc \$0, @acc[3]
adc \$0, @acc[4]
adc \$0, @acc[5]
mulx @acc[0], @acc[0], $fx # |u|*|f0| (or |v|*|g0|)
mulx @acc[1], @acc[1], %rax
add $fx, @acc[1]
___
for(my ($a,$b) = ($fx, "%rax"), $i=2; $i<5; $i++) {
$code.=<<___;
mulx @acc[$i], @acc[$i], $a
adc $b, @acc[$i]
___
($a, $b) = ($b, $a);
}
$code.=<<___ if ($j==0);
mulx @acc[$i], @acc[$i], %rax
mov $g0, $f0
adc $fx, @acc[$i]
mov @acc[0], 8*0($out_ptr) # offload |u|*|f0|
mov @acc[1], 8*1($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)
___
}
$code.=<<___;
mulx @acc[$i], @acc[$i], %rax
adc $fx, @acc[$i]
add 8*0($out_ptr), @acc[0] # accumulate |u|*|f0|
adc 8*1($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]
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 __smulx_383x63,.-__smulx_383x63
___
########################################################################
# Signed abs(|a|*|f?|+|b|*|g?|)>>k subroutines. "NNN" in the middle of
# the names refers to maximum bit-lengths of |a| and |b|. As already
# mentioned, |f?| and |g?| can be viewed as 63 bits wide, but are always
# chosen so that "bad things" don't happen. For example, so that the
# sum of the products doesn't overflow, and that the final result is
# never wider than inputs...
{
$code.=<<___;
.type __smulx_383_n_shift_by_31,\@abi-omnipotent
.align 32
__smulx_383_n_shift_by_31:
mov $f0, @acc[8]
xor @acc[6], @acc[6]
___
my $f0 = @acc[8];
for($j=0; $j<2; $j++) {
my $k = 8*6*$j;
$code.=<<___;
mov $k+8*0($in_ptr), @acc[0] # load |a| (or |b|)
mov $k+8*1($in_ptr), @acc[1]
mov $k+8*2($in_ptr), @acc[2]
mov $k+8*3($in_ptr), @acc[3]
mov $k+8*4($in_ptr), @acc[4]
mov $k+8*5($in_ptr), @acc[5]
mov %rdx, %rax
sar \$63, %rax # |f0|'s sign as mask (or |g0|'s)
xor $fx, $fx
sub %rax, $fx # |f0|'s sign as bit (or |g0|'s)
xor %rax, %rdx # conditionally negate |f0| (or |g0|)
add $fx, %rdx
xor %rax, @acc[0] # conditionally negate |a| (or |b|)
xor %rax, @acc[1]
xor %rax, @acc[2]
xor %rax, @acc[3]
xor %rax, @acc[4]
xor @acc[5], %rax
add $fx, @acc[0]
adc \$0, @acc[1]
adc \$0, @acc[2]
adc \$0, @acc[3]
adc \$0, @acc[4]
adc \$0, %rax
mulx @acc[0], @acc[0], $fx # |a|*|f0| (or |b|*|g0|)
mulx @acc[1], @acc[1], @acc[5]
add $fx, @acc[1]
___
for(my ($a,$b) = ($fx, @acc[5]), $i=2; $i<5; $i++) {
$code.=<<___;
mulx @acc[$i], @acc[$i], $a
adc $b, @acc[$i]
___
($a, $b) = ($b, $a);
}
$code.=<<___ if ($j==0);
adc \$0, $fx
imulq %rdx
add $fx, %rax
adc %rdx, @acc[6]
mov $g0, %rdx
mov @acc[0], 8*0($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 %rax, 8*5($out_ptr)
___
}
$code.=<<___;
adc \$0, $fx
imulq %rdx
add $fx, %rax
adc \$0, %rdx
add 8*0($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), %rax
adc %rdx, @acc[6]
mov $f0, %rdx
shrd \$31, @acc[1], @acc[0]
shrd \$31, @acc[2], @acc[1]
shrd \$31, @acc[3], @acc[2]
shrd \$31, @acc[4], @acc[3]
shrd \$31, %rax, @acc[4]
shrd \$31, @acc[6], %rax
sar \$63, @acc[6] # sign as mask
xor $fx, $fx
sub @acc[6], $fx # 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], %rax
add $fx, @acc[0]
adc \$0, @acc[1]
adc \$0, @acc[2]
adc \$0, @acc[3]
adc \$0, @acc[4]
adc \$0, %rax
mov @acc[0], 8*0($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 %rax, 8*5($out_ptr)
xor @acc[6], %rdx # conditionally negate |f0|
xor @acc[6], $g0 # conditionally negate |g0|
add $fx, %rdx
add $fx, $g0
ret
.size __smulx_383_n_shift_by_31,.-__smulx_383_n_shift_by_31
___
} {
$code.=<<___;
.type __smulx_191_n_shift_by_31,\@abi-omnipotent
.align 32
__smulx_191_n_shift_by_31:
mov $f0, @acc[8]
___
my $f0 = @acc[8];
for($j=0; $j<2; $j++) {
my $k = 8*6*$j;
my @acc=@acc;
@acc=@acc[3..5] if ($j);
$code.=<<___;
mov $k+8*0($in_ptr), @acc[0] # load |a| (or |b|)
mov $k+8*1($in_ptr), @acc[1]
mov $k+8*2($in_ptr), @acc[2]
mov %rdx, %rax
sar \$63, %rax # |f0|'s sign as mask (or |g0|'s)
xor $fx, $fx
sub %rax, $fx # |f0|'s sign as bit (or |g0|'s)
xor %rax, %rdx # conditionally negate |f0| (or |g0|)
add $fx, %rdx
xor %rax, @acc[0] # conditionally negate |a| (or |b|)
xor %rax, @acc[1]
xor @acc[2], %rax
add $fx, @acc[0]
adc \$0, @acc[1]
adc \$0, %rax
mulx @acc[0], @acc[0], $fx # |a|*|f0| (or |b|*|g0|)
mulx @acc[1], @acc[1], @acc[2]
add $fx, @acc[1]
adc \$0, @acc[2]
imulq %rdx
add %rax, @acc[2]
adc \$0, %rdx
___
$code.=<<___ if ($j==0);
mov %rdx, @acc[6]
mov $g0, %rdx
___
}
$code.=<<___;
add @acc[0], @acc[3]
adc @acc[1], @acc[4]
adc @acc[2], @acc[5]
adc %rdx, @acc[6]
mov $f0, %rdx
shrd \$31, @acc[4], @acc[3]
shrd \$31, @acc[5], @acc[4]
shrd \$31, @acc[6], @acc[5]
sar \$63, @acc[6] # sign as mask
xor $fx, $fx
sub @acc[6], $fx # sign as bit
xor @acc[6], @acc[3] # conditionally negate the result
xor @acc[6], @acc[4]
xor @acc[6], @acc[5]
add $fx, @acc[3]
adc \$0, @acc[4]
adc \$0, @acc[5]
mov @acc[3], 8*0($out_ptr)
mov @acc[4], 8*1($out_ptr)
mov @acc[5], 8*2($out_ptr)
xor @acc[6], %rdx # conditionally negate |f0|
xor @acc[6], $g0 # conditionally negate |g0|
add $fx, %rdx
add $fx, $g0
ret
.size __smulx_191_n_shift_by_31,.-__smulx_191_n_shift_by_31
___
} }
{
my ($a_lo, $a_hi, $b_lo, $b_hi) = map("%r$_",(8..11));
my ($t0, $t1, $t2, $t3, $t4) = ("%rax","%rbx","%rbp","%r14","%r15");
my ($fg0, $fg1, $bias) = ($g0, $g1, $t4);
my ($a_, $b_) = ($a_lo, $b_lo);
{
my @a = ($a_lo, $t1, $a_hi);
my @b = ($b_lo, $t2, $b_hi);
$code.=<<___;
.type __ab_approximation_31,\@abi-omnipotent
.align 32
__ab_approximation_31:
mov 8*5($in_ptr), @a[2] # load |a| in reverse order
mov 8*11($in_ptr), @b[2] # load |b| in reverse order
mov 8*4($in_ptr), @a[1]
mov 8*10($in_ptr), @b[1]
mov 8*3($in_ptr), @a[0]
mov 8*9($in_ptr), @b[0]
mov @a[2], $t0
or @b[2], $t0 # check top-most limbs, ...
cmovz @a[1], @a[2]
cmovz @b[1], @b[2]
cmovz @a[0], @a[1]
mov 8*2($in_ptr), @a[0]
cmovz @b[0], @b[1]
mov 8*8($in_ptr), @b[0]
mov @a[2], $t0
or @b[2], $t0 # ... ones before top-most, ...
cmovz @a[1], @a[2]
cmovz @b[1], @b[2]
cmovz @a[0], @a[1]
mov 8*1($in_ptr), @a[0]
cmovz @b[0], @b[1]
mov 8*7($in_ptr), @b[0]
mov @a[2], $t0
or @b[2], $t0 # ... and ones before that ...
cmovz @a[1], @a[2]
cmovz @b[1], @b[2]
cmovz @a[0], @a[1]
mov 8*0($in_ptr), @a[0]
cmovz @b[0], @b[1]
mov 8*6($in_ptr), @b[0]
mov @a[2], $t0
or @b[2], $t0 # ... and ones before that ...
cmovz @a[1], @a[2]
cmovz @b[1], @b[2]
cmovz @a[0], @a[1]
cmovz @b[0], @b[1]
mov @a[2], $t0
or @b[2], $t0
bsr $t0, %rcx
lea 1(%rcx), %rcx
cmovz @a[0], @a[2]
cmovz @b[0], @b[2]
cmovz $t0, %rcx
neg %rcx
#and \$63, %rcx # debugging artefact
shldq %cl, @a[1], @a[2] # align second limb to the left
shldq %cl, @b[1], @b[2]
mov \$0x7FFFFFFF, %eax
and %rax, @a[0]
and %rax, @b[0]
andn @a[2], %rax, @a[2]
andn @b[2], %rax, @b[2]
or @a[2], @a[0]
or @b[2], @b[0]
jmp __inner_loop_31
ret
.size __ab_approximation_31,.-__ab_approximation_31
___
}
$code.=<<___;
.type __inner_loop_31,\@abi-omnipotent
.align 32
__inner_loop_31: ################# by Thomas Pornin
mov \$0x7FFFFFFF80000000, $fg0 # |f0|=1, |g0|=0
mov \$0x800000007FFFFFFF, $fg1 # |f1|=0, |g1|=1
mov \$0x7FFFFFFF7FFFFFFF, $bias
.Loop_31:
cmp $b_, $a_ # if |a_|<|b_|, swap the variables
mov $a_, $t0
mov $b_, $t1
mov $fg0, $t2
mov $fg1, $t3
cmovb $b_, $a_
cmovb $t0, $b_
cmovb $fg1, $fg0
cmovb $t2, $fg1
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
shr \$1, $a_ # |a_|>>=1
add $fg1, $fg1 # |f1|<<=1, |g1|<<=1
sub $bias, $fg1
sub \$1, $cnt
jnz .Loop_31
shr \$32, $bias
mov %ecx, %edx # $fg0, $f0
mov ${fg1}d, ${f1}d
shr \$32, $g0
shr \$32, $g1
sub $bias, $f0 # remove the bias
sub $bias, $g0
sub $bias, $f1
sub $bias, $g1
ret
.size __inner_loop_31,.-__inner_loop_31
.type __inner_loop_62,\@abi-omnipotent
.align 32
__inner_loop_62:
mov \$1, $f0 # |f0|=1
xor $g0, $g0 # |g0|=0
xor $f1, $f1 # |f1|=0
mov \$1, $g1 # |g1|=1
.Loop_62:
xor $t0, $t0
test \$1, $a_lo # if |a_| is odd, then we'll be subtracting |b_|
mov $b_lo, $t1
cmovnz $b_lo, $t0
sub $a_lo, $t1 # |b_|-|a_|
mov $a_lo, $t2
sub $t0, $a_lo # |a_|-|b_| (or |a_|-0 if |a_| was even)
cmovc $t1, $a_lo # borrow means |a_|<|b_|, replace with |b_|-|a_|
cmovc $t2, $b_lo # |b_| = |a_|
mov $f0, $t0 # exchange |f0| and |f1|
cmovc $f1, $f0
cmovc $t0, $f1
mov $g0, $t1 # exchange |g0| and |g1|
cmovc $g1, $g0
cmovc $t1, $g1
xor $t0, $t0
xor $t1, $t1
shr \$1, $a_lo
test \$1, $t2 # if |a_| was odd, then we'll be subtracting...
cmovnz $f1, $t0
cmovnz $g1, $t1
add $f1, $f1 # |f1|<<=1
add $g1, $g1 # |g1|<<=1
sub $t0, $f0 # |f0|-=|f1| (or |f0-=0| if |a_| was even)
sub $t1, $g0 # |g0|-=|g1| (or |g0-=0| ...)
sub \$1, $cnt
jnz .Loop_62
ret
.size __inner_loop_62,.-__inner_loop_62
___
}
print $code;
close STDOUT;
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