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