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// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
//
// Permission to use, copy, modify, and/or distribute this software for any
// purpose with or without fee is hereby granted, provided that the above
// copyright notice and this permission notice appear in all copies.
//
// THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
// WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
// ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
// WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
// ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
// OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
// ----------------------------------------------------------------------------
// Multiply z := x * y
// Inputs x[m], y[n]; output z[k]
//
// extern void bignum_mul
// (uint64_t k, uint64_t *z,
// uint64_t m, uint64_t *x, uint64_t n, uint64_t *y);
//
// Does the "z := x * y" operation where x is m digits, y is n, result z is k.
// Truncates the result in general unless k >= m + n
//
// Standard x86-64 ABI: RDI = k, RSI = z, RDX = m, RCX = x, R8 = n, R9 = y
// Microsoft x64 ABI: RCX = k, RDX = z, R8 = m, R9 = x, [RSP+40] = n, [RSP+48] = y
// ----------------------------------------------------------------------------
#include "s2n_bignum_internal.h"
.intel_syntax noprefix
S2N_BN_SYM_VISIBILITY_DIRECTIVE(bignum_mul)
S2N_BN_SYM_PRIVACY_DIRECTIVE(bignum_mul)
.text
// These are actually right
#define p rdi
#define z rsi
#define n r8
// These are not
#define c r15
#define h r14
#define l r13
#define x r12
#define y r11
#define i rbx
#define k r10
#define m rbp
// These are always local scratch since multiplier result is in these
#define a rax
#define d rdx
S2N_BN_SYMBOL(bignum_mul):
endbr64
#if WINDOWS_ABI
push rdi
push rsi
mov rdi, rcx
mov rsi, rdx
mov rdx, r8
mov rcx, r9
mov r8, [rsp+56]
mov r9, [rsp+64]
#endif
// We use too many registers, and also we need rax:rdx for multiplications
push rbx
push rbp
push r12
push r13
push r14
push r15
mov m, rdx
// If the result size is zero, do nothing
// Note that even if either or both inputs has size zero, we can't
// just give up because we at least need to zero the output array
// If we did a multiply-add variant, however, then we could
test p, p
jz end
// Set initial 2-part sum to zero (we zero c inside the body)
xor h,h
xor l,l
// Otherwise do outer loop k = 0 ... k = p - 1
xor k, k
outerloop:
// Zero our carry term first; we eventually want it and a zero is useful now
// Set a = max 0 (k + 1 - n), i = min (k + 1) m
// This defines the range a <= j < i for the inner summation
// Note that since k < p < 2^64 we can assume k + 1 doesn't overflow
// And since we want to increment it anyway, we might as well do it now
xor c, c // c = 0
inc k // k = k + 1
mov a, k // a = k + 1
sub a, n // a = k + 1 - n
cmovc a, c // a = max 0 (k + 1 - n)
mov i, m // i = m
cmp k, m // CF <=> k + 1 < m
cmovc i, k // i = min (k + 1) m
// Turn i into a loop count, and skip things if it's <= 0
// Otherwise set up initial pointers x -> x0[a] and y -> y0[k - a]
// and then launch into the main inner loop, postdecrementing i
mov d, k
sub d, i
sub i, a
jbe innerend
lea x,[rcx+8*a]
lea y,[r9+8*d-8]
innerloop:
mov rax, [y+8*i]
mul QWORD PTR [x]
add x, 8
add l, rax
adc h, rdx
adc c, 0
dec i
jnz innerloop
innerend:
mov [z], l
mov l, h
mov h, c
add z, 8
cmp k, p
jc outerloop
end:
pop r15
pop r14
pop r13
pop r12
pop rbp
pop rbx
#if WINDOWS_ABI
pop rsi
pop rdi
#endif
ret
#if defined(__linux__) && defined(__ELF__)
.section .note.GNU-stack,"",%progbits
#endif
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