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// generated source. do not edit.
#![allow(non_upper_case_globals, unused_macros, unused_imports)]
use crate::low::macros::*;
// Copyright Amazon.com, Inc. or its affiliates. All Rights Reserved.
// SPDX-License-Identifier: Apache-2.0 OR ISC OR MIT-0
// ----------------------------------------------------------------------------
// Montgomery reduce, z := (x' / 2^{64p}) MOD m
// Inputs x[n], m[k], p; output z[k]
//
// extern void bignum_montredc(uint64_t k, uint64_t *z, uint64_t n,
// const uint64_t *x, const uint64_t *m, uint64_t p);
//
// Does a := (x' / 2^{64p}) mod m where x' = x if n <= p + k and in general
// is the lowest (p+k) digits of x, assuming x' <= 2^{64p} * m. That is,
// p-fold Montgomery reduction w.r.t. a k-digit modulus m giving a k-digit
// answer.
//
// Standard x86-64 ABI: RDI = k, RSI = z, RDX = n, RCX = x, R8 = m, R9 = p
// Microsoft x64 ABI: RCX = k, RDX = z, R8 = n, R9 = x, [RSP+40] = m, [RSP+48] = p
// ----------------------------------------------------------------------------
// We copy n into r10 but it comes in in rdx originally
macro_rules! k {
() => {
"rdi"
};
}
macro_rules! z {
() => {
"rsi"
};
}
macro_rules! n {
() => {
"r10"
};
}
macro_rules! x {
() => {
"rcx"
};
}
macro_rules! m {
() => {
"r8"
};
}
macro_rules! p {
() => {
"r9"
};
}
// General temp, low part of product and mul input
macro_rules! a {
() => {
"rax"
};
}
// General temp, High part of product
macro_rules! b {
() => {
"rdx"
};
}
// Negated modular inverse
macro_rules! w {
() => {
"QWORD PTR [rsp]"
};
}
// Inner loop counter
macro_rules! j {
() => {
"rbx"
};
}
// Home for i'th digit or Montgomery multiplier
macro_rules! d {
() => {
"rbp"
};
}
macro_rules! h {
() => {
"r11"
};
}
macro_rules! e {
() => {
"r12"
};
}
macro_rules! t {
() => {
"r13"
};
}
macro_rules! i {
() => {
"r14"
};
}
macro_rules! c {
() => {
"r15"
};
}
// Some more intuitive names for temp regs in initial word-level negmodinv.
macro_rules! t1 {
() => {
"rbx"
};
}
macro_rules! t2 {
() => {
"r14"
};
}
macro_rules! ashort {
() => {
"eax"
};
}
macro_rules! cshort {
() => {
"r15d"
};
}
macro_rules! jshort {
() => {
"ebx"
};
}
/// Montgomery reduce, z := (x' / 2^{64p}) MOD m
///
/// Inputs x[n], m[k], p; output z[k]
///
/// Does a := (x' / 2^{64p}) mod m where x' = x if n <= p + k and in general
/// is the lowest (p+k) digits of x, assuming x' <= 2^{64p} * m. That is,
/// p-fold Montgomery reduction w.r.t. a k-digit modulus m giving a k-digit
/// answer.
pub(crate) fn bignum_montredc(z: &mut [u64], x: &[u64], m: &[u64], p: u64) {
debug_assert!(z.len() == m.len());
// SAFETY: inline assembly. see [crate::low::inline_assembly_safety] for safety info.
unsafe {
core::arch::asm!(
Q!(" endbr64 " ),
// Save registers and allocate space on stack for non-register variable w
Q!(" push " "rbx"),
Q!(" push " "rbp"),
Q!(" push " "r12"),
Q!(" push " "r13"),
Q!(" push " "r14"),
Q!(" push " "r15"),
Q!(" sub " "rsp, 8"),
// If k = 0 the whole operation is trivial
Q!(" test " k!() ", " k!()),
Q!(" jz " Label!("bignum_montredc_end", 2, After)),
// Move n input into its permanent home, since we need rdx for multiplications
Q!(" mov " n!() ", rdx"),
// Compute word-level negated modular inverse w for m == m[0].
Q!(" mov " a!() ", [" m!() "]"),
Q!(" mov " t2!() ", " a!()),
Q!(" mov " t1!() ", " a!()),
Q!(" shl " t2!() ", 2"),
Q!(" sub " t1!() ", " t2!()),
Q!(" xor " t1!() ", 2"),
Q!(" mov " t2!() ", " t1!()),
Q!(" imul " t2!() ", " a!()),
Q!(" mov " ashort!() ", 2"),
Q!(" add " a!() ", " t2!()),
Q!(" add " t2!() ", 1"),
Q!(" imul " t1!() ", " a!()),
Q!(" imul " t2!() ", " t2!()),
Q!(" mov " ashort!() ", 1"),
Q!(" add " a!() ", " t2!()),
Q!(" imul " t1!() ", " a!()),
Q!(" imul " t2!() ", " t2!()),
Q!(" mov " ashort!() ", 1"),
Q!(" add " a!() ", " t2!()),
Q!(" imul " t1!() ", " a!()),
Q!(" imul " t2!() ", " t2!()),
Q!(" mov " ashort!() ", 1"),
Q!(" add " a!() ", " t2!()),
Q!(" imul " t1!() ", " a!()),
Q!(" mov " w!() ", " t1!()),
// Initialize z to the lowest k digits of the input, zero-padding if n < k.
Q!(" mov " j!() ", " k!()),
Q!(" cmp " n!() ", " k!()),
Q!(" cmovc " j!() ", " n!()),
Q!(" xor " i!() ", " i!()),
Q!(" test " j!() ", " j!()),
Q!(" jz " Label!("bignum_montredc_padloop", 3, After)),
Q!(Label!("bignum_montredc_copyloop", 4) ":"),
Q!(" mov " a!() ", [" x!() "+ 8 * " i!() "]"),
Q!(" mov " "[" z!() "+ 8 * " i!() "], " a!()),
Q!(" inc " i!()),
Q!(" cmp " i!() ", " j!()),
Q!(" jc " Label!("bignum_montredc_copyloop", 4, Before)),
Q!(" cmp " i!() ", " k!()),
Q!(" jnc " Label!("bignum_montredc_initialized", 5, After)),
Q!(" xor " j!() ", " j!()),
Q!(Label!("bignum_montredc_padloop", 3) ":"),
Q!(" mov " "[" z!() "+ 8 * " i!() "], " j!()),
Q!(" inc " i!()),
Q!(" cmp " i!() ", " k!()),
Q!(" jc " Label!("bignum_montredc_padloop", 3, Before)),
Q!(Label!("bignum_montredc_initialized", 5) ":"),
Q!(" xor " c!() ", " c!()),
// Now if p = 0 we just need the corrective tail, and even that is
// only needed for the case when the input is exactly the modulus,
// to maintain the <= 2^64p * n precondition
Q!(" test " p!() ", " p!()),
Q!(" jz " Label!("bignum_montredc_corrective", 6, After)),
// Outer loop, just doing a standard Montgomery reduction on z
Q!(" xor " i!() ", " i!()),
Q!(Label!("bignum_montredc_outerloop", 7) ":"),
Q!(" mov " e!() ", [" z!() "]"),
Q!(" mov " d!() ", " w!()),
Q!(" imul " d!() ", " e!()),
Q!(" mov " a!() ", [" m!() "]"),
Q!(" mul " d!()),
Q!(" add " a!() ", " e!()),
Q!(" mov " h!() ", rdx"),
Q!(" mov " jshort!() ", 1"),
Q!(" mov " t!() ", " k!()),
Q!(" dec " t!()),
Q!(" jz " Label!("bignum_montredc_montend", 8, After)),
Q!(Label!("bignum_montredc_montloop", 9) ":"),
Q!(" adc " h!() ", [" z!() "+ 8 * " j!() "]"),
Q!(" sbb " e!() ", " e!()),
Q!(" mov " a!() ", [" m!() "+ 8 * " j!() "]"),
Q!(" mul " d!()),
Q!(" sub " "rdx, " e!()),
Q!(" add " a!() ", " h!()),
Q!(" mov " "[" z!() "+ 8 * " j!() "-8], " a!()),
Q!(" mov " h!() ", rdx"),
Q!(" inc " j!()),
Q!(" dec " t!()),
Q!(" jnz " Label!("bignum_montredc_montloop", 9, Before)),
Q!(Label!("bignum_montredc_montend", 8) ":"),
Q!(" adc " h!() ", " c!()),
Q!(" mov " cshort!() ", 0"),
Q!(" adc " c!() ", 0"),
Q!(" add " j!() ", " i!()),
Q!(" cmp " j!() ", " n!()),
Q!(" jnc " Label!("bignum_montredc_offtheend", 12, After)),
Q!(" mov " a!() ", [" x!() "+ 8 * " j!() "]"),
Q!(" add " h!() ", " a!()),
Q!(" adc " c!() ", 0"),
Q!(Label!("bignum_montredc_offtheend", 12) ":"),
Q!(" mov " "[" z!() "+ 8 * " k!() "-8], " h!()),
// End of outer loop.
Q!(" inc " i!()),
Q!(" cmp " i!() ", " p!()),
Q!(" jc " Label!("bignum_montredc_outerloop", 7, Before)),
// Now do a comparison of (c::z) with (0::m) to set a final correction mask
// indicating that (c::z) >= m and so we need to subtract m.
Q!(Label!("bignum_montredc_corrective", 6) ":"),
Q!(" xor " j!() ", " j!()),
Q!(" mov " n!() ", " k!()),
Q!(Label!("bignum_montredc_cmploop", 13) ":"),
Q!(" mov " a!() ", [" z!() "+ 8 * " j!() "]"),
Q!(" sbb " a!() ", [" m!() "+ 8 * " j!() "]"),
Q!(" inc " j!()),
Q!(" dec " n!()),
Q!(" jnz " Label!("bignum_montredc_cmploop", 13, Before)),
Q!(" sbb " c!() ", 0"),
Q!(" sbb " d!() ", " d!()),
Q!(" not " d!()),
// Now do a masked subtraction of m for the final reduced result.
Q!(" xor " e!() ", " e!()),
Q!(" xor " j!() ", " j!()),
Q!(Label!("bignum_montredc_corrloop", 14) ":"),
Q!(" mov " a!() ", [" m!() "+ 8 * " j!() "]"),
Q!(" and " a!() ", " d!()),
Q!(" neg " e!()),
Q!(" sbb " "[" z!() "+ 8 * " j!() "], " a!()),
Q!(" sbb " e!() ", " e!()),
Q!(" inc " j!()),
Q!(" cmp " j!() ", " k!()),
Q!(" jc " Label!("bignum_montredc_corrloop", 14, Before)),
Q!(Label!("bignum_montredc_end", 2) ":"),
Q!(" add " "rsp, 8"),
Q!(" pop " "r15"),
Q!(" pop " "r14"),
Q!(" pop " "r13"),
Q!(" pop " "r12"),
Q!(" pop " "rbp"),
Q!(" pop " "rbx"),
inout("rdi") z.len() => _,
inout("rsi") z.as_mut_ptr() => _,
inout("rdx") x.len() => _,
inout("rcx") x.as_ptr() => _,
inout("r8") m.as_ptr() => _,
inout("r9") p => _,
// clobbers
out("r10") _,
out("r11") _,
out("r12") _,
out("r13") _,
out("r14") _,
out("r15") _,
out("rax") _,
)
};
}