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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 multiply, z := (x * y / 2^{64k}) mod m
// Inputs x[k], y[k], m[k]; output z[k]
//
// extern void bignum_montmul(uint64_t k, uint64_t *z, const uint64_t *x,
// const uint64_t *y, const uint64_t *m);
//
// Does z := (x * y / 2^{64k}) mod m, assuming x * y <= 2^{64k} * m, which is
// guaranteed in particular if x < m, y < m initially (the "intended" case).
//
// Standard ARM ABI: X0 = k, X1 = z, X2 = x, X3 = y, X4 = m
// ----------------------------------------------------------------------------
macro_rules! k {
() => {
"x0"
};
}
macro_rules! z {
() => {
"x1"
};
}
macro_rules! x {
() => {
"x2"
};
}
macro_rules! y {
() => {
"x3"
};
}
macro_rules! m {
() => {
"x4"
};
}
// Negated modular inverse
macro_rules! w {
() => {
"x5"
};
}
// Top carry for k'th position
macro_rules! c0 {
() => {
"x6"
};
}
// Additional top carry for (k+1)'th position
macro_rules! c1 {
() => {
"x7"
};
}
// Outer loop counter
macro_rules! i {
() => {
"x8"
};
}
// Home for i'th digit or Montgomery multiplier
macro_rules! d {
() => {
"x9"
};
}
// Inner loop counter
macro_rules! j {
() => {
"x10"
};
}
macro_rules! h {
() => {
"x11"
};
}
macro_rules! e {
() => {
"x12"
};
}
macro_rules! l {
() => {
"x13"
};
}
macro_rules! a {
() => {
"x14"
};
}
// This is just a short-term temporary used in zero-test subtraction.
// It's aliased to the same register as "a" which is always safe here.
macro_rules! t {
() => {
"x14"
};
}
// Some more intuitive names for temp regs in initial word-level negmodinv.
// These just use c0 and c1 again, which aren't initialized early on.
macro_rules! one {
() => {
"x6"
};
}
macro_rules! e1 {
() => {
"x6"
};
}
macro_rules! e2 {
() => {
"x7"
};
}
macro_rules! e4 {
() => {
"x6"
};
}
macro_rules! e8 {
() => {
"x7"
};
}
/// Montgomery multiply, z := (x * y / 2^{64k}) mod m
///
/// Inputs x[k], y[k], m[k]; output z[k]
///
/// Does z := (x * y / 2^{64k}) mod m, assuming x * y <= 2^{64k} * m, which is
/// guaranteed in particular if x < m, y < m initially (the "intended" case).
pub(crate) fn bignum_montmul(z: &mut [u64], x: &[u64], y: &[u64], m: &[u64]) {
debug_assert!(z.len() == x.len());
debug_assert!(z.len() == y.len());
debug_assert!(z.len() == m.len());
// SAFETY: inline assembly. see [crate::low::inline_assembly_safety] for safety info.
unsafe {
core::arch::asm!(
// If k = 0 the whole operation is trivial
Q!(" cbz " k!() ", " Label!("bignum_montmul_end", 2, After)),
// Compute word-level negated modular inverse w for m == m[0].
// This is essentially the same as word_negmodinv.
Q!(" ldr " a!() ", [" m!() "]"),
Q!(" lsl " w!() ", " a!() ", #2"),
Q!(" sub " w!() ", " a!() ", " w!()),
Q!(" eor " w!() ", " w!() ", #2"),
Q!(" mov " one!() ", #1"),
Q!(" madd " e1!() ", " a!() ", " w!() ", " one!()),
Q!(" mul " e2!() ", " e1!() ", " e1!()),
Q!(" madd " w!() ", " e1!() ", " w!() ", " w!()),
Q!(" mul " e4!() ", " e2!() ", " e2!()),
Q!(" madd " w!() ", " e2!() ", " w!() ", " w!()),
Q!(" mul " e8!() ", " e4!() ", " e4!()),
Q!(" madd " w!() ", " e4!() ", " w!() ", " w!()),
Q!(" madd " w!() ", " e8!() ", " w!() ", " w!()),
// Initialize the output c0::z to zero so we can then consistently add rows.
// It would be a bit more efficient to special-case the zeroth row, but
// this keeps the code slightly simpler.
Q!(" mov " i!() ", xzr"),
Q!(Label!("bignum_montmul_zoop", 3) ":"),
Q!(" str " "xzr, [" z!() ", " i!() ", lsl #3]"),
Q!(" add " i!() ", " i!() ", #1"),
Q!(" cmp " i!() ", " k!()),
Q!(" bcc " Label!("bignum_montmul_zoop", 3, Before)),
Q!(" mov " c0!() ", xzr"),
// Outer loop pulling down digits d=x[i], multiplying by y and reducing
Q!(" mov " i!() ", xzr"),
Q!(Label!("bignum_montmul_outerloop", 4) ":"),
// Multiply-add loop where we always have CF + previous high part h to add in
// Note that in general we do need yet one more carry in this phase and hence
// initialize c1 with the top carry.
Q!(" ldr " d!() ", [" x!() ", " i!() ", lsl #3]"),
Q!(" mov " j!() ", xzr"),
Q!(" adds " h!() ", xzr, xzr"),
Q!(Label!("bignum_montmul_maddloop", 5) ":"),
Q!(" ldr " a!() ", [" y!() ", " j!() ", lsl #3]"),
Q!(" ldr " e!() ", [" z!() ", " j!() ", lsl #3]"),
Q!(" mul " l!() ", " d!() ", " a!()),
Q!(" adcs " e!() ", " e!() ", " h!()),
Q!(" umulh " h!() ", " d!() ", " a!()),
Q!(" adc " h!() ", " h!() ", xzr"),
Q!(" adds " e!() ", " e!() ", " l!()),
Q!(" str " e!() ", [" z!() ", " j!() ", lsl #3]"),
Q!(" add " j!() ", " j!() ", #1"),
Q!(" sub " t!() ", " j!() ", " k!()),
Q!(" cbnz " t!() ", " Label!("bignum_montmul_maddloop", 5, Before)),
Q!(" adcs " c0!() ", " c0!() ", " h!()),
Q!(" adc " c1!() ", xzr, xzr"),
// Montgomery reduction loop, similar but offsetting writebacks
Q!(" ldr " e!() ", [" z!() "]"),
Q!(" mul " d!() ", " e!() ", " w!()),
Q!(" ldr " a!() ", [" m!() "]"),
Q!(" mul " l!() ", " d!() ", " a!()),
Q!(" umulh " h!() ", " d!() ", " a!()),
Q!(" adds " e!() ", " e!() ", " l!()),
Q!(" mov " j!() ", #1"),
Q!(" sub " t!() ", " k!() ", #1"),
Q!(" cbz " t!() ", " Label!("bignum_montmul_montend", 6, After)),
Q!(Label!("bignum_montmul_montloop", 7) ":"),
Q!(" ldr " a!() ", [" m!() ", " j!() ", lsl #3]"),
Q!(" ldr " e!() ", [" z!() ", " j!() ", lsl #3]"),
Q!(" mul " l!() ", " d!() ", " a!()),
Q!(" adcs " e!() ", " e!() ", " h!()),
Q!(" umulh " h!() ", " d!() ", " a!()),
Q!(" adc " h!() ", " h!() ", xzr"),
Q!(" adds " e!() ", " e!() ", " l!()),
Q!(" sub " l!() ", " j!() ", #1"),
Q!(" str " e!() ", [" z!() ", " l!() ", lsl #3]"),
Q!(" add " j!() ", " j!() ", #1"),
Q!(" sub " t!() ", " j!() ", " k!()),
Q!(" cbnz " t!() ", " Label!("bignum_montmul_montloop", 7, Before)),
Q!(Label!("bignum_montmul_montend", 6) ":"),
Q!(" adcs " h!() ", " c0!() ", " h!()),
Q!(" adc " c0!() ", " c1!() ", xzr"),
Q!(" sub " l!() ", " j!() ", #1"),
Q!(" str " h!() ", [" z!() ", " l!() ", lsl #3]"),
// End of outer loop
Q!(" add " i!() ", " i!() ", #1"),
Q!(" cmp " i!() ", " k!()),
Q!(" bcc " Label!("bignum_montmul_outerloop", 4, Before)),
// Now do a comparison of (c0::z) with (0::m) to set a final correction mask
// indicating that (c0::z) >= m and so we need to subtract m.
Q!(" subs " j!() ", xzr, xzr"),
Q!(Label!("bignum_montmul_cmploop", 8) ":"),
Q!(" ldr " a!() ", [" z!() ", " j!() ", lsl #3]"),
Q!(" ldr " e!() ", [" m!() ", " j!() ", lsl #3]"),
Q!(" sbcs " "xzr, " a!() ", " e!()),
Q!(" add " j!() ", " j!() ", #1"),
Q!(" sub " t!() ", " j!() ", " k!()),
Q!(" cbnz " t!() ", " Label!("bignum_montmul_cmploop", 8, Before)),
Q!(" sbcs " "xzr, " c0!() ", xzr"),
Q!(" csetm " c0!() ", cs"),
// Now do a masked subtraction of m for the final reduced result.
Q!(" subs " j!() ", xzr, xzr"),
Q!(Label!("bignum_montmul_corrloop", 9) ":"),
Q!(" ldr " a!() ", [" z!() ", " j!() ", lsl #3]"),
Q!(" ldr " e!() ", [" m!() ", " j!() ", lsl #3]"),
Q!(" and " e!() ", " e!() ", " c0!()),
Q!(" sbcs " a!() ", " a!() ", " e!()),
Q!(" str " a!() ", [" z!() ", " j!() ", lsl #3]"),
Q!(" add " j!() ", " j!() ", #1"),
Q!(" sub " t!() ", " j!() ", " k!()),
Q!(" cbnz " t!() ", " Label!("bignum_montmul_corrloop", 9, Before)),
Q!(Label!("bignum_montmul_end", 2) ":"),
inout("x0") m.len() => _,
inout("x1") z.as_mut_ptr() => _,
inout("x2") x.as_ptr() => _,
inout("x3") y.as_ptr() => _,
inout("x4") m.as_ptr() => _,
// clobbers
out("x10") _,
out("x11") _,
out("x12") _,
out("x13") _,
out("x14") _,
out("x5") _,
out("x6") _,
out("x7") _,
out("x8") _,
out("x9") _,
)
};
}