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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
// ----------------------------------------------------------------------------
// Reduce modulo basepoint order, z := x mod n_25519
// Input x[k]; output z[4]
//
// extern void bignum_mod_n25519(uint64_t z[static 4], uint64_t k,
// const uint64_t *x);
//
// Reduction is modulo the order of the curve25519/edwards25519 basepoint,
// which is n_25519 = 2^252 + 27742317777372353535851937790883648493
//
// Standard ARM ABI: X0 = z, X1 = k, X2 = x
// ----------------------------------------------------------------------------
macro_rules! z {
() => {
"x0"
};
}
macro_rules! k {
() => {
"x1"
};
}
macro_rules! x {
() => {
"x2"
};
}
macro_rules! m0 {
() => {
"x3"
};
}
macro_rules! m1 {
() => {
"x4"
};
}
macro_rules! m2 {
() => {
"x5"
};
}
macro_rules! m3 {
() => {
"x6"
};
}
macro_rules! t0 {
() => {
"x7"
};
}
macro_rules! t1 {
() => {
"x8"
};
}
macro_rules! t2 {
() => {
"x9"
};
}
macro_rules! t3 {
() => {
"x10"
};
}
macro_rules! n0 {
() => {
"x11"
};
}
macro_rules! n1 {
() => {
"x12"
};
}
// These two are aliased: we only load d when finished with q
macro_rules! q {
() => {
"x13"
};
}
macro_rules! d {
() => {
"x13"
};
}
// Loading large constants
macro_rules! movbig {
($nn:expr, $n3:expr, $n2:expr, $n1:expr, $n0:expr) => { Q!(
"movz " $nn ", " $n0 ";\n"
"movk " $nn ", " $n1 ", lsl #16;\n"
"movk " $nn ", " $n2 ", lsl #32;\n"
"movk " $nn ", " $n3 ", lsl #48"
)}
}
/// Reduce modulo basepoint order, z := x mod n_25519
///
/// Input x[k]; output z[4]
///
/// Reduction is modulo the order of the curve25519/edwards25519 basepoint,
/// which is n_25519 = 2^252 + 27742317777372353535851937790883648493
pub(crate) fn bignum_mod_n25519(z: &mut [u64; 4], x: &[u64]) {
// SAFETY: inline assembly. see [crate::low::inline_assembly_safety] for safety info.
unsafe {
core::arch::asm!(
// If the input is already <= 3 words long, go to a trivial "copy" path
Q!(" cmp " k!() ", #4"),
Q!(" bcc " Label!("bignum_mod_n25519_short", 2, After)),
// Otherwise load the top 4 digits (top-down) and reduce k by 4
// This [m3;m2;m1;m0] is the initial x where we begin reduction.
Q!(" sub " k!() ", " k!() ", #4"),
Q!(" lsl " t0!() ", " k!() ", #3"),
Q!(" add " t0!() ", " t0!() ", " x!()),
Q!(" ldp " m2!() ", " m3!() ", [" t0!() ", #16]"),
Q!(" ldp " m0!() ", " m1!() ", [" t0!() "]"),
// Load the complicated two words of n_25519 = 2^252 + [n1; n0]
movbig!(n0!(), "#0x5812", "#0x631a", "#0x5cf5", "#0xd3ed"),
movbig!(n1!(), "#0x14de", "#0xf9de", "#0xa2f7", "#0x9cd6"),
// Get the quotient estimate q = floor(x/2^252).
// Also delete it from m3, in effect doing x' = x - q * 2^252
Q!(" lsr " q!() ", " m3!() ", #60"),
Q!(" and " m3!() ", " m3!() ", #0x0FFFFFFFFFFFFFFF"),
// Multiply [t2;t1;t0] = q * [n1;n0]
Q!(" mul " t0!() ", " n0!() ", " q!()),
Q!(" mul " t1!() ", " n1!() ", " q!()),
Q!(" umulh " t2!() ", " n0!() ", " q!()),
Q!(" adds " t1!() ", " t1!() ", " t2!()),
Q!(" umulh " t2!() ", " n1!() ", " q!()),
Q!(" adc " t2!() ", " t2!() ", xzr"),
// Subtract [m3;m2;m1;m0] = x' - q * [n1;n0] = x - q * n_25519
Q!(" subs " m0!() ", " m0!() ", " t0!()),
Q!(" sbcs " m1!() ", " m1!() ", " t1!()),
Q!(" sbcs " m2!() ", " m2!() ", " t2!()),
Q!(" sbcs " m3!() ", " m3!() ", xzr"),
// If this borrows (CF = 0 because of inversion), add back n_25519.
// The masked n3 digit exploits the fact that bit 60 of n0 is set.
Q!(" csel " t0!() ", " n0!() ", xzr, cc"),
Q!(" csel " t1!() ", " n1!() ", xzr, cc"),
Q!(" adds " m0!() ", " m0!() ", " t0!()),
Q!(" adcs " m1!() ", " m1!() ", " t1!()),
Q!(" and " t0!() ", " t0!() ", #0x1000000000000000"),
Q!(" adcs " m2!() ", " m2!() ", xzr"),
Q!(" adc " m3!() ", " m3!() ", " t0!()),
// Now do (k-4) iterations of 5->4 word modular reduction. Each one
// is similar to the sequence above except for the more refined quotient
// estimation process.
Q!(" cbz " k!() ", " Label!("bignum_mod_n25519_writeback", 3, After)),
Q!(Label!("bignum_mod_n25519_loop", 4) ":"),
// Assume that the new 5-digit x is 2^64 * previous_x + next_digit.
// Get the quotient estimate q = max (floor(x/2^252)) (2^64 - 1)
// and first compute x' = x - 2^252 * q.
Q!(" extr " q!() ", " m3!() ", " m2!() ", #60"),
Q!(" and " m2!() ", " m2!() ", #0x0FFFFFFFFFFFFFFF"),
Q!(" sub " q!() ", " q!() ", " m3!() ", lsr #60"),
Q!(" and " m3!() ", " m3!() ", #0xF000000000000000"),
Q!(" add " m2!() ", " m2!() ", " m3!()),
// Multiply [t2;t1;t0] = q * [n1;n0]
Q!(" mul " t0!() ", " n0!() ", " q!()),
Q!(" mul " t1!() ", " n1!() ", " q!()),
Q!(" umulh " t2!() ", " n0!() ", " q!()),
Q!(" adds " t1!() ", " t1!() ", " t2!()),
Q!(" umulh " t2!() ", " n1!() ", " q!()),
Q!(" adc " t2!() ", " t2!() ", xzr"),
// Decrement k and load the next digit (note that d aliases to q)
Q!(" sub " k!() ", " k!() ", #1"),
Q!(" ldr " d!() ", [" x!() ", " k!() ", lsl #3]"),
// Subtract [t3;t2;t1;t0] = x' - q * [n1;n0] = x - q * n_25519
Q!(" subs " t0!() ", " d!() ", " t0!()),
Q!(" sbcs " t1!() ", " m0!() ", " t1!()),
Q!(" sbcs " t2!() ", " m1!() ", " t2!()),
Q!(" sbcs " t3!() ", " m2!() ", xzr"),
// If this borrows (CF = 0 because of inversion), add back n_25519.
// The masked n3 digit exploits the fact that bit 60 of n1 is set.
Q!(" csel " m0!() ", " n0!() ", xzr, cc"),
Q!(" csel " m1!() ", " n1!() ", xzr, cc"),
Q!(" adds " m0!() ", " t0!() ", " m0!()),
Q!(" and " m3!() ", " m1!() ", #0x1000000000000000"),
Q!(" adcs " m1!() ", " t1!() ", " m1!()),
Q!(" adcs " m2!() ", " t2!() ", xzr"),
Q!(" adc " m3!() ", " t3!() ", " m3!()),
Q!(" cbnz " k!() ", " Label!("bignum_mod_n25519_loop", 4, Before)),
// Finally write back [m3;m2;m1;m0] and return
Q!(Label!("bignum_mod_n25519_writeback", 3) ":"),
Q!(" stp " m0!() ", " m1!() ", [" z!() "]"),
Q!(" stp " m2!() ", " m3!() ", [" z!() ", #16]"),
// linear hoisting in -> b after bignum_mod_n25519_short
Q!(" b " Label!("hoist_finish", 5, After)),
// Short case: just copy the input with zero-padding
Q!(Label!("bignum_mod_n25519_short", 2) ":"),
Q!(" mov " m0!() ", xzr"),
Q!(" mov " m1!() ", xzr"),
Q!(" mov " m2!() ", xzr"),
Q!(" mov " m3!() ", xzr"),
Q!(" cbz " k!() ", " Label!("bignum_mod_n25519_writeback", 3, Before)),
Q!(" ldr " m0!() ", [" x!() "]"),
Q!(" subs " k!() ", " k!() ", #1"),
Q!(" beq " Label!("bignum_mod_n25519_writeback", 3, Before)),
Q!(" ldr " m1!() ", [" x!() ", #8]"),
Q!(" subs " k!() ", " k!() ", #1"),
Q!(" beq " Label!("bignum_mod_n25519_writeback", 3, Before)),
Q!(" ldr " m2!() ", [" x!() ", #16]"),
Q!(" b " Label!("bignum_mod_n25519_writeback", 3, Before)),
Q!(Label!("hoist_finish", 5) ":"),
inout("x0") z.as_mut_ptr() => _,
inout("x1") x.len() => _,
inout("x2") x.as_ptr() => _,
// clobbers
out("x10") _,
out("x11") _,
out("x12") _,
out("x13") _,
out("x3") _,
out("x4") _,
out("x5") _,
out("x6") _,
out("x7") _,
out("x8") _,
out("x9") _,
)
};
}