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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 x86-64 ABI: RDI = z, RSI = k, RDX = x
// Microsoft x64 ABI: RCX = z, RDX = k, R8 = x
// ----------------------------------------------------------------------------
macro_rules! z {
() => {
"rdi"
};
}
macro_rules! k {
() => {
"rsi"
};
}
macro_rules! x {
() => {
"rcx"
};
}
macro_rules! m0 {
() => {
"r8"
};
}
macro_rules! m1 {
() => {
"r9"
};
}
macro_rules! m2 {
() => {
"r10"
};
}
macro_rules! m3 {
() => {
"r11"
};
}
macro_rules! d {
() => {
"r12"
};
}
macro_rules! q {
() => {
"rbx"
};
}
/// 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!(
Q!(" endbr64 " ),
// Save extra registers
Q!(" push " "rbx"),
Q!(" push " "rbp"),
Q!(" push " "r12"),
// If the input is already <= 3 words long, go to a trivial "copy" path
Q!(" cmp " k!() ", 4"),
Q!(" jc " Label!("bignum_mod_n25519_shortinput", 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!() ", 4"),
Q!(" mov " m3!() ", [rdx + 8 * " k!() "+ 24]"),
Q!(" mov " m2!() ", [rdx + 8 * " k!() "+ 16]"),
Q!(" mov " m1!() ", [rdx + 8 * " k!() "+ 8]"),
Q!(" mov " m0!() ", [rdx + 8 * " k!() "]"),
// Move x into another register to leave rdx free for multiplies
Q!(" mov " x!() ", rdx"),
// Get the quotient estimate q = floor(x/2^252).
// Also delete it from m3, in effect doing x' = x - q * 2^252
Q!(" mov " q!() ", " m3!()),
Q!(" shr " q!() ", 60"),
Q!(" shl " m3!() ", 4"),
Q!(" shr " m3!() ", 4"),
// Let [rdx;d;rbp] = q * (n_25519 - 2^252)
Q!(" mov " "rax, 0x5812631a5cf5d3ed"),
Q!(" mul " q!()),
Q!(" mov " "rbp, rax"),
Q!(" mov " d!() ", rdx"),
Q!(" mov " "rax, 0x14def9dea2f79cd6"),
Q!(" mul " q!()),
Q!(" add " d!() ", rax"),
Q!(" adc " "rdx, 0"),
// Subtract to get x' - q * (n_25519 - 2^252) = x - q * n_25519
Q!(" sub " m0!() ", rbp"),
Q!(" sbb " m1!() ", " d!()),
Q!(" sbb " m2!() ", rdx"),
Q!(" sbb " m3!() ", 0"),
// Get a bitmask for the borrow and create a masked version of
// non-trivial digits of [rbx;0;rdx;rax] = n_25519, then add it.
// The masked n3 digit exploits the fact that bit 60 of n0 is set.
Q!(" sbb " "rbx, rbx"),
Q!(" mov " "rax, 0x5812631a5cf5d3ed"),
Q!(" and " "rax, rbx"),
Q!(" mov " "rdx, 0x14def9dea2f79cd6"),
Q!(" and " "rdx, rbx"),
Q!(" mov " "rbx, 0x1000000000000000"),
Q!(" and " "rbx, rax"),
Q!(" add " m0!() ", rax"),
Q!(" adc " m1!() ", rdx"),
Q!(" adc " m2!() ", 0"),
Q!(" adc " m3!() ", rbx"),
// 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!(" test " k!() ", " k!()),
Q!(" jz " 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!(" mov " q!() ", " m3!()),
Q!(" shld " q!() ", " m2!() ", 4"),
Q!(" shr " m3!() ", 60"),
Q!(" sub " q!() ", " m3!()),
Q!(" shl " m2!() ", 4"),
Q!(" shrd " m2!() ", " m3!() ", 4"),
// Let [rdx;m3;rbp] = q * (n_25519 - 2^252)
Q!(" mov " "rax, 0x5812631a5cf5d3ed"),
Q!(" mul " q!()),
Q!(" mov " "rbp, rax"),
Q!(" mov " m3!() ", rdx"),
Q!(" mov " "rax, 0x14def9dea2f79cd6"),
Q!(" mul " q!()),
Q!(" add " m3!() ", rax"),
Q!(" adc " "rdx, 0"),
// Load the next digit
Q!(" mov " d!() ", [" x!() "+ 8 * " k!() "-8]"),
// Subtract to get x' - q * (n_25519 - 2^252) = x - q * n_25519
Q!(" sub " d!() ", rbp"),
Q!(" sbb " m0!() ", " m3!()),
Q!(" sbb " m1!() ", rdx"),
Q!(" sbb " m2!() ", 0"),
// Get a bitmask for the borrow and create a masked version of
// non-trivial digits of [rbx;0;rdx;rax] = n_25519, then add it.
// The masked n3 digit exploits the fact that bit 60 of n0 is set.
Q!(" sbb " "rbx, rbx"),
Q!(" mov " "rax, 0x5812631a5cf5d3ed"),
Q!(" and " "rax, rbx"),
Q!(" mov " "rdx, 0x14def9dea2f79cd6"),
Q!(" and " "rdx, rbx"),
Q!(" mov " "rbx, 0x1000000000000000"),
Q!(" and " "rbx, rax"),
Q!(" add " d!() ", rax"),
Q!(" adc " m0!() ", rdx"),
Q!(" adc " m1!() ", 0"),
Q!(" adc " m2!() ", rbx"),
// Now shuffle registers up and loop
Q!(" mov " m3!() ", " m2!()),
Q!(" mov " m2!() ", " m1!()),
Q!(" mov " m1!() ", " m0!()),
Q!(" mov " m0!() ", " d!()),
Q!(" dec " k!()),
Q!(" jnz " Label!("bignum_mod_n25519_loop", 4, Before)),
// Write back
Q!(Label!("bignum_mod_n25519_writeback", 3) ":"),
Q!(" mov " "[" z!() "], " m0!()),
Q!(" mov " "[" z!() "+ 8], " m1!()),
Q!(" mov " "[" z!() "+ 16], " m2!()),
Q!(" mov " "[" z!() "+ 24], " m3!()),
// Restore registers and return
Q!(" pop " "r12"),
Q!(" pop " "rbp"),
Q!(" pop " "rbx"),
// linear hoisting in -> jmp after bignum_mod_n25519_shortinput
Q!(" jmp " Label!("hoist_finish", 5, After)),
Q!(Label!("bignum_mod_n25519_shortinput", 2) ":"),
Q!(" xor " m0!() ", " m0!()),
Q!(" xor " m1!() ", " m1!()),
Q!(" xor " m2!() ", " m2!()),
Q!(" xor " m3!() ", " m3!()),
Q!(" test " k!() ", " k!()),
Q!(" jz " Label!("bignum_mod_n25519_writeback", 3, Before)),
Q!(" mov " m0!() ", [rdx]"),
Q!(" dec " k!()),
Q!(" jz " Label!("bignum_mod_n25519_writeback", 3, Before)),
Q!(" mov " m1!() ", [rdx + 8]"),
Q!(" dec " k!()),
Q!(" jz " Label!("bignum_mod_n25519_writeback", 3, Before)),
Q!(" mov " m2!() ", [rdx + 16]"),
Q!(" jmp " Label!("bignum_mod_n25519_writeback", 3, Before)),
Q!(Label!("hoist_finish", 5) ":"),
inout("rdi") z.as_mut_ptr() => _,
inout("rsi") x.len() => _,
inout("rdx") x.as_ptr() => _,
// clobbers
out("r10") _,
out("r11") _,
out("r12") _,
out("r8") _,
out("r9") _,
out("rax") _,
out("rcx") _,
)
};
}