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curve25519-dalek-source/src/backend/avx2/field.rs
Henry de Valence bf5e3581d2 Update AVX2 docs
2017-12-04 10:37:37 -08:00

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// -*- mode: rust; coding: utf-8; -*-
//
// This file is part of curve25519-dalek.
// Copyright (c) 2016-2017 Isis Lovecruft, Henry de Valence
// See LICENSE for licensing information.
//
// Authors:
// - Isis Agora Lovecruft <isis@patternsinthevoid.net>
// - Henry de Valence <hdevalence@hdevalence.ca>
//! 4-way vectorized 32bit field arithmetic using AVX2.
//!
#![allow(bad_style)]
use std::ops::Mul;
use stdsimd::simd::{u32x8, i32x8, u64x4};
use backend::u64::field::FieldElement64;
pub(crate) static P_TIMES_2: FieldElement32x4 = FieldElement32x4([
u32x8::new(134217690, 134217690, 67108862, 67108862, 134217690, 134217690, 67108862, 67108862),
u32x8::new(134217726, 134217726, 67108862, 67108862, 134217726, 134217726, 67108862, 67108862),
u32x8::new(134217726, 134217726, 67108862, 67108862, 134217726, 134217726, 67108862, 67108862),
u32x8::new(134217726, 134217726, 67108862, 67108862, 134217726, 134217726, 67108862, 67108862),
u32x8::new(134217726, 134217726, 67108862, 67108862, 134217726, 134217726, 67108862, 67108862)
]);
/// A vector of four `FieldElements`, implemented using AVX2.
#[derive(Clone, Copy, Debug)]
pub(crate) struct FieldElement32x4(pub(crate) [u32x8; 5]);
use subtle::ConditionallyAssignable;
impl ConditionallyAssignable for FieldElement32x4 {
fn conditional_assign(&mut self, other: &FieldElement32x4, choice: u8) {
let mask = (-(choice as i32)) as u32;
let mask_vec = u32x8::splat(mask);
for i in 0..5 {
self.0[i] = self.0[i] ^ (mask_vec & (self.0[i] ^ other.0[i]));
}
}
}
impl FieldElement32x4 {
pub(crate) fn split(&self) -> [FieldElement64; 4] {
let mut out = [FieldElement64::zero(); 4];
for i in 0..5 {
let a_2i = self.0[i].extract(0) as u64; //
let b_2i = self.0[i].extract(1) as u64; //
let a_2i_1 = self.0[i].extract(2) as u64; // `.
let b_2i_1 = self.0[i].extract(3) as u64; // | pre-swapped to avoid
let c_2i = self.0[i].extract(4) as u64; // | a cross lane shuffle
let d_2i = self.0[i].extract(5) as u64; // .'
let c_2i_1 = self.0[i].extract(6) as u64; //
let d_2i_1 = self.0[i].extract(7) as u64; //
out[0].0[i] = a_2i + (a_2i_1 << 26);
out[1].0[i] = b_2i + (b_2i_1 << 26);
out[2].0[i] = c_2i + (c_2i_1 << 26);
out[3].0[i] = d_2i + (d_2i_1 << 26);
}
out
}
pub fn zero() -> FieldElement32x4 {
FieldElement32x4([u32x8::splat(0);5])
}
pub fn splat(x: &FieldElement64) -> FieldElement32x4 {
FieldElement32x4::new(x,x,x,x)
}
pub fn new(
x0: &FieldElement64,
x1: &FieldElement64,
x2: &FieldElement64,
x3: &FieldElement64,
) -> FieldElement32x4 {
let mut buf = [u32x8::splat(0); 5];
let low_26_bits = (1 << 26) - 1;
for i in 0..5 {
let a_2i = (x0.0[i] & low_26_bits) as u32;
let a_2i_1 = (x0.0[i] >> 26) as u32;
let b_2i = (x1.0[i] & low_26_bits) as u32;
let b_2i_1 = (x1.0[i] >> 26) as u32;
let c_2i = (x2.0[i] & low_26_bits) as u32;
let c_2i_1 = (x2.0[i] >> 26) as u32;
let d_2i = (x3.0[i] & low_26_bits) as u32;
let d_2i_1 = (x3.0[i] >> 26) as u32;
buf[i] = u32x8::new(a_2i, b_2i, a_2i_1, b_2i_1, c_2i, d_2i, c_2i_1, d_2i_1);
}
let mut out = FieldElement32x4(buf);
out.reduce32();
return out;
}
/// Negate variables in lanes where mask is set
/// XXX fix up api
pub fn mask_negate(&mut self, mask: u8) {
unsafe {
use stdsimd::vendor::_mm256_blend_epi32;
for i in 0..5 {
let negated = P_TIMES_2.0[i] - self.0[i];
self.0[i] = _mm256_blend_epi32(self.0[i].into(), negated.into(), mask as i32).into();
}
}
self.reduce32();
}
/// Given `self = (A,B,C,D)`, set `self = (A,B,D,C)`
pub fn swap_CD(&mut self) {
unsafe {
use stdsimd::vendor::_mm256_shuffle_epi32;
use stdsimd::vendor::_mm256_blend_epi32;
for i in 0..5 {
let swapped = _mm256_shuffle_epi32(self.0[i].into(), 0b10_11_00_01);
self.0[i] = _mm256_blend_epi32(self.0[i].into(), swapped, 0b11110000).into();
}
}
}
/// Given `self = (A,B,C,D)`, set `self = (B - A, B + A, D - C, D + C)`.
pub fn diff_sum(&mut self) {
/// (v0 v1 v2 v3 v4 v5 v6 v7) -> (v1 v0 v3 v2 v5 v4 v7 v6)
#[inline(always)]
fn alternate_32bit_lanes(v: u32x8) -> u32x8 {
unsafe {
use stdsimd::vendor::_mm256_shuffle_epi32;
_mm256_shuffle_epi32(v.as_i32x8(), 0b10_11_00_01).as_u32x8()
}
}
/// (v0 XX v2 XX v4 XX v6 XX)
/// (XX v1 XX v3 XX v5 XX v7) -> (v0 v1 v2 v3 v4 v5 v6 v7)
#[inline(always)]
fn blend_alternating_32bit_lanes(v1: u32x8, v2: u32x8) -> u32x8 {
unsafe {
use stdsimd::vendor::_mm256_blend_epi32;
_mm256_blend_epi32(v1.into(), v2.into(), 0b10101010).as_u32x8()
}
}
for i in 0..5 {
let x = self.0[i];
let p = P_TIMES_2.0[i] ;
let x_shuf = alternate_32bit_lanes(x);
let diff = (x_shuf + p) - x;
let sum = x + x_shuf;
let diff_sum = blend_alternating_32bit_lanes(diff, sum);
self.0[i] = diff_sum;
}
}
// Given `self = (A,B,C,D)`, compute `(B + A, B - A, D + C, D - C)`.
pub fn sum_diff(&self) -> FieldElement32x4 {
/// (v0 v1 v2 v3 v4 v5 v6 v7) -> (v1 v0 v3 v2 v5 v4 v7 v6)
#[inline(always)]
#[allow(dead_code)] // XXX
fn alternate_32bit_lanes(v: u32x8) -> u32x8 {
unsafe {
use stdsimd::vendor::_mm256_shuffle_epi32;
_mm256_shuffle_epi32(v.as_i32x8(), 0b10_11_00_01).as_u32x8()
}
}
/// (v0 XX v2 XX v4 XX v6 XX)
/// (XX v1 XX v3 XX v5 XX v7) -> (v0 v1 v2 v3 v4 v5 v6 v7)
#[inline(always)]
#[allow(dead_code)] // XXX
fn blend_alternating_32bit_lanes(v1: u32x8, v2: u32x8) -> u32x8 {
unsafe {
use stdsimd::vendor::_mm256_blend_epi32;
_mm256_blend_epi32(v1.into(), v2.into(), 0b10101010).as_u32x8()
}
}
let mut out = [u32x8::splat(0); 5];
for i in 0..5 {
let x = self.0[i];
let p = P_TIMES_2.0[i];
let x_shuf = alternate_32bit_lanes(x);
let sum = x + x_shuf;
let diff = (x + p) - x_shuf;
let sum_diff = blend_alternating_32bit_lanes(sum, diff);
out[i] = sum_diff;
}
FieldElement32x4(out)
}
/// Let `self` \\(= (A, B, C, D) \\).
///
/// Compute
/// $$( 121666A, 121666B, 2\cdot 121666C, -2\cdot 121665 D).$$
pub fn scale_by_curve_constants(&mut self) {
let mut b = [u64x4::splat(0); 10];
let consts = u32x8::new(121666, 0, 121666, 0, 2*121666, 0, 2*121665, 0);
let low__p20 = u64x4::splat(0x3ffffed << 20);
let even_p20 = u64x4::splat(0x3ffffff << 20);
let odd__p20 = u64x4::splat(0x1ffffff << 20);
unsafe {
use stdsimd::vendor::_mm256_mul_epu32;
use stdsimd::vendor::_mm256_blend_epi32;
let (b0, b1) = unpack_pair(self.0[0]);
let b0 = _mm256_mul_epu32(b0, consts); // need a new binding since now
let b1 = _mm256_mul_epu32(b1, consts); // b0 has type u64x4
b[0] = _mm256_blend_epi32(b0.into(), (low__p20 - b0).into(), 0b11_00_00_00).into();
b[1] = _mm256_blend_epi32(b1.into(), (odd__p20 - b1).into(), 0b11_00_00_00).into();
let (b2, b3) = unpack_pair(self.0[1]);
let b2 = _mm256_mul_epu32(b2, consts);
let b3 = _mm256_mul_epu32(b3, consts);
b[2] = _mm256_blend_epi32(b2.into(), (even_p20 - b2).into(), 0b11_00_00_00).into();
b[3] = _mm256_blend_epi32(b3.into(), (odd__p20 - b3).into(), 0b11_00_00_00).into();
let (b4, b5) = unpack_pair(self.0[2]);
let b4 = _mm256_mul_epu32(b4, consts);
let b5 = _mm256_mul_epu32(b5, consts);
b[4] = _mm256_blend_epi32(b4.into(), (even_p20 - b4).into(), 0b11_00_00_00).into();
b[5] = _mm256_blend_epi32(b5.into(), (odd__p20 - b5).into(), 0b11_00_00_00).into();
let (b6, b7) = unpack_pair(self.0[3]);
let b6 = _mm256_mul_epu32(b6, consts);
let b7 = _mm256_mul_epu32(b7, consts);
b[6] = _mm256_blend_epi32(b6.into(), (even_p20 - b6).into(), 0b11_00_00_00).into();
b[7] = _mm256_blend_epi32(b7.into(), (odd__p20 - b7).into(), 0b11_00_00_00).into();
let (b8, b9) = unpack_pair(self.0[4]);
let b8 = _mm256_mul_epu32(b8, consts);
let b9 = _mm256_mul_epu32(b9, consts);
b[8] = _mm256_blend_epi32(b8.into(), (even_p20 - b8).into(), 0b11_00_00_00).into();
b[9] = _mm256_blend_epi32(b9.into(), (odd__p20 - b9).into(), 0b11_00_00_00).into();
}
*self = FieldElement32x4::reduce64(b);
}
pub fn reduce32(&mut self) {
let shifts = i32x8::new(26,26,25,25,26,26,25,25);
let masks = u32x8::new((1<<26)-1, (1<<26)-1, (1<<25)-1, (1<<25)-1,
(1<<26)-1, (1<<26)-1, (1<<25)-1, (1<<25)-1);
let carry = |v: u32x8| -> u32x8 {
unsafe {
use stdsimd::vendor::_mm256_srlv_epi32;
_mm256_srlv_epi32(v.into(), shifts).into()
}
};
let swap_lanes = |v: u32x8| -> u32x8 {
unsafe {
use stdsimd::vendor::_mm256_shuffle_epi32;
_mm256_shuffle_epi32(v.into(), 0b01_00_11_10).into()
}
};
let combine = |v_lo: u32x8, v_hi: u32x8| -> u32x8 {
unsafe {
use stdsimd::vendor::_mm256_blend_epi32;
_mm256_blend_epi32(v_lo.into(), v_hi.into(), 0b11_00_11_00).into()
}
};
let v = &mut self.0;
let c10 = swap_lanes(carry(v[0]));
v[0] = (v[0] & masks) + combine(u32x8::splat(0), c10);
let c32 = swap_lanes(carry(v[1]));
v[1] = (v[1] & masks) + combine(c10, c32);
let c54 = swap_lanes(carry(v[2]));
v[2] = (v[2] & masks) + combine(c32, c54);
let c76 = swap_lanes(carry(v[3]));
v[3] = (v[3] & masks) + combine(c54, c76);
let c98 = swap_lanes(carry(v[4]));
v[4] = (v[4] & masks) + combine(c76, c98);
// Still need to account for c9
// c98 = (c9, c9, c8, c8, c9, c9, c8, c8)
//
let c9_19: u32x8;
unsafe {
use stdsimd::vendor::_mm256_mul_epu32;
use stdsimd::vendor::_mm256_shuffle_epi32;
let c9_spread: u32x8 = _mm256_shuffle_epi32(c98.into(), 0b11_01_10_00).into();
let c9_19_spread: u32x8 = _mm256_mul_epu32(c9_spread, u64x4::splat(19).into()).into();
c9_19 = _mm256_shuffle_epi32(c9_19_spread.into(), 0b11_01_10_00).into();
}
v[0] = v[0] + c9_19;
}
pub fn reduce64(mut z: [u64x4; 10]) -> FieldElement32x4 {
// These aren't const because splat isn't a const fn
let LOW_25_BITS: u64x4 = u64x4::splat((1<<25)-1);
let LOW_26_BITS: u64x4 = u64x4::splat((1<<26)-1);
/// XXX check whether u64x4 >> is this already
#[inline(always)]
fn shift_right(x: u64x4, s: i32) -> u64x4 {
unsafe {
use stdsimd::vendor::_mm256_srli_epi64;
_mm256_srli_epi64(x.into(), s).as_u64x4()
}
}
// Carry the value from limb i = 0..8 to limb i+1
let carry = |z: &mut [u64x4; 10], i: usize| {
debug_assert!(i < 9);
if i % 2 == 0 {
// Even limbs have 26 bits
z[i+1] = z[i+1] + shift_right(z[i], 26);
z[i] = z[i] & LOW_26_BITS;
} else {
// Odd limbs have 25 bits
z[i+1] = z[i+1] + shift_right(z[i], 25);
z[i] = z[i] & LOW_25_BITS;
}
};
// Perform two halves of the carry chain in parallel.
carry(&mut z, 0); carry(&mut z, 4);
carry(&mut z, 1); carry(&mut z, 5);
carry(&mut z, 2); carry(&mut z, 6);
carry(&mut z, 3); carry(&mut z, 7);
// Since z[3] < 2^64, c < 2^(64-25) = 2^39,
// so z[4] < 2^26 + 2^39 < 2^39.0002
carry(&mut z, 4); carry(&mut z, 8);
// Now z[4] < 2^26
// and z[5] < 2^25 + 2^13.0002 < 2^25.0004 (good enough)
// Last carry has a multiplication by 19. In the serial case we
// do a 64-bit multiplication by 19, but here we want to do a
// 32-bit multiplication. However, if we only know z[9] < 2^64,
// the carry is bounded as c < 2^(64-25) = 2^39, which is too
// big. To ensure c < 2^32, we would need z[9] < 2^57.
// Instead, we split the carry in two, with c = c_0 + c_1*2^26.
let c = shift_right(z[9], 25);
z[9] = z[9] & LOW_25_BITS;
let mut c0 = c & LOW_26_BITS; // c0 < 2^26;
let mut c1 = shift_right(c, 26); // c1 < 2^(39-26) = 2^13;
unsafe {
use stdsimd::vendor::_mm256_mul_epu32;
let x19 = u32x8::from(u64x4::splat(19));
c0 = _mm256_mul_epu32(u32x8::from(c0), x19); // c0 < 2^30.25
c1 = _mm256_mul_epu32(u32x8::from(c1), x19); // c1 < 2^17.25
}
z[0] = z[0] + c0; // z0 < 2^26 + 2^30.25 < 2^30.33
z[1] = z[1] + c1; // z1 < 2^25 + 2^17.25 < 2^25.0067
carry(&mut z, 0); // z0 < 2^26, z1 < 2^25.0067 + 2^4.33 = 2^25.007
// Now repack the [u64x4; 10] into a FieldElement32x4
FieldElement32x4([
repack_pair(z[0].into(), z[1].into()),
repack_pair(z[2].into(), z[3].into()),
repack_pair(z[4].into(), z[5].into()),
repack_pair(z[6].into(), z[7].into()),
repack_pair(z[8].into(), z[9].into()),
])
}
}
#[inline(always)]
pub fn unpack_pair(src: u32x8) -> (u32x8, u32x8) {
let a: u32x8;
let b: u32x8;
let zero = i32x8::new(0,0,0,0,0,0,0,0);
unsafe {
use stdsimd::vendor::_mm256_unpackhi_epi32;
use stdsimd::vendor::_mm256_unpacklo_epi32;
a = _mm256_unpacklo_epi32(src.as_i32x8(), zero).as_u32x8();
b = _mm256_unpackhi_epi32(src.as_i32x8(), zero).as_u32x8();
}
(a,b)
}
#[inline(always)]
pub fn repack_pair(x: u32x8, y: u32x8) -> u32x8 {
unsafe {
use stdsimd::vendor::_mm256_shuffle_epi32;
use stdsimd::vendor::_mm256_blend_epi32;
// Input: x = (a0, 0, b0, 0, c0, 0, d0)
// Input: y = (a1, 0, b1, 0, c1, 0, d1)
let x_shuffled = _mm256_shuffle_epi32(x.into(), 0b11_01_10_00);
let y_shuffled = _mm256_shuffle_epi32(y.into(), 0b10_00_11_01);
// x' = (a0, b0, 0, 0, c0, d0, 0, 0)
// y' = ( 0, 0, a1, b1, 0, 0, c1, d1)
return _mm256_blend_epi32(x_shuffled, y_shuffled, 0b11001100).as_u32x8();
}
}
impl FieldElement32x4 {
pub fn square(&self) -> FieldElement32x4 {
#[inline(always)]
fn m(x: u32x8, y: u32x8) -> u64x4 {
use stdsimd::vendor::_mm256_mul_epu32;
unsafe { _mm256_mul_epu32(x,y) }
}
#[inline(always)]
fn m_lo(x: u32x8, y: u32x8) -> u32x8 {
use stdsimd::vendor::_mm256_mul_epu32;
unsafe { u32x8::from(_mm256_mul_epu32(x,y)) }
}
let v19 = u32x8::new(19,0,19,0,19,0,19,0);
let (x0, x1) = unpack_pair(self.0[0]);
let (x2, x3) = unpack_pair(self.0[1]);
let (x4, x5) = unpack_pair(self.0[2]);
let (x6, x7) = unpack_pair(self.0[3]);
let (x8, x9) = unpack_pair(self.0[4]);
let x0_2 = x0 << 1;
let x1_2 = x1 << 1;
let x2_2 = x2 << 1;
let x3_2 = x3 << 1;
let x4_2 = x4 << 1;
let x5_2 = x5 << 1;
let x6_2 = x6 << 1;
let x7_2 = x7 << 1;
let x5_19 = m_lo(v19, x5);
let x6_19 = m_lo(v19, x6);
let x7_19 = m_lo(v19, x7);
let x8_19 = m_lo(v19, x8);
let x9_19 = m_lo(v19, x9);
let z0 = m(x0, x0) + m(x2_2,x8_19) + m(x4_2,x6_19) + ((m(x1_2,x9_19) + m(x3_2,x7_19) + m(x5,x5_19)) << 1);
let z1 = m(x0_2,x1) + m(x3_2,x8_19) + m(x5_2,x6_19) + ((m(x2,x9_19) + m(x4,x7_19)) << 1);
let z2 = m(x0_2,x2) + m(x1_2,x1) + m(x4_2,x8_19) + m(x6,x6_19) + ((m(x3_2,x9_19) + m(x5_2,x7_19)) << 1);
let z3 = m(x0_2,x3) + m(x1_2,x2) + m(x5_2,x8_19) + ((m(x4,x9_19) + m(x6,x7_19)) << 1);
let z4 = m(x0_2,x4) + m(x1_2,x3_2) + m(x2, x2) + m(x6_2,x8_19) + ((m(x5_2,x9_19) + m(x7,x7_19)) << 1);
let z5 = m(x0_2,x5) + m(x1_2,x4) + m(x2_2,x3) + m(x7_2,x8_19) + ((m(x6,x9_19)) << 1);
let z6 = m(x0_2,x6) + m(x1_2,x5_2) + m(x2_2,x4) + m(x3_2,x3) + m(x8,x8_19) + ((m(x7_2,x9_19)) << 1);
let z7 = m(x0_2,x7) + m(x1_2,x6) + m(x2_2,x5) + m(x3_2,x4) + ((m(x8,x9_19)) << 1);
let z8 = m(x0_2,x8) + m(x1_2,x7_2) + m(x2_2,x6) + m(x3_2,x5_2) + m(x4,x4) + ((m(x9,x9_19)) << 1);
let z9 = m(x0_2,x9) + m(x1_2,x8) + m(x2_2,x7) + m(x3_2,x6) + m(x4_2,x5);
FieldElement32x4::reduce64([z0, z1, z2, z3, z4, z5, z6, z7, z8, z9])
}
}
impl<'a, 'b> Mul<&'b FieldElement32x4> for &'a FieldElement32x4 {
type Output = FieldElement32x4;
fn mul(self, _rhs: &'b FieldElement32x4) -> FieldElement32x4 {
#[inline(always)]
fn m(x: u32x8, y: u32x8) -> u64x4 {
use stdsimd::vendor::_mm256_mul_epu32;
unsafe { _mm256_mul_epu32(x,y) }
}
#[inline(always)]
fn m_lo(x: u32x8, y: u32x8) -> u32x8 {
use stdsimd::vendor::_mm256_mul_epu32;
unsafe { u32x8::from(_mm256_mul_epu32(x,y)) }
}
let (x0, x1) = unpack_pair(self.0[0]);
let (x2, x3) = unpack_pair(self.0[1]);
let (x4, x5) = unpack_pair(self.0[2]);
let (x6, x7) = unpack_pair(self.0[3]);
let (x8, x9) = unpack_pair(self.0[4]);
let (y0, y1) = unpack_pair(_rhs.0[0]);
let (y2, y3) = unpack_pair(_rhs.0[1]);
let (y4, y5) = unpack_pair(_rhs.0[2]);
let (y6, y7) = unpack_pair(_rhs.0[3]);
let (y8, y9) = unpack_pair(_rhs.0[4]);
let v19 = u32x8::new(19,0,19,0,19,0,19,0);
let y1_19 = m_lo(v19, y1); // This fits in a u32
let y2_19 = m_lo(v19, y2); // iff 26 + b + lg(19) < 32
let y3_19 = m_lo(v19, y3); // if b < 32 - 26 - 4.248 = 1.752
let y4_19 = m_lo(v19, y4);
let y5_19 = m_lo(v19, y5); // below, b<2.5: this is a bottleneck,
let y6_19 = m_lo(v19, y6); // could be avoided by promoting to
let y7_19 = m_lo(v19, y7); // u64 here instead of in m()
let y8_19 = m_lo(v19, y8);
let y9_19 = m_lo(v19, y9);
let x1_2 = x1 + x1; // This fits in a u32 iff 25 + b + 1 < 32
let x3_2 = x3 + x3; // iff b < 6
let x5_2 = x5 + x5;
let x7_2 = x7 + x7;
let x9_2 = x9 + x9;
let z0 = m(x0,y0) + m(x1_2,y9_19) + m(x2,y8_19) + m(x3_2,y7_19) + m(x4,y6_19) + m(x5_2,y5_19) + m(x6,y4_19) + m(x7_2,y3_19) + m(x8,y2_19) + m(x9_2,y1_19);
let z1 = m(x0,y1) + m(x1,y0) + m(x2,y9_19) + m(x3,y8_19) + m(x4,y7_19) + m(x5,y6_19) + m(x6,y5_19) + m(x7,y4_19) + m(x8,y3_19) + m(x9,y2_19);
let z2 = m(x0,y2) + m(x1_2,y1) + m(x2,y0) + m(x3_2,y9_19) + m(x4,y8_19) + m(x5_2,y7_19) + m(x6,y6_19) + m(x7_2,y5_19) + m(x8,y4_19) + m(x9_2,y3_19);
let z3 = m(x0,y3) + m(x1,y2) + m(x2,y1) + m(x3,y0) + m(x4,y9_19) + m(x5,y8_19) + m(x6,y7_19) + m(x7,y6_19) + m(x8,y5_19) + m(x9,y4_19);
let z4 = m(x0,y4) + m(x1_2,y3) + m(x2,y2) + m(x3_2,y1) + m(x4,y0) + m(x5_2,y9_19) + m(x6,y8_19) + m(x7_2,y7_19) + m(x8,y6_19) + m(x9_2,y5_19);
let z5 = m(x0,y5) + m(x1,y4) + m(x2,y3) + m(x3,y2) + m(x4,y1) + m(x5,y0) + m(x6,y9_19) + m(x7,y8_19) + m(x8,y7_19) + m(x9,y6_19);
let z6 = m(x0,y6) + m(x1_2,y5) + m(x2,y4) + m(x3_2,y3) + m(x4,y2) + m(x5_2,y1) + m(x6,y0) + m(x7_2,y9_19) + m(x8,y8_19) + m(x9_2,y7_19);
let z7 = m(x0,y7) + m(x1,y6) + m(x2,y5) + m(x3,y4) + m(x4,y3) + m(x5,y2) + m(x6,y1) + m(x7,y0) + m(x8,y9_19) + m(x9,y8_19);
let z8 = m(x0,y8) + m(x1_2,y7) + m(x2,y6) + m(x3_2,y5) + m(x4,y4) + m(x5_2,y3) + m(x6,y2) + m(x7_2,y1) + m(x8,y0) + m(x9_2,y9_19);
let z9 = m(x0,y9) + m(x1,y8) + m(x2,y7) + m(x3,y6) + m(x4,y5) + m(x5,y4) + m(x6,y3) + m(x7,y2) + m(x8,y1) + m(x9,y0);
FieldElement32x4::reduce64([z0, z1, z2, z3, z4, z5, z6, z7, z8, z9])
}
}
#[cfg(test)]
mod test {
use super::*;
#[test]
fn scale_by_curve_constants() {
let mut x = FieldElement32x4::splat(&FieldElement64::one());
x.scale_by_curve_constants();
let xs = x.split();
assert_eq!(xs[0], FieldElement64([ 121666,0,0,0,0]));
assert_eq!(xs[1], FieldElement64([ 121666,0,0,0,0]));
assert_eq!(xs[2], FieldElement64([2*121666,0,0,0,0]));
assert_eq!(xs[3], -&FieldElement64([2*121665,0,0,0,0]));
}
#[test]
fn diff_sum_vs_serial() {
let x0 = FieldElement64([10000, 10001, 10002, 10003, 10004]);
let x1 = FieldElement64([10100, 10101, 10102, 10103, 10104]);
let x2 = FieldElement64([10200, 10201, 10202, 10203, 10204]);
let x3 = FieldElement64([10300, 10301, 10302, 10303, 10304]);
let mut vec = FieldElement32x4::new(&x0, &x1, &x2, &x3);
vec.diff_sum();
let result = vec.split();
assert_eq!(result[0], &x1 - &x0);
assert_eq!(result[1], &x1 + &x0);
assert_eq!(result[2], &x3 - &x2);
assert_eq!(result[3], &x3 + &x2);
}
#[test]
fn square_vs_serial() {
let x0 = FieldElement64([10000, 10001, 10002, 10003, 10004]);
let x1 = FieldElement64([10100, 10101, 10102, 10103, 10104]);
let x2 = FieldElement64([10200, 10201, 10202, 10203, 10204]);
let x3 = FieldElement64([10300, 10301, 10302, 10303, 10304]);
let vec = FieldElement32x4::new(&x0, &x1, &x2, &x3);
let result = vec.square().split();
assert_eq!(result[0], &x0 * &x0);
assert_eq!(result[1], &x1 * &x1);
assert_eq!(result[2], &x2 * &x2);
assert_eq!(result[3], &x3 * &x3);
}
#[test]
fn multiply_vs_serial() {
let x0 = FieldElement64([10000, 10001, 10002, 10003, 10004]);
let x1 = FieldElement64([10100, 10101, 10102, 10103, 10104]);
let x2 = FieldElement64([10200, 10201, 10202, 10203, 10204]);
let x3 = FieldElement64([10300, 10301, 10302, 10303, 10304]);
let vec = FieldElement32x4::new(&x0, &x1, &x2, &x3);
let vecprime = vec.clone();
let result = (&vec * &vecprime).split();
assert_eq!(result[0], &x0 * &x0);
assert_eq!(result[1], &x1 * &x1);
assert_eq!(result[2], &x2 * &x2);
assert_eq!(result[3], &x3 * &x3);
}
#[test]
fn test_unpack_repack_pair() {
let x0 = FieldElement64([10000 + (10001 << 26), 0, 0, 0, 0]);
let x1 = FieldElement64([10100 + (10101 << 26), 0, 0, 0, 0]);
let x2 = FieldElement64([10200 + (10201 << 26), 0, 0, 0, 0]);
let x3 = FieldElement64([10300 + (10301 << 26), 0, 0, 0, 0]);
let vec = FieldElement32x4::new(&x0, &x1, &x2, &x3);
let src = vec.0[0];
let (a,b) = unpack_pair(src);
let expected_a = u32x8::new(10000, 0, 10100, 0, 10200, 0, 10300, 0);
let expected_b = u32x8::new(10001, 0, 10101, 0, 10201, 0, 10301, 0);
assert_eq!(a, expected_a);
assert_eq!(b, expected_b);
let expected_src = repack_pair(a,b);
assert_eq!(src, expected_src);
}
#[test]
fn new_split_roundtrips() {
let x0 = FieldElement64::from_bytes(&[0x10; 32]);
let x1 = FieldElement64::from_bytes(&[0x11; 32]);
let x2 = FieldElement64::from_bytes(&[0x12; 32]);
let x3 = FieldElement64::from_bytes(&[0x13; 32]);
let vec = FieldElement32x4::new(&x0, &x1, &x2, &x3);
let splits = vec.split();
assert_eq!(x0, splits[0]);
assert_eq!(x1, splits[1]);
assert_eq!(x2, splits[2]);
assert_eq!(x3, splits[3]);
}
}
#[cfg(all(test, feature = "bench"))]
mod bench {
use test::Bencher;
use super::*;
#[bench]
fn multiply(b: &mut Bencher) {
let vec = FieldElement32x4::splat(&FieldElement64::zero());
let vecprime = vec.clone();
b.iter(|| &vec * &vecprime );
}
}
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