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fmt

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This commit is contained in:
Jean-Philippe Bossuat
2025-01-08 11:07:04 +01:00
parent bdd57b91ed
commit 160e7a33da
9 changed files with 383 additions and 207 deletions
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14
math/src/lib.rs
View File

@@ -3,10 +3,10 @@
pub mod dft;
pub mod modulus;
pub mod num_bigint;
pub mod poly;
pub mod ring;
pub mod scalar;
pub mod num_bigint;
pub const CHUNK: usize = 8;
@@ -333,11 +333,7 @@ pub mod macros {
match CHUNK {
8 => {
izip!(
$a.chunks_exact(8),
$d.chunks_exact_mut(8)
)
.for_each(|(a, d)| {
izip!($a.chunks_exact(8), $d.chunks_exact_mut(8)).for_each(|(a, d)| {
$f(&$self, &a[0], $b, $c, &mut d[0]);
$f(&$self, &a[1], $b, $c, &mut d[1]);
$f(&$self, &a[2], $b, $c, &mut d[2]);
@@ -349,11 +345,9 @@ pub mod macros {
});
let m = n - (n & 7);
izip!($a[m..].iter(), $d[m..].iter_mut()).for_each(
|(a, d)| {
izip!($a[m..].iter(), $d[m..].iter_mut()).for_each(|(a, d)| {
$f(&$self, a, $b, $c, d);
},
);
});
}
_ => {
izip!($a.iter(), $d.iter_mut()).for_each(|(a, d)| {

54
math/src/modulus.rs
View File

@@ -74,7 +74,12 @@ pub trait ScalarOperations<O> {
fn sa_add_sb_into_sb<const REDUCE: REDUCEMOD>(&self, a: &O, b: &mut O);
// Assigns a - b to c.
fn sa_sub_sb_into_sc<const SBRANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &O, b: &O, c: &mut O);
fn sa_sub_sb_into_sc<const SBRANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &O,
b: &O,
c: &mut O,
);
// Assigns a - b to b.
fn sa_sub_sb_into_sb<const SARANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &O, b: &mut O);
@@ -147,7 +152,7 @@ pub trait ScalarOperations<O> {
&self,
b: &u64,
c: &barrett::Barrett<u64>,
a: &mut u64
a: &mut u64,
);
// Assigns (a + b) * c to d.
@@ -156,25 +161,25 @@ pub trait ScalarOperations<O> {
a: &u64,
b: &u64,
c: &barrett::Barrett<u64>,
d: &mut u64
d: &mut u64,
);
// Assigns (a - b + c) * d to e.
fn sb_sub_sa_add_sc_mul_sd_into_se<const SBRANGE: u8,const REDUCE: REDUCEMOD>(
fn sb_sub_sa_add_sc_mul_sd_into_se<const SBRANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &u64,
b: &u64,
c: &u64,
d: &barrett::Barrett<u64>,
e: &mut u64
e: &mut u64,
);
fn sb_sub_sa_add_sc_mul_sd_into_sa<const SBRANGE: u8,const REDUCE: REDUCEMOD>(
fn sb_sub_sa_add_sc_mul_sd_into_sa<const SBRANGE: u8, const REDUCE: REDUCEMOD>(
&self,
b: &u64,
c: &u64,
d: &barrett::Barrett<u64>,
a: &mut u64
a: &mut u64,
);
}
@@ -206,10 +211,18 @@ pub trait VectorOperations<O> {
fn va_add_sb_into_va<const CHUNK: usize, const REDUCE: REDUCEMOD>(&self, a: &O, b: &mut [O]);
// vec(b) <- vec(a) - vec(b).
fn va_sub_vb_into_vb<const CHUNK: usize, const VBRANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &[O], b: &mut [O]);
fn va_sub_vb_into_vb<const CHUNK: usize, const VBRANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &[O],
b: &mut [O],
);
// vec(a) <- vec(a) - vec(b).
fn va_sub_vb_into_va<const CHUNK: usize, const VBRANGE: u8, const REDUCE: REDUCEMOD>(&self, b: &[O], a: &mut [O]);
fn va_sub_vb_into_va<const CHUNK: usize, const VBRANGE: u8, const REDUCE: REDUCEMOD>(
&self,
b: &[O],
a: &mut [O],
);
// vec(c) <- vec(a) - vec(b).
fn va_sub_vb_into_vc<const CHUNK: usize, const VBRANGE: u8, const REDUCE: REDUCEMOD>(
@@ -220,10 +233,17 @@ pub trait VectorOperations<O> {
);
// vec(a) <- -vec(a).
fn va_neg_into_va<const CHUNK: usize, const VARANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &mut [O]);
fn va_neg_into_va<const CHUNK: usize, const VARANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &mut [O],
);
// vec(b) <- -vec(a).
fn va_neg_into_vb<const CHUNK: usize, const VARANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &[O], b: &mut [O]);
fn va_neg_into_vb<const CHUNK: usize, const VARANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &[O],
b: &mut [O],
);
// vec(b) <- vec(a)
fn va_prep_mont_into_vb<const CHUNK: usize, const REDUCE: REDUCEMOD>(
@@ -297,7 +317,11 @@ pub trait VectorOperations<O> {
);
// vec(e) <- (vec(b) - vec(a) + scalar(c)) * scalar(e).
fn vb_sub_va_add_sc_mul_sd_into_ve<const CHUNK: usize, const VBRANGE: u8, const REDUCE: REDUCEMOD>(
fn vb_sub_va_add_sc_mul_sd_into_ve<
const CHUNK: usize,
const VBRANGE: u8,
const REDUCE: REDUCEMOD,
>(
&self,
va: &[u64],
vb: &[u64],
@@ -307,7 +331,11 @@ pub trait VectorOperations<O> {
);
// vec(a) <- (vec(b) - vec(a) + scalar(c)) * scalar(e).
fn vb_sub_va_add_sc_mul_sd_into_va<const CHUNK: usize, const VBRANGE: u8, const REDUCE: REDUCEMOD>(
fn vb_sub_va_add_sc_mul_sd_into_va<
const CHUNK: usize,
const VBRANGE: u8,
const REDUCE: REDUCEMOD,
>(
&self,
vb: &[u64],
sc: &u64,

118
math/src/modulus/impl_u64/operations.rs
View File

@@ -1,9 +1,12 @@
use crate::modulus::barrett::Barrett;
use crate::modulus::montgomery::Montgomery;
use crate::modulus::prime::Prime;
use crate::modulus::{REDUCEMOD, NONE};
use crate::modulus::{ScalarOperations, VectorOperations};
use crate::{apply_sv, apply_svv, apply_v, apply_vsv, apply_vv, apply_vvsv, apply_vvv, apply_ssv, apply_vssv, apply_vvssv};
use crate::modulus::{NONE, REDUCEMOD};
use crate::{
apply_ssv, apply_sv, apply_svv, apply_v, apply_vssv, apply_vsv, apply_vv, apply_vvssv,
apply_vvsv, apply_vvv,
};
use itertools::izip;
impl ScalarOperations<u64> for Prime<u64> {
@@ -32,11 +35,16 @@ impl ScalarOperations<u64> for Prime<u64> {
}
#[inline(always)]
fn sa_sub_sb_into_sc<const SBRANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &u64, b: &u64, c: &mut u64) {
match SBRANGE{
1 =>{*c = *a + self.q - *b}
2 =>{*c = *a + self.two_q - *b}
4 =>{*c = *a + self.four_q - *b}
fn sa_sub_sb_into_sc<const SBRANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &u64,
b: &u64,
c: &mut u64,
) {
match SBRANGE {
1 => *c = *a + self.q - *b,
2 => *c = *a + self.two_q - *b,
4 => *c = *a + self.four_q - *b,
_ => unreachable!("invalid SBRANGE argument"),
}
self.sa_reduce_into_sa::<REDUCE>(c)
@@ -44,10 +52,10 @@ impl ScalarOperations<u64> for Prime<u64> {
#[inline(always)]
fn sa_sub_sb_into_sa<const SBRANGE: u8, const REDUCE: REDUCEMOD>(&self, b: &u64, a: &mut u64) {
match SBRANGE{
1 =>{*a = *a + self.q - *b}
2 =>{*a = *a + self.two_q - *b}
4 =>{*a = *a + self.four_q - *b}
match SBRANGE {
1 => *a = *a + self.q - *b,
2 => *a = *a + self.two_q - *b,
4 => *a = *a + self.four_q - *b,
_ => unreachable!("invalid SBRANGE argument"),
}
self.sa_reduce_into_sa::<REDUCE>(a)
@@ -55,10 +63,10 @@ impl ScalarOperations<u64> for Prime<u64> {
#[inline(always)]
fn sa_sub_sb_into_sb<const SBRANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &u64, b: &mut u64) {
match SBRANGE{
1 =>{*b = *a + self.q - *b}
2 =>{*b = *a + self.two_q - *b}
4 =>{*b = *a + self.four_q - *b}
match SBRANGE {
1 => *b = *a + self.q - *b,
2 => *b = *a + self.two_q - *b,
4 => *b = *a + self.four_q - *b,
_ => unreachable!("invalid SBRANGE argument"),
}
self.sa_reduce_into_sa::<REDUCE>(b)
@@ -66,10 +74,10 @@ impl ScalarOperations<u64> for Prime<u64> {
#[inline(always)]
fn sa_neg_into_sa<const SBRANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &mut u64) {
match SBRANGE{
1 =>{*a = self.q - *a}
2 =>{*a = self.two_q - *a}
4 =>{*a = self.four_q - *a}
match SBRANGE {
1 => *a = self.q - *a,
2 => *a = self.two_q - *a,
4 => *a = self.four_q - *a,
_ => unreachable!("invalid SBRANGE argument"),
}
self.sa_reduce_into_sa::<REDUCE>(a)
@@ -77,10 +85,10 @@ impl ScalarOperations<u64> for Prime<u64> {
#[inline(always)]
fn sa_neg_into_sb<const SBRANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &u64, b: &mut u64) {
match SBRANGE{
1 =>{*b = self.q - *a}
2 =>{*b = self.two_q - *a}
4 =>{*b = self.four_q - *a}
match SBRANGE {
1 => *b = self.q - *a,
2 => *b = self.two_q - *a,
4 => *b = self.four_q - *a,
_ => unreachable!("invalid SBRANGE argument"),
}
self.sa_reduce_into_sa::<REDUCE>(b)
@@ -129,10 +137,10 @@ impl ScalarOperations<u64> for Prime<u64> {
c: &Barrett<u64>,
d: &mut u64,
) {
match VBRANGE{
1 =>{*d = a + self.q - b}
2 =>{*d = a + self.two_q - b}
4 =>{*d = a + self.four_q - b}
match VBRANGE {
1 => *d = a + self.q - b,
2 => *d = a + self.two_q - b,
4 => *d = a + self.four_q - b,
_ => unreachable!("invalid SBRANGE argument"),
}
self.barrett.mul_external_assign::<REDUCE>(*c, d);
@@ -155,7 +163,7 @@ impl ScalarOperations<u64> for Prime<u64> {
a: &u64,
b: &u64,
c: &Barrett<u64>,
d: &mut u64
d: &mut u64,
) {
*d = self.barrett.mul_external::<REDUCE>(*c, *a + *b);
}
@@ -165,7 +173,7 @@ impl ScalarOperations<u64> for Prime<u64> {
&self,
b: &u64,
c: &Barrett<u64>,
a: &mut u64
a: &mut u64,
) {
*a = self.barrett.mul_external::<REDUCE>(*c, *a + *b);
}
@@ -177,7 +185,7 @@ impl ScalarOperations<u64> for Prime<u64> {
b: &u64,
c: &u64,
d: &Barrett<u64>,
e: &mut u64
e: &mut u64,
) {
self.sa_sub_sb_into_sc::<SBRANGE, NONE>(&(b + c), a, e);
self.barrett.mul_external_assign::<REDUCE>(*d, e);
@@ -189,12 +197,11 @@ impl ScalarOperations<u64> for Prime<u64> {
b: &u64,
c: &u64,
d: &Barrett<u64>,
a: &mut u64
a: &mut u64,
) {
self.sa_sub_sb_into_sb::<SBRANGE, NONE>(&(b + c), a);
self.barrett.mul_external_assign::<REDUCE>(*d, a);
}
}
impl VectorOperations<u64> for Prime<u64> {
@@ -255,7 +262,14 @@ impl VectorOperations<u64> for Prime<u64> {
b: &[u64],
c: &mut [u64],
) {
apply_vvv!(self, Self::sa_sub_sb_into_sc::<VBRANGE, REDUCE>, a, b, c, CHUNK);
apply_vvv!(
self,
Self::sa_sub_sb_into_sc::<VBRANGE, REDUCE>,
a,
b,
c,
CHUNK
);
}
#[inline(always)]
@@ -264,7 +278,13 @@ impl VectorOperations<u64> for Prime<u64> {
b: &[u64],
a: &mut [u64],
) {
apply_vv!(self, Self::sa_sub_sb_into_sa::<VBRANGE, REDUCE>, b, a, CHUNK);
apply_vv!(
self,
Self::sa_sub_sb_into_sa::<VBRANGE, REDUCE>,
b,
a,
CHUNK
);
}
#[inline(always)]
@@ -273,11 +293,20 @@ impl VectorOperations<u64> for Prime<u64> {
a: &[u64],
b: &mut [u64],
) {
apply_vv!(self, Self::sa_sub_sb_into_sb::<VBRANGE, REDUCE>, a, b, CHUNK);
apply_vv!(
self,
Self::sa_sub_sb_into_sb::<VBRANGE, REDUCE>,
a,
b,
CHUNK
);
}
#[inline(always)]
fn va_neg_into_va<const CHUNK: usize, const VARANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &mut [u64]) {
fn va_neg_into_va<const CHUNK: usize, const VARANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &mut [u64],
) {
apply_v!(self, Self::sa_neg_into_sa::<VARANGE, REDUCE>, a, CHUNK);
}
@@ -415,14 +444,18 @@ impl VectorOperations<u64> for Prime<u64> {
}
// vec(e) <- (vec(a) - vec(b) + scalar(c)) * scalar(e).
fn vb_sub_va_add_sc_mul_sd_into_ve<const CHUNK: usize, const VBRANGE: u8, const REDUCE: REDUCEMOD>(
fn vb_sub_va_add_sc_mul_sd_into_ve<
const CHUNK: usize,
const VBRANGE: u8,
const REDUCE: REDUCEMOD,
>(
&self,
va: &[u64],
vb: &[u64],
sc: &u64,
sd: &Barrett<u64>,
ve: &mut [u64],
){
) {
apply_vvssv!(
self,
Self::sb_sub_sa_add_sc_mul_sd_into_se::<VBRANGE, REDUCE>,
@@ -436,14 +469,17 @@ impl VectorOperations<u64> for Prime<u64> {
}
// vec(a) <- (vec(b) - vec(a) + scalar(c)) * scalar(e).
fn vb_sub_va_add_sc_mul_sd_into_va<const CHUNK: usize, const VBRANGE: u8, const REDUCE: REDUCEMOD>(
fn vb_sub_va_add_sc_mul_sd_into_va<
const CHUNK: usize,
const VBRANGE: u8,
const REDUCE: REDUCEMOD,
>(
&self,
vb: &[u64],
sc: &u64,
sd: &Barrett<u64>,
va: &mut [u64],
){
) {
apply_vssv!(
self,
Self::sb_sub_sa_add_sc_mul_sd_into_sa::<VBRANGE, REDUCE>,

28
math/src/num_bigint.rs
View File

@@ -1,34 +1,32 @@
use num_bigint::BigInt;
use num_bigint::Sign;
use num_integer::Integer;
use num_traits::{Zero, One, Signed};
use num_traits::{One, Signed, Zero};
pub trait Div{
pub trait Div {
fn div_floor(&self, other: &Self) -> Self;
fn div_round(&self, other: &Self) -> Self;
}
impl Div for BigInt{
fn div_floor(&self, other:&Self) -> Self{
impl Div for BigInt {
fn div_floor(&self, other: &Self) -> Self {
let quo: BigInt = self / other;
if self.sign() == Sign::Minus {
return quo - BigInt::one()
return quo - BigInt::one();
}
return quo
return quo;
}
fn div_round(&self, other:&Self) -> Self{
fn div_round(&self, other: &Self) -> Self {
let (quo, mut rem) = self.div_rem(other);
rem <<= 1;
if rem != BigInt::zero() && &rem.abs() > other{
if self.sign() == other.sign(){
return quo + BigInt::one()
}else{
return quo - BigInt::one()
if rem != BigInt::zero() && &rem.abs() > other {
if self.sign() == other.sign() {
return quo + BigInt::one();
} else {
return quo - BigInt::one();
}
}
return quo
return quo;
}
}

44
math/src/ring/impl_u64/rescaling_rns.rs
View File

@@ -1,5 +1,5 @@
use crate::modulus::barrett::Barrett;
use crate::modulus::{NONE, ONCE, BARRETT};
use crate::modulus::{BARRETT, NONE, ONCE};
use crate::poly::PolyRNS;
use crate::ring::Ring;
use crate::ring::RingRNS;
@@ -32,8 +32,7 @@ impl RingRNS<u64> {
let rescaling_constants: ScalarRNS<Barrett<u64>> = self.rescaling_constant();
let r_last: &Ring<u64> = &self.0[level];
if ROUND{
if ROUND {
let q_level_half: u64 = r_last.modulus.q >> 1;
let (buf_q_scaling, buf_qi_scaling) = buf.0.split_at_mut(1);
@@ -56,7 +55,11 @@ impl RingRNS<u64> {
);
}
} else {
r_last.a_add_b_scalar_into_c::<ONCE>(a.at(self.level()), &q_level_half, &mut buf_q_scaling[0]);
r_last.a_add_b_scalar_into_c::<ONCE>(
a.at(self.level()),
&q_level_half,
&mut buf_q_scaling[0],
);
for (i, r) in self.0[0..level].iter().enumerate() {
r_last.a_add_b_scalar_into_c::<NONE>(
&buf_q_scaling[0],
@@ -71,7 +74,7 @@ impl RingRNS<u64> {
);
}
}
}else{
} else {
if NTT {
let (buf_ntt_q_scaling, buf_ntt_qi_scaling) = buf.0.split_at_mut(1);
self.0[level].intt::<false>(a.at(level), &mut buf_ntt_q_scaling[0]);
@@ -115,8 +118,7 @@ impl RingRNS<u64> {
let rescaling_constants: ScalarRNS<Barrett<u64>> = self.rescaling_constant();
let r_last: &Ring<u64> = &self.0[level];
if ROUND{
if ROUND {
let q_level_half: u64 = r_last.modulus.q >> 1;
let (buf_q_scaling, buf_qi_scaling) = buf.0.split_at_mut(1);
@@ -148,8 +150,7 @@ impl RingRNS<u64> {
);
}
}
}else{
} else {
if NTT {
let (buf_ntt_q_scaling, buf_ntt_qi_scaling) = buf.0.split_at_mut(1);
r_last.intt::<false>(a.at(level), &mut buf_ntt_q_scaling[0]);
@@ -161,7 +162,7 @@ impl RingRNS<u64> {
a.at_mut(i),
);
}
}else{
} else {
let (a_i, a_level) = a.0.split_at_mut(level);
for (i, r) in self.0[0..level].iter().enumerate() {
r.b_sub_a_mul_c_scalar_barrett_into_a::<2, ONCE>(
@@ -172,7 +173,6 @@ impl RingRNS<u64> {
}
}
}
}
/// Updates b to floor(a / prod_{level - nb_moduli}^{level} q[i])
@@ -213,8 +213,7 @@ impl RingRNS<u64> {
c.copy(a);
}
} else {
if NTT{
if NTT {
self.intt::<false>(a, buf);
(0..nb_moduli).for_each(|i| {
self.at_level(self.level() - i)
@@ -224,24 +223,24 @@ impl RingRNS<u64> {
)
});
self.at_level(self.level() - nb_moduli).ntt::<false>(buf, c);
}else{
} else {
println!("{} {:?}", self.level(), buf.level());
self.div_by_last_modulus::<ROUND, false>(a, buf, c);
(1..nb_moduli-1).for_each(|i| {
(1..nb_moduli - 1).for_each(|i| {
println!("{} {:?}", self.level() - i, buf.level());
self.at_level(self.level() - i)
.div_by_last_modulus_inplace::<ROUND, false>(buf, c);
});
self.at_level(self.level()-nb_moduli+1).div_by_last_modulus_inplace::<ROUND, false>(buf, c);
self.at_level(self.level() - nb_moduli + 1)
.div_by_last_modulus_inplace::<ROUND, false>(buf, c);
}
}
}
/// Updates a to floor(a / prod_{level - nb_moduli}^{level} q[i])
pub fn div_by_last_moduli_inplace<const ROUND:bool, const NTT: bool>(
pub fn div_by_last_moduli_inplace<const ROUND: bool, const NTT: bool>(
&self,
nb_moduli: usize,
buf: &mut PolyRNS<u64>,
@@ -259,15 +258,18 @@ impl RingRNS<u64> {
nb_moduli,
a.level()
);
if nb_moduli == 0{
return
if nb_moduli == 0 {
return;
}
if NTT {
self.intt::<false>(a, buf);
(0..nb_moduli).for_each(|i| {
self.at_level(self.level() - i)
.div_by_last_modulus_inplace::<ROUND, false>(&mut PolyRNS::<u64>::default(), buf)
.div_by_last_modulus_inplace::<ROUND, false>(
&mut PolyRNS::<u64>::default(),
buf,
)
});
self.at_level(self.level() - nb_moduli).ntt::<false>(buf, a);
} else {

87
math/src/ring/impl_u64/ring.rs
View File

@@ -83,7 +83,12 @@ impl Ring<u64> {
}
#[inline(always)]
pub fn a_add_b_into_c<const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &Poly<u64>, c: &mut Poly<u64>) {
pub fn a_add_b_into_c<const REDUCE: REDUCEMOD>(
&self,
a: &Poly<u64>,
b: &Poly<u64>,
c: &mut Poly<u64>,
) {
debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
debug_assert!(b.n() == self.n(), "b.n()={} != n={}", b.n(), self.n());
debug_assert!(c.n() == self.n(), "c.n()={} != n={}", c.n(), self.n());
@@ -98,7 +103,12 @@ impl Ring<u64> {
}
#[inline(always)]
pub fn a_add_b_scalar_into_c<const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &u64, c: &mut Poly<u64>) {
pub fn a_add_b_scalar_into_c<const REDUCE: REDUCEMOD>(
&self,
a: &Poly<u64>,
b: &u64,
c: &mut Poly<u64>,
) {
debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
debug_assert!(c.n() == self.n(), "c.n()={} != n={}", c.n(), self.n());
self.modulus
@@ -106,13 +116,25 @@ impl Ring<u64> {
}
#[inline(always)]
pub fn a_add_scalar_b_mul_c_scalar_barrett_into_a<const REDUCE: REDUCEMOD>(&self, b: &u64, c: &Barrett<u64>, a: &mut Poly<u64>) {
pub fn a_add_scalar_b_mul_c_scalar_barrett_into_a<const REDUCE: REDUCEMOD>(
&self,
b: &u64,
c: &Barrett<u64>,
a: &mut Poly<u64>,
) {
debug_assert!(a.n() == self.n(), "b.n()={} != n={}", a.n(), self.n());
self.modulus.va_add_sb_mul_sc_into_va::<CHUNK, REDUCE>(b, c, &mut a.0);
self.modulus
.va_add_sb_mul_sc_into_va::<CHUNK, REDUCE>(b, c, &mut a.0);
}
#[inline(always)]
pub fn add_scalar_then_mul_scalar_barrett<const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &u64, c: &Barrett<u64>, d: &mut Poly<u64>) {
pub fn add_scalar_then_mul_scalar_barrett<const REDUCE: REDUCEMOD>(
&self,
a: &Poly<u64>,
b: &u64,
c: &Barrett<u64>,
d: &mut Poly<u64>,
) {
debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
debug_assert!(d.n() == self.n(), "c.n()={} != n={}", d.n(), self.n());
self.modulus
@@ -120,7 +142,11 @@ impl Ring<u64> {
}
#[inline(always)]
pub fn a_sub_b_into_b<const BRANGE:u8, const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &mut Poly<u64>) {
pub fn a_sub_b_into_b<const BRANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &Poly<u64>,
b: &mut Poly<u64>,
) {
debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
debug_assert!(b.n() == self.n(), "b.n()={} != n={}", b.n(), self.n());
self.modulus
@@ -128,7 +154,11 @@ impl Ring<u64> {
}
#[inline(always)]
pub fn a_sub_b_into_a<const BRANGE:u8, const REDUCE: REDUCEMOD>(&self, b: &Poly<u64>, a: &mut Poly<u64>) {
pub fn a_sub_b_into_a<const BRANGE: u8, const REDUCE: REDUCEMOD>(
&self,
b: &Poly<u64>,
a: &mut Poly<u64>,
) {
debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
debug_assert!(b.n() == self.n(), "b.n()={} != n={}", b.n(), self.n());
self.modulus
@@ -136,7 +166,12 @@ impl Ring<u64> {
}
#[inline(always)]
pub fn a_sub_b_into_c<const BRANGE:u8, const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &Poly<u64>, c: &mut Poly<u64>) {
pub fn a_sub_b_into_c<const BRANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &Poly<u64>,
b: &Poly<u64>,
c: &mut Poly<u64>,
) {
debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
debug_assert!(b.n() == self.n(), "b.n()={} != n={}", b.n(), self.n());
debug_assert!(c.n() == self.n(), "c.n()={} != n={}", c.n(), self.n());
@@ -145,16 +180,22 @@ impl Ring<u64> {
}
#[inline(always)]
pub fn a_neg_into_b<const ARANGE:u8, const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &mut Poly<u64>) {
pub fn a_neg_into_b<const ARANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &Poly<u64>,
b: &mut Poly<u64>,
) {
debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
debug_assert!(b.n() == self.n(), "b.n()={} != n={}", b.n(), self.n());
self.modulus.va_neg_into_vb::<CHUNK, ARANGE, REDUCE>(&a.0, &mut b.0);
self.modulus
.va_neg_into_vb::<CHUNK, ARANGE, REDUCE>(&a.0, &mut b.0);
}
#[inline(always)]
pub fn a_neg_into_a<const ARANGE:u8,const REDUCE: REDUCEMOD>(&self, a: &mut Poly<u64>) {
pub fn a_neg_into_a<const ARANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &mut Poly<u64>) {
debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
self.modulus.va_neg_into_va::<CHUNK, ARANGE, REDUCE>(&mut a.0);
self.modulus
.va_neg_into_va::<CHUNK, ARANGE, REDUCE>(&mut a.0);
}
#[inline(always)]
@@ -184,7 +225,12 @@ impl Ring<u64> {
}
#[inline(always)]
pub fn a_mul_b_scalar_into_c<const REDUCE: REDUCEMOD>(&self, a: &Poly<u64>, b: &u64, c: &mut Poly<u64>) {
pub fn a_mul_b_scalar_into_c<const REDUCE: REDUCEMOD>(
&self,
a: &Poly<u64>,
b: &u64,
c: &mut Poly<u64>,
) {
debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
debug_assert!(c.n() == self.n(), "c.n()={} != n={}", c.n(), self.n());
self.modulus.sa_barrett_mul_vb_into_vc::<CHUNK, REDUCE>(
@@ -258,14 +304,17 @@ impl Ring<u64> {
}
#[inline(always)]
pub fn a_sub_b_add_c_scalar_mul_d_scalar_barrett_into_e<const BRANGE: u8, const REDUCE: REDUCEMOD>(
pub fn a_sub_b_add_c_scalar_mul_d_scalar_barrett_into_e<
const BRANGE: u8,
const REDUCE: REDUCEMOD,
>(
&self,
a: &Poly<u64>,
b: &Poly<u64>,
c: &u64,
d: &Barrett<u64>,
e: &mut Poly<u64>,
){
) {
debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
debug_assert!(b.n() == self.n(), "b.n()={} != n={}", b.n(), self.n());
debug_assert!(e.n() == self.n(), "e.n()={} != n={}", e.n(), self.n());
@@ -274,17 +323,19 @@ impl Ring<u64> {
}
#[inline(always)]
pub fn b_sub_a_add_c_scalar_mul_d_scalar_barrett_into_a<const BRANGE: u8, const REDUCE: REDUCEMOD>(
pub fn b_sub_a_add_c_scalar_mul_d_scalar_barrett_into_a<
const BRANGE: u8,
const REDUCE: REDUCEMOD,
>(
&self,
b: &Poly<u64>,
c: &u64,
d: &Barrett<u64>,
a: &mut Poly<u64>,
){
) {
debug_assert!(a.n() == self.n(), "a.n()={} != n={}", a.n(), self.n());
debug_assert!(b.n() == self.n(), "b.n()={} != n={}", b.n(), self.n());
self.modulus
.vb_sub_va_add_sc_mul_sd_into_va::<CHUNK, BRANGE, REDUCE>(&b.0, c, d, &mut a.0);
}
}

82
math/src/ring/impl_u64/ring_rns.rs
View File

@@ -7,8 +7,6 @@ use crate::scalar::ScalarRNS;
use num_bigint::BigInt;
use std::sync::Arc;
impl RingRNS<u64> {
pub fn new(n: usize, moduli: Vec<u64>) -> Self {
assert!(!moduli.is_empty(), "moduli cannot be empty");
@@ -198,14 +196,17 @@ impl RingRNS<u64> {
c.level(),
self.level()
);
self.0
.iter()
.enumerate()
.for_each(|(i, ring)| ring.a_sub_b_into_c::<BRANGE, REDUCE>(&a.0[i], &b.0[i], &mut c.0[i]));
self.0.iter().enumerate().for_each(|(i, ring)| {
ring.a_sub_b_into_c::<BRANGE, REDUCE>(&a.0[i], &b.0[i], &mut c.0[i])
});
}
#[inline(always)]
pub fn a_sub_b_into_b<const BRANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &PolyRNS<u64>, b: &mut PolyRNS<u64>) {
pub fn a_sub_b_into_b<const BRANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &PolyRNS<u64>,
b: &mut PolyRNS<u64>,
) {
debug_assert!(
a.level() >= self.level(),
"a.level()={} < self.level()={}",
@@ -225,7 +226,11 @@ impl RingRNS<u64> {
}
#[inline(always)]
pub fn a_sub_b_into_a<const BRANGE: u8, const REDUCE: REDUCEMOD>(&self, b: &PolyRNS<u64>, a: &mut PolyRNS<u64>) {
pub fn a_sub_b_into_a<const BRANGE: u8, const REDUCE: REDUCEMOD>(
&self,
b: &PolyRNS<u64>,
a: &mut PolyRNS<u64>,
) {
debug_assert!(
a.level() >= self.level(),
"a.level()={} < self.level()={}",
@@ -245,7 +250,11 @@ impl RingRNS<u64> {
}
#[inline(always)]
pub fn a_neg_into_b<const ARANGE: u8, const REDUCE: REDUCEMOD>(&self, a: &PolyRNS<u64>, b: &mut PolyRNS<u64>) {
pub fn a_neg_into_b<const ARANGE: u8, const REDUCE: REDUCEMOD>(
&self,
a: &PolyRNS<u64>,
b: &mut PolyRNS<u64>,
) {
debug_assert!(
a.level() >= self.level(),
"a.level()={} < self.level()={}",
@@ -326,9 +335,10 @@ impl RingRNS<u64> {
b.level(),
self.level()
);
self.0.iter().enumerate().for_each(|(i, ring)| {
ring.a_mul_b_montgomery_into_a::<REDUCE>(&a.0[i], &mut b.0[i])
});
self.0
.iter()
.enumerate()
.for_each(|(i, ring)| ring.a_mul_b_montgomery_into_a::<REDUCE>(&a.0[i], &mut b.0[i]));
}
#[inline(always)]
@@ -371,7 +381,17 @@ impl RingRNS<u64> {
}
#[inline(always)]
pub fn a_sub_b_add_scalar_mul_scalar_barrett_into_e<const BRANGE:u8, const REDUCE:REDUCEMOD>(&self, a: &PolyRNS<u64>, b: &PolyRNS<u64>, c: &u64, d: &Barrett<u64>, e: &mut PolyRNS<u64>){
pub fn a_sub_b_add_scalar_mul_scalar_barrett_into_e<
const BRANGE: u8,
const REDUCE: REDUCEMOD,
>(
&self,
a: &PolyRNS<u64>,
b: &PolyRNS<u64>,
c: &u64,
d: &Barrett<u64>,
e: &mut PolyRNS<u64>,
) {
debug_assert!(
a.level() >= self.level(),
"a.level()={} < self.level()={}",
@@ -390,14 +410,28 @@ impl RingRNS<u64> {
e.level(),
self.level()
);
self.0
.iter()
.enumerate()
.for_each(|(i, ring)| ring.a_sub_b_add_c_scalar_mul_d_scalar_barrett_into_e::<BRANGE, REDUCE>(&a.0[i], &b.0[i], c, d, &mut e.0[i]));
self.0.iter().enumerate().for_each(|(i, ring)| {
ring.a_sub_b_add_c_scalar_mul_d_scalar_barrett_into_e::<BRANGE, REDUCE>(
&a.0[i],
&b.0[i],
c,
d,
&mut e.0[i],
)
});
}
#[inline(always)]
pub fn b_sub_a_add_c_scalar_mul_d_scalar_barrett_into_a<const BRANGE:u8, const REDUCE:REDUCEMOD>(&self, b: &PolyRNS<u64>, c: &u64, d: &Barrett<u64>, a: &mut PolyRNS<u64>){
pub fn b_sub_a_add_c_scalar_mul_d_scalar_barrett_into_a<
const BRANGE: u8,
const REDUCE: REDUCEMOD,
>(
&self,
b: &PolyRNS<u64>,
c: &u64,
d: &Barrett<u64>,
a: &mut PolyRNS<u64>,
) {
debug_assert!(
a.level() >= self.level(),
"a.level()={} < self.level()={}",
@@ -410,9 +444,13 @@ impl RingRNS<u64> {
b.level(),
self.level()
);
self.0
.iter()
.enumerate()
.for_each(|(i, ring)| ring.b_sub_a_add_c_scalar_mul_d_scalar_barrett_into_a::<BRANGE, REDUCE>(&b.0[i], c, d, &mut a.0[i]));
self.0.iter().enumerate().for_each(|(i, ring)| {
ring.b_sub_a_add_c_scalar_mul_d_scalar_barrett_into_a::<BRANGE, REDUCE>(
&b.0[i],
c,
d,
&mut a.0[i],
)
});
}
}

42
math/src/ring/impl_u64/sampling.rs
View File

@@ -2,7 +2,7 @@ use crate::modulus::WordOps;
use crate::poly::{Poly, PolyRNS};
use crate::ring::{Ring, RingRNS};
use num::ToPrimitive;
use rand_distr::{Normal, Distribution};
use rand_distr::{Distribution, Normal};
use sampling::source::Source;
impl Ring<u64> {
@@ -13,21 +13,25 @@ impl Ring<u64> {
.for_each(|a| *a = source.next_u64n(max, mask));
}
pub fn fill_dist_f64<T: Distribution<f64>>(&self, source: &mut Source, dist: T, bound: f64, a: &mut Poly<u64>) {
pub fn fill_dist_f64<T: Distribution<f64>>(
&self,
source: &mut Source,
dist: T,
bound: f64,
a: &mut Poly<u64>,
) {
let max: u64 = self.modulus.q;
a.0.iter_mut()
.for_each(|a| {
a.0.iter_mut().for_each(|a| {
let mut dist_f64: f64 = dist.sample(source);
while dist_f64.abs() > bound{
while dist_f64.abs() > bound {
dist_f64 = dist.sample(source)
}
let dist_u64: u64 = (dist_f64+0.5).abs().to_u64().unwrap();
let sign: u64 = dist_f64.to_bits()>>63;
let dist_u64: u64 = (dist_f64 + 0.5).abs().to_u64().unwrap();
let sign: u64 = dist_f64.to_bits() >> 63;
*a = (dist_u64 * sign) | (max-dist_u64)*(sign^1)
*a = (dist_u64 * sign) | (max - dist_u64) * (sign ^ 1)
});
}
}
@@ -40,19 +44,25 @@ impl RingRNS<u64> {
.for_each(|(i, r)| r.fill_uniform(source, a.at_mut(i)));
}
pub fn fill_dist_f64<T: Distribution<f64>>(&self, source: &mut Source, dist: T, bound: f64, a: &mut PolyRNS<u64>) {
(0..a.n()).for_each(|j|{
pub fn fill_dist_f64<T: Distribution<f64>>(
&self,
source: &mut Source,
dist: T,
bound: f64,
a: &mut PolyRNS<u64>,
) {
(0..a.n()).for_each(|j| {
let mut dist_f64: f64 = dist.sample(source);
while dist_f64.abs() > bound{
while dist_f64.abs() > bound {
dist_f64 = dist.sample(source)
}
let dist_u64: u64 = (dist_f64+0.5).abs().to_u64().unwrap();
let sign: u64 = dist_f64.to_bits()>>63;
let dist_u64: u64 = (dist_f64 + 0.5).abs().to_u64().unwrap();
let sign: u64 = dist_f64.to_bits() >> 63;
self.0.iter().enumerate().for_each(|(i, r)|{
a.at_mut(i).0[j] = (dist_u64 * sign) | (r.modulus.q-dist_u64)*(sign^1);
self.0.iter().enumerate().for_each(|(i, r)| {
a.at_mut(i).0[j] = (dist_u64 * sign) | (r.modulus.q - dist_u64) * (sign ^ 1);
})
})
}

95
math/tests/rescaling_rns.rs
View File

@@ -1,30 +1,49 @@
use itertools::izip;
use math::num_bigint::Div;
use math::poly::PolyRNS;
use math::ring::RingRNS;
use num_bigint::BigInt;
use math::num_bigint::Div;
use sampling::source::Source;
use itertools::izip;
#[test]
fn rescaling_rns_u64() {
let n = 1 << 10;
let moduli: Vec<u64> = vec![0x1fffffffffc80001u64, 0x1fffffffffe00001u64, 0x1fffffffffb40001, 0x1fffffffff500001];
let moduli: Vec<u64> = vec![
0x1fffffffffc80001u64,
0x1fffffffffe00001u64,
0x1fffffffffb40001,
0x1fffffffff500001,
];
let ring_rns: RingRNS<u64> = RingRNS::new(n, moduli);
sub_test("test_div_by_last_modulus::<ROUND:false, NTT:false>", ||{test_div_by_last_modulus::<false, false>(&ring_rns)});
sub_test("test_div_by_last_modulus::<ROUND:false, NTT:true>", ||{test_div_by_last_modulus::<false, true>(&ring_rns)});
sub_test("test_div_by_last_modulus::<ROUND:true, NTT:false>", ||{test_div_by_last_modulus::<true, false>(&ring_rns)});
sub_test("test_div_by_last_modulus::<ROUND:true, NTT:true>", ||{test_div_by_last_modulus::<true, true>(&ring_rns)});
sub_test("test_div_by_last_modulus_inplace::<ROUND:false, NTT:false>", ||{test_div_by_last_modulus_inplace::<false, false>(&ring_rns)});
sub_test("test_div_by_last_modulus_inplace::<ROUND:false, NTT:true>", ||{test_div_by_last_modulus_inplace::<false, true>(&ring_rns)});
sub_test("test_div_by_last_modulus_inplace::<ROUND:true, NTT:true>", ||{test_div_by_last_modulus_inplace::<true, true>(&ring_rns)});
sub_test("test_div_by_last_modulus_inplace::<ROUND:true, NTT:false>", ||{test_div_by_last_modulus_inplace::<true, false>(&ring_rns)});
sub_test("test_div_by_last_modulus::<ROUND:false, NTT:false>", || {
test_div_by_last_modulus::<false, false>(&ring_rns)
});
sub_test("test_div_by_last_modulus::<ROUND:false, NTT:true>", || {
test_div_by_last_modulus::<false, true>(&ring_rns)
});
sub_test("test_div_by_last_modulus::<ROUND:true, NTT:false>", || {
test_div_by_last_modulus::<true, false>(&ring_rns)
});
sub_test("test_div_by_last_modulus::<ROUND:true, NTT:true>", || {
test_div_by_last_modulus::<true, true>(&ring_rns)
});
sub_test(
"test_div_by_last_modulus_inplace::<ROUND:false, NTT:false>",
|| test_div_by_last_modulus_inplace::<false, false>(&ring_rns),
);
sub_test(
"test_div_by_last_modulus_inplace::<ROUND:false, NTT:true>",
|| test_div_by_last_modulus_inplace::<false, true>(&ring_rns),
);
sub_test(
"test_div_by_last_modulus_inplace::<ROUND:true, NTT:true>",
|| test_div_by_last_modulus_inplace::<true, true>(&ring_rns),
);
sub_test(
"test_div_by_last_modulus_inplace::<ROUND:true, NTT:false>",
|| test_div_by_last_modulus_inplace::<true, false>(&ring_rns),
);
//sub_test("test_div_by_last_moduli::<ROUND:false, NTT:false>", ||{test_div_by_last_moduli::<false, false>(&ring_rns)});
}
@@ -34,8 +53,7 @@ fn sub_test<F: FnOnce()>(name: &str, f: F) {
f();
}
fn test_div_by_last_modulus<const ROUND:bool, const NTT:bool>(ring_rns: &RingRNS<u64>){
fn test_div_by_last_modulus<const ROUND: bool, const NTT: bool>(ring_rns: &RingRNS<u64>) {
let seed: [u8; 32] = [0; 32];
let mut source: Source = Source::new(seed);
@@ -57,8 +75,7 @@ fn test_div_by_last_modulus<const ROUND:bool, const NTT:bool>(ring_rns: &RingRNS
ring_rns.ntt_inplace::<false>(&mut a);
}
ring_rns.div_by_last_modulus::<ROUND,NTT>(&a, &mut b, &mut c);
ring_rns.div_by_last_modulus::<ROUND, NTT>(&a, &mut b, &mut c);
if NTT {
ring_rns.at_level(c.level()).intt_inplace::<false>(&mut c);
@@ -73,9 +90,9 @@ fn test_div_by_last_modulus<const ROUND:bool, const NTT:bool>(ring_rns: &RingRNS
// Performs floor division on a
let scalar_big = BigInt::from(ring_rns.0[ring_rns.level()].modulus.q);
coeffs_a.iter_mut().for_each(|a| {
if ROUND{
if ROUND {
*a = a.div_round(&scalar_big);
}else{
} else {
*a = a.div_floor(&scalar_big);
}
});
@@ -83,8 +100,7 @@ fn test_div_by_last_modulus<const ROUND:bool, const NTT:bool>(ring_rns: &RingRNS
izip!(coeffs_a, coeffs_c).for_each(|(a, b)| assert_eq!(a, b));
}
fn test_div_by_last_modulus_inplace<const ROUND:bool, const NTT:bool>(ring_rns: &RingRNS<u64>) {
fn test_div_by_last_modulus_inplace<const ROUND: bool, const NTT: bool>(ring_rns: &RingRNS<u64>) {
let seed: [u8; 32] = [0; 32];
let mut source: Source = Source::new(seed);
@@ -105,24 +121,26 @@ fn test_div_by_last_modulus_inplace<const ROUND:bool, const NTT:bool>(ring_rns:
ring_rns.ntt_inplace::<false>(&mut a);
}
ring_rns.div_by_last_modulus_inplace::<ROUND,NTT>(&mut buf, &mut a);
ring_rns.div_by_last_modulus_inplace::<ROUND, NTT>(&mut buf, &mut a);
if NTT {
ring_rns.at_level(a.level()-1).intt_inplace::<false>(&mut a);
ring_rns
.at_level(a.level() - 1)
.intt_inplace::<false>(&mut a);
}
// Exports c to coeffs_c
let mut coeffs_c = vec![BigInt::from(0); a.n()];
ring_rns
.at_level(a.level()-1)
.at_level(a.level() - 1)
.to_bigint_inplace(&a, 1, &mut coeffs_c);
// Performs floor division on a
let scalar_big = BigInt::from(ring_rns.0[ring_rns.level()].modulus.q);
coeffs_a.iter_mut().for_each(|a| {
if ROUND{
if ROUND {
*a = a.div_round(&scalar_big);
}else{
} else {
*a = a.div_floor(&scalar_big);
}
});
@@ -130,9 +148,7 @@ fn test_div_by_last_modulus_inplace<const ROUND:bool, const NTT:bool>(ring_rns:
izip!(coeffs_a, coeffs_c).for_each(|(a, b)| assert_eq!(a, b));
}
fn test_div_by_last_moduli<const ROUND:bool, const NTT:bool>(ring_rns: &RingRNS<u64>){
fn test_div_by_last_moduli<const ROUND: bool, const NTT: bool>(ring_rns: &RingRNS<u64>) {
let seed: [u8; 32] = [0; 32];
let mut source: Source = Source::new(seed);
@@ -140,7 +156,9 @@ fn test_div_by_last_moduli<const ROUND:bool, const NTT:bool>(ring_rns: &RingRNS<
let mut a: PolyRNS<u64> = ring_rns.new_polyrns();
let mut buf: PolyRNS<u64> = ring_rns.new_polyrns();
let mut c: PolyRNS<u64> = ring_rns.at_level(ring_rns.level() - nb_moduli).new_polyrns();
let mut c: PolyRNS<u64> = ring_rns
.at_level(ring_rns.level() - nb_moduli)
.new_polyrns();
// Allocates a random PolyRNS
ring_rns.fill_uniform(&mut source, &mut a);
@@ -156,7 +174,7 @@ fn test_div_by_last_moduli<const ROUND:bool, const NTT:bool>(ring_rns: &RingRNS<
ring_rns.ntt_inplace::<false>(&mut a);
}
ring_rns.div_by_last_moduli::<ROUND,NTT>(nb_moduli, &a, &mut buf, &mut c);
ring_rns.div_by_last_moduli::<ROUND, NTT>(nb_moduli, &a, &mut buf, &mut c);
if NTT {
ring_rns.at_level(c.level()).intt_inplace::<false>(&mut c);
@@ -170,11 +188,12 @@ fn test_div_by_last_moduli<const ROUND:bool, const NTT:bool>(ring_rns: &RingRNS<
// Performs floor division on a
let mut scalar_big = BigInt::from(1);
(0..nb_moduli).for_each(|i|{scalar_big *= BigInt::from(ring_rns.0[ring_rns.level()-i].modulus.q)});
(0..nb_moduli)
.for_each(|i| scalar_big *= BigInt::from(ring_rns.0[ring_rns.level() - i].modulus.q));
coeffs_a.iter_mut().for_each(|a| {
if ROUND{
if ROUND {
*a = a.div_round(&scalar_big);
}else{
} else {
*a = a.div_floor(&scalar_big);
}
});