// Copyright © 2024 Mikhail Hogrefe
//
// Uses code adopted from the FLINT Library.
//
//      Copyright © 1991, 1992, 1993, 1994, 1996, 1997, 1999, 2000, 2001, 2002, 2003, 2004, 2005
//      Free Software Foundation, Inc.
//
//      Copyright © 2006, 2007, 2008, 2009, 2010, 2015, 2016 William Hart
//
//      Copyright © 2010, 2011, 2021 Fredrik Johansson
//
//      Copyright © 2008, Peter Shrimpton
//
//      Copyright © 2009, Tom Boothby
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.

use crate::num::arithmetic::traits::{
    ModMul, ModMulAssign, ModMulPrecomputed, ModMulPrecomputedAssign, Parity, PowerOf2,
    WrappingSubAssign,
};
use crate::num::basic::integers::PrimitiveInt;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::{ExactFrom, HasHalf, JoinHalves, SplitInHalf, WrappingFrom};
use crate::num::logic::traits::LeadingZeros;

pub_test! {naive_mod_mul<T: PrimitiveUnsigned>(x: T, y: T, m: T) -> T {
    assert!(x < m, "x must be reduced mod m, but {x} >= {m}");
    assert!(y < m, "y must be reduced mod m, but {y} >= {m}");
    let (product_1, product_0) = T::x_mul_y_to_zz(x, y);
    T::xx_div_mod_y_to_qr(product_1, product_0, m).1
}}

const INVERT_U32_TABLE_LOG_SIZE: u64 = 9;

const INVERT_U32_TABLE_SIZE: usize = 1 << INVERT_U32_TABLE_LOG_SIZE;

// INVERT_U32_TABLE[i] = floor((2^24 - 2^14 + 2^9) / (2^9 + i))
const INVERT_U32_TABLE: [u32; INVERT_U32_TABLE_SIZE] = [
    32737, 32673, 32609, 32546, 32483, 32420, 32357, 32295, 32233, 32171, 32109, 32048, 31987,
    31926, 31865, 31805, 31744, 31684, 31625, 31565, 31506, 31447, 31388, 31329, 31271, 31212,
    31154, 31097, 31039, 30982, 30924, 30868, 30811, 30754, 30698, 30642, 30586, 30530, 30475,
    30419, 30364, 30309, 30255, 30200, 30146, 30092, 30038, 29984, 29930, 29877, 29824, 29771,
    29718, 29666, 29613, 29561, 29509, 29457, 29405, 29354, 29303, 29251, 29200, 29150, 29099,
    29049, 28998, 28948, 28898, 28849, 28799, 28750, 28700, 28651, 28602, 28554, 28505, 28457,
    28409, 28360, 28313, 28265, 28217, 28170, 28123, 28075, 28029, 27982, 27935, 27889, 27842,
    27796, 27750, 27704, 27658, 27613, 27568, 27522, 27477, 27432, 27387, 27343, 27298, 27254,
    27209, 27165, 27121, 27078, 27034, 26990, 26947, 26904, 26861, 26818, 26775, 26732, 26690,
    26647, 26605, 26563, 26521, 26479, 26437, 26395, 26354, 26312, 26271, 26230, 26189, 26148,
    26108, 26067, 26026, 25986, 25946, 25906, 25866, 25826, 25786, 25747, 25707, 25668, 25628,
    25589, 25550, 25511, 25473, 25434, 25395, 25357, 25319, 25281, 25242, 25205, 25167, 25129,
    25091, 25054, 25016, 24979, 24942, 24905, 24868, 24831, 24794, 24758, 24721, 24685, 24649,
    24612, 24576, 24540, 24504, 24469, 24433, 24397, 24362, 24327, 24291, 24256, 24221, 24186,
    24151, 24117, 24082, 24047, 24013, 23979, 23944, 23910, 23876, 23842, 23808, 23774, 23741,
    23707, 23674, 23640, 23607, 23574, 23541, 23508, 23475, 23442, 23409, 23377, 23344, 23312,
    23279, 23247, 23215, 23183, 23151, 23119, 23087, 23055, 23023, 22992, 22960, 22929, 22898,
    22866, 22835, 22804, 22773, 22742, 22711, 22681, 22650, 22619, 22589, 22559, 22528, 22498,
    22468, 22438, 22408, 22378, 22348, 22318, 22289, 22259, 22229, 22200, 22171, 22141, 22112,
    22083, 22054, 22025, 21996, 21967, 21938, 21910, 21881, 21853, 21824, 21796, 21767, 21739,
    21711, 21683, 21655, 21627, 21599, 21571, 21544, 21516, 21488, 21461, 21433, 21406, 21379,
    21352, 21324, 21297, 21270, 21243, 21216, 21190, 21163, 21136, 21110, 21083, 21056, 21030,
    21004, 20977, 20951, 20925, 20899, 20873, 20847, 20821, 20795, 20769, 20744, 20718, 20693,
    20667, 20642, 20616, 20591, 20566, 20540, 20515, 20490, 20465, 20440, 20415, 20390, 20366,
    20341, 20316, 20292, 20267, 20243, 20218, 20194, 20170, 20145, 20121, 20097, 20073, 20049,
    20025, 20001, 19977, 19953, 19930, 19906, 19882, 19859, 19835, 19812, 19789, 19765, 19742,
    19719, 19696, 19672, 19649, 19626, 19603, 19581, 19558, 19535, 19512, 19489, 19467, 19444,
    19422, 19399, 19377, 19354, 19332, 19310, 19288, 19265, 19243, 19221, 19199, 19177, 19155,
    19133, 19112, 19090, 19068, 19046, 19025, 19003, 18982, 18960, 18939, 18917, 18896, 18875,
    18854, 18832, 18811, 18790, 18769, 18748, 18727, 18706, 18686, 18665, 18644, 18623, 18603,
    18582, 18561, 18541, 18520, 18500, 18479, 18459, 18439, 18419, 18398, 18378, 18358, 18338,
    18318, 18298, 18278, 18258, 18238, 18218, 18199, 18179, 18159, 18139, 18120, 18100, 18081,
    18061, 18042, 18022, 18003, 17984, 17964, 17945, 17926, 17907, 17888, 17869, 17850, 17831,
    17812, 17793, 17774, 17755, 17736, 17718, 17699, 17680, 17662, 17643, 17624, 17606, 17587,
    17569, 17551, 17532, 17514, 17496, 17477, 17459, 17441, 17423, 17405, 17387, 17369, 17351,
    17333, 17315, 17297, 17279, 17261, 17244, 17226, 17208, 17191, 17173, 17155, 17138, 17120,
    17103, 17085, 17068, 17051, 17033, 17016, 16999, 16982, 16964, 16947, 16930, 16913, 16896,
    16879, 16862, 16845, 16828, 16811, 16794, 16778, 16761, 16744, 16727, 16711, 16694, 16677,
    16661, 16644, 16628, 16611, 16595, 16578, 16562, 16546, 16529, 16513, 16497, 16481, 16464,
    16448, 16432, 16416, 16400, 16384,
];

#[cfg(feature = "test_build")]
pub fn test_invert_u32_table() {
    for (i, &x) in INVERT_U32_TABLE.iter().enumerate() {
        let value = (u32::power_of_2(24) - u32::power_of_2(14) + u32::power_of_2(9))
            / (u32::power_of_2(9) + u32::exact_from(i));
        assert_eq!(
            x, value,
            "INVERT_U32_TABLE gives incorrect value, {x}, for index {i}"
        );
    }
}

// Computes
// $$
// f(x) = \left \lfloor \frac{2^{64} - 2^{32}x - 1}{x} \right \rfloor =
//     \left \lfloor \frac{2^{64}-1}{x}-2^{32} \right \rfloor.
// $$
//
// The highest bit of `x` must be set.
//
// # Worst-case complexity
// Constant time and additional memory.
//
// This is equivalent to `invert_limb` from `longlong.h`, FLINT 2.7.1, when `GMP_LIMB_BITS == 32`.
pub_crate_test! {limbs_invert_limb_u32(x: u32) -> u32 {
    assert!(x.get_highest_bit());
    let a = INVERT_U32_TABLE[usize::exact_from(x << 1 >> 23)];
    let b = (a << 4)
        .wrapping_sub((u64::from(a * a) * u64::from((x >> 11) + 1)).upper_half())
        .wrapping_sub(1);
    let mut c = b.wrapping_mul(x >> 1).wrapping_neg();
    if x.odd() {
        c.wrapping_sub_assign(b.wrapping_sub(b >> 1));
    }
    let d = (b << 15).wrapping_add((u64::from(b) * u64::from(c)).upper_half() >> 1);
    d.wrapping_sub(
        (u64::from(d) * u64::from(x))
            .wrapping_add(u64::from(x))
            .upper_half()
            .wrapping_add(x),
    )
}}

const INVERT_U64_TABLE_LOG_SIZE: u64 = 8;

const INVERT_U64_TABLE_SIZE: usize = 1 << INVERT_U64_TABLE_LOG_SIZE;

// INVERT_U32_TABLE[i] = floor((2^19 - 3*2^8) / (2^8 + i))
const INVERT_U64_TABLE: [u64; INVERT_U64_TABLE_SIZE] = [
    2045, 2037, 2029, 2021, 2013, 2005, 1998, 1990, 1983, 1975, 1968, 1960, 1953, 1946, 1938, 1931,
    1924, 1917, 1910, 1903, 1896, 1889, 1883, 1876, 1869, 1863, 1856, 1849, 1843, 1836, 1830, 1824,
    1817, 1811, 1805, 1799, 1792, 1786, 1780, 1774, 1768, 1762, 1756, 1750, 1745, 1739, 1733, 1727,
    1722, 1716, 1710, 1705, 1699, 1694, 1688, 1683, 1677, 1672, 1667, 1661, 1656, 1651, 1646, 1641,
    1636, 1630, 1625, 1620, 1615, 1610, 1605, 1600, 1596, 1591, 1586, 1581, 1576, 1572, 1567, 1562,
    1558, 1553, 1548, 1544, 1539, 1535, 1530, 1526, 1521, 1517, 1513, 1508, 1504, 1500, 1495, 1491,
    1487, 1483, 1478, 1474, 1470, 1466, 1462, 1458, 1454, 1450, 1446, 1442, 1438, 1434, 1430, 1426,
    1422, 1418, 1414, 1411, 1407, 1403, 1399, 1396, 1392, 1388, 1384, 1381, 1377, 1374, 1370, 1366,
    1363, 1359, 1356, 1352, 1349, 1345, 1342, 1338, 1335, 1332, 1328, 1325, 1322, 1318, 1315, 1312,
    1308, 1305, 1302, 1299, 1295, 1292, 1289, 1286, 1283, 1280, 1276, 1273, 1270, 1267, 1264, 1261,
    1258, 1255, 1252, 1249, 1246, 1243, 1240, 1237, 1234, 1231, 1228, 1226, 1223, 1220, 1217, 1214,
    1211, 1209, 1206, 1203, 1200, 1197, 1195, 1192, 1189, 1187, 1184, 1181, 1179, 1176, 1173, 1171,
    1168, 1165, 1163, 1160, 1158, 1155, 1153, 1150, 1148, 1145, 1143, 1140, 1138, 1135, 1133, 1130,
    1128, 1125, 1123, 1121, 1118, 1116, 1113, 1111, 1109, 1106, 1104, 1102, 1099, 1097, 1095, 1092,
    1090, 1088, 1086, 1083, 1081, 1079, 1077, 1074, 1072, 1070, 1068, 1066, 1064, 1061, 1059, 1057,
    1055, 1053, 1051, 1049, 1047, 1044, 1042, 1040, 1038, 1036, 1034, 1032, 1030, 1028, 1026, 1024,
];

/// Tests that `INVERT_U64_TABLE` is correct.
#[cfg(feature = "test_build")]
pub fn test_invert_u64_table() {
    for (i, &x) in INVERT_U64_TABLE.iter().enumerate() {
        let value = (u64::power_of_2(19) - 3 * u64::power_of_2(8))
            / (u64::power_of_2(8) + u64::exact_from(i));
        assert_eq!(
            x, value,
            "INVERT_U64_TABLE gives incorrect value, {x}, for index {i}"
        );
    }
}

// Computes
// $$
// f(x) = \left \lfloor \frac{2^{128} - 2^{64}x - 1}{x} \right \rfloor =
//     \left \lfloor \frac{2^{128}-1}{x}-2^{64} \right \rfloor.
// $$
//
// The highest bit of `x` must be set.
//
// # Worst-case complexity
// Constant time and additional memory.
//
// This is equivalent to `invert_limb` from `longlong.h`, FLINT 2.7.1, when `GMP_LIMB_BITS == 64`.
pub_crate_test! {limbs_invert_limb_u64(x: u64) -> u64 {
    assert!(x.get_highest_bit());
    let a = (x >> 24) + 1;
    let b = INVERT_U64_TABLE[usize::exact_from(x << 1 >> 56)];
    let c = (b << 11).wrapping_sub(((b * b).wrapping_mul(a) >> 40) + 1);
    let d = (c.wrapping_mul(u64::power_of_2(60).wrapping_sub(c.wrapping_mul(a))) >> 47)
        .wrapping_add(c << 13);
    let mut e = d.wrapping_mul(x >> 1).wrapping_neg();
    if x.odd() {
        e.wrapping_sub_assign(d.wrapping_sub(d >> 1));
    }
    let f = (d << 31).wrapping_add((u128::from(d) * u128::from(e)).upper_half() >> 1);
    f.wrapping_sub(
        (u128::from(f) * u128::from(x))
            .wrapping_add(u128::from(x))
            .upper_half()
            .wrapping_add(x),
    )
}}

// This is equivalent to `n_ll_mod_preinv` from `ulong_extras/ll_mod_preinv.c`, FLINT 2.7.1.
pub_test! {limbs_mod_preinverted<
    T: PrimitiveUnsigned,
    DT: From<T> + HasHalf<Half = T> + JoinHalves + PrimitiveUnsigned + SplitInHalf,
>(
    mut x_1: T,
    x_0: T,
    d: T,
    d_inv: T,
) -> T {
    assert_ne!(d, T::ZERO);
    let d_inv = DT::from(d_inv);
    let shift = LeadingZeros::leading_zeros(d);
    if shift == 0 {
        if x_1 >= d {
            x_1 -= d;
        }
        let (q_1, q_0) = (d_inv * DT::from(x_1))
            .wrapping_add(DT::join_halves(x_1, x_0))
            .split_in_half();
        let mut r = x_0.wrapping_sub(q_1.wrapping_add(T::ONE).wrapping_mul(d));
        if r > q_0 {
            r.wrapping_add_assign(d);
        }
        if r < d {
            r
        } else {
            r - d
        }
    } else {
        let mut d = d;
        if x_1 >= d {
            let y_1 = x_1 >> (T::WIDTH - shift);
            let y_0 = x_1 << shift;
            d <<= shift;
            let (q1, q0) = (d_inv * DT::from(y_1))
                .wrapping_add(DT::join_halves(y_1, y_0))
                .split_in_half();
            x_1 = y_0.wrapping_sub(q1.wrapping_add(T::ONE).wrapping_mul(d));
            if x_1 > q0 {
                x_1.wrapping_add_assign(d);
            }
            if x_1 >= d {
                x_1 -= d;
            }
        } else {
            d <<= shift;
            x_1 <<= shift;
        }
        let y_1 = x_1.wrapping_add(x_0 >> (T::WIDTH - shift));
        let y_0 = x_0 << shift;
        let (q_1, q_0) = (d_inv * DT::from(y_1))
            .wrapping_add(DT::join_halves(y_1, y_0))
            .split_in_half();
        let mut r = y_0.wrapping_sub(q_1.wrapping_add(T::ONE).wrapping_mul(d));
        if r > q_0 {
            r.wrapping_add_assign(d);
        }
        if r < d {
            r >> shift
        } else {
            (r - d) >> shift
        }
    }
}}

// This is equivalent to `n_mulmod2_preinv` from `ulong_extras.h`, FLINT 2.7.1.
pub_test! {fast_mod_mul<
    T: PrimitiveUnsigned,
    DT: From<T> + HasHalf<Half = T> + JoinHalves + PrimitiveUnsigned + SplitInHalf,
>(
    x: T,
    y: T,
    m: T,
    inv: T,
) -> T {
    assert!(x < m, "x must be reduced mod m, but {x} >= {m}");
    assert!(y < m, "y must be reduced mod m, but {y} >= {m}");
    let (product_1, product_0) = (DT::from(x) * DT::from(y)).split_in_half();
    limbs_mod_preinverted::<T, DT>(product_1, product_0, m, inv)
}}

macro_rules! impl_mod_mul_precomputed_fast {
    ($t:ident, $dt:ident, $invert_limb:ident) => {
        impl ModMulPrecomputed<$t, $t> for $t {
            type Output = $t;
            type Data = $t;

            /// Precomputes data for modular multiplication. See `mod_mul_precomputed` and
            /// [`mod_mul_precomputed_assign`](super::traits::ModMulPrecomputedAssign).
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// This is equivalent to `n_preinvert_limb` from `ulong_extras.h`, FLINT 2.7.1.
            fn precompute_mod_mul_data(&m: &$t) -> $t {
                $invert_limb(m << LeadingZeros::leading_zeros(m))
            }

            /// Multiplies two numbers modulo a third number $m$. The inputs must be already reduced
            /// modulo $m$.
            ///
            /// Some precomputed data is provided; this speeds up computations involving several
            /// modular multiplications with the same modulus. The precomputed data should be
            /// obtained using
            /// [`precompute_mod_mul_data`](ModMulPrecomputed::precompute_mod_mul_data).
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// # Panics
            /// Panics if `self` or `other` are greater than or equal to `m`.
            ///
            /// # Examples
            /// See [here](super::mod_mul#mod_mul_precomputed).
            ///
            /// This is equivalent to `n_mulmod2_preinv` from `ulong_extras.h`, FLINT 2.7.1.
            fn mod_mul_precomputed(self, other: $t, m: $t, data: &$t) -> $t {
                fast_mod_mul::<$t, $dt>(self, other, m, *data)
            }
        }
    };
}
impl_mod_mul_precomputed_fast!(u32, u64, limbs_invert_limb_u32);
impl_mod_mul_precomputed_fast!(u64, u128, limbs_invert_limb_u64);

macro_rules! impl_mod_mul_precomputed_promoted {
    ($t:ident) => {
        impl ModMulPrecomputed<$t, $t> for $t {
            type Output = $t;
            type Data = u32;

            /// Precomputes data for modular multiplication. See `mod_mul_precomputed` and
            /// [`mod_mul_precomputed_assign`](super::traits::ModMulPrecomputedAssign).
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// This is equivalent to `n_preinvert_limb` from `ulong_extras.h`, FLINT 2.7.1.
            fn precompute_mod_mul_data(&m: &$t) -> u32 {
                u32::precompute_mod_mul_data(&u32::from(m))
            }

            /// Multiplies two numbers modulo a third number $m$. The inputs must be already reduced
            /// modulo $m$.
            ///
            /// Some precomputed data is provided; this speeds up computations involving several
            /// modular multiplications with the same modulus. The precomputed data should be
            /// obtained using
            /// [`precompute_mod_mul_data`](ModMulPrecomputed::precompute_mod_mul_data).
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// # Panics
            /// Panics if `self` or `other` are greater than or equal to `m`.
            ///
            /// # Examples
            /// See [here](super::mod_mul#mod_mul_precomputed).
            ///
            /// This is equivalent to `n_mulmod2_preinv` from `ulong_extras.h`, FLINT 2.7.1.
            fn mod_mul_precomputed(self, other: $t, m: $t, data: &u32) -> $t {
                $t::wrapping_from(u32::from(self).mod_mul_precomputed(
                    u32::from(other),
                    u32::from(m),
                    data,
                ))
            }
        }
    };
}
impl_mod_mul_precomputed_promoted!(u8);
impl_mod_mul_precomputed_promoted!(u16);

impl ModMulPrecomputed<u128, u128> for u128 {
    type Output = u128;
    type Data = ();

    /// Precomputes data for modular multiplication. See `mod_mul_precomputed` and
    /// [`mod_mul_precomputed_assign`](super::traits::ModMulPrecomputedAssign).
    ///
    /// # Worst-case complexity
    /// Constant time and additional memory.
    fn precompute_mod_mul_data(_m: &u128) {}

    /// Multiplies two numbers modulo a third number $m$. The inputs must be already reduced modulo
    /// $m$.
    ///
    /// Some precomputed data is provided; this speeds up computations involving several modular
    /// multiplications with the same modulus. The precomputed data should be obtained using
    /// [`precompute_mod_mul_data`](ModMulPrecomputed::precompute_mod_mul_data).
    ///
    /// # Worst-case complexity
    /// Constant time and additional memory.
    ///
    /// # Panics
    /// Panics if `self` or `other` are greater than or equal to `m`.
    ///
    /// # Examples
    /// See [here](super::mod_mul#mod_mul_precomputed).
    ///
    /// This is equivalent to `n_mulmod2_preinv` from `ulong_extras.h`, FLINT 2.7.1.
    #[inline]
    fn mod_mul_precomputed(self, other: u128, m: u128, _data: &()) -> u128 {
        naive_mod_mul(self, other, m)
    }
}

impl ModMulPrecomputed<usize, usize> for usize {
    type Output = usize;
    type Data = usize;

    /// Precomputes data for modular multiplication. See `mod_mul_precomputed` and
    /// [`mod_mul_precomputed_assign`](super::traits::ModMulPrecomputedAssign).
    ///
    /// # Worst-case complexity
    /// Constant time and additional memory.
    ///
    /// This is equivalent to `n_preinvert_limb` from `ulong_extras.h`, FLINT 2.7.1.
    fn precompute_mod_mul_data(&m: &usize) -> usize {
        if usize::WIDTH == u32::WIDTH {
            usize::wrapping_from(u32::precompute_mod_mul_data(&u32::wrapping_from(m)))
        } else {
            usize::wrapping_from(u64::precompute_mod_mul_data(&u64::wrapping_from(m)))
        }
    }

    /// Multiplies two numbers modulo a third number $m$. The inputs must be already reduced modulo
    /// $m$.
    ///
    /// Some precomputed data is provided; this speeds up computations involving several modular
    /// multiplications with the same modulus. The precomputed data should be obtained using
    /// `precompute_mod_mul_data`.
    ///
    /// # Worst-case complexity
    /// Constant time and additional memory.
    ///
    /// # Panics
    /// Panics if `self` or `other` are greater than or equal to `m`.
    ///
    /// # Examples
    /// See [here](super::mod_mul#mod_mul_precomputed).
    ///
    /// This is equivalent to `n_mulmod2_preinv` from `ulong_extras.h`, FLINT 2.7.1.
    fn mod_mul_precomputed(self, other: usize, m: usize, data: &usize) -> usize {
        if usize::WIDTH == u32::WIDTH {
            usize::wrapping_from(u32::wrapping_from(self).mod_mul_precomputed(
                u32::wrapping_from(other),
                u32::wrapping_from(m),
                &u32::wrapping_from(*data),
            ))
        } else {
            usize::wrapping_from(u64::wrapping_from(self).mod_mul_precomputed(
                u64::wrapping_from(other),
                u64::wrapping_from(m),
                &u64::wrapping_from(*data),
            ))
        }
    }
}

macro_rules! impl_mod_mul {
    ($t:ident) => {
        impl ModMulPrecomputedAssign<$t, $t> for $t {
            /// Multiplies two numbers modulo a third number $m$, in place. The inputs must be
            /// already reduced modulo $m$.
            ///
            /// Some precomputed data is provided; this speeds up computations involving several
            /// modular multiplications with the same modulus. The precomputed data should be
            /// obtained using
            /// [`precompute_mod_mul_data`](ModMulPrecomputed::precompute_mod_mul_data).
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// # Panics
            /// Panics if `self` or `other` are greater than or equal to `m`.
            ///
            /// # Examples
            /// See [here](super::mod_mul#mod_mul_precomputed_assign).
            ///
            /// This is equivalent to `n_mulmod2_preinv` from `ulong_extras.h`, FLINT 2.7.1, where
            /// the return value is assigned to `a`.
            #[inline]
            fn mod_mul_precomputed_assign(&mut self, other: $t, m: $t, data: &Self::Data) {
                *self = self.mod_mul_precomputed(other, m, data);
            }
        }

        impl ModMul<$t> for $t {
            type Output = $t;

            /// Multiplies two numbers modulo a third number $m$. The inputs must be already reduced
            /// modulo $m$.
            ///
            /// $f(x, y, m) = z$, where $x, y, z < m$ and $xy \equiv z \mod m$.
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// # Panics
            /// Panics if `self` or `other` are greater than or equal to `m`.
            ///
            /// # Examples
            /// See [here](super::mod_mul#mod_mul).
            ///
            /// This is equivalent to `nmod_mul` from `nmod.h`, FLINT 2.7.1.
            #[inline]
            fn mod_mul(self, other: $t, m: $t) -> $t {
                naive_mod_mul(self, other, m)
            }
        }

        impl ModMulAssign<$t> for $t {
            /// Multiplies two numbers modulo a third number $m$, in place. The inputs must be
            /// already reduced modulo $m$.
            ///
            /// $x \gets z$, where $x, y, z < m$ and $xy \equiv z \mod m$.
            ///
            /// # Worst-case complexity
            /// Constant time and additional memory.
            ///
            /// # Examples
            /// See [here](super::mod_mul#mod_mul_assign).
            ///
            /// # Panics
            /// Panics if `self` or `other` are greater than or equal to `m`.
            ///
            /// This is equivalent to `nmod_mul` from `nmod.h`, FLINT 2.7.1, where the result is
            /// assigned to `a`.
            #[inline]
            fn mod_mul_assign(&mut self, other: $t, m: $t) {
                *self = naive_mod_mul(*self, other, m);
            }
        }
    };
}
apply_to_unsigneds!(impl_mod_mul);