qfall-math 0.1.1

// Copyright © 2023 Phil Milewski
//
// This file is part of qFALL-math.
//
// qFALL-math is free software: you can redistribute it and/or modify it under
// the terms of the Mozilla Public License Version 2.0 as published by the
// Mozilla Foundation. See <https://mozilla.org/en-US/MPL/2.0/>.

//! Implementation of the [`Mul`] trait for [`Zq`] values.

use super::super::Zq;
use crate::{
    error::MathError,
    integer::Z,
    macros::arithmetics::{
        arithmetic_assign_between_types, arithmetic_assign_trait_borrowed_to_owned,
        arithmetic_between_types_zq, arithmetic_trait_borrowed_to_owned,
        arithmetic_trait_mixed_borrowed_owned,
    },
    traits::CompareBase,
};
use flint_sys::{
    fmpz::fmpz,
    fmpz_mod::{fmpz_mod_mul, fmpz_mod_mul_fmpz, fmpz_mod_mul_si, fmpz_mod_mul_ui},
};
use std::ops::{Mul, MulAssign};

impl MulAssign<&Zq> for Zq {
    /// Computes the multiplication of `self` and `other` reusing
    /// the memory of `self`.
    /// [`MulAssign`] can be used on [`Zq`] in combination with
    /// [`Zq`], [`Z`], [`i64`], [`i32`], [`i16`], [`i8`], [`u64`], [`u32`], [`u16`] and [`u8`].
    ///
    /// Parameters:
    /// - `other`: specifies the value to multiply to `self`
    ///
    /// Returns the product of both numbers modulo `q` as a [`Zq`].
    ///
    /// # Examples
    /// ```
    /// use qfall_math::{integer_mod_q::Zq, integer::Z};
    ///
    /// let mut a: Zq = Zq::from((23, 42));
    /// let b: Zq = Zq::from((1, 42));
    /// let c: Z = Z::from(5);
    ///
    /// a *= &b;
    /// a *= b;
    /// a *= 5;
    /// a *= c;
    /// ```
    ///
    /// # Panics ...
    /// - if the moduli of both [`Zq`] mismatch.
    fn mul_assign(&mut self, other: &Self) {
        if !self.compare_base(other) {
            panic!("{}", self.call_compare_base_error(other).unwrap());
        }

        unsafe {
            fmpz_mod_mul(
                &mut self.value.value,
                &self.value.value,
                &other.value.value,
                self.modulus.get_fmpz_mod_ctx_struct(),
            )
        };
    }
}
impl MulAssign<i64> for Zq {
    /// Documentation at [`Zq::mul_assign`].
    fn mul_assign(&mut self, other: i64) {
        unsafe {
            fmpz_mod_mul_si(
                &mut self.value.value,
                &self.value.value,
                other,
                self.modulus.get_fmpz_mod_ctx_struct(),
            )
        };
    }
}
impl MulAssign<u64> for Zq {
    /// Documentation at [`Zq::mul_assign`].
    fn mul_assign(&mut self, other: u64) {
        unsafe {
            fmpz_mod_mul_ui(
                &mut self.value.value,
                &self.value.value,
                other,
                self.modulus.get_fmpz_mod_ctx_struct(),
            )
        };
    }
}
impl MulAssign<&Z> for Zq {
    /// Documentation at [`Zq::mul_assign`].
    fn mul_assign(&mut self, other: &Z) {
        unsafe {
            fmpz_mod_mul_fmpz(
                &mut self.value.value,
                &self.value.value,
                &other.value,
                self.modulus.get_fmpz_mod_ctx_struct(),
            )
        };
    }
}

arithmetic_assign_trait_borrowed_to_owned!(MulAssign, mul_assign, Zq, Zq);
arithmetic_assign_trait_borrowed_to_owned!(MulAssign, mul_assign, Zq, Z);
arithmetic_assign_between_types!(MulAssign, mul_assign, Zq, i64, i32 i16 i8);
arithmetic_assign_between_types!(MulAssign, mul_assign, Zq, u64, u32 u16 u8);

impl Mul for &Zq {
    type Output = Zq;
    /// Implements the [`Mul`] trait for two [`Zq`] values.
    /// [`Mul`] is implemented for any combination of [`Zq`] and borrowed [`Zq`].
    ///
    /// Parameters:
    /// - `other`: specifies the value to multiply with `self`
    ///
    /// Returns the product of both numbers as a [`Zq`].
    ///
    /// # Examples
    /// ```
    /// use qfall_math::integer_mod_q::Zq;
    ///
    /// let a: Zq = Zq::from((23, 42));
    /// let b: Zq = Zq::from((1, 42));
    ///
    /// let c: Zq = &a * &b;
    /// let d: Zq = a * b;
    /// let e: Zq = &c * d;
    /// let f: Zq = c * &e;
    /// ```
    ///
    /// # Panics ...
    /// - if the moduli of both [`Zq`] mismatch.
    fn mul(self, other: Self) -> Self::Output {
        self.mul_safe(other).unwrap()
    }
}

impl Zq {
    /// Implements multiplication for two [`Zq`] values.
    ///
    ///
    /// Parameters:
    /// - `other`: specifies the value to multiply with `self`
    ///
    /// Returns the product of both numbers as a [`Zq`] or an error if the moduli
    /// mismatch.
    ///
    /// # Examples
    /// ```
    /// use qfall_math::integer_mod_q::Zq;
    ///
    /// let a: Zq = Zq::from((23, 42));
    /// let b: Zq = Zq::from((1, 42));
    ///
    /// let c: Zq = a.mul_safe(&b).unwrap();
    /// ```
    /// # Errors
    /// - Returns a [`MathError`] of type [`MathError::MismatchingModulus`] if the moduli of
    ///   both [`Zq`] mismatch.
    pub fn mul_safe(&self, other: &Self) -> Result<Zq, MathError> {
        if !self.compare_base(other) {
            return Err(self.call_compare_base_error(other).unwrap());
        }
        let mut out_z = Z::ZERO;
        unsafe {
            fmpz_mod_mul(
                &mut out_z.value,
                &self.value.value,
                &other.value.value,
                self.modulus.get_fmpz_mod_ctx_struct(),
            )
        };

        Ok(Self {
            value: out_z,
            modulus: self.modulus.clone(),
        })
    }
}

arithmetic_trait_borrowed_to_owned!(Mul, mul, Zq, Zq, Zq);
arithmetic_trait_mixed_borrowed_owned!(Mul, mul, Zq, Zq, Zq);

impl Mul<&Z> for &Zq {
    type Output = Zq;

    /// Implements the [`Mul`] trait for [`Zq`] and [`Z`] values.
    /// [`Mul`] is implemented for any combination of owned and borrowed values.
    ///
    /// Parameters:
    ///  - `other`: specifies the value to multiply with `self`
    ///
    /// Returns the product of both numbers as a [`Zq`].
    ///
    /// # Examples
    /// ```
    /// use qfall_math::integer_mod_q::Zq;
    /// use qfall_math::integer::Z;
    /// use std::str::FromStr;
    ///
    /// let a: Zq = Zq::from((42, 19));
    /// let b: Z = Z::from(42);
    ///
    /// let c: Zq = &a * &b;
    /// let d: Zq = a * b;
    /// let e: Zq = &c * Z::from(42);
    /// let f: Zq = c * &Z::from(42);
    /// ```
    fn mul(self, other: &Z) -> Self::Output {
        let mut out = fmpz(0);
        unsafe {
            fmpz_mod_mul_fmpz(
                &mut out,
                &self.value.value,
                &other.value,
                self.modulus.get_fmpz_mod_ctx_struct(),
            );
        }
        Zq {
            modulus: self.modulus.clone(),
            value: Z { value: out },
        }
    }
}

arithmetic_trait_borrowed_to_owned!(Mul, mul, Zq, Z, Zq);
arithmetic_trait_mixed_borrowed_owned!(Mul, mul, Zq, Z, Zq);
arithmetic_between_types_zq!(Mul, mul, Zq, i64 i32 i16 i8 u64 u32 u16 u8);

#[cfg(test)]
mod test_mul_assign {
    use crate::{integer::Z, integer_mod_q::Zq};

    /// Ensure that `mul_assign` works for small numbers.
    #[test]
    fn correct_small() {
        let mut a: Zq = Zq::from((-1, 7));
        let b = Zq::from((-1, 7));
        let c = Zq::from((0, 7));

        a *= &b;
        assert_eq!(Zq::from((1, 7)), a);
        a *= &b;
        assert_eq!(Zq::from((6, 7)), a);
        a *= &c;
        assert_eq!(Zq::from((0, 7)), a);
    }

    /// Ensure that `mul_assign` works for large numbers.
    #[test]
    fn correct_large() {
        let mut a = Zq::from((i64::MAX, u64::MAX));
        let b = Zq::from((-1, u64::MAX));

        a *= &b;
        assert_eq!(Zq::from((9223372036854775808u64, u64::MAX)), a);
        a *= b;
        assert_eq!(Zq::from((i64::MAX, u64::MAX)), a);
    }

    /// Ensure that `mul_assign` is available for all types.
    #[test]
    fn availability() {
        let mut a = Zq::from((3, 7));
        let b = Zq::from((1, 7));
        let c = Z::from(1);

        a *= &b;
        a *= b;
        a *= &c;
        a *= c;
        a *= 1_u8;
        a *= 1_u16;
        a *= 1_u32;
        a *= 1_u64;
        a *= 1_i8;
        a *= 1_i16;
        a *= 1_i32;
        a *= 1_i64;
    }

    /// Ensures that mismatching moduli result in a panic.
    #[test]
    #[should_panic]
    fn mismatching_moduli() {
        let mut a = Zq::from((3, 7));
        let b = Zq::from((1, 8));

        a *= b;
    }
}

#[cfg(test)]
mod test_mul {
    use super::Zq;

    /// Testing multiplication for two [`Zq`]
    #[test]
    fn mul() {
        let a: Zq = Zq::from((11, 17));
        let b: Zq = Zq::from((12, 17));
        let c: Zq = a * b;
        assert_eq!(c, Zq::from((13, 17)));
    }

    /// Testing multiplication for two borrowed [`Zq`]
    #[test]
    fn mul_borrow() {
        let a: Zq = Zq::from((10, 11));
        let b: Zq = Zq::from((1, 11));
        let c: Zq = &a * &b;
        assert_eq!(c, Zq::from((10, 11)));
    }

    /// Testing multiplication for borrowed [`Zq`] and [`Zq`]
    #[test]
    fn mul_first_borrowed() {
        let a: Zq = Zq::from((2, 11));
        let b: Zq = Zq::from((5, 11));
        let c: Zq = &a * b;
        assert_eq!(c, Zq::from((10, 11)));
    }

    /// Testing multiplication for [`Zq`] and borrowed [`Zq`]
    #[test]
    fn mul_second_borrowed() {
        let a: Zq = Zq::from((12, 11));
        let b: Zq = Zq::from((10, 11));
        let c: Zq = a * &b;
        assert_eq!(c, Zq::from((-1, 11)));
    }

    /// Testing multiplication for large [`Zq`]
    #[test]
    fn mul_large_numbers() {
        let a: Zq = Zq::from((u32::MAX, u32::MAX - 58));
        let b: Zq = Zq::from((i32::MAX, u32::MAX - 58));
        let c: Zq = a * b;
        assert_eq!(
            c,
            Zq::from((u64::from((u32::MAX - 1) / 2) * 58, u32::MAX - 58))
        );
    }

    /// Testing multiplication for [`Zq`] with different moduli does not work
    #[test]
    #[should_panic]
    fn mul_mismatching_modulus() {
        let a: Zq = Zq::from((4, 11));
        let b: Zq = Zq::from((1, 3));
        let _c: Zq = a * b;
    }

    /// Testing whether mul_safe throws an error for mismatching moduli
    #[test]
    fn mul_safe_is_err() {
        let a: Zq = Zq::from((4, 11));
        let b: Zq = Zq::from((1, 3));
        assert!(&a.mul_safe(&b).is_err());
    }
}

#[cfg(test)]
mod test_mul_between_zq_and_z {
    use super::Z;
    use crate::integer_mod_q::Zq;

    /// Testing multiplication for [`Zq`] and [`Z`]
    #[test]
    fn mul() {
        let a: Zq = Zq::from((4, 11));
        let b: Z = Z::from(9);
        let c: Zq = a * b;
        assert_eq!(c, Zq::from((3, 11)));
    }

    /// Testing multiplication for both borrowed [`Zq`] and [`Z`]
    #[test]
    fn mul_borrow() {
        let a: Zq = Zq::from((4, 11));
        let b: Z = Z::from(9);
        let c: Zq = &a * &b;
        assert_eq!(c, Zq::from((3, 11)));
    }

    /// Testing multiplication for borrowed [`Zq`] and [`Z`]
    #[test]
    fn mul_first_borrowed() {
        let a: Zq = Zq::from((4, 11));
        let b: Z = Z::from(9);
        let c: Zq = &a * b;
        assert_eq!(c, Zq::from((3, 11)));
    }

    /// Testing multiplication for [`Zq`] and borrowed [`Z`]
    #[test]
    fn mul_second_borrowed() {
        let a: Zq = Zq::from((4, 11));
        let b: Z = Z::from(9);
        let c: Zq = a * &b;
        assert_eq!(c, Zq::from((3, 11)));
    }

    /// Testing multiplication for large numbers
    #[test]
    fn mul_large_numbers() {
        let a: Zq = Zq::from((i64::MAX, u64::MAX - 58));
        let b: Zq = Zq::from((i64::MAX - 1, i64::MAX));
        let c: Z = Z::from(u64::MAX);

        let d: Zq = a * &c;
        let e: Zq = b * c;

        assert_eq!(
            d,
            Zq::from(((u64::MAX - 1) / 2, u64::MAX - 58)) * Zq::from((u64::MAX, u64::MAX - 58))
        );
        assert_eq!(e, Zq::from((-1, i64::MAX)) * Zq::from((u64::MAX, i64::MAX)));
    }
}

#[cfg(test)]
mod test_mul_between_types {
    use crate::integer_mod_q::Zq;

    /// Testing multiplication between different types
    #[test]
    #[allow(clippy::op_ref)]
    fn mul() {
        let a: Zq = Zq::from((4, 11));
        let b: u64 = 1;
        let c: u32 = 1;
        let d: u16 = 1;
        let e: u8 = 1;
        let f: i64 = 1;
        let g: i32 = 1;
        let h: i16 = 1;
        let i: i8 = 1;

        let _: Zq = &a * &b;
        let _: Zq = &a * &c;
        let _: Zq = &a * &d;
        let _: Zq = &a * &e;
        let _: Zq = &a * &f;
        let _: Zq = &a * &g;
        let _: Zq = &a * &h;
        let _: Zq = &a * &i;

        let _: Zq = &b * &a;
        let _: Zq = &c * &a;
        let _: Zq = &d * &a;
        let _: Zq = &e * &a;
        let _: Zq = &f * &a;
        let _: Zq = &g * &a;
        let _: Zq = &h * &a;
        let _: Zq = &i * &a;

        let _: Zq = &a * b;
        let _: Zq = &a * c;
        let _: Zq = &a * d;
        let _: Zq = &a * e;
        let _: Zq = &a * f;
        let _: Zq = &a * g;
        let _: Zq = &a * h;
        let _: Zq = &a * i;

        let _: Zq = &b * Zq::from((4, 11));
        let _: Zq = &c * Zq::from((4, 11));
        let _: Zq = &d * Zq::from((4, 11));
        let _: Zq = &e * Zq::from((4, 11));
        let _: Zq = &f * Zq::from((4, 11));
        let _: Zq = &g * Zq::from((4, 11));
        let _: Zq = &h * Zq::from((4, 11));
        let _: Zq = &i * Zq::from((4, 11));

        let _: Zq = Zq::from((4, 11)) * &b;
        let _: Zq = Zq::from((4, 11)) * &c;
        let _: Zq = Zq::from((4, 11)) * &d;
        let _: Zq = Zq::from((4, 11)) * &e;
        let _: Zq = Zq::from((4, 11)) * &f;
        let _: Zq = Zq::from((4, 11)) * &g;
        let _: Zq = Zq::from((4, 11)) * &h;
        let _: Zq = Zq::from((4, 11)) * &i;

        let _: Zq = b * &a;
        let _: Zq = c * &a;
        let _: Zq = d * &a;
        let _: Zq = e * &a;
        let _: Zq = f * &a;
        let _: Zq = g * &a;
        let _: Zq = h * &a;
        let _: Zq = i * &a;

        let _: Zq = Zq::from((4, 11)) * b;
        let _: Zq = Zq::from((4, 11)) * c;
        let _: Zq = Zq::from((4, 11)) * d;
        let _: Zq = Zq::from((4, 11)) * e;
        let _: Zq = Zq::from((4, 11)) * f;
        let _: Zq = Zq::from((4, 11)) * g;
        let _: Zq = Zq::from((4, 11)) * h;
        let _: Zq = Zq::from((4, 11)) * i;

        let _: Zq = b * Zq::from((4, 11));
        let _: Zq = c * Zq::from((4, 11));
        let _: Zq = d * Zq::from((4, 11));
        let _: Zq = e * Zq::from((4, 11));
        let _: Zq = f * Zq::from((4, 11));
        let _: Zq = g * Zq::from((4, 11));
        let _: Zq = h * Zq::from((4, 11));
        let _: Zq = i * Zq::from((4, 11));
    }
}