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extern crate maths_traits; extern crate num_traits; extern crate rug; use maths_traits::{algebra,analysis}; use maths_traits::algebra::additive::*; use maths_traits::algebra::multiplicative::*; use std::fmt::{Display,Formatter,Result as FmtResult}; use std::ops; const COMPLEX_DEFAULT_PREC:(u32, u32) = (32, 32); #[derive(Clone, Debug, PartialEq)] pub struct Complex { pub val: rug::Complex } impl Display for Complex { fn fmt(&self, f: &mut Formatter<'_>) -> FmtResult { self.val.fmt(f) } } impl From<rug::Complex> for Complex { fn from(src: rug::Complex) -> Self { Complex { val: src } } } macro_rules! complex_impl_arith { ( $Imp:ident { $method:ident }, $ImpAssign:ident { $method_assign:ident } ) => { impl<B> $Imp<B> for Complex where rug::Complex: ops::$Imp<B, Output=rug::Complex> { type Output = Complex; fn $method(self, rhs: B) -> Self::Output { Complex { val: ops::$Imp::$method(self.val, rhs) } } } impl<'a, B> $Imp<B> for &'a Complex where rug::Complex: ops::$Imp<B, Output=rug::Complex> { type Output = Complex; fn $method(self, rhs: B) -> Self::Output { Complex { val: ops::$Imp::$method(self.val.clone(), rhs) } } } impl $Imp<Complex> for Complex { type Output = Complex; fn $method(self, rhs: Complex) -> Self::Output { Complex { val: ops::$Imp::$method(self.val, rhs.val) } } } impl<'a> $Imp<&'a Complex> for Complex { type Output = Complex; fn $method(self, rhs: &Complex) -> Self::Output { Complex { val: ops::$Imp::$method(self.val, &rhs.val) } } } impl<'a> $Imp<Complex> for &'a Complex { type Output = Complex; fn $method(self, rhs: Complex) -> Self::Output { Complex { val: ops::$Imp::$method(self.val.clone(), rhs.val) } } } impl<'a> $Imp<&'a Complex> for &'a Complex { type Output = Complex; fn $method(self, rhs: &'a Complex) -> Self::Output { Complex { val: ops::$Imp::$method(self.val.clone(), &rhs.val) } } } impl<B> $ImpAssign<B> for Complex where rug::Complex: $ImpAssign<B> { fn $method_assign(&mut self, rhs: B) { self.val.$method_assign(rhs); } } impl $ImpAssign<Complex> for Complex { fn $method_assign(&mut self, rhs: Complex) { self.val.$method_assign(rhs.val); } } impl<'a> $ImpAssign<&'a Complex> for Complex { fn $method_assign(&mut self, rhs: &Complex) { self.val.$method_assign(&rhs.val); } } }; } impl AddAssociative for Complex {} impl AddCommutative for Complex {} impl MulAssociative for Complex {} impl MulCommutative for Complex {} complex_impl_arith!{ Add { add }, AddAssign {add_assign} } complex_impl_arith!{ Sub { sub }, SubAssign {sub_assign} } complex_impl_arith!{ Mul { mul }, MulAssign {mul_assign} } complex_impl_arith!{ Div { div }, DivAssign {div_assign} } impl algebra::group_like::additive::Neg for Complex { type Output = Complex; fn neg(self) -> Self::Output { Complex { val: -self.val } } } impl algebra::group_like::additive::Zero for Complex { fn zero() -> Self { Complex { val: rug::Complex::new(COMPLEX_DEFAULT_PREC) } } fn is_zero(&self) -> bool { self.val == 0 } fn set_zero(&mut self) { self.val *= 0; } } impl algebra::group_like::multiplicative::One for Complex { fn one() -> Self { Complex { val: rug::Complex::with_val(COMPLEX_DEFAULT_PREC, 1) } } fn is_one(&self) -> bool { self.val == 1 } fn set_one(&mut self) { self.val *= 0; self.val += 1; } } impl algebra::group_like::multiplicative::Inv for Complex { type Output = Complex; fn inv(self) -> Self::Output { Complex { val: 1/self.val } } } impl algebra::ring_like::Distributive for Complex {} impl algebra::ring_like::Divisibility for Complex { fn divides(self, rhs: Self) -> bool { let q = rhs/self; q.val.real() == &q.val.real().clone().trunc() && q.val.imag() == &q.val.imag().clone().trunc() } fn divide(self, rhs: Self) -> Option<Self> { match self.clone().divides(rhs.clone()) { false => None, true => Some(rhs / self) } } fn unit(&self) -> bool { !self.is_zero() } fn inverse(self) -> Option<Self> { match self.unit() { false => None, true => Some(self.inv()) } } } impl algebra::ring_like::NoZeroDivisors for Complex {} impl algebra::ring_like::Exponential for Complex { fn exp(self) -> Self {Complex { val: self.val.exp() }} fn try_ln(self) -> Option<Self> { Some(Complex { val: self.val.ln() }) } } impl analysis::real::RealExponential for Complex {} macro_rules! complex_fn_trig { ($fn:ident) => { fn $fn(self) -> Self { Complex { val: self.val.$fn() } } }; } macro_rules! complex_fn_trig_try { ($fn:ident $try_fn:ident) => { fn $try_fn(self) -> Option<Self> { let result = self.val.$fn(); if result.real().is_nan() || result.imag().is_nan() {return None;} Some(Complex { val: result }) } }; } impl analysis::real::Trig for Complex { complex_fn_trig!{sin} complex_fn_trig!{cos} complex_fn_trig!{tan} complex_fn_trig!{sinh} complex_fn_trig!{cosh} complex_fn_trig!{tanh} complex_fn_trig!{asin} complex_fn_trig!{acos} complex_fn_trig!{atan} complex_fn_trig!{asinh} complex_fn_trig!{acosh} complex_fn_trig!{atanh} complex_fn_trig_try!{asin try_asin} complex_fn_trig_try!{acos try_acos} complex_fn_trig_try!{asinh try_asinh} complex_fn_trig_try!{acosh try_acosh} complex_fn_trig_try!{atanh try_atanh} fn atan2(y: Self, x: Self) -> Self { (y/x).atan() } fn pi() -> Self { Complex { val: rug::Complex::with_val(COMPLEX_DEFAULT_PREC, rug::float::Constant::Pi) } } }