/**
 * Exponential Functions
 */

use num::Num;

use ncast::*;

pub trait Exp {
    pure fn pow(n: self) -> self;
    pure fn exp() -> self;
    pure fn log_() -> self;
    pure fn exp2() -> self;
    pure fn log2() -> self;
    pure fn sqrt() -> self;
    pure fn inv_sqrt() -> self;
}

#[inline(always)] pub pure fn pow<T:Exp>(x: T, y: T) -> T { x.pow(move y) }
#[inline(always)] pub pure fn exp<T:Exp>(x: T) -> T { x.exp() }
#[inline(always)] pub pure fn log_<T:Exp>(x: T) -> T { x.log_() }
#[inline(always)] pub pure fn exp2<T:Exp>(x: T) -> T { x.exp2() }
#[inline(always)] pub pure fn log2<T:Exp>(x: T) -> T { x.log2() }
#[inline(always)] pub pure fn sqrt<T:Exp>(x: T) -> T { x.sqrt() }
#[inline(always)] pub pure fn inv_sqrt<T:Exp>(x: T) -> T { x.inv_sqrt() }

pub impl f32: Exp {
    #[inline(always)] pure fn pow(y: f32) -> f32 { f32::pow(self, y) }
    #[inline(always)] pure fn exp() -> f32 { f32::exp(self) }
    #[inline(always)] pure fn log_() -> f32 { f32::ln(self) }
    #[inline(always)] pure fn exp2() -> f32 { f32::exp2(self) }
    #[inline(always)] pure fn log2() -> f32 { f32::log2(self) }
    #[inline(always)] pure fn sqrt() -> f32 { f32::sqrt(self) }
    #[inline(always)] pure fn inv_sqrt() -> f32 { 1f32 / self.sqrt() }  // TODO: optimise? need a wizard
}

pub impl f64: Exp {
    #[inline(always)] pure fn pow(y: f64) -> f64 { f64::pow(self, y) }
    #[inline(always)] pure fn exp() -> f64 { f64::exp(self) }
    #[inline(always)] pure fn log_() -> f64 { f64::ln(self) }
    #[inline(always)] pure fn exp2() -> f64 { f64::exp2(self) }
    #[inline(always)] pure fn log2() -> f64 { f64::log2(self) }
    #[inline(always)] pure fn sqrt() -> f64 { f64::sqrt(self) }
    #[inline(always)] pure fn inv_sqrt() -> f64 { 1f64 / self.sqrt() }  // TODO: optimise? need a wizard
}

pub impl float: Exp {
    #[inline(always)] pure fn pow(y: float) -> float { cast(float::pow(cast(self), cast(y))) }
    #[inline(always)] pure fn exp() -> float { cast(float::exp(cast(self))) }
    #[inline(always)] pure fn log_() -> float { cast(float::ln(cast(self))) }
    #[inline(always)] pure fn exp2() -> float { cast(float::exp2(cast(self))) }
    #[inline(always)] pure fn log2() -> float { cast(float::log2(cast(self))) }
    #[inline(always)] pure fn sqrt() -> float { cast(float::sqrt(cast(self))) }
    #[inline(always)] pure fn inv_sqrt() -> float { 1f / self.sqrt() }  // TODO: optimise? need a wizard
}