// Copyright 2012 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.

//! Operations and constants for `float`

// Even though this module exports everything defined in it,
// because it contains re-exports, we also have to explicitly
// export locally defined things. That's a bit annoying.


// export when m_float == c_double


// PORT this must match in width according to architecture

#[allow(missing_doc)];
#[allow(non_uppercase_statics)];

use default::Default;
use num::{Zero, One, strconv};
use num::FPCategory;
use num;
use prelude::*;
use to_str;

pub static NaN: float = 0.0/0.0;

pub static infinity: float = 1.0/0.0;

pub static neg_infinity: float = -1.0/0.0;

/* Module: consts */
pub mod consts {
    // FIXME (requires Issue #1433 to fix): replace with mathematical
    // constants from cmath.
    /// Archimedes' constant
    pub static pi: float = 3.14159265358979323846264338327950288;

    /// pi/2.0
    pub static frac_pi_2: float = 1.57079632679489661923132169163975144;

    /// pi/4.0
    pub static frac_pi_4: float = 0.785398163397448309615660845819875721;

    /// 1.0/pi
    pub static frac_1_pi: float = 0.318309886183790671537767526745028724;

    /// 2.0/pi
    pub static frac_2_pi: float = 0.636619772367581343075535053490057448;

    /// 2.0/sqrt(pi)
    pub static frac_2_sqrtpi: float = 1.12837916709551257389615890312154517;

    /// sqrt(2.0)
    pub static sqrt2: float = 1.41421356237309504880168872420969808;

    /// 1.0/sqrt(2.0)
    pub static frac_1_sqrt2: float = 0.707106781186547524400844362104849039;

    /// Euler's number
    pub static e: float = 2.71828182845904523536028747135266250;

    /// log2(e)
    pub static log2_e: float = 1.44269504088896340735992468100189214;

    /// log10(e)
    pub static log10_e: float = 0.434294481903251827651128918916605082;

    /// ln(2.0)
    pub static ln_2: float = 0.693147180559945309417232121458176568;

    /// ln(10.0)
    pub static ln_10: float = 2.30258509299404568401799145468436421;
}

//
// Section: String Conversions
//

///
/// Converts a float to a string
///
/// # Arguments
///
/// * num - The float value
///
#[inline]
pub fn to_str(num: float) -> ~str {
    let (r, _) = strconv::float_to_str_common(
        num, 10u, true, strconv::SignNeg, strconv::DigAll);
    r
}

///
/// Converts a float to a string in hexadecimal format
///
/// # Arguments
///
/// * num - The float value
///
#[inline]
pub fn to_str_hex(num: float) -> ~str {
    let (r, _) = strconv::float_to_str_common(
        num, 16u, true, strconv::SignNeg, strconv::DigAll);
    r
}

///
/// Converts a float to a string in a given radix, and a flag indicating
/// whether it's a special value
///
/// # Arguments
///
/// * num - The float value
/// * radix - The base to use
///
#[inline]
pub fn to_str_radix_special(num: float, radix: uint) -> (~str, bool) {
    strconv::float_to_str_common(num, radix, true,
                           strconv::SignNeg, strconv::DigAll)
}

///
/// Converts a float to a string with exactly the number of
/// provided significant digits
///
/// # Arguments
///
/// * num - The float value
/// * digits - The number of significant digits
///
#[inline]
pub fn to_str_exact(num: float, digits: uint) -> ~str {
    let (r, _) = strconv::float_to_str_common(
        num, 10u, true, strconv::SignNeg, strconv::DigExact(digits));
    r
}

///
/// Converts a float to a string with a maximum number of
/// significant digits
///
/// # Arguments
///
/// * num - The float value
/// * digits - The number of significant digits
///
#[inline]
pub fn to_str_digits(num: float, digits: uint) -> ~str {
    let (r, _) = strconv::float_to_str_common(
        num, 10u, true, strconv::SignNeg, strconv::DigMax(digits));
    r
}

impl to_str::ToStr for float {
    #[inline]
    fn to_str(&self) -> ~str { to_str_digits(*self, 8) }
}

impl num::ToStrRadix for float {
    /// Converts a float to a string in a given radix
    ///
    /// # Arguments
    ///
    /// * num - The float value
    /// * radix - The base to use
    ///
    /// # Failure
    ///
    /// Fails if called on a special value like `inf`, `-inf` or `NaN` due to
    /// possible misinterpretation of the result at higher bases. If those values
    /// are expected, use `to_str_radix_special()` instead.
    #[inline]
    fn to_str_radix(&self, radix: uint) -> ~str {
        let (r, special) = strconv::float_to_str_common(
            *self, radix, true, strconv::SignNeg, strconv::DigAll);
        if special { fail!("number has a special value, \
                             try to_str_radix_special() if those are expected") }
        r
    }
}

///
/// Convert a string in base 16 to a float.
/// Accepts a optional binary exponent.
///
/// This function accepts strings such as
///
/// * 'a4.fe'
/// * '+a4.fe', equivalent to 'a4.fe'
/// * '-a4.fe'
/// * '2b.aP128', or equivalently, '2b.ap128'
/// * '2b.aP-128'
/// * '.' (understood as 0)
/// * 'c.'
/// * '.c', or, equivalently,  '0.c'
/// * '+inf', 'inf', '-inf', 'NaN'
///
/// Leading and trailing whitespace represent an error.
///
/// # Arguments
///
/// * num - A string
///
/// # Return value
///
/// `none` if the string did not represent a valid number.  Otherwise,
/// `Some(n)` where `n` is the floating-point number represented by `[num]`.
///
#[inline]
pub fn from_str_hex(num: &str) -> Option<float> {
    strconv::from_str_common(num, 16u, true, true, true,
                             strconv::ExpBin, false, false)
}

impl FromStr for float {
    ///
    /// Convert a string in base 10 to a float.
    /// Accepts a optional decimal exponent.
    ///
    /// This function accepts strings such as
    ///
    /// * '3.14'
    /// * '+3.14', equivalent to '3.14'
    /// * '-3.14'
    /// * '2.5E10', or equivalently, '2.5e10'
    /// * '2.5E-10'
    /// * '.' (understood as 0)
    /// * '5.'
    /// * '.5', or, equivalently,  '0.5'
    /// * '+inf', 'inf', '-inf', 'NaN'
    ///
    /// Leading and trailing whitespace represent an error.
    ///
    /// # Arguments
    ///
    /// * num - A string
    ///
    /// # Return value
    ///
    /// `none` if the string did not represent a valid number.  Otherwise,
    /// `Some(n)` where `n` is the floating-point number represented by `num`.
    ///
    #[inline]
    fn from_str(val: &str) -> Option<float> {
        strconv::from_str_common(val, 10u, true, true, true,
                                 strconv::ExpDec, false, false)
    }
}

impl num::FromStrRadix for float {
    ///
    /// Convert a string in an given base to a float.
    ///
    /// Due to possible conflicts, this function does **not** accept
    /// the special values `inf`, `-inf`, `+inf` and `NaN`, **nor**
    /// does it recognize exponents of any kind.
    ///
    /// Leading and trailing whitespace represent an error.
    ///
    /// # Arguments
    ///
    /// * num - A string
    /// * radix - The base to use. Must lie in the range [2 .. 36]
    ///
    /// # Return value
    ///
    /// `none` if the string did not represent a valid number. Otherwise,
    /// `Some(n)` where `n` is the floating-point number represented by `num`.
    ///
    #[inline]
    fn from_str_radix(val: &str, radix: uint) -> Option<float> {
        strconv::from_str_common(val, radix, true, true, false,
                                 strconv::ExpNone, false, false)
    }
}

//
// Section: Arithmetics
//

///
/// Compute the exponentiation of an integer by another integer as a float
///
/// # Arguments
///
/// * x - The base
/// * pow - The exponent
///
/// # Return value
///
/// `NaN` if both `x` and `pow` are `0u`, otherwise `x^pow`
///
pub fn pow_with_uint(base: uint, pow: uint) -> float {
    if base == 0u {
        if pow == 0u {
            return NaN as float;
        }
        return 0.;
    }
    let mut my_pow     = pow;
    let mut total      = 1f;
    let mut multiplier = base as float;
    while (my_pow > 0u) {
        if my_pow % 2u == 1u {
            total = total * multiplier;
        }
        my_pow     /= 2u;
        multiplier *= multiplier;
    }
    return total;
}

impl Num for float {}

#[cfg(not(test))]
impl Eq for float {
    #[inline]
    fn eq(&self, other: &float) -> bool { (*self) == (*other) }
}

#[cfg(not(test))]
impl ApproxEq<float> for float {
    #[inline]
    fn approx_epsilon() -> float { 1.0e-6 }

    #[inline]
    fn approx_eq(&self, other: &float) -> bool {
        self.approx_eq_eps(other, &1.0e-6)
    }

    #[inline]
    fn approx_eq_eps(&self, other: &float, approx_epsilon: &float) -> bool {
        (*self - *other).abs() < *approx_epsilon
    }
}

#[cfg(not(test))]
impl Ord for float {
    #[inline]
    fn lt(&self, other: &float) -> bool { (*self) < (*other) }
    #[inline]
    fn le(&self, other: &float) -> bool { (*self) <= (*other) }
    #[inline]
    fn ge(&self, other: &float) -> bool { (*self) >= (*other) }
    #[inline]
    fn gt(&self, other: &float) -> bool { (*self) > (*other) }
}

impl Orderable for float {
    /// Returns `NaN` if either of the numbers are `NaN`.
    #[inline]
    fn min(&self, other: &float) -> float {
        (*self as f64).min(&(*other as f64)) as float
    }

    /// Returns `NaN` if either of the numbers are `NaN`.
    #[inline]
    fn max(&self, other: &float) -> float {
        (*self as f64).max(&(*other as f64)) as float
    }

    /// Returns the number constrained within the range `mn <= self <= mx`.
    /// If any of the numbers are `NaN` then `NaN` is returned.
    #[inline]
    fn clamp(&self, mn: &float, mx: &float) -> float {
        (*self as f64).clamp(&(*mn as f64), &(*mx as f64)) as float
    }
}

impl Default for float {
    #[inline]
    fn default() -> float { 0.0 }
}

impl Zero for float {
    #[inline]
    fn zero() -> float { 0.0 }

    /// Returns true if the number is equal to either `0.0` or `-0.0`
    #[inline]
    fn is_zero(&self) -> bool { *self == 0.0 || *self == -0.0 }
}

impl One for float {
    #[inline]
    fn one() -> float { 1.0 }
}

impl Round for float {
    /// Round half-way cases toward `neg_infinity`
    #[inline]
    fn floor(&self) -> float { (*self as f64).floor() as float }

    /// Round half-way cases toward `infinity`
    #[inline]
    fn ceil(&self) -> float { (*self as f64).ceil() as float }

    /// Round half-way cases away from `0.0`
    #[inline]
    fn round(&self) -> float { (*self as f64).round() as float }

    /// The integer part of the number (rounds towards `0.0`)
    #[inline]
    fn trunc(&self) -> float { (*self as f64).trunc() as float }

    ///
    /// The fractional part of the number, satisfying:
    ///
    /// ```rust
    /// assert!(x == trunc(x) + fract(x))
    /// ```
    ///
    #[inline]
    fn fract(&self) -> float { *self - self.trunc() }
}

impl Fractional for float {
    /// The reciprocal (multiplicative inverse) of the number
    #[inline]
    fn recip(&self) -> float { 1.0 / *self }
}

impl Algebraic for float {
    #[inline]
    fn pow(&self, n: &float) -> float {
        (*self as f64).pow(&(*n as f64)) as float
    }

    #[inline]
    fn sqrt(&self) -> float {
        (*self as f64).sqrt() as float
    }

    #[inline]
    fn rsqrt(&self) -> float {
        (*self as f64).rsqrt() as float
    }

    #[inline]
    fn cbrt(&self) -> float {
        (*self as f64).cbrt() as float
    }

    #[inline]
    fn hypot(&self, other: &float) -> float {
        (*self as f64).hypot(&(*other as f64)) as float
    }
}

impl Trigonometric for float {
    #[inline]
    fn sin(&self) -> float {
        (*self as f64).sin() as float
    }

    #[inline]
    fn cos(&self) -> float {
        (*self as f64).cos() as float
    }

    #[inline]
    fn tan(&self) -> float {
        (*self as f64).tan() as float
    }

    #[inline]
    fn asin(&self) -> float {
        (*self as f64).asin() as float
    }

    #[inline]
    fn acos(&self) -> float {
        (*self as f64).acos() as float
    }

    #[inline]
    fn atan(&self) -> float {
        (*self as f64).atan() as float
    }

    #[inline]
    fn atan2(&self, other: &float) -> float {
        (*self as f64).atan2(&(*other as f64)) as float
    }

    /// Simultaneously computes the sine and cosine of the number
    #[inline]
    fn sin_cos(&self) -> (float, float) {
        match (*self as f64).sin_cos() {
            (s, c) => (s as float, c as float)
        }
    }
}

impl Exponential for float {
    /// Returns the exponential of the number
    #[inline]
    fn exp(&self) -> float {
        (*self as f64).exp() as float
    }

    /// Returns 2 raised to the power of the number
    #[inline]
    fn exp2(&self) -> float {
        (*self as f64).exp2() as float
    }

    /// Returns the natural logarithm of the number
    #[inline]
    fn ln(&self) -> float {
        (*self as f64).ln() as float
    }

    /// Returns the logarithm of the number with respect to an arbitrary base
    #[inline]
    fn log(&self, base: &float) -> float {
        (*self as f64).log(&(*base as f64)) as float
    }

    /// Returns the base 2 logarithm of the number
    #[inline]
    fn log2(&self) -> float {
        (*self as f64).log2() as float
    }

    /// Returns the base 10 logarithm of the number
    #[inline]
    fn log10(&self) -> float {
        (*self as f64).log10() as float
    }
}

impl Hyperbolic for float {
    #[inline]
    fn sinh(&self) -> float {
        (*self as f64).sinh() as float
    }

    #[inline]
    fn cosh(&self) -> float {
        (*self as f64).cosh() as float
    }

    #[inline]
    fn tanh(&self) -> float {
        (*self as f64).tanh() as float
    }

    ///
    /// Inverse hyperbolic sine
    ///
    /// # Returns
    ///
    /// - on success, the inverse hyperbolic sine of `self` will be returned
    /// - `self` if `self` is `0.0`, `-0.0`, `infinity`, or `neg_infinity`
    /// - `NaN` if `self` is `NaN`
    ///
    #[inline]
    fn asinh(&self) -> float {
        (*self as f64).asinh() as float
    }

    ///
    /// Inverse hyperbolic cosine
    ///
    /// # Returns
    ///
    /// - on success, the inverse hyperbolic cosine of `self` will be returned
    /// - `infinity` if `self` is `infinity`
    /// - `NaN` if `self` is `NaN` or `self < 1.0` (including `neg_infinity`)
    ///
    #[inline]
    fn acosh(&self) -> float {
        (*self as f64).acosh() as float
    }

    ///
    /// Inverse hyperbolic tangent
    ///
    /// # Returns
    ///
    /// - on success, the inverse hyperbolic tangent of `self` will be returned
    /// - `self` if `self` is `0.0` or `-0.0`
    /// - `infinity` if `self` is `1.0`
    /// - `neg_infinity` if `self` is `-1.0`
    /// - `NaN` if the `self` is `NaN` or outside the domain of `-1.0 <= self <= 1.0`
    ///   (including `infinity` and `neg_infinity`)
    ///
    #[inline]
    fn atanh(&self) -> float {
        (*self as f64).atanh() as float
    }
}

impl Real for float {
    /// Archimedes' constant
    #[inline]
    fn pi() -> float { 3.14159265358979323846264338327950288 }

    /// 2.0 * pi
    #[inline]
    fn two_pi() -> float { 6.28318530717958647692528676655900576 }

    /// pi / 2.0
    #[inline]
    fn frac_pi_2() -> float { 1.57079632679489661923132169163975144 }

    /// pi / 3.0
    #[inline]
    fn frac_pi_3() -> float { 1.04719755119659774615421446109316763 }

    /// pi / 4.0
    #[inline]
    fn frac_pi_4() -> float { 0.785398163397448309615660845819875721 }

    /// pi / 6.0
    #[inline]
    fn frac_pi_6() -> float { 0.52359877559829887307710723054658381 }

    /// pi / 8.0
    #[inline]
    fn frac_pi_8() -> float { 0.39269908169872415480783042290993786 }

    /// 1.0 / pi
    #[inline]
    fn frac_1_pi() -> float { 0.318309886183790671537767526745028724 }

    /// 2.0 / pi
    #[inline]
    fn frac_2_pi() -> float { 0.636619772367581343075535053490057448 }

    /// 2 .0/ sqrt(pi)
    #[inline]
    fn frac_2_sqrtpi() -> float { 1.12837916709551257389615890312154517 }

    /// sqrt(2.0)
    #[inline]
    fn sqrt2() -> float { 1.41421356237309504880168872420969808 }

    /// 1.0 / sqrt(2.0)
    #[inline]
    fn frac_1_sqrt2() -> float { 0.707106781186547524400844362104849039 }

    /// Euler's number
    #[inline]
    fn e() -> float { 2.71828182845904523536028747135266250 }

    /// log2(e)
    #[inline]
    fn log2_e() -> float { 1.44269504088896340735992468100189214 }

    /// log10(e)
    #[inline]
    fn log10_e() -> float { 0.434294481903251827651128918916605082 }

    /// ln(2.0)
    #[inline]
    fn ln_2() -> float { 0.693147180559945309417232121458176568 }

    /// ln(10.0)
    #[inline]
    fn ln_10() -> float { 2.30258509299404568401799145468436421 }

    /// Converts to degrees, assuming the number is in radians
    #[inline]
    fn to_degrees(&self) -> float { (*self as f64).to_degrees() as float }

    /// Converts to radians, assuming the number is in degrees
    #[inline]
    fn to_radians(&self) -> float { (*self as f64).to_radians() as float }
}

impl RealExt for float {
    #[inline]
    fn lgamma(&self) -> (int, float) {
        let (sign, value) = (*self as f64).lgamma();
        (sign, value as float)
    }

    #[inline]
    fn tgamma(&self) -> float { (*self as f64).tgamma() as float }

    #[inline]
    fn j0(&self) -> float { (*self as f64).j0() as float }

    #[inline]
    fn j1(&self) -> float { (*self as f64).j1() as float }

    #[inline]
    fn jn(&self, n: int) -> float { (*self as f64).jn(n) as float }

    #[inline]
    fn y0(&self) -> float { (*self as f64).y0() as float }

    #[inline]
    fn y1(&self) -> float { (*self as f64).y1() as float }

    #[inline]
    fn yn(&self, n: int) -> float { (*self as f64).yn(n) as float }
}

#[cfg(not(test))]
impl Add<float,float> for float {
    #[inline]
    fn add(&self, other: &float) -> float { *self + *other }
}

#[cfg(not(test))]
impl Sub<float,float> for float {
    #[inline]
    fn sub(&self, other: &float) -> float { *self - *other }
}

#[cfg(not(test))]
impl Mul<float,float> for float {
    #[inline]
    fn mul(&self, other: &float) -> float { *self * *other }
}

#[cfg(not(test))]
impl Div<float,float> for float {
    #[inline]
    fn div(&self, other: &float) -> float { *self / *other }
}

#[cfg(not(test))]
impl Rem<float,float> for float {
    #[inline]
    fn rem(&self, other: &float) -> float { *self % *other }
}
#[cfg(not(test))]
impl Neg<float> for float {
    #[inline]
    fn neg(&self) -> float { -*self }
}

impl Signed for float {
    /// Computes the absolute value. Returns `NaN` if the number is `NaN`.
    #[inline]
    fn abs(&self) -> float { (*self as f64).abs() as float }

    ///
    /// The positive difference of two numbers. Returns `0.0` if the number is less than or
    /// equal to `other`, otherwise the difference between`self` and `other` is returned.
    ///
    #[inline]
    fn abs_sub(&self, other: &float) -> float {
        (*self as f64).abs_sub(&(*other as f64)) as float
    }

    ///
    /// # Returns
    ///
    /// - `1.0` if the number is positive, `+0.0` or `infinity`
    /// - `-1.0` if the number is negative, `-0.0` or `neg_infinity`
    /// - `NaN` if the number is NaN
    ///
    #[inline]
    fn signum(&self) -> float {
        (*self as f64).signum() as float
    }

    /// Returns `true` if the number is positive, including `+0.0` and `infinity`
    #[inline]
    fn is_positive(&self) -> bool { *self > 0.0 || (1.0 / *self) == infinity }

    /// Returns `true` if the number is negative, including `-0.0` and `neg_infinity`
    #[inline]
    fn is_negative(&self) -> bool { *self < 0.0 || (1.0 / *self) == neg_infinity }
}

impl Bounded for float {
    #[inline]
    fn min_value() -> float {
        let x: f64 = Bounded::min_value();
        x as float
    }

    #[inline]
    fn max_value() -> float {
        let x: f64 = Bounded::max_value();
        x as float
    }
}

impl Primitive for float {
    #[inline]
    fn bits(_: Option<float>) -> uint {
        let bits: uint = Primitive::bits(Some(0f64));
        bits
    }

    #[inline]
    fn bytes(_: Option<float>) -> uint {
        let bytes: uint = Primitive::bytes(Some(0f64));
        bytes
    }
}

impl Float for float {
    #[inline]
    fn nan() -> float {
        let value: f64 = Float::nan();
        value as float
    }

    #[inline]
    fn infinity() -> float {
        let value: f64 = Float::infinity();
        value as float
    }

    #[inline]
    fn neg_infinity() -> float {
        let value: f64 = Float::neg_infinity();
        value as float
    }

    #[inline]
    fn neg_zero() -> float {
        let value: f64 = Float::neg_zero();
        value as float
    }

    /// Returns `true` if the number is NaN
    #[inline]
    fn is_nan(&self) -> bool { (*self as f64).is_nan() }

    /// Returns `true` if the number is infinite
    #[inline]
    fn is_infinite(&self) -> bool { (*self as f64).is_infinite() }

    /// Returns `true` if the number is neither infinite or NaN
    #[inline]
    fn is_finite(&self) -> bool { (*self as f64).is_finite() }

    /// Returns `true` if the number is neither zero, infinite, subnormal or NaN
    #[inline]
    fn is_normal(&self) -> bool { (*self as f64).is_normal() }

    /// Returns the floating point category of the number. If only one property is going to
    /// be tested, it is generally faster to use the specific predicate instead.
    #[inline]
    fn classify(&self) -> FPCategory { (*self as f64).classify() }

    #[inline]
    fn mantissa_digits(_: Option<float>) -> uint {
        Float::mantissa_digits(Some(0f64))
    }

    #[inline]
    fn digits(_: Option<float>) -> uint {
        Float::digits(Some(0f64))
    }

    #[inline]
    fn epsilon() -> float {
        let value: f64 = Float::epsilon();
        value as float
    }

    #[inline]
    fn min_exp(_: Option<float>) -> int {
        Float::min_exp(Some(0f64))
    }

    #[inline]
    fn max_exp(_: Option<float>) -> int {
        Float::max_exp(Some(0f64))
    }

    #[inline]
    fn min_10_exp(_: Option<float>) -> int {
        Float::min_10_exp(Some(0f64))
    }

    #[inline]
    fn max_10_exp(_: Option<float>) -> int {
        Float::max_10_exp(Some(0f64))
    }

    /// Constructs a floating point number by multiplying `x` by 2 raised to the power of `exp`
    #[inline]
    fn ldexp(x: float, exp: int) -> float {
        let value: f64 = Float::ldexp(x as f64, exp);
        value as float
    }

    ///
    /// Breaks the number into a normalized fraction and a base-2 exponent, satisfying:
    ///
    /// - `self = x * pow(2, exp)`
    /// - `0.5 <= abs(x) < 1.0`
    ///
    #[inline]
    fn frexp(&self) -> (float, int) {
        match (*self as f64).frexp() {
            (x, exp) => (x as float, exp)
        }
    }

    ///
    /// Returns the exponential of the number, minus `1`, in a way that is accurate
    /// even if the number is close to zero
    ///
    #[inline]
    fn exp_m1(&self) -> float {
        (*self as f64).exp_m1() as float
    }

    ///
    /// Returns the natural logarithm of the number plus `1` (`ln(1+n)`) more accurately
    /// than if the operations were performed separately
    ///
    #[inline]
    fn ln_1p(&self) -> float {
        (*self as f64).ln_1p() as float
    }

    ///
    /// Fused multiply-add. Computes `(self * a) + b` with only one rounding error. This
    /// produces a more accurate result with better performance than a separate multiplication
    /// operation followed by an add.
    ///
    #[inline]
    fn mul_add(&self, a: float, b: float) -> float {
        (*self as f64).mul_add(a as f64, b as f64) as float
    }

    /// Returns the next representable floating-point value in the direction of `other`
    #[inline]
    fn next_after(&self, other: float) -> float {
        (*self as f64).next_after(other as f64) as float
    }
}

#[cfg(test)]
mod tests {
    use prelude::*;
    use super::*;

    use num::*;
    use num;
    use sys;

    #[test]
    fn test_num() {
        num::test_num(10f, 2f);
    }

    #[test]
    fn test_min() {
        assert_eq!(1f.min(&2f), 1f);
        assert_eq!(2f.min(&1f), 1f);
    }

    #[test]
    fn test_max() {
        assert_eq!(1f.max(&2f), 2f);
        assert_eq!(2f.max(&1f), 2f);
    }

    #[test]
    fn test_clamp() {
        assert_eq!(1f.clamp(&2f, &4f), 2f);
        assert_eq!(8f.clamp(&2f, &4f), 4f);
        assert_eq!(3f.clamp(&2f, &4f), 3f);
        let nan: float = Float::nan();
        assert!(3f.clamp(&nan, &4f).is_nan());
        assert!(3f.clamp(&2f, &nan).is_nan());
        assert!(nan.clamp(&2f, &4f).is_nan());
    }

    #[test]
    fn test_floor() {
        assert_approx_eq!(1.0f.floor(), 1.0f);
        assert_approx_eq!(1.3f.floor(), 1.0f);
        assert_approx_eq!(1.5f.floor(), 1.0f);
        assert_approx_eq!(1.7f.floor(), 1.0f);
        assert_approx_eq!(0.0f.floor(), 0.0f);
        assert_approx_eq!((-0.0f).floor(), -0.0f);
        assert_approx_eq!((-1.0f).floor(), -1.0f);
        assert_approx_eq!((-1.3f).floor(), -2.0f);
        assert_approx_eq!((-1.5f).floor(), -2.0f);
        assert_approx_eq!((-1.7f).floor(), -2.0f);
    }

    #[test]
    fn test_ceil() {
        assert_approx_eq!(1.0f.ceil(), 1.0f);
        assert_approx_eq!(1.3f.ceil(), 2.0f);
        assert_approx_eq!(1.5f.ceil(), 2.0f);
        assert_approx_eq!(1.7f.ceil(), 2.0f);
        assert_approx_eq!(0.0f.ceil(), 0.0f);
        assert_approx_eq!((-0.0f).ceil(), -0.0f);
        assert_approx_eq!((-1.0f).ceil(), -1.0f);
        assert_approx_eq!((-1.3f).ceil(), -1.0f);
        assert_approx_eq!((-1.5f).ceil(), -1.0f);
        assert_approx_eq!((-1.7f).ceil(), -1.0f);
    }

    #[test]
    fn test_round() {
        assert_approx_eq!(1.0f.round(), 1.0f);
        assert_approx_eq!(1.3f.round(), 1.0f);
        assert_approx_eq!(1.5f.round(), 2.0f);
        assert_approx_eq!(1.7f.round(), 2.0f);
        assert_approx_eq!(0.0f.round(), 0.0f);
        assert_approx_eq!((-0.0f).round(), -0.0f);
        assert_approx_eq!((-1.0f).round(), -1.0f);
        assert_approx_eq!((-1.3f).round(), -1.0f);
        assert_approx_eq!((-1.5f).round(), -2.0f);
        assert_approx_eq!((-1.7f).round(), -2.0f);
    }

    #[test]
    fn test_trunc() {
        assert_approx_eq!(1.0f.trunc(), 1.0f);
        assert_approx_eq!(1.3f.trunc(), 1.0f);
        assert_approx_eq!(1.5f.trunc(), 1.0f);
        assert_approx_eq!(1.7f.trunc(), 1.0f);
        assert_approx_eq!(0.0f.trunc(), 0.0f);
        assert_approx_eq!((-0.0f).trunc(), -0.0f);
        assert_approx_eq!((-1.0f).trunc(), -1.0f);
        assert_approx_eq!((-1.3f).trunc(), -1.0f);
        assert_approx_eq!((-1.5f).trunc(), -1.0f);
        assert_approx_eq!((-1.7f).trunc(), -1.0f);
    }

    #[test]
    fn test_fract() {
        assert_approx_eq!(1.0f.fract(), 0.0f);
        assert_approx_eq!(1.3f.fract(), 0.3f);
        assert_approx_eq!(1.5f.fract(), 0.5f);
        assert_approx_eq!(1.7f.fract(), 0.7f);
        assert_approx_eq!(0.0f.fract(), 0.0f);
        assert_approx_eq!((-0.0f).fract(), -0.0f);
        assert_approx_eq!((-1.0f).fract(), -0.0f);
        assert_approx_eq!((-1.3f).fract(), -0.3f);
        assert_approx_eq!((-1.5f).fract(), -0.5f);
        assert_approx_eq!((-1.7f).fract(), -0.7f);
    }

    #[test]
    fn test_asinh() {
        assert_eq!(0.0f.asinh(), 0.0f);
        assert_eq!((-0.0f).asinh(), -0.0f);

        let inf: float = Float::infinity();
        let neg_inf: float = Float::neg_infinity();
        let nan: float = Float::nan();
        assert_eq!(inf.asinh(), inf);
        assert_eq!(neg_inf.asinh(), neg_inf);
        assert!(nan.asinh().is_nan());
        assert_approx_eq!(2.0f.asinh(), 1.443635475178810342493276740273105f);
        assert_approx_eq!((-2.0f).asinh(), -1.443635475178810342493276740273105f);
    }

    #[test]
    fn test_acosh() {
        assert_eq!(1.0f.acosh(), 0.0f);
        assert!(0.999f.acosh().is_nan());

        let inf: float = Float::infinity();
        let neg_inf: float = Float::neg_infinity();
        let nan: float = Float::nan();
        assert_eq!(inf.acosh(), inf);
        assert!(neg_inf.acosh().is_nan());
        assert!(nan.acosh().is_nan());
        assert_approx_eq!(2.0f.acosh(), 1.31695789692481670862504634730796844f);
        assert_approx_eq!(3.0f.acosh(), 1.76274717403908605046521864995958461f);
    }

    #[test]
    fn test_atanh() {
        assert_eq!(0.0f.atanh(), 0.0f);
        assert_eq!((-0.0f).atanh(), -0.0f);

        let inf: float = Float::infinity();
        let neg_inf: float = Float::neg_infinity();
        let inf64: f64 = Float::infinity();
        let neg_inf64: f64 = Float::neg_infinity();
        let nan: float = Float::nan();
        assert_eq!(1.0f.atanh(), inf);
        assert_eq!((-1.0f).atanh(), neg_inf);
        assert!(2f64.atanh().atanh().is_nan());
        assert!((-2f64).atanh().atanh().is_nan());
        assert!(inf64.atanh().is_nan());
        assert!(neg_inf64.atanh().is_nan());
        assert!(nan.atanh().is_nan());
        assert_approx_eq!(0.5f.atanh(), 0.54930614433405484569762261846126285f);
        assert_approx_eq!((-0.5f).atanh(), -0.54930614433405484569762261846126285f);
    }

    #[test]
    fn test_real_consts() {
        let pi: float = Real::pi();
        let two_pi: float = Real::two_pi();
        let frac_pi_2: float = Real::frac_pi_2();
        let frac_pi_3: float = Real::frac_pi_3();
        let frac_pi_4: float = Real::frac_pi_4();
        let frac_pi_6: float = Real::frac_pi_6();
        let frac_pi_8: float = Real::frac_pi_8();
        let frac_1_pi: float = Real::frac_1_pi();
        let frac_2_pi: float = Real::frac_2_pi();
        let frac_2_sqrtpi: float = Real::frac_2_sqrtpi();
        let sqrt2: float = Real::sqrt2();
        let frac_1_sqrt2: float = Real::frac_1_sqrt2();
        let e: float = Real::e();
        let log2_e: float = Real::log2_e();
        let log10_e: float = Real::log10_e();
        let ln_2: float = Real::ln_2();
        let ln_10: float = Real::ln_10();

        assert_approx_eq!(two_pi, 2f * pi);
        assert_approx_eq!(frac_pi_2, pi / 2f);
        assert_approx_eq!(frac_pi_3, pi / 3f);
        assert_approx_eq!(frac_pi_4, pi / 4f);
        assert_approx_eq!(frac_pi_6, pi / 6f);
        assert_approx_eq!(frac_pi_8, pi / 8f);
        assert_approx_eq!(frac_1_pi, 1f / pi);
        assert_approx_eq!(frac_2_pi, 2f / pi);
        assert_approx_eq!(frac_2_sqrtpi, 2f / pi.sqrt());
        assert_approx_eq!(sqrt2, 2f.sqrt());
        assert_approx_eq!(frac_1_sqrt2, 1f / 2f.sqrt());
        assert_approx_eq!(log2_e, e.log2());
        assert_approx_eq!(log10_e, e.log10());
        assert_approx_eq!(ln_2, 2f.ln());
        assert_approx_eq!(ln_10, 10f.ln());
    }

    #[test]
    fn test_abs() {
        assert_eq!(infinity.abs(), infinity);
        assert_eq!(1f.abs(), 1f);
        assert_eq!(0f.abs(), 0f);
        assert_eq!((-0f).abs(), 0f);
        assert_eq!((-1f).abs(), 1f);
        assert_eq!(neg_infinity.abs(), infinity);
        assert_eq!((1f/neg_infinity).abs(), 0f);
        assert!(NaN.abs().is_nan());
    }

    #[test]
    fn test_abs_sub() {
        assert_eq!((-1f).abs_sub(&1f), 0f);
        assert_eq!(1f.abs_sub(&1f), 0f);
        assert_eq!(1f.abs_sub(&0f), 1f);
        assert_eq!(1f.abs_sub(&-1f), 2f);
        assert_eq!(neg_infinity.abs_sub(&0f), 0f);
        assert_eq!(infinity.abs_sub(&1f), infinity);
        assert_eq!(0f.abs_sub(&neg_infinity), infinity);
        assert_eq!(0f.abs_sub(&infinity), 0f);
    }

    #[test] #[ignore(cfg(windows))] // FIXME #8663
    fn test_abs_sub_nowin() {
        assert!(NaN.abs_sub(&-1f).is_nan());
        assert!(1f.abs_sub(&NaN).is_nan());
    }

    #[test]
    fn test_signum() {
        assert_eq!(infinity.signum(), 1f);
        assert_eq!(1f.signum(), 1f);
        assert_eq!(0f.signum(), 1f);
        assert_eq!((-0f).signum(), -1f);
        assert_eq!((-1f).signum(), -1f);
        assert_eq!(neg_infinity.signum(), -1f);
        assert_eq!((1f/neg_infinity).signum(), -1f);
        assert!(NaN.signum().is_nan());
    }

    #[test]
    fn test_is_positive() {
        assert!(infinity.is_positive());
        assert!(1f.is_positive());
        assert!(0f.is_positive());
        assert!(!(-0f).is_positive());
        assert!(!(-1f).is_positive());
        assert!(!neg_infinity.is_positive());
        assert!(!(1f/neg_infinity).is_positive());
        assert!(!NaN.is_positive());
    }

    #[test]
    fn test_is_negative() {
        assert!(!infinity.is_negative());
        assert!(!1f.is_negative());
        assert!(!0f.is_negative());
        assert!((-0f).is_negative());
        assert!((-1f).is_negative());
        assert!(neg_infinity.is_negative());
        assert!((1f/neg_infinity).is_negative());
        assert!(!NaN.is_negative());
    }

    #[test]
    fn test_approx_eq() {
        assert!(1.0f.approx_eq(&1f));
        assert!(0.9999999f.approx_eq(&1f));
        assert!(1.000001f.approx_eq_eps(&1f, &1.0e-5));
        assert!(1.0000001f.approx_eq_eps(&1f, &1.0e-6));
        assert!(!1.0000001f.approx_eq_eps(&1f, &1.0e-7));
    }

    #[test]
    fn test_primitive() {
        let none: Option<float> = None;
        assert_eq!(Primitive::bits(none), sys::size_of::<float>() * 8);
        assert_eq!(Primitive::bytes(none), sys::size_of::<float>());
    }

    #[test]
    fn test_is_normal() {
        let nan: float = Float::nan();
        let inf: float = Float::infinity();
        let neg_inf: float = Float::neg_infinity();
        let zero: float = Zero::zero();
        let neg_zero: float = Float::neg_zero();
        assert!(!nan.is_normal());
        assert!(!inf.is_normal());
        assert!(!neg_inf.is_normal());
        assert!(!zero.is_normal());
        assert!(!neg_zero.is_normal());
        assert!(1f.is_normal());
        assert!(1e-307f.is_normal());
        assert!(!1e-308f.is_normal());
    }

    #[test]
    fn test_classify() {
        let nan: float = Float::nan();
        let inf: float = Float::infinity();
        let neg_inf: float = Float::neg_infinity();
        let zero: float = Zero::zero();
        let neg_zero: float = Float::neg_zero();
        assert_eq!(nan.classify(), FPNaN);
        assert_eq!(inf.classify(), FPInfinite);
        assert_eq!(neg_inf.classify(), FPInfinite);
        assert_eq!(zero.classify(), FPZero);
        assert_eq!(neg_zero.classify(), FPZero);
        assert_eq!(1f.classify(), FPNormal);
        assert_eq!(1e-307f.classify(), FPNormal);
        assert_eq!(1e-308f.classify(), FPSubnormal);
    }

    #[test]
    fn test_ldexp() {
        // We have to use from_str until base-2 exponents
        // are supported in floating-point literals
        let f1: float = from_str_hex("1p-123").unwrap();
        let f2: float = from_str_hex("1p-111").unwrap();
        assert_eq!(Float::ldexp(1f, -123), f1);
        assert_eq!(Float::ldexp(1f, -111), f2);

        assert_eq!(Float::ldexp(0f, -123), 0f);
        assert_eq!(Float::ldexp(-0f, -123), -0f);

        let inf: float = Float::infinity();
        let neg_inf: float = Float::neg_infinity();
        let nan: float = Float::nan();
        assert_eq!(Float::ldexp(inf, -123), inf);
        assert_eq!(Float::ldexp(neg_inf, -123), neg_inf);
        assert!(Float::ldexp(nan, -123).is_nan());
    }

    #[test]
    fn test_frexp() {
        // We have to use from_str until base-2 exponents
        // are supported in floating-point literals
        let f1: float = from_str_hex("1p-123").unwrap();
        let f2: float = from_str_hex("1p-111").unwrap();
        let (x1, exp1) = f1.frexp();
        let (x2, exp2) = f2.frexp();
        assert_eq!((x1, exp1), (0.5f, -122));
        assert_eq!((x2, exp2), (0.5f, -110));
        assert_eq!(Float::ldexp(x1, exp1), f1);
        assert_eq!(Float::ldexp(x2, exp2), f2);

        assert_eq!(0f.frexp(), (0f, 0));
        assert_eq!((-0f).frexp(), (-0f, 0));
    }

    #[test] #[ignore(cfg(windows))] // FIXME #8755
    fn test_frexp_nowin() {
        let inf: float = Float::infinity();
        let neg_inf: float = Float::neg_infinity();
        let nan: float = Float::nan();
        assert_eq!(match inf.frexp() { (x, _) => x }, inf);
        assert_eq!(match neg_inf.frexp() { (x, _) => x }, neg_inf);
        assert!(match nan.frexp() { (x, _) => x.is_nan() })
    }

    #[test]
    pub fn test_to_str_exact_do_decimal() {
        let s = to_str_exact(5.0, 4u);
        assert_eq!(s, ~"5.0000");
    }

    #[test]
    pub fn test_from_str() {
        assert_eq!(from_str::<float>("3"), Some(3.));
        assert_eq!(from_str::<float>("3.14"), Some(3.14));
        assert_eq!(from_str::<float>("+3.14"), Some(3.14));
        assert_eq!(from_str::<float>("-3.14"), Some(-3.14));
        assert_eq!(from_str::<float>("2.5E10"), Some(25000000000.));
        assert_eq!(from_str::<float>("2.5e10"), Some(25000000000.));
        assert_eq!(from_str::<float>("25000000000.E-10"), Some(2.5));
        assert_eq!(from_str::<float>("."), Some(0.));
        assert_eq!(from_str::<float>(".e1"), Some(0.));
        assert_eq!(from_str::<float>(".e-1"), Some(0.));
        assert_eq!(from_str::<float>("5."), Some(5.));
        assert_eq!(from_str::<float>(".5"), Some(0.5));
        assert_eq!(from_str::<float>("0.5"), Some(0.5));
        assert_eq!(from_str::<float>("-.5"), Some(-0.5));
        assert_eq!(from_str::<float>("-5"), Some(-5.));
        assert_eq!(from_str::<float>("inf"), Some(infinity));
        assert_eq!(from_str::<float>("+inf"), Some(infinity));
        assert_eq!(from_str::<float>("-inf"), Some(neg_infinity));
        // note: NaN != NaN, hence this slightly complex test
        match from_str::<float>("NaN") {
            Some(f) => assert!(f.is_nan()),
            None => fail!()
        }
        // note: -0 == 0, hence these slightly more complex tests
        match from_str::<float>("-0") {
            Some(v) if v.is_zero() => assert!(v.is_negative()),
            _ => fail!()
        }
        match from_str::<float>("0") {
            Some(v) if v.is_zero() => assert!(v.is_positive()),
            _ => fail!()
        }

        assert!(from_str::<float>("").is_none());
        assert!(from_str::<float>("x").is_none());
        assert!(from_str::<float>(" ").is_none());
        assert!(from_str::<float>("   ").is_none());
        assert!(from_str::<float>("e").is_none());
        assert!(from_str::<float>("E").is_none());
        assert!(from_str::<float>("E1").is_none());
        assert!(from_str::<float>("1e1e1").is_none());
        assert!(from_str::<float>("1e1.1").is_none());
        assert!(from_str::<float>("1e1-1").is_none());
    }

    #[test]
    pub fn test_from_str_hex() {
        assert_eq!(from_str_hex("a4"), Some(164.));
        assert_eq!(from_str_hex("a4.fe"), Some(164.9921875));
        assert_eq!(from_str_hex("-a4.fe"), Some(-164.9921875));
        assert_eq!(from_str_hex("+a4.fe"), Some(164.9921875));
        assert_eq!(from_str_hex("ff0P4"), Some(0xff00 as float));
        assert_eq!(from_str_hex("ff0p4"), Some(0xff00 as float));
        assert_eq!(from_str_hex("ff0p-4"), Some(0xff as float));
        assert_eq!(from_str_hex("."), Some(0.));
        assert_eq!(from_str_hex(".p1"), Some(0.));
        assert_eq!(from_str_hex(".p-1"), Some(0.));
        assert_eq!(from_str_hex("f."), Some(15.));
        assert_eq!(from_str_hex(".f"), Some(0.9375));
        assert_eq!(from_str_hex("0.f"), Some(0.9375));
        assert_eq!(from_str_hex("-.f"), Some(-0.9375));
        assert_eq!(from_str_hex("-f"), Some(-15.));
        assert_eq!(from_str_hex("inf"), Some(infinity));
        assert_eq!(from_str_hex("+inf"), Some(infinity));
        assert_eq!(from_str_hex("-inf"), Some(neg_infinity));
        // note: NaN != NaN, hence this slightly complex test
        match from_str_hex("NaN") {
            Some(f) => assert!(f.is_nan()),
            None => fail!()
        }
        // note: -0 == 0, hence these slightly more complex tests
        match from_str_hex("-0") {
            Some(v) if v.is_zero() => assert!(v.is_negative()),
            _ => fail!()
        }
        match from_str_hex("0") {
            Some(v) if v.is_zero() => assert!(v.is_positive()),
            _ => fail!()
        }
        assert_eq!(from_str_hex("e"), Some(14.));
        assert_eq!(from_str_hex("E"), Some(14.));
        assert_eq!(from_str_hex("E1"), Some(225.));
        assert_eq!(from_str_hex("1e1e1"), Some(123361.));
        assert_eq!(from_str_hex("1e1.1"), Some(481.0625));

        assert!(from_str_hex("").is_none());
        assert!(from_str_hex("x").is_none());
        assert!(from_str_hex(" ").is_none());
        assert!(from_str_hex("   ").is_none());
        assert!(from_str_hex("p").is_none());
        assert!(from_str_hex("P").is_none());
        assert!(from_str_hex("P1").is_none());
        assert!(from_str_hex("1p1p1").is_none());
        assert!(from_str_hex("1p1.1").is_none());
        assert!(from_str_hex("1p1-1").is_none());
    }

    #[test]
    pub fn test_to_str_hex() {
        assert_eq!(to_str_hex(164.), ~"a4");
        assert_eq!(to_str_hex(164.9921875), ~"a4.fe");
        assert_eq!(to_str_hex(-164.9921875), ~"-a4.fe");
        assert_eq!(to_str_hex(0xff00 as float), ~"ff00");
        assert_eq!(to_str_hex(-(0xff00 as float)), ~"-ff00");
        assert_eq!(to_str_hex(0.), ~"0");
        assert_eq!(to_str_hex(15.), ~"f");
        assert_eq!(to_str_hex(-15.), ~"-f");
        assert_eq!(to_str_hex(0.9375), ~"0.f");
        assert_eq!(to_str_hex(-0.9375), ~"-0.f");
        assert_eq!(to_str_hex(infinity), ~"inf");
        assert_eq!(to_str_hex(neg_infinity), ~"-inf");
        assert_eq!(to_str_hex(NaN), ~"NaN");
        assert_eq!(to_str_hex(0.), ~"0");
        assert_eq!(to_str_hex(-0.), ~"-0");
    }

    #[test]
    pub fn test_to_str_radix() {
        assert_eq!(36.0f.to_str_radix(36u), ~"10");
        assert_eq!(8.125f.to_str_radix(2u), ~"1000.001");
    }

    #[test]
    pub fn test_from_str_radix() {
        assert_eq!(from_str_radix("10", 36u), Some(36.));
        assert_eq!(from_str_radix("1000.001", 2u), Some(8.125));
    }

    #[test]
    pub fn test_to_str_inf() {
        assert_eq!(to_str_digits(infinity, 10u), ~"inf");
        assert_eq!(to_str_digits(-infinity, 10u), ~"-inf");
    }
}