rust/src/libstd/num/f64.rs
Aaron Turon b8da4d7704 add min_pos_value constant for floats
Follow-up on issue #13297 and PR #13710.  Instead of following the (confusing) C/C++ approach
of using `MIN_VALUE` for the smallest *positive* number, we introduce `MIN_POS_VALUE` (and
in the Float trait, `min_pos_value`) to represent this number.

This patch also removes a few remaining redundantly-defined constants that were missed last
time around.
2014-04-24 17:13:33 -07:00

1263 lines
37 KiB
Rust

// Copyright 2012-2014 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 64-bits floats (`f64` type)
#![allow(missing_doc)]
use prelude::*;
use cast;
use default::Default;
use from_str::FromStr;
use libc::{c_int};
use num::{FPCategory, FPNaN, FPInfinite , FPZero, FPSubnormal, FPNormal};
use num::{Zero, One, Bounded, strconv};
use num;
use intrinsics;
#[allow(dead_code)]
mod cmath {
use libc::{c_double, c_int};
#[link_name = "m"]
extern {
pub fn acos(n: c_double) -> c_double;
pub fn asin(n: c_double) -> c_double;
pub fn atan(n: c_double) -> c_double;
pub fn atan2(a: c_double, b: c_double) -> c_double;
pub fn cbrt(n: c_double) -> c_double;
pub fn cosh(n: c_double) -> c_double;
pub fn erf(n: c_double) -> c_double;
pub fn erfc(n: c_double) -> c_double;
pub fn expm1(n: c_double) -> c_double;
pub fn fdim(a: c_double, b: c_double) -> c_double;
pub fn fmax(a: c_double, b: c_double) -> c_double;
pub fn fmin(a: c_double, b: c_double) -> c_double;
pub fn fmod(a: c_double, b: c_double) -> c_double;
pub fn nextafter(x: c_double, y: c_double) -> c_double;
pub fn frexp(n: c_double, value: &mut c_int) -> c_double;
pub fn hypot(x: c_double, y: c_double) -> c_double;
pub fn ldexp(x: c_double, n: c_int) -> c_double;
pub fn logb(n: c_double) -> c_double;
pub fn log1p(n: c_double) -> c_double;
pub fn ilogb(n: c_double) -> c_int;
pub fn modf(n: c_double, iptr: &mut c_double) -> c_double;
pub fn sinh(n: c_double) -> c_double;
pub fn tan(n: c_double) -> c_double;
pub fn tanh(n: c_double) -> c_double;
pub fn tgamma(n: c_double) -> c_double;
// These are commonly only available for doubles
pub fn j0(n: c_double) -> c_double;
pub fn j1(n: c_double) -> c_double;
pub fn jn(i: c_int, n: c_double) -> c_double;
pub fn y0(n: c_double) -> c_double;
pub fn y1(n: c_double) -> c_double;
pub fn yn(i: c_int, n: c_double) -> c_double;
#[cfg(unix)]
pub fn lgamma_r(n: c_double, sign: &mut c_int) -> c_double;
#[cfg(windows)]
#[link_name="__lgamma_r"]
pub fn lgamma_r(n: c_double, sign: &mut c_int) -> c_double;
}
}
// FIXME(#5527): These constants should be deprecated once associated
// constants are implemented in favour of referencing the respective
// members of `Bounded` and `Float`.
pub static RADIX: uint = 2u;
pub static MANTISSA_DIGITS: uint = 53u;
pub static DIGITS: uint = 15u;
pub static EPSILON: f64 = 2.2204460492503131e-16_f64;
/// Smallest finite f64 value
pub static MIN_VALUE: f64 = -1.7976931348623157e+308_f64;
/// Smallest positive, normalized f64 value
pub static MIN_POS_VALUE: f64 = 2.2250738585072014e-308_f64;
/// Largest finite f64 value
pub static MAX_VALUE: f64 = 1.7976931348623157e+308_f64;
pub static MIN_EXP: int = -1021;
pub static MAX_EXP: int = 1024;
pub static MIN_10_EXP: int = -307;
pub static MAX_10_EXP: int = 308;
pub static NAN: f64 = 0.0_f64/0.0_f64;
pub static INFINITY: f64 = 1.0_f64/0.0_f64;
pub static NEG_INFINITY: f64 = -1.0_f64/0.0_f64;
/// Various useful constants.
pub mod consts {
// FIXME: replace with mathematical constants from cmath.
// FIXME(#5527): These constants should be deprecated once associated
// constants are implemented in favour of referencing the respective members
// of `Float`.
/// Archimedes' constant
pub static PI: f64 = 3.14159265358979323846264338327950288_f64;
/// pi * 2.0
pub static PI_2: f64 = 6.28318530717958647692528676655900576_f64;
/// pi/2.0
pub static FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64;
/// pi/3.0
pub static FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64;
/// pi/4.0
pub static FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64;
/// pi/6.0
pub static FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64;
/// pi/8.0
pub static FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_f64;
/// 1.0/pi
pub static FRAC_1_PI: f64 = 0.318309886183790671537767526745028724_f64;
/// 2.0/pi
pub static FRAC_2_PI: f64 = 0.636619772367581343075535053490057448_f64;
/// 2.0/sqrt(pi)
pub static FRAC_2_SQRTPI: f64 = 1.12837916709551257389615890312154517_f64;
/// sqrt(2.0)
pub static SQRT2: f64 = 1.41421356237309504880168872420969808_f64;
/// 1.0/sqrt(2.0)
pub static FRAC_1_SQRT2: f64 = 0.707106781186547524400844362104849039_f64;
/// Euler's number
pub static E: f64 = 2.71828182845904523536028747135266250_f64;
/// log2(e)
pub static LOG2_E: f64 = 1.44269504088896340735992468100189214_f64;
/// log10(e)
pub static LOG10_E: f64 = 0.434294481903251827651128918916605082_f64;
/// ln(2.0)
pub static LN_2: f64 = 0.693147180559945309417232121458176568_f64;
/// ln(10.0)
pub static LN_10: f64 = 2.30258509299404568401799145468436421_f64;
}
impl Num for f64 {}
#[cfg(not(test))]
impl Eq for f64 {
#[inline]
fn eq(&self, other: &f64) -> bool { (*self) == (*other) }
}
#[cfg(not(test))]
impl Ord for f64 {
#[inline]
fn lt(&self, other: &f64) -> bool { (*self) < (*other) }
#[inline]
fn le(&self, other: &f64) -> bool { (*self) <= (*other) }
#[inline]
fn ge(&self, other: &f64) -> bool { (*self) >= (*other) }
#[inline]
fn gt(&self, other: &f64) -> bool { (*self) > (*other) }
}
impl Default for f64 {
#[inline]
fn default() -> f64 { 0.0 }
}
impl Zero for f64 {
#[inline]
fn zero() -> f64 { 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 f64 {
#[inline]
fn one() -> f64 { 1.0 }
}
#[cfg(not(test))]
impl Add<f64,f64> for f64 {
#[inline]
fn add(&self, other: &f64) -> f64 { *self + *other }
}
#[cfg(not(test))]
impl Sub<f64,f64> for f64 {
#[inline]
fn sub(&self, other: &f64) -> f64 { *self - *other }
}
#[cfg(not(test))]
impl Mul<f64,f64> for f64 {
#[inline]
fn mul(&self, other: &f64) -> f64 { *self * *other }
}
#[cfg(not(test))]
impl Div<f64,f64> for f64 {
#[inline]
fn div(&self, other: &f64) -> f64 { *self / *other }
}
#[cfg(not(test))]
impl Rem<f64,f64> for f64 {
#[inline]
fn rem(&self, other: &f64) -> f64 {
unsafe { cmath::fmod(*self, *other) }
}
}
#[cfg(not(test))]
impl Neg<f64> for f64 {
#[inline]
fn neg(&self) -> f64 { -*self }
}
impl Signed for f64 {
/// Computes the absolute value. Returns `NAN` if the number is `NAN`.
#[inline]
fn abs(&self) -> f64 {
unsafe { intrinsics::fabsf64(*self) }
}
/// 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: &f64) -> f64 {
unsafe { cmath::fdim(*self, *other) }
}
/// # 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) -> f64 {
if self.is_nan() { NAN } else {
unsafe { intrinsics::copysignf64(1.0, *self) }
}
}
/// 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 f64 {
// NOTE: this is the smallest non-infinite f32 value, *not* MIN_VALUE
#[inline]
fn min_value() -> f64 { -MAX_VALUE }
#[inline]
fn max_value() -> f64 { MAX_VALUE }
}
impl Primitive for f64 {}
impl Float for f64 {
#[inline]
fn nan() -> f64 { NAN }
#[inline]
fn infinity() -> f64 { INFINITY }
#[inline]
fn neg_infinity() -> f64 { NEG_INFINITY }
#[inline]
fn neg_zero() -> f64 { -0.0 }
/// Returns `true` if the number is NaN
#[inline]
fn is_nan(self) -> bool { self != self }
/// Returns `true` if the number is infinite
#[inline]
fn is_infinite(self) -> bool {
self == Float::infinity() || self == Float::neg_infinity()
}
/// Returns `true` if the number is neither infinite or NaN
#[inline]
fn is_finite(self) -> bool {
!(self.is_nan() || self.is_infinite())
}
/// Returns `true` if the number is neither zero, infinite, subnormal or NaN
#[inline]
fn is_normal(self) -> bool {
self.classify() == FPNormal
}
/// 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.
fn classify(self) -> FPCategory {
static EXP_MASK: u64 = 0x7ff0000000000000;
static MAN_MASK: u64 = 0x000fffffffffffff;
let bits: u64 = unsafe { cast::transmute(self) };
match (bits & MAN_MASK, bits & EXP_MASK) {
(0, 0) => FPZero,
(_, 0) => FPSubnormal,
(0, EXP_MASK) => FPInfinite,
(_, EXP_MASK) => FPNaN,
_ => FPNormal,
}
}
#[inline]
fn mantissa_digits(_: Option<f64>) -> uint { MANTISSA_DIGITS }
#[inline]
fn digits(_: Option<f64>) -> uint { DIGITS }
#[inline]
fn epsilon() -> f64 { EPSILON }
#[inline]
fn min_exp(_: Option<f64>) -> int { MIN_EXP }
#[inline]
fn max_exp(_: Option<f64>) -> int { MAX_EXP }
#[inline]
fn min_10_exp(_: Option<f64>) -> int { MIN_10_EXP }
#[inline]
fn max_10_exp(_: Option<f64>) -> int { MAX_10_EXP }
#[inline]
fn min_pos_value(_: Option<f64>) -> f64 { MIN_POS_VALUE }
/// Constructs a floating point number by multiplying `x` by 2 raised to the
/// power of `exp`
#[inline]
fn ldexp(x: f64, exp: int) -> f64 {
unsafe { cmath::ldexp(x, exp as c_int) }
}
/// 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) -> (f64, int) {
unsafe {
let mut exp = 0;
let x = cmath::frexp(self, &mut exp);
(x, exp as int)
}
}
/// Returns the mantissa, exponent and sign as integers.
fn integer_decode(self) -> (u64, i16, i8) {
let bits: u64 = unsafe { cast::transmute(self) };
let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 };
let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16;
let mantissa = if exponent == 0 {
(bits & 0xfffffffffffff) << 1
} else {
(bits & 0xfffffffffffff) | 0x10000000000000
};
// Exponent bias + mantissa shift
exponent -= 1023 + 52;
(mantissa, exponent, sign)
}
/// Returns the next representable floating-point value in the direction of
/// `other`.
#[inline]
fn next_after(self, other: f64) -> f64 {
unsafe { cmath::nextafter(self, other) }
}
/// Round half-way cases toward `NEG_INFINITY`
#[inline]
fn floor(self) -> f64 {
unsafe { intrinsics::floorf64(self) }
}
/// Round half-way cases toward `INFINITY`
#[inline]
fn ceil(self) -> f64 {
unsafe { intrinsics::ceilf64(self) }
}
/// Round half-way cases away from `0.0`
#[inline]
fn round(self) -> f64 {
unsafe { intrinsics::roundf64(self) }
}
/// The integer part of the number (rounds towards `0.0`)
#[inline]
fn trunc(self) -> f64 {
unsafe { intrinsics::truncf64(self) }
}
/// The fractional part of the number, satisfying:
///
/// ```rust
/// let x = 1.65f64;
/// assert!(x == x.trunc() + x.fract())
/// ```
#[inline]
fn fract(self) -> f64 { self - self.trunc() }
#[inline]
fn max(self, other: f64) -> f64 {
unsafe { cmath::fmax(self, other) }
}
#[inline]
fn min(self, other: f64) -> f64 {
unsafe { cmath::fmin(self, other) }
}
/// 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: f64, b: f64) -> f64 {
unsafe { intrinsics::fmaf64(self, a, b) }
}
/// The reciprocal (multiplicative inverse) of the number
#[inline]
fn recip(self) -> f64 { 1.0 / self }
#[inline]
fn powf(self, n: f64) -> f64 {
unsafe { intrinsics::powf64(self, n) }
}
#[inline]
fn powi(self, n: i32) -> f64 {
unsafe { intrinsics::powif64(self, n) }
}
/// sqrt(2.0)
#[inline]
fn sqrt2() -> f64 { consts::SQRT2 }
/// 1.0 / sqrt(2.0)
#[inline]
fn frac_1_sqrt2() -> f64 { consts::FRAC_1_SQRT2 }
#[inline]
fn sqrt(self) -> f64 {
unsafe { intrinsics::sqrtf64(self) }
}
#[inline]
fn rsqrt(self) -> f64 { self.sqrt().recip() }
#[inline]
fn cbrt(self) -> f64 {
unsafe { cmath::cbrt(self) }
}
#[inline]
fn hypot(self, other: f64) -> f64 {
unsafe { cmath::hypot(self, other) }
}
/// Archimedes' constant
#[inline]
fn pi() -> f64 { consts::PI }
/// 2.0 * pi
#[inline]
fn two_pi() -> f64 { consts::PI_2 }
/// pi / 2.0
#[inline]
fn frac_pi_2() -> f64 { consts::FRAC_PI_2 }
/// pi / 3.0
#[inline]
fn frac_pi_3() -> f64 { consts::FRAC_PI_3 }
/// pi / 4.0
#[inline]
fn frac_pi_4() -> f64 { consts::FRAC_PI_4 }
/// pi / 6.0
#[inline]
fn frac_pi_6() -> f64 { consts::FRAC_PI_6 }
/// pi / 8.0
#[inline]
fn frac_pi_8() -> f64 { consts::FRAC_PI_8 }
/// 1.0 / pi
#[inline]
fn frac_1_pi() -> f64 { consts::FRAC_1_PI }
/// 2.0 / pi
#[inline]
fn frac_2_pi() -> f64 { consts::FRAC_2_PI }
/// 2.0 / sqrt(pi)
#[inline]
fn frac_2_sqrtpi() -> f64 { consts::FRAC_2_SQRTPI }
#[inline]
fn sin(self) -> f64 {
unsafe { intrinsics::sinf64(self) }
}
#[inline]
fn cos(self) -> f64 {
unsafe { intrinsics::cosf64(self) }
}
#[inline]
fn tan(self) -> f64 {
unsafe { cmath::tan(self) }
}
#[inline]
fn asin(self) -> f64 {
unsafe { cmath::asin(self) }
}
#[inline]
fn acos(self) -> f64 {
unsafe { cmath::acos(self) }
}
#[inline]
fn atan(self) -> f64 {
unsafe { cmath::atan(self) }
}
#[inline]
fn atan2(self, other: f64) -> f64 {
unsafe { cmath::atan2(self, other) }
}
/// Simultaneously computes the sine and cosine of the number
#[inline]
fn sin_cos(self) -> (f64, f64) {
(self.sin(), self.cos())
}
/// Euler's number
#[inline]
fn e() -> f64 { consts::E }
/// log2(e)
#[inline]
fn log2_e() -> f64 { consts::LOG2_E }
/// log10(e)
#[inline]
fn log10_e() -> f64 { consts::LOG10_E }
/// ln(2.0)
#[inline]
fn ln_2() -> f64 { consts::LN_2 }
/// ln(10.0)
#[inline]
fn ln_10() -> f64 { consts::LN_10 }
/// Returns the exponential of the number
#[inline]
fn exp(self) -> f64 {
unsafe { intrinsics::expf64(self) }
}
/// Returns 2 raised to the power of the number
#[inline]
fn exp2(self) -> f64 {
unsafe { intrinsics::exp2f64(self) }
}
/// 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) -> f64 {
unsafe { cmath::expm1(self) }
}
/// Returns the natural logarithm of the number
#[inline]
fn ln(self) -> f64 {
unsafe { intrinsics::logf64(self) }
}
/// Returns the logarithm of the number with respect to an arbitrary base
#[inline]
fn log(self, base: f64) -> f64 { self.ln() / base.ln() }
/// Returns the base 2 logarithm of the number
#[inline]
fn log2(self) -> f64 {
unsafe { intrinsics::log2f64(self) }
}
/// Returns the base 10 logarithm of the number
#[inline]
fn log10(self) -> f64 {
unsafe { intrinsics::log10f64(self) }
}
/// 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) -> f64 {
unsafe { cmath::log1p(self) }
}
#[inline]
fn sinh(self) -> f64 {
unsafe { cmath::sinh(self) }
}
#[inline]
fn cosh(self) -> f64 {
unsafe { cmath::cosh(self) }
}
#[inline]
fn tanh(self) -> f64 {
unsafe { cmath::tanh(self) }
}
/// 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) -> f64 {
match self {
NEG_INFINITY => NEG_INFINITY,
x => (x + ((x * x) + 1.0).sqrt()).ln(),
}
}
/// 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) -> f64 {
match self {
x if x < 1.0 => Float::nan(),
x => (x + ((x * x) - 1.0).sqrt()).ln(),
}
}
/// 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) -> f64 {
0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
}
/// Converts to degrees, assuming the number is in radians
#[inline]
fn to_degrees(self) -> f64 { self * (180.0f64 / Float::pi()) }
/// Converts to radians, assuming the number is in degrees
#[inline]
fn to_radians(self) -> f64 {
let value: f64 = Float::pi();
self * (value / 180.0)
}
}
//
// Section: String Conversions
//
/// Converts a float to a string
///
/// # Arguments
///
/// * num - The float value
#[inline]
pub fn to_str(num: f64) -> ~str {
let (r, _) = strconv::float_to_str_common(
num, 10u, true, strconv::SignNeg, strconv::DigAll, strconv::ExpNone, false);
r
}
/// Converts a float to a string in hexadecimal format
///
/// # Arguments
///
/// * num - The float value
#[inline]
pub fn to_str_hex(num: f64) -> ~str {
let (r, _) = strconv::float_to_str_common(
num, 16u, true, strconv::SignNeg, strconv::DigAll, strconv::ExpNone, false);
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: f64, rdx: uint) -> (~str, bool) {
strconv::float_to_str_common(num, rdx, true,
strconv::SignNeg, strconv::DigAll, strconv::ExpNone, false)
}
/// 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: f64, dig: uint) -> ~str {
let (r, _) = strconv::float_to_str_common(
num, 10u, true, strconv::SignNeg, strconv::DigExact(dig), strconv::ExpNone, false);
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: f64, dig: uint) -> ~str {
let (r, _) = strconv::float_to_str_common(
num, 10u, true, strconv::SignNeg, strconv::DigMax(dig), strconv::ExpNone, false);
r
}
/// Converts a float to a string using the exponential notation with exactly the number of
/// provided digits after the decimal point in the significand
///
/// # Arguments
///
/// * num - The float value
/// * digits - The number of digits after the decimal point
/// * upper - Use `E` instead of `e` for the exponent sign
#[inline]
pub fn to_str_exp_exact(num: f64, dig: uint, upper: bool) -> ~str {
let (r, _) = strconv::float_to_str_common(
num, 10u, true, strconv::SignNeg, strconv::DigExact(dig), strconv::ExpDec, upper);
r
}
/// Converts a float to a string using the exponential notation with the maximum number of
/// digits after the decimal point in the significand
///
/// # Arguments
///
/// * num - The float value
/// * digits - The number of digits after the decimal point
/// * upper - Use `E` instead of `e` for the exponent sign
#[inline]
pub fn to_str_exp_digits(num: f64, dig: uint, upper: bool) -> ~str {
let (r, _) = strconv::float_to_str_common(
num, 10u, true, strconv::SignNeg, strconv::DigMax(dig), strconv::ExpDec, upper);
r
}
impl num::ToStrRadix for f64 {
/// 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, rdx: uint) -> ~str {
let (r, special) = strconv::float_to_str_common(
*self, rdx, true, strconv::SignNeg, strconv::DigAll, strconv::ExpNone, false);
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 an 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<f64> {
strconv::from_str_common(num, 16u, true, true, true,
strconv::ExpBin, false, false)
}
impl FromStr for f64 {
/// Convert a string in base 10 to a float.
/// Accepts an 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<f64> {
strconv::from_str_common(val, 10u, true, true, true,
strconv::ExpDec, false, false)
}
}
impl num::FromStrRadix for f64 {
/// Convert a string in a 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, rdx: uint) -> Option<f64> {
strconv::from_str_common(val, rdx, true, true, false,
strconv::ExpNone, false, false)
}
}
#[cfg(test)]
mod tests {
use f64::*;
use num::*;
use num;
#[test]
fn test_min_nan() {
assert_eq!(NAN.min(2.0), 2.0);
assert_eq!(2.0f64.min(NAN), 2.0);
}
#[test]
fn test_max_nan() {
assert_eq!(NAN.max(2.0), 2.0);
assert_eq!(2.0f64.max(NAN), 2.0);
}
#[test]
fn test_num() {
num::test_num(10f64, 2f64);
}
#[test]
fn test_floor() {
assert_approx_eq!(1.0f64.floor(), 1.0f64);
assert_approx_eq!(1.3f64.floor(), 1.0f64);
assert_approx_eq!(1.5f64.floor(), 1.0f64);
assert_approx_eq!(1.7f64.floor(), 1.0f64);
assert_approx_eq!(0.0f64.floor(), 0.0f64);
assert_approx_eq!((-0.0f64).floor(), -0.0f64);
assert_approx_eq!((-1.0f64).floor(), -1.0f64);
assert_approx_eq!((-1.3f64).floor(), -2.0f64);
assert_approx_eq!((-1.5f64).floor(), -2.0f64);
assert_approx_eq!((-1.7f64).floor(), -2.0f64);
}
#[test]
fn test_ceil() {
assert_approx_eq!(1.0f64.ceil(), 1.0f64);
assert_approx_eq!(1.3f64.ceil(), 2.0f64);
assert_approx_eq!(1.5f64.ceil(), 2.0f64);
assert_approx_eq!(1.7f64.ceil(), 2.0f64);
assert_approx_eq!(0.0f64.ceil(), 0.0f64);
assert_approx_eq!((-0.0f64).ceil(), -0.0f64);
assert_approx_eq!((-1.0f64).ceil(), -1.0f64);
assert_approx_eq!((-1.3f64).ceil(), -1.0f64);
assert_approx_eq!((-1.5f64).ceil(), -1.0f64);
assert_approx_eq!((-1.7f64).ceil(), -1.0f64);
}
#[test]
fn test_round() {
assert_approx_eq!(1.0f64.round(), 1.0f64);
assert_approx_eq!(1.3f64.round(), 1.0f64);
assert_approx_eq!(1.5f64.round(), 2.0f64);
assert_approx_eq!(1.7f64.round(), 2.0f64);
assert_approx_eq!(0.0f64.round(), 0.0f64);
assert_approx_eq!((-0.0f64).round(), -0.0f64);
assert_approx_eq!((-1.0f64).round(), -1.0f64);
assert_approx_eq!((-1.3f64).round(), -1.0f64);
assert_approx_eq!((-1.5f64).round(), -2.0f64);
assert_approx_eq!((-1.7f64).round(), -2.0f64);
}
#[test]
fn test_trunc() {
assert_approx_eq!(1.0f64.trunc(), 1.0f64);
assert_approx_eq!(1.3f64.trunc(), 1.0f64);
assert_approx_eq!(1.5f64.trunc(), 1.0f64);
assert_approx_eq!(1.7f64.trunc(), 1.0f64);
assert_approx_eq!(0.0f64.trunc(), 0.0f64);
assert_approx_eq!((-0.0f64).trunc(), -0.0f64);
assert_approx_eq!((-1.0f64).trunc(), -1.0f64);
assert_approx_eq!((-1.3f64).trunc(), -1.0f64);
assert_approx_eq!((-1.5f64).trunc(), -1.0f64);
assert_approx_eq!((-1.7f64).trunc(), -1.0f64);
}
#[test]
fn test_fract() {
assert_approx_eq!(1.0f64.fract(), 0.0f64);
assert_approx_eq!(1.3f64.fract(), 0.3f64);
assert_approx_eq!(1.5f64.fract(), 0.5f64);
assert_approx_eq!(1.7f64.fract(), 0.7f64);
assert_approx_eq!(0.0f64.fract(), 0.0f64);
assert_approx_eq!((-0.0f64).fract(), -0.0f64);
assert_approx_eq!((-1.0f64).fract(), -0.0f64);
assert_approx_eq!((-1.3f64).fract(), -0.3f64);
assert_approx_eq!((-1.5f64).fract(), -0.5f64);
assert_approx_eq!((-1.7f64).fract(), -0.7f64);
}
#[test]
fn test_asinh() {
assert_eq!(0.0f64.asinh(), 0.0f64);
assert_eq!((-0.0f64).asinh(), -0.0f64);
let inf: f64 = Float::infinity();
let neg_inf: f64 = Float::neg_infinity();
let nan: f64 = Float::nan();
assert_eq!(inf.asinh(), inf);
assert_eq!(neg_inf.asinh(), neg_inf);
assert!(nan.asinh().is_nan());
assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64);
assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
}
#[test]
fn test_acosh() {
assert_eq!(1.0f64.acosh(), 0.0f64);
assert!(0.999f64.acosh().is_nan());
let inf: f64 = Float::infinity();
let neg_inf: f64 = Float::neg_infinity();
let nan: f64 = Float::nan();
assert_eq!(inf.acosh(), inf);
assert!(neg_inf.acosh().is_nan());
assert!(nan.acosh().is_nan());
assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
}
#[test]
fn test_atanh() {
assert_eq!(0.0f64.atanh(), 0.0f64);
assert_eq!((-0.0f64).atanh(), -0.0f64);
let inf: f64 = Float::infinity();
let neg_inf: f64 = Float::neg_infinity();
let nan: f64 = Float::nan();
assert_eq!(1.0f64.atanh(), inf);
assert_eq!((-1.0f64).atanh(), neg_inf);
assert!(2f64.atanh().atanh().is_nan());
assert!((-2f64).atanh().atanh().is_nan());
assert!(inf.atanh().is_nan());
assert!(neg_inf.atanh().is_nan());
assert!(nan.atanh().is_nan());
assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64);
assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64);
}
#[test]
fn test_real_consts() {
let pi: f64 = Float::pi();
let two_pi: f64 = Float::two_pi();
let frac_pi_2: f64 = Float::frac_pi_2();
let frac_pi_3: f64 = Float::frac_pi_3();
let frac_pi_4: f64 = Float::frac_pi_4();
let frac_pi_6: f64 = Float::frac_pi_6();
let frac_pi_8: f64 = Float::frac_pi_8();
let frac_1_pi: f64 = Float::frac_1_pi();
let frac_2_pi: f64 = Float::frac_2_pi();
let frac_2_sqrtpi: f64 = Float::frac_2_sqrtpi();
let sqrt2: f64 = Float::sqrt2();
let frac_1_sqrt2: f64 = Float::frac_1_sqrt2();
let e: f64 = Float::e();
let log2_e: f64 = Float::log2_e();
let log10_e: f64 = Float::log10_e();
let ln_2: f64 = Float::ln_2();
let ln_10: f64 = Float::ln_10();
assert_approx_eq!(two_pi, 2.0 * pi);
assert_approx_eq!(frac_pi_2, pi / 2f64);
assert_approx_eq!(frac_pi_3, pi / 3f64);
assert_approx_eq!(frac_pi_4, pi / 4f64);
assert_approx_eq!(frac_pi_6, pi / 6f64);
assert_approx_eq!(frac_pi_8, pi / 8f64);
assert_approx_eq!(frac_1_pi, 1f64 / pi);
assert_approx_eq!(frac_2_pi, 2f64 / pi);
assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt());
assert_approx_eq!(sqrt2, 2f64.sqrt());
assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt());
assert_approx_eq!(log2_e, e.log2());
assert_approx_eq!(log10_e, e.log10());
assert_approx_eq!(ln_2, 2f64.ln());
assert_approx_eq!(ln_10, 10f64.ln());
}
#[test]
pub fn test_abs() {
assert_eq!(INFINITY.abs(), INFINITY);
assert_eq!(1f64.abs(), 1f64);
assert_eq!(0f64.abs(), 0f64);
assert_eq!((-0f64).abs(), 0f64);
assert_eq!((-1f64).abs(), 1f64);
assert_eq!(NEG_INFINITY.abs(), INFINITY);
assert_eq!((1f64/NEG_INFINITY).abs(), 0f64);
assert!(NAN.abs().is_nan());
}
#[test]
fn test_abs_sub() {
assert_eq!((-1f64).abs_sub(&1f64), 0f64);
assert_eq!(1f64.abs_sub(&1f64), 0f64);
assert_eq!(1f64.abs_sub(&0f64), 1f64);
assert_eq!(1f64.abs_sub(&-1f64), 2f64);
assert_eq!(NEG_INFINITY.abs_sub(&0f64), 0f64);
assert_eq!(INFINITY.abs_sub(&1f64), INFINITY);
assert_eq!(0f64.abs_sub(&NEG_INFINITY), INFINITY);
assert_eq!(0f64.abs_sub(&INFINITY), 0f64);
}
#[test]
fn test_abs_sub_nowin() {
assert!(NAN.abs_sub(&-1f64).is_nan());
assert!(1f64.abs_sub(&NAN).is_nan());
}
#[test]
fn test_signum() {
assert_eq!(INFINITY.signum(), 1f64);
assert_eq!(1f64.signum(), 1f64);
assert_eq!(0f64.signum(), 1f64);
assert_eq!((-0f64).signum(), -1f64);
assert_eq!((-1f64).signum(), -1f64);
assert_eq!(NEG_INFINITY.signum(), -1f64);
assert_eq!((1f64/NEG_INFINITY).signum(), -1f64);
assert!(NAN.signum().is_nan());
}
#[test]
fn test_is_positive() {
assert!(INFINITY.is_positive());
assert!(1f64.is_positive());
assert!(0f64.is_positive());
assert!(!(-0f64).is_positive());
assert!(!(-1f64).is_positive());
assert!(!NEG_INFINITY.is_positive());
assert!(!(1f64/NEG_INFINITY).is_positive());
assert!(!NAN.is_positive());
}
#[test]
fn test_is_negative() {
assert!(!INFINITY.is_negative());
assert!(!1f64.is_negative());
assert!(!0f64.is_negative());
assert!((-0f64).is_negative());
assert!((-1f64).is_negative());
assert!(NEG_INFINITY.is_negative());
assert!((1f64/NEG_INFINITY).is_negative());
assert!(!NAN.is_negative());
}
#[test]
fn test_is_normal() {
let nan: f64 = Float::nan();
let inf: f64 = Float::infinity();
let neg_inf: f64 = Float::neg_infinity();
let zero: f64 = Zero::zero();
let neg_zero: f64 = 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!(1f64.is_normal());
assert!(1e-307f64.is_normal());
assert!(!1e-308f64.is_normal());
}
#[test]
fn test_classify() {
let nan: f64 = Float::nan();
let inf: f64 = Float::infinity();
let neg_inf: f64 = Float::neg_infinity();
let zero: f64 = Zero::zero();
let neg_zero: f64 = 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!(1e-307f64.classify(), FPNormal);
assert_eq!(1e-308f64.classify(), FPSubnormal);
}
#[test]
fn test_ldexp() {
// We have to use from_str until base-2 exponents
// are supported in floating-point literals
let f1: f64 = from_str_hex("1p-123").unwrap();
let f2: f64 = from_str_hex("1p-111").unwrap();
assert_eq!(Float::ldexp(1f64, -123), f1);
assert_eq!(Float::ldexp(1f64, -111), f2);
assert_eq!(Float::ldexp(0f64, -123), 0f64);
assert_eq!(Float::ldexp(-0f64, -123), -0f64);
let inf: f64 = Float::infinity();
let neg_inf: f64 = Float::neg_infinity();
let nan: f64 = 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: f64 = from_str_hex("1p-123").unwrap();
let f2: f64 = from_str_hex("1p-111").unwrap();
let (x1, exp1) = f1.frexp();
let (x2, exp2) = f2.frexp();
assert_eq!((x1, exp1), (0.5f64, -122));
assert_eq!((x2, exp2), (0.5f64, -110));
assert_eq!(Float::ldexp(x1, exp1), f1);
assert_eq!(Float::ldexp(x2, exp2), f2);
assert_eq!(0f64.frexp(), (0f64, 0));
assert_eq!((-0f64).frexp(), (-0f64, 0));
}
#[test] #[ignore(cfg(windows))] // FIXME #8755
fn test_frexp_nowin() {
let inf: f64 = Float::infinity();
let neg_inf: f64 = Float::neg_infinity();
let nan: f64 = 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]
fn test_integer_decode() {
assert_eq!(3.14159265359f64.integer_decode(), (7074237752028906u64, -51i16, 1i8));
assert_eq!((-8573.5918555f64).integer_decode(), (4713381968463931u64, -39i16, -1i8));
assert_eq!(2f64.powf(100.0).integer_decode(), (4503599627370496u64, 48i16, 1i8));
assert_eq!(0f64.integer_decode(), (0u64, -1075i16, 1i8));
assert_eq!((-0f64).integer_decode(), (0u64, -1075i16, -1i8));
assert_eq!(INFINITY.integer_decode(), (4503599627370496u64, 972i16, 1i8));
assert_eq!(NEG_INFINITY.integer_decode(), (4503599627370496, 972, -1));
assert_eq!(NAN.integer_decode(), (6755399441055744u64, 972i16, 1i8));
}
}