1755 lines
53 KiB
Rust
1755 lines
53 KiB
Rust
// Copyright 2012-2015 The Rust Project Developers. See the COPYRIGHT
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// file at the top-level directory of this distribution and at
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// http://rust-lang.org/COPYRIGHT.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! This module provides constants which are specific to the implementation
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//! of the `f32` floating point data type. Mathematically significant
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//! numbers are provided in the `consts` sub-module.
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//!
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//! *[See also the `f32` primitive type](../primitive.f32.html).*
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#![stable(feature = "rust1", since = "1.0.0")]
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#![allow(missing_docs)]
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#[cfg(not(test))]
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use core::num;
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#[cfg(not(test))]
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use intrinsics;
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#[cfg(not(test))]
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use num::FpCategory;
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#[stable(feature = "rust1", since = "1.0.0")]
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pub use core::f32::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON};
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#[stable(feature = "rust1", since = "1.0.0")]
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pub use core::f32::{MIN_EXP, MAX_EXP, MIN_10_EXP};
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#[stable(feature = "rust1", since = "1.0.0")]
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pub use core::f32::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
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#[stable(feature = "rust1", since = "1.0.0")]
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pub use core::f32::{MIN, MIN_POSITIVE, MAX};
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#[stable(feature = "rust1", since = "1.0.0")]
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pub use core::f32::consts;
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#[allow(dead_code)]
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mod cmath {
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use libc::{c_float, c_int};
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extern {
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pub fn cbrtf(n: c_float) -> c_float;
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pub fn erff(n: c_float) -> c_float;
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pub fn erfcf(n: c_float) -> c_float;
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pub fn expm1f(n: c_float) -> c_float;
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pub fn fdimf(a: c_float, b: c_float) -> c_float;
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pub fn fmodf(a: c_float, b: c_float) -> c_float;
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pub fn ilogbf(n: c_float) -> c_int;
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pub fn logbf(n: c_float) -> c_float;
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pub fn log1pf(n: c_float) -> c_float;
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pub fn modff(n: c_float, iptr: &mut c_float) -> c_float;
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pub fn nextafterf(x: c_float, y: c_float) -> c_float;
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pub fn tgammaf(n: c_float) -> c_float;
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#[cfg_attr(all(windows, target_env = "msvc"), link_name = "__lgammaf_r")]
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pub fn lgammaf_r(n: c_float, sign: &mut c_int) -> c_float;
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#[cfg_attr(all(windows, target_env = "msvc"), link_name = "_hypotf")]
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pub fn hypotf(x: c_float, y: c_float) -> c_float;
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}
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// See the comments in the `floor` function for why MSVC is special
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// here.
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#[cfg(not(target_env = "msvc"))]
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extern {
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pub fn acosf(n: c_float) -> c_float;
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pub fn asinf(n: c_float) -> c_float;
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pub fn atan2f(a: c_float, b: c_float) -> c_float;
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pub fn atanf(n: c_float) -> c_float;
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pub fn coshf(n: c_float) -> c_float;
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pub fn sinhf(n: c_float) -> c_float;
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pub fn tanf(n: c_float) -> c_float;
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pub fn tanhf(n: c_float) -> c_float;
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}
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#[cfg(target_env = "msvc")]
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pub use self::shims::*;
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#[cfg(target_env = "msvc")]
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mod shims {
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use libc::c_float;
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#[inline]
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pub unsafe fn acosf(n: c_float) -> c_float {
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f64::acos(n as f64) as c_float
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}
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#[inline]
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pub unsafe fn asinf(n: c_float) -> c_float {
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f64::asin(n as f64) as c_float
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}
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#[inline]
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pub unsafe fn atan2f(n: c_float, b: c_float) -> c_float {
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f64::atan2(n as f64, b as f64) as c_float
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}
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#[inline]
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pub unsafe fn atanf(n: c_float) -> c_float {
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f64::atan(n as f64) as c_float
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}
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#[inline]
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pub unsafe fn coshf(n: c_float) -> c_float {
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f64::cosh(n as f64) as c_float
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}
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#[inline]
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pub unsafe fn sinhf(n: c_float) -> c_float {
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f64::sinh(n as f64) as c_float
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}
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#[inline]
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pub unsafe fn tanf(n: c_float) -> c_float {
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f64::tan(n as f64) as c_float
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}
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#[inline]
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pub unsafe fn tanhf(n: c_float) -> c_float {
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f64::tanh(n as f64) as c_float
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}
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}
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}
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#[cfg(not(test))]
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#[lang = "f32"]
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impl f32 {
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/// Returns `true` if this value is `NaN` and false otherwise.
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///
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/// ```
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/// use std::f32;
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///
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/// let nan = f32::NAN;
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/// let f = 7.0_f32;
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///
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/// assert!(nan.is_nan());
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/// assert!(!f.is_nan());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_nan(self) -> bool { num::Float::is_nan(self) }
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/// Returns `true` if this value is positive infinity or negative infinity and
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/// false otherwise.
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///
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/// ```
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/// use std::f32;
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///
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/// let f = 7.0f32;
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/// let inf = f32::INFINITY;
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/// let neg_inf = f32::NEG_INFINITY;
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/// let nan = f32::NAN;
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///
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/// assert!(!f.is_infinite());
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/// assert!(!nan.is_infinite());
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///
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/// assert!(inf.is_infinite());
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/// assert!(neg_inf.is_infinite());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) }
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/// Returns `true` if this number is neither infinite nor `NaN`.
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///
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/// ```
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/// use std::f32;
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///
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/// let f = 7.0f32;
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/// let inf = f32::INFINITY;
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/// let neg_inf = f32::NEG_INFINITY;
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/// let nan = f32::NAN;
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///
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/// assert!(f.is_finite());
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///
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/// assert!(!nan.is_finite());
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/// assert!(!inf.is_finite());
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/// assert!(!neg_inf.is_finite());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_finite(self) -> bool { num::Float::is_finite(self) }
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/// Returns `true` if the number is neither zero, infinite,
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/// [subnormal][subnormal], or `NaN`.
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///
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/// ```
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/// use std::f32;
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///
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/// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
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/// let max = f32::MAX;
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/// let lower_than_min = 1.0e-40_f32;
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/// let zero = 0.0_f32;
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///
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/// assert!(min.is_normal());
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/// assert!(max.is_normal());
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///
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/// assert!(!zero.is_normal());
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/// assert!(!f32::NAN.is_normal());
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/// assert!(!f32::INFINITY.is_normal());
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/// // Values between `0` and `min` are Subnormal.
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/// assert!(!lower_than_min.is_normal());
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/// ```
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/// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_normal(self) -> bool { num::Float::is_normal(self) }
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/// Returns the floating point category of the number. If only one property
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/// is going to be tested, it is generally faster to use the specific
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/// predicate instead.
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///
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/// ```
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/// use std::num::FpCategory;
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/// use std::f32;
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///
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/// let num = 12.4_f32;
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/// let inf = f32::INFINITY;
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///
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/// assert_eq!(num.classify(), FpCategory::Normal);
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/// assert_eq!(inf.classify(), FpCategory::Infinite);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn classify(self) -> FpCategory { num::Float::classify(self) }
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/// Returns the largest integer less than or equal to a number.
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///
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/// ```
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/// let f = 3.99_f32;
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/// let g = 3.0_f32;
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///
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/// assert_eq!(f.floor(), 3.0);
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/// assert_eq!(g.floor(), 3.0);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn floor(self) -> f32 {
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// On MSVC LLVM will lower many math intrinsics to a call to the
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// corresponding function. On MSVC, however, many of these functions
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// aren't actually available as symbols to call, but rather they are all
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// `static inline` functions in header files. This means that from a C
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// perspective it's "compatible", but not so much from an ABI
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// perspective (which we're worried about).
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//
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// The inline header functions always just cast to a f64 and do their
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// operation, so we do that here as well, but only for MSVC targets.
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//
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// Note that there are many MSVC-specific float operations which
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// redirect to this comment, so `floorf` is just one case of a missing
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// function on MSVC, but there are many others elsewhere.
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#[cfg(target_env = "msvc")]
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return (self as f64).floor() as f32;
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#[cfg(not(target_env = "msvc"))]
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return unsafe { intrinsics::floorf32(self) };
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}
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/// Returns the smallest integer greater than or equal to a number.
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///
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/// ```
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/// let f = 3.01_f32;
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/// let g = 4.0_f32;
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///
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/// assert_eq!(f.ceil(), 4.0);
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/// assert_eq!(g.ceil(), 4.0);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn ceil(self) -> f32 {
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// see notes above in `floor`
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#[cfg(target_env = "msvc")]
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return (self as f64).ceil() as f32;
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#[cfg(not(target_env = "msvc"))]
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return unsafe { intrinsics::ceilf32(self) };
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}
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/// Returns the nearest integer to a number. Round half-way cases away from
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/// `0.0`.
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///
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/// ```
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/// let f = 3.3_f32;
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/// let g = -3.3_f32;
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///
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/// assert_eq!(f.round(), 3.0);
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/// assert_eq!(g.round(), -3.0);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn round(self) -> f32 {
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unsafe { intrinsics::roundf32(self) }
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}
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/// Returns the integer part of a number.
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///
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/// ```
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/// let f = 3.3_f32;
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/// let g = -3.7_f32;
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///
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/// assert_eq!(f.trunc(), 3.0);
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/// assert_eq!(g.trunc(), -3.0);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn trunc(self) -> f32 {
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unsafe { intrinsics::truncf32(self) }
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}
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/// Returns the fractional part of a number.
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///
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/// ```
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/// use std::f32;
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///
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/// let x = 3.5_f32;
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/// let y = -3.5_f32;
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/// let abs_difference_x = (x.fract() - 0.5).abs();
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/// let abs_difference_y = (y.fract() - (-0.5)).abs();
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///
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/// assert!(abs_difference_x <= f32::EPSILON);
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/// assert!(abs_difference_y <= f32::EPSILON);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn fract(self) -> f32 { self - self.trunc() }
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/// Computes the absolute value of `self`. Returns `NAN` if the
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/// number is `NAN`.
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///
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/// ```
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/// use std::f32;
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///
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/// let x = 3.5_f32;
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/// let y = -3.5_f32;
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///
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/// let abs_difference_x = (x.abs() - x).abs();
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/// let abs_difference_y = (y.abs() - (-y)).abs();
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///
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/// assert!(abs_difference_x <= f32::EPSILON);
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/// assert!(abs_difference_y <= f32::EPSILON);
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///
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/// assert!(f32::NAN.abs().is_nan());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn abs(self) -> f32 { num::Float::abs(self) }
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/// Returns a number that represents the sign of `self`.
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///
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/// - `1.0` if the number is positive, `+0.0` or `INFINITY`
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/// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
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/// - `NAN` if the number is `NAN`
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///
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/// ```
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/// use std::f32;
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///
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/// let f = 3.5_f32;
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///
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/// assert_eq!(f.signum(), 1.0);
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/// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
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///
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/// assert!(f32::NAN.signum().is_nan());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn signum(self) -> f32 { num::Float::signum(self) }
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/// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
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/// positive sign bit and positive infinity.
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///
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/// ```
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/// let f = 7.0_f32;
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/// let g = -7.0_f32;
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///
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/// assert!(f.is_sign_positive());
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/// assert!(!g.is_sign_positive());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_sign_positive(self) -> bool { num::Float::is_sign_positive(self) }
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/// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
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/// negative sign bit and negative infinity.
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///
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/// ```
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/// let f = 7.0f32;
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/// let g = -7.0f32;
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///
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/// assert!(!f.is_sign_negative());
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/// assert!(g.is_sign_negative());
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn is_sign_negative(self) -> bool { num::Float::is_sign_negative(self) }
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/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
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/// error. This produces a more accurate result with better performance than
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/// a separate multiplication operation followed by an add.
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///
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/// ```
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/// use std::f32;
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///
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/// let m = 10.0_f32;
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/// let x = 4.0_f32;
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/// let b = 60.0_f32;
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///
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/// // 100.0
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/// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn mul_add(self, a: f32, b: f32) -> f32 {
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unsafe { intrinsics::fmaf32(self, a, b) }
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}
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/// Takes the reciprocal (inverse) of a number, `1/x`.
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///
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/// ```
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/// use std::f32;
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///
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/// let x = 2.0_f32;
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/// let abs_difference = (x.recip() - (1.0/x)).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn recip(self) -> f32 { num::Float::recip(self) }
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/// Raises a number to an integer power.
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///
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/// Using this function is generally faster than using `powf`
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///
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/// ```
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/// use std::f32;
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///
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/// let x = 2.0_f32;
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/// let abs_difference = (x.powi(2) - x*x).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn powi(self, n: i32) -> f32 { num::Float::powi(self, n) }
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/// Raises a number to a floating point power.
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///
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/// ```
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/// use std::f32;
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///
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/// let x = 2.0_f32;
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/// let abs_difference = (x.powf(2.0) - x*x).abs();
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///
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/// assert!(abs_difference <= f32::EPSILON);
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/// ```
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#[stable(feature = "rust1", since = "1.0.0")]
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#[inline]
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pub fn powf(self, n: f32) -> f32 {
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// see notes above in `floor`
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#[cfg(target_env = "msvc")]
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return (self as f64).powf(n as f64) as f32;
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#[cfg(not(target_env = "msvc"))]
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return unsafe { intrinsics::powf32(self, n) };
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}
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/// Takes the square root of a number.
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///
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/// Returns NaN if `self` is a negative number.
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///
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/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let positive = 4.0_f32;
|
|
/// let negative = -4.0_f32;
|
|
///
|
|
/// let abs_difference = (positive.sqrt() - 2.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// assert!(negative.sqrt().is_nan());
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn sqrt(self) -> f32 {
|
|
if self < 0.0 {
|
|
NAN
|
|
} else {
|
|
unsafe { intrinsics::sqrtf32(self) }
|
|
}
|
|
}
|
|
|
|
/// Returns `e^(self)`, (the exponential function).
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let one = 1.0f32;
|
|
/// // e^1
|
|
/// let e = one.exp();
|
|
///
|
|
/// // ln(e) - 1 == 0
|
|
/// let abs_difference = (e.ln() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn exp(self) -> f32 {
|
|
// see notes above in `floor`
|
|
#[cfg(target_env = "msvc")]
|
|
return (self as f64).exp() as f32;
|
|
#[cfg(not(target_env = "msvc"))]
|
|
return unsafe { intrinsics::expf32(self) };
|
|
}
|
|
|
|
/// Returns `2^(self)`.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let f = 2.0f32;
|
|
///
|
|
/// // 2^2 - 4 == 0
|
|
/// let abs_difference = (f.exp2() - 4.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn exp2(self) -> f32 {
|
|
unsafe { intrinsics::exp2f32(self) }
|
|
}
|
|
|
|
/// Returns the natural logarithm of the number.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let one = 1.0f32;
|
|
/// // e^1
|
|
/// let e = one.exp();
|
|
///
|
|
/// // ln(e) - 1 == 0
|
|
/// let abs_difference = (e.ln() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn ln(self) -> f32 {
|
|
// see notes above in `floor`
|
|
#[cfg(target_env = "msvc")]
|
|
return (self as f64).ln() as f32;
|
|
#[cfg(not(target_env = "msvc"))]
|
|
return unsafe { intrinsics::logf32(self) };
|
|
}
|
|
|
|
/// Returns the logarithm of the number with respect to an arbitrary base.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let ten = 10.0f32;
|
|
/// let two = 2.0f32;
|
|
///
|
|
/// // log10(10) - 1 == 0
|
|
/// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
|
|
///
|
|
/// // log2(2) - 1 == 0
|
|
/// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference_10 <= f32::EPSILON);
|
|
/// assert!(abs_difference_2 <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn log(self, base: f32) -> f32 { self.ln() / base.ln() }
|
|
|
|
/// Returns the base 2 logarithm of the number.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let two = 2.0f32;
|
|
///
|
|
/// // log2(2) - 1 == 0
|
|
/// let abs_difference = (two.log2() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn log2(self) -> f32 {
|
|
#[cfg(target_os = "android")]
|
|
return ::sys::android::log2f32(self);
|
|
#[cfg(not(target_os = "android"))]
|
|
return unsafe { intrinsics::log2f32(self) };
|
|
}
|
|
|
|
/// Returns the base 10 logarithm of the number.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let ten = 10.0f32;
|
|
///
|
|
/// // log10(10) - 1 == 0
|
|
/// let abs_difference = (ten.log10() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn log10(self) -> f32 {
|
|
// see notes above in `floor`
|
|
#[cfg(target_env = "msvc")]
|
|
return (self as f64).log10() as f32;
|
|
#[cfg(not(target_env = "msvc"))]
|
|
return unsafe { intrinsics::log10f32(self) };
|
|
}
|
|
|
|
/// Converts radians to degrees.
|
|
///
|
|
/// ```
|
|
/// use std::f32::{self, consts};
|
|
///
|
|
/// let angle = consts::PI;
|
|
///
|
|
/// let abs_difference = (angle.to_degrees() - 180.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
|
|
#[inline]
|
|
pub fn to_degrees(self) -> f32 { num::Float::to_degrees(self) }
|
|
|
|
/// Converts degrees to radians.
|
|
///
|
|
/// ```
|
|
/// use std::f32::{self, consts};
|
|
///
|
|
/// let angle = 180.0f32;
|
|
///
|
|
/// let abs_difference = (angle.to_radians() - consts::PI).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
|
|
#[inline]
|
|
pub fn to_radians(self) -> f32 { num::Float::to_radians(self) }
|
|
|
|
/// Returns the maximum of the two numbers.
|
|
///
|
|
/// ```
|
|
/// let x = 1.0f32;
|
|
/// let y = 2.0f32;
|
|
///
|
|
/// assert_eq!(x.max(y), y);
|
|
/// ```
|
|
///
|
|
/// If one of the arguments is NaN, then the other argument is returned.
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn max(self, other: f32) -> f32 {
|
|
num::Float::max(self, other)
|
|
}
|
|
|
|
/// Returns the minimum of the two numbers.
|
|
///
|
|
/// ```
|
|
/// let x = 1.0f32;
|
|
/// let y = 2.0f32;
|
|
///
|
|
/// assert_eq!(x.min(y), x);
|
|
/// ```
|
|
///
|
|
/// If one of the arguments is NaN, then the other argument is returned.
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn min(self, other: f32) -> f32 {
|
|
num::Float::min(self, other)
|
|
}
|
|
|
|
/// The positive difference of two numbers.
|
|
///
|
|
/// * If `self <= other`: `0:0`
|
|
/// * Else: `self - other`
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let x = 3.0f32;
|
|
/// let y = -3.0f32;
|
|
///
|
|
/// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
|
|
/// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
|
|
///
|
|
/// assert!(abs_difference_x <= f32::EPSILON);
|
|
/// assert!(abs_difference_y <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
#[rustc_deprecated(since = "1.10.0",
|
|
reason = "you probably meant `(self - other).abs()`: \
|
|
this operation is `(self - other).max(0.0)` (also \
|
|
known as `fdimf` in C). If you truly need the positive \
|
|
difference, consider using that expression or the C function \
|
|
`fdimf`, depending on how you wish to handle NaN (please consider \
|
|
filing an issue describing your use-case too).")]
|
|
pub fn abs_sub(self, other: f32) -> f32 {
|
|
unsafe { cmath::fdimf(self, other) }
|
|
}
|
|
|
|
/// Takes the cubic root of a number.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let x = 8.0f32;
|
|
///
|
|
/// // x^(1/3) - 2 == 0
|
|
/// let abs_difference = (x.cbrt() - 2.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn cbrt(self) -> f32 {
|
|
unsafe { cmath::cbrtf(self) }
|
|
}
|
|
|
|
/// Calculates the length of the hypotenuse of a right-angle triangle given
|
|
/// legs of length `x` and `y`.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let x = 2.0f32;
|
|
/// let y = 3.0f32;
|
|
///
|
|
/// // sqrt(x^2 + y^2)
|
|
/// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn hypot(self, other: f32) -> f32 {
|
|
unsafe { cmath::hypotf(self, other) }
|
|
}
|
|
|
|
/// Computes the sine of a number (in radians).
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let x = f32::consts::PI/2.0;
|
|
///
|
|
/// let abs_difference = (x.sin() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn sin(self) -> f32 {
|
|
// see notes in `core::f32::Float::floor`
|
|
#[cfg(target_env = "msvc")]
|
|
return (self as f64).sin() as f32;
|
|
#[cfg(not(target_env = "msvc"))]
|
|
return unsafe { intrinsics::sinf32(self) };
|
|
}
|
|
|
|
/// Computes the cosine of a number (in radians).
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let x = 2.0*f32::consts::PI;
|
|
///
|
|
/// let abs_difference = (x.cos() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn cos(self) -> f32 {
|
|
// see notes in `core::f32::Float::floor`
|
|
#[cfg(target_env = "msvc")]
|
|
return (self as f64).cos() as f32;
|
|
#[cfg(not(target_env = "msvc"))]
|
|
return unsafe { intrinsics::cosf32(self) };
|
|
}
|
|
|
|
/// Computes the tangent of a number (in radians).
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let x = f32::consts::PI / 4.0;
|
|
/// let abs_difference = (x.tan() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn tan(self) -> f32 {
|
|
unsafe { cmath::tanf(self) }
|
|
}
|
|
|
|
/// Computes the arcsine of a number. Return value is in radians in
|
|
/// the range [-pi/2, pi/2] or NaN if the number is outside the range
|
|
/// [-1, 1].
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let f = f32::consts::PI / 2.0;
|
|
///
|
|
/// // asin(sin(pi/2))
|
|
/// let abs_difference = (f.sin().asin() - f32::consts::PI / 2.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn asin(self) -> f32 {
|
|
unsafe { cmath::asinf(self) }
|
|
}
|
|
|
|
/// Computes the arccosine of a number. Return value is in radians in
|
|
/// the range [0, pi] or NaN if the number is outside the range
|
|
/// [-1, 1].
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let f = f32::consts::PI / 4.0;
|
|
///
|
|
/// // acos(cos(pi/4))
|
|
/// let abs_difference = (f.cos().acos() - f32::consts::PI / 4.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn acos(self) -> f32 {
|
|
unsafe { cmath::acosf(self) }
|
|
}
|
|
|
|
/// Computes the arctangent of a number. Return value is in radians in the
|
|
/// range [-pi/2, pi/2];
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let f = 1.0f32;
|
|
///
|
|
/// // atan(tan(1))
|
|
/// let abs_difference = (f.tan().atan() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn atan(self) -> f32 {
|
|
unsafe { cmath::atanf(self) }
|
|
}
|
|
|
|
/// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
|
|
///
|
|
/// * `x = 0`, `y = 0`: `0`
|
|
/// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
|
|
/// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
|
|
/// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let pi = f32::consts::PI;
|
|
/// // All angles from horizontal right (+x)
|
|
/// // 45 deg counter-clockwise
|
|
/// let x1 = 3.0f32;
|
|
/// let y1 = -3.0f32;
|
|
///
|
|
/// // 135 deg clockwise
|
|
/// let x2 = -3.0f32;
|
|
/// let y2 = 3.0f32;
|
|
///
|
|
/// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
|
|
/// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
|
|
///
|
|
/// assert!(abs_difference_1 <= f32::EPSILON);
|
|
/// assert!(abs_difference_2 <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn atan2(self, other: f32) -> f32 {
|
|
unsafe { cmath::atan2f(self, other) }
|
|
}
|
|
|
|
/// Simultaneously computes the sine and cosine of the number, `x`. Returns
|
|
/// `(sin(x), cos(x))`.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let x = f32::consts::PI/4.0;
|
|
/// let f = x.sin_cos();
|
|
///
|
|
/// let abs_difference_0 = (f.0 - x.sin()).abs();
|
|
/// let abs_difference_1 = (f.1 - x.cos()).abs();
|
|
///
|
|
/// assert!(abs_difference_0 <= f32::EPSILON);
|
|
/// assert!(abs_difference_1 <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn sin_cos(self) -> (f32, f32) {
|
|
(self.sin(), self.cos())
|
|
}
|
|
|
|
/// Returns `e^(self) - 1` in a way that is accurate even if the
|
|
/// number is close to zero.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let x = 6.0f32;
|
|
///
|
|
/// // e^(ln(6)) - 1
|
|
/// let abs_difference = (x.ln().exp_m1() - 5.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn exp_m1(self) -> f32 {
|
|
unsafe { cmath::expm1f(self) }
|
|
}
|
|
|
|
/// Returns `ln(1+n)` (natural logarithm) more accurately than if
|
|
/// the operations were performed separately.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let x = f32::consts::E - 1.0;
|
|
///
|
|
/// // ln(1 + (e - 1)) == ln(e) == 1
|
|
/// let abs_difference = (x.ln_1p() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn ln_1p(self) -> f32 {
|
|
unsafe { cmath::log1pf(self) }
|
|
}
|
|
|
|
/// Hyperbolic sine function.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let e = f32::consts::E;
|
|
/// let x = 1.0f32;
|
|
///
|
|
/// let f = x.sinh();
|
|
/// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
|
|
/// let g = (e*e - 1.0)/(2.0*e);
|
|
/// let abs_difference = (f - g).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn sinh(self) -> f32 {
|
|
unsafe { cmath::sinhf(self) }
|
|
}
|
|
|
|
/// Hyperbolic cosine function.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let e = f32::consts::E;
|
|
/// let x = 1.0f32;
|
|
/// let f = x.cosh();
|
|
/// // Solving cosh() at 1 gives this result
|
|
/// let g = (e*e + 1.0)/(2.0*e);
|
|
/// let abs_difference = (f - g).abs();
|
|
///
|
|
/// // Same result
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn cosh(self) -> f32 {
|
|
unsafe { cmath::coshf(self) }
|
|
}
|
|
|
|
/// Hyperbolic tangent function.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let e = f32::consts::E;
|
|
/// let x = 1.0f32;
|
|
///
|
|
/// let f = x.tanh();
|
|
/// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
|
|
/// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
|
|
/// let abs_difference = (f - g).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn tanh(self) -> f32 {
|
|
unsafe { cmath::tanhf(self) }
|
|
}
|
|
|
|
/// Inverse hyperbolic sine function.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let x = 1.0f32;
|
|
/// let f = x.sinh().asinh();
|
|
///
|
|
/// let abs_difference = (f - x).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn asinh(self) -> f32 {
|
|
if self == NEG_INFINITY {
|
|
NEG_INFINITY
|
|
} else {
|
|
(self + ((self * self) + 1.0).sqrt()).ln()
|
|
}
|
|
}
|
|
|
|
/// Inverse hyperbolic cosine function.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let x = 1.0f32;
|
|
/// let f = x.cosh().acosh();
|
|
///
|
|
/// let abs_difference = (f - x).abs();
|
|
///
|
|
/// assert!(abs_difference <= f32::EPSILON);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn acosh(self) -> f32 {
|
|
match self {
|
|
x if x < 1.0 => ::f32::NAN,
|
|
x => (x + ((x * x) - 1.0).sqrt()).ln(),
|
|
}
|
|
}
|
|
|
|
/// Inverse hyperbolic tangent function.
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
///
|
|
/// let e = f32::consts::E;
|
|
/// let f = e.tanh().atanh();
|
|
///
|
|
/// let abs_difference = (f - e).abs();
|
|
///
|
|
/// assert!(abs_difference <= 1e-5);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn atanh(self) -> f32 {
|
|
0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
|
|
}
|
|
|
|
/// Raw transmutation to `u32`.
|
|
///
|
|
/// Converts the `f32` into its raw memory representation,
|
|
/// similar to the `transmute` function.
|
|
///
|
|
/// Note that this function is distinct from casting.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
|
|
/// assert_eq!((12.5f32).to_bits(), 0x41480000);
|
|
///
|
|
/// ```
|
|
#[stable(feature = "float_bits_conv", since = "1.21.0")]
|
|
#[inline]
|
|
pub fn to_bits(self) -> u32 {
|
|
unsafe { ::mem::transmute(self) }
|
|
}
|
|
|
|
/// Raw transmutation from `u32`.
|
|
///
|
|
/// Converts the given `u32` containing the float's raw memory
|
|
/// representation into the `f32` type, similar to the
|
|
/// `transmute` function.
|
|
///
|
|
/// There is only one difference to a bare `transmute`:
|
|
/// Due to the implications onto Rust's safety promises being
|
|
/// uncertain, if the representation of a signaling NaN "sNaN" float
|
|
/// is passed to the function, the implementation is allowed to
|
|
/// return a quiet NaN instead.
|
|
///
|
|
/// Note that this function is distinct from casting.
|
|
///
|
|
/// # Examples
|
|
///
|
|
/// ```
|
|
/// use std::f32;
|
|
/// let v = f32::from_bits(0x41480000);
|
|
/// let difference = (v - 12.5).abs();
|
|
/// assert!(difference <= 1e-5);
|
|
/// // Example for a signaling NaN value:
|
|
/// let snan = 0x7F800001;
|
|
/// assert_ne!(f32::from_bits(snan).to_bits(), snan);
|
|
/// ```
|
|
#[stable(feature = "float_bits_conv", since = "1.21.0")]
|
|
#[inline]
|
|
pub fn from_bits(mut v: u32) -> Self {
|
|
const EXP_MASK: u32 = 0x7F800000;
|
|
const FRACT_MASK: u32 = 0x007FFFFF;
|
|
if v & EXP_MASK == EXP_MASK && v & FRACT_MASK != 0 {
|
|
// While IEEE 754-2008 specifies encodings for quiet NaNs
|
|
// and signaling ones, certain MIPS and PA-RISC
|
|
// CPUs treat signaling NaNs differently.
|
|
// Therefore to be safe, we pass a known quiet NaN
|
|
// if v is any kind of NaN.
|
|
// The check above only assumes IEEE 754-1985 to be
|
|
// valid.
|
|
v = unsafe { ::mem::transmute(NAN) };
|
|
}
|
|
unsafe { ::mem::transmute(v) }
|
|
}
|
|
}
|
|
|
|
#[cfg(test)]
|
|
mod tests {
|
|
use f32;
|
|
use f32::*;
|
|
use num::*;
|
|
use num::FpCategory as Fp;
|
|
|
|
#[test]
|
|
fn test_num_f32() {
|
|
test_num(10f32, 2f32);
|
|
}
|
|
|
|
#[test]
|
|
fn test_min_nan() {
|
|
assert_eq!(NAN.min(2.0), 2.0);
|
|
assert_eq!(2.0f32.min(NAN), 2.0);
|
|
}
|
|
|
|
#[test]
|
|
fn test_max_nan() {
|
|
assert_eq!(NAN.max(2.0), 2.0);
|
|
assert_eq!(2.0f32.max(NAN), 2.0);
|
|
}
|
|
|
|
#[test]
|
|
fn test_nan() {
|
|
let nan: f32 = f32::NAN;
|
|
assert!(nan.is_nan());
|
|
assert!(!nan.is_infinite());
|
|
assert!(!nan.is_finite());
|
|
assert!(!nan.is_normal());
|
|
assert!(nan.is_sign_positive());
|
|
assert!(!nan.is_sign_negative());
|
|
assert_eq!(Fp::Nan, nan.classify());
|
|
}
|
|
|
|
#[test]
|
|
fn test_infinity() {
|
|
let inf: f32 = f32::INFINITY;
|
|
assert!(inf.is_infinite());
|
|
assert!(!inf.is_finite());
|
|
assert!(inf.is_sign_positive());
|
|
assert!(!inf.is_sign_negative());
|
|
assert!(!inf.is_nan());
|
|
assert!(!inf.is_normal());
|
|
assert_eq!(Fp::Infinite, inf.classify());
|
|
}
|
|
|
|
#[test]
|
|
fn test_neg_infinity() {
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert!(neg_inf.is_infinite());
|
|
assert!(!neg_inf.is_finite());
|
|
assert!(!neg_inf.is_sign_positive());
|
|
assert!(neg_inf.is_sign_negative());
|
|
assert!(!neg_inf.is_nan());
|
|
assert!(!neg_inf.is_normal());
|
|
assert_eq!(Fp::Infinite, neg_inf.classify());
|
|
}
|
|
|
|
#[test]
|
|
fn test_zero() {
|
|
let zero: f32 = 0.0f32;
|
|
assert_eq!(0.0, zero);
|
|
assert!(!zero.is_infinite());
|
|
assert!(zero.is_finite());
|
|
assert!(zero.is_sign_positive());
|
|
assert!(!zero.is_sign_negative());
|
|
assert!(!zero.is_nan());
|
|
assert!(!zero.is_normal());
|
|
assert_eq!(Fp::Zero, zero.classify());
|
|
}
|
|
|
|
#[test]
|
|
fn test_neg_zero() {
|
|
let neg_zero: f32 = -0.0;
|
|
assert_eq!(0.0, neg_zero);
|
|
assert!(!neg_zero.is_infinite());
|
|
assert!(neg_zero.is_finite());
|
|
assert!(!neg_zero.is_sign_positive());
|
|
assert!(neg_zero.is_sign_negative());
|
|
assert!(!neg_zero.is_nan());
|
|
assert!(!neg_zero.is_normal());
|
|
assert_eq!(Fp::Zero, neg_zero.classify());
|
|
}
|
|
|
|
#[test]
|
|
fn test_one() {
|
|
let one: f32 = 1.0f32;
|
|
assert_eq!(1.0, one);
|
|
assert!(!one.is_infinite());
|
|
assert!(one.is_finite());
|
|
assert!(one.is_sign_positive());
|
|
assert!(!one.is_sign_negative());
|
|
assert!(!one.is_nan());
|
|
assert!(one.is_normal());
|
|
assert_eq!(Fp::Normal, one.classify());
|
|
}
|
|
|
|
#[test]
|
|
fn test_is_nan() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert!(nan.is_nan());
|
|
assert!(!0.0f32.is_nan());
|
|
assert!(!5.3f32.is_nan());
|
|
assert!(!(-10.732f32).is_nan());
|
|
assert!(!inf.is_nan());
|
|
assert!(!neg_inf.is_nan());
|
|
}
|
|
|
|
#[test]
|
|
fn test_is_infinite() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert!(!nan.is_infinite());
|
|
assert!(inf.is_infinite());
|
|
assert!(neg_inf.is_infinite());
|
|
assert!(!0.0f32.is_infinite());
|
|
assert!(!42.8f32.is_infinite());
|
|
assert!(!(-109.2f32).is_infinite());
|
|
}
|
|
|
|
#[test]
|
|
fn test_is_finite() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert!(!nan.is_finite());
|
|
assert!(!inf.is_finite());
|
|
assert!(!neg_inf.is_finite());
|
|
assert!(0.0f32.is_finite());
|
|
assert!(42.8f32.is_finite());
|
|
assert!((-109.2f32).is_finite());
|
|
}
|
|
|
|
#[test]
|
|
fn test_is_normal() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
let zero: f32 = 0.0f32;
|
|
let neg_zero: f32 = -0.0;
|
|
assert!(!nan.is_normal());
|
|
assert!(!inf.is_normal());
|
|
assert!(!neg_inf.is_normal());
|
|
assert!(!zero.is_normal());
|
|
assert!(!neg_zero.is_normal());
|
|
assert!(1f32.is_normal());
|
|
assert!(1e-37f32.is_normal());
|
|
assert!(!1e-38f32.is_normal());
|
|
}
|
|
|
|
#[test]
|
|
fn test_classify() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
let zero: f32 = 0.0f32;
|
|
let neg_zero: f32 = -0.0;
|
|
assert_eq!(nan.classify(), Fp::Nan);
|
|
assert_eq!(inf.classify(), Fp::Infinite);
|
|
assert_eq!(neg_inf.classify(), Fp::Infinite);
|
|
assert_eq!(zero.classify(), Fp::Zero);
|
|
assert_eq!(neg_zero.classify(), Fp::Zero);
|
|
assert_eq!(1f32.classify(), Fp::Normal);
|
|
assert_eq!(1e-37f32.classify(), Fp::Normal);
|
|
assert_eq!(1e-38f32.classify(), Fp::Subnormal);
|
|
}
|
|
|
|
#[test]
|
|
fn test_floor() {
|
|
assert_approx_eq!(1.0f32.floor(), 1.0f32);
|
|
assert_approx_eq!(1.3f32.floor(), 1.0f32);
|
|
assert_approx_eq!(1.5f32.floor(), 1.0f32);
|
|
assert_approx_eq!(1.7f32.floor(), 1.0f32);
|
|
assert_approx_eq!(0.0f32.floor(), 0.0f32);
|
|
assert_approx_eq!((-0.0f32).floor(), -0.0f32);
|
|
assert_approx_eq!((-1.0f32).floor(), -1.0f32);
|
|
assert_approx_eq!((-1.3f32).floor(), -2.0f32);
|
|
assert_approx_eq!((-1.5f32).floor(), -2.0f32);
|
|
assert_approx_eq!((-1.7f32).floor(), -2.0f32);
|
|
}
|
|
|
|
#[test]
|
|
fn test_ceil() {
|
|
assert_approx_eq!(1.0f32.ceil(), 1.0f32);
|
|
assert_approx_eq!(1.3f32.ceil(), 2.0f32);
|
|
assert_approx_eq!(1.5f32.ceil(), 2.0f32);
|
|
assert_approx_eq!(1.7f32.ceil(), 2.0f32);
|
|
assert_approx_eq!(0.0f32.ceil(), 0.0f32);
|
|
assert_approx_eq!((-0.0f32).ceil(), -0.0f32);
|
|
assert_approx_eq!((-1.0f32).ceil(), -1.0f32);
|
|
assert_approx_eq!((-1.3f32).ceil(), -1.0f32);
|
|
assert_approx_eq!((-1.5f32).ceil(), -1.0f32);
|
|
assert_approx_eq!((-1.7f32).ceil(), -1.0f32);
|
|
}
|
|
|
|
#[test]
|
|
fn test_round() {
|
|
assert_approx_eq!(1.0f32.round(), 1.0f32);
|
|
assert_approx_eq!(1.3f32.round(), 1.0f32);
|
|
assert_approx_eq!(1.5f32.round(), 2.0f32);
|
|
assert_approx_eq!(1.7f32.round(), 2.0f32);
|
|
assert_approx_eq!(0.0f32.round(), 0.0f32);
|
|
assert_approx_eq!((-0.0f32).round(), -0.0f32);
|
|
assert_approx_eq!((-1.0f32).round(), -1.0f32);
|
|
assert_approx_eq!((-1.3f32).round(), -1.0f32);
|
|
assert_approx_eq!((-1.5f32).round(), -2.0f32);
|
|
assert_approx_eq!((-1.7f32).round(), -2.0f32);
|
|
}
|
|
|
|
#[test]
|
|
fn test_trunc() {
|
|
assert_approx_eq!(1.0f32.trunc(), 1.0f32);
|
|
assert_approx_eq!(1.3f32.trunc(), 1.0f32);
|
|
assert_approx_eq!(1.5f32.trunc(), 1.0f32);
|
|
assert_approx_eq!(1.7f32.trunc(), 1.0f32);
|
|
assert_approx_eq!(0.0f32.trunc(), 0.0f32);
|
|
assert_approx_eq!((-0.0f32).trunc(), -0.0f32);
|
|
assert_approx_eq!((-1.0f32).trunc(), -1.0f32);
|
|
assert_approx_eq!((-1.3f32).trunc(), -1.0f32);
|
|
assert_approx_eq!((-1.5f32).trunc(), -1.0f32);
|
|
assert_approx_eq!((-1.7f32).trunc(), -1.0f32);
|
|
}
|
|
|
|
#[test]
|
|
fn test_fract() {
|
|
assert_approx_eq!(1.0f32.fract(), 0.0f32);
|
|
assert_approx_eq!(1.3f32.fract(), 0.3f32);
|
|
assert_approx_eq!(1.5f32.fract(), 0.5f32);
|
|
assert_approx_eq!(1.7f32.fract(), 0.7f32);
|
|
assert_approx_eq!(0.0f32.fract(), 0.0f32);
|
|
assert_approx_eq!((-0.0f32).fract(), -0.0f32);
|
|
assert_approx_eq!((-1.0f32).fract(), -0.0f32);
|
|
assert_approx_eq!((-1.3f32).fract(), -0.3f32);
|
|
assert_approx_eq!((-1.5f32).fract(), -0.5f32);
|
|
assert_approx_eq!((-1.7f32).fract(), -0.7f32);
|
|
}
|
|
|
|
#[test]
|
|
fn test_abs() {
|
|
assert_eq!(INFINITY.abs(), INFINITY);
|
|
assert_eq!(1f32.abs(), 1f32);
|
|
assert_eq!(0f32.abs(), 0f32);
|
|
assert_eq!((-0f32).abs(), 0f32);
|
|
assert_eq!((-1f32).abs(), 1f32);
|
|
assert_eq!(NEG_INFINITY.abs(), INFINITY);
|
|
assert_eq!((1f32/NEG_INFINITY).abs(), 0f32);
|
|
assert!(NAN.abs().is_nan());
|
|
}
|
|
|
|
#[test]
|
|
fn test_signum() {
|
|
assert_eq!(INFINITY.signum(), 1f32);
|
|
assert_eq!(1f32.signum(), 1f32);
|
|
assert_eq!(0f32.signum(), 1f32);
|
|
assert_eq!((-0f32).signum(), -1f32);
|
|
assert_eq!((-1f32).signum(), -1f32);
|
|
assert_eq!(NEG_INFINITY.signum(), -1f32);
|
|
assert_eq!((1f32/NEG_INFINITY).signum(), -1f32);
|
|
assert!(NAN.signum().is_nan());
|
|
}
|
|
|
|
#[test]
|
|
fn test_is_sign_positive() {
|
|
assert!(INFINITY.is_sign_positive());
|
|
assert!(1f32.is_sign_positive());
|
|
assert!(0f32.is_sign_positive());
|
|
assert!(!(-0f32).is_sign_positive());
|
|
assert!(!(-1f32).is_sign_positive());
|
|
assert!(!NEG_INFINITY.is_sign_positive());
|
|
assert!(!(1f32/NEG_INFINITY).is_sign_positive());
|
|
assert!(NAN.is_sign_positive());
|
|
assert!(!(-NAN).is_sign_positive());
|
|
}
|
|
|
|
#[test]
|
|
fn test_is_sign_negative() {
|
|
assert!(!INFINITY.is_sign_negative());
|
|
assert!(!1f32.is_sign_negative());
|
|
assert!(!0f32.is_sign_negative());
|
|
assert!((-0f32).is_sign_negative());
|
|
assert!((-1f32).is_sign_negative());
|
|
assert!(NEG_INFINITY.is_sign_negative());
|
|
assert!((1f32/NEG_INFINITY).is_sign_negative());
|
|
assert!(!NAN.is_sign_negative());
|
|
assert!((-NAN).is_sign_negative());
|
|
}
|
|
|
|
#[test]
|
|
fn test_mul_add() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert_approx_eq!(12.3f32.mul_add(4.5, 6.7), 62.05);
|
|
assert_approx_eq!((-12.3f32).mul_add(-4.5, -6.7), 48.65);
|
|
assert_approx_eq!(0.0f32.mul_add(8.9, 1.2), 1.2);
|
|
assert_approx_eq!(3.4f32.mul_add(-0.0, 5.6), 5.6);
|
|
assert!(nan.mul_add(7.8, 9.0).is_nan());
|
|
assert_eq!(inf.mul_add(7.8, 9.0), inf);
|
|
assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
|
|
assert_eq!(8.9f32.mul_add(inf, 3.2), inf);
|
|
assert_eq!((-3.2f32).mul_add(2.4, neg_inf), neg_inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_recip() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert_eq!(1.0f32.recip(), 1.0);
|
|
assert_eq!(2.0f32.recip(), 0.5);
|
|
assert_eq!((-0.4f32).recip(), -2.5);
|
|
assert_eq!(0.0f32.recip(), inf);
|
|
assert!(nan.recip().is_nan());
|
|
assert_eq!(inf.recip(), 0.0);
|
|
assert_eq!(neg_inf.recip(), 0.0);
|
|
}
|
|
|
|
#[test]
|
|
fn test_powi() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert_eq!(1.0f32.powi(1), 1.0);
|
|
assert_approx_eq!((-3.1f32).powi(2), 9.61);
|
|
assert_approx_eq!(5.9f32.powi(-2), 0.028727);
|
|
assert_eq!(8.3f32.powi(0), 1.0);
|
|
assert!(nan.powi(2).is_nan());
|
|
assert_eq!(inf.powi(3), inf);
|
|
assert_eq!(neg_inf.powi(2), inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_powf() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert_eq!(1.0f32.powf(1.0), 1.0);
|
|
assert_approx_eq!(3.4f32.powf(4.5), 246.408218);
|
|
assert_approx_eq!(2.7f32.powf(-3.2), 0.041652);
|
|
assert_approx_eq!((-3.1f32).powf(2.0), 9.61);
|
|
assert_approx_eq!(5.9f32.powf(-2.0), 0.028727);
|
|
assert_eq!(8.3f32.powf(0.0), 1.0);
|
|
assert!(nan.powf(2.0).is_nan());
|
|
assert_eq!(inf.powf(2.0), inf);
|
|
assert_eq!(neg_inf.powf(3.0), neg_inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_sqrt_domain() {
|
|
assert!(NAN.sqrt().is_nan());
|
|
assert!(NEG_INFINITY.sqrt().is_nan());
|
|
assert!((-1.0f32).sqrt().is_nan());
|
|
assert_eq!((-0.0f32).sqrt(), -0.0);
|
|
assert_eq!(0.0f32.sqrt(), 0.0);
|
|
assert_eq!(1.0f32.sqrt(), 1.0);
|
|
assert_eq!(INFINITY.sqrt(), INFINITY);
|
|
}
|
|
|
|
#[test]
|
|
fn test_exp() {
|
|
assert_eq!(1.0, 0.0f32.exp());
|
|
assert_approx_eq!(2.718282, 1.0f32.exp());
|
|
assert_approx_eq!(148.413162, 5.0f32.exp());
|
|
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
let nan: f32 = f32::NAN;
|
|
assert_eq!(inf, inf.exp());
|
|
assert_eq!(0.0, neg_inf.exp());
|
|
assert!(nan.exp().is_nan());
|
|
}
|
|
|
|
#[test]
|
|
fn test_exp2() {
|
|
assert_eq!(32.0, 5.0f32.exp2());
|
|
assert_eq!(1.0, 0.0f32.exp2());
|
|
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
let nan: f32 = f32::NAN;
|
|
assert_eq!(inf, inf.exp2());
|
|
assert_eq!(0.0, neg_inf.exp2());
|
|
assert!(nan.exp2().is_nan());
|
|
}
|
|
|
|
#[test]
|
|
fn test_ln() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert_approx_eq!(1.0f32.exp().ln(), 1.0);
|
|
assert!(nan.ln().is_nan());
|
|
assert_eq!(inf.ln(), inf);
|
|
assert!(neg_inf.ln().is_nan());
|
|
assert!((-2.3f32).ln().is_nan());
|
|
assert_eq!((-0.0f32).ln(), neg_inf);
|
|
assert_eq!(0.0f32.ln(), neg_inf);
|
|
assert_approx_eq!(4.0f32.ln(), 1.386294);
|
|
}
|
|
|
|
#[test]
|
|
fn test_log() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert_eq!(10.0f32.log(10.0), 1.0);
|
|
assert_approx_eq!(2.3f32.log(3.5), 0.664858);
|
|
assert_eq!(1.0f32.exp().log(1.0f32.exp()), 1.0);
|
|
assert!(1.0f32.log(1.0).is_nan());
|
|
assert!(1.0f32.log(-13.9).is_nan());
|
|
assert!(nan.log(2.3).is_nan());
|
|
assert_eq!(inf.log(10.0), inf);
|
|
assert!(neg_inf.log(8.8).is_nan());
|
|
assert!((-2.3f32).log(0.1).is_nan());
|
|
assert_eq!((-0.0f32).log(2.0), neg_inf);
|
|
assert_eq!(0.0f32.log(7.0), neg_inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_log2() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert_approx_eq!(10.0f32.log2(), 3.321928);
|
|
assert_approx_eq!(2.3f32.log2(), 1.201634);
|
|
assert_approx_eq!(1.0f32.exp().log2(), 1.442695);
|
|
assert!(nan.log2().is_nan());
|
|
assert_eq!(inf.log2(), inf);
|
|
assert!(neg_inf.log2().is_nan());
|
|
assert!((-2.3f32).log2().is_nan());
|
|
assert_eq!((-0.0f32).log2(), neg_inf);
|
|
assert_eq!(0.0f32.log2(), neg_inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_log10() {
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert_eq!(10.0f32.log10(), 1.0);
|
|
assert_approx_eq!(2.3f32.log10(), 0.361728);
|
|
assert_approx_eq!(1.0f32.exp().log10(), 0.434294);
|
|
assert_eq!(1.0f32.log10(), 0.0);
|
|
assert!(nan.log10().is_nan());
|
|
assert_eq!(inf.log10(), inf);
|
|
assert!(neg_inf.log10().is_nan());
|
|
assert!((-2.3f32).log10().is_nan());
|
|
assert_eq!((-0.0f32).log10(), neg_inf);
|
|
assert_eq!(0.0f32.log10(), neg_inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_to_degrees() {
|
|
let pi: f32 = consts::PI;
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert_eq!(0.0f32.to_degrees(), 0.0);
|
|
assert_approx_eq!((-5.8f32).to_degrees(), -332.315521);
|
|
assert_eq!(pi.to_degrees(), 180.0);
|
|
assert!(nan.to_degrees().is_nan());
|
|
assert_eq!(inf.to_degrees(), inf);
|
|
assert_eq!(neg_inf.to_degrees(), neg_inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_to_radians() {
|
|
let pi: f32 = consts::PI;
|
|
let nan: f32 = f32::NAN;
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
assert_eq!(0.0f32.to_radians(), 0.0);
|
|
assert_approx_eq!(154.6f32.to_radians(), 2.698279);
|
|
assert_approx_eq!((-332.31f32).to_radians(), -5.799903);
|
|
assert_eq!(180.0f32.to_radians(), pi);
|
|
assert!(nan.to_radians().is_nan());
|
|
assert_eq!(inf.to_radians(), inf);
|
|
assert_eq!(neg_inf.to_radians(), neg_inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_asinh() {
|
|
assert_eq!(0.0f32.asinh(), 0.0f32);
|
|
assert_eq!((-0.0f32).asinh(), -0.0f32);
|
|
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
let nan: f32 = f32::NAN;
|
|
assert_eq!(inf.asinh(), inf);
|
|
assert_eq!(neg_inf.asinh(), neg_inf);
|
|
assert!(nan.asinh().is_nan());
|
|
assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32);
|
|
assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32);
|
|
}
|
|
|
|
#[test]
|
|
fn test_acosh() {
|
|
assert_eq!(1.0f32.acosh(), 0.0f32);
|
|
assert!(0.999f32.acosh().is_nan());
|
|
|
|
let inf: f32 = f32::INFINITY;
|
|
let neg_inf: f32 = f32::NEG_INFINITY;
|
|
let nan: f32 = f32::NAN;
|
|
assert_eq!(inf.acosh(), inf);
|
|
assert!(neg_inf.acosh().is_nan());
|
|
assert!(nan.acosh().is_nan());
|
|
assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32);
|
|
assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32);
|
|
}
|
|
|
|
#[test]
|
|
fn test_atanh() {
|
|
assert_eq!(0.0f32.atanh(), 0.0f32);
|
|
assert_eq!((-0.0f32).atanh(), -0.0f32);
|
|
|
|
let inf32: f32 = f32::INFINITY;
|
|
let neg_inf32: f32 = f32::NEG_INFINITY;
|
|
assert_eq!(1.0f32.atanh(), inf32);
|
|
assert_eq!((-1.0f32).atanh(), neg_inf32);
|
|
|
|
assert!(2f64.atanh().atanh().is_nan());
|
|
assert!((-2f64).atanh().atanh().is_nan());
|
|
|
|
let inf64: f32 = f32::INFINITY;
|
|
let neg_inf64: f32 = f32::NEG_INFINITY;
|
|
let nan32: f32 = f32::NAN;
|
|
assert!(inf64.atanh().is_nan());
|
|
assert!(neg_inf64.atanh().is_nan());
|
|
assert!(nan32.atanh().is_nan());
|
|
|
|
assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32);
|
|
assert_approx_eq!((-0.5f32).atanh(), -0.54930614433405484569762261846126285f32);
|
|
}
|
|
|
|
#[test]
|
|
fn test_real_consts() {
|
|
use super::consts;
|
|
|
|
let pi: f32 = consts::PI;
|
|
let frac_pi_2: f32 = consts::FRAC_PI_2;
|
|
let frac_pi_3: f32 = consts::FRAC_PI_3;
|
|
let frac_pi_4: f32 = consts::FRAC_PI_4;
|
|
let frac_pi_6: f32 = consts::FRAC_PI_6;
|
|
let frac_pi_8: f32 = consts::FRAC_PI_8;
|
|
let frac_1_pi: f32 = consts::FRAC_1_PI;
|
|
let frac_2_pi: f32 = consts::FRAC_2_PI;
|
|
let frac_2_sqrtpi: f32 = consts::FRAC_2_SQRT_PI;
|
|
let sqrt2: f32 = consts::SQRT_2;
|
|
let frac_1_sqrt2: f32 = consts::FRAC_1_SQRT_2;
|
|
let e: f32 = consts::E;
|
|
let log2_e: f32 = consts::LOG2_E;
|
|
let log10_e: f32 = consts::LOG10_E;
|
|
let ln_2: f32 = consts::LN_2;
|
|
let ln_10: f32 = consts::LN_10;
|
|
|
|
assert_approx_eq!(frac_pi_2, pi / 2f32);
|
|
assert_approx_eq!(frac_pi_3, pi / 3f32);
|
|
assert_approx_eq!(frac_pi_4, pi / 4f32);
|
|
assert_approx_eq!(frac_pi_6, pi / 6f32);
|
|
assert_approx_eq!(frac_pi_8, pi / 8f32);
|
|
assert_approx_eq!(frac_1_pi, 1f32 / pi);
|
|
assert_approx_eq!(frac_2_pi, 2f32 / pi);
|
|
assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt());
|
|
assert_approx_eq!(sqrt2, 2f32.sqrt());
|
|
assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt());
|
|
assert_approx_eq!(log2_e, e.log2());
|
|
assert_approx_eq!(log10_e, e.log10());
|
|
assert_approx_eq!(ln_2, 2f32.ln());
|
|
assert_approx_eq!(ln_10, 10f32.ln());
|
|
}
|
|
|
|
#[test]
|
|
fn test_float_bits_conv() {
|
|
assert_eq!((1f32).to_bits(), 0x3f800000);
|
|
assert_eq!((12.5f32).to_bits(), 0x41480000);
|
|
assert_eq!((1337f32).to_bits(), 0x44a72000);
|
|
assert_eq!((-14.25f32).to_bits(), 0xc1640000);
|
|
assert_approx_eq!(f32::from_bits(0x3f800000), 1.0);
|
|
assert_approx_eq!(f32::from_bits(0x41480000), 12.5);
|
|
assert_approx_eq!(f32::from_bits(0x44a72000), 1337.0);
|
|
assert_approx_eq!(f32::from_bits(0xc1640000), -14.25);
|
|
}
|
|
#[test]
|
|
fn test_snan_masking() {
|
|
// NOTE: this test assumes that our current platform
|
|
// implements IEEE 754-2008 that specifies the difference
|
|
// in encoding of quiet and signaling NaNs.
|
|
// If you are porting Rust to a platform that does not
|
|
// implement IEEE 754-2008 (but e.g. IEEE 754-1985, which
|
|
// only says that "Signaling NaNs shall be reserved operands"
|
|
// but doesn't specify the actual setup), feel free to
|
|
// cfg out this test.
|
|
let snan: u32 = 0x7F801337;
|
|
const QNAN_MASK: u32 = 0x00400000;
|
|
let nan_masked_fl = f32::from_bits(snan);
|
|
let nan_masked = nan_masked_fl.to_bits();
|
|
// Ensure that signaling NaNs don't stay the same
|
|
assert_ne!(nan_masked, snan);
|
|
// Ensure that we have a quiet NaN
|
|
assert_ne!(nan_masked & QNAN_MASK, 0);
|
|
assert!(nan_masked_fl.is_nan());
|
|
}
|
|
}
|