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// Copyright (C) 2017-2019 Baidu, Inc. All Rights Reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in
// the documentation and/or other materials provided with the
// distribution.
// * Neither the name of Baidu, Inc., nor the names of its
// contributors may be used to endorse or promote products derived
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//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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//! This module provides constants which are specific to the implementation
//! of the `f32` floating point data type.
//!
//! Mathematically significant numbers are provided in the `consts` sub-module.
//!
#![allow(missing_docs)]
use core::intrinsics;
use crate::sys::cmath;
pub use core::f32::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON};
pub use core::f32::{MIN_EXP, MAX_EXP, MIN_10_EXP};
pub use core::f32::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
pub use core::f32::{MIN, MIN_POSITIVE, MAX};
pub use core::f32::consts;
#[lang = "f32_runtime"]
impl f32 {
/// Returns the largest integer less than or equal to a number.
///
#[inline]
pub fn floor(self) -> f32 {
// On MSVC LLVM will lower many math intrinsics to a call to the
// corresponding function. On MSVC, however, many of these functions
// aren't actually available as symbols to call, but rather they are all
// `static inline` functions in header files. This means that from a C
// perspective it's "compatible", but not so much from an ABI
// perspective (which we're worried about).
//
// The inline header functions always just cast to a f64 and do their
// operation, so we do that here as well, but only for MSVC targets.
//
// Note that there are many MSVC-specific float operations which
// redirect to this comment, so `floorf` is just one case of a missing
// function on MSVC, but there are many others elsewhere.
#[cfg(target_env = "msvc")]
return (self as f64).floor() as f32;
#[cfg(not(target_env = "msvc"))]
return unsafe { intrinsics::floorf32(self) };
}
/// Returns the smallest integer greater than or equal to a number.
///
#[inline]
pub fn ceil(self) -> f32 {
// see notes above in `floor`
#[cfg(target_env = "msvc")]
return (self as f64).ceil() as f32;
#[cfg(not(target_env = "msvc"))]
return unsafe { intrinsics::ceilf32(self) };
}
/// Returns the nearest integer to a number. Round half-way cases away from
/// `0.0`.
///
#[inline]
pub fn round(self) -> f32 {
unsafe { intrinsics::roundf32(self) }
}
/// Returns the integer part of a number.
///
#[inline]
pub fn trunc(self) -> f32 {
unsafe { intrinsics::truncf32(self) }
}
/// Returns the fractional part of a number.
///
#[inline]
pub fn fract(self) -> f32 { self - self.trunc() }
/// Computes the absolute value of `self`. Returns `NAN` if the
/// number is `NAN`.
///
#[inline]
pub fn abs(self) -> f32 {
unsafe { intrinsics::fabsf32(self) }
}
/// Returns a number that represents the sign of `self`.
///
/// - `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]
pub fn signum(self) -> f32 {
if self.is_nan() {
NAN
} else {
1.0_f32.copysign(self)
}
}
/// Returns a number composed of the magnitude of `self` and the sign of
/// `sign`.
///
/// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
/// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of
/// `sign` is returned.
///
#[inline]
#[must_use]
pub fn copysign(self, sign: f32) -> f32 {
unsafe { intrinsics::copysignf32(self, sign) }
}
/// Fused multiply-add. Computes `(self * a) + b` with only one rounding
/// error, yielding a more accurate result than an unfused multiply-add.
///
/// Using `mul_add` can be more performant than an unfused multiply-add if
/// the target architecture has a dedicated `fma` CPU instruction.
///
#[inline]
pub fn mul_add(self, a: f32, b: f32) -> f32 {
unsafe { intrinsics::fmaf32(self, a, b) }
}
/// Calculates Euclidean division, the matching method for `rem_euclid`.
///
/// This computes the integer `n` such that
/// `self = n * rhs + self.rem_euclid(rhs)`.
/// In other words, the result is `self / rhs` rounded to the integer `n`
/// such that `self >= n * rhs`.
///
#[inline]
pub fn div_euclid(self, rhs: f32) -> f32 {
let q = (self / rhs).trunc();
if self % rhs < 0.0 {
return if rhs > 0.0 { q - 1.0 } else { q + 1.0 }
}
q
}
/// Calculates the least nonnegative remainder of `self (mod rhs)`.
///
/// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
/// most cases. However, due to a floating point round-off error it can
/// result in `r == rhs.abs()`, violating the mathematical definition, if
/// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
/// This result is not an element of the function's codomain, but it is the
/// closest floating point number in the real numbers and thus fulfills the
/// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
/// approximatively.
///
#[inline]
pub fn rem_euclid(self, rhs: f32) -> f32 {
let r = self % rhs;
if r < 0.0 {
r + rhs.abs()
} else {
r
}
}
/// Raises a number to an integer power.
///
/// Using this function is generally faster than using `powf`
///
#[inline]
pub fn powi(self, n: i32) -> f32 {
unsafe { intrinsics::powif32(self, n) }
}
/// Raises a number to a floating point power.
///
#[inline]
pub fn powf(self, n: f32) -> f32 {
// see notes above in `floor`
#[cfg(target_env = "msvc")]
return (self as f64).powf(n as f64) as f32;
#[cfg(not(target_env = "msvc"))]
return unsafe { intrinsics::powf32(self, n) };
}
/// Takes the square root of a number.
///
/// Returns NaN if `self` is a negative number.
///
#[inline]
pub fn sqrt(self) -> f32 {
if self < 0.0 {
NAN
} else {
unsafe { intrinsics::sqrtf32(self) }
}
}
/// Returns `e^(self)`, (the exponential function).
///
#[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)`.
///
#[inline]
pub fn exp2(self) -> f32 {
unsafe { intrinsics::exp2f32(self) }
}
/// Returns the natural logarithm of the number.
///
#[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.
///
/// The result may not be correctly rounded owing to implementation details;
/// `self.log2()` can produce more accurate results for base 2, and
/// `self.log10()` can produce more accurate results for base 10.
///
#[inline]
pub fn log(self, base: f32) -> f32 { self.ln() / base.ln() }
/// Returns the base 2 logarithm of the number.
///
#[inline]
pub fn log2(self) -> f32 {
#[cfg(target_os = "android")]
return crate::sys::android::log2f32(self);
#[cfg(not(target_os = "android"))]
return unsafe { intrinsics::log2f32(self) };
}
/// Returns the base 10 logarithm of the number.
///
#[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) };
}
/// The positive difference of two numbers.
///
/// * If `self <= other`: `0:0`
/// * Else: `self - other`
///
#[inline]
pub fn abs_sub(self, other: f32) -> f32 {
unsafe { cmath::fdimf(self, other) }
}
/// Takes the cubic root of a number.
///
#[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`.
///
#[inline]
pub fn hypot(self, other: f32) -> f32 {
unsafe { cmath::hypotf(self, other) }
}
/// Computes the sine of a number (in radians).
///
#[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).
///
#[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).
///
#[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].
///
#[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].
///
#[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];
///
#[inline]
pub fn atan(self) -> f32 {
unsafe { cmath::atanf(self) }
}
/// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
///
/// * `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)`
///
#[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))`.
///
#[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.
///
#[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.
///
#[inline]
pub fn ln_1p(self) -> f32 {
unsafe { cmath::log1pf(self) }
}
/// Hyperbolic sine function.
///
#[inline]
pub fn sinh(self) -> f32 {
unsafe { cmath::sinhf(self) }
}
/// Hyperbolic cosine function.
///
#[inline]
pub fn cosh(self) -> f32 {
unsafe { cmath::coshf(self) }
}
/// Hyperbolic tangent function.
///
#[inline]
pub fn tanh(self) -> f32 {
unsafe { cmath::tanhf(self) }
}
/// Inverse hyperbolic sine function.
///
#[inline]
pub fn asinh(self) -> f32 {
if self == NEG_INFINITY {
NEG_INFINITY
} else {
(self + ((self * self) + 1.0).sqrt()).ln()
}
}
/// Inverse hyperbolic cosine function.
///
#[inline]
pub fn acosh(self) -> f32 {
match self {
x if x < 1.0 => crate::f32::NAN,
x => (x + ((x * x) - 1.0).sqrt()).ln(),
}
}
/// Inverse hyperbolic tangent function.
///
#[inline]
pub fn atanh(self) -> f32 {
0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
}
/// Restrict a value to a certain interval unless it is NaN.
///
/// Returns `max` if `self` is greater than `max`, and `min` if `self` is
/// less than `min`. Otherwise this returns `self`.
///
/// Not that this function returns NaN if the initial value was NaN as
/// well.
///
/// # Panics
///
/// Panics if `min > max`, `min` is NaN, or `max` is NaN.
///
#[inline]
pub fn clamp(self, min: f32, max: f32) -> f32 {
assert!(min <= max);
let mut x = self;
if x < min { x = min; }
if x > max { x = max; }
x
}
}