232424d995
This commit stabilizes the `std::num` module: * The `Int` and `Float` traits are deprecated in favor of (1) the newly-added inherent methods and (2) the generic traits available in rust-lang/num. * The `Zero` and `One` traits are reintroduced in `std::num`, which together with various other traits allow you to recover the most common forms of generic programming. * The `FromStrRadix` trait, and associated free function, is deprecated in favor of inherent implementations. * A wide range of methods and constants for both integers and floating point numbers are now `#[stable]`, having been adjusted for integer guidelines. * `is_positive` and `is_negative` are renamed to `is_sign_positive` and `is_sign_negative`, in order to address #22985 * The `Wrapping` type is moved to `std::num` and stabilized; `WrappingOps` is deprecated in favor of inherent methods on the integer types, and direct implementation of operations on `Wrapping<X>` for each concrete integer type `X`. Closes #22985 Closes #21069 [breaking-change]
2105 lines
64 KiB
Rust
2105 lines
64 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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//! Operations and constants for 64-bits floats (`f64` type)
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#![stable(feature = "rust1", since = "1.0.0")]
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#![allow(missing_docs)]
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#![doc(primitive = "f64")]
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use prelude::v1::*;
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use intrinsics;
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use libc::c_int;
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use num::{Float, FpCategory};
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use num::strconv;
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use num::strconv::ExponentFormat::{ExpNone, ExpDec};
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use num::strconv::SignificantDigits::{DigAll, DigMax, DigExact};
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use num::strconv::SignFormat::SignNeg;
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use core::num;
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pub use core::f64::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON, MIN_VALUE};
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pub use core::f64::{MIN_POS_VALUE, MAX_VALUE, MIN_EXP, MAX_EXP, MIN_10_EXP};
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pub use core::f64::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
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pub use core::f64::{MIN, MIN_POSITIVE, MAX};
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pub use core::f64::consts;
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#[allow(dead_code)]
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mod cmath {
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use libc::{c_double, c_int};
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#[link_name = "m"]
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extern {
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pub fn acos(n: c_double) -> c_double;
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pub fn asin(n: c_double) -> c_double;
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pub fn atan(n: c_double) -> c_double;
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pub fn atan2(a: c_double, b: c_double) -> c_double;
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pub fn cbrt(n: c_double) -> c_double;
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pub fn cosh(n: c_double) -> c_double;
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pub fn erf(n: c_double) -> c_double;
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pub fn erfc(n: c_double) -> c_double;
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pub fn expm1(n: c_double) -> c_double;
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pub fn fdim(a: c_double, b: c_double) -> c_double;
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pub fn fmax(a: c_double, b: c_double) -> c_double;
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pub fn fmin(a: c_double, b: c_double) -> c_double;
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pub fn fmod(a: c_double, b: c_double) -> c_double;
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pub fn nextafter(x: c_double, y: c_double) -> c_double;
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pub fn frexp(n: c_double, value: &mut c_int) -> c_double;
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pub fn hypot(x: c_double, y: c_double) -> c_double;
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pub fn ldexp(x: c_double, n: c_int) -> c_double;
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pub fn logb(n: c_double) -> c_double;
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pub fn log1p(n: c_double) -> c_double;
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pub fn ilogb(n: c_double) -> c_int;
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pub fn modf(n: c_double, iptr: &mut c_double) -> c_double;
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pub fn sinh(n: c_double) -> c_double;
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pub fn tan(n: c_double) -> c_double;
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pub fn tanh(n: c_double) -> c_double;
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pub fn tgamma(n: c_double) -> c_double;
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// These are commonly only available for doubles
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pub fn j0(n: c_double) -> c_double;
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pub fn j1(n: c_double) -> c_double;
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pub fn jn(i: c_int, n: c_double) -> c_double;
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pub fn y0(n: c_double) -> c_double;
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pub fn y1(n: c_double) -> c_double;
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pub fn yn(i: c_int, n: c_double) -> c_double;
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#[cfg(unix)]
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pub fn lgamma_r(n: c_double, sign: &mut c_int) -> c_double;
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#[cfg(windows)]
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#[link_name="__lgamma_r"]
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pub fn lgamma_r(n: c_double, sign: &mut c_int) -> c_double;
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}
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}
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#[stable(feature = "rust1", since = "1.0.0")]
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#[allow(deprecated)]
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impl Float for f64 {
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// inlined methods from `num::Float`
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#[inline]
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fn nan() -> f64 { num::Float::nan() }
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#[inline]
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fn infinity() -> f64 { num::Float::infinity() }
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#[inline]
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fn neg_infinity() -> f64 { num::Float::neg_infinity() }
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#[inline]
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fn zero() -> f64 { num::Float::zero() }
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#[inline]
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fn neg_zero() -> f64 { num::Float::neg_zero() }
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#[inline]
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fn one() -> f64 { num::Float::one() }
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#[allow(deprecated)]
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#[inline]
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fn mantissa_digits(unused_self: Option<f64>) -> usize {
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num::Float::mantissa_digits(unused_self)
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}
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#[allow(deprecated)]
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#[inline]
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fn digits(unused_self: Option<f64>) -> usize { num::Float::digits(unused_self) }
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#[allow(deprecated)]
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#[inline]
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fn epsilon() -> f64 { num::Float::epsilon() }
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#[allow(deprecated)]
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#[inline]
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fn min_exp(unused_self: Option<f64>) -> isize { num::Float::min_exp(unused_self) }
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#[allow(deprecated)]
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#[inline]
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fn max_exp(unused_self: Option<f64>) -> isize { num::Float::max_exp(unused_self) }
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#[allow(deprecated)]
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#[inline]
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fn min_10_exp(unused_self: Option<f64>) -> isize { num::Float::min_10_exp(unused_self) }
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#[allow(deprecated)]
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#[inline]
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fn max_10_exp(unused_self: Option<f64>) -> isize { num::Float::max_10_exp(unused_self) }
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#[allow(deprecated)]
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#[inline]
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fn min_value() -> f64 { num::Float::min_value() }
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#[allow(deprecated)]
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#[inline]
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fn min_pos_value(unused_self: Option<f64>) -> f64 { num::Float::min_pos_value(unused_self) }
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#[allow(deprecated)]
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#[inline]
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fn max_value() -> f64 { num::Float::max_value() }
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#[inline]
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fn is_nan(self) -> bool { num::Float::is_nan(self) }
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#[inline]
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fn is_infinite(self) -> bool { num::Float::is_infinite(self) }
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#[inline]
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fn is_finite(self) -> bool { num::Float::is_finite(self) }
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#[inline]
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fn is_normal(self) -> bool { num::Float::is_normal(self) }
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#[inline]
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fn classify(self) -> FpCategory { num::Float::classify(self) }
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#[inline]
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fn integer_decode(self) -> (u64, i16, i8) { num::Float::integer_decode(self) }
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#[inline]
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fn floor(self) -> f64 { num::Float::floor(self) }
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#[inline]
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fn ceil(self) -> f64 { num::Float::ceil(self) }
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#[inline]
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fn round(self) -> f64 { num::Float::round(self) }
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#[inline]
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fn trunc(self) -> f64 { num::Float::trunc(self) }
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#[inline]
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fn fract(self) -> f64 { num::Float::fract(self) }
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#[inline]
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fn abs(self) -> f64 { num::Float::abs(self) }
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#[inline]
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fn signum(self) -> f64 { num::Float::signum(self) }
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#[inline]
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fn is_positive(self) -> bool { num::Float::is_positive(self) }
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#[inline]
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fn is_negative(self) -> bool { num::Float::is_negative(self) }
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#[inline]
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fn mul_add(self, a: f64, b: f64) -> f64 { num::Float::mul_add(self, a, b) }
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#[inline]
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fn recip(self) -> f64 { num::Float::recip(self) }
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#[inline]
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fn powi(self, n: i32) -> f64 { num::Float::powi(self, n) }
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#[inline]
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fn powf(self, n: f64) -> f64 { num::Float::powf(self, n) }
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#[inline]
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fn sqrt(self) -> f64 { num::Float::sqrt(self) }
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#[inline]
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fn rsqrt(self) -> f64 { num::Float::rsqrt(self) }
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#[inline]
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fn exp(self) -> f64 { num::Float::exp(self) }
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#[inline]
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fn exp2(self) -> f64 { num::Float::exp2(self) }
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#[inline]
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fn ln(self) -> f64 { num::Float::ln(self) }
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#[inline]
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fn log(self, base: f64) -> f64 { num::Float::log(self, base) }
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#[inline]
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fn log2(self) -> f64 { num::Float::log2(self) }
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#[inline]
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fn log10(self) -> f64 { num::Float::log10(self) }
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#[inline]
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fn to_degrees(self) -> f64 { num::Float::to_degrees(self) }
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#[inline]
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fn to_radians(self) -> f64 { num::Float::to_radians(self) }
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#[inline]
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fn ldexp(self, exp: isize) -> f64 {
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unsafe { cmath::ldexp(self, exp as c_int) }
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}
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/// Breaks the number into a normalized fraction and a base-2 exponent,
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/// satisfying:
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///
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/// - `self = x * pow(2, exp)`
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/// - `0.5 <= abs(x) < 1.0`
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#[inline]
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fn frexp(self) -> (f64, isize) {
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unsafe {
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let mut exp = 0;
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let x = cmath::frexp(self, &mut exp);
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(x, exp as isize)
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}
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}
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/// Returns the next representable floating-point value in the direction of
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/// `other`.
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#[inline]
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fn next_after(self, other: f64) -> f64 {
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unsafe { cmath::nextafter(self, other) }
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}
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#[inline]
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fn max(self, other: f64) -> f64 {
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unsafe { cmath::fmax(self, other) }
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}
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#[inline]
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fn min(self, other: f64) -> f64 {
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unsafe { cmath::fmin(self, other) }
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}
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#[inline]
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fn abs_sub(self, other: f64) -> f64 {
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unsafe { cmath::fdim(self, other) }
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}
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#[inline]
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fn cbrt(self) -> f64 {
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unsafe { cmath::cbrt(self) }
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}
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#[inline]
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fn hypot(self, other: f64) -> f64 {
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unsafe { cmath::hypot(self, other) }
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}
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#[inline]
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fn sin(self) -> f64 {
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unsafe { intrinsics::sinf64(self) }
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}
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#[inline]
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fn cos(self) -> f64 {
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unsafe { intrinsics::cosf64(self) }
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}
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#[inline]
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fn tan(self) -> f64 {
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unsafe { cmath::tan(self) }
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}
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#[inline]
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fn asin(self) -> f64 {
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unsafe { cmath::asin(self) }
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}
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#[inline]
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fn acos(self) -> f64 {
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unsafe { cmath::acos(self) }
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}
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#[inline]
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fn atan(self) -> f64 {
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unsafe { cmath::atan(self) }
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}
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#[inline]
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fn atan2(self, other: f64) -> f64 {
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unsafe { cmath::atan2(self, other) }
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}
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/// Simultaneously computes the sine and cosine of the number
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#[inline]
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fn sin_cos(self) -> (f64, f64) {
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(self.sin(), self.cos())
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}
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/// Returns the exponential of the number, minus `1`, in a way that is
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/// accurate even if the number is close to zero
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#[inline]
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fn exp_m1(self) -> f64 {
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unsafe { cmath::expm1(self) }
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}
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/// Returns the natural logarithm of the number plus `1` (`ln(1+n)`) more
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/// accurately than if the operations were performed separately
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#[inline]
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fn ln_1p(self) -> f64 {
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unsafe { cmath::log1p(self) }
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}
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#[inline]
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fn sinh(self) -> f64 {
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unsafe { cmath::sinh(self) }
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}
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#[inline]
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fn cosh(self) -> f64 {
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unsafe { cmath::cosh(self) }
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}
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#[inline]
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fn tanh(self) -> f64 {
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unsafe { cmath::tanh(self) }
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}
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/// Inverse hyperbolic sine
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///
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/// # Returns
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///
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/// - on success, the inverse hyperbolic sine of `self` will be returned
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/// - `self` if `self` is `0.0`, `-0.0`, `INFINITY`, or `NEG_INFINITY`
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/// - `NAN` if `self` is `NAN`
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#[inline]
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fn asinh(self) -> f64 {
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match self {
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NEG_INFINITY => NEG_INFINITY,
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x => (x + ((x * x) + 1.0).sqrt()).ln(),
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}
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}
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/// Inverse hyperbolic cosine
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///
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/// # Returns
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///
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/// - on success, the inverse hyperbolic cosine of `self` will be returned
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/// - `INFINITY` if `self` is `INFINITY`
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/// - `NAN` if `self` is `NAN` or `self < 1.0` (including `NEG_INFINITY`)
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#[inline]
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fn acosh(self) -> f64 {
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match self {
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x if x < 1.0 => Float::nan(),
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x => (x + ((x * x) - 1.0).sqrt()).ln(),
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}
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}
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/// Inverse hyperbolic tangent
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///
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/// # Returns
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///
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/// - on success, the inverse hyperbolic tangent of `self` will be returned
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/// - `self` if `self` is `0.0` or `-0.0`
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/// - `INFINITY` if `self` is `1.0`
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/// - `NEG_INFINITY` if `self` is `-1.0`
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/// - `NAN` if the `self` is `NAN` or outside the domain of `-1.0 <= self <= 1.0`
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/// (including `INFINITY` and `NEG_INFINITY`)
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#[inline]
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fn atanh(self) -> f64 {
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0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
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}
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}
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#[cfg(not(test))]
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#[lang = "f64"]
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#[stable(feature = "rust1", since = "1.0.0")]
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impl f64 {
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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::f64;
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///
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/// let nan = f64::NAN;
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/// let f = 7.0_f64;
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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::f64;
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///
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/// let f = 7.0f64;
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/// let inf = f64::INFINITY;
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/// let neg_inf = f64::NEG_INFINITY;
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/// let nan = f64::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::f64;
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///
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/// let f = 7.0f64;
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/// let inf: f64 = f64::INFINITY;
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/// let neg_inf: f64 = f64::NEG_INFINITY;
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/// let nan: f64 = f64::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-38f64
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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 = 0.0f32;
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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]: http://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
|
|
/// is going to be tested, it is generally faster to use the specific
|
|
/// predicate instead.
|
|
///
|
|
/// ```
|
|
/// use std::num::FpCategory;
|
|
/// use std::f64;
|
|
///
|
|
/// let num = 12.4_f64;
|
|
/// let inf = f64::INFINITY;
|
|
///
|
|
/// assert_eq!(num.classify(), FpCategory::Normal);
|
|
/// assert_eq!(inf.classify(), FpCategory::Infinite);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn classify(self) -> FpCategory { num::Float::classify(self) }
|
|
|
|
/// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
|
|
/// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
|
|
/// The floating point encoding is documented in the [Reference][floating-point].
|
|
///
|
|
/// ```
|
|
/// # #![feature(std_misc)]
|
|
/// let num = 2.0f64;
|
|
///
|
|
/// // (8388608, -22, 1)
|
|
/// let (mantissa, exponent, sign) = num.integer_decode();
|
|
/// let sign_f = sign as f64;
|
|
/// let mantissa_f = mantissa as f64;
|
|
/// let exponent_f = num.powf(exponent as f64);
|
|
///
|
|
/// // 1 * 8388608 * 2^(-22) == 2
|
|
/// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
/// [floating-point]: ../../../../../reference.html#machine-types
|
|
#[unstable(feature = "std_misc", reason = "signature is undecided")]
|
|
#[inline]
|
|
pub fn integer_decode(self) -> (u64, i16, i8) { num::Float::integer_decode(self) }
|
|
|
|
/// Returns the largest integer less than or equal to a number.
|
|
///
|
|
/// ```
|
|
/// let f = 3.99_f64;
|
|
/// let g = 3.0_f64;
|
|
///
|
|
/// assert_eq!(f.floor(), 3.0);
|
|
/// assert_eq!(g.floor(), 3.0);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn floor(self) -> f64 { num::Float::floor(self) }
|
|
|
|
/// Returns the smallest integer greater than or equal to a number.
|
|
///
|
|
/// ```
|
|
/// let f = 3.01_f64;
|
|
/// let g = 4.0_f64;
|
|
///
|
|
/// assert_eq!(f.ceil(), 4.0);
|
|
/// assert_eq!(g.ceil(), 4.0);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn ceil(self) -> f64 { num::Float::ceil(self) }
|
|
|
|
/// Returns the nearest integer to a number. Round half-way cases away from
|
|
/// `0.0`.
|
|
///
|
|
/// ```
|
|
/// let f = 3.3_f64;
|
|
/// let g = -3.3_f64;
|
|
///
|
|
/// assert_eq!(f.round(), 3.0);
|
|
/// assert_eq!(g.round(), -3.0);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn round(self) -> f64 { num::Float::round(self) }
|
|
|
|
/// Return the integer part of a number.
|
|
///
|
|
/// ```
|
|
/// let f = 3.3_f64;
|
|
/// let g = -3.7_f64;
|
|
///
|
|
/// assert_eq!(f.trunc(), 3.0);
|
|
/// assert_eq!(g.trunc(), -3.0);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn trunc(self) -> f64 { num::Float::trunc(self) }
|
|
|
|
/// Returns the fractional part of a number.
|
|
///
|
|
/// ```
|
|
/// let x = 3.5_f64;
|
|
/// let y = -3.5_f64;
|
|
/// let abs_difference_x = (x.fract() - 0.5).abs();
|
|
/// let abs_difference_y = (y.fract() - (-0.5)).abs();
|
|
///
|
|
/// assert!(abs_difference_x < 1e-10);
|
|
/// assert!(abs_difference_y < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn fract(self) -> f64 { num::Float::fract(self) }
|
|
|
|
/// Computes the absolute value of `self`. Returns `NAN` if the
|
|
/// number is `NAN`.
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let x = 3.5_f64;
|
|
/// let y = -3.5_f64;
|
|
///
|
|
/// let abs_difference_x = (x.abs() - x).abs();
|
|
/// let abs_difference_y = (y.abs() - (-y)).abs();
|
|
///
|
|
/// assert!(abs_difference_x < 1e-10);
|
|
/// assert!(abs_difference_y < 1e-10);
|
|
///
|
|
/// assert!(f64::NAN.abs().is_nan());
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn abs(self) -> f64 { num::Float::abs(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`
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let f = 3.5_f64;
|
|
///
|
|
/// assert_eq!(f.signum(), 1.0);
|
|
/// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
|
|
///
|
|
/// assert!(f64::NAN.signum().is_nan());
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn signum(self) -> f64 { num::Float::signum(self) }
|
|
|
|
/// Returns `true` if `self`'s sign bit is positive, including
|
|
/// `+0.0` and `INFINITY`.
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let nan: f64 = f64::NAN;
|
|
///
|
|
/// let f = 7.0_f64;
|
|
/// let g = -7.0_f64;
|
|
///
|
|
/// assert!(f.is_sign_positive());
|
|
/// assert!(!g.is_sign_positive());
|
|
/// // Requires both tests to determine if is `NaN`
|
|
/// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn is_sign_positive(self) -> bool { num::Float::is_positive(self) }
|
|
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[deprecated(since = "1.0.0", reason = "renamed to is_sign_positive")]
|
|
#[inline]
|
|
pub fn is_positive(self) -> bool { num::Float::is_positive(self) }
|
|
|
|
/// Returns `true` if `self`'s sign is negative, including `-0.0`
|
|
/// and `NEG_INFINITY`.
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let nan = f64::NAN;
|
|
///
|
|
/// let f = 7.0_f64;
|
|
/// let g = -7.0_f64;
|
|
///
|
|
/// assert!(!f.is_sign_negative());
|
|
/// assert!(g.is_sign_negative());
|
|
/// // Requires both tests to determine if is `NaN`.
|
|
/// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn is_sign_negative(self) -> bool { num::Float::is_negative(self) }
|
|
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[deprecated(since = "1.0.0", reason = "renamed to is_sign_negative")]
|
|
#[inline]
|
|
pub fn is_negative(self) -> bool { num::Float::is_negative(self) }
|
|
|
|
/// 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.
|
|
///
|
|
/// ```
|
|
/// let m = 10.0_f64;
|
|
/// let x = 4.0_f64;
|
|
/// let b = 60.0_f64;
|
|
///
|
|
/// // 100.0
|
|
/// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn mul_add(self, a: f64, b: f64) -> f64 { num::Float::mul_add(self, a, b) }
|
|
|
|
/// Take the reciprocal (inverse) of a number, `1/x`.
|
|
///
|
|
/// ```
|
|
/// let x = 2.0_f64;
|
|
/// let abs_difference = (x.recip() - (1.0/x)).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn recip(self) -> f64 { num::Float::recip(self) }
|
|
|
|
/// Raise a number to an integer power.
|
|
///
|
|
/// Using this function is generally faster than using `powf`
|
|
///
|
|
/// ```
|
|
/// let x = 2.0_f64;
|
|
/// let abs_difference = (x.powi(2) - x*x).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn powi(self, n: i32) -> f64 { num::Float::powi(self, n) }
|
|
|
|
/// Raise a number to a floating point power.
|
|
///
|
|
/// ```
|
|
/// let x = 2.0_f64;
|
|
/// let abs_difference = (x.powf(2.0) - x*x).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn powf(self, n: f64) -> f64 { num::Float::powf(self, n) }
|
|
|
|
/// Take the square root of a number.
|
|
///
|
|
/// Returns NaN if `self` is a negative number.
|
|
///
|
|
/// ```
|
|
/// let positive = 4.0_f64;
|
|
/// let negative = -4.0_f64;
|
|
///
|
|
/// let abs_difference = (positive.sqrt() - 2.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// assert!(negative.sqrt().is_nan());
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn sqrt(self) -> f64 { num::Float::sqrt(self) }
|
|
|
|
/// Take the reciprocal (inverse) square root of a number, `1/sqrt(x)`.
|
|
///
|
|
/// ```
|
|
/// # #![feature(std_misc)]
|
|
/// let f = 4.0_f64;
|
|
///
|
|
/// let abs_difference = (f.rsqrt() - 0.5).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[unstable(feature = "std_misc",
|
|
reason = "unsure about its place in the world")]
|
|
#[deprecated(since = "1.0.0", reason = "use self.sqrt().recip() instead")]
|
|
#[inline]
|
|
pub fn rsqrt(self) -> f64 { num::Float::rsqrt(self) }
|
|
|
|
/// Returns `e^(self)`, (the exponential function).
|
|
///
|
|
/// ```
|
|
/// let one = 1.0_f64;
|
|
/// // e^1
|
|
/// let e = one.exp();
|
|
///
|
|
/// // ln(e) - 1 == 0
|
|
/// let abs_difference = (e.ln() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn exp(self) -> f64 { num::Float::exp(self) }
|
|
|
|
/// Returns `2^(self)`.
|
|
///
|
|
/// ```
|
|
/// let f = 2.0_f64;
|
|
///
|
|
/// // 2^2 - 4 == 0
|
|
/// let abs_difference = (f.exp2() - 4.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn exp2(self) -> f64 { num::Float::exp2(self) }
|
|
|
|
/// Returns the natural logarithm of the number.
|
|
///
|
|
/// ```
|
|
/// let one = 1.0_f64;
|
|
/// // e^1
|
|
/// let e = one.exp();
|
|
///
|
|
/// // ln(e) - 1 == 0
|
|
/// let abs_difference = (e.ln() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn ln(self) -> f64 { num::Float::ln(self) }
|
|
|
|
/// Returns the logarithm of the number with respect to an arbitrary base.
|
|
///
|
|
/// ```
|
|
/// let ten = 10.0_f64;
|
|
/// let two = 2.0_f64;
|
|
///
|
|
/// // 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 < 1e-10);
|
|
/// assert!(abs_difference_2 < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn log(self, base: f64) -> f64 { num::Float::log(self, base) }
|
|
|
|
/// Returns the base 2 logarithm of the number.
|
|
///
|
|
/// ```
|
|
/// let two = 2.0_f64;
|
|
///
|
|
/// // log2(2) - 1 == 0
|
|
/// let abs_difference = (two.log2() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn log2(self) -> f64 { num::Float::log2(self) }
|
|
|
|
/// Returns the base 10 logarithm of the number.
|
|
///
|
|
/// ```
|
|
/// let ten = 10.0_f64;
|
|
///
|
|
/// // log10(10) - 1 == 0
|
|
/// let abs_difference = (ten.log10() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn log10(self) -> f64 { num::Float::log10(self) }
|
|
|
|
/// Convert radians to degrees.
|
|
///
|
|
/// ```
|
|
/// use std::f64::consts;
|
|
///
|
|
/// let angle = consts::PI;
|
|
///
|
|
/// let abs_difference = (angle.to_degrees() - 180.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn to_degrees(self) -> f64 { num::Float::to_degrees(self) }
|
|
|
|
/// Convert degrees to radians.
|
|
///
|
|
/// ```
|
|
/// use std::f64::consts;
|
|
///
|
|
/// let angle = 180.0_f64;
|
|
///
|
|
/// let abs_difference = (angle.to_radians() - consts::PI).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn to_radians(self) -> f64 { num::Float::to_radians(self) }
|
|
|
|
/// Constructs a floating point number of `x*2^exp`.
|
|
///
|
|
/// ```
|
|
/// # #![feature(std_misc)]
|
|
/// // 3*2^2 - 12 == 0
|
|
/// let abs_difference = (f64::ldexp(3.0, 2) - 12.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[unstable(feature = "std_misc",
|
|
reason = "pending integer conventions")]
|
|
#[inline]
|
|
pub fn ldexp(x: f64, exp: isize) -> f64 {
|
|
unsafe { cmath::ldexp(x, exp as c_int) }
|
|
}
|
|
|
|
/// Breaks the number into a normalized fraction and a base-2 exponent,
|
|
/// satisfying:
|
|
///
|
|
/// * `self = x * 2^exp`
|
|
/// * `0.5 <= abs(x) < 1.0`
|
|
///
|
|
/// ```
|
|
/// # #![feature(std_misc)]
|
|
/// let x = 4.0_f64;
|
|
///
|
|
/// // (1/2)*2^3 -> 1 * 8/2 -> 4.0
|
|
/// let f = x.frexp();
|
|
/// let abs_difference_0 = (f.0 - 0.5).abs();
|
|
/// let abs_difference_1 = (f.1 as f64 - 3.0).abs();
|
|
///
|
|
/// assert!(abs_difference_0 < 1e-10);
|
|
/// assert!(abs_difference_1 < 1e-10);
|
|
/// ```
|
|
#[unstable(feature = "std_misc",
|
|
reason = "pending integer conventions")]
|
|
#[inline]
|
|
pub fn frexp(self) -> (f64, isize) {
|
|
unsafe {
|
|
let mut exp = 0;
|
|
let x = cmath::frexp(self, &mut exp);
|
|
(x, exp as isize)
|
|
}
|
|
}
|
|
|
|
/// Returns the next representable floating-point value in the direction of
|
|
/// `other`.
|
|
///
|
|
/// ```
|
|
/// # #![feature(std_misc)]
|
|
///
|
|
/// let x = 1.0f32;
|
|
///
|
|
/// let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs();
|
|
///
|
|
/// assert!(abs_diff < 1e-10);
|
|
/// ```
|
|
#[unstable(feature = "std_misc",
|
|
reason = "unsure about its place in the world")]
|
|
#[inline]
|
|
pub fn next_after(self, other: f64) -> f64 {
|
|
unsafe { cmath::nextafter(self, other) }
|
|
}
|
|
|
|
/// Returns the maximum of the two numbers.
|
|
///
|
|
/// ```
|
|
/// let x = 1.0_f64;
|
|
/// let y = 2.0_f64;
|
|
///
|
|
/// assert_eq!(x.max(y), y);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn max(self, other: f64) -> f64 {
|
|
unsafe { cmath::fmax(self, other) }
|
|
}
|
|
|
|
/// Returns the minimum of the two numbers.
|
|
///
|
|
/// ```
|
|
/// let x = 1.0_f64;
|
|
/// let y = 2.0_f64;
|
|
///
|
|
/// assert_eq!(x.min(y), x);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn min(self, other: f64) -> f64 {
|
|
unsafe { cmath::fmin(self, other) }
|
|
}
|
|
|
|
/// The positive difference of two numbers.
|
|
///
|
|
/// * If `self <= other`: `0:0`
|
|
/// * Else: `self - other`
|
|
///
|
|
/// ```
|
|
/// let x = 3.0_f64;
|
|
/// let y = -3.0_f64;
|
|
///
|
|
/// 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 < 1e-10);
|
|
/// assert!(abs_difference_y < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn abs_sub(self, other: f64) -> f64 {
|
|
unsafe { cmath::fdim(self, other) }
|
|
}
|
|
|
|
/// Take the cubic root of a number.
|
|
///
|
|
/// ```
|
|
/// let x = 8.0_f64;
|
|
///
|
|
/// // x^(1/3) - 2 == 0
|
|
/// let abs_difference = (x.cbrt() - 2.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn cbrt(self) -> f64 {
|
|
unsafe { cmath::cbrt(self) }
|
|
}
|
|
|
|
/// Calculate the length of the hypotenuse of a right-angle triangle given
|
|
/// legs of length `x` and `y`.
|
|
///
|
|
/// ```
|
|
/// let x = 2.0_f64;
|
|
/// let y = 3.0_f64;
|
|
///
|
|
/// // sqrt(x^2 + y^2)
|
|
/// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn hypot(self, other: f64) -> f64 {
|
|
unsafe { cmath::hypot(self, other) }
|
|
}
|
|
|
|
/// Computes the sine of a number (in radians).
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let x = f64::consts::PI/2.0;
|
|
///
|
|
/// let abs_difference = (x.sin() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn sin(self) -> f64 {
|
|
unsafe { intrinsics::sinf64(self) }
|
|
}
|
|
|
|
/// Computes the cosine of a number (in radians).
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let x = 2.0*f64::consts::PI;
|
|
///
|
|
/// let abs_difference = (x.cos() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn cos(self) -> f64 {
|
|
unsafe { intrinsics::cosf64(self) }
|
|
}
|
|
|
|
/// Computes the tangent of a number (in radians).
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let x = f64::consts::PI/4.0;
|
|
/// let abs_difference = (x.tan() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-14);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn tan(self) -> f64 {
|
|
unsafe { cmath::tan(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::f64;
|
|
///
|
|
/// let f = f64::consts::PI / 2.0;
|
|
///
|
|
/// // asin(sin(pi/2))
|
|
/// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn asin(self) -> f64 {
|
|
unsafe { cmath::asin(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::f64;
|
|
///
|
|
/// let f = f64::consts::PI / 4.0;
|
|
///
|
|
/// // acos(cos(pi/4))
|
|
/// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn acos(self) -> f64 {
|
|
unsafe { cmath::acos(self) }
|
|
}
|
|
|
|
/// Computes the arctangent of a number. Return value is in radians in the
|
|
/// range [-pi/2, pi/2];
|
|
///
|
|
/// ```
|
|
/// let f = 1.0_f64;
|
|
///
|
|
/// // atan(tan(1))
|
|
/// let abs_difference = (f.tan().atan() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn atan(self) -> f64 {
|
|
unsafe { cmath::atan(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::f64;
|
|
///
|
|
/// let pi = f64::consts::PI;
|
|
/// // All angles from horizontal right (+x)
|
|
/// // 45 deg counter-clockwise
|
|
/// let x1 = 3.0_f64;
|
|
/// let y1 = -3.0_f64;
|
|
///
|
|
/// // 135 deg clockwise
|
|
/// let x2 = -3.0_f64;
|
|
/// let y2 = 3.0_f64;
|
|
///
|
|
/// 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 < 1e-10);
|
|
/// assert!(abs_difference_2 < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn atan2(self, other: f64) -> f64 {
|
|
unsafe { cmath::atan2(self, other) }
|
|
}
|
|
|
|
/// Simultaneously computes the sine and cosine of the number, `x`. Returns
|
|
/// `(sin(x), cos(x))`.
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let x = f64::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 < 1e-10);
|
|
/// assert!(abs_difference_0 < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn sin_cos(self) -> (f64, f64) {
|
|
(self.sin(), self.cos())
|
|
}
|
|
|
|
/// Returns `e^(self) - 1` in a way that is accurate even if the
|
|
/// number is close to zero.
|
|
///
|
|
/// ```
|
|
/// let x = 7.0_f64;
|
|
///
|
|
/// // e^(ln(7)) - 1
|
|
/// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn exp_m1(self) -> f64 {
|
|
unsafe { cmath::expm1(self) }
|
|
}
|
|
|
|
/// Returns `ln(1+n)` (natural logarithm) more accurately than if
|
|
/// the operations were performed separately.
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let x = f64::consts::E - 1.0;
|
|
///
|
|
/// // ln(1 + (e - 1)) == ln(e) == 1
|
|
/// let abs_difference = (x.ln_1p() - 1.0).abs();
|
|
///
|
|
/// assert!(abs_difference < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn ln_1p(self) -> f64 {
|
|
unsafe { cmath::log1p(self) }
|
|
}
|
|
|
|
/// Hyperbolic sine function.
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let e = f64::consts::E;
|
|
/// let x = 1.0_f64;
|
|
///
|
|
/// 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 < 1e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn sinh(self) -> f64 {
|
|
unsafe { cmath::sinh(self) }
|
|
}
|
|
|
|
/// Hyperbolic cosine function.
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let e = f64::consts::E;
|
|
/// let x = 1.0_f64;
|
|
/// 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 < 1.0e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn cosh(self) -> f64 {
|
|
unsafe { cmath::cosh(self) }
|
|
}
|
|
|
|
/// Hyperbolic tangent function.
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let e = f64::consts::E;
|
|
/// let x = 1.0_f64;
|
|
///
|
|
/// 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 < 1.0e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn tanh(self) -> f64 {
|
|
unsafe { cmath::tanh(self) }
|
|
}
|
|
|
|
/// Inverse hyperbolic sine function.
|
|
///
|
|
/// ```
|
|
/// let x = 1.0_f64;
|
|
/// let f = x.sinh().asinh();
|
|
///
|
|
/// let abs_difference = (f - x).abs();
|
|
///
|
|
/// assert!(abs_difference < 1.0e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn asinh(self) -> f64 {
|
|
match self {
|
|
NEG_INFINITY => NEG_INFINITY,
|
|
x => (x + ((x * x) + 1.0).sqrt()).ln(),
|
|
}
|
|
}
|
|
|
|
/// Inverse hyperbolic cosine function.
|
|
///
|
|
/// ```
|
|
/// let x = 1.0_f64;
|
|
/// let f = x.cosh().acosh();
|
|
///
|
|
/// let abs_difference = (f - x).abs();
|
|
///
|
|
/// assert!(abs_difference < 1.0e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn acosh(self) -> f64 {
|
|
match self {
|
|
x if x < 1.0 => Float::nan(),
|
|
x => (x + ((x * x) - 1.0).sqrt()).ln(),
|
|
}
|
|
}
|
|
|
|
/// Inverse hyperbolic tangent function.
|
|
///
|
|
/// ```
|
|
/// use std::f64;
|
|
///
|
|
/// let e = f64::consts::E;
|
|
/// let f = e.tanh().atanh();
|
|
///
|
|
/// let abs_difference = (f - e).abs();
|
|
///
|
|
/// assert!(abs_difference < 1.0e-10);
|
|
/// ```
|
|
#[stable(feature = "rust1", since = "1.0.0")]
|
|
#[inline]
|
|
pub fn atanh(self) -> f64 {
|
|
0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
|
|
}
|
|
}
|
|
|
|
//
|
|
// Section: String Conversions
|
|
//
|
|
|
|
/// Converts a float to a string
|
|
///
|
|
/// # Arguments
|
|
///
|
|
/// * num - The float value
|
|
#[inline]
|
|
#[unstable(feature = "std_misc", reason = "may be removed or relocated")]
|
|
#[deprecated(since = "1.0.0", reason = "use the ToString trait instead")]
|
|
pub fn to_string(num: f64) -> String {
|
|
let (r, _) = strconv::float_to_str_common(
|
|
num, 10, true, SignNeg, DigAll, ExpNone, false);
|
|
r
|
|
}
|
|
|
|
/// Converts a float to a string in hexadecimal format
|
|
///
|
|
/// # Arguments
|
|
///
|
|
/// * num - The float value
|
|
#[inline]
|
|
#[unstable(feature = "std_misc", reason = "may be removed or relocated")]
|
|
#[deprecated(since = "1.0.0", reason = "use format! instead")]
|
|
pub fn to_str_hex(num: f64) -> String {
|
|
let (r, _) = strconv::float_to_str_common(
|
|
num, 16, true, SignNeg, DigAll, 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]
|
|
#[unstable(feature = "std_misc", reason = "may be removed or relocated")]
|
|
#[deprecated(since = "1.0.0", reason = "use format! instead")]
|
|
pub fn to_str_radix_special(num: f64, rdx: u32) -> (String, bool) {
|
|
strconv::float_to_str_common(num, rdx, true, SignNeg, DigAll, 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]
|
|
#[unstable(feature = "std_misc", reason = "may be removed or relocated")]
|
|
pub fn to_str_exact(num: f64, dig: usize) -> String {
|
|
let (r, _) = strconv::float_to_str_common(
|
|
num, 10, true, SignNeg, DigExact(dig), 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]
|
|
#[unstable(feature = "std_misc", reason = "may be removed or relocated")]
|
|
pub fn to_str_digits(num: f64, dig: usize) -> String {
|
|
let (r, _) = strconv::float_to_str_common(
|
|
num, 10, true, SignNeg, DigMax(dig), 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]
|
|
#[unstable(feature = "std_misc", reason = "may be removed or relocated")]
|
|
pub fn to_str_exp_exact(num: f64, dig: usize, upper: bool) -> String {
|
|
let (r, _) = strconv::float_to_str_common(
|
|
num, 10, true, SignNeg, DigExact(dig), 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]
|
|
#[unstable(feature = "std_misc", reason = "may be removed or relocated")]
|
|
pub fn to_str_exp_digits(num: f64, dig: usize, upper: bool) -> String {
|
|
let (r, _) = strconv::float_to_str_common(
|
|
num, 10, true, SignNeg, DigMax(dig), ExpDec, upper);
|
|
r
|
|
}
|
|
|
|
#[cfg(test)]
|
|
mod tests {
|
|
use f64::*;
|
|
use num::*;
|
|
use num::FpCategory as Fp;
|
|
|
|
#[test]
|
|
fn test_num_f64() {
|
|
test_num(10f64, 2f64);
|
|
}
|
|
|
|
#[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_nan() {
|
|
let nan: f64 = Float::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: f64 = Float::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: f64 = Float::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: f64 = Float::zero();
|
|
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: f64 = Float::neg_zero();
|
|
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: f64 = Float::one();
|
|
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: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert!(nan.is_nan());
|
|
assert!(!0.0f64.is_nan());
|
|
assert!(!5.3f64.is_nan());
|
|
assert!(!(-10.732f64).is_nan());
|
|
assert!(!inf.is_nan());
|
|
assert!(!neg_inf.is_nan());
|
|
}
|
|
|
|
#[test]
|
|
fn test_is_infinite() {
|
|
let nan: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert!(!nan.is_infinite());
|
|
assert!(inf.is_infinite());
|
|
assert!(neg_inf.is_infinite());
|
|
assert!(!0.0f64.is_infinite());
|
|
assert!(!42.8f64.is_infinite());
|
|
assert!(!(-109.2f64).is_infinite());
|
|
}
|
|
|
|
#[test]
|
|
fn test_is_finite() {
|
|
let nan: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert!(!nan.is_finite());
|
|
assert!(!inf.is_finite());
|
|
assert!(!neg_inf.is_finite());
|
|
assert!(0.0f64.is_finite());
|
|
assert!(42.8f64.is_finite());
|
|
assert!((-109.2f64).is_finite());
|
|
}
|
|
|
|
#[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 = Float::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 = Float::zero();
|
|
let neg_zero: f64 = Float::neg_zero();
|
|
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!(1e-307f64.classify(), Fp::Normal);
|
|
assert_eq!(1e-308f64.classify(), Fp::Subnormal);
|
|
}
|
|
|
|
#[test]
|
|
fn test_integer_decode() {
|
|
assert_eq!(3.14159265359f64.integer_decode(), (7074237752028906, -51, 1));
|
|
assert_eq!((-8573.5918555f64).integer_decode(), (4713381968463931, -39, -1));
|
|
assert_eq!(2f64.powf(100.0).integer_decode(), (4503599627370496, 48, 1));
|
|
assert_eq!(0f64.integer_decode(), (0, -1075, 1));
|
|
assert_eq!((-0f64).integer_decode(), (0, -1075, -1));
|
|
assert_eq!(INFINITY.integer_decode(), (4503599627370496, 972, 1));
|
|
assert_eq!(NEG_INFINITY.integer_decode(), (4503599627370496, 972, -1));
|
|
assert_eq!(NAN.integer_decode(), (6755399441055744, 972, 1));
|
|
}
|
|
|
|
#[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_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_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_sign_positive() {
|
|
assert!(INFINITY.is_sign_positive());
|
|
assert!(1f64.is_sign_positive());
|
|
assert!(0f64.is_sign_positive());
|
|
assert!(!(-0f64).is_sign_positive());
|
|
assert!(!(-1f64).is_sign_positive());
|
|
assert!(!NEG_INFINITY.is_sign_positive());
|
|
assert!(!(1f64/NEG_INFINITY).is_sign_positive());
|
|
assert!(!NAN.is_sign_positive());
|
|
}
|
|
|
|
#[test]
|
|
fn test_is_sign_negative() {
|
|
assert!(!INFINITY.is_sign_negative());
|
|
assert!(!1f64.is_sign_negative());
|
|
assert!(!0f64.is_sign_negative());
|
|
assert!((-0f64).is_sign_negative());
|
|
assert!((-1f64).is_sign_negative());
|
|
assert!(NEG_INFINITY.is_sign_negative());
|
|
assert!((1f64/NEG_INFINITY).is_sign_negative());
|
|
assert!(!NAN.is_sign_negative());
|
|
}
|
|
|
|
#[test]
|
|
fn test_mul_add() {
|
|
let nan: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05);
|
|
assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65);
|
|
assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2);
|
|
assert_approx_eq!(3.4f64.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!(8.9f64.mul_add(inf, 3.2), inf);
|
|
assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_recip() {
|
|
let nan: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert_eq!(1.0f64.recip(), 1.0);
|
|
assert_eq!(2.0f64.recip(), 0.5);
|
|
assert_eq!((-0.4f64).recip(), -2.5);
|
|
assert_eq!(0.0f64.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: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert_eq!(1.0f64.powi(1), 1.0);
|
|
assert_approx_eq!((-3.1f64).powi(2), 9.61);
|
|
assert_approx_eq!(5.9f64.powi(-2), 0.028727);
|
|
assert_eq!(8.3f64.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: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert_eq!(1.0f64.powf(1.0), 1.0);
|
|
assert_approx_eq!(3.4f64.powf(4.5), 246.408183);
|
|
assert_approx_eq!(2.7f64.powf(-3.2), 0.041652);
|
|
assert_approx_eq!((-3.1f64).powf(2.0), 9.61);
|
|
assert_approx_eq!(5.9f64.powf(-2.0), 0.028727);
|
|
assert_eq!(8.3f64.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!((-1.0f64).sqrt().is_nan());
|
|
assert_eq!((-0.0f64).sqrt(), -0.0);
|
|
assert_eq!(0.0f64.sqrt(), 0.0);
|
|
assert_eq!(1.0f64.sqrt(), 1.0);
|
|
assert_eq!(INFINITY.sqrt(), INFINITY);
|
|
}
|
|
|
|
#[test]
|
|
fn test_rsqrt() {
|
|
let nan: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert!(nan.rsqrt().is_nan());
|
|
assert_eq!(inf.rsqrt(), 0.0);
|
|
assert!(neg_inf.rsqrt().is_nan());
|
|
assert!((-1.0f64).rsqrt().is_nan());
|
|
assert_eq!((-0.0f64).rsqrt(), neg_inf);
|
|
assert_eq!(0.0f64.rsqrt(), inf);
|
|
assert_eq!(1.0f64.rsqrt(), 1.0);
|
|
assert_eq!(4.0f64.rsqrt(), 0.5);
|
|
}
|
|
|
|
#[test]
|
|
fn test_exp() {
|
|
assert_eq!(1.0, 0.0f64.exp());
|
|
assert_approx_eq!(2.718282, 1.0f64.exp());
|
|
assert_approx_eq!(148.413159, 5.0f64.exp());
|
|
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
let nan: f64 = Float::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, 5.0f64.exp2());
|
|
assert_eq!(1.0, 0.0f64.exp2());
|
|
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
let nan: f64 = Float::nan();
|
|
assert_eq!(inf, inf.exp2());
|
|
assert_eq!(0.0, neg_inf.exp2());
|
|
assert!(nan.exp2().is_nan());
|
|
}
|
|
|
|
#[test]
|
|
fn test_ln() {
|
|
let nan: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert_approx_eq!(1.0f64.exp().ln(), 1.0);
|
|
assert!(nan.ln().is_nan());
|
|
assert_eq!(inf.ln(), inf);
|
|
assert!(neg_inf.ln().is_nan());
|
|
assert!((-2.3f64).ln().is_nan());
|
|
assert_eq!((-0.0f64).ln(), neg_inf);
|
|
assert_eq!(0.0f64.ln(), neg_inf);
|
|
assert_approx_eq!(4.0f64.ln(), 1.386294);
|
|
}
|
|
|
|
#[test]
|
|
fn test_log() {
|
|
let nan: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert_eq!(10.0f64.log(10.0), 1.0);
|
|
assert_approx_eq!(2.3f64.log(3.5), 0.664858);
|
|
assert_eq!(1.0f64.exp().log(1.0.exp()), 1.0);
|
|
assert!(1.0f64.log(1.0).is_nan());
|
|
assert!(1.0f64.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!((-2.3f64).log(0.1).is_nan());
|
|
assert_eq!((-0.0f64).log(2.0), neg_inf);
|
|
assert_eq!(0.0f64.log(7.0), neg_inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_log2() {
|
|
let nan: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert_approx_eq!(10.0f64.log2(), 3.321928);
|
|
assert_approx_eq!(2.3f64.log2(), 1.201634);
|
|
assert_approx_eq!(1.0f64.exp().log2(), 1.442695);
|
|
assert!(nan.log2().is_nan());
|
|
assert_eq!(inf.log2(), inf);
|
|
assert!(neg_inf.log2().is_nan());
|
|
assert!((-2.3f64).log2().is_nan());
|
|
assert_eq!((-0.0f64).log2(), neg_inf);
|
|
assert_eq!(0.0f64.log2(), neg_inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_log10() {
|
|
let nan: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert_eq!(10.0f64.log10(), 1.0);
|
|
assert_approx_eq!(2.3f64.log10(), 0.361728);
|
|
assert_approx_eq!(1.0f64.exp().log10(), 0.434294);
|
|
assert_eq!(1.0f64.log10(), 0.0);
|
|
assert!(nan.log10().is_nan());
|
|
assert_eq!(inf.log10(), inf);
|
|
assert!(neg_inf.log10().is_nan());
|
|
assert!((-2.3f64).log10().is_nan());
|
|
assert_eq!((-0.0f64).log10(), neg_inf);
|
|
assert_eq!(0.0f64.log10(), neg_inf);
|
|
}
|
|
|
|
#[test]
|
|
fn test_to_degrees() {
|
|
let pi: f64 = consts::PI;
|
|
let nan: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert_eq!(0.0f64.to_degrees(), 0.0);
|
|
assert_approx_eq!((-5.8f64).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: f64 = consts::PI;
|
|
let nan: f64 = Float::nan();
|
|
let inf: f64 = Float::infinity();
|
|
let neg_inf: f64 = Float::neg_infinity();
|
|
assert_eq!(0.0f64.to_radians(), 0.0);
|
|
assert_approx_eq!(154.6f64.to_radians(), 2.698279);
|
|
assert_approx_eq!((-332.31f64).to_radians(), -5.799903);
|
|
assert_eq!(180.0f64.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_ldexp() {
|
|
// We have to use from_str until base-2 exponents
|
|
// are supported in floating-point literals
|
|
let f1: f64 = FromStrRadix::from_str_radix("1p-123", 16).unwrap();
|
|
let f2: f64 = FromStrRadix::from_str_radix("1p-111", 16).unwrap();
|
|
let f3: f64 = FromStrRadix::from_str_radix("1.Cp-12", 16).unwrap();
|
|
assert_eq!(1f64.ldexp(-123), f1);
|
|
assert_eq!(1f64.ldexp(-111), f2);
|
|
assert_eq!(Float::ldexp(1.75f64, -12), f3);
|
|
|
|
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 = FromStrRadix::from_str_radix("1p-123", 16).unwrap();
|
|
let f2: f64 = FromStrRadix::from_str_radix("1p-111", 16).unwrap();
|
|
let f3: f64 = FromStrRadix::from_str_radix("1.Cp-123", 16).unwrap();
|
|
let (x1, exp1) = f1.frexp();
|
|
let (x2, exp2) = f2.frexp();
|
|
let (x3, exp3) = f3.frexp();
|
|
assert_eq!((x1, exp1), (0.5f64, -122));
|
|
assert_eq!((x2, exp2), (0.5f64, -110));
|
|
assert_eq!((x3, exp3), (0.875f64, -122));
|
|
assert_eq!(Float::ldexp(x1, exp1), f1);
|
|
assert_eq!(Float::ldexp(x2, exp2), f2);
|
|
assert_eq!(Float::ldexp(x3, exp3), f3);
|
|
|
|
assert_eq!(0f64.frexp(), (0f64, 0));
|
|
assert_eq!((-0f64).frexp(), (-0f64, 0));
|
|
}
|
|
|
|
#[test] #[cfg_attr(windows, ignore)] // 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_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_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() {
|
|
use super::consts;
|
|
let pi: f64 = consts::PI;
|
|
let two_pi: f64 = consts::PI_2;
|
|
let frac_pi_2: f64 = consts::FRAC_PI_2;
|
|
let frac_pi_3: f64 = consts::FRAC_PI_3;
|
|
let frac_pi_4: f64 = consts::FRAC_PI_4;
|
|
let frac_pi_6: f64 = consts::FRAC_PI_6;
|
|
let frac_pi_8: f64 = consts::FRAC_PI_8;
|
|
let frac_1_pi: f64 = consts::FRAC_1_PI;
|
|
let frac_2_pi: f64 = consts::FRAC_2_PI;
|
|
let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRTPI;
|
|
let sqrt2: f64 = consts::SQRT2;
|
|
let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT2;
|
|
let e: f64 = consts::E;
|
|
let log2_e: f64 = consts::LOG2_E;
|
|
let log10_e: f64 = consts::LOG10_E;
|
|
let ln_2: f64 = consts::LN_2;
|
|
let ln_10: f64 = consts::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());
|
|
}
|
|
}
|