1 // Copyright 2012-2015 The Rust Project Developers. See the COPYRIGHT
2 // file at the top-level directory of this distribution and at
3 // http://rust-lang.org/COPYRIGHT.
5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8 // option. This file may not be copied, modified, or distributed
9 // except according to those terms.
11 //! This module provides constants which are specific to the implementation
12 //! of the `f32` floating point data type.
14 //! Mathematically significant numbers are provided in the `consts` sub-module.
16 //! *[See also the `f32` primitive type](../../std/primitive.f32.html).*
18 #![stable(feature = "rust1", since = "1.0.0")]
19 #![allow(missing_docs)]
30 #[stable(feature = "rust1", since = "1.0.0")]
31 pub use core::f32::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON};
32 #[stable(feature = "rust1", since = "1.0.0")]
33 pub use core::f32::{MIN_EXP, MAX_EXP, MIN_10_EXP};
34 #[stable(feature = "rust1", since = "1.0.0")]
35 pub use core::f32::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
36 #[stable(feature = "rust1", since = "1.0.0")]
37 pub use core::f32::{MIN, MIN_POSITIVE, MAX};
38 #[stable(feature = "rust1", since = "1.0.0")]
39 pub use core::f32::consts;
44 /// Returns `true` if this value is `NaN` and false otherwise.
49 /// let nan = f32::NAN;
52 /// assert!(nan.is_nan());
53 /// assert!(!f.is_nan());
55 #[stable(feature = "rust1", since = "1.0.0")]
57 pub fn is_nan(self) -> bool { num::Float::is_nan(self) }
59 /// Returns `true` if this value is positive infinity or negative infinity and
66 /// let inf = f32::INFINITY;
67 /// let neg_inf = f32::NEG_INFINITY;
68 /// let nan = f32::NAN;
70 /// assert!(!f.is_infinite());
71 /// assert!(!nan.is_infinite());
73 /// assert!(inf.is_infinite());
74 /// assert!(neg_inf.is_infinite());
76 #[stable(feature = "rust1", since = "1.0.0")]
78 pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) }
80 /// Returns `true` if this number is neither infinite nor `NaN`.
86 /// let inf = f32::INFINITY;
87 /// let neg_inf = f32::NEG_INFINITY;
88 /// let nan = f32::NAN;
90 /// assert!(f.is_finite());
92 /// assert!(!nan.is_finite());
93 /// assert!(!inf.is_finite());
94 /// assert!(!neg_inf.is_finite());
96 #[stable(feature = "rust1", since = "1.0.0")]
98 pub fn is_finite(self) -> bool { num::Float::is_finite(self) }
100 /// Returns `true` if the number is neither zero, infinite,
101 /// [subnormal][subnormal], or `NaN`.
106 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
107 /// let max = f32::MAX;
108 /// let lower_than_min = 1.0e-40_f32;
109 /// let zero = 0.0_f32;
111 /// assert!(min.is_normal());
112 /// assert!(max.is_normal());
114 /// assert!(!zero.is_normal());
115 /// assert!(!f32::NAN.is_normal());
116 /// assert!(!f32::INFINITY.is_normal());
117 /// // Values between `0` and `min` are Subnormal.
118 /// assert!(!lower_than_min.is_normal());
120 /// [subnormal]: https://en.wikipedia.org/wiki/Denormal_number
121 #[stable(feature = "rust1", since = "1.0.0")]
123 pub fn is_normal(self) -> bool { num::Float::is_normal(self) }
125 /// Returns the floating point category of the number. If only one property
126 /// is going to be tested, it is generally faster to use the specific
127 /// predicate instead.
130 /// use std::num::FpCategory;
133 /// let num = 12.4_f32;
134 /// let inf = f32::INFINITY;
136 /// assert_eq!(num.classify(), FpCategory::Normal);
137 /// assert_eq!(inf.classify(), FpCategory::Infinite);
139 #[stable(feature = "rust1", since = "1.0.0")]
141 pub fn classify(self) -> FpCategory { num::Float::classify(self) }
143 /// Returns the largest integer less than or equal to a number.
146 /// let f = 3.99_f32;
149 /// assert_eq!(f.floor(), 3.0);
150 /// assert_eq!(g.floor(), 3.0);
152 #[stable(feature = "rust1", since = "1.0.0")]
154 pub fn floor(self) -> f32 {
155 // On MSVC LLVM will lower many math intrinsics to a call to the
156 // corresponding function. On MSVC, however, many of these functions
157 // aren't actually available as symbols to call, but rather they are all
158 // `static inline` functions in header files. This means that from a C
159 // perspective it's "compatible", but not so much from an ABI
160 // perspective (which we're worried about).
162 // The inline header functions always just cast to a f64 and do their
163 // operation, so we do that here as well, but only for MSVC targets.
165 // Note that there are many MSVC-specific float operations which
166 // redirect to this comment, so `floorf` is just one case of a missing
167 // function on MSVC, but there are many others elsewhere.
168 #[cfg(target_env = "msvc")]
169 return (self as f64).floor() as f32;
170 #[cfg(not(target_env = "msvc"))]
171 return unsafe { intrinsics::floorf32(self) };
174 /// Returns the smallest integer greater than or equal to a number.
177 /// let f = 3.01_f32;
180 /// assert_eq!(f.ceil(), 4.0);
181 /// assert_eq!(g.ceil(), 4.0);
183 #[stable(feature = "rust1", since = "1.0.0")]
185 pub fn ceil(self) -> f32 {
186 // see notes above in `floor`
187 #[cfg(target_env = "msvc")]
188 return (self as f64).ceil() as f32;
189 #[cfg(not(target_env = "msvc"))]
190 return unsafe { intrinsics::ceilf32(self) };
193 /// Returns the nearest integer to a number. Round half-way cases away from
198 /// let g = -3.3_f32;
200 /// assert_eq!(f.round(), 3.0);
201 /// assert_eq!(g.round(), -3.0);
203 #[stable(feature = "rust1", since = "1.0.0")]
205 pub fn round(self) -> f32 {
206 unsafe { intrinsics::roundf32(self) }
209 /// Returns the integer part of a number.
213 /// let g = -3.7_f32;
215 /// assert_eq!(f.trunc(), 3.0);
216 /// assert_eq!(g.trunc(), -3.0);
218 #[stable(feature = "rust1", since = "1.0.0")]
220 pub fn trunc(self) -> f32 {
221 unsafe { intrinsics::truncf32(self) }
224 /// Returns the fractional part of a number.
230 /// let y = -3.5_f32;
231 /// let abs_difference_x = (x.fract() - 0.5).abs();
232 /// let abs_difference_y = (y.fract() - (-0.5)).abs();
234 /// assert!(abs_difference_x <= f32::EPSILON);
235 /// assert!(abs_difference_y <= f32::EPSILON);
237 #[stable(feature = "rust1", since = "1.0.0")]
239 pub fn fract(self) -> f32 { self - self.trunc() }
241 /// Computes the absolute value of `self`. Returns `NAN` if the
248 /// let y = -3.5_f32;
250 /// let abs_difference_x = (x.abs() - x).abs();
251 /// let abs_difference_y = (y.abs() - (-y)).abs();
253 /// assert!(abs_difference_x <= f32::EPSILON);
254 /// assert!(abs_difference_y <= f32::EPSILON);
256 /// assert!(f32::NAN.abs().is_nan());
258 #[stable(feature = "rust1", since = "1.0.0")]
260 pub fn abs(self) -> f32 { num::Float::abs(self) }
262 /// Returns a number that represents the sign of `self`.
264 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
265 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
266 /// - `NAN` if the number is `NAN`
273 /// assert_eq!(f.signum(), 1.0);
274 /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
276 /// assert!(f32::NAN.signum().is_nan());
278 #[stable(feature = "rust1", since = "1.0.0")]
280 pub fn signum(self) -> f32 { num::Float::signum(self) }
282 /// Returns `true` if and only if `self` has a positive sign, including `+0.0`, `NaN`s with
283 /// positive sign bit and positive infinity.
287 /// let g = -7.0_f32;
289 /// assert!(f.is_sign_positive());
290 /// assert!(!g.is_sign_positive());
292 #[stable(feature = "rust1", since = "1.0.0")]
294 pub fn is_sign_positive(self) -> bool { num::Float::is_sign_positive(self) }
296 /// Returns `true` if and only if `self` has a negative sign, including `-0.0`, `NaN`s with
297 /// negative sign bit and negative infinity.
303 /// assert!(!f.is_sign_negative());
304 /// assert!(g.is_sign_negative());
306 #[stable(feature = "rust1", since = "1.0.0")]
308 pub fn is_sign_negative(self) -> bool { num::Float::is_sign_negative(self) }
310 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
311 /// error. This produces a more accurate result with better performance than
312 /// a separate multiplication operation followed by an add.
317 /// let m = 10.0_f32;
319 /// let b = 60.0_f32;
322 /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
324 /// assert!(abs_difference <= f32::EPSILON);
326 #[stable(feature = "rust1", since = "1.0.0")]
328 pub fn mul_add(self, a: f32, b: f32) -> f32 {
329 unsafe { intrinsics::fmaf32(self, a, b) }
332 /// Takes the reciprocal (inverse) of a number, `1/x`.
338 /// let abs_difference = (x.recip() - (1.0/x)).abs();
340 /// assert!(abs_difference <= f32::EPSILON);
342 #[stable(feature = "rust1", since = "1.0.0")]
344 pub fn recip(self) -> f32 { num::Float::recip(self) }
346 /// Raises a number to an integer power.
348 /// Using this function is generally faster than using `powf`
354 /// let abs_difference = (x.powi(2) - x*x).abs();
356 /// assert!(abs_difference <= f32::EPSILON);
358 #[stable(feature = "rust1", since = "1.0.0")]
360 pub fn powi(self, n: i32) -> f32 { num::Float::powi(self, n) }
362 /// Raises a number to a floating point power.
368 /// let abs_difference = (x.powf(2.0) - x*x).abs();
370 /// assert!(abs_difference <= f32::EPSILON);
372 #[stable(feature = "rust1", since = "1.0.0")]
374 pub fn powf(self, n: f32) -> f32 {
375 // see notes above in `floor`
376 #[cfg(target_env = "msvc")]
377 return (self as f64).powf(n as f64) as f32;
378 #[cfg(not(target_env = "msvc"))]
379 return unsafe { intrinsics::powf32(self, n) };
382 /// Takes the square root of a number.
384 /// Returns NaN if `self` is a negative number.
389 /// let positive = 4.0_f32;
390 /// let negative = -4.0_f32;
392 /// let abs_difference = (positive.sqrt() - 2.0).abs();
394 /// assert!(abs_difference <= f32::EPSILON);
395 /// assert!(negative.sqrt().is_nan());
397 #[stable(feature = "rust1", since = "1.0.0")]
399 pub fn sqrt(self) -> f32 {
403 unsafe { intrinsics::sqrtf32(self) }
407 /// Returns `e^(self)`, (the exponential function).
412 /// let one = 1.0f32;
414 /// let e = one.exp();
416 /// // ln(e) - 1 == 0
417 /// let abs_difference = (e.ln() - 1.0).abs();
419 /// assert!(abs_difference <= f32::EPSILON);
421 #[stable(feature = "rust1", since = "1.0.0")]
423 pub fn exp(self) -> f32 {
424 // see notes above in `floor`
425 #[cfg(target_env = "msvc")]
426 return (self as f64).exp() as f32;
427 #[cfg(not(target_env = "msvc"))]
428 return unsafe { intrinsics::expf32(self) };
431 /// Returns `2^(self)`.
439 /// let abs_difference = (f.exp2() - 4.0).abs();
441 /// assert!(abs_difference <= f32::EPSILON);
443 #[stable(feature = "rust1", since = "1.0.0")]
445 pub fn exp2(self) -> f32 {
446 unsafe { intrinsics::exp2f32(self) }
449 /// Returns the natural logarithm of the number.
454 /// let one = 1.0f32;
456 /// let e = one.exp();
458 /// // ln(e) - 1 == 0
459 /// let abs_difference = (e.ln() - 1.0).abs();
461 /// assert!(abs_difference <= f32::EPSILON);
463 #[stable(feature = "rust1", since = "1.0.0")]
465 pub fn ln(self) -> f32 {
466 // see notes above in `floor`
467 #[cfg(target_env = "msvc")]
468 return (self as f64).ln() as f32;
469 #[cfg(not(target_env = "msvc"))]
470 return unsafe { intrinsics::logf32(self) };
473 /// Returns the logarithm of the number with respect to an arbitrary base.
475 /// The result may not be correctly rounded owing to implementation details;
476 /// `self.log2()` can produce more accurate results for base 2, and
477 /// `self.log10()` can produce more accurate results for base 10.
482 /// let five = 5.0f32;
484 /// // log5(5) - 1 == 0
485 /// let abs_difference = (five.log(5.0) - 1.0).abs();
487 /// assert!(abs_difference <= f32::EPSILON);
489 #[stable(feature = "rust1", since = "1.0.0")]
491 pub fn log(self, base: f32) -> f32 { self.ln() / base.ln() }
493 /// Returns the base 2 logarithm of the number.
498 /// let two = 2.0f32;
500 /// // log2(2) - 1 == 0
501 /// let abs_difference = (two.log2() - 1.0).abs();
503 /// assert!(abs_difference <= f32::EPSILON);
505 #[stable(feature = "rust1", since = "1.0.0")]
507 pub fn log2(self) -> f32 {
508 #[cfg(target_os = "android")]
509 return ::sys::android::log2f32(self);
510 #[cfg(not(target_os = "android"))]
511 return unsafe { intrinsics::log2f32(self) };
514 /// Returns the base 10 logarithm of the number.
519 /// let ten = 10.0f32;
521 /// // log10(10) - 1 == 0
522 /// let abs_difference = (ten.log10() - 1.0).abs();
524 /// assert!(abs_difference <= f32::EPSILON);
526 #[stable(feature = "rust1", since = "1.0.0")]
528 pub fn log10(self) -> f32 {
529 // see notes above in `floor`
530 #[cfg(target_env = "msvc")]
531 return (self as f64).log10() as f32;
532 #[cfg(not(target_env = "msvc"))]
533 return unsafe { intrinsics::log10f32(self) };
536 /// Converts radians to degrees.
539 /// use std::f32::{self, consts};
541 /// let angle = consts::PI;
543 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
545 /// assert!(abs_difference <= f32::EPSILON);
547 #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
549 pub fn to_degrees(self) -> f32 { num::Float::to_degrees(self) }
551 /// Converts degrees to radians.
554 /// use std::f32::{self, consts};
556 /// let angle = 180.0f32;
558 /// let abs_difference = (angle.to_radians() - consts::PI).abs();
560 /// assert!(abs_difference <= f32::EPSILON);
562 #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
564 pub fn to_radians(self) -> f32 { num::Float::to_radians(self) }
566 /// Returns the maximum of the two numbers.
572 /// assert_eq!(x.max(y), y);
575 /// If one of the arguments is NaN, then the other argument is returned.
576 #[stable(feature = "rust1", since = "1.0.0")]
578 pub fn max(self, other: f32) -> f32 {
579 num::Float::max(self, other)
582 /// Returns the minimum of the two numbers.
588 /// assert_eq!(x.min(y), x);
591 /// If one of the arguments is NaN, then the other argument is returned.
592 #[stable(feature = "rust1", since = "1.0.0")]
594 pub fn min(self, other: f32) -> f32 {
595 num::Float::min(self, other)
598 /// The positive difference of two numbers.
600 /// * If `self <= other`: `0:0`
601 /// * Else: `self - other`
609 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
610 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
612 /// assert!(abs_difference_x <= f32::EPSILON);
613 /// assert!(abs_difference_y <= f32::EPSILON);
615 #[stable(feature = "rust1", since = "1.0.0")]
617 #[rustc_deprecated(since = "1.10.0",
618 reason = "you probably meant `(self - other).abs()`: \
619 this operation is `(self - other).max(0.0)` (also \
620 known as `fdimf` in C). If you truly need the positive \
621 difference, consider using that expression or the C function \
622 `fdimf`, depending on how you wish to handle NaN (please consider \
623 filing an issue describing your use-case too).")]
624 pub fn abs_sub(self, other: f32) -> f32 {
625 unsafe { cmath::fdimf(self, other) }
628 /// Takes the cubic root of a number.
635 /// // x^(1/3) - 2 == 0
636 /// let abs_difference = (x.cbrt() - 2.0).abs();
638 /// assert!(abs_difference <= f32::EPSILON);
640 #[stable(feature = "rust1", since = "1.0.0")]
642 pub fn cbrt(self) -> f32 {
643 unsafe { cmath::cbrtf(self) }
646 /// Calculates the length of the hypotenuse of a right-angle triangle given
647 /// legs of length `x` and `y`.
655 /// // sqrt(x^2 + y^2)
656 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
658 /// assert!(abs_difference <= f32::EPSILON);
660 #[stable(feature = "rust1", since = "1.0.0")]
662 pub fn hypot(self, other: f32) -> f32 {
663 unsafe { cmath::hypotf(self, other) }
666 /// Computes the sine of a number (in radians).
671 /// let x = f32::consts::PI/2.0;
673 /// let abs_difference = (x.sin() - 1.0).abs();
675 /// assert!(abs_difference <= f32::EPSILON);
677 #[stable(feature = "rust1", since = "1.0.0")]
679 pub fn sin(self) -> f32 {
680 // see notes in `core::f32::Float::floor`
681 #[cfg(target_env = "msvc")]
682 return (self as f64).sin() as f32;
683 #[cfg(not(target_env = "msvc"))]
684 return unsafe { intrinsics::sinf32(self) };
687 /// Computes the cosine of a number (in radians).
692 /// let x = 2.0*f32::consts::PI;
694 /// let abs_difference = (x.cos() - 1.0).abs();
696 /// assert!(abs_difference <= f32::EPSILON);
698 #[stable(feature = "rust1", since = "1.0.0")]
700 pub fn cos(self) -> f32 {
701 // see notes in `core::f32::Float::floor`
702 #[cfg(target_env = "msvc")]
703 return (self as f64).cos() as f32;
704 #[cfg(not(target_env = "msvc"))]
705 return unsafe { intrinsics::cosf32(self) };
708 /// Computes the tangent of a number (in radians).
713 /// let x = f32::consts::PI / 4.0;
714 /// let abs_difference = (x.tan() - 1.0).abs();
716 /// assert!(abs_difference <= f32::EPSILON);
718 #[stable(feature = "rust1", since = "1.0.0")]
720 pub fn tan(self) -> f32 {
721 unsafe { cmath::tanf(self) }
724 /// Computes the arcsine of a number. Return value is in radians in
725 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
731 /// let f = f32::consts::PI / 2.0;
733 /// // asin(sin(pi/2))
734 /// let abs_difference = (f.sin().asin() - f32::consts::PI / 2.0).abs();
736 /// assert!(abs_difference <= f32::EPSILON);
738 #[stable(feature = "rust1", since = "1.0.0")]
740 pub fn asin(self) -> f32 {
741 unsafe { cmath::asinf(self) }
744 /// Computes the arccosine of a number. Return value is in radians in
745 /// the range [0, pi] or NaN if the number is outside the range
751 /// let f = f32::consts::PI / 4.0;
753 /// // acos(cos(pi/4))
754 /// let abs_difference = (f.cos().acos() - f32::consts::PI / 4.0).abs();
756 /// assert!(abs_difference <= f32::EPSILON);
758 #[stable(feature = "rust1", since = "1.0.0")]
760 pub fn acos(self) -> f32 {
761 unsafe { cmath::acosf(self) }
764 /// Computes the arctangent of a number. Return value is in radians in the
765 /// range [-pi/2, pi/2];
773 /// let abs_difference = (f.tan().atan() - 1.0).abs();
775 /// assert!(abs_difference <= f32::EPSILON);
777 #[stable(feature = "rust1", since = "1.0.0")]
779 pub fn atan(self) -> f32 {
780 unsafe { cmath::atanf(self) }
783 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
785 /// * `x = 0`, `y = 0`: `0`
786 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
787 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
788 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
793 /// let pi = f32::consts::PI;
794 /// // All angles from horizontal right (+x)
795 /// // 45 deg counter-clockwise
797 /// let y1 = -3.0f32;
799 /// // 135 deg clockwise
800 /// let x2 = -3.0f32;
803 /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
804 /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
806 /// assert!(abs_difference_1 <= f32::EPSILON);
807 /// assert!(abs_difference_2 <= f32::EPSILON);
809 #[stable(feature = "rust1", since = "1.0.0")]
811 pub fn atan2(self, other: f32) -> f32 {
812 unsafe { cmath::atan2f(self, other) }
815 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
816 /// `(sin(x), cos(x))`.
821 /// let x = f32::consts::PI/4.0;
822 /// let f = x.sin_cos();
824 /// let abs_difference_0 = (f.0 - x.sin()).abs();
825 /// let abs_difference_1 = (f.1 - x.cos()).abs();
827 /// assert!(abs_difference_0 <= f32::EPSILON);
828 /// assert!(abs_difference_1 <= f32::EPSILON);
830 #[stable(feature = "rust1", since = "1.0.0")]
832 pub fn sin_cos(self) -> (f32, f32) {
833 (self.sin(), self.cos())
836 /// Returns `e^(self) - 1` in a way that is accurate even if the
837 /// number is close to zero.
845 /// let abs_difference = (x.ln().exp_m1() - 5.0).abs();
847 /// assert!(abs_difference <= f32::EPSILON);
849 #[stable(feature = "rust1", since = "1.0.0")]
851 pub fn exp_m1(self) -> f32 {
852 unsafe { cmath::expm1f(self) }
855 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
856 /// the operations were performed separately.
861 /// let x = f32::consts::E - 1.0;
863 /// // ln(1 + (e - 1)) == ln(e) == 1
864 /// let abs_difference = (x.ln_1p() - 1.0).abs();
866 /// assert!(abs_difference <= f32::EPSILON);
868 #[stable(feature = "rust1", since = "1.0.0")]
870 pub fn ln_1p(self) -> f32 {
871 unsafe { cmath::log1pf(self) }
874 /// Hyperbolic sine function.
879 /// let e = f32::consts::E;
882 /// let f = x.sinh();
883 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
884 /// let g = (e*e - 1.0)/(2.0*e);
885 /// let abs_difference = (f - g).abs();
887 /// assert!(abs_difference <= f32::EPSILON);
889 #[stable(feature = "rust1", since = "1.0.0")]
891 pub fn sinh(self) -> f32 {
892 unsafe { cmath::sinhf(self) }
895 /// Hyperbolic cosine function.
900 /// let e = f32::consts::E;
902 /// let f = x.cosh();
903 /// // Solving cosh() at 1 gives this result
904 /// let g = (e*e + 1.0)/(2.0*e);
905 /// let abs_difference = (f - g).abs();
908 /// assert!(abs_difference <= f32::EPSILON);
910 #[stable(feature = "rust1", since = "1.0.0")]
912 pub fn cosh(self) -> f32 {
913 unsafe { cmath::coshf(self) }
916 /// Hyperbolic tangent function.
921 /// let e = f32::consts::E;
924 /// let f = x.tanh();
925 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
926 /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
927 /// let abs_difference = (f - g).abs();
929 /// assert!(abs_difference <= f32::EPSILON);
931 #[stable(feature = "rust1", since = "1.0.0")]
933 pub fn tanh(self) -> f32 {
934 unsafe { cmath::tanhf(self) }
937 /// Inverse hyperbolic sine function.
943 /// let f = x.sinh().asinh();
945 /// let abs_difference = (f - x).abs();
947 /// assert!(abs_difference <= f32::EPSILON);
949 #[stable(feature = "rust1", since = "1.0.0")]
951 pub fn asinh(self) -> f32 {
952 if self == NEG_INFINITY {
955 (self + ((self * self) + 1.0).sqrt()).ln()
959 /// Inverse hyperbolic cosine function.
965 /// let f = x.cosh().acosh();
967 /// let abs_difference = (f - x).abs();
969 /// assert!(abs_difference <= f32::EPSILON);
971 #[stable(feature = "rust1", since = "1.0.0")]
973 pub fn acosh(self) -> f32 {
975 x if x < 1.0 => ::f32::NAN,
976 x => (x + ((x * x) - 1.0).sqrt()).ln(),
980 /// Inverse hyperbolic tangent function.
985 /// let e = f32::consts::E;
986 /// let f = e.tanh().atanh();
988 /// let abs_difference = (f - e).abs();
990 /// assert!(abs_difference <= 1e-5);
992 #[stable(feature = "rust1", since = "1.0.0")]
994 pub fn atanh(self) -> f32 {
995 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
998 /// Raw transmutation to `u32`.
1000 /// This is currently identical to `transmute::<f32, u32>(self)` on all platforms.
1002 /// See `from_bits` for some discussion of the portability of this operation
1003 /// (there are almost no issues).
1005 /// Note that this function is distinct from `as` casting, which attempts to
1006 /// preserve the *numeric* value, and not the bitwise value.
1011 /// assert_ne!((1f32).to_bits(), 1f32 as u32); // to_bits() is not casting!
1012 /// assert_eq!((12.5f32).to_bits(), 0x41480000);
1015 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1017 pub fn to_bits(self) -> u32 {
1018 num::Float::to_bits(self)
1021 /// Raw transmutation from `u32`.
1023 /// This is currently identical to `transmute::<u32, f32>(v)` on all platforms.
1024 /// It turns out this is incredibly portable, for two reasons:
1026 /// * Floats and Ints have the same endianess on all supported platforms.
1027 /// * IEEE-754 very precisely specifies the bit layout of floats.
1029 /// However there is one caveat: prior to the 2008 version of IEEE-754, how
1030 /// to interpret the NaN signaling bit wasn't actually specified. Most platforms
1031 /// (notably x86 and ARM) picked the interpretation that was ultimately
1032 /// standardized in 2008, but some didn't (notably MIPS). As a result, all
1033 /// signaling NaNs on MIPS are quiet NaNs on x86, and vice-versa.
1035 /// Rather than trying to preserve signaling-ness cross-platform, this
1036 /// implementation favours preserving the exact bits. This means that
1037 /// any payloads encoded in NaNs will be preserved even if the result of
1038 /// this method is sent over the network from an x86 machine to a MIPS one.
1040 /// If the results of this method are only manipulated by the same
1041 /// architecture that produced them, then there is no portability concern.
1043 /// If the input isn't NaN, then there is no portability concern.
1045 /// If you don't care about signalingness (very likely), then there is no
1046 /// portability concern.
1048 /// Note that this function is distinct from `as` casting, which attempts to
1049 /// preserve the *numeric* value, and not the bitwise value.
1055 /// let v = f32::from_bits(0x41480000);
1056 /// let difference = (v - 12.5).abs();
1057 /// assert!(difference <= 1e-5);
1059 #[stable(feature = "float_bits_conv", since = "1.20.0")]
1061 pub fn from_bits(v: u32) -> Self {
1062 num::Float::from_bits(v)
1071 use num::FpCategory as Fp;
1075 test_num(10f32, 2f32);
1080 assert_eq!(NAN.min(2.0), 2.0);
1081 assert_eq!(2.0f32.min(NAN), 2.0);
1086 assert_eq!(NAN.max(2.0), 2.0);
1087 assert_eq!(2.0f32.max(NAN), 2.0);
1092 let nan: f32 = f32::NAN;
1093 assert!(nan.is_nan());
1094 assert!(!nan.is_infinite());
1095 assert!(!nan.is_finite());
1096 assert!(!nan.is_normal());
1097 assert!(nan.is_sign_positive());
1098 assert!(!nan.is_sign_negative());
1099 assert_eq!(Fp::Nan, nan.classify());
1103 fn test_infinity() {
1104 let inf: f32 = f32::INFINITY;
1105 assert!(inf.is_infinite());
1106 assert!(!inf.is_finite());
1107 assert!(inf.is_sign_positive());
1108 assert!(!inf.is_sign_negative());
1109 assert!(!inf.is_nan());
1110 assert!(!inf.is_normal());
1111 assert_eq!(Fp::Infinite, inf.classify());
1115 fn test_neg_infinity() {
1116 let neg_inf: f32 = f32::NEG_INFINITY;
1117 assert!(neg_inf.is_infinite());
1118 assert!(!neg_inf.is_finite());
1119 assert!(!neg_inf.is_sign_positive());
1120 assert!(neg_inf.is_sign_negative());
1121 assert!(!neg_inf.is_nan());
1122 assert!(!neg_inf.is_normal());
1123 assert_eq!(Fp::Infinite, neg_inf.classify());
1128 let zero: f32 = 0.0f32;
1129 assert_eq!(0.0, zero);
1130 assert!(!zero.is_infinite());
1131 assert!(zero.is_finite());
1132 assert!(zero.is_sign_positive());
1133 assert!(!zero.is_sign_negative());
1134 assert!(!zero.is_nan());
1135 assert!(!zero.is_normal());
1136 assert_eq!(Fp::Zero, zero.classify());
1140 fn test_neg_zero() {
1141 let neg_zero: f32 = -0.0;
1142 assert_eq!(0.0, neg_zero);
1143 assert!(!neg_zero.is_infinite());
1144 assert!(neg_zero.is_finite());
1145 assert!(!neg_zero.is_sign_positive());
1146 assert!(neg_zero.is_sign_negative());
1147 assert!(!neg_zero.is_nan());
1148 assert!(!neg_zero.is_normal());
1149 assert_eq!(Fp::Zero, neg_zero.classify());
1154 let one: f32 = 1.0f32;
1155 assert_eq!(1.0, one);
1156 assert!(!one.is_infinite());
1157 assert!(one.is_finite());
1158 assert!(one.is_sign_positive());
1159 assert!(!one.is_sign_negative());
1160 assert!(!one.is_nan());
1161 assert!(one.is_normal());
1162 assert_eq!(Fp::Normal, one.classify());
1167 let nan: f32 = f32::NAN;
1168 let inf: f32 = f32::INFINITY;
1169 let neg_inf: f32 = f32::NEG_INFINITY;
1170 assert!(nan.is_nan());
1171 assert!(!0.0f32.is_nan());
1172 assert!(!5.3f32.is_nan());
1173 assert!(!(-10.732f32).is_nan());
1174 assert!(!inf.is_nan());
1175 assert!(!neg_inf.is_nan());
1179 fn test_is_infinite() {
1180 let nan: f32 = f32::NAN;
1181 let inf: f32 = f32::INFINITY;
1182 let neg_inf: f32 = f32::NEG_INFINITY;
1183 assert!(!nan.is_infinite());
1184 assert!(inf.is_infinite());
1185 assert!(neg_inf.is_infinite());
1186 assert!(!0.0f32.is_infinite());
1187 assert!(!42.8f32.is_infinite());
1188 assert!(!(-109.2f32).is_infinite());
1192 fn test_is_finite() {
1193 let nan: f32 = f32::NAN;
1194 let inf: f32 = f32::INFINITY;
1195 let neg_inf: f32 = f32::NEG_INFINITY;
1196 assert!(!nan.is_finite());
1197 assert!(!inf.is_finite());
1198 assert!(!neg_inf.is_finite());
1199 assert!(0.0f32.is_finite());
1200 assert!(42.8f32.is_finite());
1201 assert!((-109.2f32).is_finite());
1205 fn test_is_normal() {
1206 let nan: f32 = f32::NAN;
1207 let inf: f32 = f32::INFINITY;
1208 let neg_inf: f32 = f32::NEG_INFINITY;
1209 let zero: f32 = 0.0f32;
1210 let neg_zero: f32 = -0.0;
1211 assert!(!nan.is_normal());
1212 assert!(!inf.is_normal());
1213 assert!(!neg_inf.is_normal());
1214 assert!(!zero.is_normal());
1215 assert!(!neg_zero.is_normal());
1216 assert!(1f32.is_normal());
1217 assert!(1e-37f32.is_normal());
1218 assert!(!1e-38f32.is_normal());
1222 fn test_classify() {
1223 let nan: f32 = f32::NAN;
1224 let inf: f32 = f32::INFINITY;
1225 let neg_inf: f32 = f32::NEG_INFINITY;
1226 let zero: f32 = 0.0f32;
1227 let neg_zero: f32 = -0.0;
1228 assert_eq!(nan.classify(), Fp::Nan);
1229 assert_eq!(inf.classify(), Fp::Infinite);
1230 assert_eq!(neg_inf.classify(), Fp::Infinite);
1231 assert_eq!(zero.classify(), Fp::Zero);
1232 assert_eq!(neg_zero.classify(), Fp::Zero);
1233 assert_eq!(1f32.classify(), Fp::Normal);
1234 assert_eq!(1e-37f32.classify(), Fp::Normal);
1235 assert_eq!(1e-38f32.classify(), Fp::Subnormal);
1240 assert_approx_eq!(1.0f32.floor(), 1.0f32);
1241 assert_approx_eq!(1.3f32.floor(), 1.0f32);
1242 assert_approx_eq!(1.5f32.floor(), 1.0f32);
1243 assert_approx_eq!(1.7f32.floor(), 1.0f32);
1244 assert_approx_eq!(0.0f32.floor(), 0.0f32);
1245 assert_approx_eq!((-0.0f32).floor(), -0.0f32);
1246 assert_approx_eq!((-1.0f32).floor(), -1.0f32);
1247 assert_approx_eq!((-1.3f32).floor(), -2.0f32);
1248 assert_approx_eq!((-1.5f32).floor(), -2.0f32);
1249 assert_approx_eq!((-1.7f32).floor(), -2.0f32);
1254 assert_approx_eq!(1.0f32.ceil(), 1.0f32);
1255 assert_approx_eq!(1.3f32.ceil(), 2.0f32);
1256 assert_approx_eq!(1.5f32.ceil(), 2.0f32);
1257 assert_approx_eq!(1.7f32.ceil(), 2.0f32);
1258 assert_approx_eq!(0.0f32.ceil(), 0.0f32);
1259 assert_approx_eq!((-0.0f32).ceil(), -0.0f32);
1260 assert_approx_eq!((-1.0f32).ceil(), -1.0f32);
1261 assert_approx_eq!((-1.3f32).ceil(), -1.0f32);
1262 assert_approx_eq!((-1.5f32).ceil(), -1.0f32);
1263 assert_approx_eq!((-1.7f32).ceil(), -1.0f32);
1268 assert_approx_eq!(1.0f32.round(), 1.0f32);
1269 assert_approx_eq!(1.3f32.round(), 1.0f32);
1270 assert_approx_eq!(1.5f32.round(), 2.0f32);
1271 assert_approx_eq!(1.7f32.round(), 2.0f32);
1272 assert_approx_eq!(0.0f32.round(), 0.0f32);
1273 assert_approx_eq!((-0.0f32).round(), -0.0f32);
1274 assert_approx_eq!((-1.0f32).round(), -1.0f32);
1275 assert_approx_eq!((-1.3f32).round(), -1.0f32);
1276 assert_approx_eq!((-1.5f32).round(), -2.0f32);
1277 assert_approx_eq!((-1.7f32).round(), -2.0f32);
1282 assert_approx_eq!(1.0f32.trunc(), 1.0f32);
1283 assert_approx_eq!(1.3f32.trunc(), 1.0f32);
1284 assert_approx_eq!(1.5f32.trunc(), 1.0f32);
1285 assert_approx_eq!(1.7f32.trunc(), 1.0f32);
1286 assert_approx_eq!(0.0f32.trunc(), 0.0f32);
1287 assert_approx_eq!((-0.0f32).trunc(), -0.0f32);
1288 assert_approx_eq!((-1.0f32).trunc(), -1.0f32);
1289 assert_approx_eq!((-1.3f32).trunc(), -1.0f32);
1290 assert_approx_eq!((-1.5f32).trunc(), -1.0f32);
1291 assert_approx_eq!((-1.7f32).trunc(), -1.0f32);
1296 assert_approx_eq!(1.0f32.fract(), 0.0f32);
1297 assert_approx_eq!(1.3f32.fract(), 0.3f32);
1298 assert_approx_eq!(1.5f32.fract(), 0.5f32);
1299 assert_approx_eq!(1.7f32.fract(), 0.7f32);
1300 assert_approx_eq!(0.0f32.fract(), 0.0f32);
1301 assert_approx_eq!((-0.0f32).fract(), -0.0f32);
1302 assert_approx_eq!((-1.0f32).fract(), -0.0f32);
1303 assert_approx_eq!((-1.3f32).fract(), -0.3f32);
1304 assert_approx_eq!((-1.5f32).fract(), -0.5f32);
1305 assert_approx_eq!((-1.7f32).fract(), -0.7f32);
1310 assert_eq!(INFINITY.abs(), INFINITY);
1311 assert_eq!(1f32.abs(), 1f32);
1312 assert_eq!(0f32.abs(), 0f32);
1313 assert_eq!((-0f32).abs(), 0f32);
1314 assert_eq!((-1f32).abs(), 1f32);
1315 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1316 assert_eq!((1f32/NEG_INFINITY).abs(), 0f32);
1317 assert!(NAN.abs().is_nan());
1322 assert_eq!(INFINITY.signum(), 1f32);
1323 assert_eq!(1f32.signum(), 1f32);
1324 assert_eq!(0f32.signum(), 1f32);
1325 assert_eq!((-0f32).signum(), -1f32);
1326 assert_eq!((-1f32).signum(), -1f32);
1327 assert_eq!(NEG_INFINITY.signum(), -1f32);
1328 assert_eq!((1f32/NEG_INFINITY).signum(), -1f32);
1329 assert!(NAN.signum().is_nan());
1333 fn test_is_sign_positive() {
1334 assert!(INFINITY.is_sign_positive());
1335 assert!(1f32.is_sign_positive());
1336 assert!(0f32.is_sign_positive());
1337 assert!(!(-0f32).is_sign_positive());
1338 assert!(!(-1f32).is_sign_positive());
1339 assert!(!NEG_INFINITY.is_sign_positive());
1340 assert!(!(1f32/NEG_INFINITY).is_sign_positive());
1341 assert!(NAN.is_sign_positive());
1342 assert!(!(-NAN).is_sign_positive());
1346 fn test_is_sign_negative() {
1347 assert!(!INFINITY.is_sign_negative());
1348 assert!(!1f32.is_sign_negative());
1349 assert!(!0f32.is_sign_negative());
1350 assert!((-0f32).is_sign_negative());
1351 assert!((-1f32).is_sign_negative());
1352 assert!(NEG_INFINITY.is_sign_negative());
1353 assert!((1f32/NEG_INFINITY).is_sign_negative());
1354 assert!(!NAN.is_sign_negative());
1355 assert!((-NAN).is_sign_negative());
1360 let nan: f32 = f32::NAN;
1361 let inf: f32 = f32::INFINITY;
1362 let neg_inf: f32 = f32::NEG_INFINITY;
1363 assert_approx_eq!(12.3f32.mul_add(4.5, 6.7), 62.05);
1364 assert_approx_eq!((-12.3f32).mul_add(-4.5, -6.7), 48.65);
1365 assert_approx_eq!(0.0f32.mul_add(8.9, 1.2), 1.2);
1366 assert_approx_eq!(3.4f32.mul_add(-0.0, 5.6), 5.6);
1367 assert!(nan.mul_add(7.8, 9.0).is_nan());
1368 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1369 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1370 assert_eq!(8.9f32.mul_add(inf, 3.2), inf);
1371 assert_eq!((-3.2f32).mul_add(2.4, neg_inf), neg_inf);
1376 let nan: f32 = f32::NAN;
1377 let inf: f32 = f32::INFINITY;
1378 let neg_inf: f32 = f32::NEG_INFINITY;
1379 assert_eq!(1.0f32.recip(), 1.0);
1380 assert_eq!(2.0f32.recip(), 0.5);
1381 assert_eq!((-0.4f32).recip(), -2.5);
1382 assert_eq!(0.0f32.recip(), inf);
1383 assert!(nan.recip().is_nan());
1384 assert_eq!(inf.recip(), 0.0);
1385 assert_eq!(neg_inf.recip(), 0.0);
1390 let nan: f32 = f32::NAN;
1391 let inf: f32 = f32::INFINITY;
1392 let neg_inf: f32 = f32::NEG_INFINITY;
1393 assert_eq!(1.0f32.powi(1), 1.0);
1394 assert_approx_eq!((-3.1f32).powi(2), 9.61);
1395 assert_approx_eq!(5.9f32.powi(-2), 0.028727);
1396 assert_eq!(8.3f32.powi(0), 1.0);
1397 assert!(nan.powi(2).is_nan());
1398 assert_eq!(inf.powi(3), inf);
1399 assert_eq!(neg_inf.powi(2), inf);
1404 let nan: f32 = f32::NAN;
1405 let inf: f32 = f32::INFINITY;
1406 let neg_inf: f32 = f32::NEG_INFINITY;
1407 assert_eq!(1.0f32.powf(1.0), 1.0);
1408 assert_approx_eq!(3.4f32.powf(4.5), 246.408218);
1409 assert_approx_eq!(2.7f32.powf(-3.2), 0.041652);
1410 assert_approx_eq!((-3.1f32).powf(2.0), 9.61);
1411 assert_approx_eq!(5.9f32.powf(-2.0), 0.028727);
1412 assert_eq!(8.3f32.powf(0.0), 1.0);
1413 assert!(nan.powf(2.0).is_nan());
1414 assert_eq!(inf.powf(2.0), inf);
1415 assert_eq!(neg_inf.powf(3.0), neg_inf);
1419 fn test_sqrt_domain() {
1420 assert!(NAN.sqrt().is_nan());
1421 assert!(NEG_INFINITY.sqrt().is_nan());
1422 assert!((-1.0f32).sqrt().is_nan());
1423 assert_eq!((-0.0f32).sqrt(), -0.0);
1424 assert_eq!(0.0f32.sqrt(), 0.0);
1425 assert_eq!(1.0f32.sqrt(), 1.0);
1426 assert_eq!(INFINITY.sqrt(), INFINITY);
1431 assert_eq!(1.0, 0.0f32.exp());
1432 assert_approx_eq!(2.718282, 1.0f32.exp());
1433 assert_approx_eq!(148.413162, 5.0f32.exp());
1435 let inf: f32 = f32::INFINITY;
1436 let neg_inf: f32 = f32::NEG_INFINITY;
1437 let nan: f32 = f32::NAN;
1438 assert_eq!(inf, inf.exp());
1439 assert_eq!(0.0, neg_inf.exp());
1440 assert!(nan.exp().is_nan());
1445 assert_eq!(32.0, 5.0f32.exp2());
1446 assert_eq!(1.0, 0.0f32.exp2());
1448 let inf: f32 = f32::INFINITY;
1449 let neg_inf: f32 = f32::NEG_INFINITY;
1450 let nan: f32 = f32::NAN;
1451 assert_eq!(inf, inf.exp2());
1452 assert_eq!(0.0, neg_inf.exp2());
1453 assert!(nan.exp2().is_nan());
1458 let nan: f32 = f32::NAN;
1459 let inf: f32 = f32::INFINITY;
1460 let neg_inf: f32 = f32::NEG_INFINITY;
1461 assert_approx_eq!(1.0f32.exp().ln(), 1.0);
1462 assert!(nan.ln().is_nan());
1463 assert_eq!(inf.ln(), inf);
1464 assert!(neg_inf.ln().is_nan());
1465 assert!((-2.3f32).ln().is_nan());
1466 assert_eq!((-0.0f32).ln(), neg_inf);
1467 assert_eq!(0.0f32.ln(), neg_inf);
1468 assert_approx_eq!(4.0f32.ln(), 1.386294);
1473 let nan: f32 = f32::NAN;
1474 let inf: f32 = f32::INFINITY;
1475 let neg_inf: f32 = f32::NEG_INFINITY;
1476 assert_eq!(10.0f32.log(10.0), 1.0);
1477 assert_approx_eq!(2.3f32.log(3.5), 0.664858);
1478 assert_eq!(1.0f32.exp().log(1.0f32.exp()), 1.0);
1479 assert!(1.0f32.log(1.0).is_nan());
1480 assert!(1.0f32.log(-13.9).is_nan());
1481 assert!(nan.log(2.3).is_nan());
1482 assert_eq!(inf.log(10.0), inf);
1483 assert!(neg_inf.log(8.8).is_nan());
1484 assert!((-2.3f32).log(0.1).is_nan());
1485 assert_eq!((-0.0f32).log(2.0), neg_inf);
1486 assert_eq!(0.0f32.log(7.0), neg_inf);
1491 let nan: f32 = f32::NAN;
1492 let inf: f32 = f32::INFINITY;
1493 let neg_inf: f32 = f32::NEG_INFINITY;
1494 assert_approx_eq!(10.0f32.log2(), 3.321928);
1495 assert_approx_eq!(2.3f32.log2(), 1.201634);
1496 assert_approx_eq!(1.0f32.exp().log2(), 1.442695);
1497 assert!(nan.log2().is_nan());
1498 assert_eq!(inf.log2(), inf);
1499 assert!(neg_inf.log2().is_nan());
1500 assert!((-2.3f32).log2().is_nan());
1501 assert_eq!((-0.0f32).log2(), neg_inf);
1502 assert_eq!(0.0f32.log2(), neg_inf);
1507 let nan: f32 = f32::NAN;
1508 let inf: f32 = f32::INFINITY;
1509 let neg_inf: f32 = f32::NEG_INFINITY;
1510 assert_eq!(10.0f32.log10(), 1.0);
1511 assert_approx_eq!(2.3f32.log10(), 0.361728);
1512 assert_approx_eq!(1.0f32.exp().log10(), 0.434294);
1513 assert_eq!(1.0f32.log10(), 0.0);
1514 assert!(nan.log10().is_nan());
1515 assert_eq!(inf.log10(), inf);
1516 assert!(neg_inf.log10().is_nan());
1517 assert!((-2.3f32).log10().is_nan());
1518 assert_eq!((-0.0f32).log10(), neg_inf);
1519 assert_eq!(0.0f32.log10(), neg_inf);
1523 fn test_to_degrees() {
1524 let pi: f32 = consts::PI;
1525 let nan: f32 = f32::NAN;
1526 let inf: f32 = f32::INFINITY;
1527 let neg_inf: f32 = f32::NEG_INFINITY;
1528 assert_eq!(0.0f32.to_degrees(), 0.0);
1529 assert_approx_eq!((-5.8f32).to_degrees(), -332.315521);
1530 assert_eq!(pi.to_degrees(), 180.0);
1531 assert!(nan.to_degrees().is_nan());
1532 assert_eq!(inf.to_degrees(), inf);
1533 assert_eq!(neg_inf.to_degrees(), neg_inf);
1537 fn test_to_radians() {
1538 let pi: f32 = consts::PI;
1539 let nan: f32 = f32::NAN;
1540 let inf: f32 = f32::INFINITY;
1541 let neg_inf: f32 = f32::NEG_INFINITY;
1542 assert_eq!(0.0f32.to_radians(), 0.0);
1543 assert_approx_eq!(154.6f32.to_radians(), 2.698279);
1544 assert_approx_eq!((-332.31f32).to_radians(), -5.799903);
1545 assert_eq!(180.0f32.to_radians(), pi);
1546 assert!(nan.to_radians().is_nan());
1547 assert_eq!(inf.to_radians(), inf);
1548 assert_eq!(neg_inf.to_radians(), neg_inf);
1553 assert_eq!(0.0f32.asinh(), 0.0f32);
1554 assert_eq!((-0.0f32).asinh(), -0.0f32);
1556 let inf: f32 = f32::INFINITY;
1557 let neg_inf: f32 = f32::NEG_INFINITY;
1558 let nan: f32 = f32::NAN;
1559 assert_eq!(inf.asinh(), inf);
1560 assert_eq!(neg_inf.asinh(), neg_inf);
1561 assert!(nan.asinh().is_nan());
1562 assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32);
1563 assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32);
1568 assert_eq!(1.0f32.acosh(), 0.0f32);
1569 assert!(0.999f32.acosh().is_nan());
1571 let inf: f32 = f32::INFINITY;
1572 let neg_inf: f32 = f32::NEG_INFINITY;
1573 let nan: f32 = f32::NAN;
1574 assert_eq!(inf.acosh(), inf);
1575 assert!(neg_inf.acosh().is_nan());
1576 assert!(nan.acosh().is_nan());
1577 assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32);
1578 assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32);
1583 assert_eq!(0.0f32.atanh(), 0.0f32);
1584 assert_eq!((-0.0f32).atanh(), -0.0f32);
1586 let inf32: f32 = f32::INFINITY;
1587 let neg_inf32: f32 = f32::NEG_INFINITY;
1588 assert_eq!(1.0f32.atanh(), inf32);
1589 assert_eq!((-1.0f32).atanh(), neg_inf32);
1591 assert!(2f64.atanh().atanh().is_nan());
1592 assert!((-2f64).atanh().atanh().is_nan());
1594 let inf64: f32 = f32::INFINITY;
1595 let neg_inf64: f32 = f32::NEG_INFINITY;
1596 let nan32: f32 = f32::NAN;
1597 assert!(inf64.atanh().is_nan());
1598 assert!(neg_inf64.atanh().is_nan());
1599 assert!(nan32.atanh().is_nan());
1601 assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32);
1602 assert_approx_eq!((-0.5f32).atanh(), -0.54930614433405484569762261846126285f32);
1606 fn test_real_consts() {
1609 let pi: f32 = consts::PI;
1610 let frac_pi_2: f32 = consts::FRAC_PI_2;
1611 let frac_pi_3: f32 = consts::FRAC_PI_3;
1612 let frac_pi_4: f32 = consts::FRAC_PI_4;
1613 let frac_pi_6: f32 = consts::FRAC_PI_6;
1614 let frac_pi_8: f32 = consts::FRAC_PI_8;
1615 let frac_1_pi: f32 = consts::FRAC_1_PI;
1616 let frac_2_pi: f32 = consts::FRAC_2_PI;
1617 let frac_2_sqrtpi: f32 = consts::FRAC_2_SQRT_PI;
1618 let sqrt2: f32 = consts::SQRT_2;
1619 let frac_1_sqrt2: f32 = consts::FRAC_1_SQRT_2;
1620 let e: f32 = consts::E;
1621 let log2_e: f32 = consts::LOG2_E;
1622 let log10_e: f32 = consts::LOG10_E;
1623 let ln_2: f32 = consts::LN_2;
1624 let ln_10: f32 = consts::LN_10;
1626 assert_approx_eq!(frac_pi_2, pi / 2f32);
1627 assert_approx_eq!(frac_pi_3, pi / 3f32);
1628 assert_approx_eq!(frac_pi_4, pi / 4f32);
1629 assert_approx_eq!(frac_pi_6, pi / 6f32);
1630 assert_approx_eq!(frac_pi_8, pi / 8f32);
1631 assert_approx_eq!(frac_1_pi, 1f32 / pi);
1632 assert_approx_eq!(frac_2_pi, 2f32 / pi);
1633 assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt());
1634 assert_approx_eq!(sqrt2, 2f32.sqrt());
1635 assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt());
1636 assert_approx_eq!(log2_e, e.log2());
1637 assert_approx_eq!(log10_e, e.log10());
1638 assert_approx_eq!(ln_2, 2f32.ln());
1639 assert_approx_eq!(ln_10, 10f32.ln());
1643 fn test_float_bits_conv() {
1644 assert_eq!((1f32).to_bits(), 0x3f800000);
1645 assert_eq!((12.5f32).to_bits(), 0x41480000);
1646 assert_eq!((1337f32).to_bits(), 0x44a72000);
1647 assert_eq!((-14.25f32).to_bits(), 0xc1640000);
1648 assert_approx_eq!(f32::from_bits(0x3f800000), 1.0);
1649 assert_approx_eq!(f32::from_bits(0x41480000), 12.5);
1650 assert_approx_eq!(f32::from_bits(0x44a72000), 1337.0);
1651 assert_approx_eq!(f32::from_bits(0xc1640000), -14.25);
1653 // Check that NaNs roundtrip their bits regardless of signalingness
1654 // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits
1655 let masked_nan1 = f32::NAN.to_bits() ^ 0x002A_AAAA;
1656 let masked_nan2 = f32::NAN.to_bits() ^ 0x0055_5555;
1657 assert!(f32::from_bits(masked_nan1).is_nan());
1658 assert!(f32::from_bits(masked_nan2).is_nan());
1660 assert_eq!(f32::from_bits(masked_nan1).to_bits(), masked_nan1);
1661 assert_eq!(f32::from_bits(masked_nan2).to_bits(), masked_nan2);