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 //! The 32-bit floating point type.
13 //! *[See also the `f32` primitive type](../primitive.f32.html).*
15 #![stable(feature = "rust1", since = "1.0.0")]
16 #![allow(missing_docs)]
28 #[stable(feature = "rust1", since = "1.0.0")]
29 pub use core::f32::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON};
30 #[stable(feature = "rust1", since = "1.0.0")]
31 pub use core::f32::{MIN_EXP, MAX_EXP, MIN_10_EXP};
32 #[stable(feature = "rust1", since = "1.0.0")]
33 pub use core::f32::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
34 #[stable(feature = "rust1", since = "1.0.0")]
35 pub use core::f32::{MIN, MIN_POSITIVE, MAX};
36 #[stable(feature = "rust1", since = "1.0.0")]
37 pub use core::f32::consts;
41 use libc::{c_float, c_int};
44 pub fn cbrtf(n: c_float) -> c_float;
45 pub fn erff(n: c_float) -> c_float;
46 pub fn erfcf(n: c_float) -> c_float;
47 pub fn expm1f(n: c_float) -> c_float;
48 pub fn fdimf(a: c_float, b: c_float) -> c_float;
49 pub fn fmaxf(a: c_float, b: c_float) -> c_float;
50 pub fn fminf(a: c_float, b: c_float) -> c_float;
51 pub fn fmodf(a: c_float, b: c_float) -> c_float;
52 pub fn ilogbf(n: c_float) -> c_int;
53 pub fn logbf(n: c_float) -> c_float;
54 pub fn log1pf(n: c_float) -> c_float;
55 pub fn modff(n: c_float, iptr: &mut c_float) -> c_float;
56 pub fn nextafterf(x: c_float, y: c_float) -> c_float;
57 pub fn tgammaf(n: c_float) -> c_float;
59 #[cfg_attr(all(windows, target_env = "msvc"), link_name = "__lgammaf_r")]
60 pub fn lgammaf_r(n: c_float, sign: &mut c_int) -> c_float;
61 #[cfg_attr(all(windows, target_env = "msvc"), link_name = "_hypotf")]
62 pub fn hypotf(x: c_float, y: c_float) -> c_float;
65 // See the comments in `core::float::Float::floor` for why MSVC is special
67 #[cfg(not(target_env = "msvc"))]
69 pub fn acosf(n: c_float) -> c_float;
70 pub fn asinf(n: c_float) -> c_float;
71 pub fn atan2f(a: c_float, b: c_float) -> c_float;
72 pub fn atanf(n: c_float) -> c_float;
73 pub fn coshf(n: c_float) -> c_float;
74 pub fn frexpf(n: c_float, value: &mut c_int) -> c_float;
75 pub fn ldexpf(x: c_float, n: c_int) -> c_float;
76 pub fn sinhf(n: c_float) -> c_float;
77 pub fn tanf(n: c_float) -> c_float;
78 pub fn tanhf(n: c_float) -> c_float;
81 #[cfg(target_env = "msvc")]
82 pub use self::shims::*;
83 #[cfg(target_env = "msvc")]
85 use libc::{c_float, c_int};
88 pub unsafe fn acosf(n: c_float) -> c_float {
89 f64::acos(n as f64) as c_float
93 pub unsafe fn asinf(n: c_float) -> c_float {
94 f64::asin(n as f64) as c_float
98 pub unsafe fn atan2f(n: c_float, b: c_float) -> c_float {
99 f64::atan2(n as f64, b as f64) as c_float
103 pub unsafe fn atanf(n: c_float) -> c_float {
104 f64::atan(n as f64) as c_float
108 pub unsafe fn coshf(n: c_float) -> c_float {
109 f64::cosh(n as f64) as c_float
113 pub unsafe fn frexpf(x: c_float, value: &mut c_int) -> c_float {
114 let (a, b) = f64::frexp(x as f64);
120 pub unsafe fn ldexpf(x: c_float, n: c_int) -> c_float {
121 f64::ldexp(x as f64, n as isize) as c_float
125 pub unsafe fn sinhf(n: c_float) -> c_float {
126 f64::sinh(n as f64) as c_float
130 pub unsafe fn tanf(n: c_float) -> c_float {
131 f64::tan(n as f64) as c_float
135 pub unsafe fn tanhf(n: c_float) -> c_float {
136 f64::tanh(n as f64) as c_float
144 /// Returns `true` if this value is `NaN` and false otherwise.
149 /// let nan = f32::NAN;
152 /// assert!(nan.is_nan());
153 /// assert!(!f.is_nan());
155 #[stable(feature = "rust1", since = "1.0.0")]
157 pub fn is_nan(self) -> bool { num::Float::is_nan(self) }
159 /// Returns `true` if this value is positive infinity or negative infinity and
166 /// let inf = f32::INFINITY;
167 /// let neg_inf = f32::NEG_INFINITY;
168 /// let nan = f32::NAN;
170 /// assert!(!f.is_infinite());
171 /// assert!(!nan.is_infinite());
173 /// assert!(inf.is_infinite());
174 /// assert!(neg_inf.is_infinite());
176 #[stable(feature = "rust1", since = "1.0.0")]
178 pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) }
180 /// Returns `true` if this number is neither infinite nor `NaN`.
186 /// let inf = f32::INFINITY;
187 /// let neg_inf = f32::NEG_INFINITY;
188 /// let nan = f32::NAN;
190 /// assert!(f.is_finite());
192 /// assert!(!nan.is_finite());
193 /// assert!(!inf.is_finite());
194 /// assert!(!neg_inf.is_finite());
196 #[stable(feature = "rust1", since = "1.0.0")]
198 pub fn is_finite(self) -> bool { num::Float::is_finite(self) }
200 /// Returns `true` if the number is neither zero, infinite,
201 /// [subnormal][subnormal], or `NaN`.
206 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
207 /// let max = f32::MAX;
208 /// let lower_than_min = 1.0e-40_f32;
209 /// let zero = 0.0_f32;
211 /// assert!(min.is_normal());
212 /// assert!(max.is_normal());
214 /// assert!(!zero.is_normal());
215 /// assert!(!f32::NAN.is_normal());
216 /// assert!(!f32::INFINITY.is_normal());
217 /// // Values between `0` and `min` are Subnormal.
218 /// assert!(!lower_than_min.is_normal());
220 /// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number
221 #[stable(feature = "rust1", since = "1.0.0")]
223 pub fn is_normal(self) -> bool { num::Float::is_normal(self) }
225 /// Returns the floating point category of the number. If only one property
226 /// is going to be tested, it is generally faster to use the specific
227 /// predicate instead.
230 /// use std::num::FpCategory;
233 /// let num = 12.4_f32;
234 /// let inf = f32::INFINITY;
236 /// assert_eq!(num.classify(), FpCategory::Normal);
237 /// assert_eq!(inf.classify(), FpCategory::Infinite);
239 #[stable(feature = "rust1", since = "1.0.0")]
241 pub fn classify(self) -> FpCategory { num::Float::classify(self) }
243 /// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
244 /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
245 /// The floating point encoding is documented in the [Reference][floating-point].
248 /// #![feature(float_extras)]
252 /// let num = 2.0f32;
254 /// // (8388608, -22, 1)
255 /// let (mantissa, exponent, sign) = num.integer_decode();
256 /// let sign_f = sign as f32;
257 /// let mantissa_f = mantissa as f32;
258 /// let exponent_f = num.powf(exponent as f32);
260 /// // 1 * 8388608 * 2^(-22) == 2
261 /// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
263 /// assert!(abs_difference <= f32::EPSILON);
265 /// [floating-point]: ../../../../../reference.html#machine-types
266 #[unstable(feature = "float_extras", reason = "signature is undecided",
269 pub fn integer_decode(self) -> (u64, i16, i8) {
270 num::Float::integer_decode(self)
273 /// Returns the largest integer less than or equal to a number.
276 /// let f = 3.99_f32;
279 /// assert_eq!(f.floor(), 3.0);
280 /// assert_eq!(g.floor(), 3.0);
282 #[stable(feature = "rust1", since = "1.0.0")]
284 pub fn floor(self) -> f32 {
285 // On MSVC LLVM will lower many math intrinsics to a call to the
286 // corresponding function. On MSVC, however, many of these functions
287 // aren't actually available as symbols to call, but rather they are all
288 // `static inline` functions in header files. This means that from a C
289 // perspective it's "compatible", but not so much from an ABI
290 // perspective (which we're worried about).
292 // The inline header functions always just cast to a f64 and do their
293 // operation, so we do that here as well, but only for MSVC targets.
295 // Note that there are many MSVC-specific float operations which
296 // redirect to this comment, so `floorf` is just one case of a missing
297 // function on MSVC, but there are many others elsewhere.
298 #[cfg(target_env = "msvc")]
299 return (self as f64).floor() as f32;
300 #[cfg(not(target_env = "msvc"))]
301 return unsafe { intrinsics::floorf32(self) };
304 /// Returns the smallest integer greater than or equal to a number.
307 /// let f = 3.01_f32;
310 /// assert_eq!(f.ceil(), 4.0);
311 /// assert_eq!(g.ceil(), 4.0);
313 #[stable(feature = "rust1", since = "1.0.0")]
315 pub fn ceil(self) -> f32 {
316 // see notes above in `floor`
317 #[cfg(target_env = "msvc")]
318 return (self as f64).ceil() as f32;
319 #[cfg(not(target_env = "msvc"))]
320 return unsafe { intrinsics::ceilf32(self) };
323 /// Returns the nearest integer to a number. Round half-way cases away from
328 /// let g = -3.3_f32;
330 /// assert_eq!(f.round(), 3.0);
331 /// assert_eq!(g.round(), -3.0);
333 #[stable(feature = "rust1", since = "1.0.0")]
335 pub fn round(self) -> f32 {
336 unsafe { intrinsics::roundf32(self) }
339 /// Returns the integer part of a number.
343 /// let g = -3.7_f32;
345 /// assert_eq!(f.trunc(), 3.0);
346 /// assert_eq!(g.trunc(), -3.0);
348 #[stable(feature = "rust1", since = "1.0.0")]
350 pub fn trunc(self) -> f32 {
351 unsafe { intrinsics::truncf32(self) }
354 /// Returns the fractional part of a number.
360 /// let y = -3.5_f32;
361 /// let abs_difference_x = (x.fract() - 0.5).abs();
362 /// let abs_difference_y = (y.fract() - (-0.5)).abs();
364 /// assert!(abs_difference_x <= f32::EPSILON);
365 /// assert!(abs_difference_y <= f32::EPSILON);
367 #[stable(feature = "rust1", since = "1.0.0")]
369 pub fn fract(self) -> f32 { self - self.trunc() }
371 /// Computes the absolute value of `self`. Returns `NAN` if the
378 /// let y = -3.5_f32;
380 /// let abs_difference_x = (x.abs() - x).abs();
381 /// let abs_difference_y = (y.abs() - (-y)).abs();
383 /// assert!(abs_difference_x <= f32::EPSILON);
384 /// assert!(abs_difference_y <= f32::EPSILON);
386 /// assert!(f32::NAN.abs().is_nan());
388 #[stable(feature = "rust1", since = "1.0.0")]
390 pub fn abs(self) -> f32 { num::Float::abs(self) }
392 /// Returns a number that represents the sign of `self`.
394 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
395 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
396 /// - `NAN` if the number is `NAN`
403 /// assert_eq!(f.signum(), 1.0);
404 /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
406 /// assert!(f32::NAN.signum().is_nan());
408 #[stable(feature = "rust1", since = "1.0.0")]
410 pub fn signum(self) -> f32 { num::Float::signum(self) }
412 /// Returns `true` if `self`'s sign bit is positive, including
413 /// `+0.0` and `INFINITY`.
418 /// let nan = f32::NAN;
420 /// let g = -7.0_f32;
422 /// assert!(f.is_sign_positive());
423 /// assert!(!g.is_sign_positive());
424 /// // Requires both tests to determine if is `NaN`
425 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
427 #[stable(feature = "rust1", since = "1.0.0")]
429 pub fn is_sign_positive(self) -> bool { num::Float::is_sign_positive(self) }
431 /// Returns `true` if `self`'s sign is negative, including `-0.0`
432 /// and `NEG_INFINITY`.
437 /// let nan = f32::NAN;
441 /// assert!(!f.is_sign_negative());
442 /// assert!(g.is_sign_negative());
443 /// // Requires both tests to determine if is `NaN`.
444 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
446 #[stable(feature = "rust1", since = "1.0.0")]
448 pub fn is_sign_negative(self) -> bool { num::Float::is_sign_negative(self) }
450 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
451 /// error. This produces a more accurate result with better performance than
452 /// a separate multiplication operation followed by an add.
457 /// let m = 10.0_f32;
459 /// let b = 60.0_f32;
462 /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
464 /// assert!(abs_difference <= f32::EPSILON);
466 #[stable(feature = "rust1", since = "1.0.0")]
468 pub fn mul_add(self, a: f32, b: f32) -> f32 {
469 unsafe { intrinsics::fmaf32(self, a, b) }
472 /// Takes the reciprocal (inverse) of a number, `1/x`.
478 /// let abs_difference = (x.recip() - (1.0/x)).abs();
480 /// assert!(abs_difference <= f32::EPSILON);
482 #[stable(feature = "rust1", since = "1.0.0")]
484 pub fn recip(self) -> f32 { num::Float::recip(self) }
486 /// Raises a number to an integer power.
488 /// Using this function is generally faster than using `powf`
494 /// let abs_difference = (x.powi(2) - x*x).abs();
496 /// assert!(abs_difference <= f32::EPSILON);
498 #[stable(feature = "rust1", since = "1.0.0")]
500 pub fn powi(self, n: i32) -> f32 { num::Float::powi(self, n) }
502 /// Raises a number to a floating point power.
508 /// let abs_difference = (x.powf(2.0) - x*x).abs();
510 /// assert!(abs_difference <= f32::EPSILON);
512 #[stable(feature = "rust1", since = "1.0.0")]
514 pub fn powf(self, n: f32) -> f32 {
515 // see notes above in `floor`
516 #[cfg(target_env = "msvc")]
517 return (self as f64).powf(n as f64) as f32;
518 #[cfg(not(target_env = "msvc"))]
519 return unsafe { intrinsics::powf32(self, n) };
522 /// Takes the square root of a number.
524 /// Returns NaN if `self` is a negative number.
529 /// let positive = 4.0_f32;
530 /// let negative = -4.0_f32;
532 /// let abs_difference = (positive.sqrt() - 2.0).abs();
534 /// assert!(abs_difference <= f32::EPSILON);
535 /// assert!(negative.sqrt().is_nan());
537 #[stable(feature = "rust1", since = "1.0.0")]
539 pub fn sqrt(self) -> f32 {
543 unsafe { intrinsics::sqrtf32(self) }
547 /// Returns `e^(self)`, (the exponential function).
552 /// let one = 1.0f32;
554 /// let e = one.exp();
556 /// // ln(e) - 1 == 0
557 /// let abs_difference = (e.ln() - 1.0).abs();
559 /// assert!(abs_difference <= f32::EPSILON);
561 #[stable(feature = "rust1", since = "1.0.0")]
563 pub fn exp(self) -> f32 {
564 // see notes above in `floor`
565 #[cfg(target_env = "msvc")]
566 return (self as f64).exp() as f32;
567 #[cfg(not(target_env = "msvc"))]
568 return unsafe { intrinsics::expf32(self) };
571 /// Returns `2^(self)`.
579 /// let abs_difference = (f.exp2() - 4.0).abs();
581 /// assert!(abs_difference <= f32::EPSILON);
583 #[stable(feature = "rust1", since = "1.0.0")]
585 pub fn exp2(self) -> f32 {
586 unsafe { intrinsics::exp2f32(self) }
589 /// Returns the natural logarithm of the number.
594 /// let one = 1.0f32;
596 /// let e = one.exp();
598 /// // ln(e) - 1 == 0
599 /// let abs_difference = (e.ln() - 1.0).abs();
601 /// assert!(abs_difference <= f32::EPSILON);
603 #[stable(feature = "rust1", since = "1.0.0")]
605 pub fn ln(self) -> f32 {
606 // see notes above in `floor`
607 #[cfg(target_env = "msvc")]
608 return (self as f64).ln() as f32;
609 #[cfg(not(target_env = "msvc"))]
610 return unsafe { intrinsics::logf32(self) };
613 /// Returns the logarithm of the number with respect to an arbitrary base.
618 /// let ten = 10.0f32;
619 /// let two = 2.0f32;
621 /// // log10(10) - 1 == 0
622 /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
624 /// // log2(2) - 1 == 0
625 /// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
627 /// assert!(abs_difference_10 <= f32::EPSILON);
628 /// assert!(abs_difference_2 <= f32::EPSILON);
630 #[stable(feature = "rust1", since = "1.0.0")]
632 pub fn log(self, base: f32) -> f32 { self.ln() / base.ln() }
634 /// Returns the base 2 logarithm of the number.
639 /// let two = 2.0f32;
641 /// // log2(2) - 1 == 0
642 /// let abs_difference = (two.log2() - 1.0).abs();
644 /// assert!(abs_difference <= f32::EPSILON);
646 #[stable(feature = "rust1", since = "1.0.0")]
648 pub fn log2(self) -> f32 {
649 unsafe { intrinsics::log2f32(self) }
652 /// Returns the base 10 logarithm of the number.
657 /// let ten = 10.0f32;
659 /// // log10(10) - 1 == 0
660 /// let abs_difference = (ten.log10() - 1.0).abs();
662 /// assert!(abs_difference <= f32::EPSILON);
664 #[stable(feature = "rust1", since = "1.0.0")]
666 pub fn log10(self) -> f32 {
667 // see notes above in `floor`
668 #[cfg(target_env = "msvc")]
669 return (self as f64).log10() as f32;
670 #[cfg(not(target_env = "msvc"))]
671 return unsafe { intrinsics::log10f32(self) };
674 /// Converts radians to degrees.
677 /// use std::f32::{self, consts};
679 /// let angle = consts::PI;
681 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
683 /// assert!(abs_difference <= f32::EPSILON);
685 #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
687 pub fn to_degrees(self) -> f32 { num::Float::to_degrees(self) }
689 /// Converts degrees to radians.
692 /// use std::f32::{self, consts};
694 /// let angle = 180.0f32;
696 /// let abs_difference = (angle.to_radians() - consts::PI).abs();
698 /// assert!(abs_difference <= f32::EPSILON);
700 #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
702 pub fn to_radians(self) -> f32 { num::Float::to_radians(self) }
704 /// Constructs a floating point number of `x*2^exp`.
707 /// #![feature(float_extras)]
710 /// // 3*2^2 - 12 == 0
711 /// let abs_difference = (f32::ldexp(3.0, 2) - 12.0).abs();
713 /// assert!(abs_difference <= f32::EPSILON);
715 #[unstable(feature = "float_extras",
716 reason = "pending integer conventions",
719 pub fn ldexp(x: f32, exp: isize) -> f32 {
720 unsafe { cmath::ldexpf(x, exp as c_int) }
723 /// Breaks the number into a normalized fraction and a base-2 exponent,
726 /// * `self = x * 2^exp`
727 /// * `0.5 <= abs(x) < 1.0`
730 /// #![feature(float_extras)]
736 /// // (1/2)*2^3 -> 1 * 8/2 -> 4.0
737 /// let f = x.frexp();
738 /// let abs_difference_0 = (f.0 - 0.5).abs();
739 /// let abs_difference_1 = (f.1 as f32 - 3.0).abs();
741 /// assert!(abs_difference_0 <= f32::EPSILON);
742 /// assert!(abs_difference_1 <= f32::EPSILON);
744 #[unstable(feature = "float_extras",
745 reason = "pending integer conventions",
748 pub fn frexp(self) -> (f32, isize) {
751 let x = cmath::frexpf(self, &mut exp);
756 /// Returns the next representable floating-point value in the direction of
760 /// #![feature(float_extras)]
766 /// let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs();
768 /// assert!(abs_diff <= f32::EPSILON);
770 #[unstable(feature = "float_extras",
771 reason = "unsure about its place in the world",
774 pub fn next_after(self, other: f32) -> f32 {
775 unsafe { cmath::nextafterf(self, other) }
778 /// Returns the maximum of the two numbers.
784 /// assert_eq!(x.max(y), y);
787 /// If one of the arguments is NaN, then the other argument is returned.
788 #[stable(feature = "rust1", since = "1.0.0")]
790 pub fn max(self, other: f32) -> f32 {
791 unsafe { cmath::fmaxf(self, other) }
794 /// Returns the minimum of the two numbers.
800 /// assert_eq!(x.min(y), x);
803 /// If one of the arguments is NaN, then the other argument is returned.
804 #[stable(feature = "rust1", since = "1.0.0")]
806 pub fn min(self, other: f32) -> f32 {
807 unsafe { cmath::fminf(self, other) }
810 /// The positive difference of two numbers.
812 /// * If `self <= other`: `0:0`
813 /// * Else: `self - other`
821 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
822 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
824 /// assert!(abs_difference_x <= f32::EPSILON);
825 /// assert!(abs_difference_y <= f32::EPSILON);
827 #[stable(feature = "rust1", since = "1.0.0")]
829 pub fn abs_sub(self, other: f32) -> f32 {
830 unsafe { cmath::fdimf(self, other) }
833 /// Takes the cubic root of a number.
840 /// // x^(1/3) - 2 == 0
841 /// let abs_difference = (x.cbrt() - 2.0).abs();
843 /// assert!(abs_difference <= f32::EPSILON);
845 #[stable(feature = "rust1", since = "1.0.0")]
847 pub fn cbrt(self) -> f32 {
848 unsafe { cmath::cbrtf(self) }
851 /// Calculates the length of the hypotenuse of a right-angle triangle given
852 /// legs of length `x` and `y`.
860 /// // sqrt(x^2 + y^2)
861 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
863 /// assert!(abs_difference <= f32::EPSILON);
865 #[stable(feature = "rust1", since = "1.0.0")]
867 pub fn hypot(self, other: f32) -> f32 {
868 unsafe { cmath::hypotf(self, other) }
871 /// Computes the sine of a number (in radians).
876 /// let x = f32::consts::PI/2.0;
878 /// let abs_difference = (x.sin() - 1.0).abs();
880 /// assert!(abs_difference <= f32::EPSILON);
882 #[stable(feature = "rust1", since = "1.0.0")]
884 pub fn sin(self) -> f32 {
885 // see notes in `core::f32::Float::floor`
886 #[cfg(target_env = "msvc")]
887 return (self as f64).sin() as f32;
888 #[cfg(not(target_env = "msvc"))]
889 return unsafe { intrinsics::sinf32(self) };
892 /// Computes the cosine of a number (in radians).
897 /// let x = 2.0*f32::consts::PI;
899 /// let abs_difference = (x.cos() - 1.0).abs();
901 /// assert!(abs_difference <= f32::EPSILON);
903 #[stable(feature = "rust1", since = "1.0.0")]
905 pub fn cos(self) -> f32 {
906 // see notes in `core::f32::Float::floor`
907 #[cfg(target_env = "msvc")]
908 return (self as f64).cos() as f32;
909 #[cfg(not(target_env = "msvc"))]
910 return unsafe { intrinsics::cosf32(self) };
913 /// Computes the tangent of a number (in radians).
918 /// let x = f64::consts::PI/4.0;
919 /// let abs_difference = (x.tan() - 1.0).abs();
921 /// assert!(abs_difference < 1e-10);
923 #[stable(feature = "rust1", since = "1.0.0")]
925 pub fn tan(self) -> f32 {
926 unsafe { cmath::tanf(self) }
929 /// Computes the arcsine of a number. Return value is in radians in
930 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
936 /// let f = f32::consts::PI / 2.0;
938 /// // asin(sin(pi/2))
939 /// let abs_difference = f.sin().asin().abs_sub(f32::consts::PI / 2.0);
941 /// assert!(abs_difference <= f32::EPSILON);
943 #[stable(feature = "rust1", since = "1.0.0")]
945 pub fn asin(self) -> f32 {
946 unsafe { cmath::asinf(self) }
949 /// Computes the arccosine of a number. Return value is in radians in
950 /// the range [0, pi] or NaN if the number is outside the range
956 /// let f = f32::consts::PI / 4.0;
958 /// // acos(cos(pi/4))
959 /// let abs_difference = f.cos().acos().abs_sub(f32::consts::PI / 4.0);
961 /// assert!(abs_difference <= f32::EPSILON);
963 #[stable(feature = "rust1", since = "1.0.0")]
965 pub fn acos(self) -> f32 {
966 unsafe { cmath::acosf(self) }
969 /// Computes the arctangent of a number. Return value is in radians in the
970 /// range [-pi/2, pi/2];
978 /// let abs_difference = f.tan().atan().abs_sub(1.0);
980 /// assert!(abs_difference <= f32::EPSILON);
982 #[stable(feature = "rust1", since = "1.0.0")]
984 pub fn atan(self) -> f32 {
985 unsafe { cmath::atanf(self) }
988 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
990 /// * `x = 0`, `y = 0`: `0`
991 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
992 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
993 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
998 /// let pi = f32::consts::PI;
999 /// // All angles from horizontal right (+x)
1000 /// // 45 deg counter-clockwise
1001 /// let x1 = 3.0f32;
1002 /// let y1 = -3.0f32;
1004 /// // 135 deg clockwise
1005 /// let x2 = -3.0f32;
1006 /// let y2 = 3.0f32;
1008 /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
1009 /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
1011 /// assert!(abs_difference_1 <= f32::EPSILON);
1012 /// assert!(abs_difference_2 <= f32::EPSILON);
1014 #[stable(feature = "rust1", since = "1.0.0")]
1016 pub fn atan2(self, other: f32) -> f32 {
1017 unsafe { cmath::atan2f(self, other) }
1020 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
1021 /// `(sin(x), cos(x))`.
1026 /// let x = f32::consts::PI/4.0;
1027 /// let f = x.sin_cos();
1029 /// let abs_difference_0 = (f.0 - x.sin()).abs();
1030 /// let abs_difference_1 = (f.1 - x.cos()).abs();
1032 /// assert!(abs_difference_0 <= f32::EPSILON);
1033 /// assert!(abs_difference_0 <= f32::EPSILON);
1035 #[stable(feature = "rust1", since = "1.0.0")]
1037 pub fn sin_cos(self) -> (f32, f32) {
1038 (self.sin(), self.cos())
1041 /// Returns `e^(self) - 1` in a way that is accurate even if the
1042 /// number is close to zero.
1047 /// // e^(ln(7)) - 1
1048 /// let abs_difference = x.ln().exp_m1().abs_sub(6.0);
1050 /// assert!(abs_difference < 1e-10);
1052 #[stable(feature = "rust1", since = "1.0.0")]
1054 pub fn exp_m1(self) -> f32 {
1055 unsafe { cmath::expm1f(self) }
1058 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
1059 /// the operations were performed separately.
1064 /// let x = f32::consts::E - 1.0;
1066 /// // ln(1 + (e - 1)) == ln(e) == 1
1067 /// let abs_difference = (x.ln_1p() - 1.0).abs();
1069 /// assert!(abs_difference <= f32::EPSILON);
1071 #[stable(feature = "rust1", since = "1.0.0")]
1073 pub fn ln_1p(self) -> f32 {
1074 unsafe { cmath::log1pf(self) }
1077 /// Hyperbolic sine function.
1082 /// let e = f32::consts::E;
1085 /// let f = x.sinh();
1086 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
1087 /// let g = (e*e - 1.0)/(2.0*e);
1088 /// let abs_difference = (f - g).abs();
1090 /// assert!(abs_difference <= f32::EPSILON);
1092 #[stable(feature = "rust1", since = "1.0.0")]
1094 pub fn sinh(self) -> f32 {
1095 unsafe { cmath::sinhf(self) }
1098 /// Hyperbolic cosine function.
1103 /// let e = f32::consts::E;
1105 /// let f = x.cosh();
1106 /// // Solving cosh() at 1 gives this result
1107 /// let g = (e*e + 1.0)/(2.0*e);
1108 /// let abs_difference = f.abs_sub(g);
1111 /// assert!(abs_difference <= f32::EPSILON);
1113 #[stable(feature = "rust1", since = "1.0.0")]
1115 pub fn cosh(self) -> f32 {
1116 unsafe { cmath::coshf(self) }
1119 /// Hyperbolic tangent function.
1124 /// let e = f32::consts::E;
1127 /// let f = x.tanh();
1128 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1129 /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
1130 /// let abs_difference = (f - g).abs();
1132 /// assert!(abs_difference <= f32::EPSILON);
1134 #[stable(feature = "rust1", since = "1.0.0")]
1136 pub fn tanh(self) -> f32 {
1137 unsafe { cmath::tanhf(self) }
1140 /// Inverse hyperbolic sine function.
1146 /// let f = x.sinh().asinh();
1148 /// let abs_difference = (f - x).abs();
1150 /// assert!(abs_difference <= f32::EPSILON);
1152 #[stable(feature = "rust1", since = "1.0.0")]
1154 pub fn asinh(self) -> f32 {
1156 NEG_INFINITY => NEG_INFINITY,
1157 x => (x + ((x * x) + 1.0).sqrt()).ln(),
1161 /// Inverse hyperbolic cosine function.
1167 /// let f = x.cosh().acosh();
1169 /// let abs_difference = (f - x).abs();
1171 /// assert!(abs_difference <= f32::EPSILON);
1173 #[stable(feature = "rust1", since = "1.0.0")]
1175 pub fn acosh(self) -> f32 {
1177 x if x < 1.0 => ::f32::NAN,
1178 x => (x + ((x * x) - 1.0).sqrt()).ln(),
1182 /// Inverse hyperbolic tangent function.
1187 /// let e = f32::consts::E;
1188 /// let f = e.tanh().atanh();
1190 /// let abs_difference = f.abs_sub(e);
1192 /// assert!(abs_difference <= f32::EPSILON);
1194 #[stable(feature = "rust1", since = "1.0.0")]
1196 pub fn atanh(self) -> f32 {
1197 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1206 use num::FpCategory as Fp;
1210 test_num(10f32, 2f32);
1215 assert_eq!(NAN.min(2.0), 2.0);
1216 assert_eq!(2.0f32.min(NAN), 2.0);
1221 assert_eq!(NAN.max(2.0), 2.0);
1222 assert_eq!(2.0f32.max(NAN), 2.0);
1227 let nan: f32 = f32::NAN;
1228 assert!(nan.is_nan());
1229 assert!(!nan.is_infinite());
1230 assert!(!nan.is_finite());
1231 assert!(!nan.is_normal());
1232 assert!(!nan.is_sign_positive());
1233 assert!(!nan.is_sign_negative());
1234 assert_eq!(Fp::Nan, nan.classify());
1238 fn test_infinity() {
1239 let inf: f32 = f32::INFINITY;
1240 assert!(inf.is_infinite());
1241 assert!(!inf.is_finite());
1242 assert!(inf.is_sign_positive());
1243 assert!(!inf.is_sign_negative());
1244 assert!(!inf.is_nan());
1245 assert!(!inf.is_normal());
1246 assert_eq!(Fp::Infinite, inf.classify());
1250 fn test_neg_infinity() {
1251 let neg_inf: f32 = f32::NEG_INFINITY;
1252 assert!(neg_inf.is_infinite());
1253 assert!(!neg_inf.is_finite());
1254 assert!(!neg_inf.is_sign_positive());
1255 assert!(neg_inf.is_sign_negative());
1256 assert!(!neg_inf.is_nan());
1257 assert!(!neg_inf.is_normal());
1258 assert_eq!(Fp::Infinite, neg_inf.classify());
1263 let zero: f32 = 0.0f32;
1264 assert_eq!(0.0, zero);
1265 assert!(!zero.is_infinite());
1266 assert!(zero.is_finite());
1267 assert!(zero.is_sign_positive());
1268 assert!(!zero.is_sign_negative());
1269 assert!(!zero.is_nan());
1270 assert!(!zero.is_normal());
1271 assert_eq!(Fp::Zero, zero.classify());
1275 fn test_neg_zero() {
1276 let neg_zero: f32 = -0.0;
1277 assert_eq!(0.0, neg_zero);
1278 assert!(!neg_zero.is_infinite());
1279 assert!(neg_zero.is_finite());
1280 assert!(!neg_zero.is_sign_positive());
1281 assert!(neg_zero.is_sign_negative());
1282 assert!(!neg_zero.is_nan());
1283 assert!(!neg_zero.is_normal());
1284 assert_eq!(Fp::Zero, neg_zero.classify());
1289 let one: f32 = 1.0f32;
1290 assert_eq!(1.0, one);
1291 assert!(!one.is_infinite());
1292 assert!(one.is_finite());
1293 assert!(one.is_sign_positive());
1294 assert!(!one.is_sign_negative());
1295 assert!(!one.is_nan());
1296 assert!(one.is_normal());
1297 assert_eq!(Fp::Normal, one.classify());
1302 let nan: f32 = f32::NAN;
1303 let inf: f32 = f32::INFINITY;
1304 let neg_inf: f32 = f32::NEG_INFINITY;
1305 assert!(nan.is_nan());
1306 assert!(!0.0f32.is_nan());
1307 assert!(!5.3f32.is_nan());
1308 assert!(!(-10.732f32).is_nan());
1309 assert!(!inf.is_nan());
1310 assert!(!neg_inf.is_nan());
1314 fn test_is_infinite() {
1315 let nan: f32 = f32::NAN;
1316 let inf: f32 = f32::INFINITY;
1317 let neg_inf: f32 = f32::NEG_INFINITY;
1318 assert!(!nan.is_infinite());
1319 assert!(inf.is_infinite());
1320 assert!(neg_inf.is_infinite());
1321 assert!(!0.0f32.is_infinite());
1322 assert!(!42.8f32.is_infinite());
1323 assert!(!(-109.2f32).is_infinite());
1327 fn test_is_finite() {
1328 let nan: f32 = f32::NAN;
1329 let inf: f32 = f32::INFINITY;
1330 let neg_inf: f32 = f32::NEG_INFINITY;
1331 assert!(!nan.is_finite());
1332 assert!(!inf.is_finite());
1333 assert!(!neg_inf.is_finite());
1334 assert!(0.0f32.is_finite());
1335 assert!(42.8f32.is_finite());
1336 assert!((-109.2f32).is_finite());
1340 fn test_is_normal() {
1341 let nan: f32 = f32::NAN;
1342 let inf: f32 = f32::INFINITY;
1343 let neg_inf: f32 = f32::NEG_INFINITY;
1344 let zero: f32 = 0.0f32;
1345 let neg_zero: f32 = -0.0;
1346 assert!(!nan.is_normal());
1347 assert!(!inf.is_normal());
1348 assert!(!neg_inf.is_normal());
1349 assert!(!zero.is_normal());
1350 assert!(!neg_zero.is_normal());
1351 assert!(1f32.is_normal());
1352 assert!(1e-37f32.is_normal());
1353 assert!(!1e-38f32.is_normal());
1357 fn test_classify() {
1358 let nan: f32 = f32::NAN;
1359 let inf: f32 = f32::INFINITY;
1360 let neg_inf: f32 = f32::NEG_INFINITY;
1361 let zero: f32 = 0.0f32;
1362 let neg_zero: f32 = -0.0;
1363 assert_eq!(nan.classify(), Fp::Nan);
1364 assert_eq!(inf.classify(), Fp::Infinite);
1365 assert_eq!(neg_inf.classify(), Fp::Infinite);
1366 assert_eq!(zero.classify(), Fp::Zero);
1367 assert_eq!(neg_zero.classify(), Fp::Zero);
1368 assert_eq!(1f32.classify(), Fp::Normal);
1369 assert_eq!(1e-37f32.classify(), Fp::Normal);
1370 assert_eq!(1e-38f32.classify(), Fp::Subnormal);
1374 fn test_integer_decode() {
1375 assert_eq!(3.14159265359f32.integer_decode(), (13176795, -22, 1));
1376 assert_eq!((-8573.5918555f32).integer_decode(), (8779358, -10, -1));
1377 assert_eq!(2f32.powf(100.0).integer_decode(), (8388608, 77, 1));
1378 assert_eq!(0f32.integer_decode(), (0, -150, 1));
1379 assert_eq!((-0f32).integer_decode(), (0, -150, -1));
1380 assert_eq!(INFINITY.integer_decode(), (8388608, 105, 1));
1381 assert_eq!(NEG_INFINITY.integer_decode(), (8388608, 105, -1));
1382 assert_eq!(NAN.integer_decode(), (12582912, 105, 1));
1387 assert_approx_eq!(1.0f32.floor(), 1.0f32);
1388 assert_approx_eq!(1.3f32.floor(), 1.0f32);
1389 assert_approx_eq!(1.5f32.floor(), 1.0f32);
1390 assert_approx_eq!(1.7f32.floor(), 1.0f32);
1391 assert_approx_eq!(0.0f32.floor(), 0.0f32);
1392 assert_approx_eq!((-0.0f32).floor(), -0.0f32);
1393 assert_approx_eq!((-1.0f32).floor(), -1.0f32);
1394 assert_approx_eq!((-1.3f32).floor(), -2.0f32);
1395 assert_approx_eq!((-1.5f32).floor(), -2.0f32);
1396 assert_approx_eq!((-1.7f32).floor(), -2.0f32);
1401 assert_approx_eq!(1.0f32.ceil(), 1.0f32);
1402 assert_approx_eq!(1.3f32.ceil(), 2.0f32);
1403 assert_approx_eq!(1.5f32.ceil(), 2.0f32);
1404 assert_approx_eq!(1.7f32.ceil(), 2.0f32);
1405 assert_approx_eq!(0.0f32.ceil(), 0.0f32);
1406 assert_approx_eq!((-0.0f32).ceil(), -0.0f32);
1407 assert_approx_eq!((-1.0f32).ceil(), -1.0f32);
1408 assert_approx_eq!((-1.3f32).ceil(), -1.0f32);
1409 assert_approx_eq!((-1.5f32).ceil(), -1.0f32);
1410 assert_approx_eq!((-1.7f32).ceil(), -1.0f32);
1415 assert_approx_eq!(1.0f32.round(), 1.0f32);
1416 assert_approx_eq!(1.3f32.round(), 1.0f32);
1417 assert_approx_eq!(1.5f32.round(), 2.0f32);
1418 assert_approx_eq!(1.7f32.round(), 2.0f32);
1419 assert_approx_eq!(0.0f32.round(), 0.0f32);
1420 assert_approx_eq!((-0.0f32).round(), -0.0f32);
1421 assert_approx_eq!((-1.0f32).round(), -1.0f32);
1422 assert_approx_eq!((-1.3f32).round(), -1.0f32);
1423 assert_approx_eq!((-1.5f32).round(), -2.0f32);
1424 assert_approx_eq!((-1.7f32).round(), -2.0f32);
1429 assert_approx_eq!(1.0f32.trunc(), 1.0f32);
1430 assert_approx_eq!(1.3f32.trunc(), 1.0f32);
1431 assert_approx_eq!(1.5f32.trunc(), 1.0f32);
1432 assert_approx_eq!(1.7f32.trunc(), 1.0f32);
1433 assert_approx_eq!(0.0f32.trunc(), 0.0f32);
1434 assert_approx_eq!((-0.0f32).trunc(), -0.0f32);
1435 assert_approx_eq!((-1.0f32).trunc(), -1.0f32);
1436 assert_approx_eq!((-1.3f32).trunc(), -1.0f32);
1437 assert_approx_eq!((-1.5f32).trunc(), -1.0f32);
1438 assert_approx_eq!((-1.7f32).trunc(), -1.0f32);
1443 assert_approx_eq!(1.0f32.fract(), 0.0f32);
1444 assert_approx_eq!(1.3f32.fract(), 0.3f32);
1445 assert_approx_eq!(1.5f32.fract(), 0.5f32);
1446 assert_approx_eq!(1.7f32.fract(), 0.7f32);
1447 assert_approx_eq!(0.0f32.fract(), 0.0f32);
1448 assert_approx_eq!((-0.0f32).fract(), -0.0f32);
1449 assert_approx_eq!((-1.0f32).fract(), -0.0f32);
1450 assert_approx_eq!((-1.3f32).fract(), -0.3f32);
1451 assert_approx_eq!((-1.5f32).fract(), -0.5f32);
1452 assert_approx_eq!((-1.7f32).fract(), -0.7f32);
1457 assert_eq!(INFINITY.abs(), INFINITY);
1458 assert_eq!(1f32.abs(), 1f32);
1459 assert_eq!(0f32.abs(), 0f32);
1460 assert_eq!((-0f32).abs(), 0f32);
1461 assert_eq!((-1f32).abs(), 1f32);
1462 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1463 assert_eq!((1f32/NEG_INFINITY).abs(), 0f32);
1464 assert!(NAN.abs().is_nan());
1469 assert_eq!(INFINITY.signum(), 1f32);
1470 assert_eq!(1f32.signum(), 1f32);
1471 assert_eq!(0f32.signum(), 1f32);
1472 assert_eq!((-0f32).signum(), -1f32);
1473 assert_eq!((-1f32).signum(), -1f32);
1474 assert_eq!(NEG_INFINITY.signum(), -1f32);
1475 assert_eq!((1f32/NEG_INFINITY).signum(), -1f32);
1476 assert!(NAN.signum().is_nan());
1480 fn test_is_sign_positive() {
1481 assert!(INFINITY.is_sign_positive());
1482 assert!(1f32.is_sign_positive());
1483 assert!(0f32.is_sign_positive());
1484 assert!(!(-0f32).is_sign_positive());
1485 assert!(!(-1f32).is_sign_positive());
1486 assert!(!NEG_INFINITY.is_sign_positive());
1487 assert!(!(1f32/NEG_INFINITY).is_sign_positive());
1488 assert!(!NAN.is_sign_positive());
1492 fn test_is_sign_negative() {
1493 assert!(!INFINITY.is_sign_negative());
1494 assert!(!1f32.is_sign_negative());
1495 assert!(!0f32.is_sign_negative());
1496 assert!((-0f32).is_sign_negative());
1497 assert!((-1f32).is_sign_negative());
1498 assert!(NEG_INFINITY.is_sign_negative());
1499 assert!((1f32/NEG_INFINITY).is_sign_negative());
1500 assert!(!NAN.is_sign_negative());
1505 let nan: f32 = f32::NAN;
1506 let inf: f32 = f32::INFINITY;
1507 let neg_inf: f32 = f32::NEG_INFINITY;
1508 assert_approx_eq!(12.3f32.mul_add(4.5, 6.7), 62.05);
1509 assert_approx_eq!((-12.3f32).mul_add(-4.5, -6.7), 48.65);
1510 assert_approx_eq!(0.0f32.mul_add(8.9, 1.2), 1.2);
1511 assert_approx_eq!(3.4f32.mul_add(-0.0, 5.6), 5.6);
1512 assert!(nan.mul_add(7.8, 9.0).is_nan());
1513 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1514 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1515 assert_eq!(8.9f32.mul_add(inf, 3.2), inf);
1516 assert_eq!((-3.2f32).mul_add(2.4, neg_inf), neg_inf);
1521 let nan: f32 = f32::NAN;
1522 let inf: f32 = f32::INFINITY;
1523 let neg_inf: f32 = f32::NEG_INFINITY;
1524 assert_eq!(1.0f32.recip(), 1.0);
1525 assert_eq!(2.0f32.recip(), 0.5);
1526 assert_eq!((-0.4f32).recip(), -2.5);
1527 assert_eq!(0.0f32.recip(), inf);
1528 assert!(nan.recip().is_nan());
1529 assert_eq!(inf.recip(), 0.0);
1530 assert_eq!(neg_inf.recip(), 0.0);
1535 let nan: f32 = f32::NAN;
1536 let inf: f32 = f32::INFINITY;
1537 let neg_inf: f32 = f32::NEG_INFINITY;
1538 assert_eq!(1.0f32.powi(1), 1.0);
1539 assert_approx_eq!((-3.1f32).powi(2), 9.61);
1540 assert_approx_eq!(5.9f32.powi(-2), 0.028727);
1541 assert_eq!(8.3f32.powi(0), 1.0);
1542 assert!(nan.powi(2).is_nan());
1543 assert_eq!(inf.powi(3), inf);
1544 assert_eq!(neg_inf.powi(2), inf);
1549 let nan: f32 = f32::NAN;
1550 let inf: f32 = f32::INFINITY;
1551 let neg_inf: f32 = f32::NEG_INFINITY;
1552 assert_eq!(1.0f32.powf(1.0), 1.0);
1553 assert_approx_eq!(3.4f32.powf(4.5), 246.408218);
1554 assert_approx_eq!(2.7f32.powf(-3.2), 0.041652);
1555 assert_approx_eq!((-3.1f32).powf(2.0), 9.61);
1556 assert_approx_eq!(5.9f32.powf(-2.0), 0.028727);
1557 assert_eq!(8.3f32.powf(0.0), 1.0);
1558 assert!(nan.powf(2.0).is_nan());
1559 assert_eq!(inf.powf(2.0), inf);
1560 assert_eq!(neg_inf.powf(3.0), neg_inf);
1564 fn test_sqrt_domain() {
1565 assert!(NAN.sqrt().is_nan());
1566 assert!(NEG_INFINITY.sqrt().is_nan());
1567 assert!((-1.0f32).sqrt().is_nan());
1568 assert_eq!((-0.0f32).sqrt(), -0.0);
1569 assert_eq!(0.0f32.sqrt(), 0.0);
1570 assert_eq!(1.0f32.sqrt(), 1.0);
1571 assert_eq!(INFINITY.sqrt(), INFINITY);
1576 assert_eq!(1.0, 0.0f32.exp());
1577 assert_approx_eq!(2.718282, 1.0f32.exp());
1578 assert_approx_eq!(148.413162, 5.0f32.exp());
1580 let inf: f32 = f32::INFINITY;
1581 let neg_inf: f32 = f32::NEG_INFINITY;
1582 let nan: f32 = f32::NAN;
1583 assert_eq!(inf, inf.exp());
1584 assert_eq!(0.0, neg_inf.exp());
1585 assert!(nan.exp().is_nan());
1590 assert_eq!(32.0, 5.0f32.exp2());
1591 assert_eq!(1.0, 0.0f32.exp2());
1593 let inf: f32 = f32::INFINITY;
1594 let neg_inf: f32 = f32::NEG_INFINITY;
1595 let nan: f32 = f32::NAN;
1596 assert_eq!(inf, inf.exp2());
1597 assert_eq!(0.0, neg_inf.exp2());
1598 assert!(nan.exp2().is_nan());
1603 let nan: f32 = f32::NAN;
1604 let inf: f32 = f32::INFINITY;
1605 let neg_inf: f32 = f32::NEG_INFINITY;
1606 assert_approx_eq!(1.0f32.exp().ln(), 1.0);
1607 assert!(nan.ln().is_nan());
1608 assert_eq!(inf.ln(), inf);
1609 assert!(neg_inf.ln().is_nan());
1610 assert!((-2.3f32).ln().is_nan());
1611 assert_eq!((-0.0f32).ln(), neg_inf);
1612 assert_eq!(0.0f32.ln(), neg_inf);
1613 assert_approx_eq!(4.0f32.ln(), 1.386294);
1618 let nan: f32 = f32::NAN;
1619 let inf: f32 = f32::INFINITY;
1620 let neg_inf: f32 = f32::NEG_INFINITY;
1621 assert_eq!(10.0f32.log(10.0), 1.0);
1622 assert_approx_eq!(2.3f32.log(3.5), 0.664858);
1623 assert_eq!(1.0f32.exp().log(1.0f32.exp()), 1.0);
1624 assert!(1.0f32.log(1.0).is_nan());
1625 assert!(1.0f32.log(-13.9).is_nan());
1626 assert!(nan.log(2.3).is_nan());
1627 assert_eq!(inf.log(10.0), inf);
1628 assert!(neg_inf.log(8.8).is_nan());
1629 assert!((-2.3f32).log(0.1).is_nan());
1630 assert_eq!((-0.0f32).log(2.0), neg_inf);
1631 assert_eq!(0.0f32.log(7.0), neg_inf);
1636 let nan: f32 = f32::NAN;
1637 let inf: f32 = f32::INFINITY;
1638 let neg_inf: f32 = f32::NEG_INFINITY;
1639 assert_approx_eq!(10.0f32.log2(), 3.321928);
1640 assert_approx_eq!(2.3f32.log2(), 1.201634);
1641 assert_approx_eq!(1.0f32.exp().log2(), 1.442695);
1642 assert!(nan.log2().is_nan());
1643 assert_eq!(inf.log2(), inf);
1644 assert!(neg_inf.log2().is_nan());
1645 assert!((-2.3f32).log2().is_nan());
1646 assert_eq!((-0.0f32).log2(), neg_inf);
1647 assert_eq!(0.0f32.log2(), neg_inf);
1652 let nan: f32 = f32::NAN;
1653 let inf: f32 = f32::INFINITY;
1654 let neg_inf: f32 = f32::NEG_INFINITY;
1655 assert_eq!(10.0f32.log10(), 1.0);
1656 assert_approx_eq!(2.3f32.log10(), 0.361728);
1657 assert_approx_eq!(1.0f32.exp().log10(), 0.434294);
1658 assert_eq!(1.0f32.log10(), 0.0);
1659 assert!(nan.log10().is_nan());
1660 assert_eq!(inf.log10(), inf);
1661 assert!(neg_inf.log10().is_nan());
1662 assert!((-2.3f32).log10().is_nan());
1663 assert_eq!((-0.0f32).log10(), neg_inf);
1664 assert_eq!(0.0f32.log10(), neg_inf);
1668 fn test_to_degrees() {
1669 let pi: f32 = consts::PI;
1670 let nan: f32 = f32::NAN;
1671 let inf: f32 = f32::INFINITY;
1672 let neg_inf: f32 = f32::NEG_INFINITY;
1673 assert_eq!(0.0f32.to_degrees(), 0.0);
1674 assert_approx_eq!((-5.8f32).to_degrees(), -332.315521);
1675 assert_eq!(pi.to_degrees(), 180.0);
1676 assert!(nan.to_degrees().is_nan());
1677 assert_eq!(inf.to_degrees(), inf);
1678 assert_eq!(neg_inf.to_degrees(), neg_inf);
1682 fn test_to_radians() {
1683 let pi: f32 = consts::PI;
1684 let nan: f32 = f32::NAN;
1685 let inf: f32 = f32::INFINITY;
1686 let neg_inf: f32 = f32::NEG_INFINITY;
1687 assert_eq!(0.0f32.to_radians(), 0.0);
1688 assert_approx_eq!(154.6f32.to_radians(), 2.698279);
1689 assert_approx_eq!((-332.31f32).to_radians(), -5.799903);
1690 assert_eq!(180.0f32.to_radians(), pi);
1691 assert!(nan.to_radians().is_nan());
1692 assert_eq!(inf.to_radians(), inf);
1693 assert_eq!(neg_inf.to_radians(), neg_inf);
1698 let f1 = 2.0f32.powi(-123);
1699 let f2 = 2.0f32.powi(-111);
1700 let f3 = 1.75 * 2.0f32.powi(-12);
1701 assert_eq!(f32::ldexp(1f32, -123), f1);
1702 assert_eq!(f32::ldexp(1f32, -111), f2);
1703 assert_eq!(f32::ldexp(1.75f32, -12), f3);
1705 assert_eq!(f32::ldexp(0f32, -123), 0f32);
1706 assert_eq!(f32::ldexp(-0f32, -123), -0f32);
1708 let inf: f32 = f32::INFINITY;
1709 let neg_inf: f32 = f32::NEG_INFINITY;
1710 let nan: f32 = f32::NAN;
1711 assert_eq!(f32::ldexp(inf, -123), inf);
1712 assert_eq!(f32::ldexp(neg_inf, -123), neg_inf);
1713 assert!(f32::ldexp(nan, -123).is_nan());
1718 let f1 = 2.0f32.powi(-123);
1719 let f2 = 2.0f32.powi(-111);
1720 let f3 = 1.75 * 2.0f32.powi(-123);
1721 let (x1, exp1) = f1.frexp();
1722 let (x2, exp2) = f2.frexp();
1723 let (x3, exp3) = f3.frexp();
1724 assert_eq!((x1, exp1), (0.5f32, -122));
1725 assert_eq!((x2, exp2), (0.5f32, -110));
1726 assert_eq!((x3, exp3), (0.875f32, -122));
1727 assert_eq!(f32::ldexp(x1, exp1), f1);
1728 assert_eq!(f32::ldexp(x2, exp2), f2);
1729 assert_eq!(f32::ldexp(x3, exp3), f3);
1731 assert_eq!(0f32.frexp(), (0f32, 0));
1732 assert_eq!((-0f32).frexp(), (-0f32, 0));
1735 #[test] #[cfg_attr(windows, ignore)] // FIXME #8755
1736 fn test_frexp_nowin() {
1737 let inf: f32 = f32::INFINITY;
1738 let neg_inf: f32 = f32::NEG_INFINITY;
1739 let nan: f32 = f32::NAN;
1740 assert_eq!(match inf.frexp() { (x, _) => x }, inf);
1741 assert_eq!(match neg_inf.frexp() { (x, _) => x }, neg_inf);
1742 assert!(match nan.frexp() { (x, _) => x.is_nan() })
1747 assert_eq!((-1f32).abs_sub(1f32), 0f32);
1748 assert_eq!(1f32.abs_sub(1f32), 0f32);
1749 assert_eq!(1f32.abs_sub(0f32), 1f32);
1750 assert_eq!(1f32.abs_sub(-1f32), 2f32);
1751 assert_eq!(NEG_INFINITY.abs_sub(0f32), 0f32);
1752 assert_eq!(INFINITY.abs_sub(1f32), INFINITY);
1753 assert_eq!(0f32.abs_sub(NEG_INFINITY), INFINITY);
1754 assert_eq!(0f32.abs_sub(INFINITY), 0f32);
1758 fn test_abs_sub_nowin() {
1759 assert!(NAN.abs_sub(-1f32).is_nan());
1760 assert!(1f32.abs_sub(NAN).is_nan());
1765 assert_eq!(0.0f32.asinh(), 0.0f32);
1766 assert_eq!((-0.0f32).asinh(), -0.0f32);
1768 let inf: f32 = f32::INFINITY;
1769 let neg_inf: f32 = f32::NEG_INFINITY;
1770 let nan: f32 = f32::NAN;
1771 assert_eq!(inf.asinh(), inf);
1772 assert_eq!(neg_inf.asinh(), neg_inf);
1773 assert!(nan.asinh().is_nan());
1774 assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32);
1775 assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32);
1780 assert_eq!(1.0f32.acosh(), 0.0f32);
1781 assert!(0.999f32.acosh().is_nan());
1783 let inf: f32 = f32::INFINITY;
1784 let neg_inf: f32 = f32::NEG_INFINITY;
1785 let nan: f32 = f32::NAN;
1786 assert_eq!(inf.acosh(), inf);
1787 assert!(neg_inf.acosh().is_nan());
1788 assert!(nan.acosh().is_nan());
1789 assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32);
1790 assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32);
1795 assert_eq!(0.0f32.atanh(), 0.0f32);
1796 assert_eq!((-0.0f32).atanh(), -0.0f32);
1798 let inf32: f32 = f32::INFINITY;
1799 let neg_inf32: f32 = f32::NEG_INFINITY;
1800 assert_eq!(1.0f32.atanh(), inf32);
1801 assert_eq!((-1.0f32).atanh(), neg_inf32);
1803 assert!(2f64.atanh().atanh().is_nan());
1804 assert!((-2f64).atanh().atanh().is_nan());
1806 let inf64: f32 = f32::INFINITY;
1807 let neg_inf64: f32 = f32::NEG_INFINITY;
1808 let nan32: f32 = f32::NAN;
1809 assert!(inf64.atanh().is_nan());
1810 assert!(neg_inf64.atanh().is_nan());
1811 assert!(nan32.atanh().is_nan());
1813 assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32);
1814 assert_approx_eq!((-0.5f32).atanh(), -0.54930614433405484569762261846126285f32);
1818 fn test_real_consts() {
1821 let pi: f32 = consts::PI;
1822 let frac_pi_2: f32 = consts::FRAC_PI_2;
1823 let frac_pi_3: f32 = consts::FRAC_PI_3;
1824 let frac_pi_4: f32 = consts::FRAC_PI_4;
1825 let frac_pi_6: f32 = consts::FRAC_PI_6;
1826 let frac_pi_8: f32 = consts::FRAC_PI_8;
1827 let frac_1_pi: f32 = consts::FRAC_1_PI;
1828 let frac_2_pi: f32 = consts::FRAC_2_PI;
1829 let frac_2_sqrtpi: f32 = consts::FRAC_2_SQRT_PI;
1830 let sqrt2: f32 = consts::SQRT_2;
1831 let frac_1_sqrt2: f32 = consts::FRAC_1_SQRT_2;
1832 let e: f32 = consts::E;
1833 let log2_e: f32 = consts::LOG2_E;
1834 let log10_e: f32 = consts::LOG10_E;
1835 let ln_2: f32 = consts::LN_2;
1836 let ln_10: f32 = consts::LN_10;
1838 assert_approx_eq!(frac_pi_2, pi / 2f32);
1839 assert_approx_eq!(frac_pi_3, pi / 3f32);
1840 assert_approx_eq!(frac_pi_4, pi / 4f32);
1841 assert_approx_eq!(frac_pi_6, pi / 6f32);
1842 assert_approx_eq!(frac_pi_8, pi / 8f32);
1843 assert_approx_eq!(frac_1_pi, 1f32 / pi);
1844 assert_approx_eq!(frac_2_pi, 2f32 / pi);
1845 assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt());
1846 assert_approx_eq!(sqrt2, 2f32.sqrt());
1847 assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt());
1848 assert_approx_eq!(log2_e, e.log2());
1849 assert_approx_eq!(log10_e, e.log10());
1850 assert_approx_eq!(ln_2, 2f32.ln());
1851 assert_approx_eq!(ln_10, 10f32.ln());