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};
87 pub unsafe fn acosf(n: c_float) -> c_float {
88 f64::acos(n as f64) as c_float
91 pub unsafe fn asinf(n: c_float) -> c_float {
92 f64::asin(n as f64) as c_float
95 pub unsafe fn atan2f(n: c_float, b: c_float) -> c_float {
96 f64::atan2(n as f64, b as f64) as c_float
99 pub unsafe fn atanf(n: c_float) -> c_float {
100 f64::atan(n as f64) as c_float
103 pub unsafe fn coshf(n: c_float) -> c_float {
104 f64::cosh(n as f64) as c_float
107 pub unsafe fn frexpf(x: c_float, value: &mut c_int) -> c_float {
108 let (a, b) = f64::frexp(x as f64);
113 pub unsafe fn ldexpf(x: c_float, n: c_int) -> c_float {
114 f64::ldexp(x as f64, n as isize) as c_float
117 pub unsafe fn sinhf(n: c_float) -> c_float {
118 f64::sinh(n as f64) as c_float
121 pub unsafe fn tanf(n: c_float) -> c_float {
122 f64::tan(n as f64) as c_float
125 pub unsafe fn tanhf(n: c_float) -> c_float {
126 f64::tanh(n as f64) as c_float
134 /// Returns `true` if this value is `NaN` and false otherwise.
139 /// let nan = f32::NAN;
142 /// assert!(nan.is_nan());
143 /// assert!(!f.is_nan());
145 #[stable(feature = "rust1", since = "1.0.0")]
147 pub fn is_nan(self) -> bool { num::Float::is_nan(self) }
149 /// Returns `true` if this value is positive infinity or negative infinity and
156 /// let inf = f32::INFINITY;
157 /// let neg_inf = f32::NEG_INFINITY;
158 /// let nan = f32::NAN;
160 /// assert!(!f.is_infinite());
161 /// assert!(!nan.is_infinite());
163 /// assert!(inf.is_infinite());
164 /// assert!(neg_inf.is_infinite());
166 #[stable(feature = "rust1", since = "1.0.0")]
168 pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) }
170 /// Returns `true` if this number is neither infinite nor `NaN`.
176 /// let inf = f32::INFINITY;
177 /// let neg_inf = f32::NEG_INFINITY;
178 /// let nan = f32::NAN;
180 /// assert!(f.is_finite());
182 /// assert!(!nan.is_finite());
183 /// assert!(!inf.is_finite());
184 /// assert!(!neg_inf.is_finite());
186 #[stable(feature = "rust1", since = "1.0.0")]
188 pub fn is_finite(self) -> bool { num::Float::is_finite(self) }
190 /// Returns `true` if the number is neither zero, infinite,
191 /// [subnormal][subnormal], or `NaN`.
196 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
197 /// let max = f32::MAX;
198 /// let lower_than_min = 1.0e-40_f32;
199 /// let zero = 0.0_f32;
201 /// assert!(min.is_normal());
202 /// assert!(max.is_normal());
204 /// assert!(!zero.is_normal());
205 /// assert!(!f32::NAN.is_normal());
206 /// assert!(!f32::INFINITY.is_normal());
207 /// // Values between `0` and `min` are Subnormal.
208 /// assert!(!lower_than_min.is_normal());
210 /// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number
211 #[stable(feature = "rust1", since = "1.0.0")]
213 pub fn is_normal(self) -> bool { num::Float::is_normal(self) }
215 /// Returns the floating point category of the number. If only one property
216 /// is going to be tested, it is generally faster to use the specific
217 /// predicate instead.
220 /// use std::num::FpCategory;
223 /// let num = 12.4_f32;
224 /// let inf = f32::INFINITY;
226 /// assert_eq!(num.classify(), FpCategory::Normal);
227 /// assert_eq!(inf.classify(), FpCategory::Infinite);
229 #[stable(feature = "rust1", since = "1.0.0")]
231 pub fn classify(self) -> FpCategory { num::Float::classify(self) }
233 /// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
234 /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
235 /// The floating point encoding is documented in the [Reference][floating-point].
238 /// #![feature(float_extras)]
242 /// let num = 2.0f32;
244 /// // (8388608, -22, 1)
245 /// let (mantissa, exponent, sign) = num.integer_decode();
246 /// let sign_f = sign as f32;
247 /// let mantissa_f = mantissa as f32;
248 /// let exponent_f = num.powf(exponent as f32);
250 /// // 1 * 8388608 * 2^(-22) == 2
251 /// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
253 /// assert!(abs_difference <= f32::EPSILON);
255 /// [floating-point]: ../../../../../reference.html#machine-types
256 #[unstable(feature = "float_extras", reason = "signature is undecided",
259 pub fn integer_decode(self) -> (u64, i16, i8) {
260 num::Float::integer_decode(self)
263 /// Returns the largest integer less than or equal to a number.
266 /// let f = 3.99_f32;
269 /// assert_eq!(f.floor(), 3.0);
270 /// assert_eq!(g.floor(), 3.0);
272 #[stable(feature = "rust1", since = "1.0.0")]
274 pub fn floor(self) -> f32 {
277 // On MSVC LLVM will lower many math intrinsics to a call to the
278 // corresponding function. On MSVC, however, many of these functions
279 // aren't actually available as symbols to call, but rather they are all
280 // `static inline` functions in header files. This means that from a C
281 // perspective it's "compatible", but not so much from an ABI
282 // perspective (which we're worried about).
284 // The inline header functions always just cast to a f64 and do their
285 // operation, so we do that here as well, but only for MSVC targets.
287 // Note that there are many MSVC-specific float operations which
288 // redirect to this comment, so `floorf` is just one case of a missing
289 // function on MSVC, but there are many others elsewhere.
290 #[cfg(target_env = "msvc")]
291 fn floorf(f: f32) -> f32 { (f as f64).floor() as f32 }
292 #[cfg(not(target_env = "msvc"))]
293 fn floorf(f: f32) -> f32 { unsafe { intrinsics::floorf32(f) } }
296 /// Returns the smallest integer greater than or equal to a number.
299 /// let f = 3.01_f32;
302 /// assert_eq!(f.ceil(), 4.0);
303 /// assert_eq!(g.ceil(), 4.0);
305 #[stable(feature = "rust1", since = "1.0.0")]
307 pub fn ceil(self) -> f32 {
310 // see notes above in `floor`
311 #[cfg(target_env = "msvc")]
312 fn ceilf(f: f32) -> f32 { (f as f64).ceil() as f32 }
313 #[cfg(not(target_env = "msvc"))]
314 fn ceilf(f: f32) -> f32 { unsafe { intrinsics::ceilf32(f) } }
317 /// Returns the nearest integer to a number. Round half-way cases away from
322 /// let g = -3.3_f32;
324 /// assert_eq!(f.round(), 3.0);
325 /// assert_eq!(g.round(), -3.0);
327 #[stable(feature = "rust1", since = "1.0.0")]
329 pub fn round(self) -> f32 {
330 unsafe { intrinsics::roundf32(self) }
333 /// Returns the integer part of a number.
337 /// let g = -3.7_f32;
339 /// assert_eq!(f.trunc(), 3.0);
340 /// assert_eq!(g.trunc(), -3.0);
342 #[stable(feature = "rust1", since = "1.0.0")]
344 pub fn trunc(self) -> f32 {
345 unsafe { intrinsics::truncf32(self) }
348 /// Returns the fractional part of a number.
354 /// let y = -3.5_f32;
355 /// let abs_difference_x = (x.fract() - 0.5).abs();
356 /// let abs_difference_y = (y.fract() - (-0.5)).abs();
358 /// assert!(abs_difference_x <= f32::EPSILON);
359 /// assert!(abs_difference_y <= f32::EPSILON);
361 #[stable(feature = "rust1", since = "1.0.0")]
363 pub fn fract(self) -> f32 { self - self.trunc() }
365 /// Computes the absolute value of `self`. Returns `NAN` if the
372 /// let y = -3.5_f32;
374 /// let abs_difference_x = (x.abs() - x).abs();
375 /// let abs_difference_y = (y.abs() - (-y)).abs();
377 /// assert!(abs_difference_x <= f32::EPSILON);
378 /// assert!(abs_difference_y <= f32::EPSILON);
380 /// assert!(f32::NAN.abs().is_nan());
382 #[stable(feature = "rust1", since = "1.0.0")]
384 pub fn abs(self) -> f32 { num::Float::abs(self) }
386 /// Returns a number that represents the sign of `self`.
388 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
389 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
390 /// - `NAN` if the number is `NAN`
397 /// assert_eq!(f.signum(), 1.0);
398 /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
400 /// assert!(f32::NAN.signum().is_nan());
402 #[stable(feature = "rust1", since = "1.0.0")]
404 pub fn signum(self) -> f32 { num::Float::signum(self) }
406 /// Returns `true` if `self`'s sign bit is positive, including
407 /// `+0.0` and `INFINITY`.
412 /// let nan = f32::NAN;
414 /// let g = -7.0_f32;
416 /// assert!(f.is_sign_positive());
417 /// assert!(!g.is_sign_positive());
418 /// // Requires both tests to determine if is `NaN`
419 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
421 #[stable(feature = "rust1", since = "1.0.0")]
423 pub fn is_sign_positive(self) -> bool { num::Float::is_sign_positive(self) }
425 /// Returns `true` if `self`'s sign is negative, including `-0.0`
426 /// and `NEG_INFINITY`.
431 /// let nan = f32::NAN;
435 /// assert!(!f.is_sign_negative());
436 /// assert!(g.is_sign_negative());
437 /// // Requires both tests to determine if is `NaN`.
438 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
440 #[stable(feature = "rust1", since = "1.0.0")]
442 pub fn is_sign_negative(self) -> bool { num::Float::is_sign_negative(self) }
444 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
445 /// error. This produces a more accurate result with better performance than
446 /// a separate multiplication operation followed by an add.
451 /// let m = 10.0_f32;
453 /// let b = 60.0_f32;
456 /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
458 /// assert!(abs_difference <= f32::EPSILON);
460 #[stable(feature = "rust1", since = "1.0.0")]
462 pub fn mul_add(self, a: f32, b: f32) -> f32 {
463 unsafe { intrinsics::fmaf32(self, a, b) }
466 /// Takes the reciprocal (inverse) of a number, `1/x`.
472 /// let abs_difference = (x.recip() - (1.0/x)).abs();
474 /// assert!(abs_difference <= f32::EPSILON);
476 #[stable(feature = "rust1", since = "1.0.0")]
478 pub fn recip(self) -> f32 { num::Float::recip(self) }
480 /// Raises a number to an integer power.
482 /// Using this function is generally faster than using `powf`
488 /// let abs_difference = (x.powi(2) - x*x).abs();
490 /// assert!(abs_difference <= f32::EPSILON);
492 #[stable(feature = "rust1", since = "1.0.0")]
494 pub fn powi(self, n: i32) -> f32 { num::Float::powi(self, n) }
496 /// Raises a number to a floating point power.
502 /// let abs_difference = (x.powf(2.0) - x*x).abs();
504 /// assert!(abs_difference <= f32::EPSILON);
506 #[stable(feature = "rust1", since = "1.0.0")]
508 pub fn powf(self, n: f32) -> f32 {
509 return powf(self, n);
511 // see notes above in `floor`
512 #[cfg(target_env = "msvc")]
513 fn powf(f: f32, n: f32) -> f32 { (f as f64).powf(n as f64) as f32 }
514 #[cfg(not(target_env = "msvc"))]
515 fn powf(f: f32, n: f32) -> f32 { unsafe { intrinsics::powf32(f, n) } }
518 /// Takes the square root of a number.
520 /// Returns NaN if `self` is a negative number.
525 /// let positive = 4.0_f32;
526 /// let negative = -4.0_f32;
528 /// let abs_difference = (positive.sqrt() - 2.0).abs();
530 /// assert!(abs_difference <= f32::EPSILON);
531 /// assert!(negative.sqrt().is_nan());
533 #[stable(feature = "rust1", since = "1.0.0")]
535 pub fn sqrt(self) -> f32 {
539 unsafe { intrinsics::sqrtf32(self) }
543 /// Returns `e^(self)`, (the exponential function).
548 /// let one = 1.0f32;
550 /// let e = one.exp();
552 /// // ln(e) - 1 == 0
553 /// let abs_difference = (e.ln() - 1.0).abs();
555 /// assert!(abs_difference <= f32::EPSILON);
557 #[stable(feature = "rust1", since = "1.0.0")]
559 pub fn exp(self) -> f32 {
562 // see notes above in `floor`
563 #[cfg(target_env = "msvc")]
564 fn expf(f: f32) -> f32 { (f as f64).exp() as f32 }
565 #[cfg(not(target_env = "msvc"))]
566 fn expf(f: f32) -> f32 { unsafe { intrinsics::expf32(f) } }
569 /// Returns `2^(self)`.
577 /// let abs_difference = (f.exp2() - 4.0).abs();
579 /// assert!(abs_difference <= f32::EPSILON);
581 #[stable(feature = "rust1", since = "1.0.0")]
583 pub fn exp2(self) -> f32 {
584 unsafe { intrinsics::exp2f32(self) }
587 /// Returns the natural logarithm of the number.
592 /// let one = 1.0f32;
594 /// let e = one.exp();
596 /// // ln(e) - 1 == 0
597 /// let abs_difference = (e.ln() - 1.0).abs();
599 /// assert!(abs_difference <= f32::EPSILON);
601 #[stable(feature = "rust1", since = "1.0.0")]
603 pub fn ln(self) -> f32 {
606 // see notes above in `floor`
607 #[cfg(target_env = "msvc")]
608 fn logf(f: f32) -> f32 { (f as f64).ln() as f32 }
609 #[cfg(not(target_env = "msvc"))]
610 fn logf(f: f32) -> f32 { unsafe { intrinsics::logf32(f) } }
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 {
669 // see notes above in `floor`
670 #[cfg(target_env = "msvc")]
671 fn log10f(f: f32) -> f32 { (f as f64).log10() as f32 }
672 #[cfg(not(target_env = "msvc"))]
673 fn log10f(f: f32) -> f32 { unsafe { intrinsics::log10f32(f) } }
676 /// Converts radians to degrees.
679 /// use std::f32::{self, consts};
681 /// let angle = consts::PI;
683 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
685 /// assert!(abs_difference <= f32::EPSILON);
687 #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
689 pub fn to_degrees(self) -> f32 { num::Float::to_degrees(self) }
691 /// Converts degrees to radians.
694 /// use std::f32::{self, consts};
696 /// let angle = 180.0f32;
698 /// let abs_difference = (angle.to_radians() - consts::PI).abs();
700 /// assert!(abs_difference <= f32::EPSILON);
702 #[stable(feature = "f32_deg_rad_conversions", since="1.7.0")]
704 pub fn to_radians(self) -> f32 { num::Float::to_radians(self) }
706 /// Constructs a floating point number of `x*2^exp`.
709 /// #![feature(float_extras)]
712 /// // 3*2^2 - 12 == 0
713 /// let abs_difference = (f32::ldexp(3.0, 2) - 12.0).abs();
715 /// assert!(abs_difference <= f32::EPSILON);
717 #[unstable(feature = "float_extras",
718 reason = "pending integer conventions",
721 pub fn ldexp(x: f32, exp: isize) -> f32 {
722 unsafe { cmath::ldexpf(x, exp as c_int) }
725 /// Breaks the number into a normalized fraction and a base-2 exponent,
728 /// * `self = x * 2^exp`
729 /// * `0.5 <= abs(x) < 1.0`
732 /// #![feature(float_extras)]
738 /// // (1/2)*2^3 -> 1 * 8/2 -> 4.0
739 /// let f = x.frexp();
740 /// let abs_difference_0 = (f.0 - 0.5).abs();
741 /// let abs_difference_1 = (f.1 as f32 - 3.0).abs();
743 /// assert!(abs_difference_0 <= f32::EPSILON);
744 /// assert!(abs_difference_1 <= f32::EPSILON);
746 #[unstable(feature = "float_extras",
747 reason = "pending integer conventions",
750 pub fn frexp(self) -> (f32, isize) {
753 let x = cmath::frexpf(self, &mut exp);
758 /// Returns the next representable floating-point value in the direction of
762 /// #![feature(float_extras)]
768 /// let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs();
770 /// assert!(abs_diff <= f32::EPSILON);
772 #[unstable(feature = "float_extras",
773 reason = "unsure about its place in the world",
776 pub fn next_after(self, other: f32) -> f32 {
777 unsafe { cmath::nextafterf(self, other) }
780 /// Returns the maximum of the two numbers.
786 /// assert_eq!(x.max(y), y);
789 /// If one of the arguments is NaN, then the other argument is returned.
790 #[stable(feature = "rust1", since = "1.0.0")]
792 pub fn max(self, other: f32) -> f32 {
793 unsafe { cmath::fmaxf(self, other) }
796 /// Returns the minimum of the two numbers.
802 /// assert_eq!(x.min(y), x);
805 /// If one of the arguments is NaN, then the other argument is returned.
806 #[stable(feature = "rust1", since = "1.0.0")]
808 pub fn min(self, other: f32) -> f32 {
809 unsafe { cmath::fminf(self, other) }
812 /// The positive difference of two numbers.
814 /// * If `self <= other`: `0:0`
815 /// * Else: `self - other`
823 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
824 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
826 /// assert!(abs_difference_x <= f32::EPSILON);
827 /// assert!(abs_difference_y <= f32::EPSILON);
829 #[stable(feature = "rust1", since = "1.0.0")]
831 pub fn abs_sub(self, other: f32) -> f32 {
832 unsafe { cmath::fdimf(self, other) }
835 /// Takes the cubic root of a number.
842 /// // x^(1/3) - 2 == 0
843 /// let abs_difference = (x.cbrt() - 2.0).abs();
845 /// assert!(abs_difference <= f32::EPSILON);
847 #[stable(feature = "rust1", since = "1.0.0")]
849 pub fn cbrt(self) -> f32 {
850 unsafe { cmath::cbrtf(self) }
853 /// Calculates the length of the hypotenuse of a right-angle triangle given
854 /// legs of length `x` and `y`.
862 /// // sqrt(x^2 + y^2)
863 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
865 /// assert!(abs_difference <= f32::EPSILON);
867 #[stable(feature = "rust1", since = "1.0.0")]
869 pub fn hypot(self, other: f32) -> f32 {
870 unsafe { cmath::hypotf(self, other) }
873 /// Computes the sine of a number (in radians).
878 /// let x = f32::consts::PI/2.0;
880 /// let abs_difference = (x.sin() - 1.0).abs();
882 /// assert!(abs_difference <= f32::EPSILON);
884 #[stable(feature = "rust1", since = "1.0.0")]
886 pub fn sin(self) -> f32 {
889 // see notes in `core::f32::Float::floor`
890 #[cfg(target_env = "msvc")]
891 fn sinf(f: f32) -> f32 { (f as f64).sin() as f32 }
892 #[cfg(not(target_env = "msvc"))]
893 fn sinf(f: f32) -> f32 { unsafe { intrinsics::sinf32(f) } }
896 /// Computes the cosine of a number (in radians).
901 /// let x = 2.0*f32::consts::PI;
903 /// let abs_difference = (x.cos() - 1.0).abs();
905 /// assert!(abs_difference <= f32::EPSILON);
907 #[stable(feature = "rust1", since = "1.0.0")]
909 pub fn cos(self) -> f32 {
912 // see notes in `core::f32::Float::floor`
913 #[cfg(target_env = "msvc")]
914 fn cosf(f: f32) -> f32 { (f as f64).cos() as f32 }
915 #[cfg(not(target_env = "msvc"))]
916 fn cosf(f: f32) -> f32 { unsafe { intrinsics::cosf32(f) } }
919 /// Computes the tangent of a number (in radians).
924 /// let x = f64::consts::PI/4.0;
925 /// let abs_difference = (x.tan() - 1.0).abs();
927 /// assert!(abs_difference < 1e-10);
929 #[stable(feature = "rust1", since = "1.0.0")]
931 pub fn tan(self) -> f32 {
932 unsafe { cmath::tanf(self) }
935 /// Computes the arcsine of a number. Return value is in radians in
936 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
942 /// let f = f32::consts::PI / 2.0;
944 /// // asin(sin(pi/2))
945 /// let abs_difference = f.sin().asin().abs_sub(f32::consts::PI / 2.0);
947 /// assert!(abs_difference <= f32::EPSILON);
949 #[stable(feature = "rust1", since = "1.0.0")]
951 pub fn asin(self) -> f32 {
952 unsafe { cmath::asinf(self) }
955 /// Computes the arccosine of a number. Return value is in radians in
956 /// the range [0, pi] or NaN if the number is outside the range
962 /// let f = f32::consts::PI / 4.0;
964 /// // acos(cos(pi/4))
965 /// let abs_difference = f.cos().acos().abs_sub(f32::consts::PI / 4.0);
967 /// assert!(abs_difference <= f32::EPSILON);
969 #[stable(feature = "rust1", since = "1.0.0")]
971 pub fn acos(self) -> f32 {
972 unsafe { cmath::acosf(self) }
975 /// Computes the arctangent of a number. Return value is in radians in the
976 /// range [-pi/2, pi/2];
984 /// let abs_difference = f.tan().atan().abs_sub(1.0);
986 /// assert!(abs_difference <= f32::EPSILON);
988 #[stable(feature = "rust1", since = "1.0.0")]
990 pub fn atan(self) -> f32 {
991 unsafe { cmath::atanf(self) }
994 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
996 /// * `x = 0`, `y = 0`: `0`
997 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
998 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
999 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
1004 /// let pi = f32::consts::PI;
1005 /// // All angles from horizontal right (+x)
1006 /// // 45 deg counter-clockwise
1007 /// let x1 = 3.0f32;
1008 /// let y1 = -3.0f32;
1010 /// // 135 deg clockwise
1011 /// let x2 = -3.0f32;
1012 /// let y2 = 3.0f32;
1014 /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
1015 /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
1017 /// assert!(abs_difference_1 <= f32::EPSILON);
1018 /// assert!(abs_difference_2 <= f32::EPSILON);
1020 #[stable(feature = "rust1", since = "1.0.0")]
1022 pub fn atan2(self, other: f32) -> f32 {
1023 unsafe { cmath::atan2f(self, other) }
1026 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
1027 /// `(sin(x), cos(x))`.
1032 /// let x = f32::consts::PI/4.0;
1033 /// let f = x.sin_cos();
1035 /// let abs_difference_0 = (f.0 - x.sin()).abs();
1036 /// let abs_difference_1 = (f.1 - x.cos()).abs();
1038 /// assert!(abs_difference_0 <= f32::EPSILON);
1039 /// assert!(abs_difference_0 <= f32::EPSILON);
1041 #[stable(feature = "rust1", since = "1.0.0")]
1043 pub fn sin_cos(self) -> (f32, f32) {
1044 (self.sin(), self.cos())
1047 /// Returns `e^(self) - 1` in a way that is accurate even if the
1048 /// number is close to zero.
1053 /// // e^(ln(7)) - 1
1054 /// let abs_difference = x.ln().exp_m1().abs_sub(6.0);
1056 /// assert!(abs_difference < 1e-10);
1058 #[stable(feature = "rust1", since = "1.0.0")]
1060 pub fn exp_m1(self) -> f32 {
1061 unsafe { cmath::expm1f(self) }
1064 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
1065 /// the operations were performed separately.
1070 /// let x = f32::consts::E - 1.0;
1072 /// // ln(1 + (e - 1)) == ln(e) == 1
1073 /// let abs_difference = (x.ln_1p() - 1.0).abs();
1075 /// assert!(abs_difference <= f32::EPSILON);
1077 #[stable(feature = "rust1", since = "1.0.0")]
1079 pub fn ln_1p(self) -> f32 {
1080 unsafe { cmath::log1pf(self) }
1083 /// Hyperbolic sine function.
1088 /// let e = f32::consts::E;
1091 /// let f = x.sinh();
1092 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
1093 /// let g = (e*e - 1.0)/(2.0*e);
1094 /// let abs_difference = (f - g).abs();
1096 /// assert!(abs_difference <= f32::EPSILON);
1098 #[stable(feature = "rust1", since = "1.0.0")]
1100 pub fn sinh(self) -> f32 {
1101 unsafe { cmath::sinhf(self) }
1104 /// Hyperbolic cosine function.
1109 /// let e = f32::consts::E;
1111 /// let f = x.cosh();
1112 /// // Solving cosh() at 1 gives this result
1113 /// let g = (e*e + 1.0)/(2.0*e);
1114 /// let abs_difference = f.abs_sub(g);
1117 /// assert!(abs_difference <= f32::EPSILON);
1119 #[stable(feature = "rust1", since = "1.0.0")]
1121 pub fn cosh(self) -> f32 {
1122 unsafe { cmath::coshf(self) }
1125 /// Hyperbolic tangent function.
1130 /// let e = f32::consts::E;
1133 /// let f = x.tanh();
1134 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1135 /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
1136 /// let abs_difference = (f - g).abs();
1138 /// assert!(abs_difference <= f32::EPSILON);
1140 #[stable(feature = "rust1", since = "1.0.0")]
1142 pub fn tanh(self) -> f32 {
1143 unsafe { cmath::tanhf(self) }
1146 /// Inverse hyperbolic sine function.
1152 /// let f = x.sinh().asinh();
1154 /// let abs_difference = (f - x).abs();
1156 /// assert!(abs_difference <= f32::EPSILON);
1158 #[stable(feature = "rust1", since = "1.0.0")]
1160 pub fn asinh(self) -> f32 {
1162 NEG_INFINITY => NEG_INFINITY,
1163 x => (x + ((x * x) + 1.0).sqrt()).ln(),
1167 /// Inverse hyperbolic cosine function.
1173 /// let f = x.cosh().acosh();
1175 /// let abs_difference = (f - x).abs();
1177 /// assert!(abs_difference <= f32::EPSILON);
1179 #[stable(feature = "rust1", since = "1.0.0")]
1181 pub fn acosh(self) -> f32 {
1183 x if x < 1.0 => ::f32::NAN,
1184 x => (x + ((x * x) - 1.0).sqrt()).ln(),
1188 /// Inverse hyperbolic tangent function.
1193 /// let e = f32::consts::E;
1194 /// let f = e.tanh().atanh();
1196 /// let abs_difference = f.abs_sub(e);
1198 /// assert!(abs_difference <= f32::EPSILON);
1200 #[stable(feature = "rust1", since = "1.0.0")]
1202 pub fn atanh(self) -> f32 {
1203 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1212 use num::FpCategory as Fp;
1216 test_num(10f32, 2f32);
1221 assert_eq!(NAN.min(2.0), 2.0);
1222 assert_eq!(2.0f32.min(NAN), 2.0);
1227 assert_eq!(NAN.max(2.0), 2.0);
1228 assert_eq!(2.0f32.max(NAN), 2.0);
1233 let nan: f32 = f32::NAN;
1234 assert!(nan.is_nan());
1235 assert!(!nan.is_infinite());
1236 assert!(!nan.is_finite());
1237 assert!(!nan.is_normal());
1238 assert!(!nan.is_sign_positive());
1239 assert!(!nan.is_sign_negative());
1240 assert_eq!(Fp::Nan, nan.classify());
1244 fn test_infinity() {
1245 let inf: f32 = f32::INFINITY;
1246 assert!(inf.is_infinite());
1247 assert!(!inf.is_finite());
1248 assert!(inf.is_sign_positive());
1249 assert!(!inf.is_sign_negative());
1250 assert!(!inf.is_nan());
1251 assert!(!inf.is_normal());
1252 assert_eq!(Fp::Infinite, inf.classify());
1256 fn test_neg_infinity() {
1257 let neg_inf: f32 = f32::NEG_INFINITY;
1258 assert!(neg_inf.is_infinite());
1259 assert!(!neg_inf.is_finite());
1260 assert!(!neg_inf.is_sign_positive());
1261 assert!(neg_inf.is_sign_negative());
1262 assert!(!neg_inf.is_nan());
1263 assert!(!neg_inf.is_normal());
1264 assert_eq!(Fp::Infinite, neg_inf.classify());
1269 let zero: f32 = 0.0f32;
1270 assert_eq!(0.0, zero);
1271 assert!(!zero.is_infinite());
1272 assert!(zero.is_finite());
1273 assert!(zero.is_sign_positive());
1274 assert!(!zero.is_sign_negative());
1275 assert!(!zero.is_nan());
1276 assert!(!zero.is_normal());
1277 assert_eq!(Fp::Zero, zero.classify());
1281 fn test_neg_zero() {
1282 let neg_zero: f32 = -0.0;
1283 assert_eq!(0.0, neg_zero);
1284 assert!(!neg_zero.is_infinite());
1285 assert!(neg_zero.is_finite());
1286 assert!(!neg_zero.is_sign_positive());
1287 assert!(neg_zero.is_sign_negative());
1288 assert!(!neg_zero.is_nan());
1289 assert!(!neg_zero.is_normal());
1290 assert_eq!(Fp::Zero, neg_zero.classify());
1295 let one: f32 = 1.0f32;
1296 assert_eq!(1.0, one);
1297 assert!(!one.is_infinite());
1298 assert!(one.is_finite());
1299 assert!(one.is_sign_positive());
1300 assert!(!one.is_sign_negative());
1301 assert!(!one.is_nan());
1302 assert!(one.is_normal());
1303 assert_eq!(Fp::Normal, one.classify());
1308 let nan: f32 = f32::NAN;
1309 let inf: f32 = f32::INFINITY;
1310 let neg_inf: f32 = f32::NEG_INFINITY;
1311 assert!(nan.is_nan());
1312 assert!(!0.0f32.is_nan());
1313 assert!(!5.3f32.is_nan());
1314 assert!(!(-10.732f32).is_nan());
1315 assert!(!inf.is_nan());
1316 assert!(!neg_inf.is_nan());
1320 fn test_is_infinite() {
1321 let nan: f32 = f32::NAN;
1322 let inf: f32 = f32::INFINITY;
1323 let neg_inf: f32 = f32::NEG_INFINITY;
1324 assert!(!nan.is_infinite());
1325 assert!(inf.is_infinite());
1326 assert!(neg_inf.is_infinite());
1327 assert!(!0.0f32.is_infinite());
1328 assert!(!42.8f32.is_infinite());
1329 assert!(!(-109.2f32).is_infinite());
1333 fn test_is_finite() {
1334 let nan: f32 = f32::NAN;
1335 let inf: f32 = f32::INFINITY;
1336 let neg_inf: f32 = f32::NEG_INFINITY;
1337 assert!(!nan.is_finite());
1338 assert!(!inf.is_finite());
1339 assert!(!neg_inf.is_finite());
1340 assert!(0.0f32.is_finite());
1341 assert!(42.8f32.is_finite());
1342 assert!((-109.2f32).is_finite());
1346 fn test_is_normal() {
1347 let nan: f32 = f32::NAN;
1348 let inf: f32 = f32::INFINITY;
1349 let neg_inf: f32 = f32::NEG_INFINITY;
1350 let zero: f32 = 0.0f32;
1351 let neg_zero: f32 = -0.0;
1352 assert!(!nan.is_normal());
1353 assert!(!inf.is_normal());
1354 assert!(!neg_inf.is_normal());
1355 assert!(!zero.is_normal());
1356 assert!(!neg_zero.is_normal());
1357 assert!(1f32.is_normal());
1358 assert!(1e-37f32.is_normal());
1359 assert!(!1e-38f32.is_normal());
1363 fn test_classify() {
1364 let nan: f32 = f32::NAN;
1365 let inf: f32 = f32::INFINITY;
1366 let neg_inf: f32 = f32::NEG_INFINITY;
1367 let zero: f32 = 0.0f32;
1368 let neg_zero: f32 = -0.0;
1369 assert_eq!(nan.classify(), Fp::Nan);
1370 assert_eq!(inf.classify(), Fp::Infinite);
1371 assert_eq!(neg_inf.classify(), Fp::Infinite);
1372 assert_eq!(zero.classify(), Fp::Zero);
1373 assert_eq!(neg_zero.classify(), Fp::Zero);
1374 assert_eq!(1f32.classify(), Fp::Normal);
1375 assert_eq!(1e-37f32.classify(), Fp::Normal);
1376 assert_eq!(1e-38f32.classify(), Fp::Subnormal);
1380 fn test_integer_decode() {
1381 assert_eq!(3.14159265359f32.integer_decode(), (13176795, -22, 1));
1382 assert_eq!((-8573.5918555f32).integer_decode(), (8779358, -10, -1));
1383 assert_eq!(2f32.powf(100.0).integer_decode(), (8388608, 77, 1));
1384 assert_eq!(0f32.integer_decode(), (0, -150, 1));
1385 assert_eq!((-0f32).integer_decode(), (0, -150, -1));
1386 assert_eq!(INFINITY.integer_decode(), (8388608, 105, 1));
1387 assert_eq!(NEG_INFINITY.integer_decode(), (8388608, 105, -1));
1388 assert_eq!(NAN.integer_decode(), (12582912, 105, 1));
1393 assert_approx_eq!(1.0f32.floor(), 1.0f32);
1394 assert_approx_eq!(1.3f32.floor(), 1.0f32);
1395 assert_approx_eq!(1.5f32.floor(), 1.0f32);
1396 assert_approx_eq!(1.7f32.floor(), 1.0f32);
1397 assert_approx_eq!(0.0f32.floor(), 0.0f32);
1398 assert_approx_eq!((-0.0f32).floor(), -0.0f32);
1399 assert_approx_eq!((-1.0f32).floor(), -1.0f32);
1400 assert_approx_eq!((-1.3f32).floor(), -2.0f32);
1401 assert_approx_eq!((-1.5f32).floor(), -2.0f32);
1402 assert_approx_eq!((-1.7f32).floor(), -2.0f32);
1407 assert_approx_eq!(1.0f32.ceil(), 1.0f32);
1408 assert_approx_eq!(1.3f32.ceil(), 2.0f32);
1409 assert_approx_eq!(1.5f32.ceil(), 2.0f32);
1410 assert_approx_eq!(1.7f32.ceil(), 2.0f32);
1411 assert_approx_eq!(0.0f32.ceil(), 0.0f32);
1412 assert_approx_eq!((-0.0f32).ceil(), -0.0f32);
1413 assert_approx_eq!((-1.0f32).ceil(), -1.0f32);
1414 assert_approx_eq!((-1.3f32).ceil(), -1.0f32);
1415 assert_approx_eq!((-1.5f32).ceil(), -1.0f32);
1416 assert_approx_eq!((-1.7f32).ceil(), -1.0f32);
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);
1425 assert_approx_eq!(0.0f32.round(), 0.0f32);
1426 assert_approx_eq!((-0.0f32).round(), -0.0f32);
1427 assert_approx_eq!((-1.0f32).round(), -1.0f32);
1428 assert_approx_eq!((-1.3f32).round(), -1.0f32);
1429 assert_approx_eq!((-1.5f32).round(), -2.0f32);
1430 assert_approx_eq!((-1.7f32).round(), -2.0f32);
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);
1439 assert_approx_eq!(0.0f32.trunc(), 0.0f32);
1440 assert_approx_eq!((-0.0f32).trunc(), -0.0f32);
1441 assert_approx_eq!((-1.0f32).trunc(), -1.0f32);
1442 assert_approx_eq!((-1.3f32).trunc(), -1.0f32);
1443 assert_approx_eq!((-1.5f32).trunc(), -1.0f32);
1444 assert_approx_eq!((-1.7f32).trunc(), -1.0f32);
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);
1453 assert_approx_eq!(0.0f32.fract(), 0.0f32);
1454 assert_approx_eq!((-0.0f32).fract(), -0.0f32);
1455 assert_approx_eq!((-1.0f32).fract(), -0.0f32);
1456 assert_approx_eq!((-1.3f32).fract(), -0.3f32);
1457 assert_approx_eq!((-1.5f32).fract(), -0.5f32);
1458 assert_approx_eq!((-1.7f32).fract(), -0.7f32);
1463 assert_eq!(INFINITY.abs(), INFINITY);
1464 assert_eq!(1f32.abs(), 1f32);
1465 assert_eq!(0f32.abs(), 0f32);
1466 assert_eq!((-0f32).abs(), 0f32);
1467 assert_eq!((-1f32).abs(), 1f32);
1468 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1469 assert_eq!((1f32/NEG_INFINITY).abs(), 0f32);
1470 assert!(NAN.abs().is_nan());
1475 assert_eq!(INFINITY.signum(), 1f32);
1476 assert_eq!(1f32.signum(), 1f32);
1477 assert_eq!(0f32.signum(), 1f32);
1478 assert_eq!((-0f32).signum(), -1f32);
1479 assert_eq!((-1f32).signum(), -1f32);
1480 assert_eq!(NEG_INFINITY.signum(), -1f32);
1481 assert_eq!((1f32/NEG_INFINITY).signum(), -1f32);
1482 assert!(NAN.signum().is_nan());
1486 fn test_is_sign_positive() {
1487 assert!(INFINITY.is_sign_positive());
1488 assert!(1f32.is_sign_positive());
1489 assert!(0f32.is_sign_positive());
1490 assert!(!(-0f32).is_sign_positive());
1491 assert!(!(-1f32).is_sign_positive());
1492 assert!(!NEG_INFINITY.is_sign_positive());
1493 assert!(!(1f32/NEG_INFINITY).is_sign_positive());
1494 assert!(!NAN.is_sign_positive());
1498 fn test_is_sign_negative() {
1499 assert!(!INFINITY.is_sign_negative());
1500 assert!(!1f32.is_sign_negative());
1501 assert!(!0f32.is_sign_negative());
1502 assert!((-0f32).is_sign_negative());
1503 assert!((-1f32).is_sign_negative());
1504 assert!(NEG_INFINITY.is_sign_negative());
1505 assert!((1f32/NEG_INFINITY).is_sign_negative());
1506 assert!(!NAN.is_sign_negative());
1511 let nan: f32 = f32::NAN;
1512 let inf: f32 = f32::INFINITY;
1513 let neg_inf: f32 = f32::NEG_INFINITY;
1514 assert_approx_eq!(12.3f32.mul_add(4.5, 6.7), 62.05);
1515 assert_approx_eq!((-12.3f32).mul_add(-4.5, -6.7), 48.65);
1516 assert_approx_eq!(0.0f32.mul_add(8.9, 1.2), 1.2);
1517 assert_approx_eq!(3.4f32.mul_add(-0.0, 5.6), 5.6);
1518 assert!(nan.mul_add(7.8, 9.0).is_nan());
1519 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1520 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1521 assert_eq!(8.9f32.mul_add(inf, 3.2), inf);
1522 assert_eq!((-3.2f32).mul_add(2.4, neg_inf), neg_inf);
1527 let nan: f32 = f32::NAN;
1528 let inf: f32 = f32::INFINITY;
1529 let neg_inf: f32 = f32::NEG_INFINITY;
1530 assert_eq!(1.0f32.recip(), 1.0);
1531 assert_eq!(2.0f32.recip(), 0.5);
1532 assert_eq!((-0.4f32).recip(), -2.5);
1533 assert_eq!(0.0f32.recip(), inf);
1534 assert!(nan.recip().is_nan());
1535 assert_eq!(inf.recip(), 0.0);
1536 assert_eq!(neg_inf.recip(), 0.0);
1541 let nan: f32 = f32::NAN;
1542 let inf: f32 = f32::INFINITY;
1543 let neg_inf: f32 = f32::NEG_INFINITY;
1544 assert_eq!(1.0f32.powi(1), 1.0);
1545 assert_approx_eq!((-3.1f32).powi(2), 9.61);
1546 assert_approx_eq!(5.9f32.powi(-2), 0.028727);
1547 assert_eq!(8.3f32.powi(0), 1.0);
1548 assert!(nan.powi(2).is_nan());
1549 assert_eq!(inf.powi(3), inf);
1550 assert_eq!(neg_inf.powi(2), inf);
1555 let nan: f32 = f32::NAN;
1556 let inf: f32 = f32::INFINITY;
1557 let neg_inf: f32 = f32::NEG_INFINITY;
1558 assert_eq!(1.0f32.powf(1.0), 1.0);
1559 assert_approx_eq!(3.4f32.powf(4.5), 246.408218);
1560 assert_approx_eq!(2.7f32.powf(-3.2), 0.041652);
1561 assert_approx_eq!((-3.1f32).powf(2.0), 9.61);
1562 assert_approx_eq!(5.9f32.powf(-2.0), 0.028727);
1563 assert_eq!(8.3f32.powf(0.0), 1.0);
1564 assert!(nan.powf(2.0).is_nan());
1565 assert_eq!(inf.powf(2.0), inf);
1566 assert_eq!(neg_inf.powf(3.0), neg_inf);
1570 fn test_sqrt_domain() {
1571 assert!(NAN.sqrt().is_nan());
1572 assert!(NEG_INFINITY.sqrt().is_nan());
1573 assert!((-1.0f32).sqrt().is_nan());
1574 assert_eq!((-0.0f32).sqrt(), -0.0);
1575 assert_eq!(0.0f32.sqrt(), 0.0);
1576 assert_eq!(1.0f32.sqrt(), 1.0);
1577 assert_eq!(INFINITY.sqrt(), INFINITY);
1582 assert_eq!(1.0, 0.0f32.exp());
1583 assert_approx_eq!(2.718282, 1.0f32.exp());
1584 assert_approx_eq!(148.413162, 5.0f32.exp());
1586 let inf: f32 = f32::INFINITY;
1587 let neg_inf: f32 = f32::NEG_INFINITY;
1588 let nan: f32 = f32::NAN;
1589 assert_eq!(inf, inf.exp());
1590 assert_eq!(0.0, neg_inf.exp());
1591 assert!(nan.exp().is_nan());
1596 assert_eq!(32.0, 5.0f32.exp2());
1597 assert_eq!(1.0, 0.0f32.exp2());
1599 let inf: f32 = f32::INFINITY;
1600 let neg_inf: f32 = f32::NEG_INFINITY;
1601 let nan: f32 = f32::NAN;
1602 assert_eq!(inf, inf.exp2());
1603 assert_eq!(0.0, neg_inf.exp2());
1604 assert!(nan.exp2().is_nan());
1609 let nan: f32 = f32::NAN;
1610 let inf: f32 = f32::INFINITY;
1611 let neg_inf: f32 = f32::NEG_INFINITY;
1612 assert_approx_eq!(1.0f32.exp().ln(), 1.0);
1613 assert!(nan.ln().is_nan());
1614 assert_eq!(inf.ln(), inf);
1615 assert!(neg_inf.ln().is_nan());
1616 assert!((-2.3f32).ln().is_nan());
1617 assert_eq!((-0.0f32).ln(), neg_inf);
1618 assert_eq!(0.0f32.ln(), neg_inf);
1619 assert_approx_eq!(4.0f32.ln(), 1.386294);
1624 let nan: f32 = f32::NAN;
1625 let inf: f32 = f32::INFINITY;
1626 let neg_inf: f32 = f32::NEG_INFINITY;
1627 assert_eq!(10.0f32.log(10.0), 1.0);
1628 assert_approx_eq!(2.3f32.log(3.5), 0.664858);
1629 assert_eq!(1.0f32.exp().log(1.0f32.exp()), 1.0);
1630 assert!(1.0f32.log(1.0).is_nan());
1631 assert!(1.0f32.log(-13.9).is_nan());
1632 assert!(nan.log(2.3).is_nan());
1633 assert_eq!(inf.log(10.0), inf);
1634 assert!(neg_inf.log(8.8).is_nan());
1635 assert!((-2.3f32).log(0.1).is_nan());
1636 assert_eq!((-0.0f32).log(2.0), neg_inf);
1637 assert_eq!(0.0f32.log(7.0), neg_inf);
1642 let nan: f32 = f32::NAN;
1643 let inf: f32 = f32::INFINITY;
1644 let neg_inf: f32 = f32::NEG_INFINITY;
1645 assert_approx_eq!(10.0f32.log2(), 3.321928);
1646 assert_approx_eq!(2.3f32.log2(), 1.201634);
1647 assert_approx_eq!(1.0f32.exp().log2(), 1.442695);
1648 assert!(nan.log2().is_nan());
1649 assert_eq!(inf.log2(), inf);
1650 assert!(neg_inf.log2().is_nan());
1651 assert!((-2.3f32).log2().is_nan());
1652 assert_eq!((-0.0f32).log2(), neg_inf);
1653 assert_eq!(0.0f32.log2(), neg_inf);
1658 let nan: f32 = f32::NAN;
1659 let inf: f32 = f32::INFINITY;
1660 let neg_inf: f32 = f32::NEG_INFINITY;
1661 assert_eq!(10.0f32.log10(), 1.0);
1662 assert_approx_eq!(2.3f32.log10(), 0.361728);
1663 assert_approx_eq!(1.0f32.exp().log10(), 0.434294);
1664 assert_eq!(1.0f32.log10(), 0.0);
1665 assert!(nan.log10().is_nan());
1666 assert_eq!(inf.log10(), inf);
1667 assert!(neg_inf.log10().is_nan());
1668 assert!((-2.3f32).log10().is_nan());
1669 assert_eq!((-0.0f32).log10(), neg_inf);
1670 assert_eq!(0.0f32.log10(), neg_inf);
1674 fn test_to_degrees() {
1675 let pi: f32 = consts::PI;
1676 let nan: f32 = f32::NAN;
1677 let inf: f32 = f32::INFINITY;
1678 let neg_inf: f32 = f32::NEG_INFINITY;
1679 assert_eq!(0.0f32.to_degrees(), 0.0);
1680 assert_approx_eq!((-5.8f32).to_degrees(), -332.315521);
1681 assert_eq!(pi.to_degrees(), 180.0);
1682 assert!(nan.to_degrees().is_nan());
1683 assert_eq!(inf.to_degrees(), inf);
1684 assert_eq!(neg_inf.to_degrees(), neg_inf);
1688 fn test_to_radians() {
1689 let pi: f32 = consts::PI;
1690 let nan: f32 = f32::NAN;
1691 let inf: f32 = f32::INFINITY;
1692 let neg_inf: f32 = f32::NEG_INFINITY;
1693 assert_eq!(0.0f32.to_radians(), 0.0);
1694 assert_approx_eq!(154.6f32.to_radians(), 2.698279);
1695 assert_approx_eq!((-332.31f32).to_radians(), -5.799903);
1696 assert_eq!(180.0f32.to_radians(), pi);
1697 assert!(nan.to_radians().is_nan());
1698 assert_eq!(inf.to_radians(), inf);
1699 assert_eq!(neg_inf.to_radians(), neg_inf);
1704 let f1 = 2.0f32.powi(-123);
1705 let f2 = 2.0f32.powi(-111);
1706 let f3 = 1.75 * 2.0f32.powi(-12);
1707 assert_eq!(f32::ldexp(1f32, -123), f1);
1708 assert_eq!(f32::ldexp(1f32, -111), f2);
1709 assert_eq!(f32::ldexp(1.75f32, -12), f3);
1711 assert_eq!(f32::ldexp(0f32, -123), 0f32);
1712 assert_eq!(f32::ldexp(-0f32, -123), -0f32);
1714 let inf: f32 = f32::INFINITY;
1715 let neg_inf: f32 = f32::NEG_INFINITY;
1716 let nan: f32 = f32::NAN;
1717 assert_eq!(f32::ldexp(inf, -123), inf);
1718 assert_eq!(f32::ldexp(neg_inf, -123), neg_inf);
1719 assert!(f32::ldexp(nan, -123).is_nan());
1724 let f1 = 2.0f32.powi(-123);
1725 let f2 = 2.0f32.powi(-111);
1726 let f3 = 1.75 * 2.0f32.powi(-123);
1727 let (x1, exp1) = f1.frexp();
1728 let (x2, exp2) = f2.frexp();
1729 let (x3, exp3) = f3.frexp();
1730 assert_eq!((x1, exp1), (0.5f32, -122));
1731 assert_eq!((x2, exp2), (0.5f32, -110));
1732 assert_eq!((x3, exp3), (0.875f32, -122));
1733 assert_eq!(f32::ldexp(x1, exp1), f1);
1734 assert_eq!(f32::ldexp(x2, exp2), f2);
1735 assert_eq!(f32::ldexp(x3, exp3), f3);
1737 assert_eq!(0f32.frexp(), (0f32, 0));
1738 assert_eq!((-0f32).frexp(), (-0f32, 0));
1741 #[test] #[cfg_attr(windows, ignore)] // FIXME #8755
1742 fn test_frexp_nowin() {
1743 let inf: f32 = f32::INFINITY;
1744 let neg_inf: f32 = f32::NEG_INFINITY;
1745 let nan: f32 = f32::NAN;
1746 assert_eq!(match inf.frexp() { (x, _) => x }, inf);
1747 assert_eq!(match neg_inf.frexp() { (x, _) => x }, neg_inf);
1748 assert!(match nan.frexp() { (x, _) => x.is_nan() })
1753 assert_eq!((-1f32).abs_sub(1f32), 0f32);
1754 assert_eq!(1f32.abs_sub(1f32), 0f32);
1755 assert_eq!(1f32.abs_sub(0f32), 1f32);
1756 assert_eq!(1f32.abs_sub(-1f32), 2f32);
1757 assert_eq!(NEG_INFINITY.abs_sub(0f32), 0f32);
1758 assert_eq!(INFINITY.abs_sub(1f32), INFINITY);
1759 assert_eq!(0f32.abs_sub(NEG_INFINITY), INFINITY);
1760 assert_eq!(0f32.abs_sub(INFINITY), 0f32);
1764 fn test_abs_sub_nowin() {
1765 assert!(NAN.abs_sub(-1f32).is_nan());
1766 assert!(1f32.abs_sub(NAN).is_nan());
1771 assert_eq!(0.0f32.asinh(), 0.0f32);
1772 assert_eq!((-0.0f32).asinh(), -0.0f32);
1774 let inf: f32 = f32::INFINITY;
1775 let neg_inf: f32 = f32::NEG_INFINITY;
1776 let nan: f32 = f32::NAN;
1777 assert_eq!(inf.asinh(), inf);
1778 assert_eq!(neg_inf.asinh(), neg_inf);
1779 assert!(nan.asinh().is_nan());
1780 assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32);
1781 assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32);
1786 assert_eq!(1.0f32.acosh(), 0.0f32);
1787 assert!(0.999f32.acosh().is_nan());
1789 let inf: f32 = f32::INFINITY;
1790 let neg_inf: f32 = f32::NEG_INFINITY;
1791 let nan: f32 = f32::NAN;
1792 assert_eq!(inf.acosh(), inf);
1793 assert!(neg_inf.acosh().is_nan());
1794 assert!(nan.acosh().is_nan());
1795 assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32);
1796 assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32);
1801 assert_eq!(0.0f32.atanh(), 0.0f32);
1802 assert_eq!((-0.0f32).atanh(), -0.0f32);
1804 let inf32: f32 = f32::INFINITY;
1805 let neg_inf32: f32 = f32::NEG_INFINITY;
1806 assert_eq!(1.0f32.atanh(), inf32);
1807 assert_eq!((-1.0f32).atanh(), neg_inf32);
1809 assert!(2f64.atanh().atanh().is_nan());
1810 assert!((-2f64).atanh().atanh().is_nan());
1812 let inf64: f32 = f32::INFINITY;
1813 let neg_inf64: f32 = f32::NEG_INFINITY;
1814 let nan32: f32 = f32::NAN;
1815 assert!(inf64.atanh().is_nan());
1816 assert!(neg_inf64.atanh().is_nan());
1817 assert!(nan32.atanh().is_nan());
1819 assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32);
1820 assert_approx_eq!((-0.5f32).atanh(), -0.54930614433405484569762261846126285f32);
1824 fn test_real_consts() {
1827 let pi: f32 = consts::PI;
1828 let frac_pi_2: f32 = consts::FRAC_PI_2;
1829 let frac_pi_3: f32 = consts::FRAC_PI_3;
1830 let frac_pi_4: f32 = consts::FRAC_PI_4;
1831 let frac_pi_6: f32 = consts::FRAC_PI_6;
1832 let frac_pi_8: f32 = consts::FRAC_PI_8;
1833 let frac_1_pi: f32 = consts::FRAC_1_PI;
1834 let frac_2_pi: f32 = consts::FRAC_2_PI;
1835 let frac_2_sqrtpi: f32 = consts::FRAC_2_SQRT_PI;
1836 let sqrt2: f32 = consts::SQRT_2;
1837 let frac_1_sqrt2: f32 = consts::FRAC_1_SQRT_2;
1838 let e: f32 = consts::E;
1839 let log2_e: f32 = consts::LOG2_E;
1840 let log10_e: f32 = consts::LOG10_E;
1841 let ln_2: f32 = consts::LN_2;
1842 let ln_10: f32 = consts::LN_10;
1844 assert_approx_eq!(frac_pi_2, pi / 2f32);
1845 assert_approx_eq!(frac_pi_3, pi / 3f32);
1846 assert_approx_eq!(frac_pi_4, pi / 4f32);
1847 assert_approx_eq!(frac_pi_6, pi / 6f32);
1848 assert_approx_eq!(frac_pi_8, pi / 8f32);
1849 assert_approx_eq!(frac_1_pi, 1f32 / pi);
1850 assert_approx_eq!(frac_2_pi, 2f32 / pi);
1851 assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt());
1852 assert_approx_eq!(sqrt2, 2f32.sqrt());
1853 assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt());
1854 assert_approx_eq!(log2_e, e.log2());
1855 assert_approx_eq!(log10_e, e.log10());
1856 assert_approx_eq!(ln_2, 2f32.ln());
1857 assert_approx_eq!(ln_10, 10f32.ln());