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)]
19 #[cfg(not(target_env = "msvc"))]
22 use num::{FpCategory, ParseFloatError};
24 pub use core::f32::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON};
25 pub use core::f32::{MIN_EXP, MAX_EXP, MIN_10_EXP};
26 pub use core::f32::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
27 pub use core::f32::{MIN, MIN_POSITIVE, MAX};
28 pub use core::f32::consts;
32 use libc::{c_float, c_int};
35 pub fn cbrtf(n: c_float) -> c_float;
36 pub fn erff(n: c_float) -> c_float;
37 pub fn erfcf(n: c_float) -> c_float;
38 pub fn expm1f(n: c_float) -> c_float;
39 pub fn fdimf(a: c_float, b: c_float) -> c_float;
40 pub fn fmaxf(a: c_float, b: c_float) -> c_float;
41 pub fn fminf(a: c_float, b: c_float) -> c_float;
42 pub fn fmodf(a: c_float, b: c_float) -> c_float;
43 pub fn nextafterf(x: c_float, y: c_float) -> c_float;
44 pub fn logbf(n: c_float) -> c_float;
45 pub fn log1pf(n: c_float) -> c_float;
46 pub fn ilogbf(n: c_float) -> c_int;
47 pub fn modff(n: c_float, iptr: &mut c_float) -> c_float;
48 pub fn tgammaf(n: c_float) -> c_float;
50 #[cfg_attr(all(windows, target_env = "msvc"), link_name = "__lgammaf_r")]
51 pub fn lgammaf_r(n: c_float, sign: &mut c_int) -> c_float;
52 #[cfg_attr(all(windows, target_env = "msvc"), link_name = "_hypotf")]
53 pub fn hypotf(x: c_float, y: c_float) -> c_float;
56 // See the comments in `core::float::Float::floor` for why MSVC is special
58 #[cfg(not(target_env = "msvc"))]
60 pub fn acosf(n: c_float) -> c_float;
61 pub fn asinf(n: c_float) -> c_float;
62 pub fn atan2f(a: c_float, b: c_float) -> c_float;
63 pub fn atanf(n: c_float) -> c_float;
64 pub fn coshf(n: c_float) -> c_float;
65 pub fn frexpf(n: c_float, value: &mut c_int) -> c_float;
66 pub fn ldexpf(x: c_float, n: c_int) -> c_float;
67 pub fn sinhf(n: c_float) -> c_float;
68 pub fn tanf(n: c_float) -> c_float;
69 pub fn tanhf(n: c_float) -> c_float;
72 #[cfg(target_env = "msvc")]
73 pub use self::shims::*;
74 #[cfg(target_env = "msvc")]
76 use libc::{c_float, c_int};
78 pub unsafe fn acosf(n: c_float) -> c_float {
79 f64::acos(n as f64) as c_float
82 pub unsafe fn asinf(n: c_float) -> c_float {
83 f64::asin(n as f64) as c_float
86 pub unsafe fn atan2f(n: c_float, b: c_float) -> c_float {
87 f64::atan2(n as f64, b as f64) as c_float
90 pub unsafe fn atanf(n: c_float) -> c_float {
91 f64::atan(n as f64) as c_float
94 pub unsafe fn coshf(n: c_float) -> c_float {
95 f64::cosh(n as f64) as c_float
98 pub unsafe fn frexpf(x: c_float, value: &mut c_int) -> c_float {
99 let (a, b) = f64::frexp(x as f64);
104 pub unsafe fn ldexpf(x: c_float, n: c_int) -> c_float {
105 f64::ldexp(x as f64, n as isize) as c_float
108 pub unsafe fn sinhf(n: c_float) -> c_float {
109 f64::sinh(n as f64) as c_float
112 pub unsafe fn tanf(n: c_float) -> c_float {
113 f64::tan(n as f64) as c_float
116 pub unsafe fn tanhf(n: c_float) -> c_float {
117 f64::tanh(n as f64) as c_float
124 #[stable(feature = "rust1", since = "1.0.0")]
126 /// Parses a float as with a given radix
127 #[unstable(feature = "float_from_str_radix", reason = "recently moved API",
129 pub fn from_str_radix(s: &str, radix: u32) -> Result<f32, ParseFloatError> {
130 num::Float::from_str_radix(s, radix)
133 /// Returns `true` if this value is `NaN` and false otherwise.
138 /// let nan = f32::NAN;
141 /// assert!(nan.is_nan());
142 /// assert!(!f.is_nan());
144 #[stable(feature = "rust1", since = "1.0.0")]
146 pub fn is_nan(self) -> bool { num::Float::is_nan(self) }
148 /// Returns `true` if this value is positive infinity or negative infinity and
155 /// let inf = f32::INFINITY;
156 /// let neg_inf = f32::NEG_INFINITY;
157 /// let nan = f32::NAN;
159 /// assert!(!f.is_infinite());
160 /// assert!(!nan.is_infinite());
162 /// assert!(inf.is_infinite());
163 /// assert!(neg_inf.is_infinite());
165 #[stable(feature = "rust1", since = "1.0.0")]
167 pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) }
169 /// Returns `true` if this number is neither infinite nor `NaN`.
175 /// let inf = f32::INFINITY;
176 /// let neg_inf = f32::NEG_INFINITY;
177 /// let nan = f32::NAN;
179 /// assert!(f.is_finite());
181 /// assert!(!nan.is_finite());
182 /// assert!(!inf.is_finite());
183 /// assert!(!neg_inf.is_finite());
185 #[stable(feature = "rust1", since = "1.0.0")]
187 pub fn is_finite(self) -> bool { num::Float::is_finite(self) }
189 /// Returns `true` if the number is neither zero, infinite,
190 /// [subnormal][subnormal], or `NaN`.
195 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
196 /// let max = f32::MAX;
197 /// let lower_than_min = 1.0e-40_f32;
198 /// let zero = 0.0_f32;
200 /// assert!(min.is_normal());
201 /// assert!(max.is_normal());
203 /// assert!(!zero.is_normal());
204 /// assert!(!f32::NAN.is_normal());
205 /// assert!(!f32::INFINITY.is_normal());
206 /// // Values between `0` and `min` are Subnormal.
207 /// assert!(!lower_than_min.is_normal());
209 /// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number
210 #[stable(feature = "rust1", since = "1.0.0")]
212 pub fn is_normal(self) -> bool { num::Float::is_normal(self) }
214 /// Returns the floating point category of the number. If only one property
215 /// is going to be tested, it is generally faster to use the specific
216 /// predicate instead.
219 /// use std::num::FpCategory;
222 /// let num = 12.4_f32;
223 /// let inf = f32::INFINITY;
225 /// assert_eq!(num.classify(), FpCategory::Normal);
226 /// assert_eq!(inf.classify(), FpCategory::Infinite);
228 #[stable(feature = "rust1", since = "1.0.0")]
230 pub fn classify(self) -> FpCategory { num::Float::classify(self) }
232 /// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
233 /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
234 /// The floating point encoding is documented in the [Reference][floating-point].
237 /// #![feature(float_extras)]
241 /// let num = 2.0f32;
243 /// // (8388608, -22, 1)
244 /// let (mantissa, exponent, sign) = num.integer_decode();
245 /// let sign_f = sign as f32;
246 /// let mantissa_f = mantissa as f32;
247 /// let exponent_f = num.powf(exponent as f32);
249 /// // 1 * 8388608 * 2^(-22) == 2
250 /// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
252 /// assert!(abs_difference <= f32::EPSILON);
254 /// [floating-point]: ../../../../../reference.html#machine-types
255 #[unstable(feature = "float_extras", reason = "signature is undecided",
258 pub fn integer_decode(self) -> (u64, i16, i8) {
259 num::Float::integer_decode(self)
262 /// Returns the largest integer less than or equal to a number.
265 /// let f = 3.99_f32;
268 /// assert_eq!(f.floor(), 3.0);
269 /// assert_eq!(g.floor(), 3.0);
271 #[stable(feature = "rust1", since = "1.0.0")]
273 pub fn floor(self) -> f32 { num::Float::floor(self) }
275 /// Returns the smallest integer greater than or equal to a number.
278 /// let f = 3.01_f32;
281 /// assert_eq!(f.ceil(), 4.0);
282 /// assert_eq!(g.ceil(), 4.0);
284 #[stable(feature = "rust1", since = "1.0.0")]
286 pub fn ceil(self) -> f32 { num::Float::ceil(self) }
288 /// Returns the nearest integer to a number. Round half-way cases away from
293 /// let g = -3.3_f32;
295 /// assert_eq!(f.round(), 3.0);
296 /// assert_eq!(g.round(), -3.0);
298 #[stable(feature = "rust1", since = "1.0.0")]
300 pub fn round(self) -> f32 { num::Float::round(self) }
302 /// Returns the integer part of a number.
306 /// let g = -3.7_f32;
308 /// assert_eq!(f.trunc(), 3.0);
309 /// assert_eq!(g.trunc(), -3.0);
311 #[stable(feature = "rust1", since = "1.0.0")]
313 pub fn trunc(self) -> f32 { num::Float::trunc(self) }
315 /// Returns the fractional part of a number.
321 /// let y = -3.5_f32;
322 /// let abs_difference_x = (x.fract() - 0.5).abs();
323 /// let abs_difference_y = (y.fract() - (-0.5)).abs();
325 /// assert!(abs_difference_x <= f32::EPSILON);
326 /// assert!(abs_difference_y <= f32::EPSILON);
328 #[stable(feature = "rust1", since = "1.0.0")]
330 pub fn fract(self) -> f32 { num::Float::fract(self) }
332 /// Computes the absolute value of `self`. Returns `NAN` if the
339 /// let y = -3.5_f32;
341 /// let abs_difference_x = (x.abs() - x).abs();
342 /// let abs_difference_y = (y.abs() - (-y)).abs();
344 /// assert!(abs_difference_x <= f32::EPSILON);
345 /// assert!(abs_difference_y <= f32::EPSILON);
347 /// assert!(f32::NAN.abs().is_nan());
349 #[stable(feature = "rust1", since = "1.0.0")]
351 pub fn abs(self) -> f32 { num::Float::abs(self) }
353 /// Returns a number that represents the sign of `self`.
355 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
356 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
357 /// - `NAN` if the number is `NAN`
364 /// assert_eq!(f.signum(), 1.0);
365 /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
367 /// assert!(f32::NAN.signum().is_nan());
369 #[stable(feature = "rust1", since = "1.0.0")]
371 pub fn signum(self) -> f32 { num::Float::signum(self) }
373 /// Returns `true` if `self`'s sign bit is positive, including
374 /// `+0.0` and `INFINITY`.
379 /// let nan = f32::NAN;
381 /// let g = -7.0_f32;
383 /// assert!(f.is_sign_positive());
384 /// assert!(!g.is_sign_positive());
385 /// // Requires both tests to determine if is `NaN`
386 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
388 #[stable(feature = "rust1", since = "1.0.0")]
390 pub fn is_sign_positive(self) -> bool { num::Float::is_positive(self) }
392 /// Returns `true` if `self`'s sign is negative, including `-0.0`
393 /// and `NEG_INFINITY`.
398 /// let nan = f32::NAN;
402 /// assert!(!f.is_sign_negative());
403 /// assert!(g.is_sign_negative());
404 /// // Requires both tests to determine if is `NaN`.
405 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
407 #[stable(feature = "rust1", since = "1.0.0")]
409 pub fn is_sign_negative(self) -> bool { num::Float::is_negative(self) }
411 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
412 /// error. This produces a more accurate result with better performance than
413 /// a separate multiplication operation followed by an add.
418 /// let m = 10.0_f32;
420 /// let b = 60.0_f32;
423 /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
425 /// assert!(abs_difference <= f32::EPSILON);
427 #[stable(feature = "rust1", since = "1.0.0")]
429 pub fn mul_add(self, a: f32, b: f32) -> f32 { num::Float::mul_add(self, a, b) }
431 /// Takes the reciprocal (inverse) of a number, `1/x`.
437 /// let abs_difference = (x.recip() - (1.0/x)).abs();
439 /// assert!(abs_difference <= f32::EPSILON);
441 #[stable(feature = "rust1", since = "1.0.0")]
443 pub fn recip(self) -> f32 { num::Float::recip(self) }
445 /// Raises a number to an integer power.
447 /// Using this function is generally faster than using `powf`
453 /// let abs_difference = (x.powi(2) - x*x).abs();
455 /// assert!(abs_difference <= f32::EPSILON);
457 #[stable(feature = "rust1", since = "1.0.0")]
459 pub fn powi(self, n: i32) -> f32 { num::Float::powi(self, n) }
461 /// Raises a number to a floating point power.
467 /// let abs_difference = (x.powf(2.0) - x*x).abs();
469 /// assert!(abs_difference <= f32::EPSILON);
471 #[stable(feature = "rust1", since = "1.0.0")]
473 pub fn powf(self, n: f32) -> f32 { num::Float::powf(self, n) }
475 /// Takes the square root of a number.
477 /// Returns NaN if `self` is a negative number.
482 /// let positive = 4.0_f32;
483 /// let negative = -4.0_f32;
485 /// let abs_difference = (positive.sqrt() - 2.0).abs();
487 /// assert!(abs_difference <= f32::EPSILON);
488 /// assert!(negative.sqrt().is_nan());
490 #[stable(feature = "rust1", since = "1.0.0")]
492 pub fn sqrt(self) -> f32 { num::Float::sqrt(self) }
494 /// Returns `e^(self)`, (the exponential function).
499 /// let one = 1.0f32;
501 /// let e = one.exp();
503 /// // ln(e) - 1 == 0
504 /// let abs_difference = (e.ln() - 1.0).abs();
506 /// assert!(abs_difference <= f32::EPSILON);
508 #[stable(feature = "rust1", since = "1.0.0")]
510 pub fn exp(self) -> f32 { num::Float::exp(self) }
512 /// Returns `2^(self)`.
520 /// let abs_difference = (f.exp2() - 4.0).abs();
522 /// assert!(abs_difference <= f32::EPSILON);
524 #[stable(feature = "rust1", since = "1.0.0")]
526 pub fn exp2(self) -> f32 { num::Float::exp2(self) }
528 /// Returns the natural logarithm of the number.
533 /// let one = 1.0f32;
535 /// let e = one.exp();
537 /// // ln(e) - 1 == 0
538 /// let abs_difference = (e.ln() - 1.0).abs();
540 /// assert!(abs_difference <= f32::EPSILON);
542 #[stable(feature = "rust1", since = "1.0.0")]
544 pub fn ln(self) -> f32 { num::Float::ln(self) }
546 /// Returns the logarithm of the number with respect to an arbitrary base.
551 /// let ten = 10.0f32;
552 /// let two = 2.0f32;
554 /// // log10(10) - 1 == 0
555 /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
557 /// // log2(2) - 1 == 0
558 /// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
560 /// assert!(abs_difference_10 <= f32::EPSILON);
561 /// assert!(abs_difference_2 <= f32::EPSILON);
563 #[stable(feature = "rust1", since = "1.0.0")]
565 pub fn log(self, base: f32) -> f32 { num::Float::log(self, base) }
567 /// Returns the base 2 logarithm of the number.
572 /// let two = 2.0f32;
574 /// // log2(2) - 1 == 0
575 /// let abs_difference = (two.log2() - 1.0).abs();
577 /// assert!(abs_difference <= f32::EPSILON);
579 #[stable(feature = "rust1", since = "1.0.0")]
581 pub fn log2(self) -> f32 { num::Float::log2(self) }
583 /// Returns the base 10 logarithm of the number.
588 /// let ten = 10.0f32;
590 /// // log10(10) - 1 == 0
591 /// let abs_difference = (ten.log10() - 1.0).abs();
593 /// assert!(abs_difference <= f32::EPSILON);
595 #[stable(feature = "rust1", since = "1.0.0")]
597 pub fn log10(self) -> f32 { num::Float::log10(self) }
599 /// Converts radians to degrees.
602 /// #![feature(float_extras)]
604 /// use std::f32::{self, consts};
606 /// let angle = consts::PI;
608 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
610 /// assert!(abs_difference <= f32::EPSILON);
612 #[unstable(feature = "float_extras", reason = "desirability is unclear",
615 pub fn to_degrees(self) -> f32 { num::Float::to_degrees(self) }
617 /// Converts degrees to radians.
620 /// #![feature(float_extras)]
622 /// use std::f32::{self, consts};
624 /// let angle = 180.0f32;
626 /// let abs_difference = (angle.to_radians() - consts::PI).abs();
628 /// assert!(abs_difference <= f32::EPSILON);
630 #[unstable(feature = "float_extras", reason = "desirability is unclear",
633 pub fn to_radians(self) -> f32 { num::Float::to_radians(self) }
635 /// Constructs a floating point number of `x*2^exp`.
638 /// #![feature(float_extras)]
641 /// // 3*2^2 - 12 == 0
642 /// let abs_difference = (f32::ldexp(3.0, 2) - 12.0).abs();
644 /// assert!(abs_difference <= f32::EPSILON);
646 #[unstable(feature = "float_extras",
647 reason = "pending integer conventions",
650 pub fn ldexp(x: f32, exp: isize) -> f32 {
651 unsafe { cmath::ldexpf(x, exp as c_int) }
654 /// Breaks the number into a normalized fraction and a base-2 exponent,
657 /// * `self = x * 2^exp`
658 /// * `0.5 <= abs(x) < 1.0`
661 /// #![feature(float_extras)]
667 /// // (1/2)*2^3 -> 1 * 8/2 -> 4.0
668 /// let f = x.frexp();
669 /// let abs_difference_0 = (f.0 - 0.5).abs();
670 /// let abs_difference_1 = (f.1 as f32 - 3.0).abs();
672 /// assert!(abs_difference_0 <= f32::EPSILON);
673 /// assert!(abs_difference_1 <= f32::EPSILON);
675 #[unstable(feature = "float_extras",
676 reason = "pending integer conventions",
679 pub fn frexp(self) -> (f32, isize) {
682 let x = cmath::frexpf(self, &mut exp);
687 /// Returns the next representable floating-point value in the direction of
691 /// #![feature(float_extras)]
697 /// let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs();
699 /// assert!(abs_diff <= f32::EPSILON);
701 #[unstable(feature = "float_extras",
702 reason = "unsure about its place in the world",
705 pub fn next_after(self, other: f32) -> f32 {
706 unsafe { cmath::nextafterf(self, other) }
709 /// Returns the maximum of the two numbers.
715 /// assert_eq!(x.max(y), y);
718 /// If one of the arguments is NaN, then the other argument is returned.
719 #[stable(feature = "rust1", since = "1.0.0")]
721 pub fn max(self, other: f32) -> f32 {
722 unsafe { cmath::fmaxf(self, other) }
725 /// Returns the minimum of the two numbers.
731 /// assert_eq!(x.min(y), x);
734 /// If one of the arguments is NaN, then the other argument is returned.
735 #[stable(feature = "rust1", since = "1.0.0")]
737 pub fn min(self, other: f32) -> f32 {
738 unsafe { cmath::fminf(self, other) }
741 /// The positive difference of two numbers.
743 /// * If `self <= other`: `0:0`
744 /// * Else: `self - other`
752 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
753 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
755 /// assert!(abs_difference_x <= f32::EPSILON);
756 /// assert!(abs_difference_y <= f32::EPSILON);
758 #[stable(feature = "rust1", since = "1.0.0")]
760 pub fn abs_sub(self, other: f32) -> f32 {
761 unsafe { cmath::fdimf(self, other) }
764 /// Takes the cubic root of a number.
771 /// // x^(1/3) - 2 == 0
772 /// let abs_difference = (x.cbrt() - 2.0).abs();
774 /// assert!(abs_difference <= f32::EPSILON);
776 #[stable(feature = "rust1", since = "1.0.0")]
778 pub fn cbrt(self) -> f32 {
779 unsafe { cmath::cbrtf(self) }
782 /// Calculates the length of the hypotenuse of a right-angle triangle given
783 /// legs of length `x` and `y`.
791 /// // sqrt(x^2 + y^2)
792 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
794 /// assert!(abs_difference <= f32::EPSILON);
796 #[stable(feature = "rust1", since = "1.0.0")]
798 pub fn hypot(self, other: f32) -> f32 {
799 unsafe { cmath::hypotf(self, other) }
802 /// Computes the sine of a number (in radians).
807 /// let x = f32::consts::PI/2.0;
809 /// let abs_difference = (x.sin() - 1.0).abs();
811 /// assert!(abs_difference <= f32::EPSILON);
813 #[stable(feature = "rust1", since = "1.0.0")]
815 pub fn sin(self) -> f32 {
818 // see notes in `core::f32::Float::floor`
819 #[cfg(target_env = "msvc")]
820 fn sinf(f: f32) -> f32 { (f as f64).sin() as f32 }
821 #[cfg(not(target_env = "msvc"))]
822 fn sinf(f: f32) -> f32 { unsafe { intrinsics::sinf32(f) } }
825 /// Computes the cosine of a number (in radians).
830 /// let x = 2.0*f32::consts::PI;
832 /// let abs_difference = (x.cos() - 1.0).abs();
834 /// assert!(abs_difference <= f32::EPSILON);
836 #[stable(feature = "rust1", since = "1.0.0")]
838 pub fn cos(self) -> f32 {
841 // see notes in `core::f32::Float::floor`
842 #[cfg(target_env = "msvc")]
843 fn cosf(f: f32) -> f32 { (f as f64).cos() as f32 }
844 #[cfg(not(target_env = "msvc"))]
845 fn cosf(f: f32) -> f32 { unsafe { intrinsics::cosf32(f) } }
848 /// Computes the tangent of a number (in radians).
853 /// let x = f64::consts::PI/4.0;
854 /// let abs_difference = (x.tan() - 1.0).abs();
856 /// assert!(abs_difference < 1e-10);
858 #[stable(feature = "rust1", since = "1.0.0")]
860 pub fn tan(self) -> f32 {
861 unsafe { cmath::tanf(self) }
864 /// Computes the arcsine of a number. Return value is in radians in
865 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
871 /// let f = f32::consts::PI / 2.0;
873 /// // asin(sin(pi/2))
874 /// let abs_difference = f.sin().asin().abs_sub(f32::consts::PI / 2.0);
876 /// assert!(abs_difference <= f32::EPSILON);
878 #[stable(feature = "rust1", since = "1.0.0")]
880 pub fn asin(self) -> f32 {
881 unsafe { cmath::asinf(self) }
884 /// Computes the arccosine of a number. Return value is in radians in
885 /// the range [0, pi] or NaN if the number is outside the range
891 /// let f = f32::consts::PI / 4.0;
893 /// // acos(cos(pi/4))
894 /// let abs_difference = f.cos().acos().abs_sub(f32::consts::PI / 4.0);
896 /// assert!(abs_difference <= f32::EPSILON);
898 #[stable(feature = "rust1", since = "1.0.0")]
900 pub fn acos(self) -> f32 {
901 unsafe { cmath::acosf(self) }
904 /// Computes the arctangent of a number. Return value is in radians in the
905 /// range [-pi/2, pi/2];
913 /// let abs_difference = f.tan().atan().abs_sub(1.0);
915 /// assert!(abs_difference <= f32::EPSILON);
917 #[stable(feature = "rust1", since = "1.0.0")]
919 pub fn atan(self) -> f32 {
920 unsafe { cmath::atanf(self) }
923 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
925 /// * `x = 0`, `y = 0`: `0`
926 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
927 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
928 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
933 /// let pi = f32::consts::PI;
934 /// // All angles from horizontal right (+x)
935 /// // 45 deg counter-clockwise
937 /// let y1 = -3.0f32;
939 /// // 135 deg clockwise
940 /// let x2 = -3.0f32;
943 /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
944 /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
946 /// assert!(abs_difference_1 <= f32::EPSILON);
947 /// assert!(abs_difference_2 <= f32::EPSILON);
949 #[stable(feature = "rust1", since = "1.0.0")]
951 pub fn atan2(self, other: f32) -> f32 {
952 unsafe { cmath::atan2f(self, other) }
955 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
956 /// `(sin(x), cos(x))`.
961 /// let x = f32::consts::PI/4.0;
962 /// let f = x.sin_cos();
964 /// let abs_difference_0 = (f.0 - x.sin()).abs();
965 /// let abs_difference_1 = (f.1 - x.cos()).abs();
967 /// assert!(abs_difference_0 <= f32::EPSILON);
968 /// assert!(abs_difference_0 <= f32::EPSILON);
970 #[stable(feature = "rust1", since = "1.0.0")]
972 pub fn sin_cos(self) -> (f32, f32) {
973 (self.sin(), self.cos())
976 /// Returns `e^(self) - 1` in a way that is accurate even if the
977 /// number is close to zero.
983 /// let abs_difference = x.ln().exp_m1().abs_sub(6.0);
985 /// assert!(abs_difference < 1e-10);
987 #[stable(feature = "rust1", since = "1.0.0")]
989 pub fn exp_m1(self) -> f32 {
990 unsafe { cmath::expm1f(self) }
993 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
994 /// the operations were performed separately.
999 /// let x = f32::consts::E - 1.0;
1001 /// // ln(1 + (e - 1)) == ln(e) == 1
1002 /// let abs_difference = (x.ln_1p() - 1.0).abs();
1004 /// assert!(abs_difference <= f32::EPSILON);
1006 #[stable(feature = "rust1", since = "1.0.0")]
1008 pub fn ln_1p(self) -> f32 {
1009 unsafe { cmath::log1pf(self) }
1012 /// Hyperbolic sine function.
1017 /// let e = f32::consts::E;
1020 /// let f = x.sinh();
1021 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
1022 /// let g = (e*e - 1.0)/(2.0*e);
1023 /// let abs_difference = (f - g).abs();
1025 /// assert!(abs_difference <= f32::EPSILON);
1027 #[stable(feature = "rust1", since = "1.0.0")]
1029 pub fn sinh(self) -> f32 {
1030 unsafe { cmath::sinhf(self) }
1033 /// Hyperbolic cosine function.
1038 /// let e = f32::consts::E;
1040 /// let f = x.cosh();
1041 /// // Solving cosh() at 1 gives this result
1042 /// let g = (e*e + 1.0)/(2.0*e);
1043 /// let abs_difference = f.abs_sub(g);
1046 /// assert!(abs_difference <= f32::EPSILON);
1048 #[stable(feature = "rust1", since = "1.0.0")]
1050 pub fn cosh(self) -> f32 {
1051 unsafe { cmath::coshf(self) }
1054 /// Hyperbolic tangent function.
1059 /// let e = f32::consts::E;
1062 /// let f = x.tanh();
1063 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1064 /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
1065 /// let abs_difference = (f - g).abs();
1067 /// assert!(abs_difference <= f32::EPSILON);
1069 #[stable(feature = "rust1", since = "1.0.0")]
1071 pub fn tanh(self) -> f32 {
1072 unsafe { cmath::tanhf(self) }
1075 /// Inverse hyperbolic sine function.
1081 /// let f = x.sinh().asinh();
1083 /// let abs_difference = (f - x).abs();
1085 /// assert!(abs_difference <= f32::EPSILON);
1087 #[stable(feature = "rust1", since = "1.0.0")]
1089 pub fn asinh(self) -> f32 {
1091 NEG_INFINITY => NEG_INFINITY,
1092 x => (x + ((x * x) + 1.0).sqrt()).ln(),
1096 /// Inverse hyperbolic cosine function.
1102 /// let f = x.cosh().acosh();
1104 /// let abs_difference = (f - x).abs();
1106 /// assert!(abs_difference <= f32::EPSILON);
1108 #[stable(feature = "rust1", since = "1.0.0")]
1110 pub fn acosh(self) -> f32 {
1112 x if x < 1.0 => ::f32::NAN,
1113 x => (x + ((x * x) - 1.0).sqrt()).ln(),
1117 /// Inverse hyperbolic tangent function.
1122 /// let e = f32::consts::E;
1123 /// let f = e.tanh().atanh();
1125 /// let abs_difference = f.abs_sub(e);
1127 /// assert!(abs_difference <= f32::EPSILON);
1129 #[stable(feature = "rust1", since = "1.0.0")]
1131 pub fn atanh(self) -> f32 {
1132 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1141 use num::FpCategory as Fp;
1145 test_num(10f32, 2f32);
1150 assert_eq!(NAN.min(2.0), 2.0);
1151 assert_eq!(2.0f32.min(NAN), 2.0);
1156 assert_eq!(NAN.max(2.0), 2.0);
1157 assert_eq!(2.0f32.max(NAN), 2.0);
1162 let nan: f32 = f32::NAN;
1163 assert!(nan.is_nan());
1164 assert!(!nan.is_infinite());
1165 assert!(!nan.is_finite());
1166 assert!(!nan.is_normal());
1167 assert!(!nan.is_sign_positive());
1168 assert!(!nan.is_sign_negative());
1169 assert_eq!(Fp::Nan, nan.classify());
1173 fn test_infinity() {
1174 let inf: f32 = f32::INFINITY;
1175 assert!(inf.is_infinite());
1176 assert!(!inf.is_finite());
1177 assert!(inf.is_sign_positive());
1178 assert!(!inf.is_sign_negative());
1179 assert!(!inf.is_nan());
1180 assert!(!inf.is_normal());
1181 assert_eq!(Fp::Infinite, inf.classify());
1185 fn test_neg_infinity() {
1186 let neg_inf: f32 = f32::NEG_INFINITY;
1187 assert!(neg_inf.is_infinite());
1188 assert!(!neg_inf.is_finite());
1189 assert!(!neg_inf.is_sign_positive());
1190 assert!(neg_inf.is_sign_negative());
1191 assert!(!neg_inf.is_nan());
1192 assert!(!neg_inf.is_normal());
1193 assert_eq!(Fp::Infinite, neg_inf.classify());
1198 let zero: f32 = 0.0f32;
1199 assert_eq!(0.0, zero);
1200 assert!(!zero.is_infinite());
1201 assert!(zero.is_finite());
1202 assert!(zero.is_sign_positive());
1203 assert!(!zero.is_sign_negative());
1204 assert!(!zero.is_nan());
1205 assert!(!zero.is_normal());
1206 assert_eq!(Fp::Zero, zero.classify());
1210 fn test_neg_zero() {
1211 let neg_zero: f32 = -0.0;
1212 assert_eq!(0.0, neg_zero);
1213 assert!(!neg_zero.is_infinite());
1214 assert!(neg_zero.is_finite());
1215 assert!(!neg_zero.is_sign_positive());
1216 assert!(neg_zero.is_sign_negative());
1217 assert!(!neg_zero.is_nan());
1218 assert!(!neg_zero.is_normal());
1219 assert_eq!(Fp::Zero, neg_zero.classify());
1224 let one: f32 = 1.0f32;
1225 assert_eq!(1.0, one);
1226 assert!(!one.is_infinite());
1227 assert!(one.is_finite());
1228 assert!(one.is_sign_positive());
1229 assert!(!one.is_sign_negative());
1230 assert!(!one.is_nan());
1231 assert!(one.is_normal());
1232 assert_eq!(Fp::Normal, one.classify());
1237 let nan: f32 = f32::NAN;
1238 let inf: f32 = f32::INFINITY;
1239 let neg_inf: f32 = f32::NEG_INFINITY;
1240 assert!(nan.is_nan());
1241 assert!(!0.0f32.is_nan());
1242 assert!(!5.3f32.is_nan());
1243 assert!(!(-10.732f32).is_nan());
1244 assert!(!inf.is_nan());
1245 assert!(!neg_inf.is_nan());
1249 fn test_is_infinite() {
1250 let nan: f32 = f32::NAN;
1251 let inf: f32 = f32::INFINITY;
1252 let neg_inf: f32 = f32::NEG_INFINITY;
1253 assert!(!nan.is_infinite());
1254 assert!(inf.is_infinite());
1255 assert!(neg_inf.is_infinite());
1256 assert!(!0.0f32.is_infinite());
1257 assert!(!42.8f32.is_infinite());
1258 assert!(!(-109.2f32).is_infinite());
1262 fn test_is_finite() {
1263 let nan: f32 = f32::NAN;
1264 let inf: f32 = f32::INFINITY;
1265 let neg_inf: f32 = f32::NEG_INFINITY;
1266 assert!(!nan.is_finite());
1267 assert!(!inf.is_finite());
1268 assert!(!neg_inf.is_finite());
1269 assert!(0.0f32.is_finite());
1270 assert!(42.8f32.is_finite());
1271 assert!((-109.2f32).is_finite());
1275 fn test_is_normal() {
1276 let nan: f32 = f32::NAN;
1277 let inf: f32 = f32::INFINITY;
1278 let neg_inf: f32 = f32::NEG_INFINITY;
1279 let zero: f32 = 0.0f32;
1280 let neg_zero: f32 = -0.0;
1281 assert!(!nan.is_normal());
1282 assert!(!inf.is_normal());
1283 assert!(!neg_inf.is_normal());
1284 assert!(!zero.is_normal());
1285 assert!(!neg_zero.is_normal());
1286 assert!(1f32.is_normal());
1287 assert!(1e-37f32.is_normal());
1288 assert!(!1e-38f32.is_normal());
1292 fn test_classify() {
1293 let nan: f32 = f32::NAN;
1294 let inf: f32 = f32::INFINITY;
1295 let neg_inf: f32 = f32::NEG_INFINITY;
1296 let zero: f32 = 0.0f32;
1297 let neg_zero: f32 = -0.0;
1298 assert_eq!(nan.classify(), Fp::Nan);
1299 assert_eq!(inf.classify(), Fp::Infinite);
1300 assert_eq!(neg_inf.classify(), Fp::Infinite);
1301 assert_eq!(zero.classify(), Fp::Zero);
1302 assert_eq!(neg_zero.classify(), Fp::Zero);
1303 assert_eq!(1f32.classify(), Fp::Normal);
1304 assert_eq!(1e-37f32.classify(), Fp::Normal);
1305 assert_eq!(1e-38f32.classify(), Fp::Subnormal);
1309 fn test_integer_decode() {
1310 assert_eq!(3.14159265359f32.integer_decode(), (13176795, -22, 1));
1311 assert_eq!((-8573.5918555f32).integer_decode(), (8779358, -10, -1));
1312 assert_eq!(2f32.powf(100.0).integer_decode(), (8388608, 77, 1));
1313 assert_eq!(0f32.integer_decode(), (0, -150, 1));
1314 assert_eq!((-0f32).integer_decode(), (0, -150, -1));
1315 assert_eq!(INFINITY.integer_decode(), (8388608, 105, 1));
1316 assert_eq!(NEG_INFINITY.integer_decode(), (8388608, 105, -1));
1317 assert_eq!(NAN.integer_decode(), (12582912, 105, 1));
1322 assert_approx_eq!(1.0f32.floor(), 1.0f32);
1323 assert_approx_eq!(1.3f32.floor(), 1.0f32);
1324 assert_approx_eq!(1.5f32.floor(), 1.0f32);
1325 assert_approx_eq!(1.7f32.floor(), 1.0f32);
1326 assert_approx_eq!(0.0f32.floor(), 0.0f32);
1327 assert_approx_eq!((-0.0f32).floor(), -0.0f32);
1328 assert_approx_eq!((-1.0f32).floor(), -1.0f32);
1329 assert_approx_eq!((-1.3f32).floor(), -2.0f32);
1330 assert_approx_eq!((-1.5f32).floor(), -2.0f32);
1331 assert_approx_eq!((-1.7f32).floor(), -2.0f32);
1336 assert_approx_eq!(1.0f32.ceil(), 1.0f32);
1337 assert_approx_eq!(1.3f32.ceil(), 2.0f32);
1338 assert_approx_eq!(1.5f32.ceil(), 2.0f32);
1339 assert_approx_eq!(1.7f32.ceil(), 2.0f32);
1340 assert_approx_eq!(0.0f32.ceil(), 0.0f32);
1341 assert_approx_eq!((-0.0f32).ceil(), -0.0f32);
1342 assert_approx_eq!((-1.0f32).ceil(), -1.0f32);
1343 assert_approx_eq!((-1.3f32).ceil(), -1.0f32);
1344 assert_approx_eq!((-1.5f32).ceil(), -1.0f32);
1345 assert_approx_eq!((-1.7f32).ceil(), -1.0f32);
1350 assert_approx_eq!(1.0f32.round(), 1.0f32);
1351 assert_approx_eq!(1.3f32.round(), 1.0f32);
1352 assert_approx_eq!(1.5f32.round(), 2.0f32);
1353 assert_approx_eq!(1.7f32.round(), 2.0f32);
1354 assert_approx_eq!(0.0f32.round(), 0.0f32);
1355 assert_approx_eq!((-0.0f32).round(), -0.0f32);
1356 assert_approx_eq!((-1.0f32).round(), -1.0f32);
1357 assert_approx_eq!((-1.3f32).round(), -1.0f32);
1358 assert_approx_eq!((-1.5f32).round(), -2.0f32);
1359 assert_approx_eq!((-1.7f32).round(), -2.0f32);
1364 assert_approx_eq!(1.0f32.trunc(), 1.0f32);
1365 assert_approx_eq!(1.3f32.trunc(), 1.0f32);
1366 assert_approx_eq!(1.5f32.trunc(), 1.0f32);
1367 assert_approx_eq!(1.7f32.trunc(), 1.0f32);
1368 assert_approx_eq!(0.0f32.trunc(), 0.0f32);
1369 assert_approx_eq!((-0.0f32).trunc(), -0.0f32);
1370 assert_approx_eq!((-1.0f32).trunc(), -1.0f32);
1371 assert_approx_eq!((-1.3f32).trunc(), -1.0f32);
1372 assert_approx_eq!((-1.5f32).trunc(), -1.0f32);
1373 assert_approx_eq!((-1.7f32).trunc(), -1.0f32);
1378 assert_approx_eq!(1.0f32.fract(), 0.0f32);
1379 assert_approx_eq!(1.3f32.fract(), 0.3f32);
1380 assert_approx_eq!(1.5f32.fract(), 0.5f32);
1381 assert_approx_eq!(1.7f32.fract(), 0.7f32);
1382 assert_approx_eq!(0.0f32.fract(), 0.0f32);
1383 assert_approx_eq!((-0.0f32).fract(), -0.0f32);
1384 assert_approx_eq!((-1.0f32).fract(), -0.0f32);
1385 assert_approx_eq!((-1.3f32).fract(), -0.3f32);
1386 assert_approx_eq!((-1.5f32).fract(), -0.5f32);
1387 assert_approx_eq!((-1.7f32).fract(), -0.7f32);
1392 assert_eq!(INFINITY.abs(), INFINITY);
1393 assert_eq!(1f32.abs(), 1f32);
1394 assert_eq!(0f32.abs(), 0f32);
1395 assert_eq!((-0f32).abs(), 0f32);
1396 assert_eq!((-1f32).abs(), 1f32);
1397 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1398 assert_eq!((1f32/NEG_INFINITY).abs(), 0f32);
1399 assert!(NAN.abs().is_nan());
1404 assert_eq!(INFINITY.signum(), 1f32);
1405 assert_eq!(1f32.signum(), 1f32);
1406 assert_eq!(0f32.signum(), 1f32);
1407 assert_eq!((-0f32).signum(), -1f32);
1408 assert_eq!((-1f32).signum(), -1f32);
1409 assert_eq!(NEG_INFINITY.signum(), -1f32);
1410 assert_eq!((1f32/NEG_INFINITY).signum(), -1f32);
1411 assert!(NAN.signum().is_nan());
1415 fn test_is_sign_positive() {
1416 assert!(INFINITY.is_sign_positive());
1417 assert!(1f32.is_sign_positive());
1418 assert!(0f32.is_sign_positive());
1419 assert!(!(-0f32).is_sign_positive());
1420 assert!(!(-1f32).is_sign_positive());
1421 assert!(!NEG_INFINITY.is_sign_positive());
1422 assert!(!(1f32/NEG_INFINITY).is_sign_positive());
1423 assert!(!NAN.is_sign_positive());
1427 fn test_is_sign_negative() {
1428 assert!(!INFINITY.is_sign_negative());
1429 assert!(!1f32.is_sign_negative());
1430 assert!(!0f32.is_sign_negative());
1431 assert!((-0f32).is_sign_negative());
1432 assert!((-1f32).is_sign_negative());
1433 assert!(NEG_INFINITY.is_sign_negative());
1434 assert!((1f32/NEG_INFINITY).is_sign_negative());
1435 assert!(!NAN.is_sign_negative());
1440 let nan: f32 = f32::NAN;
1441 let inf: f32 = f32::INFINITY;
1442 let neg_inf: f32 = f32::NEG_INFINITY;
1443 assert_approx_eq!(12.3f32.mul_add(4.5, 6.7), 62.05);
1444 assert_approx_eq!((-12.3f32).mul_add(-4.5, -6.7), 48.65);
1445 assert_approx_eq!(0.0f32.mul_add(8.9, 1.2), 1.2);
1446 assert_approx_eq!(3.4f32.mul_add(-0.0, 5.6), 5.6);
1447 assert!(nan.mul_add(7.8, 9.0).is_nan());
1448 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1449 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1450 assert_eq!(8.9f32.mul_add(inf, 3.2), inf);
1451 assert_eq!((-3.2f32).mul_add(2.4, neg_inf), neg_inf);
1456 let nan: f32 = f32::NAN;
1457 let inf: f32 = f32::INFINITY;
1458 let neg_inf: f32 = f32::NEG_INFINITY;
1459 assert_eq!(1.0f32.recip(), 1.0);
1460 assert_eq!(2.0f32.recip(), 0.5);
1461 assert_eq!((-0.4f32).recip(), -2.5);
1462 assert_eq!(0.0f32.recip(), inf);
1463 assert!(nan.recip().is_nan());
1464 assert_eq!(inf.recip(), 0.0);
1465 assert_eq!(neg_inf.recip(), 0.0);
1470 let nan: f32 = f32::NAN;
1471 let inf: f32 = f32::INFINITY;
1472 let neg_inf: f32 = f32::NEG_INFINITY;
1473 assert_eq!(1.0f32.powi(1), 1.0);
1474 assert_approx_eq!((-3.1f32).powi(2), 9.61);
1475 assert_approx_eq!(5.9f32.powi(-2), 0.028727);
1476 assert_eq!(8.3f32.powi(0), 1.0);
1477 assert!(nan.powi(2).is_nan());
1478 assert_eq!(inf.powi(3), inf);
1479 assert_eq!(neg_inf.powi(2), inf);
1484 let nan: f32 = f32::NAN;
1485 let inf: f32 = f32::INFINITY;
1486 let neg_inf: f32 = f32::NEG_INFINITY;
1487 assert_eq!(1.0f32.powf(1.0), 1.0);
1488 assert_approx_eq!(3.4f32.powf(4.5), 246.408218);
1489 assert_approx_eq!(2.7f32.powf(-3.2), 0.041652);
1490 assert_approx_eq!((-3.1f32).powf(2.0), 9.61);
1491 assert_approx_eq!(5.9f32.powf(-2.0), 0.028727);
1492 assert_eq!(8.3f32.powf(0.0), 1.0);
1493 assert!(nan.powf(2.0).is_nan());
1494 assert_eq!(inf.powf(2.0), inf);
1495 assert_eq!(neg_inf.powf(3.0), neg_inf);
1499 fn test_sqrt_domain() {
1500 assert!(NAN.sqrt().is_nan());
1501 assert!(NEG_INFINITY.sqrt().is_nan());
1502 assert!((-1.0f32).sqrt().is_nan());
1503 assert_eq!((-0.0f32).sqrt(), -0.0);
1504 assert_eq!(0.0f32.sqrt(), 0.0);
1505 assert_eq!(1.0f32.sqrt(), 1.0);
1506 assert_eq!(INFINITY.sqrt(), INFINITY);
1511 assert_eq!(1.0, 0.0f32.exp());
1512 assert_approx_eq!(2.718282, 1.0f32.exp());
1513 assert_approx_eq!(148.413162, 5.0f32.exp());
1515 let inf: f32 = f32::INFINITY;
1516 let neg_inf: f32 = f32::NEG_INFINITY;
1517 let nan: f32 = f32::NAN;
1518 assert_eq!(inf, inf.exp());
1519 assert_eq!(0.0, neg_inf.exp());
1520 assert!(nan.exp().is_nan());
1525 assert_eq!(32.0, 5.0f32.exp2());
1526 assert_eq!(1.0, 0.0f32.exp2());
1528 let inf: f32 = f32::INFINITY;
1529 let neg_inf: f32 = f32::NEG_INFINITY;
1530 let nan: f32 = f32::NAN;
1531 assert_eq!(inf, inf.exp2());
1532 assert_eq!(0.0, neg_inf.exp2());
1533 assert!(nan.exp2().is_nan());
1538 let nan: f32 = f32::NAN;
1539 let inf: f32 = f32::INFINITY;
1540 let neg_inf: f32 = f32::NEG_INFINITY;
1541 assert_approx_eq!(1.0f32.exp().ln(), 1.0);
1542 assert!(nan.ln().is_nan());
1543 assert_eq!(inf.ln(), inf);
1544 assert!(neg_inf.ln().is_nan());
1545 assert!((-2.3f32).ln().is_nan());
1546 assert_eq!((-0.0f32).ln(), neg_inf);
1547 assert_eq!(0.0f32.ln(), neg_inf);
1548 assert_approx_eq!(4.0f32.ln(), 1.386294);
1553 let nan: f32 = f32::NAN;
1554 let inf: f32 = f32::INFINITY;
1555 let neg_inf: f32 = f32::NEG_INFINITY;
1556 assert_eq!(10.0f32.log(10.0), 1.0);
1557 assert_approx_eq!(2.3f32.log(3.5), 0.664858);
1558 assert_eq!(1.0f32.exp().log(1.0f32.exp()), 1.0);
1559 assert!(1.0f32.log(1.0).is_nan());
1560 assert!(1.0f32.log(-13.9).is_nan());
1561 assert!(nan.log(2.3).is_nan());
1562 assert_eq!(inf.log(10.0), inf);
1563 assert!(neg_inf.log(8.8).is_nan());
1564 assert!((-2.3f32).log(0.1).is_nan());
1565 assert_eq!((-0.0f32).log(2.0), neg_inf);
1566 assert_eq!(0.0f32.log(7.0), neg_inf);
1571 let nan: f32 = f32::NAN;
1572 let inf: f32 = f32::INFINITY;
1573 let neg_inf: f32 = f32::NEG_INFINITY;
1574 assert_approx_eq!(10.0f32.log2(), 3.321928);
1575 assert_approx_eq!(2.3f32.log2(), 1.201634);
1576 assert_approx_eq!(1.0f32.exp().log2(), 1.442695);
1577 assert!(nan.log2().is_nan());
1578 assert_eq!(inf.log2(), inf);
1579 assert!(neg_inf.log2().is_nan());
1580 assert!((-2.3f32).log2().is_nan());
1581 assert_eq!((-0.0f32).log2(), neg_inf);
1582 assert_eq!(0.0f32.log2(), neg_inf);
1587 let nan: f32 = f32::NAN;
1588 let inf: f32 = f32::INFINITY;
1589 let neg_inf: f32 = f32::NEG_INFINITY;
1590 assert_eq!(10.0f32.log10(), 1.0);
1591 assert_approx_eq!(2.3f32.log10(), 0.361728);
1592 assert_approx_eq!(1.0f32.exp().log10(), 0.434294);
1593 assert_eq!(1.0f32.log10(), 0.0);
1594 assert!(nan.log10().is_nan());
1595 assert_eq!(inf.log10(), inf);
1596 assert!(neg_inf.log10().is_nan());
1597 assert!((-2.3f32).log10().is_nan());
1598 assert_eq!((-0.0f32).log10(), neg_inf);
1599 assert_eq!(0.0f32.log10(), neg_inf);
1603 fn test_to_degrees() {
1604 let pi: f32 = consts::PI;
1605 let nan: f32 = f32::NAN;
1606 let inf: f32 = f32::INFINITY;
1607 let neg_inf: f32 = f32::NEG_INFINITY;
1608 assert_eq!(0.0f32.to_degrees(), 0.0);
1609 assert_approx_eq!((-5.8f32).to_degrees(), -332.315521);
1610 assert_eq!(pi.to_degrees(), 180.0);
1611 assert!(nan.to_degrees().is_nan());
1612 assert_eq!(inf.to_degrees(), inf);
1613 assert_eq!(neg_inf.to_degrees(), neg_inf);
1617 fn test_to_radians() {
1618 let pi: f32 = consts::PI;
1619 let nan: f32 = f32::NAN;
1620 let inf: f32 = f32::INFINITY;
1621 let neg_inf: f32 = f32::NEG_INFINITY;
1622 assert_eq!(0.0f32.to_radians(), 0.0);
1623 assert_approx_eq!(154.6f32.to_radians(), 2.698279);
1624 assert_approx_eq!((-332.31f32).to_radians(), -5.799903);
1625 assert_eq!(180.0f32.to_radians(), pi);
1626 assert!(nan.to_radians().is_nan());
1627 assert_eq!(inf.to_radians(), inf);
1628 assert_eq!(neg_inf.to_radians(), neg_inf);
1633 // We have to use from_str until base-2 exponents
1634 // are supported in floating-point literals
1635 let f1: f32 = f32::from_str_radix("1p-123", 16).unwrap();
1636 let f2: f32 = f32::from_str_radix("1p-111", 16).unwrap();
1637 let f3: f32 = f32::from_str_radix("1.Cp-12", 16).unwrap();
1638 assert_eq!(f32::ldexp(1f32, -123), f1);
1639 assert_eq!(f32::ldexp(1f32, -111), f2);
1640 assert_eq!(f32::ldexp(1.75f32, -12), f3);
1642 assert_eq!(f32::ldexp(0f32, -123), 0f32);
1643 assert_eq!(f32::ldexp(-0f32, -123), -0f32);
1645 let inf: f32 = f32::INFINITY;
1646 let neg_inf: f32 = f32::NEG_INFINITY;
1647 let nan: f32 = f32::NAN;
1648 assert_eq!(f32::ldexp(inf, -123), inf);
1649 assert_eq!(f32::ldexp(neg_inf, -123), neg_inf);
1650 assert!(f32::ldexp(nan, -123).is_nan());
1655 // We have to use from_str until base-2 exponents
1656 // are supported in floating-point literals
1657 let f1: f32 = f32::from_str_radix("1p-123", 16).unwrap();
1658 let f2: f32 = f32::from_str_radix("1p-111", 16).unwrap();
1659 let f3: f32 = f32::from_str_radix("1.Cp-123", 16).unwrap();
1660 let (x1, exp1) = f1.frexp();
1661 let (x2, exp2) = f2.frexp();
1662 let (x3, exp3) = f3.frexp();
1663 assert_eq!((x1, exp1), (0.5f32, -122));
1664 assert_eq!((x2, exp2), (0.5f32, -110));
1665 assert_eq!((x3, exp3), (0.875f32, -122));
1666 assert_eq!(f32::ldexp(x1, exp1), f1);
1667 assert_eq!(f32::ldexp(x2, exp2), f2);
1668 assert_eq!(f32::ldexp(x3, exp3), f3);
1670 assert_eq!(0f32.frexp(), (0f32, 0));
1671 assert_eq!((-0f32).frexp(), (-0f32, 0));
1674 #[test] #[cfg_attr(windows, ignore)] // FIXME #8755
1675 fn test_frexp_nowin() {
1676 let inf: f32 = f32::INFINITY;
1677 let neg_inf: f32 = f32::NEG_INFINITY;
1678 let nan: f32 = f32::NAN;
1679 assert_eq!(match inf.frexp() { (x, _) => x }, inf);
1680 assert_eq!(match neg_inf.frexp() { (x, _) => x }, neg_inf);
1681 assert!(match nan.frexp() { (x, _) => x.is_nan() })
1686 assert_eq!((-1f32).abs_sub(1f32), 0f32);
1687 assert_eq!(1f32.abs_sub(1f32), 0f32);
1688 assert_eq!(1f32.abs_sub(0f32), 1f32);
1689 assert_eq!(1f32.abs_sub(-1f32), 2f32);
1690 assert_eq!(NEG_INFINITY.abs_sub(0f32), 0f32);
1691 assert_eq!(INFINITY.abs_sub(1f32), INFINITY);
1692 assert_eq!(0f32.abs_sub(NEG_INFINITY), INFINITY);
1693 assert_eq!(0f32.abs_sub(INFINITY), 0f32);
1697 fn test_abs_sub_nowin() {
1698 assert!(NAN.abs_sub(-1f32).is_nan());
1699 assert!(1f32.abs_sub(NAN).is_nan());
1704 assert_eq!(0.0f32.asinh(), 0.0f32);
1705 assert_eq!((-0.0f32).asinh(), -0.0f32);
1707 let inf: f32 = f32::INFINITY;
1708 let neg_inf: f32 = f32::NEG_INFINITY;
1709 let nan: f32 = f32::NAN;
1710 assert_eq!(inf.asinh(), inf);
1711 assert_eq!(neg_inf.asinh(), neg_inf);
1712 assert!(nan.asinh().is_nan());
1713 assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32);
1714 assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32);
1719 assert_eq!(1.0f32.acosh(), 0.0f32);
1720 assert!(0.999f32.acosh().is_nan());
1722 let inf: f32 = f32::INFINITY;
1723 let neg_inf: f32 = f32::NEG_INFINITY;
1724 let nan: f32 = f32::NAN;
1725 assert_eq!(inf.acosh(), inf);
1726 assert!(neg_inf.acosh().is_nan());
1727 assert!(nan.acosh().is_nan());
1728 assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32);
1729 assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32);
1734 assert_eq!(0.0f32.atanh(), 0.0f32);
1735 assert_eq!((-0.0f32).atanh(), -0.0f32);
1737 let inf32: f32 = f32::INFINITY;
1738 let neg_inf32: f32 = f32::NEG_INFINITY;
1739 assert_eq!(1.0f32.atanh(), inf32);
1740 assert_eq!((-1.0f32).atanh(), neg_inf32);
1742 assert!(2f64.atanh().atanh().is_nan());
1743 assert!((-2f64).atanh().atanh().is_nan());
1745 let inf64: f32 = f32::INFINITY;
1746 let neg_inf64: f32 = f32::NEG_INFINITY;
1747 let nan32: f32 = f32::NAN;
1748 assert!(inf64.atanh().is_nan());
1749 assert!(neg_inf64.atanh().is_nan());
1750 assert!(nan32.atanh().is_nan());
1752 assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32);
1753 assert_approx_eq!((-0.5f32).atanh(), -0.54930614433405484569762261846126285f32);
1757 fn test_real_consts() {
1760 let pi: f32 = consts::PI;
1761 let frac_pi_2: f32 = consts::FRAC_PI_2;
1762 let frac_pi_3: f32 = consts::FRAC_PI_3;
1763 let frac_pi_4: f32 = consts::FRAC_PI_4;
1764 let frac_pi_6: f32 = consts::FRAC_PI_6;
1765 let frac_pi_8: f32 = consts::FRAC_PI_8;
1766 let frac_1_pi: f32 = consts::FRAC_1_PI;
1767 let frac_2_pi: f32 = consts::FRAC_2_PI;
1768 let frac_2_sqrtpi: f32 = consts::FRAC_2_SQRT_PI;
1769 let sqrt2: f32 = consts::SQRT_2;
1770 let frac_1_sqrt2: f32 = consts::FRAC_1_SQRT_2;
1771 let e: f32 = consts::E;
1772 let log2_e: f32 = consts::LOG2_E;
1773 let log10_e: f32 = consts::LOG10_E;
1774 let ln_2: f32 = consts::LN_2;
1775 let ln_10: f32 = consts::LN_10;
1777 assert_approx_eq!(frac_pi_2, pi / 2f32);
1778 assert_approx_eq!(frac_pi_3, pi / 3f32);
1779 assert_approx_eq!(frac_pi_4, pi / 4f32);
1780 assert_approx_eq!(frac_pi_6, pi / 6f32);
1781 assert_approx_eq!(frac_pi_8, pi / 8f32);
1782 assert_approx_eq!(frac_1_pi, 1f32 / pi);
1783 assert_approx_eq!(frac_2_pi, 2f32 / pi);
1784 assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt());
1785 assert_approx_eq!(sqrt2, 2f32.sqrt());
1786 assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt());
1787 assert_approx_eq!(log2_e, e.log2());
1788 assert_approx_eq!(log10_e, e.log10());
1789 assert_approx_eq!(ln_2, 2f32.ln());
1790 assert_approx_eq!(ln_10, 10f32.ln());