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)]
22 #[cfg(not(target_env = "msvc"))]
25 use num::{FpCategory, ParseFloatError};
27 pub use core::f32::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON};
28 pub use core::f32::{MIN_EXP, MAX_EXP, MIN_10_EXP};
29 pub use core::f32::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
30 pub use core::f32::{MIN, MIN_POSITIVE, MAX};
31 pub use core::f32::consts;
35 use libc::{c_float, c_int};
38 pub fn cbrtf(n: c_float) -> c_float;
39 pub fn erff(n: c_float) -> c_float;
40 pub fn erfcf(n: c_float) -> c_float;
41 pub fn expm1f(n: c_float) -> c_float;
42 pub fn fdimf(a: c_float, b: c_float) -> c_float;
43 pub fn fmaxf(a: c_float, b: c_float) -> c_float;
44 pub fn fminf(a: c_float, b: c_float) -> c_float;
45 pub fn fmodf(a: c_float, b: c_float) -> c_float;
46 pub fn nextafterf(x: c_float, y: c_float) -> c_float;
47 pub fn logbf(n: c_float) -> c_float;
48 pub fn log1pf(n: c_float) -> c_float;
49 pub fn ilogbf(n: c_float) -> c_int;
50 pub fn modff(n: c_float, iptr: &mut c_float) -> c_float;
51 pub fn tgammaf(n: c_float) -> c_float;
53 #[cfg_attr(all(windows, target_env = "msvc"), link_name = "__lgammaf_r")]
54 pub fn lgammaf_r(n: c_float, sign: &mut c_int) -> c_float;
55 #[cfg_attr(all(windows, target_env = "msvc"), link_name = "_hypotf")]
56 pub fn hypotf(x: c_float, y: c_float) -> c_float;
59 // See the comments in `core::float::Float::floor` for why MSVC is special
61 #[cfg(not(target_env = "msvc"))]
63 pub fn acosf(n: c_float) -> c_float;
64 pub fn asinf(n: c_float) -> c_float;
65 pub fn atan2f(a: c_float, b: c_float) -> c_float;
66 pub fn atanf(n: c_float) -> c_float;
67 pub fn coshf(n: c_float) -> c_float;
68 pub fn frexpf(n: c_float, value: &mut c_int) -> c_float;
69 pub fn ldexpf(x: c_float, n: c_int) -> c_float;
70 pub fn sinhf(n: c_float) -> c_float;
71 pub fn tanf(n: c_float) -> c_float;
72 pub fn tanhf(n: c_float) -> c_float;
75 #[cfg(target_env = "msvc")]
76 pub use self::shims::*;
77 #[cfg(target_env = "msvc")]
79 use libc::{c_float, c_int};
81 pub unsafe fn acosf(n: c_float) -> c_float {
82 f64::acos(n as f64) as c_float
85 pub unsafe fn asinf(n: c_float) -> c_float {
86 f64::asin(n as f64) as c_float
89 pub unsafe fn atan2f(n: c_float, b: c_float) -> c_float {
90 f64::atan2(n as f64, b as f64) as c_float
93 pub unsafe fn atanf(n: c_float) -> c_float {
94 f64::atan(n as f64) as c_float
97 pub unsafe fn coshf(n: c_float) -> c_float {
98 f64::cosh(n as f64) as c_float
101 pub unsafe fn frexpf(x: c_float, value: &mut c_int) -> c_float {
102 let (a, b) = f64::frexp(x as f64);
107 pub unsafe fn ldexpf(x: c_float, n: c_int) -> c_float {
108 f64::ldexp(x as f64, n as isize) as c_float
111 pub unsafe fn sinhf(n: c_float) -> c_float {
112 f64::sinh(n as f64) as c_float
115 pub unsafe fn tanf(n: c_float) -> c_float {
116 f64::tan(n as f64) as c_float
119 pub unsafe fn tanhf(n: c_float) -> c_float {
120 f64::tanh(n as f64) as c_float
127 #[stable(feature = "rust1", since = "1.0.0")]
129 /// Parses a float as with a given radix
130 #[unstable(feature = "float_from_str_radix", reason = "recently moved API")]
131 pub fn from_str_radix(s: &str, radix: u32) -> Result<f32, ParseFloatError> {
132 num::Float::from_str_radix(s, radix)
135 /// Returns `true` if this value is `NaN` and false otherwise.
140 /// let nan = f32::NAN;
143 /// assert!(nan.is_nan());
144 /// assert!(!f.is_nan());
146 #[stable(feature = "rust1", since = "1.0.0")]
148 pub fn is_nan(self) -> bool { num::Float::is_nan(self) }
150 /// Returns `true` if this value is positive infinity or negative infinity and
157 /// let inf = f32::INFINITY;
158 /// let neg_inf = f32::NEG_INFINITY;
159 /// let nan = f32::NAN;
161 /// assert!(!f.is_infinite());
162 /// assert!(!nan.is_infinite());
164 /// assert!(inf.is_infinite());
165 /// assert!(neg_inf.is_infinite());
167 #[stable(feature = "rust1", since = "1.0.0")]
169 pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) }
171 /// Returns `true` if this number is neither infinite nor `NaN`.
177 /// let inf = f32::INFINITY;
178 /// let neg_inf = f32::NEG_INFINITY;
179 /// let nan = f32::NAN;
181 /// assert!(f.is_finite());
183 /// assert!(!nan.is_finite());
184 /// assert!(!inf.is_finite());
185 /// assert!(!neg_inf.is_finite());
187 #[stable(feature = "rust1", since = "1.0.0")]
189 pub fn is_finite(self) -> bool { num::Float::is_finite(self) }
191 /// Returns `true` if the number is neither zero, infinite,
192 /// [subnormal][subnormal], or `NaN`.
197 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
198 /// let max = f32::MAX;
199 /// let lower_than_min = 1.0e-40_f32;
200 /// let zero = 0.0_f32;
202 /// assert!(min.is_normal());
203 /// assert!(max.is_normal());
205 /// assert!(!zero.is_normal());
206 /// assert!(!f32::NAN.is_normal());
207 /// assert!(!f32::INFINITY.is_normal());
208 /// // Values between `0` and `min` are Subnormal.
209 /// assert!(!lower_than_min.is_normal());
211 /// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number
212 #[stable(feature = "rust1", since = "1.0.0")]
214 pub fn is_normal(self) -> bool { num::Float::is_normal(self) }
216 /// Returns the floating point category of the number. If only one property
217 /// is going to be tested, it is generally faster to use the specific
218 /// predicate instead.
221 /// use std::num::FpCategory;
224 /// let num = 12.4_f32;
225 /// let inf = f32::INFINITY;
227 /// assert_eq!(num.classify(), FpCategory::Normal);
228 /// assert_eq!(inf.classify(), FpCategory::Infinite);
230 #[stable(feature = "rust1", since = "1.0.0")]
232 pub fn classify(self) -> FpCategory { num::Float::classify(self) }
234 /// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
235 /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
236 /// The floating point encoding is documented in the [Reference][floating-point].
239 /// #![feature(float_extras)]
243 /// let num = 2.0f32;
245 /// // (8388608, -22, 1)
246 /// let (mantissa, exponent, sign) = num.integer_decode();
247 /// let sign_f = sign as f32;
248 /// let mantissa_f = mantissa as f32;
249 /// let exponent_f = num.powf(exponent as f32);
251 /// // 1 * 8388608 * 2^(-22) == 2
252 /// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
254 /// assert!(abs_difference <= f32::EPSILON);
256 /// [floating-point]: ../../../../../reference.html#machine-types
257 #[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 { num::Float::floor(self) }
276 /// Returns the smallest integer greater than or equal to a number.
279 /// let f = 3.01_f32;
282 /// assert_eq!(f.ceil(), 4.0);
283 /// assert_eq!(g.ceil(), 4.0);
285 #[stable(feature = "rust1", since = "1.0.0")]
287 pub fn ceil(self) -> f32 { num::Float::ceil(self) }
289 /// Returns the nearest integer to a number. Round half-way cases away from
294 /// let g = -3.3_f32;
296 /// assert_eq!(f.round(), 3.0);
297 /// assert_eq!(g.round(), -3.0);
299 #[stable(feature = "rust1", since = "1.0.0")]
301 pub fn round(self) -> f32 { num::Float::round(self) }
303 /// Returns the integer part of a number.
307 /// let g = -3.7_f32;
309 /// assert_eq!(f.trunc(), 3.0);
310 /// assert_eq!(g.trunc(), -3.0);
312 #[stable(feature = "rust1", since = "1.0.0")]
314 pub fn trunc(self) -> f32 { num::Float::trunc(self) }
316 /// Returns the fractional part of a number.
322 /// let y = -3.5_f32;
323 /// let abs_difference_x = (x.fract() - 0.5).abs();
324 /// let abs_difference_y = (y.fract() - (-0.5)).abs();
326 /// assert!(abs_difference_x <= f32::EPSILON);
327 /// assert!(abs_difference_y <= f32::EPSILON);
329 #[stable(feature = "rust1", since = "1.0.0")]
331 pub fn fract(self) -> f32 { num::Float::fract(self) }
333 /// Computes the absolute value of `self`. Returns `NAN` if the
340 /// let y = -3.5_f32;
342 /// let abs_difference_x = (x.abs() - x).abs();
343 /// let abs_difference_y = (y.abs() - (-y)).abs();
345 /// assert!(abs_difference_x <= f32::EPSILON);
346 /// assert!(abs_difference_y <= f32::EPSILON);
348 /// assert!(f32::NAN.abs().is_nan());
350 #[stable(feature = "rust1", since = "1.0.0")]
352 pub fn abs(self) -> f32 { num::Float::abs(self) }
354 /// Returns a number that represents the sign of `self`.
356 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
357 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
358 /// - `NAN` if the number is `NAN`
365 /// assert_eq!(f.signum(), 1.0);
366 /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
368 /// assert!(f32::NAN.signum().is_nan());
370 #[stable(feature = "rust1", since = "1.0.0")]
372 pub fn signum(self) -> f32 { num::Float::signum(self) }
374 /// Returns `true` if `self`'s sign bit is positive, including
375 /// `+0.0` and `INFINITY`.
380 /// let nan = f32::NAN;
382 /// let g = -7.0_f32;
384 /// assert!(f.is_sign_positive());
385 /// assert!(!g.is_sign_positive());
386 /// // Requires both tests to determine if is `NaN`
387 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
389 #[stable(feature = "rust1", since = "1.0.0")]
391 pub fn is_sign_positive(self) -> bool { num::Float::is_positive(self) }
393 /// Returns `true` if `self`'s sign is negative, including `-0.0`
394 /// and `NEG_INFINITY`.
399 /// let nan = f32::NAN;
403 /// assert!(!f.is_sign_negative());
404 /// assert!(g.is_sign_negative());
405 /// // Requires both tests to determine if is `NaN`.
406 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
408 #[stable(feature = "rust1", since = "1.0.0")]
410 pub fn is_sign_negative(self) -> bool { num::Float::is_negative(self) }
412 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
413 /// error. This produces a more accurate result with better performance than
414 /// a separate multiplication operation followed by an add.
419 /// let m = 10.0_f32;
421 /// let b = 60.0_f32;
424 /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
426 /// assert!(abs_difference <= f32::EPSILON);
428 #[stable(feature = "rust1", since = "1.0.0")]
430 pub fn mul_add(self, a: f32, b: f32) -> f32 { num::Float::mul_add(self, a, b) }
432 /// Takes the reciprocal (inverse) of a number, `1/x`.
438 /// let abs_difference = (x.recip() - (1.0/x)).abs();
440 /// assert!(abs_difference <= f32::EPSILON);
442 #[stable(feature = "rust1", since = "1.0.0")]
444 pub fn recip(self) -> f32 { num::Float::recip(self) }
446 /// Raises a number to an integer power.
448 /// Using this function is generally faster than using `powf`
454 /// let abs_difference = (x.powi(2) - x*x).abs();
456 /// assert!(abs_difference <= f32::EPSILON);
458 #[stable(feature = "rust1", since = "1.0.0")]
460 pub fn powi(self, n: i32) -> f32 { num::Float::powi(self, n) }
462 /// Raises a number to a floating point power.
468 /// let abs_difference = (x.powf(2.0) - x*x).abs();
470 /// assert!(abs_difference <= f32::EPSILON);
472 #[stable(feature = "rust1", since = "1.0.0")]
474 pub fn powf(self, n: f32) -> f32 { num::Float::powf(self, n) }
476 /// Takes the square root of a number.
478 /// Returns NaN if `self` is a negative number.
483 /// let positive = 4.0_f32;
484 /// let negative = -4.0_f32;
486 /// let abs_difference = (positive.sqrt() - 2.0).abs();
488 /// assert!(abs_difference <= f32::EPSILON);
489 /// assert!(negative.sqrt().is_nan());
491 #[stable(feature = "rust1", since = "1.0.0")]
493 pub fn sqrt(self) -> f32 { num::Float::sqrt(self) }
495 /// Returns `e^(self)`, (the exponential function).
500 /// let one = 1.0f32;
502 /// let e = one.exp();
504 /// // ln(e) - 1 == 0
505 /// let abs_difference = (e.ln() - 1.0).abs();
507 /// assert!(abs_difference <= f32::EPSILON);
509 #[stable(feature = "rust1", since = "1.0.0")]
511 pub fn exp(self) -> f32 { num::Float::exp(self) }
513 /// Returns `2^(self)`.
521 /// let abs_difference = (f.exp2() - 4.0).abs();
523 /// assert!(abs_difference <= f32::EPSILON);
525 #[stable(feature = "rust1", since = "1.0.0")]
527 pub fn exp2(self) -> f32 { num::Float::exp2(self) }
529 /// Returns the natural logarithm of the number.
534 /// let one = 1.0f32;
536 /// let e = one.exp();
538 /// // ln(e) - 1 == 0
539 /// let abs_difference = (e.ln() - 1.0).abs();
541 /// assert!(abs_difference <= f32::EPSILON);
543 #[stable(feature = "rust1", since = "1.0.0")]
545 pub fn ln(self) -> f32 { num::Float::ln(self) }
547 /// Returns the logarithm of the number with respect to an arbitrary base.
552 /// let ten = 10.0f32;
553 /// let two = 2.0f32;
555 /// // log10(10) - 1 == 0
556 /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
558 /// // log2(2) - 1 == 0
559 /// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
561 /// assert!(abs_difference_10 <= f32::EPSILON);
562 /// assert!(abs_difference_2 <= f32::EPSILON);
564 #[stable(feature = "rust1", since = "1.0.0")]
566 pub fn log(self, base: f32) -> f32 { num::Float::log(self, base) }
568 /// Returns the base 2 logarithm of the number.
573 /// let two = 2.0f32;
575 /// // log2(2) - 1 == 0
576 /// let abs_difference = (two.log2() - 1.0).abs();
578 /// assert!(abs_difference <= f32::EPSILON);
580 #[stable(feature = "rust1", since = "1.0.0")]
582 pub fn log2(self) -> f32 { num::Float::log2(self) }
584 /// Returns the base 10 logarithm of the number.
589 /// let ten = 10.0f32;
591 /// // log10(10) - 1 == 0
592 /// let abs_difference = (ten.log10() - 1.0).abs();
594 /// assert!(abs_difference <= f32::EPSILON);
596 #[stable(feature = "rust1", since = "1.0.0")]
598 pub fn log10(self) -> f32 { num::Float::log10(self) }
600 /// Converts radians to degrees.
603 /// #![feature(float_extras)]
605 /// use std::f32::{self, consts};
607 /// let angle = consts::PI;
609 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
611 /// assert!(abs_difference <= f32::EPSILON);
613 #[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")]
632 pub fn to_radians(self) -> f32 { num::Float::to_radians(self) }
634 /// Constructs a floating point number of `x*2^exp`.
637 /// #![feature(float_extras)]
640 /// // 3*2^2 - 12 == 0
641 /// let abs_difference = (f32::ldexp(3.0, 2) - 12.0).abs();
643 /// assert!(abs_difference <= f32::EPSILON);
645 #[unstable(feature = "float_extras",
646 reason = "pending integer conventions")]
648 pub fn ldexp(x: f32, exp: isize) -> f32 {
649 unsafe { cmath::ldexpf(x, exp as c_int) }
652 /// Breaks the number into a normalized fraction and a base-2 exponent,
655 /// * `self = x * 2^exp`
656 /// * `0.5 <= abs(x) < 1.0`
659 /// #![feature(float_extras)]
665 /// // (1/2)*2^3 -> 1 * 8/2 -> 4.0
666 /// let f = x.frexp();
667 /// let abs_difference_0 = (f.0 - 0.5).abs();
668 /// let abs_difference_1 = (f.1 as f32 - 3.0).abs();
670 /// assert!(abs_difference_0 <= f32::EPSILON);
671 /// assert!(abs_difference_1 <= f32::EPSILON);
673 #[unstable(feature = "float_extras",
674 reason = "pending integer conventions")]
676 pub fn frexp(self) -> (f32, isize) {
679 let x = cmath::frexpf(self, &mut exp);
684 /// Returns the next representable floating-point value in the direction of
688 /// #![feature(float_extras)]
694 /// let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs();
696 /// assert!(abs_diff <= f32::EPSILON);
698 #[unstable(feature = "float_extras",
699 reason = "unsure about its place in the world")]
701 pub fn next_after(self, other: f32) -> f32 {
702 unsafe { cmath::nextafterf(self, other) }
705 /// Returns the maximum of the two numbers.
711 /// assert_eq!(x.max(y), y);
714 /// If one of the arguments is NaN, then the other argument is returned.
715 #[stable(feature = "rust1", since = "1.0.0")]
717 pub fn max(self, other: f32) -> f32 {
718 unsafe { cmath::fmaxf(self, other) }
721 /// Returns the minimum of the two numbers.
727 /// assert_eq!(x.min(y), x);
730 /// If one of the arguments is NaN, then the other argument is returned.
731 #[stable(feature = "rust1", since = "1.0.0")]
733 pub fn min(self, other: f32) -> f32 {
734 unsafe { cmath::fminf(self, other) }
737 /// The positive difference of two numbers.
739 /// * If `self <= other`: `0:0`
740 /// * Else: `self - other`
748 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
749 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
751 /// assert!(abs_difference_x <= f32::EPSILON);
752 /// assert!(abs_difference_y <= f32::EPSILON);
754 #[stable(feature = "rust1", since = "1.0.0")]
756 pub fn abs_sub(self, other: f32) -> f32 {
757 unsafe { cmath::fdimf(self, other) }
760 /// Takes the cubic root of a number.
767 /// // x^(1/3) - 2 == 0
768 /// let abs_difference = (x.cbrt() - 2.0).abs();
770 /// assert!(abs_difference <= f32::EPSILON);
772 #[stable(feature = "rust1", since = "1.0.0")]
774 pub fn cbrt(self) -> f32 {
775 unsafe { cmath::cbrtf(self) }
778 /// Calculates the length of the hypotenuse of a right-angle triangle given
779 /// legs of length `x` and `y`.
787 /// // sqrt(x^2 + y^2)
788 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
790 /// assert!(abs_difference <= f32::EPSILON);
792 #[stable(feature = "rust1", since = "1.0.0")]
794 pub fn hypot(self, other: f32) -> f32 {
795 unsafe { cmath::hypotf(self, other) }
798 /// Computes the sine of a number (in radians).
803 /// let x = f32::consts::PI/2.0;
805 /// let abs_difference = (x.sin() - 1.0).abs();
807 /// assert!(abs_difference <= f32::EPSILON);
809 #[stable(feature = "rust1", since = "1.0.0")]
811 pub fn sin(self) -> f32 {
814 // see notes in `core::f32::Float::floor`
815 #[cfg(target_env = "msvc")]
816 fn sinf(f: f32) -> f32 { (f as f64).sin() as f32 }
817 #[cfg(not(target_env = "msvc"))]
818 fn sinf(f: f32) -> f32 { unsafe { intrinsics::sinf32(f) } }
821 /// Computes the cosine of a number (in radians).
826 /// let x = 2.0*f32::consts::PI;
828 /// let abs_difference = (x.cos() - 1.0).abs();
830 /// assert!(abs_difference <= f32::EPSILON);
832 #[stable(feature = "rust1", since = "1.0.0")]
834 pub fn cos(self) -> f32 {
837 // see notes in `core::f32::Float::floor`
838 #[cfg(target_env = "msvc")]
839 fn cosf(f: f32) -> f32 { (f as f64).cos() as f32 }
840 #[cfg(not(target_env = "msvc"))]
841 fn cosf(f: f32) -> f32 { unsafe { intrinsics::cosf32(f) } }
844 /// Computes the tangent of a number (in radians).
849 /// let x = f64::consts::PI/4.0;
850 /// let abs_difference = (x.tan() - 1.0).abs();
852 /// assert!(abs_difference < 1e-10);
854 #[stable(feature = "rust1", since = "1.0.0")]
856 pub fn tan(self) -> f32 {
857 unsafe { cmath::tanf(self) }
860 /// Computes the arcsine of a number. Return value is in radians in
861 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
867 /// let f = f32::consts::PI / 2.0;
869 /// // asin(sin(pi/2))
870 /// let abs_difference = f.sin().asin().abs_sub(f32::consts::PI / 2.0);
872 /// assert!(abs_difference <= f32::EPSILON);
874 #[stable(feature = "rust1", since = "1.0.0")]
876 pub fn asin(self) -> f32 {
877 unsafe { cmath::asinf(self) }
880 /// Computes the arccosine of a number. Return value is in radians in
881 /// the range [0, pi] or NaN if the number is outside the range
887 /// let f = f32::consts::PI / 4.0;
889 /// // acos(cos(pi/4))
890 /// let abs_difference = f.cos().acos().abs_sub(f32::consts::PI / 4.0);
892 /// assert!(abs_difference <= f32::EPSILON);
894 #[stable(feature = "rust1", since = "1.0.0")]
896 pub fn acos(self) -> f32 {
897 unsafe { cmath::acosf(self) }
900 /// Computes the arctangent of a number. Return value is in radians in the
901 /// range [-pi/2, pi/2];
909 /// let abs_difference = f.tan().atan().abs_sub(1.0);
911 /// assert!(abs_difference <= f32::EPSILON);
913 #[stable(feature = "rust1", since = "1.0.0")]
915 pub fn atan(self) -> f32 {
916 unsafe { cmath::atanf(self) }
919 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
921 /// * `x = 0`, `y = 0`: `0`
922 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
923 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
924 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
929 /// let pi = f32::consts::PI;
930 /// // All angles from horizontal right (+x)
931 /// // 45 deg counter-clockwise
933 /// let y1 = -3.0f32;
935 /// // 135 deg clockwise
936 /// let x2 = -3.0f32;
939 /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
940 /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
942 /// assert!(abs_difference_1 <= f32::EPSILON);
943 /// assert!(abs_difference_2 <= f32::EPSILON);
945 #[stable(feature = "rust1", since = "1.0.0")]
947 pub fn atan2(self, other: f32) -> f32 {
948 unsafe { cmath::atan2f(self, other) }
951 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
952 /// `(sin(x), cos(x))`.
957 /// let x = f32::consts::PI/4.0;
958 /// let f = x.sin_cos();
960 /// let abs_difference_0 = (f.0 - x.sin()).abs();
961 /// let abs_difference_1 = (f.1 - x.cos()).abs();
963 /// assert!(abs_difference_0 <= f32::EPSILON);
964 /// assert!(abs_difference_0 <= f32::EPSILON);
966 #[stable(feature = "rust1", since = "1.0.0")]
968 pub fn sin_cos(self) -> (f32, f32) {
969 (self.sin(), self.cos())
972 /// Returns `e^(self) - 1` in a way that is accurate even if the
973 /// number is close to zero.
979 /// let abs_difference = x.ln().exp_m1().abs_sub(6.0);
981 /// assert!(abs_difference < 1e-10);
983 #[stable(feature = "rust1", since = "1.0.0")]
985 pub fn exp_m1(self) -> f32 {
986 unsafe { cmath::expm1f(self) }
989 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
990 /// the operations were performed separately.
995 /// let x = f32::consts::E - 1.0;
997 /// // ln(1 + (e - 1)) == ln(e) == 1
998 /// let abs_difference = (x.ln_1p() - 1.0).abs();
1000 /// assert!(abs_difference <= f32::EPSILON);
1002 #[stable(feature = "rust1", since = "1.0.0")]
1004 pub fn ln_1p(self) -> f32 {
1005 unsafe { cmath::log1pf(self) }
1008 /// Hyperbolic sine function.
1013 /// let e = f32::consts::E;
1016 /// let f = x.sinh();
1017 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
1018 /// let g = (e*e - 1.0)/(2.0*e);
1019 /// let abs_difference = (f - g).abs();
1021 /// assert!(abs_difference <= f32::EPSILON);
1023 #[stable(feature = "rust1", since = "1.0.0")]
1025 pub fn sinh(self) -> f32 {
1026 unsafe { cmath::sinhf(self) }
1029 /// Hyperbolic cosine function.
1034 /// let e = f32::consts::E;
1036 /// let f = x.cosh();
1037 /// // Solving cosh() at 1 gives this result
1038 /// let g = (e*e + 1.0)/(2.0*e);
1039 /// let abs_difference = f.abs_sub(g);
1042 /// assert!(abs_difference <= f32::EPSILON);
1044 #[stable(feature = "rust1", since = "1.0.0")]
1046 pub fn cosh(self) -> f32 {
1047 unsafe { cmath::coshf(self) }
1050 /// Hyperbolic tangent function.
1055 /// let e = f32::consts::E;
1058 /// let f = x.tanh();
1059 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1060 /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
1061 /// let abs_difference = (f - g).abs();
1063 /// assert!(abs_difference <= f32::EPSILON);
1065 #[stable(feature = "rust1", since = "1.0.0")]
1067 pub fn tanh(self) -> f32 {
1068 unsafe { cmath::tanhf(self) }
1071 /// Inverse hyperbolic sine function.
1077 /// let f = x.sinh().asinh();
1079 /// let abs_difference = (f - x).abs();
1081 /// assert!(abs_difference <= f32::EPSILON);
1083 #[stable(feature = "rust1", since = "1.0.0")]
1085 pub fn asinh(self) -> f32 {
1087 NEG_INFINITY => NEG_INFINITY,
1088 x => (x + ((x * x) + 1.0).sqrt()).ln(),
1092 /// Inverse hyperbolic cosine function.
1098 /// let f = x.cosh().acosh();
1100 /// let abs_difference = (f - x).abs();
1102 /// assert!(abs_difference <= f32::EPSILON);
1104 #[stable(feature = "rust1", since = "1.0.0")]
1106 pub fn acosh(self) -> f32 {
1108 x if x < 1.0 => ::f32::NAN,
1109 x => (x + ((x * x) - 1.0).sqrt()).ln(),
1113 /// Inverse hyperbolic tangent function.
1118 /// let e = f32::consts::E;
1119 /// let f = e.tanh().atanh();
1121 /// let abs_difference = f.abs_sub(e);
1123 /// assert!(abs_difference <= f32::EPSILON);
1125 #[stable(feature = "rust1", since = "1.0.0")]
1127 pub fn atanh(self) -> f32 {
1128 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1137 use num::FpCategory as Fp;
1141 test_num(10f32, 2f32);
1146 assert_eq!(NAN.min(2.0), 2.0);
1147 assert_eq!(2.0f32.min(NAN), 2.0);
1152 assert_eq!(NAN.max(2.0), 2.0);
1153 assert_eq!(2.0f32.max(NAN), 2.0);
1158 let nan: f32 = f32::NAN;
1159 assert!(nan.is_nan());
1160 assert!(!nan.is_infinite());
1161 assert!(!nan.is_finite());
1162 assert!(!nan.is_normal());
1163 assert!(!nan.is_sign_positive());
1164 assert!(!nan.is_sign_negative());
1165 assert_eq!(Fp::Nan, nan.classify());
1169 fn test_infinity() {
1170 let inf: f32 = f32::INFINITY;
1171 assert!(inf.is_infinite());
1172 assert!(!inf.is_finite());
1173 assert!(inf.is_sign_positive());
1174 assert!(!inf.is_sign_negative());
1175 assert!(!inf.is_nan());
1176 assert!(!inf.is_normal());
1177 assert_eq!(Fp::Infinite, inf.classify());
1181 fn test_neg_infinity() {
1182 let neg_inf: f32 = f32::NEG_INFINITY;
1183 assert!(neg_inf.is_infinite());
1184 assert!(!neg_inf.is_finite());
1185 assert!(!neg_inf.is_sign_positive());
1186 assert!(neg_inf.is_sign_negative());
1187 assert!(!neg_inf.is_nan());
1188 assert!(!neg_inf.is_normal());
1189 assert_eq!(Fp::Infinite, neg_inf.classify());
1194 let zero: f32 = 0.0f32;
1195 assert_eq!(0.0, zero);
1196 assert!(!zero.is_infinite());
1197 assert!(zero.is_finite());
1198 assert!(zero.is_sign_positive());
1199 assert!(!zero.is_sign_negative());
1200 assert!(!zero.is_nan());
1201 assert!(!zero.is_normal());
1202 assert_eq!(Fp::Zero, zero.classify());
1206 fn test_neg_zero() {
1207 let neg_zero: f32 = -0.0;
1208 assert_eq!(0.0, neg_zero);
1209 assert!(!neg_zero.is_infinite());
1210 assert!(neg_zero.is_finite());
1211 assert!(!neg_zero.is_sign_positive());
1212 assert!(neg_zero.is_sign_negative());
1213 assert!(!neg_zero.is_nan());
1214 assert!(!neg_zero.is_normal());
1215 assert_eq!(Fp::Zero, neg_zero.classify());
1220 let one: f32 = 1.0f32;
1221 assert_eq!(1.0, one);
1222 assert!(!one.is_infinite());
1223 assert!(one.is_finite());
1224 assert!(one.is_sign_positive());
1225 assert!(!one.is_sign_negative());
1226 assert!(!one.is_nan());
1227 assert!(one.is_normal());
1228 assert_eq!(Fp::Normal, one.classify());
1233 let nan: f32 = f32::NAN;
1234 let inf: f32 = f32::INFINITY;
1235 let neg_inf: f32 = f32::NEG_INFINITY;
1236 assert!(nan.is_nan());
1237 assert!(!0.0f32.is_nan());
1238 assert!(!5.3f32.is_nan());
1239 assert!(!(-10.732f32).is_nan());
1240 assert!(!inf.is_nan());
1241 assert!(!neg_inf.is_nan());
1245 fn test_is_infinite() {
1246 let nan: f32 = f32::NAN;
1247 let inf: f32 = f32::INFINITY;
1248 let neg_inf: f32 = f32::NEG_INFINITY;
1249 assert!(!nan.is_infinite());
1250 assert!(inf.is_infinite());
1251 assert!(neg_inf.is_infinite());
1252 assert!(!0.0f32.is_infinite());
1253 assert!(!42.8f32.is_infinite());
1254 assert!(!(-109.2f32).is_infinite());
1258 fn test_is_finite() {
1259 let nan: f32 = f32::NAN;
1260 let inf: f32 = f32::INFINITY;
1261 let neg_inf: f32 = f32::NEG_INFINITY;
1262 assert!(!nan.is_finite());
1263 assert!(!inf.is_finite());
1264 assert!(!neg_inf.is_finite());
1265 assert!(0.0f32.is_finite());
1266 assert!(42.8f32.is_finite());
1267 assert!((-109.2f32).is_finite());
1271 fn test_is_normal() {
1272 let nan: f32 = f32::NAN;
1273 let inf: f32 = f32::INFINITY;
1274 let neg_inf: f32 = f32::NEG_INFINITY;
1275 let zero: f32 = 0.0f32;
1276 let neg_zero: f32 = -0.0;
1277 assert!(!nan.is_normal());
1278 assert!(!inf.is_normal());
1279 assert!(!neg_inf.is_normal());
1280 assert!(!zero.is_normal());
1281 assert!(!neg_zero.is_normal());
1282 assert!(1f32.is_normal());
1283 assert!(1e-37f32.is_normal());
1284 assert!(!1e-38f32.is_normal());
1288 fn test_classify() {
1289 let nan: f32 = f32::NAN;
1290 let inf: f32 = f32::INFINITY;
1291 let neg_inf: f32 = f32::NEG_INFINITY;
1292 let zero: f32 = 0.0f32;
1293 let neg_zero: f32 = -0.0;
1294 assert_eq!(nan.classify(), Fp::Nan);
1295 assert_eq!(inf.classify(), Fp::Infinite);
1296 assert_eq!(neg_inf.classify(), Fp::Infinite);
1297 assert_eq!(zero.classify(), Fp::Zero);
1298 assert_eq!(neg_zero.classify(), Fp::Zero);
1299 assert_eq!(1f32.classify(), Fp::Normal);
1300 assert_eq!(1e-37f32.classify(), Fp::Normal);
1301 assert_eq!(1e-38f32.classify(), Fp::Subnormal);
1305 fn test_integer_decode() {
1306 assert_eq!(3.14159265359f32.integer_decode(), (13176795, -22, 1));
1307 assert_eq!((-8573.5918555f32).integer_decode(), (8779358, -10, -1));
1308 assert_eq!(2f32.powf(100.0).integer_decode(), (8388608, 77, 1));
1309 assert_eq!(0f32.integer_decode(), (0, -150, 1));
1310 assert_eq!((-0f32).integer_decode(), (0, -150, -1));
1311 assert_eq!(INFINITY.integer_decode(), (8388608, 105, 1));
1312 assert_eq!(NEG_INFINITY.integer_decode(), (8388608, 105, -1));
1313 assert_eq!(NAN.integer_decode(), (12582912, 105, 1));
1318 assert_approx_eq!(1.0f32.floor(), 1.0f32);
1319 assert_approx_eq!(1.3f32.floor(), 1.0f32);
1320 assert_approx_eq!(1.5f32.floor(), 1.0f32);
1321 assert_approx_eq!(1.7f32.floor(), 1.0f32);
1322 assert_approx_eq!(0.0f32.floor(), 0.0f32);
1323 assert_approx_eq!((-0.0f32).floor(), -0.0f32);
1324 assert_approx_eq!((-1.0f32).floor(), -1.0f32);
1325 assert_approx_eq!((-1.3f32).floor(), -2.0f32);
1326 assert_approx_eq!((-1.5f32).floor(), -2.0f32);
1327 assert_approx_eq!((-1.7f32).floor(), -2.0f32);
1332 assert_approx_eq!(1.0f32.ceil(), 1.0f32);
1333 assert_approx_eq!(1.3f32.ceil(), 2.0f32);
1334 assert_approx_eq!(1.5f32.ceil(), 2.0f32);
1335 assert_approx_eq!(1.7f32.ceil(), 2.0f32);
1336 assert_approx_eq!(0.0f32.ceil(), 0.0f32);
1337 assert_approx_eq!((-0.0f32).ceil(), -0.0f32);
1338 assert_approx_eq!((-1.0f32).ceil(), -1.0f32);
1339 assert_approx_eq!((-1.3f32).ceil(), -1.0f32);
1340 assert_approx_eq!((-1.5f32).ceil(), -1.0f32);
1341 assert_approx_eq!((-1.7f32).ceil(), -1.0f32);
1346 assert_approx_eq!(1.0f32.round(), 1.0f32);
1347 assert_approx_eq!(1.3f32.round(), 1.0f32);
1348 assert_approx_eq!(1.5f32.round(), 2.0f32);
1349 assert_approx_eq!(1.7f32.round(), 2.0f32);
1350 assert_approx_eq!(0.0f32.round(), 0.0f32);
1351 assert_approx_eq!((-0.0f32).round(), -0.0f32);
1352 assert_approx_eq!((-1.0f32).round(), -1.0f32);
1353 assert_approx_eq!((-1.3f32).round(), -1.0f32);
1354 assert_approx_eq!((-1.5f32).round(), -2.0f32);
1355 assert_approx_eq!((-1.7f32).round(), -2.0f32);
1360 assert_approx_eq!(1.0f32.trunc(), 1.0f32);
1361 assert_approx_eq!(1.3f32.trunc(), 1.0f32);
1362 assert_approx_eq!(1.5f32.trunc(), 1.0f32);
1363 assert_approx_eq!(1.7f32.trunc(), 1.0f32);
1364 assert_approx_eq!(0.0f32.trunc(), 0.0f32);
1365 assert_approx_eq!((-0.0f32).trunc(), -0.0f32);
1366 assert_approx_eq!((-1.0f32).trunc(), -1.0f32);
1367 assert_approx_eq!((-1.3f32).trunc(), -1.0f32);
1368 assert_approx_eq!((-1.5f32).trunc(), -1.0f32);
1369 assert_approx_eq!((-1.7f32).trunc(), -1.0f32);
1374 assert_approx_eq!(1.0f32.fract(), 0.0f32);
1375 assert_approx_eq!(1.3f32.fract(), 0.3f32);
1376 assert_approx_eq!(1.5f32.fract(), 0.5f32);
1377 assert_approx_eq!(1.7f32.fract(), 0.7f32);
1378 assert_approx_eq!(0.0f32.fract(), 0.0f32);
1379 assert_approx_eq!((-0.0f32).fract(), -0.0f32);
1380 assert_approx_eq!((-1.0f32).fract(), -0.0f32);
1381 assert_approx_eq!((-1.3f32).fract(), -0.3f32);
1382 assert_approx_eq!((-1.5f32).fract(), -0.5f32);
1383 assert_approx_eq!((-1.7f32).fract(), -0.7f32);
1388 assert_eq!(INFINITY.abs(), INFINITY);
1389 assert_eq!(1f32.abs(), 1f32);
1390 assert_eq!(0f32.abs(), 0f32);
1391 assert_eq!((-0f32).abs(), 0f32);
1392 assert_eq!((-1f32).abs(), 1f32);
1393 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1394 assert_eq!((1f32/NEG_INFINITY).abs(), 0f32);
1395 assert!(NAN.abs().is_nan());
1400 assert_eq!(INFINITY.signum(), 1f32);
1401 assert_eq!(1f32.signum(), 1f32);
1402 assert_eq!(0f32.signum(), 1f32);
1403 assert_eq!((-0f32).signum(), -1f32);
1404 assert_eq!((-1f32).signum(), -1f32);
1405 assert_eq!(NEG_INFINITY.signum(), -1f32);
1406 assert_eq!((1f32/NEG_INFINITY).signum(), -1f32);
1407 assert!(NAN.signum().is_nan());
1411 fn test_is_sign_positive() {
1412 assert!(INFINITY.is_sign_positive());
1413 assert!(1f32.is_sign_positive());
1414 assert!(0f32.is_sign_positive());
1415 assert!(!(-0f32).is_sign_positive());
1416 assert!(!(-1f32).is_sign_positive());
1417 assert!(!NEG_INFINITY.is_sign_positive());
1418 assert!(!(1f32/NEG_INFINITY).is_sign_positive());
1419 assert!(!NAN.is_sign_positive());
1423 fn test_is_sign_negative() {
1424 assert!(!INFINITY.is_sign_negative());
1425 assert!(!1f32.is_sign_negative());
1426 assert!(!0f32.is_sign_negative());
1427 assert!((-0f32).is_sign_negative());
1428 assert!((-1f32).is_sign_negative());
1429 assert!(NEG_INFINITY.is_sign_negative());
1430 assert!((1f32/NEG_INFINITY).is_sign_negative());
1431 assert!(!NAN.is_sign_negative());
1436 let nan: f32 = f32::NAN;
1437 let inf: f32 = f32::INFINITY;
1438 let neg_inf: f32 = f32::NEG_INFINITY;
1439 assert_approx_eq!(12.3f32.mul_add(4.5, 6.7), 62.05);
1440 assert_approx_eq!((-12.3f32).mul_add(-4.5, -6.7), 48.65);
1441 assert_approx_eq!(0.0f32.mul_add(8.9, 1.2), 1.2);
1442 assert_approx_eq!(3.4f32.mul_add(-0.0, 5.6), 5.6);
1443 assert!(nan.mul_add(7.8, 9.0).is_nan());
1444 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1445 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1446 assert_eq!(8.9f32.mul_add(inf, 3.2), inf);
1447 assert_eq!((-3.2f32).mul_add(2.4, neg_inf), neg_inf);
1452 let nan: f32 = f32::NAN;
1453 let inf: f32 = f32::INFINITY;
1454 let neg_inf: f32 = f32::NEG_INFINITY;
1455 assert_eq!(1.0f32.recip(), 1.0);
1456 assert_eq!(2.0f32.recip(), 0.5);
1457 assert_eq!((-0.4f32).recip(), -2.5);
1458 assert_eq!(0.0f32.recip(), inf);
1459 assert!(nan.recip().is_nan());
1460 assert_eq!(inf.recip(), 0.0);
1461 assert_eq!(neg_inf.recip(), 0.0);
1466 let nan: f32 = f32::NAN;
1467 let inf: f32 = f32::INFINITY;
1468 let neg_inf: f32 = f32::NEG_INFINITY;
1469 assert_eq!(1.0f32.powi(1), 1.0);
1470 assert_approx_eq!((-3.1f32).powi(2), 9.61);
1471 assert_approx_eq!(5.9f32.powi(-2), 0.028727);
1472 assert_eq!(8.3f32.powi(0), 1.0);
1473 assert!(nan.powi(2).is_nan());
1474 assert_eq!(inf.powi(3), inf);
1475 assert_eq!(neg_inf.powi(2), inf);
1480 let nan: f32 = f32::NAN;
1481 let inf: f32 = f32::INFINITY;
1482 let neg_inf: f32 = f32::NEG_INFINITY;
1483 assert_eq!(1.0f32.powf(1.0), 1.0);
1484 assert_approx_eq!(3.4f32.powf(4.5), 246.408218);
1485 assert_approx_eq!(2.7f32.powf(-3.2), 0.041652);
1486 assert_approx_eq!((-3.1f32).powf(2.0), 9.61);
1487 assert_approx_eq!(5.9f32.powf(-2.0), 0.028727);
1488 assert_eq!(8.3f32.powf(0.0), 1.0);
1489 assert!(nan.powf(2.0).is_nan());
1490 assert_eq!(inf.powf(2.0), inf);
1491 assert_eq!(neg_inf.powf(3.0), neg_inf);
1495 fn test_sqrt_domain() {
1496 assert!(NAN.sqrt().is_nan());
1497 assert!(NEG_INFINITY.sqrt().is_nan());
1498 assert!((-1.0f32).sqrt().is_nan());
1499 assert_eq!((-0.0f32).sqrt(), -0.0);
1500 assert_eq!(0.0f32.sqrt(), 0.0);
1501 assert_eq!(1.0f32.sqrt(), 1.0);
1502 assert_eq!(INFINITY.sqrt(), INFINITY);
1507 assert_eq!(1.0, 0.0f32.exp());
1508 assert_approx_eq!(2.718282, 1.0f32.exp());
1509 assert_approx_eq!(148.413162, 5.0f32.exp());
1511 let inf: f32 = f32::INFINITY;
1512 let neg_inf: f32 = f32::NEG_INFINITY;
1513 let nan: f32 = f32::NAN;
1514 assert_eq!(inf, inf.exp());
1515 assert_eq!(0.0, neg_inf.exp());
1516 assert!(nan.exp().is_nan());
1521 assert_eq!(32.0, 5.0f32.exp2());
1522 assert_eq!(1.0, 0.0f32.exp2());
1524 let inf: f32 = f32::INFINITY;
1525 let neg_inf: f32 = f32::NEG_INFINITY;
1526 let nan: f32 = f32::NAN;
1527 assert_eq!(inf, inf.exp2());
1528 assert_eq!(0.0, neg_inf.exp2());
1529 assert!(nan.exp2().is_nan());
1534 let nan: f32 = f32::NAN;
1535 let inf: f32 = f32::INFINITY;
1536 let neg_inf: f32 = f32::NEG_INFINITY;
1537 assert_approx_eq!(1.0f32.exp().ln(), 1.0);
1538 assert!(nan.ln().is_nan());
1539 assert_eq!(inf.ln(), inf);
1540 assert!(neg_inf.ln().is_nan());
1541 assert!((-2.3f32).ln().is_nan());
1542 assert_eq!((-0.0f32).ln(), neg_inf);
1543 assert_eq!(0.0f32.ln(), neg_inf);
1544 assert_approx_eq!(4.0f32.ln(), 1.386294);
1549 let nan: f32 = f32::NAN;
1550 let inf: f32 = f32::INFINITY;
1551 let neg_inf: f32 = f32::NEG_INFINITY;
1552 assert_eq!(10.0f32.log(10.0), 1.0);
1553 assert_approx_eq!(2.3f32.log(3.5), 0.664858);
1554 assert_eq!(1.0f32.exp().log(1.0f32.exp()), 1.0);
1555 assert!(1.0f32.log(1.0).is_nan());
1556 assert!(1.0f32.log(-13.9).is_nan());
1557 assert!(nan.log(2.3).is_nan());
1558 assert_eq!(inf.log(10.0), inf);
1559 assert!(neg_inf.log(8.8).is_nan());
1560 assert!((-2.3f32).log(0.1).is_nan());
1561 assert_eq!((-0.0f32).log(2.0), neg_inf);
1562 assert_eq!(0.0f32.log(7.0), neg_inf);
1567 let nan: f32 = f32::NAN;
1568 let inf: f32 = f32::INFINITY;
1569 let neg_inf: f32 = f32::NEG_INFINITY;
1570 assert_approx_eq!(10.0f32.log2(), 3.321928);
1571 assert_approx_eq!(2.3f32.log2(), 1.201634);
1572 assert_approx_eq!(1.0f32.exp().log2(), 1.442695);
1573 assert!(nan.log2().is_nan());
1574 assert_eq!(inf.log2(), inf);
1575 assert!(neg_inf.log2().is_nan());
1576 assert!((-2.3f32).log2().is_nan());
1577 assert_eq!((-0.0f32).log2(), neg_inf);
1578 assert_eq!(0.0f32.log2(), neg_inf);
1583 let nan: f32 = f32::NAN;
1584 let inf: f32 = f32::INFINITY;
1585 let neg_inf: f32 = f32::NEG_INFINITY;
1586 assert_eq!(10.0f32.log10(), 1.0);
1587 assert_approx_eq!(2.3f32.log10(), 0.361728);
1588 assert_approx_eq!(1.0f32.exp().log10(), 0.434294);
1589 assert_eq!(1.0f32.log10(), 0.0);
1590 assert!(nan.log10().is_nan());
1591 assert_eq!(inf.log10(), inf);
1592 assert!(neg_inf.log10().is_nan());
1593 assert!((-2.3f32).log10().is_nan());
1594 assert_eq!((-0.0f32).log10(), neg_inf);
1595 assert_eq!(0.0f32.log10(), neg_inf);
1599 fn test_to_degrees() {
1600 let pi: f32 = consts::PI;
1601 let nan: f32 = f32::NAN;
1602 let inf: f32 = f32::INFINITY;
1603 let neg_inf: f32 = f32::NEG_INFINITY;
1604 assert_eq!(0.0f32.to_degrees(), 0.0);
1605 assert_approx_eq!((-5.8f32).to_degrees(), -332.315521);
1606 assert_eq!(pi.to_degrees(), 180.0);
1607 assert!(nan.to_degrees().is_nan());
1608 assert_eq!(inf.to_degrees(), inf);
1609 assert_eq!(neg_inf.to_degrees(), neg_inf);
1613 fn test_to_radians() {
1614 let pi: f32 = consts::PI;
1615 let nan: f32 = f32::NAN;
1616 let inf: f32 = f32::INFINITY;
1617 let neg_inf: f32 = f32::NEG_INFINITY;
1618 assert_eq!(0.0f32.to_radians(), 0.0);
1619 assert_approx_eq!(154.6f32.to_radians(), 2.698279);
1620 assert_approx_eq!((-332.31f32).to_radians(), -5.799903);
1621 assert_eq!(180.0f32.to_radians(), pi);
1622 assert!(nan.to_radians().is_nan());
1623 assert_eq!(inf.to_radians(), inf);
1624 assert_eq!(neg_inf.to_radians(), neg_inf);
1629 // We have to use from_str until base-2 exponents
1630 // are supported in floating-point literals
1631 let f1: f32 = f32::from_str_radix("1p-123", 16).unwrap();
1632 let f2: f32 = f32::from_str_radix("1p-111", 16).unwrap();
1633 let f3: f32 = f32::from_str_radix("1.Cp-12", 16).unwrap();
1634 assert_eq!(f32::ldexp(1f32, -123), f1);
1635 assert_eq!(f32::ldexp(1f32, -111), f2);
1636 assert_eq!(f32::ldexp(1.75f32, -12), f3);
1638 assert_eq!(f32::ldexp(0f32, -123), 0f32);
1639 assert_eq!(f32::ldexp(-0f32, -123), -0f32);
1641 let inf: f32 = f32::INFINITY;
1642 let neg_inf: f32 = f32::NEG_INFINITY;
1643 let nan: f32 = f32::NAN;
1644 assert_eq!(f32::ldexp(inf, -123), inf);
1645 assert_eq!(f32::ldexp(neg_inf, -123), neg_inf);
1646 assert!(f32::ldexp(nan, -123).is_nan());
1651 // We have to use from_str until base-2 exponents
1652 // are supported in floating-point literals
1653 let f1: f32 = f32::from_str_radix("1p-123", 16).unwrap();
1654 let f2: f32 = f32::from_str_radix("1p-111", 16).unwrap();
1655 let f3: f32 = f32::from_str_radix("1.Cp-123", 16).unwrap();
1656 let (x1, exp1) = f1.frexp();
1657 let (x2, exp2) = f2.frexp();
1658 let (x3, exp3) = f3.frexp();
1659 assert_eq!((x1, exp1), (0.5f32, -122));
1660 assert_eq!((x2, exp2), (0.5f32, -110));
1661 assert_eq!((x3, exp3), (0.875f32, -122));
1662 assert_eq!(f32::ldexp(x1, exp1), f1);
1663 assert_eq!(f32::ldexp(x2, exp2), f2);
1664 assert_eq!(f32::ldexp(x3, exp3), f3);
1666 assert_eq!(0f32.frexp(), (0f32, 0));
1667 assert_eq!((-0f32).frexp(), (-0f32, 0));
1670 #[test] #[cfg_attr(windows, ignore)] // FIXME #8755
1671 fn test_frexp_nowin() {
1672 let inf: f32 = f32::INFINITY;
1673 let neg_inf: f32 = f32::NEG_INFINITY;
1674 let nan: f32 = f32::NAN;
1675 assert_eq!(match inf.frexp() { (x, _) => x }, inf);
1676 assert_eq!(match neg_inf.frexp() { (x, _) => x }, neg_inf);
1677 assert!(match nan.frexp() { (x, _) => x.is_nan() })
1682 assert_eq!((-1f32).abs_sub(1f32), 0f32);
1683 assert_eq!(1f32.abs_sub(1f32), 0f32);
1684 assert_eq!(1f32.abs_sub(0f32), 1f32);
1685 assert_eq!(1f32.abs_sub(-1f32), 2f32);
1686 assert_eq!(NEG_INFINITY.abs_sub(0f32), 0f32);
1687 assert_eq!(INFINITY.abs_sub(1f32), INFINITY);
1688 assert_eq!(0f32.abs_sub(NEG_INFINITY), INFINITY);
1689 assert_eq!(0f32.abs_sub(INFINITY), 0f32);
1693 fn test_abs_sub_nowin() {
1694 assert!(NAN.abs_sub(-1f32).is_nan());
1695 assert!(1f32.abs_sub(NAN).is_nan());
1700 assert_eq!(0.0f32.asinh(), 0.0f32);
1701 assert_eq!((-0.0f32).asinh(), -0.0f32);
1703 let inf: f32 = f32::INFINITY;
1704 let neg_inf: f32 = f32::NEG_INFINITY;
1705 let nan: f32 = f32::NAN;
1706 assert_eq!(inf.asinh(), inf);
1707 assert_eq!(neg_inf.asinh(), neg_inf);
1708 assert!(nan.asinh().is_nan());
1709 assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32);
1710 assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32);
1715 assert_eq!(1.0f32.acosh(), 0.0f32);
1716 assert!(0.999f32.acosh().is_nan());
1718 let inf: f32 = f32::INFINITY;
1719 let neg_inf: f32 = f32::NEG_INFINITY;
1720 let nan: f32 = f32::NAN;
1721 assert_eq!(inf.acosh(), inf);
1722 assert!(neg_inf.acosh().is_nan());
1723 assert!(nan.acosh().is_nan());
1724 assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32);
1725 assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32);
1730 assert_eq!(0.0f32.atanh(), 0.0f32);
1731 assert_eq!((-0.0f32).atanh(), -0.0f32);
1733 let inf32: f32 = f32::INFINITY;
1734 let neg_inf32: f32 = f32::NEG_INFINITY;
1735 assert_eq!(1.0f32.atanh(), inf32);
1736 assert_eq!((-1.0f32).atanh(), neg_inf32);
1738 assert!(2f64.atanh().atanh().is_nan());
1739 assert!((-2f64).atanh().atanh().is_nan());
1741 let inf64: f32 = f32::INFINITY;
1742 let neg_inf64: f32 = f32::NEG_INFINITY;
1743 let nan32: f32 = f32::NAN;
1744 assert!(inf64.atanh().is_nan());
1745 assert!(neg_inf64.atanh().is_nan());
1746 assert!(nan32.atanh().is_nan());
1748 assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32);
1749 assert_approx_eq!((-0.5f32).atanh(), -0.54930614433405484569762261846126285f32);
1753 fn test_real_consts() {
1756 let pi: f32 = consts::PI;
1757 let two_pi: f32 = consts::PI_2;
1758 let frac_pi_2: f32 = consts::FRAC_PI_2;
1759 let frac_pi_3: f32 = consts::FRAC_PI_3;
1760 let frac_pi_4: f32 = consts::FRAC_PI_4;
1761 let frac_pi_6: f32 = consts::FRAC_PI_6;
1762 let frac_pi_8: f32 = consts::FRAC_PI_8;
1763 let frac_1_pi: f32 = consts::FRAC_1_PI;
1764 let frac_2_pi: f32 = consts::FRAC_2_PI;
1765 let frac_2_sqrtpi: f32 = consts::FRAC_2_SQRT_PI;
1766 let sqrt2: f32 = consts::SQRT_2;
1767 let frac_1_sqrt2: f32 = consts::FRAC_1_SQRT_2;
1768 let e: f32 = consts::E;
1769 let log2_e: f32 = consts::LOG2_E;
1770 let log10_e: f32 = consts::LOG10_E;
1771 let ln_2: f32 = consts::LN_2;
1772 let ln_10: f32 = consts::LN_10;
1774 assert_approx_eq!(two_pi, 2f32 * pi);
1775 assert_approx_eq!(frac_pi_2, pi / 2f32);
1776 assert_approx_eq!(frac_pi_3, pi / 3f32);
1777 assert_approx_eq!(frac_pi_4, pi / 4f32);
1778 assert_approx_eq!(frac_pi_6, pi / 6f32);
1779 assert_approx_eq!(frac_pi_8, pi / 8f32);
1780 assert_approx_eq!(frac_1_pi, 1f32 / pi);
1781 assert_approx_eq!(frac_2_pi, 2f32 / pi);
1782 assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt());
1783 assert_approx_eq!(sqrt2, 2f32.sqrt());
1784 assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt());
1785 assert_approx_eq!(log2_e, e.log2());
1786 assert_approx_eq!(log10_e, e.log10());
1787 assert_approx_eq!(ln_2, 2f32.ln());
1788 assert_approx_eq!(ln_10, 10f32.ln());