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")]
128 pub fn from_str_radix(s: &str, radix: u32) -> Result<f32, ParseFloatError> {
129 num::Float::from_str_radix(s, radix)
132 /// Returns `true` if this value is `NaN` and false otherwise.
137 /// let nan = f32::NAN;
140 /// assert!(nan.is_nan());
141 /// assert!(!f.is_nan());
143 #[stable(feature = "rust1", since = "1.0.0")]
145 pub fn is_nan(self) -> bool { num::Float::is_nan(self) }
147 /// Returns `true` if this value is positive infinity or negative infinity and
154 /// let inf = f32::INFINITY;
155 /// let neg_inf = f32::NEG_INFINITY;
156 /// let nan = f32::NAN;
158 /// assert!(!f.is_infinite());
159 /// assert!(!nan.is_infinite());
161 /// assert!(inf.is_infinite());
162 /// assert!(neg_inf.is_infinite());
164 #[stable(feature = "rust1", since = "1.0.0")]
166 pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) }
168 /// Returns `true` if this number is neither infinite nor `NaN`.
174 /// let inf = f32::INFINITY;
175 /// let neg_inf = f32::NEG_INFINITY;
176 /// let nan = f32::NAN;
178 /// assert!(f.is_finite());
180 /// assert!(!nan.is_finite());
181 /// assert!(!inf.is_finite());
182 /// assert!(!neg_inf.is_finite());
184 #[stable(feature = "rust1", since = "1.0.0")]
186 pub fn is_finite(self) -> bool { num::Float::is_finite(self) }
188 /// Returns `true` if the number is neither zero, infinite,
189 /// [subnormal][subnormal], or `NaN`.
194 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f32
195 /// let max = f32::MAX;
196 /// let lower_than_min = 1.0e-40_f32;
197 /// let zero = 0.0_f32;
199 /// assert!(min.is_normal());
200 /// assert!(max.is_normal());
202 /// assert!(!zero.is_normal());
203 /// assert!(!f32::NAN.is_normal());
204 /// assert!(!f32::INFINITY.is_normal());
205 /// // Values between `0` and `min` are Subnormal.
206 /// assert!(!lower_than_min.is_normal());
208 /// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number
209 #[stable(feature = "rust1", since = "1.0.0")]
211 pub fn is_normal(self) -> bool { num::Float::is_normal(self) }
213 /// Returns the floating point category of the number. If only one property
214 /// is going to be tested, it is generally faster to use the specific
215 /// predicate instead.
218 /// use std::num::FpCategory;
221 /// let num = 12.4_f32;
222 /// let inf = f32::INFINITY;
224 /// assert_eq!(num.classify(), FpCategory::Normal);
225 /// assert_eq!(inf.classify(), FpCategory::Infinite);
227 #[stable(feature = "rust1", since = "1.0.0")]
229 pub fn classify(self) -> FpCategory { num::Float::classify(self) }
231 /// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
232 /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
233 /// The floating point encoding is documented in the [Reference][floating-point].
236 /// #![feature(float_extras)]
240 /// let num = 2.0f32;
242 /// // (8388608, -22, 1)
243 /// let (mantissa, exponent, sign) = num.integer_decode();
244 /// let sign_f = sign as f32;
245 /// let mantissa_f = mantissa as f32;
246 /// let exponent_f = num.powf(exponent as f32);
248 /// // 1 * 8388608 * 2^(-22) == 2
249 /// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
251 /// assert!(abs_difference <= f32::EPSILON);
253 /// [floating-point]: ../../../../../reference.html#machine-types
254 #[unstable(feature = "float_extras", reason = "signature is undecided")]
256 pub fn integer_decode(self) -> (u64, i16, i8) {
257 num::Float::integer_decode(self)
260 /// Returns the largest integer less than or equal to a number.
263 /// let f = 3.99_f32;
266 /// assert_eq!(f.floor(), 3.0);
267 /// assert_eq!(g.floor(), 3.0);
269 #[stable(feature = "rust1", since = "1.0.0")]
271 pub fn floor(self) -> f32 { num::Float::floor(self) }
273 /// Returns the smallest integer greater than or equal to a number.
276 /// let f = 3.01_f32;
279 /// assert_eq!(f.ceil(), 4.0);
280 /// assert_eq!(g.ceil(), 4.0);
282 #[stable(feature = "rust1", since = "1.0.0")]
284 pub fn ceil(self) -> f32 { num::Float::ceil(self) }
286 /// Returns the nearest integer to a number. Round half-way cases away from
291 /// let g = -3.3_f32;
293 /// assert_eq!(f.round(), 3.0);
294 /// assert_eq!(g.round(), -3.0);
296 #[stable(feature = "rust1", since = "1.0.0")]
298 pub fn round(self) -> f32 { num::Float::round(self) }
300 /// Returns the integer part of a number.
304 /// let g = -3.7_f32;
306 /// assert_eq!(f.trunc(), 3.0);
307 /// assert_eq!(g.trunc(), -3.0);
309 #[stable(feature = "rust1", since = "1.0.0")]
311 pub fn trunc(self) -> f32 { num::Float::trunc(self) }
313 /// Returns the fractional part of a number.
319 /// let y = -3.5_f32;
320 /// let abs_difference_x = (x.fract() - 0.5).abs();
321 /// let abs_difference_y = (y.fract() - (-0.5)).abs();
323 /// assert!(abs_difference_x <= f32::EPSILON);
324 /// assert!(abs_difference_y <= f32::EPSILON);
326 #[stable(feature = "rust1", since = "1.0.0")]
328 pub fn fract(self) -> f32 { num::Float::fract(self) }
330 /// Computes the absolute value of `self`. Returns `NAN` if the
337 /// let y = -3.5_f32;
339 /// let abs_difference_x = (x.abs() - x).abs();
340 /// let abs_difference_y = (y.abs() - (-y)).abs();
342 /// assert!(abs_difference_x <= f32::EPSILON);
343 /// assert!(abs_difference_y <= f32::EPSILON);
345 /// assert!(f32::NAN.abs().is_nan());
347 #[stable(feature = "rust1", since = "1.0.0")]
349 pub fn abs(self) -> f32 { num::Float::abs(self) }
351 /// Returns a number that represents the sign of `self`.
353 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
354 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
355 /// - `NAN` if the number is `NAN`
362 /// assert_eq!(f.signum(), 1.0);
363 /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
365 /// assert!(f32::NAN.signum().is_nan());
367 #[stable(feature = "rust1", since = "1.0.0")]
369 pub fn signum(self) -> f32 { num::Float::signum(self) }
371 /// Returns `true` if `self`'s sign bit is positive, including
372 /// `+0.0` and `INFINITY`.
377 /// let nan = f32::NAN;
379 /// let g = -7.0_f32;
381 /// assert!(f.is_sign_positive());
382 /// assert!(!g.is_sign_positive());
383 /// // Requires both tests to determine if is `NaN`
384 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
386 #[stable(feature = "rust1", since = "1.0.0")]
388 pub fn is_sign_positive(self) -> bool { num::Float::is_positive(self) }
390 /// Returns `true` if `self`'s sign is negative, including `-0.0`
391 /// and `NEG_INFINITY`.
396 /// let nan = f32::NAN;
400 /// assert!(!f.is_sign_negative());
401 /// assert!(g.is_sign_negative());
402 /// // Requires both tests to determine if is `NaN`.
403 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
405 #[stable(feature = "rust1", since = "1.0.0")]
407 pub fn is_sign_negative(self) -> bool { num::Float::is_negative(self) }
409 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
410 /// error. This produces a more accurate result with better performance than
411 /// a separate multiplication operation followed by an add.
416 /// let m = 10.0_f32;
418 /// let b = 60.0_f32;
421 /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
423 /// assert!(abs_difference <= f32::EPSILON);
425 #[stable(feature = "rust1", since = "1.0.0")]
427 pub fn mul_add(self, a: f32, b: f32) -> f32 { num::Float::mul_add(self, a, b) }
429 /// Takes the reciprocal (inverse) of a number, `1/x`.
435 /// let abs_difference = (x.recip() - (1.0/x)).abs();
437 /// assert!(abs_difference <= f32::EPSILON);
439 #[stable(feature = "rust1", since = "1.0.0")]
441 pub fn recip(self) -> f32 { num::Float::recip(self) }
443 /// Raises a number to an integer power.
445 /// Using this function is generally faster than using `powf`
451 /// let abs_difference = (x.powi(2) - x*x).abs();
453 /// assert!(abs_difference <= f32::EPSILON);
455 #[stable(feature = "rust1", since = "1.0.0")]
457 pub fn powi(self, n: i32) -> f32 { num::Float::powi(self, n) }
459 /// Raises a number to a floating point power.
465 /// let abs_difference = (x.powf(2.0) - x*x).abs();
467 /// assert!(abs_difference <= f32::EPSILON);
469 #[stable(feature = "rust1", since = "1.0.0")]
471 pub fn powf(self, n: f32) -> f32 { num::Float::powf(self, n) }
473 /// Takes the square root of a number.
475 /// Returns NaN if `self` is a negative number.
480 /// let positive = 4.0_f32;
481 /// let negative = -4.0_f32;
483 /// let abs_difference = (positive.sqrt() - 2.0).abs();
485 /// assert!(abs_difference <= f32::EPSILON);
486 /// assert!(negative.sqrt().is_nan());
488 #[stable(feature = "rust1", since = "1.0.0")]
490 pub fn sqrt(self) -> f32 { num::Float::sqrt(self) }
492 /// Returns `e^(self)`, (the exponential function).
497 /// let one = 1.0f32;
499 /// let e = one.exp();
501 /// // ln(e) - 1 == 0
502 /// let abs_difference = (e.ln() - 1.0).abs();
504 /// assert!(abs_difference <= f32::EPSILON);
506 #[stable(feature = "rust1", since = "1.0.0")]
508 pub fn exp(self) -> f32 { num::Float::exp(self) }
510 /// Returns `2^(self)`.
518 /// let abs_difference = (f.exp2() - 4.0).abs();
520 /// assert!(abs_difference <= f32::EPSILON);
522 #[stable(feature = "rust1", since = "1.0.0")]
524 pub fn exp2(self) -> f32 { num::Float::exp2(self) }
526 /// Returns the natural logarithm of the number.
531 /// let one = 1.0f32;
533 /// let e = one.exp();
535 /// // ln(e) - 1 == 0
536 /// let abs_difference = (e.ln() - 1.0).abs();
538 /// assert!(abs_difference <= f32::EPSILON);
540 #[stable(feature = "rust1", since = "1.0.0")]
542 pub fn ln(self) -> f32 { num::Float::ln(self) }
544 /// Returns the logarithm of the number with respect to an arbitrary base.
549 /// let ten = 10.0f32;
550 /// let two = 2.0f32;
552 /// // log10(10) - 1 == 0
553 /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
555 /// // log2(2) - 1 == 0
556 /// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
558 /// assert!(abs_difference_10 <= f32::EPSILON);
559 /// assert!(abs_difference_2 <= f32::EPSILON);
561 #[stable(feature = "rust1", since = "1.0.0")]
563 pub fn log(self, base: f32) -> f32 { num::Float::log(self, base) }
565 /// Returns the base 2 logarithm of the number.
570 /// let two = 2.0f32;
572 /// // log2(2) - 1 == 0
573 /// let abs_difference = (two.log2() - 1.0).abs();
575 /// assert!(abs_difference <= f32::EPSILON);
577 #[stable(feature = "rust1", since = "1.0.0")]
579 pub fn log2(self) -> f32 { num::Float::log2(self) }
581 /// Returns the base 10 logarithm of the number.
586 /// let ten = 10.0f32;
588 /// // log10(10) - 1 == 0
589 /// let abs_difference = (ten.log10() - 1.0).abs();
591 /// assert!(abs_difference <= f32::EPSILON);
593 #[stable(feature = "rust1", since = "1.0.0")]
595 pub fn log10(self) -> f32 { num::Float::log10(self) }
597 /// Converts radians to degrees.
600 /// #![feature(float_extras)]
602 /// use std::f32::{self, consts};
604 /// let angle = consts::PI;
606 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
608 /// assert!(abs_difference <= f32::EPSILON);
610 #[unstable(feature = "float_extras", reason = "desirability is unclear")]
612 pub fn to_degrees(self) -> f32 { num::Float::to_degrees(self) }
614 /// Converts degrees to radians.
617 /// #![feature(float_extras)]
619 /// use std::f32::{self, consts};
621 /// let angle = 180.0f32;
623 /// let abs_difference = (angle.to_radians() - consts::PI).abs();
625 /// assert!(abs_difference <= f32::EPSILON);
627 #[unstable(feature = "float_extras", reason = "desirability is unclear")]
629 pub fn to_radians(self) -> f32 { num::Float::to_radians(self) }
631 /// Constructs a floating point number of `x*2^exp`.
634 /// #![feature(float_extras)]
637 /// // 3*2^2 - 12 == 0
638 /// let abs_difference = (f32::ldexp(3.0, 2) - 12.0).abs();
640 /// assert!(abs_difference <= f32::EPSILON);
642 #[unstable(feature = "float_extras",
643 reason = "pending integer conventions")]
645 pub fn ldexp(x: f32, exp: isize) -> f32 {
646 unsafe { cmath::ldexpf(x, exp as c_int) }
649 /// Breaks the number into a normalized fraction and a base-2 exponent,
652 /// * `self = x * 2^exp`
653 /// * `0.5 <= abs(x) < 1.0`
656 /// #![feature(float_extras)]
662 /// // (1/2)*2^3 -> 1 * 8/2 -> 4.0
663 /// let f = x.frexp();
664 /// let abs_difference_0 = (f.0 - 0.5).abs();
665 /// let abs_difference_1 = (f.1 as f32 - 3.0).abs();
667 /// assert!(abs_difference_0 <= f32::EPSILON);
668 /// assert!(abs_difference_1 <= f32::EPSILON);
670 #[unstable(feature = "float_extras",
671 reason = "pending integer conventions")]
673 pub fn frexp(self) -> (f32, isize) {
676 let x = cmath::frexpf(self, &mut exp);
681 /// Returns the next representable floating-point value in the direction of
685 /// #![feature(float_extras)]
691 /// let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs();
693 /// assert!(abs_diff <= f32::EPSILON);
695 #[unstable(feature = "float_extras",
696 reason = "unsure about its place in the world")]
698 pub fn next_after(self, other: f32) -> f32 {
699 unsafe { cmath::nextafterf(self, other) }
702 /// Returns the maximum of the two numbers.
708 /// assert_eq!(x.max(y), y);
711 /// If one of the arguments is NaN, then the other argument is returned.
712 #[stable(feature = "rust1", since = "1.0.0")]
714 pub fn max(self, other: f32) -> f32 {
715 unsafe { cmath::fmaxf(self, other) }
718 /// Returns the minimum of the two numbers.
724 /// assert_eq!(x.min(y), x);
727 /// If one of the arguments is NaN, then the other argument is returned.
728 #[stable(feature = "rust1", since = "1.0.0")]
730 pub fn min(self, other: f32) -> f32 {
731 unsafe { cmath::fminf(self, other) }
734 /// The positive difference of two numbers.
736 /// * If `self <= other`: `0:0`
737 /// * Else: `self - other`
745 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
746 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
748 /// assert!(abs_difference_x <= f32::EPSILON);
749 /// assert!(abs_difference_y <= f32::EPSILON);
751 #[stable(feature = "rust1", since = "1.0.0")]
753 pub fn abs_sub(self, other: f32) -> f32 {
754 unsafe { cmath::fdimf(self, other) }
757 /// Takes the cubic root of a number.
764 /// // x^(1/3) - 2 == 0
765 /// let abs_difference = (x.cbrt() - 2.0).abs();
767 /// assert!(abs_difference <= f32::EPSILON);
769 #[stable(feature = "rust1", since = "1.0.0")]
771 pub fn cbrt(self) -> f32 {
772 unsafe { cmath::cbrtf(self) }
775 /// Calculates the length of the hypotenuse of a right-angle triangle given
776 /// legs of length `x` and `y`.
784 /// // sqrt(x^2 + y^2)
785 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
787 /// assert!(abs_difference <= f32::EPSILON);
789 #[stable(feature = "rust1", since = "1.0.0")]
791 pub fn hypot(self, other: f32) -> f32 {
792 unsafe { cmath::hypotf(self, other) }
795 /// Computes the sine of a number (in radians).
800 /// let x = f32::consts::PI/2.0;
802 /// let abs_difference = (x.sin() - 1.0).abs();
804 /// assert!(abs_difference <= f32::EPSILON);
806 #[stable(feature = "rust1", since = "1.0.0")]
808 pub fn sin(self) -> f32 {
811 // see notes in `core::f32::Float::floor`
812 #[cfg(target_env = "msvc")]
813 fn sinf(f: f32) -> f32 { (f as f64).sin() as f32 }
814 #[cfg(not(target_env = "msvc"))]
815 fn sinf(f: f32) -> f32 { unsafe { intrinsics::sinf32(f) } }
818 /// Computes the cosine of a number (in radians).
823 /// let x = 2.0*f32::consts::PI;
825 /// let abs_difference = (x.cos() - 1.0).abs();
827 /// assert!(abs_difference <= f32::EPSILON);
829 #[stable(feature = "rust1", since = "1.0.0")]
831 pub fn cos(self) -> f32 {
834 // see notes in `core::f32::Float::floor`
835 #[cfg(target_env = "msvc")]
836 fn cosf(f: f32) -> f32 { (f as f64).cos() as f32 }
837 #[cfg(not(target_env = "msvc"))]
838 fn cosf(f: f32) -> f32 { unsafe { intrinsics::cosf32(f) } }
841 /// Computes the tangent of a number (in radians).
846 /// let x = f64::consts::PI/4.0;
847 /// let abs_difference = (x.tan() - 1.0).abs();
849 /// assert!(abs_difference < 1e-10);
851 #[stable(feature = "rust1", since = "1.0.0")]
853 pub fn tan(self) -> f32 {
854 unsafe { cmath::tanf(self) }
857 /// Computes the arcsine of a number. Return value is in radians in
858 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
864 /// let f = f32::consts::PI / 2.0;
866 /// // asin(sin(pi/2))
867 /// let abs_difference = f.sin().asin().abs_sub(f32::consts::PI / 2.0);
869 /// assert!(abs_difference <= f32::EPSILON);
871 #[stable(feature = "rust1", since = "1.0.0")]
873 pub fn asin(self) -> f32 {
874 unsafe { cmath::asinf(self) }
877 /// Computes the arccosine of a number. Return value is in radians in
878 /// the range [0, pi] or NaN if the number is outside the range
884 /// let f = f32::consts::PI / 4.0;
886 /// // acos(cos(pi/4))
887 /// let abs_difference = f.cos().acos().abs_sub(f32::consts::PI / 4.0);
889 /// assert!(abs_difference <= f32::EPSILON);
891 #[stable(feature = "rust1", since = "1.0.0")]
893 pub fn acos(self) -> f32 {
894 unsafe { cmath::acosf(self) }
897 /// Computes the arctangent of a number. Return value is in radians in the
898 /// range [-pi/2, pi/2];
906 /// let abs_difference = f.tan().atan().abs_sub(1.0);
908 /// assert!(abs_difference <= f32::EPSILON);
910 #[stable(feature = "rust1", since = "1.0.0")]
912 pub fn atan(self) -> f32 {
913 unsafe { cmath::atanf(self) }
916 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
918 /// * `x = 0`, `y = 0`: `0`
919 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
920 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
921 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
926 /// let pi = f32::consts::PI;
927 /// // All angles from horizontal right (+x)
928 /// // 45 deg counter-clockwise
930 /// let y1 = -3.0f32;
932 /// // 135 deg clockwise
933 /// let x2 = -3.0f32;
936 /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
937 /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
939 /// assert!(abs_difference_1 <= f32::EPSILON);
940 /// assert!(abs_difference_2 <= f32::EPSILON);
942 #[stable(feature = "rust1", since = "1.0.0")]
944 pub fn atan2(self, other: f32) -> f32 {
945 unsafe { cmath::atan2f(self, other) }
948 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
949 /// `(sin(x), cos(x))`.
954 /// let x = f32::consts::PI/4.0;
955 /// let f = x.sin_cos();
957 /// let abs_difference_0 = (f.0 - x.sin()).abs();
958 /// let abs_difference_1 = (f.1 - x.cos()).abs();
960 /// assert!(abs_difference_0 <= f32::EPSILON);
961 /// assert!(abs_difference_0 <= f32::EPSILON);
963 #[stable(feature = "rust1", since = "1.0.0")]
965 pub fn sin_cos(self) -> (f32, f32) {
966 (self.sin(), self.cos())
969 /// Returns `e^(self) - 1` in a way that is accurate even if the
970 /// number is close to zero.
976 /// let abs_difference = x.ln().exp_m1().abs_sub(6.0);
978 /// assert!(abs_difference < 1e-10);
980 #[stable(feature = "rust1", since = "1.0.0")]
982 pub fn exp_m1(self) -> f32 {
983 unsafe { cmath::expm1f(self) }
986 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
987 /// the operations were performed separately.
992 /// let x = f32::consts::E - 1.0;
994 /// // ln(1 + (e - 1)) == ln(e) == 1
995 /// let abs_difference = (x.ln_1p() - 1.0).abs();
997 /// assert!(abs_difference <= f32::EPSILON);
999 #[stable(feature = "rust1", since = "1.0.0")]
1001 pub fn ln_1p(self) -> f32 {
1002 unsafe { cmath::log1pf(self) }
1005 /// Hyperbolic sine function.
1010 /// let e = f32::consts::E;
1013 /// let f = x.sinh();
1014 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
1015 /// let g = (e*e - 1.0)/(2.0*e);
1016 /// let abs_difference = (f - g).abs();
1018 /// assert!(abs_difference <= f32::EPSILON);
1020 #[stable(feature = "rust1", since = "1.0.0")]
1022 pub fn sinh(self) -> f32 {
1023 unsafe { cmath::sinhf(self) }
1026 /// Hyperbolic cosine function.
1031 /// let e = f32::consts::E;
1033 /// let f = x.cosh();
1034 /// // Solving cosh() at 1 gives this result
1035 /// let g = (e*e + 1.0)/(2.0*e);
1036 /// let abs_difference = f.abs_sub(g);
1039 /// assert!(abs_difference <= f32::EPSILON);
1041 #[stable(feature = "rust1", since = "1.0.0")]
1043 pub fn cosh(self) -> f32 {
1044 unsafe { cmath::coshf(self) }
1047 /// Hyperbolic tangent function.
1052 /// let e = f32::consts::E;
1055 /// let f = x.tanh();
1056 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1057 /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
1058 /// let abs_difference = (f - g).abs();
1060 /// assert!(abs_difference <= f32::EPSILON);
1062 #[stable(feature = "rust1", since = "1.0.0")]
1064 pub fn tanh(self) -> f32 {
1065 unsafe { cmath::tanhf(self) }
1068 /// Inverse hyperbolic sine function.
1074 /// let f = x.sinh().asinh();
1076 /// let abs_difference = (f - x).abs();
1078 /// assert!(abs_difference <= f32::EPSILON);
1080 #[stable(feature = "rust1", since = "1.0.0")]
1082 pub fn asinh(self) -> f32 {
1084 NEG_INFINITY => NEG_INFINITY,
1085 x => (x + ((x * x) + 1.0).sqrt()).ln(),
1089 /// Inverse hyperbolic cosine function.
1095 /// let f = x.cosh().acosh();
1097 /// let abs_difference = (f - x).abs();
1099 /// assert!(abs_difference <= f32::EPSILON);
1101 #[stable(feature = "rust1", since = "1.0.0")]
1103 pub fn acosh(self) -> f32 {
1105 x if x < 1.0 => ::f32::NAN,
1106 x => (x + ((x * x) - 1.0).sqrt()).ln(),
1110 /// Inverse hyperbolic tangent function.
1115 /// let e = f32::consts::E;
1116 /// let f = e.tanh().atanh();
1118 /// let abs_difference = f.abs_sub(e);
1120 /// assert!(abs_difference <= f32::EPSILON);
1122 #[stable(feature = "rust1", since = "1.0.0")]
1124 pub fn atanh(self) -> f32 {
1125 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1134 use num::FpCategory as Fp;
1138 test_num(10f32, 2f32);
1143 assert_eq!(NAN.min(2.0), 2.0);
1144 assert_eq!(2.0f32.min(NAN), 2.0);
1149 assert_eq!(NAN.max(2.0), 2.0);
1150 assert_eq!(2.0f32.max(NAN), 2.0);
1155 let nan: f32 = f32::NAN;
1156 assert!(nan.is_nan());
1157 assert!(!nan.is_infinite());
1158 assert!(!nan.is_finite());
1159 assert!(!nan.is_normal());
1160 assert!(!nan.is_sign_positive());
1161 assert!(!nan.is_sign_negative());
1162 assert_eq!(Fp::Nan, nan.classify());
1166 fn test_infinity() {
1167 let inf: f32 = f32::INFINITY;
1168 assert!(inf.is_infinite());
1169 assert!(!inf.is_finite());
1170 assert!(inf.is_sign_positive());
1171 assert!(!inf.is_sign_negative());
1172 assert!(!inf.is_nan());
1173 assert!(!inf.is_normal());
1174 assert_eq!(Fp::Infinite, inf.classify());
1178 fn test_neg_infinity() {
1179 let neg_inf: f32 = f32::NEG_INFINITY;
1180 assert!(neg_inf.is_infinite());
1181 assert!(!neg_inf.is_finite());
1182 assert!(!neg_inf.is_sign_positive());
1183 assert!(neg_inf.is_sign_negative());
1184 assert!(!neg_inf.is_nan());
1185 assert!(!neg_inf.is_normal());
1186 assert_eq!(Fp::Infinite, neg_inf.classify());
1191 let zero: f32 = 0.0f32;
1192 assert_eq!(0.0, zero);
1193 assert!(!zero.is_infinite());
1194 assert!(zero.is_finite());
1195 assert!(zero.is_sign_positive());
1196 assert!(!zero.is_sign_negative());
1197 assert!(!zero.is_nan());
1198 assert!(!zero.is_normal());
1199 assert_eq!(Fp::Zero, zero.classify());
1203 fn test_neg_zero() {
1204 let neg_zero: f32 = -0.0;
1205 assert_eq!(0.0, neg_zero);
1206 assert!(!neg_zero.is_infinite());
1207 assert!(neg_zero.is_finite());
1208 assert!(!neg_zero.is_sign_positive());
1209 assert!(neg_zero.is_sign_negative());
1210 assert!(!neg_zero.is_nan());
1211 assert!(!neg_zero.is_normal());
1212 assert_eq!(Fp::Zero, neg_zero.classify());
1217 let one: f32 = 1.0f32;
1218 assert_eq!(1.0, one);
1219 assert!(!one.is_infinite());
1220 assert!(one.is_finite());
1221 assert!(one.is_sign_positive());
1222 assert!(!one.is_sign_negative());
1223 assert!(!one.is_nan());
1224 assert!(one.is_normal());
1225 assert_eq!(Fp::Normal, one.classify());
1230 let nan: f32 = f32::NAN;
1231 let inf: f32 = f32::INFINITY;
1232 let neg_inf: f32 = f32::NEG_INFINITY;
1233 assert!(nan.is_nan());
1234 assert!(!0.0f32.is_nan());
1235 assert!(!5.3f32.is_nan());
1236 assert!(!(-10.732f32).is_nan());
1237 assert!(!inf.is_nan());
1238 assert!(!neg_inf.is_nan());
1242 fn test_is_infinite() {
1243 let nan: f32 = f32::NAN;
1244 let inf: f32 = f32::INFINITY;
1245 let neg_inf: f32 = f32::NEG_INFINITY;
1246 assert!(!nan.is_infinite());
1247 assert!(inf.is_infinite());
1248 assert!(neg_inf.is_infinite());
1249 assert!(!0.0f32.is_infinite());
1250 assert!(!42.8f32.is_infinite());
1251 assert!(!(-109.2f32).is_infinite());
1255 fn test_is_finite() {
1256 let nan: f32 = f32::NAN;
1257 let inf: f32 = f32::INFINITY;
1258 let neg_inf: f32 = f32::NEG_INFINITY;
1259 assert!(!nan.is_finite());
1260 assert!(!inf.is_finite());
1261 assert!(!neg_inf.is_finite());
1262 assert!(0.0f32.is_finite());
1263 assert!(42.8f32.is_finite());
1264 assert!((-109.2f32).is_finite());
1268 fn test_is_normal() {
1269 let nan: f32 = f32::NAN;
1270 let inf: f32 = f32::INFINITY;
1271 let neg_inf: f32 = f32::NEG_INFINITY;
1272 let zero: f32 = 0.0f32;
1273 let neg_zero: f32 = -0.0;
1274 assert!(!nan.is_normal());
1275 assert!(!inf.is_normal());
1276 assert!(!neg_inf.is_normal());
1277 assert!(!zero.is_normal());
1278 assert!(!neg_zero.is_normal());
1279 assert!(1f32.is_normal());
1280 assert!(1e-37f32.is_normal());
1281 assert!(!1e-38f32.is_normal());
1285 fn test_classify() {
1286 let nan: f32 = f32::NAN;
1287 let inf: f32 = f32::INFINITY;
1288 let neg_inf: f32 = f32::NEG_INFINITY;
1289 let zero: f32 = 0.0f32;
1290 let neg_zero: f32 = -0.0;
1291 assert_eq!(nan.classify(), Fp::Nan);
1292 assert_eq!(inf.classify(), Fp::Infinite);
1293 assert_eq!(neg_inf.classify(), Fp::Infinite);
1294 assert_eq!(zero.classify(), Fp::Zero);
1295 assert_eq!(neg_zero.classify(), Fp::Zero);
1296 assert_eq!(1f32.classify(), Fp::Normal);
1297 assert_eq!(1e-37f32.classify(), Fp::Normal);
1298 assert_eq!(1e-38f32.classify(), Fp::Subnormal);
1302 fn test_integer_decode() {
1303 assert_eq!(3.14159265359f32.integer_decode(), (13176795, -22, 1));
1304 assert_eq!((-8573.5918555f32).integer_decode(), (8779358, -10, -1));
1305 assert_eq!(2f32.powf(100.0).integer_decode(), (8388608, 77, 1));
1306 assert_eq!(0f32.integer_decode(), (0, -150, 1));
1307 assert_eq!((-0f32).integer_decode(), (0, -150, -1));
1308 assert_eq!(INFINITY.integer_decode(), (8388608, 105, 1));
1309 assert_eq!(NEG_INFINITY.integer_decode(), (8388608, 105, -1));
1310 assert_eq!(NAN.integer_decode(), (12582912, 105, 1));
1315 assert_approx_eq!(1.0f32.floor(), 1.0f32);
1316 assert_approx_eq!(1.3f32.floor(), 1.0f32);
1317 assert_approx_eq!(1.5f32.floor(), 1.0f32);
1318 assert_approx_eq!(1.7f32.floor(), 1.0f32);
1319 assert_approx_eq!(0.0f32.floor(), 0.0f32);
1320 assert_approx_eq!((-0.0f32).floor(), -0.0f32);
1321 assert_approx_eq!((-1.0f32).floor(), -1.0f32);
1322 assert_approx_eq!((-1.3f32).floor(), -2.0f32);
1323 assert_approx_eq!((-1.5f32).floor(), -2.0f32);
1324 assert_approx_eq!((-1.7f32).floor(), -2.0f32);
1329 assert_approx_eq!(1.0f32.ceil(), 1.0f32);
1330 assert_approx_eq!(1.3f32.ceil(), 2.0f32);
1331 assert_approx_eq!(1.5f32.ceil(), 2.0f32);
1332 assert_approx_eq!(1.7f32.ceil(), 2.0f32);
1333 assert_approx_eq!(0.0f32.ceil(), 0.0f32);
1334 assert_approx_eq!((-0.0f32).ceil(), -0.0f32);
1335 assert_approx_eq!((-1.0f32).ceil(), -1.0f32);
1336 assert_approx_eq!((-1.3f32).ceil(), -1.0f32);
1337 assert_approx_eq!((-1.5f32).ceil(), -1.0f32);
1338 assert_approx_eq!((-1.7f32).ceil(), -1.0f32);
1343 assert_approx_eq!(1.0f32.round(), 1.0f32);
1344 assert_approx_eq!(1.3f32.round(), 1.0f32);
1345 assert_approx_eq!(1.5f32.round(), 2.0f32);
1346 assert_approx_eq!(1.7f32.round(), 2.0f32);
1347 assert_approx_eq!(0.0f32.round(), 0.0f32);
1348 assert_approx_eq!((-0.0f32).round(), -0.0f32);
1349 assert_approx_eq!((-1.0f32).round(), -1.0f32);
1350 assert_approx_eq!((-1.3f32).round(), -1.0f32);
1351 assert_approx_eq!((-1.5f32).round(), -2.0f32);
1352 assert_approx_eq!((-1.7f32).round(), -2.0f32);
1357 assert_approx_eq!(1.0f32.trunc(), 1.0f32);
1358 assert_approx_eq!(1.3f32.trunc(), 1.0f32);
1359 assert_approx_eq!(1.5f32.trunc(), 1.0f32);
1360 assert_approx_eq!(1.7f32.trunc(), 1.0f32);
1361 assert_approx_eq!(0.0f32.trunc(), 0.0f32);
1362 assert_approx_eq!((-0.0f32).trunc(), -0.0f32);
1363 assert_approx_eq!((-1.0f32).trunc(), -1.0f32);
1364 assert_approx_eq!((-1.3f32).trunc(), -1.0f32);
1365 assert_approx_eq!((-1.5f32).trunc(), -1.0f32);
1366 assert_approx_eq!((-1.7f32).trunc(), -1.0f32);
1371 assert_approx_eq!(1.0f32.fract(), 0.0f32);
1372 assert_approx_eq!(1.3f32.fract(), 0.3f32);
1373 assert_approx_eq!(1.5f32.fract(), 0.5f32);
1374 assert_approx_eq!(1.7f32.fract(), 0.7f32);
1375 assert_approx_eq!(0.0f32.fract(), 0.0f32);
1376 assert_approx_eq!((-0.0f32).fract(), -0.0f32);
1377 assert_approx_eq!((-1.0f32).fract(), -0.0f32);
1378 assert_approx_eq!((-1.3f32).fract(), -0.3f32);
1379 assert_approx_eq!((-1.5f32).fract(), -0.5f32);
1380 assert_approx_eq!((-1.7f32).fract(), -0.7f32);
1385 assert_eq!(INFINITY.abs(), INFINITY);
1386 assert_eq!(1f32.abs(), 1f32);
1387 assert_eq!(0f32.abs(), 0f32);
1388 assert_eq!((-0f32).abs(), 0f32);
1389 assert_eq!((-1f32).abs(), 1f32);
1390 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1391 assert_eq!((1f32/NEG_INFINITY).abs(), 0f32);
1392 assert!(NAN.abs().is_nan());
1397 assert_eq!(INFINITY.signum(), 1f32);
1398 assert_eq!(1f32.signum(), 1f32);
1399 assert_eq!(0f32.signum(), 1f32);
1400 assert_eq!((-0f32).signum(), -1f32);
1401 assert_eq!((-1f32).signum(), -1f32);
1402 assert_eq!(NEG_INFINITY.signum(), -1f32);
1403 assert_eq!((1f32/NEG_INFINITY).signum(), -1f32);
1404 assert!(NAN.signum().is_nan());
1408 fn test_is_sign_positive() {
1409 assert!(INFINITY.is_sign_positive());
1410 assert!(1f32.is_sign_positive());
1411 assert!(0f32.is_sign_positive());
1412 assert!(!(-0f32).is_sign_positive());
1413 assert!(!(-1f32).is_sign_positive());
1414 assert!(!NEG_INFINITY.is_sign_positive());
1415 assert!(!(1f32/NEG_INFINITY).is_sign_positive());
1416 assert!(!NAN.is_sign_positive());
1420 fn test_is_sign_negative() {
1421 assert!(!INFINITY.is_sign_negative());
1422 assert!(!1f32.is_sign_negative());
1423 assert!(!0f32.is_sign_negative());
1424 assert!((-0f32).is_sign_negative());
1425 assert!((-1f32).is_sign_negative());
1426 assert!(NEG_INFINITY.is_sign_negative());
1427 assert!((1f32/NEG_INFINITY).is_sign_negative());
1428 assert!(!NAN.is_sign_negative());
1433 let nan: f32 = f32::NAN;
1434 let inf: f32 = f32::INFINITY;
1435 let neg_inf: f32 = f32::NEG_INFINITY;
1436 assert_approx_eq!(12.3f32.mul_add(4.5, 6.7), 62.05);
1437 assert_approx_eq!((-12.3f32).mul_add(-4.5, -6.7), 48.65);
1438 assert_approx_eq!(0.0f32.mul_add(8.9, 1.2), 1.2);
1439 assert_approx_eq!(3.4f32.mul_add(-0.0, 5.6), 5.6);
1440 assert!(nan.mul_add(7.8, 9.0).is_nan());
1441 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1442 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1443 assert_eq!(8.9f32.mul_add(inf, 3.2), inf);
1444 assert_eq!((-3.2f32).mul_add(2.4, neg_inf), neg_inf);
1449 let nan: f32 = f32::NAN;
1450 let inf: f32 = f32::INFINITY;
1451 let neg_inf: f32 = f32::NEG_INFINITY;
1452 assert_eq!(1.0f32.recip(), 1.0);
1453 assert_eq!(2.0f32.recip(), 0.5);
1454 assert_eq!((-0.4f32).recip(), -2.5);
1455 assert_eq!(0.0f32.recip(), inf);
1456 assert!(nan.recip().is_nan());
1457 assert_eq!(inf.recip(), 0.0);
1458 assert_eq!(neg_inf.recip(), 0.0);
1463 let nan: f32 = f32::NAN;
1464 let inf: f32 = f32::INFINITY;
1465 let neg_inf: f32 = f32::NEG_INFINITY;
1466 assert_eq!(1.0f32.powi(1), 1.0);
1467 assert_approx_eq!((-3.1f32).powi(2), 9.61);
1468 assert_approx_eq!(5.9f32.powi(-2), 0.028727);
1469 assert_eq!(8.3f32.powi(0), 1.0);
1470 assert!(nan.powi(2).is_nan());
1471 assert_eq!(inf.powi(3), inf);
1472 assert_eq!(neg_inf.powi(2), inf);
1477 let nan: f32 = f32::NAN;
1478 let inf: f32 = f32::INFINITY;
1479 let neg_inf: f32 = f32::NEG_INFINITY;
1480 assert_eq!(1.0f32.powf(1.0), 1.0);
1481 assert_approx_eq!(3.4f32.powf(4.5), 246.408218);
1482 assert_approx_eq!(2.7f32.powf(-3.2), 0.041652);
1483 assert_approx_eq!((-3.1f32).powf(2.0), 9.61);
1484 assert_approx_eq!(5.9f32.powf(-2.0), 0.028727);
1485 assert_eq!(8.3f32.powf(0.0), 1.0);
1486 assert!(nan.powf(2.0).is_nan());
1487 assert_eq!(inf.powf(2.0), inf);
1488 assert_eq!(neg_inf.powf(3.0), neg_inf);
1492 fn test_sqrt_domain() {
1493 assert!(NAN.sqrt().is_nan());
1494 assert!(NEG_INFINITY.sqrt().is_nan());
1495 assert!((-1.0f32).sqrt().is_nan());
1496 assert_eq!((-0.0f32).sqrt(), -0.0);
1497 assert_eq!(0.0f32.sqrt(), 0.0);
1498 assert_eq!(1.0f32.sqrt(), 1.0);
1499 assert_eq!(INFINITY.sqrt(), INFINITY);
1504 assert_eq!(1.0, 0.0f32.exp());
1505 assert_approx_eq!(2.718282, 1.0f32.exp());
1506 assert_approx_eq!(148.413162, 5.0f32.exp());
1508 let inf: f32 = f32::INFINITY;
1509 let neg_inf: f32 = f32::NEG_INFINITY;
1510 let nan: f32 = f32::NAN;
1511 assert_eq!(inf, inf.exp());
1512 assert_eq!(0.0, neg_inf.exp());
1513 assert!(nan.exp().is_nan());
1518 assert_eq!(32.0, 5.0f32.exp2());
1519 assert_eq!(1.0, 0.0f32.exp2());
1521 let inf: f32 = f32::INFINITY;
1522 let neg_inf: f32 = f32::NEG_INFINITY;
1523 let nan: f32 = f32::NAN;
1524 assert_eq!(inf, inf.exp2());
1525 assert_eq!(0.0, neg_inf.exp2());
1526 assert!(nan.exp2().is_nan());
1531 let nan: f32 = f32::NAN;
1532 let inf: f32 = f32::INFINITY;
1533 let neg_inf: f32 = f32::NEG_INFINITY;
1534 assert_approx_eq!(1.0f32.exp().ln(), 1.0);
1535 assert!(nan.ln().is_nan());
1536 assert_eq!(inf.ln(), inf);
1537 assert!(neg_inf.ln().is_nan());
1538 assert!((-2.3f32).ln().is_nan());
1539 assert_eq!((-0.0f32).ln(), neg_inf);
1540 assert_eq!(0.0f32.ln(), neg_inf);
1541 assert_approx_eq!(4.0f32.ln(), 1.386294);
1546 let nan: f32 = f32::NAN;
1547 let inf: f32 = f32::INFINITY;
1548 let neg_inf: f32 = f32::NEG_INFINITY;
1549 assert_eq!(10.0f32.log(10.0), 1.0);
1550 assert_approx_eq!(2.3f32.log(3.5), 0.664858);
1551 assert_eq!(1.0f32.exp().log(1.0f32.exp()), 1.0);
1552 assert!(1.0f32.log(1.0).is_nan());
1553 assert!(1.0f32.log(-13.9).is_nan());
1554 assert!(nan.log(2.3).is_nan());
1555 assert_eq!(inf.log(10.0), inf);
1556 assert!(neg_inf.log(8.8).is_nan());
1557 assert!((-2.3f32).log(0.1).is_nan());
1558 assert_eq!((-0.0f32).log(2.0), neg_inf);
1559 assert_eq!(0.0f32.log(7.0), neg_inf);
1564 let nan: f32 = f32::NAN;
1565 let inf: f32 = f32::INFINITY;
1566 let neg_inf: f32 = f32::NEG_INFINITY;
1567 assert_approx_eq!(10.0f32.log2(), 3.321928);
1568 assert_approx_eq!(2.3f32.log2(), 1.201634);
1569 assert_approx_eq!(1.0f32.exp().log2(), 1.442695);
1570 assert!(nan.log2().is_nan());
1571 assert_eq!(inf.log2(), inf);
1572 assert!(neg_inf.log2().is_nan());
1573 assert!((-2.3f32).log2().is_nan());
1574 assert_eq!((-0.0f32).log2(), neg_inf);
1575 assert_eq!(0.0f32.log2(), neg_inf);
1580 let nan: f32 = f32::NAN;
1581 let inf: f32 = f32::INFINITY;
1582 let neg_inf: f32 = f32::NEG_INFINITY;
1583 assert_eq!(10.0f32.log10(), 1.0);
1584 assert_approx_eq!(2.3f32.log10(), 0.361728);
1585 assert_approx_eq!(1.0f32.exp().log10(), 0.434294);
1586 assert_eq!(1.0f32.log10(), 0.0);
1587 assert!(nan.log10().is_nan());
1588 assert_eq!(inf.log10(), inf);
1589 assert!(neg_inf.log10().is_nan());
1590 assert!((-2.3f32).log10().is_nan());
1591 assert_eq!((-0.0f32).log10(), neg_inf);
1592 assert_eq!(0.0f32.log10(), neg_inf);
1596 fn test_to_degrees() {
1597 let pi: f32 = consts::PI;
1598 let nan: f32 = f32::NAN;
1599 let inf: f32 = f32::INFINITY;
1600 let neg_inf: f32 = f32::NEG_INFINITY;
1601 assert_eq!(0.0f32.to_degrees(), 0.0);
1602 assert_approx_eq!((-5.8f32).to_degrees(), -332.315521);
1603 assert_eq!(pi.to_degrees(), 180.0);
1604 assert!(nan.to_degrees().is_nan());
1605 assert_eq!(inf.to_degrees(), inf);
1606 assert_eq!(neg_inf.to_degrees(), neg_inf);
1610 fn test_to_radians() {
1611 let pi: f32 = consts::PI;
1612 let nan: f32 = f32::NAN;
1613 let inf: f32 = f32::INFINITY;
1614 let neg_inf: f32 = f32::NEG_INFINITY;
1615 assert_eq!(0.0f32.to_radians(), 0.0);
1616 assert_approx_eq!(154.6f32.to_radians(), 2.698279);
1617 assert_approx_eq!((-332.31f32).to_radians(), -5.799903);
1618 assert_eq!(180.0f32.to_radians(), pi);
1619 assert!(nan.to_radians().is_nan());
1620 assert_eq!(inf.to_radians(), inf);
1621 assert_eq!(neg_inf.to_radians(), neg_inf);
1626 // We have to use from_str until base-2 exponents
1627 // are supported in floating-point literals
1628 let f1: f32 = f32::from_str_radix("1p-123", 16).unwrap();
1629 let f2: f32 = f32::from_str_radix("1p-111", 16).unwrap();
1630 let f3: f32 = f32::from_str_radix("1.Cp-12", 16).unwrap();
1631 assert_eq!(f32::ldexp(1f32, -123), f1);
1632 assert_eq!(f32::ldexp(1f32, -111), f2);
1633 assert_eq!(f32::ldexp(1.75f32, -12), f3);
1635 assert_eq!(f32::ldexp(0f32, -123), 0f32);
1636 assert_eq!(f32::ldexp(-0f32, -123), -0f32);
1638 let inf: f32 = f32::INFINITY;
1639 let neg_inf: f32 = f32::NEG_INFINITY;
1640 let nan: f32 = f32::NAN;
1641 assert_eq!(f32::ldexp(inf, -123), inf);
1642 assert_eq!(f32::ldexp(neg_inf, -123), neg_inf);
1643 assert!(f32::ldexp(nan, -123).is_nan());
1648 // We have to use from_str until base-2 exponents
1649 // are supported in floating-point literals
1650 let f1: f32 = f32::from_str_radix("1p-123", 16).unwrap();
1651 let f2: f32 = f32::from_str_radix("1p-111", 16).unwrap();
1652 let f3: f32 = f32::from_str_radix("1.Cp-123", 16).unwrap();
1653 let (x1, exp1) = f1.frexp();
1654 let (x2, exp2) = f2.frexp();
1655 let (x3, exp3) = f3.frexp();
1656 assert_eq!((x1, exp1), (0.5f32, -122));
1657 assert_eq!((x2, exp2), (0.5f32, -110));
1658 assert_eq!((x3, exp3), (0.875f32, -122));
1659 assert_eq!(f32::ldexp(x1, exp1), f1);
1660 assert_eq!(f32::ldexp(x2, exp2), f2);
1661 assert_eq!(f32::ldexp(x3, exp3), f3);
1663 assert_eq!(0f32.frexp(), (0f32, 0));
1664 assert_eq!((-0f32).frexp(), (-0f32, 0));
1667 #[test] #[cfg_attr(windows, ignore)] // FIXME #8755
1668 fn test_frexp_nowin() {
1669 let inf: f32 = f32::INFINITY;
1670 let neg_inf: f32 = f32::NEG_INFINITY;
1671 let nan: f32 = f32::NAN;
1672 assert_eq!(match inf.frexp() { (x, _) => x }, inf);
1673 assert_eq!(match neg_inf.frexp() { (x, _) => x }, neg_inf);
1674 assert!(match nan.frexp() { (x, _) => x.is_nan() })
1679 assert_eq!((-1f32).abs_sub(1f32), 0f32);
1680 assert_eq!(1f32.abs_sub(1f32), 0f32);
1681 assert_eq!(1f32.abs_sub(0f32), 1f32);
1682 assert_eq!(1f32.abs_sub(-1f32), 2f32);
1683 assert_eq!(NEG_INFINITY.abs_sub(0f32), 0f32);
1684 assert_eq!(INFINITY.abs_sub(1f32), INFINITY);
1685 assert_eq!(0f32.abs_sub(NEG_INFINITY), INFINITY);
1686 assert_eq!(0f32.abs_sub(INFINITY), 0f32);
1690 fn test_abs_sub_nowin() {
1691 assert!(NAN.abs_sub(-1f32).is_nan());
1692 assert!(1f32.abs_sub(NAN).is_nan());
1697 assert_eq!(0.0f32.asinh(), 0.0f32);
1698 assert_eq!((-0.0f32).asinh(), -0.0f32);
1700 let inf: f32 = f32::INFINITY;
1701 let neg_inf: f32 = f32::NEG_INFINITY;
1702 let nan: f32 = f32::NAN;
1703 assert_eq!(inf.asinh(), inf);
1704 assert_eq!(neg_inf.asinh(), neg_inf);
1705 assert!(nan.asinh().is_nan());
1706 assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32);
1707 assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32);
1712 assert_eq!(1.0f32.acosh(), 0.0f32);
1713 assert!(0.999f32.acosh().is_nan());
1715 let inf: f32 = f32::INFINITY;
1716 let neg_inf: f32 = f32::NEG_INFINITY;
1717 let nan: f32 = f32::NAN;
1718 assert_eq!(inf.acosh(), inf);
1719 assert!(neg_inf.acosh().is_nan());
1720 assert!(nan.acosh().is_nan());
1721 assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32);
1722 assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32);
1727 assert_eq!(0.0f32.atanh(), 0.0f32);
1728 assert_eq!((-0.0f32).atanh(), -0.0f32);
1730 let inf32: f32 = f32::INFINITY;
1731 let neg_inf32: f32 = f32::NEG_INFINITY;
1732 assert_eq!(1.0f32.atanh(), inf32);
1733 assert_eq!((-1.0f32).atanh(), neg_inf32);
1735 assert!(2f64.atanh().atanh().is_nan());
1736 assert!((-2f64).atanh().atanh().is_nan());
1738 let inf64: f32 = f32::INFINITY;
1739 let neg_inf64: f32 = f32::NEG_INFINITY;
1740 let nan32: f32 = f32::NAN;
1741 assert!(inf64.atanh().is_nan());
1742 assert!(neg_inf64.atanh().is_nan());
1743 assert!(nan32.atanh().is_nan());
1745 assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32);
1746 assert_approx_eq!((-0.5f32).atanh(), -0.54930614433405484569762261846126285f32);
1750 fn test_real_consts() {
1753 let pi: f32 = consts::PI;
1754 let two_pi: f32 = consts::PI_2;
1755 let frac_pi_2: f32 = consts::FRAC_PI_2;
1756 let frac_pi_3: f32 = consts::FRAC_PI_3;
1757 let frac_pi_4: f32 = consts::FRAC_PI_4;
1758 let frac_pi_6: f32 = consts::FRAC_PI_6;
1759 let frac_pi_8: f32 = consts::FRAC_PI_8;
1760 let frac_1_pi: f32 = consts::FRAC_1_PI;
1761 let frac_2_pi: f32 = consts::FRAC_2_PI;
1762 let frac_2_sqrtpi: f32 = consts::FRAC_2_SQRT_PI;
1763 let sqrt2: f32 = consts::SQRT_2;
1764 let frac_1_sqrt2: f32 = consts::FRAC_1_SQRT_2;
1765 let e: f32 = consts::E;
1766 let log2_e: f32 = consts::LOG2_E;
1767 let log10_e: f32 = consts::LOG10_E;
1768 let ln_2: f32 = consts::LN_2;
1769 let ln_10: f32 = consts::LN_10;
1771 assert_approx_eq!(two_pi, 2f32 * pi);
1772 assert_approx_eq!(frac_pi_2, pi / 2f32);
1773 assert_approx_eq!(frac_pi_3, pi / 3f32);
1774 assert_approx_eq!(frac_pi_4, pi / 4f32);
1775 assert_approx_eq!(frac_pi_6, pi / 6f32);
1776 assert_approx_eq!(frac_pi_8, pi / 8f32);
1777 assert_approx_eq!(frac_1_pi, 1f32 / pi);
1778 assert_approx_eq!(frac_2_pi, 2f32 / pi);
1779 assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt());
1780 assert_approx_eq!(sqrt2, 2f32.sqrt());
1781 assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt());
1782 assert_approx_eq!(log2_e, e.log2());
1783 assert_approx_eq!(log10_e, e.log10());
1784 assert_approx_eq!(ln_2, 2f32.ln());
1785 assert_approx_eq!(ln_10, 10f32.ln());