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 64-bit floating point type.
13 //! *[See also the `f64` primitive type](../primitive.f64.html).*
15 #![stable(feature = "rust1", since = "1.0.0")]
16 #![allow(missing_docs)]
27 #[stable(feature = "rust1", since = "1.0.0")]
28 pub use core::f64::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON};
29 #[stable(feature = "rust1", since = "1.0.0")]
30 pub use core::f64::{MIN_EXP, MAX_EXP, MIN_10_EXP};
31 #[stable(feature = "rust1", since = "1.0.0")]
32 pub use core::f64::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
33 #[stable(feature = "rust1", since = "1.0.0")]
34 pub use core::f64::{MIN, MIN_POSITIVE, MAX};
35 #[stable(feature = "rust1", since = "1.0.0")]
36 pub use core::f64::consts;
40 use libc::{c_double, c_int};
44 pub fn acos(n: c_double) -> c_double;
45 pub fn asin(n: c_double) -> c_double;
46 pub fn atan(n: c_double) -> c_double;
47 pub fn atan2(a: c_double, b: c_double) -> c_double;
48 pub fn cbrt(n: c_double) -> c_double;
49 pub fn cosh(n: c_double) -> c_double;
50 pub fn erf(n: c_double) -> c_double;
51 pub fn erfc(n: c_double) -> c_double;
52 pub fn expm1(n: c_double) -> c_double;
53 pub fn fdim(a: c_double, b: c_double) -> c_double;
54 pub fn fmax(a: c_double, b: c_double) -> c_double;
55 pub fn fmin(a: c_double, b: c_double) -> c_double;
56 pub fn fmod(a: c_double, b: c_double) -> c_double;
57 pub fn frexp(n: c_double, value: &mut c_int) -> c_double;
58 pub fn ilogb(n: c_double) -> c_int;
59 pub fn ldexp(x: c_double, n: c_int) -> c_double;
60 pub fn logb(n: c_double) -> c_double;
61 pub fn log1p(n: c_double) -> c_double;
62 pub fn nextafter(x: c_double, y: c_double) -> c_double;
63 pub fn modf(n: c_double, iptr: &mut c_double) -> c_double;
64 pub fn sinh(n: c_double) -> c_double;
65 pub fn tan(n: c_double) -> c_double;
66 pub fn tanh(n: c_double) -> c_double;
67 pub fn tgamma(n: c_double) -> c_double;
69 // These are commonly only available for doubles
71 pub fn j0(n: c_double) -> c_double;
72 pub fn j1(n: c_double) -> c_double;
73 pub fn jn(i: c_int, n: c_double) -> c_double;
75 pub fn y0(n: c_double) -> c_double;
76 pub fn y1(n: c_double) -> c_double;
77 pub fn yn(i: c_int, n: c_double) -> c_double;
79 #[cfg_attr(all(windows, target_env = "msvc"), link_name = "__lgamma_r")]
80 pub fn lgamma_r(n: c_double, sign: &mut c_int) -> c_double;
82 #[cfg_attr(all(windows, target_env = "msvc"), link_name = "_hypot")]
83 pub fn hypot(x: c_double, y: c_double) -> c_double;
90 /// Returns `true` if this value is `NaN` and false otherwise.
95 /// let nan = f64::NAN;
98 /// assert!(nan.is_nan());
99 /// assert!(!f.is_nan());
101 #[stable(feature = "rust1", since = "1.0.0")]
103 pub fn is_nan(self) -> bool { num::Float::is_nan(self) }
105 /// Returns `true` if this value is positive infinity or negative infinity and
112 /// let inf = f64::INFINITY;
113 /// let neg_inf = f64::NEG_INFINITY;
114 /// let nan = f64::NAN;
116 /// assert!(!f.is_infinite());
117 /// assert!(!nan.is_infinite());
119 /// assert!(inf.is_infinite());
120 /// assert!(neg_inf.is_infinite());
122 #[stable(feature = "rust1", since = "1.0.0")]
124 pub fn is_infinite(self) -> bool { num::Float::is_infinite(self) }
126 /// Returns `true` if this number is neither infinite nor `NaN`.
132 /// let inf: f64 = f64::INFINITY;
133 /// let neg_inf: f64 = f64::NEG_INFINITY;
134 /// let nan: f64 = f64::NAN;
136 /// assert!(f.is_finite());
138 /// assert!(!nan.is_finite());
139 /// assert!(!inf.is_finite());
140 /// assert!(!neg_inf.is_finite());
142 #[stable(feature = "rust1", since = "1.0.0")]
144 pub fn is_finite(self) -> bool { num::Float::is_finite(self) }
146 /// Returns `true` if the number is neither zero, infinite,
147 /// [subnormal][subnormal], or `NaN`.
152 /// let min = f32::MIN_POSITIVE; // 1.17549435e-38f64
153 /// let max = f32::MAX;
154 /// let lower_than_min = 1.0e-40_f32;
155 /// let zero = 0.0f32;
157 /// assert!(min.is_normal());
158 /// assert!(max.is_normal());
160 /// assert!(!zero.is_normal());
161 /// assert!(!f32::NAN.is_normal());
162 /// assert!(!f32::INFINITY.is_normal());
163 /// // Values between `0` and `min` are Subnormal.
164 /// assert!(!lower_than_min.is_normal());
166 /// [subnormal]: http://en.wikipedia.org/wiki/Denormal_number
167 #[stable(feature = "rust1", since = "1.0.0")]
169 pub fn is_normal(self) -> bool { num::Float::is_normal(self) }
171 /// Returns the floating point category of the number. If only one property
172 /// is going to be tested, it is generally faster to use the specific
173 /// predicate instead.
176 /// use std::num::FpCategory;
179 /// let num = 12.4_f64;
180 /// let inf = f64::INFINITY;
182 /// assert_eq!(num.classify(), FpCategory::Normal);
183 /// assert_eq!(inf.classify(), FpCategory::Infinite);
185 #[stable(feature = "rust1", since = "1.0.0")]
187 pub fn classify(self) -> FpCategory { num::Float::classify(self) }
189 /// Returns the mantissa, base 2 exponent, and sign as integers, respectively.
190 /// The original number can be recovered by `sign * mantissa * 2 ^ exponent`.
191 /// The floating point encoding is documented in the [Reference][floating-point].
194 /// #![feature(float_extras)]
196 /// let num = 2.0f64;
198 /// // (8388608, -22, 1)
199 /// let (mantissa, exponent, sign) = num.integer_decode();
200 /// let sign_f = sign as f64;
201 /// let mantissa_f = mantissa as f64;
202 /// let exponent_f = num.powf(exponent as f64);
204 /// // 1 * 8388608 * 2^(-22) == 2
205 /// let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs();
207 /// assert!(abs_difference < 1e-10);
209 /// [floating-point]: ../../../../../reference.html#machine-types
210 #[unstable(feature = "float_extras", reason = "signature is undecided",
213 pub fn integer_decode(self) -> (u64, i16, i8) { num::Float::integer_decode(self) }
215 /// Returns the largest integer less than or equal to a number.
218 /// let f = 3.99_f64;
221 /// assert_eq!(f.floor(), 3.0);
222 /// assert_eq!(g.floor(), 3.0);
224 #[stable(feature = "rust1", since = "1.0.0")]
226 pub fn floor(self) -> f64 {
227 unsafe { intrinsics::floorf64(self) }
230 /// Returns the smallest integer greater than or equal to a number.
233 /// let f = 3.01_f64;
236 /// assert_eq!(f.ceil(), 4.0);
237 /// assert_eq!(g.ceil(), 4.0);
239 #[stable(feature = "rust1", since = "1.0.0")]
241 pub fn ceil(self) -> f64 {
242 unsafe { intrinsics::ceilf64(self) }
245 /// Returns the nearest integer to a number. Round half-way cases away from
250 /// let g = -3.3_f64;
252 /// assert_eq!(f.round(), 3.0);
253 /// assert_eq!(g.round(), -3.0);
255 #[stable(feature = "rust1", since = "1.0.0")]
257 pub fn round(self) -> f64 {
258 unsafe { intrinsics::roundf64(self) }
261 /// Returns the integer part of a number.
265 /// let g = -3.7_f64;
267 /// assert_eq!(f.trunc(), 3.0);
268 /// assert_eq!(g.trunc(), -3.0);
270 #[stable(feature = "rust1", since = "1.0.0")]
272 pub fn trunc(self) -> f64 {
273 unsafe { intrinsics::truncf64(self) }
276 /// Returns the fractional part of a number.
280 /// let y = -3.5_f64;
281 /// let abs_difference_x = (x.fract() - 0.5).abs();
282 /// let abs_difference_y = (y.fract() - (-0.5)).abs();
284 /// assert!(abs_difference_x < 1e-10);
285 /// assert!(abs_difference_y < 1e-10);
287 #[stable(feature = "rust1", since = "1.0.0")]
289 pub fn fract(self) -> f64 { self - self.trunc() }
291 /// Computes the absolute value of `self`. Returns `NAN` if the
298 /// let y = -3.5_f64;
300 /// let abs_difference_x = (x.abs() - x).abs();
301 /// let abs_difference_y = (y.abs() - (-y)).abs();
303 /// assert!(abs_difference_x < 1e-10);
304 /// assert!(abs_difference_y < 1e-10);
306 /// assert!(f64::NAN.abs().is_nan());
308 #[stable(feature = "rust1", since = "1.0.0")]
310 pub fn abs(self) -> f64 { num::Float::abs(self) }
312 /// Returns a number that represents the sign of `self`.
314 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
315 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
316 /// - `NAN` if the number is `NAN`
323 /// assert_eq!(f.signum(), 1.0);
324 /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
326 /// assert!(f64::NAN.signum().is_nan());
328 #[stable(feature = "rust1", since = "1.0.0")]
330 pub fn signum(self) -> f64 { num::Float::signum(self) }
332 /// Returns `true` if `self`'s sign bit is positive, including
333 /// `+0.0` and `INFINITY`.
338 /// let nan: f64 = f64::NAN;
341 /// let g = -7.0_f64;
343 /// assert!(f.is_sign_positive());
344 /// assert!(!g.is_sign_positive());
345 /// // Requires both tests to determine if is `NaN`
346 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
348 #[stable(feature = "rust1", since = "1.0.0")]
350 pub fn is_sign_positive(self) -> bool { num::Float::is_sign_positive(self) }
352 #[stable(feature = "rust1", since = "1.0.0")]
353 #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_positive")]
355 pub fn is_positive(self) -> bool { num::Float::is_sign_positive(self) }
357 /// Returns `true` if `self`'s sign is negative, including `-0.0`
358 /// and `NEG_INFINITY`.
363 /// let nan = f64::NAN;
366 /// let g = -7.0_f64;
368 /// assert!(!f.is_sign_negative());
369 /// assert!(g.is_sign_negative());
370 /// // Requires both tests to determine if is `NaN`.
371 /// assert!(!nan.is_sign_positive() && !nan.is_sign_negative());
373 #[stable(feature = "rust1", since = "1.0.0")]
375 pub fn is_sign_negative(self) -> bool { num::Float::is_sign_negative(self) }
377 #[stable(feature = "rust1", since = "1.0.0")]
378 #[rustc_deprecated(since = "1.0.0", reason = "renamed to is_sign_negative")]
380 pub fn is_negative(self) -> bool { num::Float::is_sign_negative(self) }
382 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
383 /// error. This produces a more accurate result with better performance than
384 /// a separate multiplication operation followed by an add.
387 /// let m = 10.0_f64;
389 /// let b = 60.0_f64;
392 /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
394 /// assert!(abs_difference < 1e-10);
396 #[stable(feature = "rust1", since = "1.0.0")]
398 pub fn mul_add(self, a: f64, b: f64) -> f64 {
399 unsafe { intrinsics::fmaf64(self, a, b) }
402 /// Takes the reciprocal (inverse) of a number, `1/x`.
406 /// let abs_difference = (x.recip() - (1.0/x)).abs();
408 /// assert!(abs_difference < 1e-10);
410 #[stable(feature = "rust1", since = "1.0.0")]
412 pub fn recip(self) -> f64 { num::Float::recip(self) }
414 /// Raises a number to an integer power.
416 /// Using this function is generally faster than using `powf`
420 /// let abs_difference = (x.powi(2) - x*x).abs();
422 /// assert!(abs_difference < 1e-10);
424 #[stable(feature = "rust1", since = "1.0.0")]
426 pub fn powi(self, n: i32) -> f64 { num::Float::powi(self, n) }
428 /// Raises a number to a floating point power.
432 /// let abs_difference = (x.powf(2.0) - x*x).abs();
434 /// assert!(abs_difference < 1e-10);
436 #[stable(feature = "rust1", since = "1.0.0")]
438 pub fn powf(self, n: f64) -> f64 {
439 unsafe { intrinsics::powf64(self, n) }
442 /// Takes the square root of a number.
444 /// Returns NaN if `self` is a negative number.
447 /// let positive = 4.0_f64;
448 /// let negative = -4.0_f64;
450 /// let abs_difference = (positive.sqrt() - 2.0).abs();
452 /// assert!(abs_difference < 1e-10);
453 /// assert!(negative.sqrt().is_nan());
455 #[stable(feature = "rust1", since = "1.0.0")]
457 pub fn sqrt(self) -> f64 {
461 unsafe { intrinsics::sqrtf64(self) }
465 /// Returns `e^(self)`, (the exponential function).
468 /// let one = 1.0_f64;
470 /// let e = one.exp();
472 /// // ln(e) - 1 == 0
473 /// let abs_difference = (e.ln() - 1.0).abs();
475 /// assert!(abs_difference < 1e-10);
477 #[stable(feature = "rust1", since = "1.0.0")]
479 pub fn exp(self) -> f64 {
480 unsafe { intrinsics::expf64(self) }
483 /// Returns `2^(self)`.
489 /// let abs_difference = (f.exp2() - 4.0).abs();
491 /// assert!(abs_difference < 1e-10);
493 #[stable(feature = "rust1", since = "1.0.0")]
495 pub fn exp2(self) -> f64 {
496 unsafe { intrinsics::exp2f64(self) }
499 /// Returns the natural logarithm of the number.
502 /// let one = 1.0_f64;
504 /// let e = one.exp();
506 /// // ln(e) - 1 == 0
507 /// let abs_difference = (e.ln() - 1.0).abs();
509 /// assert!(abs_difference < 1e-10);
511 #[stable(feature = "rust1", since = "1.0.0")]
513 pub fn ln(self) -> f64 {
514 unsafe { intrinsics::logf64(self) }
517 /// Returns the logarithm of the number with respect to an arbitrary base.
520 /// let ten = 10.0_f64;
521 /// let two = 2.0_f64;
523 /// // log10(10) - 1 == 0
524 /// let abs_difference_10 = (ten.log(10.0) - 1.0).abs();
526 /// // log2(2) - 1 == 0
527 /// let abs_difference_2 = (two.log(2.0) - 1.0).abs();
529 /// assert!(abs_difference_10 < 1e-10);
530 /// assert!(abs_difference_2 < 1e-10);
532 #[stable(feature = "rust1", since = "1.0.0")]
534 pub fn log(self, base: f64) -> f64 { self.ln() / base.ln() }
536 /// Returns the base 2 logarithm of the number.
539 /// let two = 2.0_f64;
541 /// // log2(2) - 1 == 0
542 /// let abs_difference = (two.log2() - 1.0).abs();
544 /// assert!(abs_difference < 1e-10);
546 #[stable(feature = "rust1", since = "1.0.0")]
548 pub fn log2(self) -> f64 {
549 unsafe { intrinsics::log2f64(self) }
552 /// Returns the base 10 logarithm of the number.
555 /// let ten = 10.0_f64;
557 /// // log10(10) - 1 == 0
558 /// let abs_difference = (ten.log10() - 1.0).abs();
560 /// assert!(abs_difference < 1e-10);
562 #[stable(feature = "rust1", since = "1.0.0")]
564 pub fn log10(self) -> f64 {
565 unsafe { intrinsics::log10f64(self) }
568 /// Converts radians to degrees.
571 /// use std::f64::consts;
573 /// let angle = consts::PI;
575 /// let abs_difference = (angle.to_degrees() - 180.0).abs();
577 /// assert!(abs_difference < 1e-10);
579 #[stable(feature = "rust1", since = "1.0.0")]
581 pub fn to_degrees(self) -> f64 { num::Float::to_degrees(self) }
583 /// Converts degrees to radians.
586 /// use std::f64::consts;
588 /// let angle = 180.0_f64;
590 /// let abs_difference = (angle.to_radians() - consts::PI).abs();
592 /// assert!(abs_difference < 1e-10);
594 #[stable(feature = "rust1", since = "1.0.0")]
596 pub fn to_radians(self) -> f64 { num::Float::to_radians(self) }
598 /// Constructs a floating point number of `x*2^exp`.
601 /// #![feature(float_extras)]
603 /// // 3*2^2 - 12 == 0
604 /// let abs_difference = (f64::ldexp(3.0, 2) - 12.0).abs();
606 /// assert!(abs_difference < 1e-10);
608 #[unstable(feature = "float_extras",
609 reason = "pending integer conventions",
612 pub fn ldexp(x: f64, exp: isize) -> f64 {
613 unsafe { cmath::ldexp(x, exp as c_int) }
616 /// Breaks the number into a normalized fraction and a base-2 exponent,
619 /// * `self = x * 2^exp`
620 /// * `0.5 <= abs(x) < 1.0`
623 /// #![feature(float_extras)]
627 /// // (1/2)*2^3 -> 1 * 8/2 -> 4.0
628 /// let f = x.frexp();
629 /// let abs_difference_0 = (f.0 - 0.5).abs();
630 /// let abs_difference_1 = (f.1 as f64 - 3.0).abs();
632 /// assert!(abs_difference_0 < 1e-10);
633 /// assert!(abs_difference_1 < 1e-10);
635 #[unstable(feature = "float_extras",
636 reason = "pending integer conventions",
639 pub fn frexp(self) -> (f64, isize) {
642 let x = cmath::frexp(self, &mut exp);
647 /// Returns the next representable floating-point value in the direction of
651 /// #![feature(float_extras)]
655 /// let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs();
657 /// assert!(abs_diff < 1e-10);
659 #[unstable(feature = "float_extras",
660 reason = "unsure about its place in the world",
663 pub fn next_after(self, other: f64) -> f64 {
664 unsafe { cmath::nextafter(self, other) }
667 /// Returns the maximum of the two numbers.
673 /// assert_eq!(x.max(y), y);
676 /// If one of the arguments is NaN, then the other argument is returned.
677 #[stable(feature = "rust1", since = "1.0.0")]
679 pub fn max(self, other: f64) -> f64 {
680 unsafe { cmath::fmax(self, other) }
683 /// Returns the minimum of the two numbers.
689 /// assert_eq!(x.min(y), x);
692 /// If one of the arguments is NaN, then the other argument is returned.
693 #[stable(feature = "rust1", since = "1.0.0")]
695 pub fn min(self, other: f64) -> f64 {
696 unsafe { cmath::fmin(self, other) }
699 /// The positive difference of two numbers.
701 /// * If `self <= other`: `0:0`
702 /// * Else: `self - other`
706 /// let y = -3.0_f64;
708 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
709 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
711 /// assert!(abs_difference_x < 1e-10);
712 /// assert!(abs_difference_y < 1e-10);
714 #[stable(feature = "rust1", since = "1.0.0")]
716 pub fn abs_sub(self, other: f64) -> f64 {
717 unsafe { cmath::fdim(self, other) }
720 /// Takes the cubic root of a number.
725 /// // x^(1/3) - 2 == 0
726 /// let abs_difference = (x.cbrt() - 2.0).abs();
728 /// assert!(abs_difference < 1e-10);
730 #[stable(feature = "rust1", since = "1.0.0")]
732 pub fn cbrt(self) -> f64 {
733 unsafe { cmath::cbrt(self) }
736 /// Calculates the length of the hypotenuse of a right-angle triangle given
737 /// legs of length `x` and `y`.
743 /// // sqrt(x^2 + y^2)
744 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
746 /// assert!(abs_difference < 1e-10);
748 #[stable(feature = "rust1", since = "1.0.0")]
750 pub fn hypot(self, other: f64) -> f64 {
751 unsafe { cmath::hypot(self, other) }
754 /// Computes the sine of a number (in radians).
759 /// let x = f64::consts::PI/2.0;
761 /// let abs_difference = (x.sin() - 1.0).abs();
763 /// assert!(abs_difference < 1e-10);
765 #[stable(feature = "rust1", since = "1.0.0")]
767 pub fn sin(self) -> f64 {
768 unsafe { intrinsics::sinf64(self) }
771 /// Computes the cosine of a number (in radians).
776 /// let x = 2.0*f64::consts::PI;
778 /// let abs_difference = (x.cos() - 1.0).abs();
780 /// assert!(abs_difference < 1e-10);
782 #[stable(feature = "rust1", since = "1.0.0")]
784 pub fn cos(self) -> f64 {
785 unsafe { intrinsics::cosf64(self) }
788 /// Computes the tangent of a number (in radians).
793 /// let x = f64::consts::PI/4.0;
794 /// let abs_difference = (x.tan() - 1.0).abs();
796 /// assert!(abs_difference < 1e-14);
798 #[stable(feature = "rust1", since = "1.0.0")]
800 pub fn tan(self) -> f64 {
801 unsafe { cmath::tan(self) }
804 /// Computes the arcsine of a number. Return value is in radians in
805 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
811 /// let f = f64::consts::PI / 2.0;
813 /// // asin(sin(pi/2))
814 /// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
816 /// assert!(abs_difference < 1e-10);
818 #[stable(feature = "rust1", since = "1.0.0")]
820 pub fn asin(self) -> f64 {
821 unsafe { cmath::asin(self) }
824 /// Computes the arccosine of a number. Return value is in radians in
825 /// the range [0, pi] or NaN if the number is outside the range
831 /// let f = f64::consts::PI / 4.0;
833 /// // acos(cos(pi/4))
834 /// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
836 /// assert!(abs_difference < 1e-10);
838 #[stable(feature = "rust1", since = "1.0.0")]
840 pub fn acos(self) -> f64 {
841 unsafe { cmath::acos(self) }
844 /// Computes the arctangent of a number. Return value is in radians in the
845 /// range [-pi/2, pi/2];
851 /// let abs_difference = (f.tan().atan() - 1.0).abs();
853 /// assert!(abs_difference < 1e-10);
855 #[stable(feature = "rust1", since = "1.0.0")]
857 pub fn atan(self) -> f64 {
858 unsafe { cmath::atan(self) }
861 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).
863 /// * `x = 0`, `y = 0`: `0`
864 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
865 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
866 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
871 /// let pi = f64::consts::PI;
872 /// // All angles from horizontal right (+x)
873 /// // 45 deg counter-clockwise
874 /// let x1 = 3.0_f64;
875 /// let y1 = -3.0_f64;
877 /// // 135 deg clockwise
878 /// let x2 = -3.0_f64;
879 /// let y2 = 3.0_f64;
881 /// let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs();
882 /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs();
884 /// assert!(abs_difference_1 < 1e-10);
885 /// assert!(abs_difference_2 < 1e-10);
887 #[stable(feature = "rust1", since = "1.0.0")]
889 pub fn atan2(self, other: f64) -> f64 {
890 unsafe { cmath::atan2(self, other) }
893 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
894 /// `(sin(x), cos(x))`.
899 /// let x = f64::consts::PI/4.0;
900 /// let f = x.sin_cos();
902 /// let abs_difference_0 = (f.0 - x.sin()).abs();
903 /// let abs_difference_1 = (f.1 - x.cos()).abs();
905 /// assert!(abs_difference_0 < 1e-10);
906 /// assert!(abs_difference_0 < 1e-10);
908 #[stable(feature = "rust1", since = "1.0.0")]
910 pub fn sin_cos(self) -> (f64, f64) {
911 (self.sin(), self.cos())
914 /// Returns `e^(self) - 1` in a way that is accurate even if the
915 /// number is close to zero.
921 /// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
923 /// assert!(abs_difference < 1e-10);
925 #[stable(feature = "rust1", since = "1.0.0")]
927 pub fn exp_m1(self) -> f64 {
928 unsafe { cmath::expm1(self) }
931 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
932 /// the operations were performed separately.
937 /// let x = f64::consts::E - 1.0;
939 /// // ln(1 + (e - 1)) == ln(e) == 1
940 /// let abs_difference = (x.ln_1p() - 1.0).abs();
942 /// assert!(abs_difference < 1e-10);
944 #[stable(feature = "rust1", since = "1.0.0")]
946 pub fn ln_1p(self) -> f64 {
947 unsafe { cmath::log1p(self) }
950 /// Hyperbolic sine function.
955 /// let e = f64::consts::E;
958 /// let f = x.sinh();
959 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
960 /// let g = (e*e - 1.0)/(2.0*e);
961 /// let abs_difference = (f - g).abs();
963 /// assert!(abs_difference < 1e-10);
965 #[stable(feature = "rust1", since = "1.0.0")]
967 pub fn sinh(self) -> f64 {
968 unsafe { cmath::sinh(self) }
971 /// Hyperbolic cosine function.
976 /// let e = f64::consts::E;
978 /// let f = x.cosh();
979 /// // Solving cosh() at 1 gives this result
980 /// let g = (e*e + 1.0)/(2.0*e);
981 /// let abs_difference = (f - g).abs();
984 /// assert!(abs_difference < 1.0e-10);
986 #[stable(feature = "rust1", since = "1.0.0")]
988 pub fn cosh(self) -> f64 {
989 unsafe { cmath::cosh(self) }
992 /// Hyperbolic tangent function.
997 /// let e = f64::consts::E;
1000 /// let f = x.tanh();
1001 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
1002 /// let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2));
1003 /// let abs_difference = (f - g).abs();
1005 /// assert!(abs_difference < 1.0e-10);
1007 #[stable(feature = "rust1", since = "1.0.0")]
1009 pub fn tanh(self) -> f64 {
1010 unsafe { cmath::tanh(self) }
1013 /// Inverse hyperbolic sine function.
1016 /// let x = 1.0_f64;
1017 /// let f = x.sinh().asinh();
1019 /// let abs_difference = (f - x).abs();
1021 /// assert!(abs_difference < 1.0e-10);
1023 #[stable(feature = "rust1", since = "1.0.0")]
1025 pub fn asinh(self) -> f64 {
1027 NEG_INFINITY => NEG_INFINITY,
1028 x => (x + ((x * x) + 1.0).sqrt()).ln(),
1032 /// Inverse hyperbolic cosine function.
1035 /// let x = 1.0_f64;
1036 /// let f = x.cosh().acosh();
1038 /// let abs_difference = (f - x).abs();
1040 /// assert!(abs_difference < 1.0e-10);
1042 #[stable(feature = "rust1", since = "1.0.0")]
1044 pub fn acosh(self) -> f64 {
1046 x if x < 1.0 => NAN,
1047 x => (x + ((x * x) - 1.0).sqrt()).ln(),
1051 /// Inverse hyperbolic tangent function.
1056 /// let e = f64::consts::E;
1057 /// let f = e.tanh().atanh();
1059 /// let abs_difference = (f - e).abs();
1061 /// assert!(abs_difference < 1.0e-10);
1063 #[stable(feature = "rust1", since = "1.0.0")]
1065 pub fn atanh(self) -> f64 {
1066 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1075 use num::FpCategory as Fp;
1079 test_num(10f64, 2f64);
1084 assert_eq!(NAN.min(2.0), 2.0);
1085 assert_eq!(2.0f64.min(NAN), 2.0);
1090 assert_eq!(NAN.max(2.0), 2.0);
1091 assert_eq!(2.0f64.max(NAN), 2.0);
1097 assert!(nan.is_nan());
1098 assert!(!nan.is_infinite());
1099 assert!(!nan.is_finite());
1100 assert!(!nan.is_normal());
1101 assert!(!nan.is_sign_positive());
1102 assert!(!nan.is_sign_negative());
1103 assert_eq!(Fp::Nan, nan.classify());
1107 fn test_infinity() {
1108 let inf: f64 = INFINITY;
1109 assert!(inf.is_infinite());
1110 assert!(!inf.is_finite());
1111 assert!(inf.is_sign_positive());
1112 assert!(!inf.is_sign_negative());
1113 assert!(!inf.is_nan());
1114 assert!(!inf.is_normal());
1115 assert_eq!(Fp::Infinite, inf.classify());
1119 fn test_neg_infinity() {
1120 let neg_inf: f64 = NEG_INFINITY;
1121 assert!(neg_inf.is_infinite());
1122 assert!(!neg_inf.is_finite());
1123 assert!(!neg_inf.is_sign_positive());
1124 assert!(neg_inf.is_sign_negative());
1125 assert!(!neg_inf.is_nan());
1126 assert!(!neg_inf.is_normal());
1127 assert_eq!(Fp::Infinite, neg_inf.classify());
1132 let zero: f64 = 0.0f64;
1133 assert_eq!(0.0, zero);
1134 assert!(!zero.is_infinite());
1135 assert!(zero.is_finite());
1136 assert!(zero.is_sign_positive());
1137 assert!(!zero.is_sign_negative());
1138 assert!(!zero.is_nan());
1139 assert!(!zero.is_normal());
1140 assert_eq!(Fp::Zero, zero.classify());
1144 fn test_neg_zero() {
1145 let neg_zero: f64 = -0.0;
1146 assert_eq!(0.0, neg_zero);
1147 assert!(!neg_zero.is_infinite());
1148 assert!(neg_zero.is_finite());
1149 assert!(!neg_zero.is_sign_positive());
1150 assert!(neg_zero.is_sign_negative());
1151 assert!(!neg_zero.is_nan());
1152 assert!(!neg_zero.is_normal());
1153 assert_eq!(Fp::Zero, neg_zero.classify());
1158 let one: f64 = 1.0f64;
1159 assert_eq!(1.0, one);
1160 assert!(!one.is_infinite());
1161 assert!(one.is_finite());
1162 assert!(one.is_sign_positive());
1163 assert!(!one.is_sign_negative());
1164 assert!(!one.is_nan());
1165 assert!(one.is_normal());
1166 assert_eq!(Fp::Normal, one.classify());
1172 let inf: f64 = INFINITY;
1173 let neg_inf: f64 = NEG_INFINITY;
1174 assert!(nan.is_nan());
1175 assert!(!0.0f64.is_nan());
1176 assert!(!5.3f64.is_nan());
1177 assert!(!(-10.732f64).is_nan());
1178 assert!(!inf.is_nan());
1179 assert!(!neg_inf.is_nan());
1183 fn test_is_infinite() {
1185 let inf: f64 = INFINITY;
1186 let neg_inf: f64 = NEG_INFINITY;
1187 assert!(!nan.is_infinite());
1188 assert!(inf.is_infinite());
1189 assert!(neg_inf.is_infinite());
1190 assert!(!0.0f64.is_infinite());
1191 assert!(!42.8f64.is_infinite());
1192 assert!(!(-109.2f64).is_infinite());
1196 fn test_is_finite() {
1198 let inf: f64 = INFINITY;
1199 let neg_inf: f64 = NEG_INFINITY;
1200 assert!(!nan.is_finite());
1201 assert!(!inf.is_finite());
1202 assert!(!neg_inf.is_finite());
1203 assert!(0.0f64.is_finite());
1204 assert!(42.8f64.is_finite());
1205 assert!((-109.2f64).is_finite());
1209 fn test_is_normal() {
1211 let inf: f64 = INFINITY;
1212 let neg_inf: f64 = NEG_INFINITY;
1213 let zero: f64 = 0.0f64;
1214 let neg_zero: f64 = -0.0;
1215 assert!(!nan.is_normal());
1216 assert!(!inf.is_normal());
1217 assert!(!neg_inf.is_normal());
1218 assert!(!zero.is_normal());
1219 assert!(!neg_zero.is_normal());
1220 assert!(1f64.is_normal());
1221 assert!(1e-307f64.is_normal());
1222 assert!(!1e-308f64.is_normal());
1226 fn test_classify() {
1228 let inf: f64 = INFINITY;
1229 let neg_inf: f64 = NEG_INFINITY;
1230 let zero: f64 = 0.0f64;
1231 let neg_zero: f64 = -0.0;
1232 assert_eq!(nan.classify(), Fp::Nan);
1233 assert_eq!(inf.classify(), Fp::Infinite);
1234 assert_eq!(neg_inf.classify(), Fp::Infinite);
1235 assert_eq!(zero.classify(), Fp::Zero);
1236 assert_eq!(neg_zero.classify(), Fp::Zero);
1237 assert_eq!(1e-307f64.classify(), Fp::Normal);
1238 assert_eq!(1e-308f64.classify(), Fp::Subnormal);
1242 fn test_integer_decode() {
1243 assert_eq!(3.14159265359f64.integer_decode(), (7074237752028906, -51, 1));
1244 assert_eq!((-8573.5918555f64).integer_decode(), (4713381968463931, -39, -1));
1245 assert_eq!(2f64.powf(100.0).integer_decode(), (4503599627370496, 48, 1));
1246 assert_eq!(0f64.integer_decode(), (0, -1075, 1));
1247 assert_eq!((-0f64).integer_decode(), (0, -1075, -1));
1248 assert_eq!(INFINITY.integer_decode(), (4503599627370496, 972, 1));
1249 assert_eq!(NEG_INFINITY.integer_decode(), (4503599627370496, 972, -1));
1250 assert_eq!(NAN.integer_decode(), (6755399441055744, 972, 1));
1255 assert_approx_eq!(1.0f64.floor(), 1.0f64);
1256 assert_approx_eq!(1.3f64.floor(), 1.0f64);
1257 assert_approx_eq!(1.5f64.floor(), 1.0f64);
1258 assert_approx_eq!(1.7f64.floor(), 1.0f64);
1259 assert_approx_eq!(0.0f64.floor(), 0.0f64);
1260 assert_approx_eq!((-0.0f64).floor(), -0.0f64);
1261 assert_approx_eq!((-1.0f64).floor(), -1.0f64);
1262 assert_approx_eq!((-1.3f64).floor(), -2.0f64);
1263 assert_approx_eq!((-1.5f64).floor(), -2.0f64);
1264 assert_approx_eq!((-1.7f64).floor(), -2.0f64);
1269 assert_approx_eq!(1.0f64.ceil(), 1.0f64);
1270 assert_approx_eq!(1.3f64.ceil(), 2.0f64);
1271 assert_approx_eq!(1.5f64.ceil(), 2.0f64);
1272 assert_approx_eq!(1.7f64.ceil(), 2.0f64);
1273 assert_approx_eq!(0.0f64.ceil(), 0.0f64);
1274 assert_approx_eq!((-0.0f64).ceil(), -0.0f64);
1275 assert_approx_eq!((-1.0f64).ceil(), -1.0f64);
1276 assert_approx_eq!((-1.3f64).ceil(), -1.0f64);
1277 assert_approx_eq!((-1.5f64).ceil(), -1.0f64);
1278 assert_approx_eq!((-1.7f64).ceil(), -1.0f64);
1283 assert_approx_eq!(1.0f64.round(), 1.0f64);
1284 assert_approx_eq!(1.3f64.round(), 1.0f64);
1285 assert_approx_eq!(1.5f64.round(), 2.0f64);
1286 assert_approx_eq!(1.7f64.round(), 2.0f64);
1287 assert_approx_eq!(0.0f64.round(), 0.0f64);
1288 assert_approx_eq!((-0.0f64).round(), -0.0f64);
1289 assert_approx_eq!((-1.0f64).round(), -1.0f64);
1290 assert_approx_eq!((-1.3f64).round(), -1.0f64);
1291 assert_approx_eq!((-1.5f64).round(), -2.0f64);
1292 assert_approx_eq!((-1.7f64).round(), -2.0f64);
1297 assert_approx_eq!(1.0f64.trunc(), 1.0f64);
1298 assert_approx_eq!(1.3f64.trunc(), 1.0f64);
1299 assert_approx_eq!(1.5f64.trunc(), 1.0f64);
1300 assert_approx_eq!(1.7f64.trunc(), 1.0f64);
1301 assert_approx_eq!(0.0f64.trunc(), 0.0f64);
1302 assert_approx_eq!((-0.0f64).trunc(), -0.0f64);
1303 assert_approx_eq!((-1.0f64).trunc(), -1.0f64);
1304 assert_approx_eq!((-1.3f64).trunc(), -1.0f64);
1305 assert_approx_eq!((-1.5f64).trunc(), -1.0f64);
1306 assert_approx_eq!((-1.7f64).trunc(), -1.0f64);
1311 assert_approx_eq!(1.0f64.fract(), 0.0f64);
1312 assert_approx_eq!(1.3f64.fract(), 0.3f64);
1313 assert_approx_eq!(1.5f64.fract(), 0.5f64);
1314 assert_approx_eq!(1.7f64.fract(), 0.7f64);
1315 assert_approx_eq!(0.0f64.fract(), 0.0f64);
1316 assert_approx_eq!((-0.0f64).fract(), -0.0f64);
1317 assert_approx_eq!((-1.0f64).fract(), -0.0f64);
1318 assert_approx_eq!((-1.3f64).fract(), -0.3f64);
1319 assert_approx_eq!((-1.5f64).fract(), -0.5f64);
1320 assert_approx_eq!((-1.7f64).fract(), -0.7f64);
1325 assert_eq!(INFINITY.abs(), INFINITY);
1326 assert_eq!(1f64.abs(), 1f64);
1327 assert_eq!(0f64.abs(), 0f64);
1328 assert_eq!((-0f64).abs(), 0f64);
1329 assert_eq!((-1f64).abs(), 1f64);
1330 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1331 assert_eq!((1f64/NEG_INFINITY).abs(), 0f64);
1332 assert!(NAN.abs().is_nan());
1337 assert_eq!(INFINITY.signum(), 1f64);
1338 assert_eq!(1f64.signum(), 1f64);
1339 assert_eq!(0f64.signum(), 1f64);
1340 assert_eq!((-0f64).signum(), -1f64);
1341 assert_eq!((-1f64).signum(), -1f64);
1342 assert_eq!(NEG_INFINITY.signum(), -1f64);
1343 assert_eq!((1f64/NEG_INFINITY).signum(), -1f64);
1344 assert!(NAN.signum().is_nan());
1348 fn test_is_sign_positive() {
1349 assert!(INFINITY.is_sign_positive());
1350 assert!(1f64.is_sign_positive());
1351 assert!(0f64.is_sign_positive());
1352 assert!(!(-0f64).is_sign_positive());
1353 assert!(!(-1f64).is_sign_positive());
1354 assert!(!NEG_INFINITY.is_sign_positive());
1355 assert!(!(1f64/NEG_INFINITY).is_sign_positive());
1356 assert!(!NAN.is_sign_positive());
1360 fn test_is_sign_negative() {
1361 assert!(!INFINITY.is_sign_negative());
1362 assert!(!1f64.is_sign_negative());
1363 assert!(!0f64.is_sign_negative());
1364 assert!((-0f64).is_sign_negative());
1365 assert!((-1f64).is_sign_negative());
1366 assert!(NEG_INFINITY.is_sign_negative());
1367 assert!((1f64/NEG_INFINITY).is_sign_negative());
1368 assert!(!NAN.is_sign_negative());
1374 let inf: f64 = INFINITY;
1375 let neg_inf: f64 = NEG_INFINITY;
1376 assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05);
1377 assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65);
1378 assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2);
1379 assert_approx_eq!(3.4f64.mul_add(-0.0, 5.6), 5.6);
1380 assert!(nan.mul_add(7.8, 9.0).is_nan());
1381 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1382 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1383 assert_eq!(8.9f64.mul_add(inf, 3.2), inf);
1384 assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf);
1390 let inf: f64 = INFINITY;
1391 let neg_inf: f64 = NEG_INFINITY;
1392 assert_eq!(1.0f64.recip(), 1.0);
1393 assert_eq!(2.0f64.recip(), 0.5);
1394 assert_eq!((-0.4f64).recip(), -2.5);
1395 assert_eq!(0.0f64.recip(), inf);
1396 assert!(nan.recip().is_nan());
1397 assert_eq!(inf.recip(), 0.0);
1398 assert_eq!(neg_inf.recip(), 0.0);
1404 let inf: f64 = INFINITY;
1405 let neg_inf: f64 = NEG_INFINITY;
1406 assert_eq!(1.0f64.powi(1), 1.0);
1407 assert_approx_eq!((-3.1f64).powi(2), 9.61);
1408 assert_approx_eq!(5.9f64.powi(-2), 0.028727);
1409 assert_eq!(8.3f64.powi(0), 1.0);
1410 assert!(nan.powi(2).is_nan());
1411 assert_eq!(inf.powi(3), inf);
1412 assert_eq!(neg_inf.powi(2), inf);
1418 let inf: f64 = INFINITY;
1419 let neg_inf: f64 = NEG_INFINITY;
1420 assert_eq!(1.0f64.powf(1.0), 1.0);
1421 assert_approx_eq!(3.4f64.powf(4.5), 246.408183);
1422 assert_approx_eq!(2.7f64.powf(-3.2), 0.041652);
1423 assert_approx_eq!((-3.1f64).powf(2.0), 9.61);
1424 assert_approx_eq!(5.9f64.powf(-2.0), 0.028727);
1425 assert_eq!(8.3f64.powf(0.0), 1.0);
1426 assert!(nan.powf(2.0).is_nan());
1427 assert_eq!(inf.powf(2.0), inf);
1428 assert_eq!(neg_inf.powf(3.0), neg_inf);
1432 fn test_sqrt_domain() {
1433 assert!(NAN.sqrt().is_nan());
1434 assert!(NEG_INFINITY.sqrt().is_nan());
1435 assert!((-1.0f64).sqrt().is_nan());
1436 assert_eq!((-0.0f64).sqrt(), -0.0);
1437 assert_eq!(0.0f64.sqrt(), 0.0);
1438 assert_eq!(1.0f64.sqrt(), 1.0);
1439 assert_eq!(INFINITY.sqrt(), INFINITY);
1444 assert_eq!(1.0, 0.0f64.exp());
1445 assert_approx_eq!(2.718282, 1.0f64.exp());
1446 assert_approx_eq!(148.413159, 5.0f64.exp());
1448 let inf: f64 = INFINITY;
1449 let neg_inf: f64 = NEG_INFINITY;
1451 assert_eq!(inf, inf.exp());
1452 assert_eq!(0.0, neg_inf.exp());
1453 assert!(nan.exp().is_nan());
1458 assert_eq!(32.0, 5.0f64.exp2());
1459 assert_eq!(1.0, 0.0f64.exp2());
1461 let inf: f64 = INFINITY;
1462 let neg_inf: f64 = NEG_INFINITY;
1464 assert_eq!(inf, inf.exp2());
1465 assert_eq!(0.0, neg_inf.exp2());
1466 assert!(nan.exp2().is_nan());
1472 let inf: f64 = INFINITY;
1473 let neg_inf: f64 = NEG_INFINITY;
1474 assert_approx_eq!(1.0f64.exp().ln(), 1.0);
1475 assert!(nan.ln().is_nan());
1476 assert_eq!(inf.ln(), inf);
1477 assert!(neg_inf.ln().is_nan());
1478 assert!((-2.3f64).ln().is_nan());
1479 assert_eq!((-0.0f64).ln(), neg_inf);
1480 assert_eq!(0.0f64.ln(), neg_inf);
1481 assert_approx_eq!(4.0f64.ln(), 1.386294);
1487 let inf: f64 = INFINITY;
1488 let neg_inf: f64 = NEG_INFINITY;
1489 assert_eq!(10.0f64.log(10.0), 1.0);
1490 assert_approx_eq!(2.3f64.log(3.5), 0.664858);
1491 assert_eq!(1.0f64.exp().log(1.0f64.exp()), 1.0);
1492 assert!(1.0f64.log(1.0).is_nan());
1493 assert!(1.0f64.log(-13.9).is_nan());
1494 assert!(nan.log(2.3).is_nan());
1495 assert_eq!(inf.log(10.0), inf);
1496 assert!(neg_inf.log(8.8).is_nan());
1497 assert!((-2.3f64).log(0.1).is_nan());
1498 assert_eq!((-0.0f64).log(2.0), neg_inf);
1499 assert_eq!(0.0f64.log(7.0), neg_inf);
1505 let inf: f64 = INFINITY;
1506 let neg_inf: f64 = NEG_INFINITY;
1507 assert_approx_eq!(10.0f64.log2(), 3.321928);
1508 assert_approx_eq!(2.3f64.log2(), 1.201634);
1509 assert_approx_eq!(1.0f64.exp().log2(), 1.442695);
1510 assert!(nan.log2().is_nan());
1511 assert_eq!(inf.log2(), inf);
1512 assert!(neg_inf.log2().is_nan());
1513 assert!((-2.3f64).log2().is_nan());
1514 assert_eq!((-0.0f64).log2(), neg_inf);
1515 assert_eq!(0.0f64.log2(), neg_inf);
1521 let inf: f64 = INFINITY;
1522 let neg_inf: f64 = NEG_INFINITY;
1523 assert_eq!(10.0f64.log10(), 1.0);
1524 assert_approx_eq!(2.3f64.log10(), 0.361728);
1525 assert_approx_eq!(1.0f64.exp().log10(), 0.434294);
1526 assert_eq!(1.0f64.log10(), 0.0);
1527 assert!(nan.log10().is_nan());
1528 assert_eq!(inf.log10(), inf);
1529 assert!(neg_inf.log10().is_nan());
1530 assert!((-2.3f64).log10().is_nan());
1531 assert_eq!((-0.0f64).log10(), neg_inf);
1532 assert_eq!(0.0f64.log10(), neg_inf);
1536 fn test_to_degrees() {
1537 let pi: f64 = consts::PI;
1539 let inf: f64 = INFINITY;
1540 let neg_inf: f64 = NEG_INFINITY;
1541 assert_eq!(0.0f64.to_degrees(), 0.0);
1542 assert_approx_eq!((-5.8f64).to_degrees(), -332.315521);
1543 assert_eq!(pi.to_degrees(), 180.0);
1544 assert!(nan.to_degrees().is_nan());
1545 assert_eq!(inf.to_degrees(), inf);
1546 assert_eq!(neg_inf.to_degrees(), neg_inf);
1550 fn test_to_radians() {
1551 let pi: f64 = consts::PI;
1553 let inf: f64 = INFINITY;
1554 let neg_inf: f64 = NEG_INFINITY;
1555 assert_eq!(0.0f64.to_radians(), 0.0);
1556 assert_approx_eq!(154.6f64.to_radians(), 2.698279);
1557 assert_approx_eq!((-332.31f64).to_radians(), -5.799903);
1558 assert_eq!(180.0f64.to_radians(), pi);
1559 assert!(nan.to_radians().is_nan());
1560 assert_eq!(inf.to_radians(), inf);
1561 assert_eq!(neg_inf.to_radians(), neg_inf);
1566 let f1 = 2.0f64.powi(-123);
1567 let f2 = 2.0f64.powi(-111);
1568 let f3 = 1.75 * 2.0f64.powi(-12);
1569 assert_eq!(f64::ldexp(1f64, -123), f1);
1570 assert_eq!(f64::ldexp(1f64, -111), f2);
1571 assert_eq!(f64::ldexp(1.75f64, -12), f3);
1573 assert_eq!(f64::ldexp(0f64, -123), 0f64);
1574 assert_eq!(f64::ldexp(-0f64, -123), -0f64);
1576 let inf: f64 = INFINITY;
1577 let neg_inf: f64 = NEG_INFINITY;
1579 assert_eq!(f64::ldexp(inf, -123), inf);
1580 assert_eq!(f64::ldexp(neg_inf, -123), neg_inf);
1581 assert!(f64::ldexp(nan, -123).is_nan());
1586 let f1 = 2.0f64.powi(-123);
1587 let f2 = 2.0f64.powi(-111);
1588 let f3 = 1.75 * 2.0f64.powi(-123);
1589 let (x1, exp1) = f1.frexp();
1590 let (x2, exp2) = f2.frexp();
1591 let (x3, exp3) = f3.frexp();
1592 assert_eq!((x1, exp1), (0.5f64, -122));
1593 assert_eq!((x2, exp2), (0.5f64, -110));
1594 assert_eq!((x3, exp3), (0.875f64, -122));
1595 assert_eq!(f64::ldexp(x1, exp1), f1);
1596 assert_eq!(f64::ldexp(x2, exp2), f2);
1597 assert_eq!(f64::ldexp(x3, exp3), f3);
1599 assert_eq!(0f64.frexp(), (0f64, 0));
1600 assert_eq!((-0f64).frexp(), (-0f64, 0));
1603 #[test] #[cfg_attr(windows, ignore)] // FIXME #8755
1604 fn test_frexp_nowin() {
1605 let inf: f64 = INFINITY;
1606 let neg_inf: f64 = NEG_INFINITY;
1608 assert_eq!(match inf.frexp() { (x, _) => x }, inf);
1609 assert_eq!(match neg_inf.frexp() { (x, _) => x }, neg_inf);
1610 assert!(match nan.frexp() { (x, _) => x.is_nan() })
1615 assert_eq!((-1f64).abs_sub(1f64), 0f64);
1616 assert_eq!(1f64.abs_sub(1f64), 0f64);
1617 assert_eq!(1f64.abs_sub(0f64), 1f64);
1618 assert_eq!(1f64.abs_sub(-1f64), 2f64);
1619 assert_eq!(NEG_INFINITY.abs_sub(0f64), 0f64);
1620 assert_eq!(INFINITY.abs_sub(1f64), INFINITY);
1621 assert_eq!(0f64.abs_sub(NEG_INFINITY), INFINITY);
1622 assert_eq!(0f64.abs_sub(INFINITY), 0f64);
1626 fn test_abs_sub_nowin() {
1627 assert!(NAN.abs_sub(-1f64).is_nan());
1628 assert!(1f64.abs_sub(NAN).is_nan());
1633 assert_eq!(0.0f64.asinh(), 0.0f64);
1634 assert_eq!((-0.0f64).asinh(), -0.0f64);
1636 let inf: f64 = INFINITY;
1637 let neg_inf: f64 = NEG_INFINITY;
1639 assert_eq!(inf.asinh(), inf);
1640 assert_eq!(neg_inf.asinh(), neg_inf);
1641 assert!(nan.asinh().is_nan());
1642 assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64);
1643 assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
1648 assert_eq!(1.0f64.acosh(), 0.0f64);
1649 assert!(0.999f64.acosh().is_nan());
1651 let inf: f64 = INFINITY;
1652 let neg_inf: f64 = NEG_INFINITY;
1654 assert_eq!(inf.acosh(), inf);
1655 assert!(neg_inf.acosh().is_nan());
1656 assert!(nan.acosh().is_nan());
1657 assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
1658 assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
1663 assert_eq!(0.0f64.atanh(), 0.0f64);
1664 assert_eq!((-0.0f64).atanh(), -0.0f64);
1666 let inf: f64 = INFINITY;
1667 let neg_inf: f64 = NEG_INFINITY;
1669 assert_eq!(1.0f64.atanh(), inf);
1670 assert_eq!((-1.0f64).atanh(), neg_inf);
1671 assert!(2f64.atanh().atanh().is_nan());
1672 assert!((-2f64).atanh().atanh().is_nan());
1673 assert!(inf.atanh().is_nan());
1674 assert!(neg_inf.atanh().is_nan());
1675 assert!(nan.atanh().is_nan());
1676 assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64);
1677 assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64);
1681 fn test_real_consts() {
1683 let pi: f64 = consts::PI;
1684 let frac_pi_2: f64 = consts::FRAC_PI_2;
1685 let frac_pi_3: f64 = consts::FRAC_PI_3;
1686 let frac_pi_4: f64 = consts::FRAC_PI_4;
1687 let frac_pi_6: f64 = consts::FRAC_PI_6;
1688 let frac_pi_8: f64 = consts::FRAC_PI_8;
1689 let frac_1_pi: f64 = consts::FRAC_1_PI;
1690 let frac_2_pi: f64 = consts::FRAC_2_PI;
1691 let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRT_PI;
1692 let sqrt2: f64 = consts::SQRT_2;
1693 let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT_2;
1694 let e: f64 = consts::E;
1695 let log2_e: f64 = consts::LOG2_E;
1696 let log10_e: f64 = consts::LOG10_E;
1697 let ln_2: f64 = consts::LN_2;
1698 let ln_10: f64 = consts::LN_10;
1700 assert_approx_eq!(frac_pi_2, pi / 2f64);
1701 assert_approx_eq!(frac_pi_3, pi / 3f64);
1702 assert_approx_eq!(frac_pi_4, pi / 4f64);
1703 assert_approx_eq!(frac_pi_6, pi / 6f64);
1704 assert_approx_eq!(frac_pi_8, pi / 8f64);
1705 assert_approx_eq!(frac_1_pi, 1f64 / pi);
1706 assert_approx_eq!(frac_2_pi, 2f64 / pi);
1707 assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt());
1708 assert_approx_eq!(sqrt2, 2f64.sqrt());
1709 assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt());
1710 assert_approx_eq!(log2_e, e.log2());
1711 assert_approx_eq!(log10_e, e.log10());
1712 assert_approx_eq!(ln_2, 2f64.ln());
1713 assert_approx_eq!(ln_10, 10f64.ln());