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 self.log_wrapper(|n
| { unsafe { intrinsics::logf64(n) }
})
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 self.log_wrapper(|n
| { unsafe { intrinsics::log2f64(n) }
})
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 self.log_wrapper(|n
| { unsafe { intrinsics::log10f64(n) }
})
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 {
1026 if self == NEG_INFINITY
{
1029 (self + ((self * self) + 1.0).sqrt()).ln()
1033 /// Inverse hyperbolic cosine function.
1036 /// let x = 1.0_f64;
1037 /// let f = x.cosh().acosh();
1039 /// let abs_difference = (f - x).abs();
1041 /// assert!(abs_difference < 1.0e-10);
1043 #[stable(feature = "rust1", since = "1.0.0")]
1045 pub fn acosh(self) -> f64 {
1047 x
if x
< 1.0 => NAN
,
1048 x
=> (x
+ ((x
* x
) - 1.0).sqrt()).ln(),
1052 /// Inverse hyperbolic tangent function.
1057 /// let e = f64::consts::E;
1058 /// let f = e.tanh().atanh();
1060 /// let abs_difference = (f - e).abs();
1062 /// assert!(abs_difference < 1.0e-10);
1064 #[stable(feature = "rust1", since = "1.0.0")]
1066 pub fn atanh(self) -> f64 {
1067 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
1070 // Solaris/Illumos requires a wrapper around log, log2, and log10 functions
1071 // because of their non-standard behavior (e.g. log(-n) returns -Inf instead
1072 // of expected NaN).
1073 fn log_wrapper
<F
: Fn(f64) -> f64>(self, log_fn
: F
) -> f64 {
1074 if !cfg
!(target_os
= "solaris") {
1077 if self.is_finite() {
1080 } else if self == 0.0 {
1081 NEG_INFINITY
// log(0) = -Inf
1083 NAN
// log(-n) = NaN
1085 } else if self.is_nan() {
1086 self // log(NaN) = NaN
1087 } else if self > 0.0 {
1088 self // log(Inf) = Inf
1090 NAN
// log(-Inf) = NaN
1101 use num
::FpCategory
as Fp
;
1105 test_num(10f64, 2f64);
1110 assert_eq
!(NAN
.min(2.0), 2.0);
1111 assert_eq
!(2.0f64.min(NAN
), 2.0);
1116 assert_eq
!(NAN
.max(2.0), 2.0);
1117 assert_eq
!(2.0f64.max(NAN
), 2.0);
1123 assert
!(nan
.is_nan());
1124 assert
!(!nan
.is_infinite());
1125 assert
!(!nan
.is_finite());
1126 assert
!(!nan
.is_normal());
1127 assert
!(!nan
.is_sign_positive());
1128 assert
!(!nan
.is_sign_negative());
1129 assert_eq
!(Fp
::Nan
, nan
.classify());
1133 fn test_infinity() {
1134 let inf
: f64 = INFINITY
;
1135 assert
!(inf
.is_infinite());
1136 assert
!(!inf
.is_finite());
1137 assert
!(inf
.is_sign_positive());
1138 assert
!(!inf
.is_sign_negative());
1139 assert
!(!inf
.is_nan());
1140 assert
!(!inf
.is_normal());
1141 assert_eq
!(Fp
::Infinite
, inf
.classify());
1145 fn test_neg_infinity() {
1146 let neg_inf
: f64 = NEG_INFINITY
;
1147 assert
!(neg_inf
.is_infinite());
1148 assert
!(!neg_inf
.is_finite());
1149 assert
!(!neg_inf
.is_sign_positive());
1150 assert
!(neg_inf
.is_sign_negative());
1151 assert
!(!neg_inf
.is_nan());
1152 assert
!(!neg_inf
.is_normal());
1153 assert_eq
!(Fp
::Infinite
, neg_inf
.classify());
1158 let zero
: f64 = 0.0f64;
1159 assert_eq
!(0.0, zero
);
1160 assert
!(!zero
.is_infinite());
1161 assert
!(zero
.is_finite());
1162 assert
!(zero
.is_sign_positive());
1163 assert
!(!zero
.is_sign_negative());
1164 assert
!(!zero
.is_nan());
1165 assert
!(!zero
.is_normal());
1166 assert_eq
!(Fp
::Zero
, zero
.classify());
1170 fn test_neg_zero() {
1171 let neg_zero
: f64 = -0.0;
1172 assert_eq
!(0.0, neg_zero
);
1173 assert
!(!neg_zero
.is_infinite());
1174 assert
!(neg_zero
.is_finite());
1175 assert
!(!neg_zero
.is_sign_positive());
1176 assert
!(neg_zero
.is_sign_negative());
1177 assert
!(!neg_zero
.is_nan());
1178 assert
!(!neg_zero
.is_normal());
1179 assert_eq
!(Fp
::Zero
, neg_zero
.classify());
1184 let one
: f64 = 1.0f64;
1185 assert_eq
!(1.0, one
);
1186 assert
!(!one
.is_infinite());
1187 assert
!(one
.is_finite());
1188 assert
!(one
.is_sign_positive());
1189 assert
!(!one
.is_sign_negative());
1190 assert
!(!one
.is_nan());
1191 assert
!(one
.is_normal());
1192 assert_eq
!(Fp
::Normal
, one
.classify());
1198 let inf
: f64 = INFINITY
;
1199 let neg_inf
: f64 = NEG_INFINITY
;
1200 assert
!(nan
.is_nan());
1201 assert
!(!0.0f64.is_nan());
1202 assert
!(!5.3f64.is_nan());
1203 assert
!(!(-10.732f64).is_nan());
1204 assert
!(!inf
.is_nan());
1205 assert
!(!neg_inf
.is_nan());
1209 fn test_is_infinite() {
1211 let inf
: f64 = INFINITY
;
1212 let neg_inf
: f64 = NEG_INFINITY
;
1213 assert
!(!nan
.is_infinite());
1214 assert
!(inf
.is_infinite());
1215 assert
!(neg_inf
.is_infinite());
1216 assert
!(!0.0f64.is_infinite());
1217 assert
!(!42.8f64.is_infinite());
1218 assert
!(!(-109.2f64).is_infinite());
1222 fn test_is_finite() {
1224 let inf
: f64 = INFINITY
;
1225 let neg_inf
: f64 = NEG_INFINITY
;
1226 assert
!(!nan
.is_finite());
1227 assert
!(!inf
.is_finite());
1228 assert
!(!neg_inf
.is_finite());
1229 assert
!(0.0f64.is_finite());
1230 assert
!(42.8f64.is_finite());
1231 assert
!((-109.2f64).is_finite());
1235 fn test_is_normal() {
1237 let inf
: f64 = INFINITY
;
1238 let neg_inf
: f64 = NEG_INFINITY
;
1239 let zero
: f64 = 0.0f64;
1240 let neg_zero
: f64 = -0.0;
1241 assert
!(!nan
.is_normal());
1242 assert
!(!inf
.is_normal());
1243 assert
!(!neg_inf
.is_normal());
1244 assert
!(!zero
.is_normal());
1245 assert
!(!neg_zero
.is_normal());
1246 assert
!(1f64.is_normal());
1247 assert
!(1e
-307f64.is_normal());
1248 assert
!(!1e
-308f64.is_normal());
1252 fn test_classify() {
1254 let inf
: f64 = INFINITY
;
1255 let neg_inf
: f64 = NEG_INFINITY
;
1256 let zero
: f64 = 0.0f64;
1257 let neg_zero
: f64 = -0.0;
1258 assert_eq
!(nan
.classify(), Fp
::Nan
);
1259 assert_eq
!(inf
.classify(), Fp
::Infinite
);
1260 assert_eq
!(neg_inf
.classify(), Fp
::Infinite
);
1261 assert_eq
!(zero
.classify(), Fp
::Zero
);
1262 assert_eq
!(neg_zero
.classify(), Fp
::Zero
);
1263 assert_eq
!(1e
-307f64.classify(), Fp
::Normal
);
1264 assert_eq
!(1e
-308f64.classify(), Fp
::Subnormal
);
1268 #[rustc_no_mir] // FIXME #27840 MIR NAN ends up negative.
1269 fn test_integer_decode() {
1270 assert_eq
!(3.14159265359f64.integer_decode(), (7074237752028906, -51, 1));
1271 assert_eq
!((-8573.5918555f64).integer_decode(), (4713381968463931, -39, -1));
1272 assert_eq
!(2f64.powf(100.0).integer_decode(), (4503599627370496, 48, 1));
1273 assert_eq
!(0f64.integer_decode(), (0, -1075, 1));
1274 assert_eq
!((-0f64).integer_decode(), (0, -1075, -1));
1275 assert_eq
!(INFINITY
.integer_decode(), (4503599627370496, 972, 1));
1276 assert_eq
!(NEG_INFINITY
.integer_decode(), (4503599627370496, 972, -1));
1277 assert_eq
!(NAN
.integer_decode(), (6755399441055744, 972, 1));
1282 assert_approx_eq
!(1.0f64.floor(), 1.0f64);
1283 assert_approx_eq
!(1.3f64.floor(), 1.0f64);
1284 assert_approx_eq
!(1.5f64.floor(), 1.0f64);
1285 assert_approx_eq
!(1.7f64.floor(), 1.0f64);
1286 assert_approx_eq
!(0.0f64.floor(), 0.0f64);
1287 assert_approx_eq
!((-0.0f64).floor(), -0.0f64);
1288 assert_approx_eq
!((-1.0f64).floor(), -1.0f64);
1289 assert_approx_eq
!((-1.3f64).floor(), -2.0f64);
1290 assert_approx_eq
!((-1.5f64).floor(), -2.0f64);
1291 assert_approx_eq
!((-1.7f64).floor(), -2.0f64);
1296 assert_approx_eq
!(1.0f64.ceil(), 1.0f64);
1297 assert_approx_eq
!(1.3f64.ceil(), 2.0f64);
1298 assert_approx_eq
!(1.5f64.ceil(), 2.0f64);
1299 assert_approx_eq
!(1.7f64.ceil(), 2.0f64);
1300 assert_approx_eq
!(0.0f64.ceil(), 0.0f64);
1301 assert_approx_eq
!((-0.0f64).ceil(), -0.0f64);
1302 assert_approx_eq
!((-1.0f64).ceil(), -1.0f64);
1303 assert_approx_eq
!((-1.3f64).ceil(), -1.0f64);
1304 assert_approx_eq
!((-1.5f64).ceil(), -1.0f64);
1305 assert_approx_eq
!((-1.7f64).ceil(), -1.0f64);
1310 assert_approx_eq
!(1.0f64.round(), 1.0f64);
1311 assert_approx_eq
!(1.3f64.round(), 1.0f64);
1312 assert_approx_eq
!(1.5f64.round(), 2.0f64);
1313 assert_approx_eq
!(1.7f64.round(), 2.0f64);
1314 assert_approx_eq
!(0.0f64.round(), 0.0f64);
1315 assert_approx_eq
!((-0.0f64).round(), -0.0f64);
1316 assert_approx_eq
!((-1.0f64).round(), -1.0f64);
1317 assert_approx_eq
!((-1.3f64).round(), -1.0f64);
1318 assert_approx_eq
!((-1.5f64).round(), -2.0f64);
1319 assert_approx_eq
!((-1.7f64).round(), -2.0f64);
1324 assert_approx_eq
!(1.0f64.trunc(), 1.0f64);
1325 assert_approx_eq
!(1.3f64.trunc(), 1.0f64);
1326 assert_approx_eq
!(1.5f64.trunc(), 1.0f64);
1327 assert_approx_eq
!(1.7f64.trunc(), 1.0f64);
1328 assert_approx_eq
!(0.0f64.trunc(), 0.0f64);
1329 assert_approx_eq
!((-0.0f64).trunc(), -0.0f64);
1330 assert_approx_eq
!((-1.0f64).trunc(), -1.0f64);
1331 assert_approx_eq
!((-1.3f64).trunc(), -1.0f64);
1332 assert_approx_eq
!((-1.5f64).trunc(), -1.0f64);
1333 assert_approx_eq
!((-1.7f64).trunc(), -1.0f64);
1338 assert_approx_eq
!(1.0f64.fract(), 0.0f64);
1339 assert_approx_eq
!(1.3f64.fract(), 0.3f64);
1340 assert_approx_eq
!(1.5f64.fract(), 0.5f64);
1341 assert_approx_eq
!(1.7f64.fract(), 0.7f64);
1342 assert_approx_eq
!(0.0f64.fract(), 0.0f64);
1343 assert_approx_eq
!((-0.0f64).fract(), -0.0f64);
1344 assert_approx_eq
!((-1.0f64).fract(), -0.0f64);
1345 assert_approx_eq
!((-1.3f64).fract(), -0.3f64);
1346 assert_approx_eq
!((-1.5f64).fract(), -0.5f64);
1347 assert_approx_eq
!((-1.7f64).fract(), -0.7f64);
1352 assert_eq
!(INFINITY
.abs(), INFINITY
);
1353 assert_eq
!(1f64.abs(), 1f64);
1354 assert_eq
!(0f64.abs(), 0f64);
1355 assert_eq
!((-0f64).abs(), 0f64);
1356 assert_eq
!((-1f64).abs(), 1f64);
1357 assert_eq
!(NEG_INFINITY
.abs(), INFINITY
);
1358 assert_eq
!((1f64/NEG_INFINITY
).abs(), 0f64);
1359 assert
!(NAN
.abs().is_nan());
1364 assert_eq
!(INFINITY
.signum(), 1f64);
1365 assert_eq
!(1f64.signum(), 1f64);
1366 assert_eq
!(0f64.signum(), 1f64);
1367 assert_eq
!((-0f64).signum(), -1f64);
1368 assert_eq
!((-1f64).signum(), -1f64);
1369 assert_eq
!(NEG_INFINITY
.signum(), -1f64);
1370 assert_eq
!((1f64/NEG_INFINITY
).signum(), -1f64);
1371 assert
!(NAN
.signum().is_nan());
1375 fn test_is_sign_positive() {
1376 assert
!(INFINITY
.is_sign_positive());
1377 assert
!(1f64.is_sign_positive());
1378 assert
!(0f64.is_sign_positive());
1379 assert
!(!(-0f64).is_sign_positive());
1380 assert
!(!(-1f64).is_sign_positive());
1381 assert
!(!NEG_INFINITY
.is_sign_positive());
1382 assert
!(!(1f64/NEG_INFINITY
).is_sign_positive());
1383 assert
!(!NAN
.is_sign_positive());
1387 fn test_is_sign_negative() {
1388 assert
!(!INFINITY
.is_sign_negative());
1389 assert
!(!1f64.is_sign_negative());
1390 assert
!(!0f64.is_sign_negative());
1391 assert
!((-0f64).is_sign_negative());
1392 assert
!((-1f64).is_sign_negative());
1393 assert
!(NEG_INFINITY
.is_sign_negative());
1394 assert
!((1f64/NEG_INFINITY
).is_sign_negative());
1395 assert
!(!NAN
.is_sign_negative());
1401 let inf
: f64 = INFINITY
;
1402 let neg_inf
: f64 = NEG_INFINITY
;
1403 assert_approx_eq
!(12.3f64.mul_add(4.5, 6.7), 62.05);
1404 assert_approx_eq
!((-12.3f64).mul_add(-4.5, -6.7), 48.65);
1405 assert_approx_eq
!(0.0f64.mul_add(8.9, 1.2), 1.2);
1406 assert_approx_eq
!(3.4f64.mul_add(-0.0, 5.6), 5.6);
1407 assert
!(nan
.mul_add(7.8, 9.0).is_nan());
1408 assert_eq
!(inf
.mul_add(7.8, 9.0), inf
);
1409 assert_eq
!(neg_inf
.mul_add(7.8, 9.0), neg_inf
);
1410 assert_eq
!(8.9f64.mul_add(inf
, 3.2), inf
);
1411 assert_eq
!((-3.2f64).mul_add(2.4, neg_inf
), neg_inf
);
1417 let inf
: f64 = INFINITY
;
1418 let neg_inf
: f64 = NEG_INFINITY
;
1419 assert_eq
!(1.0f64.recip(), 1.0);
1420 assert_eq
!(2.0f64.recip(), 0.5);
1421 assert_eq
!((-0.4f64).recip(), -2.5);
1422 assert_eq
!(0.0f64.recip(), inf
);
1423 assert
!(nan
.recip().is_nan());
1424 assert_eq
!(inf
.recip(), 0.0);
1425 assert_eq
!(neg_inf
.recip(), 0.0);
1431 let inf
: f64 = INFINITY
;
1432 let neg_inf
: f64 = NEG_INFINITY
;
1433 assert_eq
!(1.0f64.powi(1), 1.0);
1434 assert_approx_eq
!((-3.1f64).powi(2), 9.61);
1435 assert_approx_eq
!(5.9f64.powi(-2), 0.028727);
1436 assert_eq
!(8.3f64.powi(0), 1.0);
1437 assert
!(nan
.powi(2).is_nan());
1438 assert_eq
!(inf
.powi(3), inf
);
1439 assert_eq
!(neg_inf
.powi(2), inf
);
1445 let inf
: f64 = INFINITY
;
1446 let neg_inf
: f64 = NEG_INFINITY
;
1447 assert_eq
!(1.0f64.powf(1.0), 1.0);
1448 assert_approx_eq
!(3.4f64.powf(4.5), 246.408183);
1449 assert_approx_eq
!(2.7f64.powf(-3.2), 0.041652);
1450 assert_approx_eq
!((-3.1f64).powf(2.0), 9.61);
1451 assert_approx_eq
!(5.9f64.powf(-2.0), 0.028727);
1452 assert_eq
!(8.3f64.powf(0.0), 1.0);
1453 assert
!(nan
.powf(2.0).is_nan());
1454 assert_eq
!(inf
.powf(2.0), inf
);
1455 assert_eq
!(neg_inf
.powf(3.0), neg_inf
);
1459 fn test_sqrt_domain() {
1460 assert
!(NAN
.sqrt().is_nan());
1461 assert
!(NEG_INFINITY
.sqrt().is_nan());
1462 assert
!((-1.0f64).sqrt().is_nan());
1463 assert_eq
!((-0.0f64).sqrt(), -0.0);
1464 assert_eq
!(0.0f64.sqrt(), 0.0);
1465 assert_eq
!(1.0f64.sqrt(), 1.0);
1466 assert_eq
!(INFINITY
.sqrt(), INFINITY
);
1471 assert_eq
!(1.0, 0.0f64.exp());
1472 assert_approx_eq
!(2.718282, 1.0f64.exp());
1473 assert_approx_eq
!(148.413159, 5.0f64.exp());
1475 let inf
: f64 = INFINITY
;
1476 let neg_inf
: f64 = NEG_INFINITY
;
1478 assert_eq
!(inf
, inf
.exp());
1479 assert_eq
!(0.0, neg_inf
.exp());
1480 assert
!(nan
.exp().is_nan());
1485 assert_eq
!(32.0, 5.0f64.exp2());
1486 assert_eq
!(1.0, 0.0f64.exp2());
1488 let inf
: f64 = INFINITY
;
1489 let neg_inf
: f64 = NEG_INFINITY
;
1491 assert_eq
!(inf
, inf
.exp2());
1492 assert_eq
!(0.0, neg_inf
.exp2());
1493 assert
!(nan
.exp2().is_nan());
1499 let inf
: f64 = INFINITY
;
1500 let neg_inf
: f64 = NEG_INFINITY
;
1501 assert_approx_eq
!(1.0f64.exp().ln(), 1.0);
1502 assert
!(nan
.ln().is_nan());
1503 assert_eq
!(inf
.ln(), inf
);
1504 assert
!(neg_inf
.ln().is_nan());
1505 assert
!((-2.3f64).ln().is_nan());
1506 assert_eq
!((-0.0f64).ln(), neg_inf
);
1507 assert_eq
!(0.0f64.ln(), neg_inf
);
1508 assert_approx_eq
!(4.0f64.ln(), 1.386294);
1514 let inf
: f64 = INFINITY
;
1515 let neg_inf
: f64 = NEG_INFINITY
;
1516 assert_eq
!(10.0f64.log(10.0), 1.0);
1517 assert_approx_eq
!(2.3f64.log(3.5), 0.664858);
1518 assert_eq
!(1.0f64.exp().log(1.0f64.exp()), 1.0);
1519 assert
!(1.0f64.log(1.0).is_nan());
1520 assert
!(1.0f64.log(-13.9).is_nan());
1521 assert
!(nan
.log(2.3).is_nan());
1522 assert_eq
!(inf
.log(10.0), inf
);
1523 assert
!(neg_inf
.log(8.8).is_nan());
1524 assert
!((-2.3f64).log(0.1).is_nan());
1525 assert_eq
!((-0.0f64).log(2.0), neg_inf
);
1526 assert_eq
!(0.0f64.log(7.0), neg_inf
);
1532 let inf
: f64 = INFINITY
;
1533 let neg_inf
: f64 = NEG_INFINITY
;
1534 assert_approx_eq
!(10.0f64.log2(), 3.321928);
1535 assert_approx_eq
!(2.3f64.log2(), 1.201634);
1536 assert_approx_eq
!(1.0f64.exp().log2(), 1.442695);
1537 assert
!(nan
.log2().is_nan());
1538 assert_eq
!(inf
.log2(), inf
);
1539 assert
!(neg_inf
.log2().is_nan());
1540 assert
!((-2.3f64).log2().is_nan());
1541 assert_eq
!((-0.0f64).log2(), neg_inf
);
1542 assert_eq
!(0.0f64.log2(), neg_inf
);
1548 let inf
: f64 = INFINITY
;
1549 let neg_inf
: f64 = NEG_INFINITY
;
1550 assert_eq
!(10.0f64.log10(), 1.0);
1551 assert_approx_eq
!(2.3f64.log10(), 0.361728);
1552 assert_approx_eq
!(1.0f64.exp().log10(), 0.434294);
1553 assert_eq
!(1.0f64.log10(), 0.0);
1554 assert
!(nan
.log10().is_nan());
1555 assert_eq
!(inf
.log10(), inf
);
1556 assert
!(neg_inf
.log10().is_nan());
1557 assert
!((-2.3f64).log10().is_nan());
1558 assert_eq
!((-0.0f64).log10(), neg_inf
);
1559 assert_eq
!(0.0f64.log10(), neg_inf
);
1563 fn test_to_degrees() {
1564 let pi
: f64 = consts
::PI
;
1566 let inf
: f64 = INFINITY
;
1567 let neg_inf
: f64 = NEG_INFINITY
;
1568 assert_eq
!(0.0f64.to_degrees(), 0.0);
1569 assert_approx_eq
!((-5.8f64).to_degrees(), -332.315521);
1570 assert_eq
!(pi
.to_degrees(), 180.0);
1571 assert
!(nan
.to_degrees().is_nan());
1572 assert_eq
!(inf
.to_degrees(), inf
);
1573 assert_eq
!(neg_inf
.to_degrees(), neg_inf
);
1577 fn test_to_radians() {
1578 let pi
: f64 = consts
::PI
;
1580 let inf
: f64 = INFINITY
;
1581 let neg_inf
: f64 = NEG_INFINITY
;
1582 assert_eq
!(0.0f64.to_radians(), 0.0);
1583 assert_approx_eq
!(154.6f64.to_radians(), 2.698279);
1584 assert_approx_eq
!((-332.31f64).to_radians(), -5.799903);
1585 assert_eq
!(180.0f64.to_radians(), pi
);
1586 assert
!(nan
.to_radians().is_nan());
1587 assert_eq
!(inf
.to_radians(), inf
);
1588 assert_eq
!(neg_inf
.to_radians(), neg_inf
);
1593 let f1
= 2.0f64.powi(-123);
1594 let f2
= 2.0f64.powi(-111);
1595 let f3
= 1.75 * 2.0f64.powi(-12);
1596 assert_eq
!(f64::ldexp(1f64, -123), f1
);
1597 assert_eq
!(f64::ldexp(1f64, -111), f2
);
1598 assert_eq
!(f64::ldexp(1.75f64, -12), f3
);
1600 assert_eq
!(f64::ldexp(0f64, -123), 0f64);
1601 assert_eq
!(f64::ldexp(-0f64, -123), -0f64);
1603 let inf
: f64 = INFINITY
;
1604 let neg_inf
: f64 = NEG_INFINITY
;
1606 assert_eq
!(f64::ldexp(inf
, -123), inf
);
1607 assert_eq
!(f64::ldexp(neg_inf
, -123), neg_inf
);
1608 assert
!(f64::ldexp(nan
, -123).is_nan());
1613 let f1
= 2.0f64.powi(-123);
1614 let f2
= 2.0f64.powi(-111);
1615 let f3
= 1.75 * 2.0f64.powi(-123);
1616 let (x1
, exp1
) = f1
.frexp();
1617 let (x2
, exp2
) = f2
.frexp();
1618 let (x3
, exp3
) = f3
.frexp();
1619 assert_eq
!((x1
, exp1
), (0.5f64, -122));
1620 assert_eq
!((x2
, exp2
), (0.5f64, -110));
1621 assert_eq
!((x3
, exp3
), (0.875f64, -122));
1622 assert_eq
!(f64::ldexp(x1
, exp1
), f1
);
1623 assert_eq
!(f64::ldexp(x2
, exp2
), f2
);
1624 assert_eq
!(f64::ldexp(x3
, exp3
), f3
);
1626 assert_eq
!(0f64.frexp(), (0f64, 0));
1627 assert_eq
!((-0f64).frexp(), (-0f64, 0));
1630 #[test] #[cfg_attr(windows, ignore)] // FIXME #8755
1631 fn test_frexp_nowin() {
1632 let inf
: f64 = INFINITY
;
1633 let neg_inf
: f64 = NEG_INFINITY
;
1635 assert_eq
!(match inf
.frexp() { (x, _) => x }
, inf
);
1636 assert_eq
!(match neg_inf
.frexp() { (x, _) => x }
, neg_inf
);
1637 assert
!(match nan
.frexp() { (x, _) => x.is_nan() }
)
1642 assert_eq
!((-1f64).abs_sub(1f64), 0f64);
1643 assert_eq
!(1f64.abs_sub(1f64), 0f64);
1644 assert_eq
!(1f64.abs_sub(0f64), 1f64);
1645 assert_eq
!(1f64.abs_sub(-1f64), 2f64);
1646 assert_eq
!(NEG_INFINITY
.abs_sub(0f64), 0f64);
1647 assert_eq
!(INFINITY
.abs_sub(1f64), INFINITY
);
1648 assert_eq
!(0f64.abs_sub(NEG_INFINITY
), INFINITY
);
1649 assert_eq
!(0f64.abs_sub(INFINITY
), 0f64);
1653 fn test_abs_sub_nowin() {
1654 assert
!(NAN
.abs_sub(-1f64).is_nan());
1655 assert
!(1f64.abs_sub(NAN
).is_nan());
1660 assert_eq
!(0.0f64.asinh(), 0.0f64);
1661 assert_eq
!((-0.0f64).asinh(), -0.0f64);
1663 let inf
: f64 = INFINITY
;
1664 let neg_inf
: f64 = NEG_INFINITY
;
1666 assert_eq
!(inf
.asinh(), inf
);
1667 assert_eq
!(neg_inf
.asinh(), neg_inf
);
1668 assert
!(nan
.asinh().is_nan());
1669 assert_approx_eq
!(2.0f64.asinh(), 1.443635475178810342493276740273105f64);
1670 assert_approx_eq
!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
1675 assert_eq
!(1.0f64.acosh(), 0.0f64);
1676 assert
!(0.999f64.acosh().is_nan());
1678 let inf
: f64 = INFINITY
;
1679 let neg_inf
: f64 = NEG_INFINITY
;
1681 assert_eq
!(inf
.acosh(), inf
);
1682 assert
!(neg_inf
.acosh().is_nan());
1683 assert
!(nan
.acosh().is_nan());
1684 assert_approx_eq
!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
1685 assert_approx_eq
!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
1690 assert_eq
!(0.0f64.atanh(), 0.0f64);
1691 assert_eq
!((-0.0f64).atanh(), -0.0f64);
1693 let inf
: f64 = INFINITY
;
1694 let neg_inf
: f64 = NEG_INFINITY
;
1696 assert_eq
!(1.0f64.atanh(), inf
);
1697 assert_eq
!((-1.0f64).atanh(), neg_inf
);
1698 assert
!(2f64.atanh().atanh().is_nan());
1699 assert
!((-2f64).atanh().atanh().is_nan());
1700 assert
!(inf
.atanh().is_nan());
1701 assert
!(neg_inf
.atanh().is_nan());
1702 assert
!(nan
.atanh().is_nan());
1703 assert_approx_eq
!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64);
1704 assert_approx_eq
!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64);
1708 fn test_real_consts() {
1710 let pi
: f64 = consts
::PI
;
1711 let frac_pi_2
: f64 = consts
::FRAC_PI_2
;
1712 let frac_pi_3
: f64 = consts
::FRAC_PI_3
;
1713 let frac_pi_4
: f64 = consts
::FRAC_PI_4
;
1714 let frac_pi_6
: f64 = consts
::FRAC_PI_6
;
1715 let frac_pi_8
: f64 = consts
::FRAC_PI_8
;
1716 let frac_1_pi
: f64 = consts
::FRAC_1_PI
;
1717 let frac_2_pi
: f64 = consts
::FRAC_2_PI
;
1718 let frac_2_sqrtpi
: f64 = consts
::FRAC_2_SQRT_PI
;
1719 let sqrt2
: f64 = consts
::SQRT_2
;
1720 let frac_1_sqrt2
: f64 = consts
::FRAC_1_SQRT_2
;
1721 let e
: f64 = consts
::E
;
1722 let log2_e
: f64 = consts
::LOG2_E
;
1723 let log10_e
: f64 = consts
::LOG10_E
;
1724 let ln_2
: f64 = consts
::LN_2
;
1725 let ln_10
: f64 = consts
::LN_10
;
1727 assert_approx_eq
!(frac_pi_2
, pi
/ 2f64);
1728 assert_approx_eq
!(frac_pi_3
, pi
/ 3f64);
1729 assert_approx_eq
!(frac_pi_4
, pi
/ 4f64);
1730 assert_approx_eq
!(frac_pi_6
, pi
/ 6f64);
1731 assert_approx_eq
!(frac_pi_8
, pi
/ 8f64);
1732 assert_approx_eq
!(frac_1_pi
, 1f64 / pi
);
1733 assert_approx_eq
!(frac_2_pi
, 2f64 / pi
);
1734 assert_approx_eq
!(frac_2_sqrtpi
, 2f64 / pi
.sqrt());
1735 assert_approx_eq
!(sqrt2
, 2f64.sqrt());
1736 assert_approx_eq
!(frac_1_sqrt2
, 1f64 / 2f64.sqrt());
1737 assert_approx_eq
!(log2_e
, e
.log2());
1738 assert_approx_eq
!(log10_e
, e
.log10());
1739 assert_approx_eq
!(ln_2
, 2f64.ln());
1740 assert_approx_eq
!(ln_10
, 10f64.ln());