1 //! This module provides constants which are specific to the implementation
2 //! of the `f64` floating point data type.
4 //! *[See also the `f64` primitive type](../../std/primitive.f64.html).*
6 //! Mathematically significant numbers are provided in the `consts` sub-module.
8 //! Although using these constants won’t cause compilation warnings,
9 //! new code should use the associated constants directly on the primitive type.
11 #![stable(feature = "rust1", since = "1.0.0")]
12 #![allow(missing_docs)]
15 use crate::intrinsics;
17 use crate::sys::cmath;
19 #[stable(feature = "rust1", since = "1.0.0")]
20 pub use core::f64::consts;
21 #[stable(feature = "rust1", since = "1.0.0")]
22 pub use core::f64::{DIGITS, EPSILON, MANTISSA_DIGITS, RADIX};
23 #[stable(feature = "rust1", since = "1.0.0")]
24 pub use core::f64::{INFINITY, MAX_10_EXP, NAN, NEG_INFINITY};
25 #[stable(feature = "rust1", since = "1.0.0")]
26 pub use core::f64::{MAX, MIN, MIN_POSITIVE};
27 #[stable(feature = "rust1", since = "1.0.0")]
28 pub use core::f64::{MAX_EXP, MIN_10_EXP, MIN_EXP};
31 #[lang = "f64_runtime"]
33 /// Returns the largest integer less than or equal to a number.
42 /// assert_eq!(f.floor(), 3.0);
43 /// assert_eq!(g.floor(), 3.0);
44 /// assert_eq!(h.floor(), -4.0);
46 #[must_use = "method returns a new number and does not mutate the original value"]
47 #[stable(feature = "rust1", since = "1.0.0")]
49 pub fn floor(self) -> f64 {
50 unsafe { intrinsics::floorf64(self) }
53 /// Returns the smallest integer greater than or equal to a number.
61 /// assert_eq!(f.ceil(), 4.0);
62 /// assert_eq!(g.ceil(), 4.0);
64 #[must_use = "method returns a new number and does not mutate the original value"]
65 #[stable(feature = "rust1", since = "1.0.0")]
67 pub fn ceil(self) -> f64 {
68 unsafe { intrinsics::ceilf64(self) }
71 /// Returns the nearest integer to a number. Round half-way cases away from
80 /// assert_eq!(f.round(), 3.0);
81 /// assert_eq!(g.round(), -3.0);
83 #[must_use = "method returns a new number and does not mutate the original value"]
84 #[stable(feature = "rust1", since = "1.0.0")]
86 pub fn round(self) -> f64 {
87 unsafe { intrinsics::roundf64(self) }
90 /// Returns the integer part of a number.
99 /// assert_eq!(f.trunc(), 3.0);
100 /// assert_eq!(g.trunc(), 3.0);
101 /// assert_eq!(h.trunc(), -3.0);
103 #[must_use = "method returns a new number and does not mutate the original value"]
104 #[stable(feature = "rust1", since = "1.0.0")]
106 pub fn trunc(self) -> f64 {
107 unsafe { intrinsics::truncf64(self) }
110 /// Returns the fractional part of a number.
116 /// let y = -3.6_f64;
117 /// let abs_difference_x = (x.fract() - 0.6).abs();
118 /// let abs_difference_y = (y.fract() - (-0.6)).abs();
120 /// assert!(abs_difference_x < 1e-10);
121 /// assert!(abs_difference_y < 1e-10);
123 #[must_use = "method returns a new number and does not mutate the original value"]
124 #[stable(feature = "rust1", since = "1.0.0")]
126 pub fn fract(self) -> f64 {
130 /// Computes the absolute value of `self`. Returns `NAN` if the
137 /// let y = -3.5_f64;
139 /// let abs_difference_x = (x.abs() - x).abs();
140 /// let abs_difference_y = (y.abs() - (-y)).abs();
142 /// assert!(abs_difference_x < 1e-10);
143 /// assert!(abs_difference_y < 1e-10);
145 /// assert!(f64::NAN.abs().is_nan());
147 #[must_use = "method returns a new number and does not mutate the original value"]
148 #[stable(feature = "rust1", since = "1.0.0")]
150 pub fn abs(self) -> f64 {
151 unsafe { intrinsics::fabsf64(self) }
154 /// Returns a number that represents the sign of `self`.
156 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
157 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
158 /// - `NAN` if the number is `NAN`
165 /// assert_eq!(f.signum(), 1.0);
166 /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
168 /// assert!(f64::NAN.signum().is_nan());
170 #[must_use = "method returns a new number and does not mutate the original value"]
171 #[stable(feature = "rust1", since = "1.0.0")]
173 pub fn signum(self) -> f64 {
174 if self.is_nan() { Self::NAN } else { 1.0_f64.copysign(self) }
177 /// Returns a number composed of the magnitude of `self` and the sign of
180 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
181 /// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of
182 /// `sign` is returned.
189 /// assert_eq!(f.copysign(0.42), 3.5_f64);
190 /// assert_eq!(f.copysign(-0.42), -3.5_f64);
191 /// assert_eq!((-f).copysign(0.42), 3.5_f64);
192 /// assert_eq!((-f).copysign(-0.42), -3.5_f64);
194 /// assert!(f64::NAN.copysign(1.0).is_nan());
196 #[must_use = "method returns a new number and does not mutate the original value"]
197 #[stable(feature = "copysign", since = "1.35.0")]
199 pub fn copysign(self, sign: f64) -> f64 {
200 unsafe { intrinsics::copysignf64(self, sign) }
203 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
204 /// error, yielding a more accurate result than an unfused multiply-add.
206 /// Using `mul_add` can be more performant than an unfused multiply-add if
207 /// the target architecture has a dedicated `fma` CPU instruction.
212 /// let m = 10.0_f64;
214 /// let b = 60.0_f64;
217 /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs();
219 /// assert!(abs_difference < 1e-10);
221 #[must_use = "method returns a new number and does not mutate the original value"]
222 #[stable(feature = "rust1", since = "1.0.0")]
224 pub fn mul_add(self, a: f64, b: f64) -> f64 {
225 unsafe { intrinsics::fmaf64(self, a, b) }
228 /// Calculates Euclidean division, the matching method for `rem_euclid`.
230 /// This computes the integer `n` such that
231 /// `self = n * rhs + self.rem_euclid(rhs)`.
232 /// In other words, the result is `self / rhs` rounded to the integer `n`
233 /// such that `self >= n * rhs`.
238 /// let a: f64 = 7.0;
240 /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
241 /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
242 /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
243 /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0
245 #[must_use = "method returns a new number and does not mutate the original value"]
247 #[stable(feature = "euclidean_division", since = "1.38.0")]
248 pub fn div_euclid(self, rhs: f64) -> f64 {
249 let q = (self / rhs).trunc();
250 if self % rhs < 0.0 {
251 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
256 /// Calculates the least nonnegative remainder of `self (mod rhs)`.
258 /// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
259 /// most cases. However, due to a floating point round-off error it can
260 /// result in `r == rhs.abs()`, violating the mathematical definition, if
261 /// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
262 /// This result is not an element of the function's codomain, but it is the
263 /// closest floating point number in the real numbers and thus fulfills the
264 /// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
270 /// let a: f64 = 7.0;
272 /// assert_eq!(a.rem_euclid(b), 3.0);
273 /// assert_eq!((-a).rem_euclid(b), 1.0);
274 /// assert_eq!(a.rem_euclid(-b), 3.0);
275 /// assert_eq!((-a).rem_euclid(-b), 1.0);
276 /// // limitation due to round-off error
277 /// assert!((-f64::EPSILON).rem_euclid(3.0) != 0.0);
279 #[must_use = "method returns a new number and does not mutate the original value"]
281 #[stable(feature = "euclidean_division", since = "1.38.0")]
282 pub fn rem_euclid(self, rhs: f64) -> f64 {
284 if r < 0.0 { r + rhs.abs() } else { r }
287 /// Raises a number to an integer power.
289 /// Using this function is generally faster than using `powf`
295 /// let abs_difference = (x.powi(2) - (x * x)).abs();
297 /// assert!(abs_difference < 1e-10);
299 #[must_use = "method returns a new number and does not mutate the original value"]
300 #[stable(feature = "rust1", since = "1.0.0")]
302 pub fn powi(self, n: i32) -> f64 {
303 unsafe { intrinsics::powif64(self, n) }
306 /// Raises a number to a floating point power.
312 /// let abs_difference = (x.powf(2.0) - (x * x)).abs();
314 /// assert!(abs_difference < 1e-10);
316 #[must_use = "method returns a new number and does not mutate the original value"]
317 #[stable(feature = "rust1", since = "1.0.0")]
319 pub fn powf(self, n: f64) -> f64 {
320 unsafe { intrinsics::powf64(self, n) }
323 /// Returns the square root of a number.
325 /// Returns NaN if `self` is a negative number.
330 /// let positive = 4.0_f64;
331 /// let negative = -4.0_f64;
333 /// let abs_difference = (positive.sqrt() - 2.0).abs();
335 /// assert!(abs_difference < 1e-10);
336 /// assert!(negative.sqrt().is_nan());
338 #[must_use = "method returns a new number and does not mutate the original value"]
339 #[stable(feature = "rust1", since = "1.0.0")]
341 pub fn sqrt(self) -> f64 {
342 unsafe { intrinsics::sqrtf64(self) }
345 /// Returns `e^(self)`, (the exponential function).
350 /// let one = 1.0_f64;
352 /// let e = one.exp();
354 /// // ln(e) - 1 == 0
355 /// let abs_difference = (e.ln() - 1.0).abs();
357 /// assert!(abs_difference < 1e-10);
359 #[must_use = "method returns a new number and does not mutate the original value"]
360 #[stable(feature = "rust1", since = "1.0.0")]
362 pub fn exp(self) -> f64 {
363 unsafe { intrinsics::expf64(self) }
366 /// Returns `2^(self)`.
374 /// let abs_difference = (f.exp2() - 4.0).abs();
376 /// assert!(abs_difference < 1e-10);
378 #[must_use = "method returns a new number and does not mutate the original value"]
379 #[stable(feature = "rust1", since = "1.0.0")]
381 pub fn exp2(self) -> f64 {
382 unsafe { intrinsics::exp2f64(self) }
385 /// Returns the natural logarithm of the number.
390 /// let one = 1.0_f64;
392 /// let e = one.exp();
394 /// // ln(e) - 1 == 0
395 /// let abs_difference = (e.ln() - 1.0).abs();
397 /// assert!(abs_difference < 1e-10);
399 #[must_use = "method returns a new number and does not mutate the original value"]
400 #[stable(feature = "rust1", since = "1.0.0")]
402 pub fn ln(self) -> f64 {
403 self.log_wrapper(|n| unsafe { intrinsics::logf64(n) })
406 /// Returns the logarithm of the number with respect to an arbitrary base.
408 /// The result may not be correctly rounded owing to implementation details;
409 /// `self.log2()` can produce more accurate results for base 2, and
410 /// `self.log10()` can produce more accurate results for base 10.
415 /// let twenty_five = 25.0_f64;
417 /// // log5(25) - 2 == 0
418 /// let abs_difference = (twenty_five.log(5.0) - 2.0).abs();
420 /// assert!(abs_difference < 1e-10);
422 #[must_use = "method returns a new number and does not mutate the original value"]
423 #[stable(feature = "rust1", since = "1.0.0")]
425 pub fn log(self, base: f64) -> f64 {
426 self.ln() / base.ln()
429 /// Returns the base 2 logarithm of the number.
434 /// let four = 4.0_f64;
436 /// // log2(4) - 2 == 0
437 /// let abs_difference = (four.log2() - 2.0).abs();
439 /// assert!(abs_difference < 1e-10);
441 #[must_use = "method returns a new number and does not mutate the original value"]
442 #[stable(feature = "rust1", since = "1.0.0")]
444 pub fn log2(self) -> f64 {
445 self.log_wrapper(|n| {
446 #[cfg(target_os = "android")]
447 return crate::sys::android::log2f64(n);
448 #[cfg(not(target_os = "android"))]
449 return unsafe { intrinsics::log2f64(n) };
453 /// Returns the base 10 logarithm of the number.
458 /// let hundred = 100.0_f64;
460 /// // log10(100) - 2 == 0
461 /// let abs_difference = (hundred.log10() - 2.0).abs();
463 /// assert!(abs_difference < 1e-10);
465 #[must_use = "method returns a new number and does not mutate the original value"]
466 #[stable(feature = "rust1", since = "1.0.0")]
468 pub fn log10(self) -> f64 {
469 self.log_wrapper(|n| unsafe { intrinsics::log10f64(n) })
472 /// The positive difference of two numbers.
474 /// * If `self <= other`: `0:0`
475 /// * Else: `self - other`
481 /// let y = -3.0_f64;
483 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
484 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
486 /// assert!(abs_difference_x < 1e-10);
487 /// assert!(abs_difference_y < 1e-10);
489 #[must_use = "method returns a new number and does not mutate the original value"]
490 #[stable(feature = "rust1", since = "1.0.0")]
494 reason = "you probably meant `(self - other).abs()`: \
495 this operation is `(self - other).max(0.0)` \
496 except that `abs_sub` also propagates NaNs (also \
497 known as `fdim` in C). If you truly need the positive \
498 difference, consider using that expression or the C function \
499 `fdim`, depending on how you wish to handle NaN (please consider \
500 filing an issue describing your use-case too)."
502 pub fn abs_sub(self, other: f64) -> f64 {
503 unsafe { cmath::fdim(self, other) }
506 /// Returns the cubic root of a number.
513 /// // x^(1/3) - 2 == 0
514 /// let abs_difference = (x.cbrt() - 2.0).abs();
516 /// assert!(abs_difference < 1e-10);
518 #[must_use = "method returns a new number and does not mutate the original value"]
519 #[stable(feature = "rust1", since = "1.0.0")]
521 pub fn cbrt(self) -> f64 {
522 unsafe { cmath::cbrt(self) }
525 /// Calculates the length of the hypotenuse of a right-angle triangle given
526 /// legs of length `x` and `y`.
534 /// // sqrt(x^2 + y^2)
535 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
537 /// assert!(abs_difference < 1e-10);
539 #[must_use = "method returns a new number and does not mutate the original value"]
540 #[stable(feature = "rust1", since = "1.0.0")]
542 pub fn hypot(self, other: f64) -> f64 {
543 unsafe { cmath::hypot(self, other) }
546 /// Computes the sine of a number (in radians).
551 /// let x = std::f64::consts::FRAC_PI_2;
553 /// let abs_difference = (x.sin() - 1.0).abs();
555 /// assert!(abs_difference < 1e-10);
557 #[must_use = "method returns a new number and does not mutate the original value"]
558 #[stable(feature = "rust1", since = "1.0.0")]
560 pub fn sin(self) -> f64 {
561 unsafe { intrinsics::sinf64(self) }
564 /// Computes the cosine of a number (in radians).
569 /// let x = 2.0 * std::f64::consts::PI;
571 /// let abs_difference = (x.cos() - 1.0).abs();
573 /// assert!(abs_difference < 1e-10);
575 #[must_use = "method returns a new number and does not mutate the original value"]
576 #[stable(feature = "rust1", since = "1.0.0")]
578 pub fn cos(self) -> f64 {
579 unsafe { intrinsics::cosf64(self) }
582 /// Computes the tangent of a number (in radians).
587 /// let x = std::f64::consts::FRAC_PI_4;
588 /// let abs_difference = (x.tan() - 1.0).abs();
590 /// assert!(abs_difference < 1e-14);
592 #[must_use = "method returns a new number and does not mutate the original value"]
593 #[stable(feature = "rust1", since = "1.0.0")]
595 pub fn tan(self) -> f64 {
596 unsafe { cmath::tan(self) }
599 /// Computes the arcsine of a number. Return value is in radians in
600 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
606 /// let f = std::f64::consts::FRAC_PI_2;
608 /// // asin(sin(pi/2))
609 /// let abs_difference = (f.sin().asin() - std::f64::consts::FRAC_PI_2).abs();
611 /// assert!(abs_difference < 1e-10);
613 #[must_use = "method returns a new number and does not mutate the original value"]
614 #[stable(feature = "rust1", since = "1.0.0")]
616 pub fn asin(self) -> f64 {
617 unsafe { cmath::asin(self) }
620 /// Computes the arccosine of a number. Return value is in radians in
621 /// the range [0, pi] or NaN if the number is outside the range
627 /// let f = std::f64::consts::FRAC_PI_4;
629 /// // acos(cos(pi/4))
630 /// let abs_difference = (f.cos().acos() - std::f64::consts::FRAC_PI_4).abs();
632 /// assert!(abs_difference < 1e-10);
634 #[must_use = "method returns a new number and does not mutate the original value"]
635 #[stable(feature = "rust1", since = "1.0.0")]
637 pub fn acos(self) -> f64 {
638 unsafe { cmath::acos(self) }
641 /// Computes the arctangent of a number. Return value is in radians in the
642 /// range [-pi/2, pi/2];
650 /// let abs_difference = (f.tan().atan() - 1.0).abs();
652 /// assert!(abs_difference < 1e-10);
654 #[must_use = "method returns a new number and does not mutate the original value"]
655 #[stable(feature = "rust1", since = "1.0.0")]
657 pub fn atan(self) -> f64 {
658 unsafe { cmath::atan(self) }
661 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
663 /// * `x = 0`, `y = 0`: `0`
664 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
665 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
666 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
671 /// // Positive angles measured counter-clockwise
672 /// // from positive x axis
673 /// // -pi/4 radians (45 deg clockwise)
674 /// let x1 = 3.0_f64;
675 /// let y1 = -3.0_f64;
677 /// // 3pi/4 radians (135 deg counter-clockwise)
678 /// let x2 = -3.0_f64;
679 /// let y2 = 3.0_f64;
681 /// let abs_difference_1 = (y1.atan2(x1) - (-std::f64::consts::FRAC_PI_4)).abs();
682 /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f64::consts::FRAC_PI_4)).abs();
684 /// assert!(abs_difference_1 < 1e-10);
685 /// assert!(abs_difference_2 < 1e-10);
687 #[must_use = "method returns a new number and does not mutate the original value"]
688 #[stable(feature = "rust1", since = "1.0.0")]
690 pub fn atan2(self, other: f64) -> f64 {
691 unsafe { cmath::atan2(self, other) }
694 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
695 /// `(sin(x), cos(x))`.
700 /// let x = std::f64::consts::FRAC_PI_4;
701 /// let f = x.sin_cos();
703 /// let abs_difference_0 = (f.0 - x.sin()).abs();
704 /// let abs_difference_1 = (f.1 - x.cos()).abs();
706 /// assert!(abs_difference_0 < 1e-10);
707 /// assert!(abs_difference_1 < 1e-10);
709 #[stable(feature = "rust1", since = "1.0.0")]
711 pub fn sin_cos(self) -> (f64, f64) {
712 (self.sin(), self.cos())
715 /// Returns `e^(self) - 1` in a way that is accurate even if the
716 /// number is close to zero.
724 /// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
726 /// assert!(abs_difference < 1e-10);
728 #[must_use = "method returns a new number and does not mutate the original value"]
729 #[stable(feature = "rust1", since = "1.0.0")]
731 pub fn exp_m1(self) -> f64 {
732 unsafe { cmath::expm1(self) }
735 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
736 /// the operations were performed separately.
741 /// let x = std::f64::consts::E - 1.0;
743 /// // ln(1 + (e - 1)) == ln(e) == 1
744 /// let abs_difference = (x.ln_1p() - 1.0).abs();
746 /// assert!(abs_difference < 1e-10);
748 #[must_use = "method returns a new number and does not mutate the original value"]
749 #[stable(feature = "rust1", since = "1.0.0")]
751 pub fn ln_1p(self) -> f64 {
752 unsafe { cmath::log1p(self) }
755 /// Hyperbolic sine function.
760 /// let e = std::f64::consts::E;
763 /// let f = x.sinh();
764 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
765 /// let g = ((e * e) - 1.0) / (2.0 * e);
766 /// let abs_difference = (f - g).abs();
768 /// assert!(abs_difference < 1e-10);
770 #[must_use = "method returns a new number and does not mutate the original value"]
771 #[stable(feature = "rust1", since = "1.0.0")]
773 pub fn sinh(self) -> f64 {
774 unsafe { cmath::sinh(self) }
777 /// Hyperbolic cosine function.
782 /// let e = std::f64::consts::E;
784 /// let f = x.cosh();
785 /// // Solving cosh() at 1 gives this result
786 /// let g = ((e * e) + 1.0) / (2.0 * e);
787 /// let abs_difference = (f - g).abs();
790 /// assert!(abs_difference < 1.0e-10);
792 #[must_use = "method returns a new number and does not mutate the original value"]
793 #[stable(feature = "rust1", since = "1.0.0")]
795 pub fn cosh(self) -> f64 {
796 unsafe { cmath::cosh(self) }
799 /// Hyperbolic tangent function.
804 /// let e = std::f64::consts::E;
807 /// let f = x.tanh();
808 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
809 /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
810 /// let abs_difference = (f - g).abs();
812 /// assert!(abs_difference < 1.0e-10);
814 #[must_use = "method returns a new number and does not mutate the original value"]
815 #[stable(feature = "rust1", since = "1.0.0")]
817 pub fn tanh(self) -> f64 {
818 unsafe { cmath::tanh(self) }
821 /// Inverse hyperbolic sine function.
827 /// let f = x.sinh().asinh();
829 /// let abs_difference = (f - x).abs();
831 /// assert!(abs_difference < 1.0e-10);
833 #[must_use = "method returns a new number and does not mutate the original value"]
834 #[stable(feature = "rust1", since = "1.0.0")]
836 pub fn asinh(self) -> f64 {
837 if self == Self::NEG_INFINITY {
840 (self + ((self * self) + 1.0).sqrt()).ln().copysign(self)
844 /// Inverse hyperbolic cosine function.
850 /// let f = x.cosh().acosh();
852 /// let abs_difference = (f - x).abs();
854 /// assert!(abs_difference < 1.0e-10);
856 #[must_use = "method returns a new number and does not mutate the original value"]
857 #[stable(feature = "rust1", since = "1.0.0")]
859 pub fn acosh(self) -> f64 {
860 if self < 1.0 { Self::NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() }
863 /// Inverse hyperbolic tangent function.
868 /// let e = std::f64::consts::E;
869 /// let f = e.tanh().atanh();
871 /// let abs_difference = (f - e).abs();
873 /// assert!(abs_difference < 1.0e-10);
875 #[must_use = "method returns a new number and does not mutate the original value"]
876 #[stable(feature = "rust1", since = "1.0.0")]
878 pub fn atanh(self) -> f64 {
879 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
882 /// Restrict a value to a certain interval unless it is NaN.
884 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
885 /// less than `min`. Otherwise this returns `self`.
887 /// Note that this function returns NaN if the initial value was NaN as
892 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
897 /// #![feature(clamp)]
898 /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
899 /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
900 /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
901 /// assert!((f64::NAN).clamp(-2.0, 1.0).is_nan());
903 #[must_use = "method returns a new number and does not mutate the original value"]
904 #[unstable(feature = "clamp", issue = "44095")]
906 pub fn clamp(self, min: f64, max: f64) -> f64 {
918 // Solaris/Illumos requires a wrapper around log, log2, and log10 functions
919 // because of their non-standard behavior (e.g., log(-n) returns -Inf instead
921 fn log_wrapper<F: Fn(f64) -> f64>(self, log_fn: F) -> f64 {
922 if !cfg!(any(target_os = "solaris", target_os = "illumos")) {
925 if self.is_finite() {
928 } else if self == 0.0 {
929 Self::NEG_INFINITY // log(0) = -Inf
931 Self::NAN // log(-n) = NaN
933 } else if self.is_nan() {
934 self // log(NaN) = NaN
935 } else if self > 0.0 {
936 self // log(Inf) = Inf
938 Self::NAN // log(-Inf) = NaN
948 use crate::num::FpCategory as Fp;
953 test_num(10f64, 2f64);
958 assert_eq!(NAN.min(2.0), 2.0);
959 assert_eq!(2.0f64.min(NAN), 2.0);
964 assert_eq!(NAN.max(2.0), 2.0);
965 assert_eq!(2.0f64.max(NAN), 2.0);
971 assert!(nan.is_nan());
972 assert!(!nan.is_infinite());
973 assert!(!nan.is_finite());
974 assert!(!nan.is_normal());
975 assert!(nan.is_sign_positive());
976 assert!(!nan.is_sign_negative());
977 assert_eq!(Fp::Nan, nan.classify());
982 let inf: f64 = INFINITY;
983 assert!(inf.is_infinite());
984 assert!(!inf.is_finite());
985 assert!(inf.is_sign_positive());
986 assert!(!inf.is_sign_negative());
987 assert!(!inf.is_nan());
988 assert!(!inf.is_normal());
989 assert_eq!(Fp::Infinite, inf.classify());
993 fn test_neg_infinity() {
994 let neg_inf: f64 = NEG_INFINITY;
995 assert!(neg_inf.is_infinite());
996 assert!(!neg_inf.is_finite());
997 assert!(!neg_inf.is_sign_positive());
998 assert!(neg_inf.is_sign_negative());
999 assert!(!neg_inf.is_nan());
1000 assert!(!neg_inf.is_normal());
1001 assert_eq!(Fp::Infinite, neg_inf.classify());
1006 let zero: f64 = 0.0f64;
1007 assert_eq!(0.0, zero);
1008 assert!(!zero.is_infinite());
1009 assert!(zero.is_finite());
1010 assert!(zero.is_sign_positive());
1011 assert!(!zero.is_sign_negative());
1012 assert!(!zero.is_nan());
1013 assert!(!zero.is_normal());
1014 assert_eq!(Fp::Zero, zero.classify());
1018 fn test_neg_zero() {
1019 let neg_zero: f64 = -0.0;
1020 assert_eq!(0.0, neg_zero);
1021 assert!(!neg_zero.is_infinite());
1022 assert!(neg_zero.is_finite());
1023 assert!(!neg_zero.is_sign_positive());
1024 assert!(neg_zero.is_sign_negative());
1025 assert!(!neg_zero.is_nan());
1026 assert!(!neg_zero.is_normal());
1027 assert_eq!(Fp::Zero, neg_zero.classify());
1030 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1033 let one: f64 = 1.0f64;
1034 assert_eq!(1.0, one);
1035 assert!(!one.is_infinite());
1036 assert!(one.is_finite());
1037 assert!(one.is_sign_positive());
1038 assert!(!one.is_sign_negative());
1039 assert!(!one.is_nan());
1040 assert!(one.is_normal());
1041 assert_eq!(Fp::Normal, one.classify());
1047 let inf: f64 = INFINITY;
1048 let neg_inf: f64 = NEG_INFINITY;
1049 assert!(nan.is_nan());
1050 assert!(!0.0f64.is_nan());
1051 assert!(!5.3f64.is_nan());
1052 assert!(!(-10.732f64).is_nan());
1053 assert!(!inf.is_nan());
1054 assert!(!neg_inf.is_nan());
1058 fn test_is_infinite() {
1060 let inf: f64 = INFINITY;
1061 let neg_inf: f64 = NEG_INFINITY;
1062 assert!(!nan.is_infinite());
1063 assert!(inf.is_infinite());
1064 assert!(neg_inf.is_infinite());
1065 assert!(!0.0f64.is_infinite());
1066 assert!(!42.8f64.is_infinite());
1067 assert!(!(-109.2f64).is_infinite());
1071 fn test_is_finite() {
1073 let inf: f64 = INFINITY;
1074 let neg_inf: f64 = NEG_INFINITY;
1075 assert!(!nan.is_finite());
1076 assert!(!inf.is_finite());
1077 assert!(!neg_inf.is_finite());
1078 assert!(0.0f64.is_finite());
1079 assert!(42.8f64.is_finite());
1080 assert!((-109.2f64).is_finite());
1083 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1085 fn test_is_normal() {
1087 let inf: f64 = INFINITY;
1088 let neg_inf: f64 = NEG_INFINITY;
1089 let zero: f64 = 0.0f64;
1090 let neg_zero: f64 = -0.0;
1091 assert!(!nan.is_normal());
1092 assert!(!inf.is_normal());
1093 assert!(!neg_inf.is_normal());
1094 assert!(!zero.is_normal());
1095 assert!(!neg_zero.is_normal());
1096 assert!(1f64.is_normal());
1097 assert!(1e-307f64.is_normal());
1098 assert!(!1e-308f64.is_normal());
1101 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1103 fn test_classify() {
1105 let inf: f64 = INFINITY;
1106 let neg_inf: f64 = NEG_INFINITY;
1107 let zero: f64 = 0.0f64;
1108 let neg_zero: f64 = -0.0;
1109 assert_eq!(nan.classify(), Fp::Nan);
1110 assert_eq!(inf.classify(), Fp::Infinite);
1111 assert_eq!(neg_inf.classify(), Fp::Infinite);
1112 assert_eq!(zero.classify(), Fp::Zero);
1113 assert_eq!(neg_zero.classify(), Fp::Zero);
1114 assert_eq!(1e-307f64.classify(), Fp::Normal);
1115 assert_eq!(1e-308f64.classify(), Fp::Subnormal);
1120 assert_approx_eq!(1.0f64.floor(), 1.0f64);
1121 assert_approx_eq!(1.3f64.floor(), 1.0f64);
1122 assert_approx_eq!(1.5f64.floor(), 1.0f64);
1123 assert_approx_eq!(1.7f64.floor(), 1.0f64);
1124 assert_approx_eq!(0.0f64.floor(), 0.0f64);
1125 assert_approx_eq!((-0.0f64).floor(), -0.0f64);
1126 assert_approx_eq!((-1.0f64).floor(), -1.0f64);
1127 assert_approx_eq!((-1.3f64).floor(), -2.0f64);
1128 assert_approx_eq!((-1.5f64).floor(), -2.0f64);
1129 assert_approx_eq!((-1.7f64).floor(), -2.0f64);
1134 assert_approx_eq!(1.0f64.ceil(), 1.0f64);
1135 assert_approx_eq!(1.3f64.ceil(), 2.0f64);
1136 assert_approx_eq!(1.5f64.ceil(), 2.0f64);
1137 assert_approx_eq!(1.7f64.ceil(), 2.0f64);
1138 assert_approx_eq!(0.0f64.ceil(), 0.0f64);
1139 assert_approx_eq!((-0.0f64).ceil(), -0.0f64);
1140 assert_approx_eq!((-1.0f64).ceil(), -1.0f64);
1141 assert_approx_eq!((-1.3f64).ceil(), -1.0f64);
1142 assert_approx_eq!((-1.5f64).ceil(), -1.0f64);
1143 assert_approx_eq!((-1.7f64).ceil(), -1.0f64);
1148 assert_approx_eq!(1.0f64.round(), 1.0f64);
1149 assert_approx_eq!(1.3f64.round(), 1.0f64);
1150 assert_approx_eq!(1.5f64.round(), 2.0f64);
1151 assert_approx_eq!(1.7f64.round(), 2.0f64);
1152 assert_approx_eq!(0.0f64.round(), 0.0f64);
1153 assert_approx_eq!((-0.0f64).round(), -0.0f64);
1154 assert_approx_eq!((-1.0f64).round(), -1.0f64);
1155 assert_approx_eq!((-1.3f64).round(), -1.0f64);
1156 assert_approx_eq!((-1.5f64).round(), -2.0f64);
1157 assert_approx_eq!((-1.7f64).round(), -2.0f64);
1162 assert_approx_eq!(1.0f64.trunc(), 1.0f64);
1163 assert_approx_eq!(1.3f64.trunc(), 1.0f64);
1164 assert_approx_eq!(1.5f64.trunc(), 1.0f64);
1165 assert_approx_eq!(1.7f64.trunc(), 1.0f64);
1166 assert_approx_eq!(0.0f64.trunc(), 0.0f64);
1167 assert_approx_eq!((-0.0f64).trunc(), -0.0f64);
1168 assert_approx_eq!((-1.0f64).trunc(), -1.0f64);
1169 assert_approx_eq!((-1.3f64).trunc(), -1.0f64);
1170 assert_approx_eq!((-1.5f64).trunc(), -1.0f64);
1171 assert_approx_eq!((-1.7f64).trunc(), -1.0f64);
1176 assert_approx_eq!(1.0f64.fract(), 0.0f64);
1177 assert_approx_eq!(1.3f64.fract(), 0.3f64);
1178 assert_approx_eq!(1.5f64.fract(), 0.5f64);
1179 assert_approx_eq!(1.7f64.fract(), 0.7f64);
1180 assert_approx_eq!(0.0f64.fract(), 0.0f64);
1181 assert_approx_eq!((-0.0f64).fract(), -0.0f64);
1182 assert_approx_eq!((-1.0f64).fract(), -0.0f64);
1183 assert_approx_eq!((-1.3f64).fract(), -0.3f64);
1184 assert_approx_eq!((-1.5f64).fract(), -0.5f64);
1185 assert_approx_eq!((-1.7f64).fract(), -0.7f64);
1190 assert_eq!(INFINITY.abs(), INFINITY);
1191 assert_eq!(1f64.abs(), 1f64);
1192 assert_eq!(0f64.abs(), 0f64);
1193 assert_eq!((-0f64).abs(), 0f64);
1194 assert_eq!((-1f64).abs(), 1f64);
1195 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1196 assert_eq!((1f64 / NEG_INFINITY).abs(), 0f64);
1197 assert!(NAN.abs().is_nan());
1202 assert_eq!(INFINITY.signum(), 1f64);
1203 assert_eq!(1f64.signum(), 1f64);
1204 assert_eq!(0f64.signum(), 1f64);
1205 assert_eq!((-0f64).signum(), -1f64);
1206 assert_eq!((-1f64).signum(), -1f64);
1207 assert_eq!(NEG_INFINITY.signum(), -1f64);
1208 assert_eq!((1f64 / NEG_INFINITY).signum(), -1f64);
1209 assert!(NAN.signum().is_nan());
1213 fn test_is_sign_positive() {
1214 assert!(INFINITY.is_sign_positive());
1215 assert!(1f64.is_sign_positive());
1216 assert!(0f64.is_sign_positive());
1217 assert!(!(-0f64).is_sign_positive());
1218 assert!(!(-1f64).is_sign_positive());
1219 assert!(!NEG_INFINITY.is_sign_positive());
1220 assert!(!(1f64 / NEG_INFINITY).is_sign_positive());
1221 assert!(NAN.is_sign_positive());
1222 assert!(!(-NAN).is_sign_positive());
1226 fn test_is_sign_negative() {
1227 assert!(!INFINITY.is_sign_negative());
1228 assert!(!1f64.is_sign_negative());
1229 assert!(!0f64.is_sign_negative());
1230 assert!((-0f64).is_sign_negative());
1231 assert!((-1f64).is_sign_negative());
1232 assert!(NEG_INFINITY.is_sign_negative());
1233 assert!((1f64 / NEG_INFINITY).is_sign_negative());
1234 assert!(!NAN.is_sign_negative());
1235 assert!((-NAN).is_sign_negative());
1241 let inf: f64 = INFINITY;
1242 let neg_inf: f64 = NEG_INFINITY;
1243 assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05);
1244 assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65);
1245 assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2);
1246 assert_approx_eq!(3.4f64.mul_add(-0.0, 5.6), 5.6);
1247 assert!(nan.mul_add(7.8, 9.0).is_nan());
1248 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1249 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1250 assert_eq!(8.9f64.mul_add(inf, 3.2), inf);
1251 assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf);
1257 let inf: f64 = INFINITY;
1258 let neg_inf: f64 = NEG_INFINITY;
1259 assert_eq!(1.0f64.recip(), 1.0);
1260 assert_eq!(2.0f64.recip(), 0.5);
1261 assert_eq!((-0.4f64).recip(), -2.5);
1262 assert_eq!(0.0f64.recip(), inf);
1263 assert!(nan.recip().is_nan());
1264 assert_eq!(inf.recip(), 0.0);
1265 assert_eq!(neg_inf.recip(), 0.0);
1271 let inf: f64 = INFINITY;
1272 let neg_inf: f64 = NEG_INFINITY;
1273 assert_eq!(1.0f64.powi(1), 1.0);
1274 assert_approx_eq!((-3.1f64).powi(2), 9.61);
1275 assert_approx_eq!(5.9f64.powi(-2), 0.028727);
1276 assert_eq!(8.3f64.powi(0), 1.0);
1277 assert!(nan.powi(2).is_nan());
1278 assert_eq!(inf.powi(3), inf);
1279 assert_eq!(neg_inf.powi(2), inf);
1285 let inf: f64 = INFINITY;
1286 let neg_inf: f64 = NEG_INFINITY;
1287 assert_eq!(1.0f64.powf(1.0), 1.0);
1288 assert_approx_eq!(3.4f64.powf(4.5), 246.408183);
1289 assert_approx_eq!(2.7f64.powf(-3.2), 0.041652);
1290 assert_approx_eq!((-3.1f64).powf(2.0), 9.61);
1291 assert_approx_eq!(5.9f64.powf(-2.0), 0.028727);
1292 assert_eq!(8.3f64.powf(0.0), 1.0);
1293 assert!(nan.powf(2.0).is_nan());
1294 assert_eq!(inf.powf(2.0), inf);
1295 assert_eq!(neg_inf.powf(3.0), neg_inf);
1299 fn test_sqrt_domain() {
1300 assert!(NAN.sqrt().is_nan());
1301 assert!(NEG_INFINITY.sqrt().is_nan());
1302 assert!((-1.0f64).sqrt().is_nan());
1303 assert_eq!((-0.0f64).sqrt(), -0.0);
1304 assert_eq!(0.0f64.sqrt(), 0.0);
1305 assert_eq!(1.0f64.sqrt(), 1.0);
1306 assert_eq!(INFINITY.sqrt(), INFINITY);
1311 assert_eq!(1.0, 0.0f64.exp());
1312 assert_approx_eq!(2.718282, 1.0f64.exp());
1313 assert_approx_eq!(148.413159, 5.0f64.exp());
1315 let inf: f64 = INFINITY;
1316 let neg_inf: f64 = NEG_INFINITY;
1318 assert_eq!(inf, inf.exp());
1319 assert_eq!(0.0, neg_inf.exp());
1320 assert!(nan.exp().is_nan());
1325 assert_eq!(32.0, 5.0f64.exp2());
1326 assert_eq!(1.0, 0.0f64.exp2());
1328 let inf: f64 = INFINITY;
1329 let neg_inf: f64 = NEG_INFINITY;
1331 assert_eq!(inf, inf.exp2());
1332 assert_eq!(0.0, neg_inf.exp2());
1333 assert!(nan.exp2().is_nan());
1339 let inf: f64 = INFINITY;
1340 let neg_inf: f64 = NEG_INFINITY;
1341 assert_approx_eq!(1.0f64.exp().ln(), 1.0);
1342 assert!(nan.ln().is_nan());
1343 assert_eq!(inf.ln(), inf);
1344 assert!(neg_inf.ln().is_nan());
1345 assert!((-2.3f64).ln().is_nan());
1346 assert_eq!((-0.0f64).ln(), neg_inf);
1347 assert_eq!(0.0f64.ln(), neg_inf);
1348 assert_approx_eq!(4.0f64.ln(), 1.386294);
1354 let inf: f64 = INFINITY;
1355 let neg_inf: f64 = NEG_INFINITY;
1356 assert_eq!(10.0f64.log(10.0), 1.0);
1357 assert_approx_eq!(2.3f64.log(3.5), 0.664858);
1358 assert_eq!(1.0f64.exp().log(1.0f64.exp()), 1.0);
1359 assert!(1.0f64.log(1.0).is_nan());
1360 assert!(1.0f64.log(-13.9).is_nan());
1361 assert!(nan.log(2.3).is_nan());
1362 assert_eq!(inf.log(10.0), inf);
1363 assert!(neg_inf.log(8.8).is_nan());
1364 assert!((-2.3f64).log(0.1).is_nan());
1365 assert_eq!((-0.0f64).log(2.0), neg_inf);
1366 assert_eq!(0.0f64.log(7.0), neg_inf);
1372 let inf: f64 = INFINITY;
1373 let neg_inf: f64 = NEG_INFINITY;
1374 assert_approx_eq!(10.0f64.log2(), 3.321928);
1375 assert_approx_eq!(2.3f64.log2(), 1.201634);
1376 assert_approx_eq!(1.0f64.exp().log2(), 1.442695);
1377 assert!(nan.log2().is_nan());
1378 assert_eq!(inf.log2(), inf);
1379 assert!(neg_inf.log2().is_nan());
1380 assert!((-2.3f64).log2().is_nan());
1381 assert_eq!((-0.0f64).log2(), neg_inf);
1382 assert_eq!(0.0f64.log2(), neg_inf);
1388 let inf: f64 = INFINITY;
1389 let neg_inf: f64 = NEG_INFINITY;
1390 assert_eq!(10.0f64.log10(), 1.0);
1391 assert_approx_eq!(2.3f64.log10(), 0.361728);
1392 assert_approx_eq!(1.0f64.exp().log10(), 0.434294);
1393 assert_eq!(1.0f64.log10(), 0.0);
1394 assert!(nan.log10().is_nan());
1395 assert_eq!(inf.log10(), inf);
1396 assert!(neg_inf.log10().is_nan());
1397 assert!((-2.3f64).log10().is_nan());
1398 assert_eq!((-0.0f64).log10(), neg_inf);
1399 assert_eq!(0.0f64.log10(), neg_inf);
1403 fn test_to_degrees() {
1404 let pi: f64 = consts::PI;
1406 let inf: f64 = INFINITY;
1407 let neg_inf: f64 = NEG_INFINITY;
1408 assert_eq!(0.0f64.to_degrees(), 0.0);
1409 assert_approx_eq!((-5.8f64).to_degrees(), -332.315521);
1410 assert_eq!(pi.to_degrees(), 180.0);
1411 assert!(nan.to_degrees().is_nan());
1412 assert_eq!(inf.to_degrees(), inf);
1413 assert_eq!(neg_inf.to_degrees(), neg_inf);
1417 fn test_to_radians() {
1418 let pi: f64 = consts::PI;
1420 let inf: f64 = INFINITY;
1421 let neg_inf: f64 = NEG_INFINITY;
1422 assert_eq!(0.0f64.to_radians(), 0.0);
1423 assert_approx_eq!(154.6f64.to_radians(), 2.698279);
1424 assert_approx_eq!((-332.31f64).to_radians(), -5.799903);
1425 assert_eq!(180.0f64.to_radians(), pi);
1426 assert!(nan.to_radians().is_nan());
1427 assert_eq!(inf.to_radians(), inf);
1428 assert_eq!(neg_inf.to_radians(), neg_inf);
1433 assert_eq!(0.0f64.asinh(), 0.0f64);
1434 assert_eq!((-0.0f64).asinh(), -0.0f64);
1436 let inf: f64 = INFINITY;
1437 let neg_inf: f64 = NEG_INFINITY;
1439 assert_eq!(inf.asinh(), inf);
1440 assert_eq!(neg_inf.asinh(), neg_inf);
1441 assert!(nan.asinh().is_nan());
1442 assert!((-0.0f64).asinh().is_sign_negative());
1444 assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64);
1445 assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
1450 assert_eq!(1.0f64.acosh(), 0.0f64);
1451 assert!(0.999f64.acosh().is_nan());
1453 let inf: f64 = INFINITY;
1454 let neg_inf: f64 = NEG_INFINITY;
1456 assert_eq!(inf.acosh(), inf);
1457 assert!(neg_inf.acosh().is_nan());
1458 assert!(nan.acosh().is_nan());
1459 assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
1460 assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
1465 assert_eq!(0.0f64.atanh(), 0.0f64);
1466 assert_eq!((-0.0f64).atanh(), -0.0f64);
1468 let inf: f64 = INFINITY;
1469 let neg_inf: f64 = NEG_INFINITY;
1471 assert_eq!(1.0f64.atanh(), inf);
1472 assert_eq!((-1.0f64).atanh(), neg_inf);
1473 assert!(2f64.atanh().atanh().is_nan());
1474 assert!((-2f64).atanh().atanh().is_nan());
1475 assert!(inf.atanh().is_nan());
1476 assert!(neg_inf.atanh().is_nan());
1477 assert!(nan.atanh().is_nan());
1478 assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64);
1479 assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64);
1483 fn test_real_consts() {
1485 let pi: f64 = consts::PI;
1486 let frac_pi_2: f64 = consts::FRAC_PI_2;
1487 let frac_pi_3: f64 = consts::FRAC_PI_3;
1488 let frac_pi_4: f64 = consts::FRAC_PI_4;
1489 let frac_pi_6: f64 = consts::FRAC_PI_6;
1490 let frac_pi_8: f64 = consts::FRAC_PI_8;
1491 let frac_1_pi: f64 = consts::FRAC_1_PI;
1492 let frac_2_pi: f64 = consts::FRAC_2_PI;
1493 let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRT_PI;
1494 let sqrt2: f64 = consts::SQRT_2;
1495 let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT_2;
1496 let e: f64 = consts::E;
1497 let log2_e: f64 = consts::LOG2_E;
1498 let log10_e: f64 = consts::LOG10_E;
1499 let ln_2: f64 = consts::LN_2;
1500 let ln_10: f64 = consts::LN_10;
1502 assert_approx_eq!(frac_pi_2, pi / 2f64);
1503 assert_approx_eq!(frac_pi_3, pi / 3f64);
1504 assert_approx_eq!(frac_pi_4, pi / 4f64);
1505 assert_approx_eq!(frac_pi_6, pi / 6f64);
1506 assert_approx_eq!(frac_pi_8, pi / 8f64);
1507 assert_approx_eq!(frac_1_pi, 1f64 / pi);
1508 assert_approx_eq!(frac_2_pi, 2f64 / pi);
1509 assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt());
1510 assert_approx_eq!(sqrt2, 2f64.sqrt());
1511 assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt());
1512 assert_approx_eq!(log2_e, e.log2());
1513 assert_approx_eq!(log10_e, e.log10());
1514 assert_approx_eq!(ln_2, 2f64.ln());
1515 assert_approx_eq!(ln_10, 10f64.ln());
1519 fn test_float_bits_conv() {
1520 assert_eq!((1f64).to_bits(), 0x3ff0000000000000);
1521 assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
1522 assert_eq!((1337f64).to_bits(), 0x4094e40000000000);
1523 assert_eq!((-14.25f64).to_bits(), 0xc02c800000000000);
1524 assert_approx_eq!(f64::from_bits(0x3ff0000000000000), 1.0);
1525 assert_approx_eq!(f64::from_bits(0x4029000000000000), 12.5);
1526 assert_approx_eq!(f64::from_bits(0x4094e40000000000), 1337.0);
1527 assert_approx_eq!(f64::from_bits(0xc02c800000000000), -14.25);
1529 // Check that NaNs roundtrip their bits regardless of signalingness
1530 // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits
1531 let masked_nan1 = f64::NAN.to_bits() ^ 0x000A_AAAA_AAAA_AAAA;
1532 let masked_nan2 = f64::NAN.to_bits() ^ 0x0005_5555_5555_5555;
1533 assert!(f64::from_bits(masked_nan1).is_nan());
1534 assert!(f64::from_bits(masked_nan2).is_nan());
1536 assert_eq!(f64::from_bits(masked_nan1).to_bits(), masked_nan1);
1537 assert_eq!(f64::from_bits(masked_nan2).to_bits(), masked_nan2);
1542 fn test_clamp_min_greater_than_max() {
1543 let _ = 1.0f64.clamp(3.0, 1.0);
1548 fn test_clamp_min_is_nan() {
1549 let _ = 1.0f64.clamp(NAN, 1.0);
1554 fn test_clamp_max_is_nan() {
1555 let _ = 1.0f64.clamp(3.0, NAN);
1559 fn test_total_cmp() {
1560 use core::cmp::Ordering;
1562 fn quiet_bit_mask() -> u64 {
1563 1 << (f64::MANTISSA_DIGITS - 2)
1566 fn min_subnorm() -> f64 {
1567 f64::MIN_POSITIVE / f64::powf(2.0, f64::MANTISSA_DIGITS as f64 - 1.0)
1570 fn max_subnorm() -> f64 {
1571 f64::MIN_POSITIVE - min_subnorm()
1575 f64::from_bits(f64::NAN.to_bits() | quiet_bit_mask())
1579 f64::from_bits((f64::NAN.to_bits() & !quiet_bit_mask()) + 42)
1582 assert_eq!(Ordering::Equal, (-q_nan()).total_cmp(&-q_nan()));
1583 assert_eq!(Ordering::Equal, (-s_nan()).total_cmp(&-s_nan()));
1584 assert_eq!(Ordering::Equal, (-f64::INFINITY).total_cmp(&-f64::INFINITY));
1585 assert_eq!(Ordering::Equal, (-f64::MAX).total_cmp(&-f64::MAX));
1586 assert_eq!(Ordering::Equal, (-2.5_f64).total_cmp(&-2.5));
1587 assert_eq!(Ordering::Equal, (-1.0_f64).total_cmp(&-1.0));
1588 assert_eq!(Ordering::Equal, (-1.5_f64).total_cmp(&-1.5));
1589 assert_eq!(Ordering::Equal, (-0.5_f64).total_cmp(&-0.5));
1590 assert_eq!(Ordering::Equal, (-f64::MIN_POSITIVE).total_cmp(&-f64::MIN_POSITIVE));
1591 assert_eq!(Ordering::Equal, (-max_subnorm()).total_cmp(&-max_subnorm()));
1592 assert_eq!(Ordering::Equal, (-min_subnorm()).total_cmp(&-min_subnorm()));
1593 assert_eq!(Ordering::Equal, (-0.0_f64).total_cmp(&-0.0));
1594 assert_eq!(Ordering::Equal, 0.0_f64.total_cmp(&0.0));
1595 assert_eq!(Ordering::Equal, min_subnorm().total_cmp(&min_subnorm()));
1596 assert_eq!(Ordering::Equal, max_subnorm().total_cmp(&max_subnorm()));
1597 assert_eq!(Ordering::Equal, f64::MIN_POSITIVE.total_cmp(&f64::MIN_POSITIVE));
1598 assert_eq!(Ordering::Equal, 0.5_f64.total_cmp(&0.5));
1599 assert_eq!(Ordering::Equal, 1.0_f64.total_cmp(&1.0));
1600 assert_eq!(Ordering::Equal, 1.5_f64.total_cmp(&1.5));
1601 assert_eq!(Ordering::Equal, 2.5_f64.total_cmp(&2.5));
1602 assert_eq!(Ordering::Equal, f64::MAX.total_cmp(&f64::MAX));
1603 assert_eq!(Ordering::Equal, f64::INFINITY.total_cmp(&f64::INFINITY));
1604 assert_eq!(Ordering::Equal, s_nan().total_cmp(&s_nan()));
1605 assert_eq!(Ordering::Equal, q_nan().total_cmp(&q_nan()));
1607 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-s_nan()));
1608 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::INFINITY));
1609 assert_eq!(Ordering::Less, (-f64::INFINITY).total_cmp(&-f64::MAX));
1610 assert_eq!(Ordering::Less, (-f64::MAX).total_cmp(&-2.5));
1611 assert_eq!(Ordering::Less, (-2.5_f64).total_cmp(&-1.5));
1612 assert_eq!(Ordering::Less, (-1.5_f64).total_cmp(&-1.0));
1613 assert_eq!(Ordering::Less, (-1.0_f64).total_cmp(&-0.5));
1614 assert_eq!(Ordering::Less, (-0.5_f64).total_cmp(&-f64::MIN_POSITIVE));
1615 assert_eq!(Ordering::Less, (-f64::MIN_POSITIVE).total_cmp(&-max_subnorm()));
1616 assert_eq!(Ordering::Less, (-max_subnorm()).total_cmp(&-min_subnorm()));
1617 assert_eq!(Ordering::Less, (-min_subnorm()).total_cmp(&-0.0));
1618 assert_eq!(Ordering::Less, (-0.0_f64).total_cmp(&0.0));
1619 assert_eq!(Ordering::Less, 0.0_f64.total_cmp(&min_subnorm()));
1620 assert_eq!(Ordering::Less, min_subnorm().total_cmp(&max_subnorm()));
1621 assert_eq!(Ordering::Less, max_subnorm().total_cmp(&f64::MIN_POSITIVE));
1622 assert_eq!(Ordering::Less, f64::MIN_POSITIVE.total_cmp(&0.5));
1623 assert_eq!(Ordering::Less, 0.5_f64.total_cmp(&1.0));
1624 assert_eq!(Ordering::Less, 1.0_f64.total_cmp(&1.5));
1625 assert_eq!(Ordering::Less, 1.5_f64.total_cmp(&2.5));
1626 assert_eq!(Ordering::Less, 2.5_f64.total_cmp(&f64::MAX));
1627 assert_eq!(Ordering::Less, f64::MAX.total_cmp(&f64::INFINITY));
1628 assert_eq!(Ordering::Less, f64::INFINITY.total_cmp(&s_nan()));
1629 assert_eq!(Ordering::Less, s_nan().total_cmp(&q_nan()));
1631 assert_eq!(Ordering::Greater, (-s_nan()).total_cmp(&-q_nan()));
1632 assert_eq!(Ordering::Greater, (-f64::INFINITY).total_cmp(&-s_nan()));
1633 assert_eq!(Ordering::Greater, (-f64::MAX).total_cmp(&-f64::INFINITY));
1634 assert_eq!(Ordering::Greater, (-2.5_f64).total_cmp(&-f64::MAX));
1635 assert_eq!(Ordering::Greater, (-1.5_f64).total_cmp(&-2.5));
1636 assert_eq!(Ordering::Greater, (-1.0_f64).total_cmp(&-1.5));
1637 assert_eq!(Ordering::Greater, (-0.5_f64).total_cmp(&-1.0));
1638 assert_eq!(Ordering::Greater, (-f64::MIN_POSITIVE).total_cmp(&-0.5));
1639 assert_eq!(Ordering::Greater, (-max_subnorm()).total_cmp(&-f64::MIN_POSITIVE));
1640 assert_eq!(Ordering::Greater, (-min_subnorm()).total_cmp(&-max_subnorm()));
1641 assert_eq!(Ordering::Greater, (-0.0_f64).total_cmp(&-min_subnorm()));
1642 assert_eq!(Ordering::Greater, 0.0_f64.total_cmp(&-0.0));
1643 assert_eq!(Ordering::Greater, min_subnorm().total_cmp(&0.0));
1644 assert_eq!(Ordering::Greater, max_subnorm().total_cmp(&min_subnorm()));
1645 assert_eq!(Ordering::Greater, f64::MIN_POSITIVE.total_cmp(&max_subnorm()));
1646 assert_eq!(Ordering::Greater, 0.5_f64.total_cmp(&f64::MIN_POSITIVE));
1647 assert_eq!(Ordering::Greater, 1.0_f64.total_cmp(&0.5));
1648 assert_eq!(Ordering::Greater, 1.5_f64.total_cmp(&1.0));
1649 assert_eq!(Ordering::Greater, 2.5_f64.total_cmp(&1.5));
1650 assert_eq!(Ordering::Greater, f64::MAX.total_cmp(&2.5));
1651 assert_eq!(Ordering::Greater, f64::INFINITY.total_cmp(&f64::MAX));
1652 assert_eq!(Ordering::Greater, s_nan().total_cmp(&f64::INFINITY));
1653 assert_eq!(Ordering::Greater, q_nan().total_cmp(&s_nan()));
1655 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-s_nan()));
1656 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::INFINITY));
1657 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::MAX));
1658 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-2.5));
1659 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-1.5));
1660 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-1.0));
1661 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-0.5));
1662 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-f64::MIN_POSITIVE));
1663 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-max_subnorm()));
1664 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-min_subnorm()));
1665 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&-0.0));
1666 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&0.0));
1667 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&min_subnorm()));
1668 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&max_subnorm()));
1669 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::MIN_POSITIVE));
1670 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&0.5));
1671 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&1.0));
1672 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&1.5));
1673 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&2.5));
1674 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::MAX));
1675 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&f64::INFINITY));
1676 assert_eq!(Ordering::Less, (-q_nan()).total_cmp(&s_nan()));
1678 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::INFINITY));
1679 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::MAX));
1680 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-2.5));
1681 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-1.5));
1682 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-1.0));
1683 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-0.5));
1684 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-f64::MIN_POSITIVE));
1685 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-max_subnorm()));
1686 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-min_subnorm()));
1687 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&-0.0));
1688 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&0.0));
1689 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&min_subnorm()));
1690 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&max_subnorm()));
1691 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::MIN_POSITIVE));
1692 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&0.5));
1693 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&1.0));
1694 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&1.5));
1695 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&2.5));
1696 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::MAX));
1697 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&f64::INFINITY));
1698 assert_eq!(Ordering::Less, (-s_nan()).total_cmp(&s_nan()));