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 #![stable(feature = "rust1", since = "1.0.0")]
9 #![allow(missing_docs)]
12 use crate::intrinsics;
14 use crate::sys::cmath;
16 #[stable(feature = "rust1", since = "1.0.0")]
17 pub use core::f64::consts;
18 #[stable(feature = "rust1", since = "1.0.0")]
19 pub use core::f64::{DIGITS, EPSILON, MANTISSA_DIGITS, RADIX};
20 #[stable(feature = "rust1", since = "1.0.0")]
21 pub use core::f64::{INFINITY, MAX_10_EXP, NAN, NEG_INFINITY};
22 #[stable(feature = "rust1", since = "1.0.0")]
23 pub use core::f64::{MAX, MIN, MIN_POSITIVE};
24 #[stable(feature = "rust1", since = "1.0.0")]
25 pub use core::f64::{MAX_EXP, MIN_10_EXP, MIN_EXP};
28 #[lang = "f64_runtime"]
30 /// Returns the largest integer less than or equal to a number.
39 /// assert_eq!(f.floor(), 3.0);
40 /// assert_eq!(g.floor(), 3.0);
41 /// assert_eq!(h.floor(), -4.0);
43 #[must_use = "method returns a new number and does not mutate the original value"]
44 #[stable(feature = "rust1", since = "1.0.0")]
46 pub fn floor(self) -> f64 {
47 unsafe { intrinsics::floorf64(self) }
50 /// Returns the smallest integer greater than or equal to a number.
58 /// assert_eq!(f.ceil(), 4.0);
59 /// assert_eq!(g.ceil(), 4.0);
61 #[must_use = "method returns a new number and does not mutate the original value"]
62 #[stable(feature = "rust1", since = "1.0.0")]
64 pub fn ceil(self) -> f64 {
65 unsafe { intrinsics::ceilf64(self) }
68 /// Returns the nearest integer to a number. Round half-way cases away from
77 /// assert_eq!(f.round(), 3.0);
78 /// assert_eq!(g.round(), -3.0);
80 #[must_use = "method returns a new number and does not mutate the original value"]
81 #[stable(feature = "rust1", since = "1.0.0")]
83 pub fn round(self) -> f64 {
84 unsafe { intrinsics::roundf64(self) }
87 /// Returns the integer part of a number.
96 /// assert_eq!(f.trunc(), 3.0);
97 /// assert_eq!(g.trunc(), 3.0);
98 /// assert_eq!(h.trunc(), -3.0);
100 #[must_use = "method returns a new number and does not mutate the original value"]
101 #[stable(feature = "rust1", since = "1.0.0")]
103 pub fn trunc(self) -> f64 {
104 unsafe { intrinsics::truncf64(self) }
107 /// Returns the fractional part of a number.
113 /// let y = -3.6_f64;
114 /// let abs_difference_x = (x.fract() - 0.6).abs();
115 /// let abs_difference_y = (y.fract() - (-0.6)).abs();
117 /// assert!(abs_difference_x < 1e-10);
118 /// assert!(abs_difference_y < 1e-10);
120 #[must_use = "method returns a new number and does not mutate the original value"]
121 #[stable(feature = "rust1", since = "1.0.0")]
123 pub fn fract(self) -> f64 {
127 /// Computes the absolute value of `self`. Returns `NAN` if the
136 /// let y = -3.5_f64;
138 /// let abs_difference_x = (x.abs() - x).abs();
139 /// let abs_difference_y = (y.abs() - (-y)).abs();
141 /// assert!(abs_difference_x < 1e-10);
142 /// assert!(abs_difference_y < 1e-10);
144 /// assert!(f64::NAN.abs().is_nan());
146 #[must_use = "method returns a new number and does not mutate the original value"]
147 #[stable(feature = "rust1", since = "1.0.0")]
149 pub fn abs(self) -> f64 {
150 unsafe { intrinsics::fabsf64(self) }
153 /// Returns a number that represents the sign of `self`.
155 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
156 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
157 /// - `NAN` if the number is `NAN`
166 /// assert_eq!(f.signum(), 1.0);
167 /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
169 /// assert!(f64::NAN.signum().is_nan());
171 #[must_use = "method returns a new number and does not mutate the original value"]
172 #[stable(feature = "rust1", since = "1.0.0")]
174 pub fn signum(self) -> f64 {
175 if self.is_nan() { NAN } else { 1.0_f64.copysign(self) }
178 /// Returns a number composed of the magnitude of `self` and the sign of
181 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
182 /// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of
183 /// `sign` is returned.
192 /// assert_eq!(f.copysign(0.42), 3.5_f64);
193 /// assert_eq!(f.copysign(-0.42), -3.5_f64);
194 /// assert_eq!((-f).copysign(0.42), 3.5_f64);
195 /// assert_eq!((-f).copysign(-0.42), -3.5_f64);
197 /// assert!(f64::NAN.copysign(1.0).is_nan());
199 #[must_use = "method returns a new number and does not mutate the original value"]
200 #[stable(feature = "copysign", since = "1.35.0")]
202 pub fn copysign(self, sign: f64) -> f64 {
203 unsafe { intrinsics::copysignf64(self, sign) }
206 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
207 /// error, yielding a more accurate result than an unfused multiply-add.
209 /// Using `mul_add` can be more performant than an unfused multiply-add if
210 /// the target architecture has a dedicated `fma` CPU instruction.
215 /// let m = 10.0_f64;
217 /// let b = 60.0_f64;
220 /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs();
222 /// assert!(abs_difference < 1e-10);
224 #[must_use = "method returns a new number and does not mutate the original value"]
225 #[stable(feature = "rust1", since = "1.0.0")]
227 pub fn mul_add(self, a: f64, b: f64) -> f64 {
228 unsafe { intrinsics::fmaf64(self, a, b) }
231 /// Calculates Euclidean division, the matching method for `rem_euclid`.
233 /// This computes the integer `n` such that
234 /// `self = n * rhs + self.rem_euclid(rhs)`.
235 /// In other words, the result is `self / rhs` rounded to the integer `n`
236 /// such that `self >= n * rhs`.
241 /// let a: f64 = 7.0;
243 /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
244 /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
245 /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
246 /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0
248 #[must_use = "method returns a new number and does not mutate the original value"]
250 #[stable(feature = "euclidean_division", since = "1.38.0")]
251 pub fn div_euclid(self, rhs: f64) -> f64 {
252 let q = (self / rhs).trunc();
253 if self % rhs < 0.0 {
254 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
259 /// Calculates the least nonnegative remainder of `self (mod rhs)`.
261 /// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
262 /// most cases. However, due to a floating point round-off error it can
263 /// result in `r == rhs.abs()`, violating the mathematical definition, if
264 /// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
265 /// This result is not an element of the function's codomain, but it is the
266 /// closest floating point number in the real numbers and thus fulfills the
267 /// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
273 /// let a: f64 = 7.0;
275 /// assert_eq!(a.rem_euclid(b), 3.0);
276 /// assert_eq!((-a).rem_euclid(b), 1.0);
277 /// assert_eq!(a.rem_euclid(-b), 3.0);
278 /// assert_eq!((-a).rem_euclid(-b), 1.0);
279 /// // limitation due to round-off error
280 /// assert!((-std::f64::EPSILON).rem_euclid(3.0) != 0.0);
282 #[must_use = "method returns a new number and does not mutate the original value"]
284 #[stable(feature = "euclidean_division", since = "1.38.0")]
285 pub fn rem_euclid(self, rhs: f64) -> f64 {
287 if r < 0.0 { r + rhs.abs() } else { r }
290 /// Raises a number to an integer power.
292 /// Using this function is generally faster than using `powf`
298 /// let abs_difference = (x.powi(2) - (x * x)).abs();
300 /// assert!(abs_difference < 1e-10);
302 #[must_use = "method returns a new number and does not mutate the original value"]
303 #[stable(feature = "rust1", since = "1.0.0")]
305 pub fn powi(self, n: i32) -> f64 {
306 unsafe { intrinsics::powif64(self, n) }
309 /// Raises a number to a floating point power.
315 /// let abs_difference = (x.powf(2.0) - (x * x)).abs();
317 /// assert!(abs_difference < 1e-10);
319 #[must_use = "method returns a new number and does not mutate the original value"]
320 #[stable(feature = "rust1", since = "1.0.0")]
322 pub fn powf(self, n: f64) -> f64 {
323 unsafe { intrinsics::powf64(self, n) }
326 /// Returns the square root of a number.
328 /// Returns NaN if `self` is a negative number.
333 /// let positive = 4.0_f64;
334 /// let negative = -4.0_f64;
336 /// let abs_difference = (positive.sqrt() - 2.0).abs();
338 /// assert!(abs_difference < 1e-10);
339 /// assert!(negative.sqrt().is_nan());
341 #[must_use = "method returns a new number and does not mutate the original value"]
342 #[stable(feature = "rust1", since = "1.0.0")]
344 pub fn sqrt(self) -> f64 {
345 unsafe { intrinsics::sqrtf64(self) }
348 /// Returns `e^(self)`, (the exponential function).
353 /// let one = 1.0_f64;
355 /// let e = one.exp();
357 /// // ln(e) - 1 == 0
358 /// let abs_difference = (e.ln() - 1.0).abs();
360 /// assert!(abs_difference < 1e-10);
362 #[must_use = "method returns a new number and does not mutate the original value"]
363 #[stable(feature = "rust1", since = "1.0.0")]
365 pub fn exp(self) -> f64 {
366 unsafe { intrinsics::expf64(self) }
369 /// Returns `2^(self)`.
377 /// let abs_difference = (f.exp2() - 4.0).abs();
379 /// assert!(abs_difference < 1e-10);
381 #[must_use = "method returns a new number and does not mutate the original value"]
382 #[stable(feature = "rust1", since = "1.0.0")]
384 pub fn exp2(self) -> f64 {
385 unsafe { intrinsics::exp2f64(self) }
388 /// Returns the natural logarithm of the number.
393 /// let one = 1.0_f64;
395 /// let e = one.exp();
397 /// // ln(e) - 1 == 0
398 /// let abs_difference = (e.ln() - 1.0).abs();
400 /// assert!(abs_difference < 1e-10);
402 #[must_use = "method returns a new number and does not mutate the original value"]
403 #[stable(feature = "rust1", since = "1.0.0")]
405 pub fn ln(self) -> f64 {
406 self.log_wrapper(|n| unsafe { intrinsics::logf64(n) })
409 /// Returns the logarithm of the number with respect to an arbitrary base.
411 /// The result may not be correctly rounded owing to implementation details;
412 /// `self.log2()` can produce more accurate results for base 2, and
413 /// `self.log10()` can produce more accurate results for base 10.
418 /// let twenty_five = 25.0_f64;
420 /// // log5(25) - 2 == 0
421 /// let abs_difference = (twenty_five.log(5.0) - 2.0).abs();
423 /// assert!(abs_difference < 1e-10);
425 #[must_use = "method returns a new number and does not mutate the original value"]
426 #[stable(feature = "rust1", since = "1.0.0")]
428 pub fn log(self, base: f64) -> f64 {
429 self.ln() / base.ln()
432 /// Returns the base 2 logarithm of the number.
437 /// let four = 4.0_f64;
439 /// // log2(4) - 2 == 0
440 /// let abs_difference = (four.log2() - 2.0).abs();
442 /// assert!(abs_difference < 1e-10);
444 #[must_use = "method returns a new number and does not mutate the original value"]
445 #[stable(feature = "rust1", since = "1.0.0")]
447 pub fn log2(self) -> f64 {
448 self.log_wrapper(|n| {
449 #[cfg(target_os = "android")]
450 return crate::sys::android::log2f64(n);
451 #[cfg(not(target_os = "android"))]
452 return unsafe { intrinsics::log2f64(n) };
456 /// Returns the base 10 logarithm of the number.
461 /// let hundred = 100.0_f64;
463 /// // log10(100) - 2 == 0
464 /// let abs_difference = (hundred.log10() - 2.0).abs();
466 /// assert!(abs_difference < 1e-10);
468 #[must_use = "method returns a new number and does not mutate the original value"]
469 #[stable(feature = "rust1", since = "1.0.0")]
471 pub fn log10(self) -> f64 {
472 self.log_wrapper(|n| unsafe { intrinsics::log10f64(n) })
475 /// The positive difference of two numbers.
477 /// * If `self <= other`: `0:0`
478 /// * Else: `self - other`
484 /// let y = -3.0_f64;
486 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
487 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
489 /// assert!(abs_difference_x < 1e-10);
490 /// assert!(abs_difference_y < 1e-10);
492 #[must_use = "method returns a new number and does not mutate the original value"]
493 #[stable(feature = "rust1", since = "1.0.0")]
497 reason = "you probably meant `(self - other).abs()`: \
498 this operation is `(self - other).max(0.0)` \
499 except that `abs_sub` also propagates NaNs (also \
500 known as `fdim` in C). If you truly need the positive \
501 difference, consider using that expression or the C function \
502 `fdim`, depending on how you wish to handle NaN (please consider \
503 filing an issue describing your use-case too)."
505 pub fn abs_sub(self, other: f64) -> f64 {
506 unsafe { cmath::fdim(self, other) }
509 /// Returns the cubic root of a number.
516 /// // x^(1/3) - 2 == 0
517 /// let abs_difference = (x.cbrt() - 2.0).abs();
519 /// assert!(abs_difference < 1e-10);
521 #[must_use = "method returns a new number and does not mutate the original value"]
522 #[stable(feature = "rust1", since = "1.0.0")]
524 pub fn cbrt(self) -> f64 {
525 unsafe { cmath::cbrt(self) }
528 /// Calculates the length of the hypotenuse of a right-angle triangle given
529 /// legs of length `x` and `y`.
537 /// // sqrt(x^2 + y^2)
538 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
540 /// assert!(abs_difference < 1e-10);
542 #[must_use = "method returns a new number and does not mutate the original value"]
543 #[stable(feature = "rust1", since = "1.0.0")]
545 pub fn hypot(self, other: f64) -> f64 {
546 unsafe { cmath::hypot(self, other) }
549 /// Computes the sine of a number (in radians).
556 /// let x = f64::consts::FRAC_PI_2;
558 /// let abs_difference = (x.sin() - 1.0).abs();
560 /// assert!(abs_difference < 1e-10);
562 #[must_use = "method returns a new number and does not mutate the original value"]
563 #[stable(feature = "rust1", since = "1.0.0")]
565 pub fn sin(self) -> f64 {
566 unsafe { intrinsics::sinf64(self) }
569 /// Computes the cosine of a number (in radians).
576 /// let x = 2.0 * f64::consts::PI;
578 /// let abs_difference = (x.cos() - 1.0).abs();
580 /// assert!(abs_difference < 1e-10);
582 #[must_use = "method returns a new number and does not mutate the original value"]
583 #[stable(feature = "rust1", since = "1.0.0")]
585 pub fn cos(self) -> f64 {
586 unsafe { intrinsics::cosf64(self) }
589 /// Computes the tangent of a number (in radians).
596 /// let x = f64::consts::FRAC_PI_4;
597 /// let abs_difference = (x.tan() - 1.0).abs();
599 /// assert!(abs_difference < 1e-14);
601 #[must_use = "method returns a new number and does not mutate the original value"]
602 #[stable(feature = "rust1", since = "1.0.0")]
604 pub fn tan(self) -> f64 {
605 unsafe { cmath::tan(self) }
608 /// Computes the arcsine of a number. Return value is in radians in
609 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
617 /// let f = f64::consts::FRAC_PI_2;
619 /// // asin(sin(pi/2))
620 /// let abs_difference = (f.sin().asin() - f64::consts::FRAC_PI_2).abs();
622 /// assert!(abs_difference < 1e-10);
624 #[must_use = "method returns a new number and does not mutate the original value"]
625 #[stable(feature = "rust1", since = "1.0.0")]
627 pub fn asin(self) -> f64 {
628 unsafe { cmath::asin(self) }
631 /// Computes the arccosine of a number. Return value is in radians in
632 /// the range [0, pi] or NaN if the number is outside the range
640 /// let f = f64::consts::FRAC_PI_4;
642 /// // acos(cos(pi/4))
643 /// let abs_difference = (f.cos().acos() - f64::consts::FRAC_PI_4).abs();
645 /// assert!(abs_difference < 1e-10);
647 #[must_use = "method returns a new number and does not mutate the original value"]
648 #[stable(feature = "rust1", since = "1.0.0")]
650 pub fn acos(self) -> f64 {
651 unsafe { cmath::acos(self) }
654 /// Computes the arctangent of a number. Return value is in radians in the
655 /// range [-pi/2, pi/2];
663 /// let abs_difference = (f.tan().atan() - 1.0).abs();
665 /// assert!(abs_difference < 1e-10);
667 #[must_use = "method returns a new number and does not mutate the original value"]
668 #[stable(feature = "rust1", since = "1.0.0")]
670 pub fn atan(self) -> f64 {
671 unsafe { cmath::atan(self) }
674 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
676 /// * `x = 0`, `y = 0`: `0`
677 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
678 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
679 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
686 /// // Positive angles measured counter-clockwise
687 /// // from positive x axis
688 /// // -pi/4 radians (45 deg clockwise)
689 /// let x1 = 3.0_f64;
690 /// let y1 = -3.0_f64;
692 /// // 3pi/4 radians (135 deg counter-clockwise)
693 /// let x2 = -3.0_f64;
694 /// let y2 = 3.0_f64;
696 /// let abs_difference_1 = (y1.atan2(x1) - (-f64::consts::FRAC_PI_4)).abs();
697 /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * f64::consts::FRAC_PI_4)).abs();
699 /// assert!(abs_difference_1 < 1e-10);
700 /// assert!(abs_difference_2 < 1e-10);
702 #[must_use = "method returns a new number and does not mutate the original value"]
703 #[stable(feature = "rust1", since = "1.0.0")]
705 pub fn atan2(self, other: f64) -> f64 {
706 unsafe { cmath::atan2(self, other) }
709 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
710 /// `(sin(x), cos(x))`.
717 /// let x = f64::consts::FRAC_PI_4;
718 /// let f = x.sin_cos();
720 /// let abs_difference_0 = (f.0 - x.sin()).abs();
721 /// let abs_difference_1 = (f.1 - x.cos()).abs();
723 /// assert!(abs_difference_0 < 1e-10);
724 /// assert!(abs_difference_1 < 1e-10);
726 #[stable(feature = "rust1", since = "1.0.0")]
728 pub fn sin_cos(self) -> (f64, f64) {
729 (self.sin(), self.cos())
732 /// Returns `e^(self) - 1` in a way that is accurate even if the
733 /// number is close to zero.
741 /// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
743 /// assert!(abs_difference < 1e-10);
745 #[must_use = "method returns a new number and does not mutate the original value"]
746 #[stable(feature = "rust1", since = "1.0.0")]
748 pub fn exp_m1(self) -> f64 {
749 unsafe { cmath::expm1(self) }
752 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
753 /// the operations were performed separately.
760 /// let x = f64::consts::E - 1.0;
762 /// // ln(1 + (e - 1)) == ln(e) == 1
763 /// let abs_difference = (x.ln_1p() - 1.0).abs();
765 /// assert!(abs_difference < 1e-10);
767 #[must_use = "method returns a new number and does not mutate the original value"]
768 #[stable(feature = "rust1", since = "1.0.0")]
770 pub fn ln_1p(self) -> f64 {
771 unsafe { cmath::log1p(self) }
774 /// Hyperbolic sine function.
781 /// let e = f64::consts::E;
784 /// let f = x.sinh();
785 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
786 /// let g = ((e * e) - 1.0) / (2.0 * e);
787 /// let abs_difference = (f - g).abs();
789 /// assert!(abs_difference < 1e-10);
791 #[must_use = "method returns a new number and does not mutate the original value"]
792 #[stable(feature = "rust1", since = "1.0.0")]
794 pub fn sinh(self) -> f64 {
795 unsafe { cmath::sinh(self) }
798 /// Hyperbolic cosine function.
805 /// let e = f64::consts::E;
807 /// let f = x.cosh();
808 /// // Solving cosh() at 1 gives this result
809 /// let g = ((e * e) + 1.0) / (2.0 * e);
810 /// let abs_difference = (f - g).abs();
813 /// assert!(abs_difference < 1.0e-10);
815 #[must_use = "method returns a new number and does not mutate the original value"]
816 #[stable(feature = "rust1", since = "1.0.0")]
818 pub fn cosh(self) -> f64 {
819 unsafe { cmath::cosh(self) }
822 /// Hyperbolic tangent function.
829 /// let e = f64::consts::E;
832 /// let f = x.tanh();
833 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
834 /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
835 /// let abs_difference = (f - g).abs();
837 /// assert!(abs_difference < 1.0e-10);
839 #[must_use = "method returns a new number and does not mutate the original value"]
840 #[stable(feature = "rust1", since = "1.0.0")]
842 pub fn tanh(self) -> f64 {
843 unsafe { cmath::tanh(self) }
846 /// Inverse hyperbolic sine function.
852 /// let f = x.sinh().asinh();
854 /// let abs_difference = (f - x).abs();
856 /// assert!(abs_difference < 1.0e-10);
858 #[must_use = "method returns a new number and does not mutate the original value"]
859 #[stable(feature = "rust1", since = "1.0.0")]
861 pub fn asinh(self) -> f64 {
862 if self == NEG_INFINITY {
865 (self + ((self * self) + 1.0).sqrt()).ln().copysign(self)
869 /// Inverse hyperbolic cosine function.
875 /// let f = x.cosh().acosh();
877 /// let abs_difference = (f - x).abs();
879 /// assert!(abs_difference < 1.0e-10);
881 #[must_use = "method returns a new number and does not mutate the original value"]
882 #[stable(feature = "rust1", since = "1.0.0")]
884 pub fn acosh(self) -> f64 {
885 if self < 1.0 { NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() }
888 /// Inverse hyperbolic tangent function.
895 /// let e = f64::consts::E;
896 /// let f = e.tanh().atanh();
898 /// let abs_difference = (f - e).abs();
900 /// assert!(abs_difference < 1.0e-10);
902 #[must_use = "method returns a new number and does not mutate the original value"]
903 #[stable(feature = "rust1", since = "1.0.0")]
905 pub fn atanh(self) -> f64 {
906 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
909 /// Restrict a value to a certain interval unless it is NaN.
911 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
912 /// less than `min`. Otherwise this returns `self`.
914 /// Not that this function returns NaN if the initial value was NaN as
919 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
924 /// #![feature(clamp)]
925 /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
926 /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
927 /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
928 /// assert!((std::f64::NAN).clamp(-2.0, 1.0).is_nan());
930 #[must_use = "method returns a new number and does not mutate the original value"]
931 #[unstable(feature = "clamp", issue = "44095")]
933 pub fn clamp(self, min: f64, max: f64) -> f64 {
945 // Solaris/Illumos requires a wrapper around log, log2, and log10 functions
946 // because of their non-standard behavior (e.g., log(-n) returns -Inf instead
948 fn log_wrapper<F: Fn(f64) -> f64>(self, log_fn: F) -> f64 {
949 if !cfg!(target_os = "solaris") {
952 if self.is_finite() {
955 } else if self == 0.0 {
956 NEG_INFINITY // log(0) = -Inf
960 } else if self.is_nan() {
961 self // log(NaN) = NaN
962 } else if self > 0.0 {
963 self // log(Inf) = Inf
965 NAN // log(-Inf) = NaN
975 use crate::num::FpCategory as Fp;
980 test_num(10f64, 2f64);
985 assert_eq!(NAN.min(2.0), 2.0);
986 assert_eq!(2.0f64.min(NAN), 2.0);
991 assert_eq!(NAN.max(2.0), 2.0);
992 assert_eq!(2.0f64.max(NAN), 2.0);
998 assert!(nan.is_nan());
999 assert!(!nan.is_infinite());
1000 assert!(!nan.is_finite());
1001 assert!(!nan.is_normal());
1002 assert!(nan.is_sign_positive());
1003 assert!(!nan.is_sign_negative());
1004 assert_eq!(Fp::Nan, nan.classify());
1008 fn test_infinity() {
1009 let inf: f64 = INFINITY;
1010 assert!(inf.is_infinite());
1011 assert!(!inf.is_finite());
1012 assert!(inf.is_sign_positive());
1013 assert!(!inf.is_sign_negative());
1014 assert!(!inf.is_nan());
1015 assert!(!inf.is_normal());
1016 assert_eq!(Fp::Infinite, inf.classify());
1020 fn test_neg_infinity() {
1021 let neg_inf: f64 = NEG_INFINITY;
1022 assert!(neg_inf.is_infinite());
1023 assert!(!neg_inf.is_finite());
1024 assert!(!neg_inf.is_sign_positive());
1025 assert!(neg_inf.is_sign_negative());
1026 assert!(!neg_inf.is_nan());
1027 assert!(!neg_inf.is_normal());
1028 assert_eq!(Fp::Infinite, neg_inf.classify());
1033 let zero: f64 = 0.0f64;
1034 assert_eq!(0.0, zero);
1035 assert!(!zero.is_infinite());
1036 assert!(zero.is_finite());
1037 assert!(zero.is_sign_positive());
1038 assert!(!zero.is_sign_negative());
1039 assert!(!zero.is_nan());
1040 assert!(!zero.is_normal());
1041 assert_eq!(Fp::Zero, zero.classify());
1045 fn test_neg_zero() {
1046 let neg_zero: f64 = -0.0;
1047 assert_eq!(0.0, neg_zero);
1048 assert!(!neg_zero.is_infinite());
1049 assert!(neg_zero.is_finite());
1050 assert!(!neg_zero.is_sign_positive());
1051 assert!(neg_zero.is_sign_negative());
1052 assert!(!neg_zero.is_nan());
1053 assert!(!neg_zero.is_normal());
1054 assert_eq!(Fp::Zero, neg_zero.classify());
1057 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1060 let one: f64 = 1.0f64;
1061 assert_eq!(1.0, one);
1062 assert!(!one.is_infinite());
1063 assert!(one.is_finite());
1064 assert!(one.is_sign_positive());
1065 assert!(!one.is_sign_negative());
1066 assert!(!one.is_nan());
1067 assert!(one.is_normal());
1068 assert_eq!(Fp::Normal, one.classify());
1074 let inf: f64 = INFINITY;
1075 let neg_inf: f64 = NEG_INFINITY;
1076 assert!(nan.is_nan());
1077 assert!(!0.0f64.is_nan());
1078 assert!(!5.3f64.is_nan());
1079 assert!(!(-10.732f64).is_nan());
1080 assert!(!inf.is_nan());
1081 assert!(!neg_inf.is_nan());
1085 fn test_is_infinite() {
1087 let inf: f64 = INFINITY;
1088 let neg_inf: f64 = NEG_INFINITY;
1089 assert!(!nan.is_infinite());
1090 assert!(inf.is_infinite());
1091 assert!(neg_inf.is_infinite());
1092 assert!(!0.0f64.is_infinite());
1093 assert!(!42.8f64.is_infinite());
1094 assert!(!(-109.2f64).is_infinite());
1098 fn test_is_finite() {
1100 let inf: f64 = INFINITY;
1101 let neg_inf: f64 = NEG_INFINITY;
1102 assert!(!nan.is_finite());
1103 assert!(!inf.is_finite());
1104 assert!(!neg_inf.is_finite());
1105 assert!(0.0f64.is_finite());
1106 assert!(42.8f64.is_finite());
1107 assert!((-109.2f64).is_finite());
1110 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1112 fn test_is_normal() {
1114 let inf: f64 = INFINITY;
1115 let neg_inf: f64 = NEG_INFINITY;
1116 let zero: f64 = 0.0f64;
1117 let neg_zero: f64 = -0.0;
1118 assert!(!nan.is_normal());
1119 assert!(!inf.is_normal());
1120 assert!(!neg_inf.is_normal());
1121 assert!(!zero.is_normal());
1122 assert!(!neg_zero.is_normal());
1123 assert!(1f64.is_normal());
1124 assert!(1e-307f64.is_normal());
1125 assert!(!1e-308f64.is_normal());
1128 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1130 fn test_classify() {
1132 let inf: f64 = INFINITY;
1133 let neg_inf: f64 = NEG_INFINITY;
1134 let zero: f64 = 0.0f64;
1135 let neg_zero: f64 = -0.0;
1136 assert_eq!(nan.classify(), Fp::Nan);
1137 assert_eq!(inf.classify(), Fp::Infinite);
1138 assert_eq!(neg_inf.classify(), Fp::Infinite);
1139 assert_eq!(zero.classify(), Fp::Zero);
1140 assert_eq!(neg_zero.classify(), Fp::Zero);
1141 assert_eq!(1e-307f64.classify(), Fp::Normal);
1142 assert_eq!(1e-308f64.classify(), Fp::Subnormal);
1147 assert_approx_eq!(1.0f64.floor(), 1.0f64);
1148 assert_approx_eq!(1.3f64.floor(), 1.0f64);
1149 assert_approx_eq!(1.5f64.floor(), 1.0f64);
1150 assert_approx_eq!(1.7f64.floor(), 1.0f64);
1151 assert_approx_eq!(0.0f64.floor(), 0.0f64);
1152 assert_approx_eq!((-0.0f64).floor(), -0.0f64);
1153 assert_approx_eq!((-1.0f64).floor(), -1.0f64);
1154 assert_approx_eq!((-1.3f64).floor(), -2.0f64);
1155 assert_approx_eq!((-1.5f64).floor(), -2.0f64);
1156 assert_approx_eq!((-1.7f64).floor(), -2.0f64);
1161 assert_approx_eq!(1.0f64.ceil(), 1.0f64);
1162 assert_approx_eq!(1.3f64.ceil(), 2.0f64);
1163 assert_approx_eq!(1.5f64.ceil(), 2.0f64);
1164 assert_approx_eq!(1.7f64.ceil(), 2.0f64);
1165 assert_approx_eq!(0.0f64.ceil(), 0.0f64);
1166 assert_approx_eq!((-0.0f64).ceil(), -0.0f64);
1167 assert_approx_eq!((-1.0f64).ceil(), -1.0f64);
1168 assert_approx_eq!((-1.3f64).ceil(), -1.0f64);
1169 assert_approx_eq!((-1.5f64).ceil(), -1.0f64);
1170 assert_approx_eq!((-1.7f64).ceil(), -1.0f64);
1175 assert_approx_eq!(1.0f64.round(), 1.0f64);
1176 assert_approx_eq!(1.3f64.round(), 1.0f64);
1177 assert_approx_eq!(1.5f64.round(), 2.0f64);
1178 assert_approx_eq!(1.7f64.round(), 2.0f64);
1179 assert_approx_eq!(0.0f64.round(), 0.0f64);
1180 assert_approx_eq!((-0.0f64).round(), -0.0f64);
1181 assert_approx_eq!((-1.0f64).round(), -1.0f64);
1182 assert_approx_eq!((-1.3f64).round(), -1.0f64);
1183 assert_approx_eq!((-1.5f64).round(), -2.0f64);
1184 assert_approx_eq!((-1.7f64).round(), -2.0f64);
1189 assert_approx_eq!(1.0f64.trunc(), 1.0f64);
1190 assert_approx_eq!(1.3f64.trunc(), 1.0f64);
1191 assert_approx_eq!(1.5f64.trunc(), 1.0f64);
1192 assert_approx_eq!(1.7f64.trunc(), 1.0f64);
1193 assert_approx_eq!(0.0f64.trunc(), 0.0f64);
1194 assert_approx_eq!((-0.0f64).trunc(), -0.0f64);
1195 assert_approx_eq!((-1.0f64).trunc(), -1.0f64);
1196 assert_approx_eq!((-1.3f64).trunc(), -1.0f64);
1197 assert_approx_eq!((-1.5f64).trunc(), -1.0f64);
1198 assert_approx_eq!((-1.7f64).trunc(), -1.0f64);
1203 assert_approx_eq!(1.0f64.fract(), 0.0f64);
1204 assert_approx_eq!(1.3f64.fract(), 0.3f64);
1205 assert_approx_eq!(1.5f64.fract(), 0.5f64);
1206 assert_approx_eq!(1.7f64.fract(), 0.7f64);
1207 assert_approx_eq!(0.0f64.fract(), 0.0f64);
1208 assert_approx_eq!((-0.0f64).fract(), -0.0f64);
1209 assert_approx_eq!((-1.0f64).fract(), -0.0f64);
1210 assert_approx_eq!((-1.3f64).fract(), -0.3f64);
1211 assert_approx_eq!((-1.5f64).fract(), -0.5f64);
1212 assert_approx_eq!((-1.7f64).fract(), -0.7f64);
1217 assert_eq!(INFINITY.abs(), INFINITY);
1218 assert_eq!(1f64.abs(), 1f64);
1219 assert_eq!(0f64.abs(), 0f64);
1220 assert_eq!((-0f64).abs(), 0f64);
1221 assert_eq!((-1f64).abs(), 1f64);
1222 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1223 assert_eq!((1f64 / NEG_INFINITY).abs(), 0f64);
1224 assert!(NAN.abs().is_nan());
1229 assert_eq!(INFINITY.signum(), 1f64);
1230 assert_eq!(1f64.signum(), 1f64);
1231 assert_eq!(0f64.signum(), 1f64);
1232 assert_eq!((-0f64).signum(), -1f64);
1233 assert_eq!((-1f64).signum(), -1f64);
1234 assert_eq!(NEG_INFINITY.signum(), -1f64);
1235 assert_eq!((1f64 / NEG_INFINITY).signum(), -1f64);
1236 assert!(NAN.signum().is_nan());
1240 fn test_is_sign_positive() {
1241 assert!(INFINITY.is_sign_positive());
1242 assert!(1f64.is_sign_positive());
1243 assert!(0f64.is_sign_positive());
1244 assert!(!(-0f64).is_sign_positive());
1245 assert!(!(-1f64).is_sign_positive());
1246 assert!(!NEG_INFINITY.is_sign_positive());
1247 assert!(!(1f64 / NEG_INFINITY).is_sign_positive());
1248 assert!(NAN.is_sign_positive());
1249 assert!(!(-NAN).is_sign_positive());
1253 fn test_is_sign_negative() {
1254 assert!(!INFINITY.is_sign_negative());
1255 assert!(!1f64.is_sign_negative());
1256 assert!(!0f64.is_sign_negative());
1257 assert!((-0f64).is_sign_negative());
1258 assert!((-1f64).is_sign_negative());
1259 assert!(NEG_INFINITY.is_sign_negative());
1260 assert!((1f64 / NEG_INFINITY).is_sign_negative());
1261 assert!(!NAN.is_sign_negative());
1262 assert!((-NAN).is_sign_negative());
1268 let inf: f64 = INFINITY;
1269 let neg_inf: f64 = NEG_INFINITY;
1270 assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05);
1271 assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65);
1272 assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2);
1273 assert_approx_eq!(3.4f64.mul_add(-0.0, 5.6), 5.6);
1274 assert!(nan.mul_add(7.8, 9.0).is_nan());
1275 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1276 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1277 assert_eq!(8.9f64.mul_add(inf, 3.2), inf);
1278 assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf);
1284 let inf: f64 = INFINITY;
1285 let neg_inf: f64 = NEG_INFINITY;
1286 assert_eq!(1.0f64.recip(), 1.0);
1287 assert_eq!(2.0f64.recip(), 0.5);
1288 assert_eq!((-0.4f64).recip(), -2.5);
1289 assert_eq!(0.0f64.recip(), inf);
1290 assert!(nan.recip().is_nan());
1291 assert_eq!(inf.recip(), 0.0);
1292 assert_eq!(neg_inf.recip(), 0.0);
1298 let inf: f64 = INFINITY;
1299 let neg_inf: f64 = NEG_INFINITY;
1300 assert_eq!(1.0f64.powi(1), 1.0);
1301 assert_approx_eq!((-3.1f64).powi(2), 9.61);
1302 assert_approx_eq!(5.9f64.powi(-2), 0.028727);
1303 assert_eq!(8.3f64.powi(0), 1.0);
1304 assert!(nan.powi(2).is_nan());
1305 assert_eq!(inf.powi(3), inf);
1306 assert_eq!(neg_inf.powi(2), inf);
1312 let inf: f64 = INFINITY;
1313 let neg_inf: f64 = NEG_INFINITY;
1314 assert_eq!(1.0f64.powf(1.0), 1.0);
1315 assert_approx_eq!(3.4f64.powf(4.5), 246.408183);
1316 assert_approx_eq!(2.7f64.powf(-3.2), 0.041652);
1317 assert_approx_eq!((-3.1f64).powf(2.0), 9.61);
1318 assert_approx_eq!(5.9f64.powf(-2.0), 0.028727);
1319 assert_eq!(8.3f64.powf(0.0), 1.0);
1320 assert!(nan.powf(2.0).is_nan());
1321 assert_eq!(inf.powf(2.0), inf);
1322 assert_eq!(neg_inf.powf(3.0), neg_inf);
1326 fn test_sqrt_domain() {
1327 assert!(NAN.sqrt().is_nan());
1328 assert!(NEG_INFINITY.sqrt().is_nan());
1329 assert!((-1.0f64).sqrt().is_nan());
1330 assert_eq!((-0.0f64).sqrt(), -0.0);
1331 assert_eq!(0.0f64.sqrt(), 0.0);
1332 assert_eq!(1.0f64.sqrt(), 1.0);
1333 assert_eq!(INFINITY.sqrt(), INFINITY);
1338 assert_eq!(1.0, 0.0f64.exp());
1339 assert_approx_eq!(2.718282, 1.0f64.exp());
1340 assert_approx_eq!(148.413159, 5.0f64.exp());
1342 let inf: f64 = INFINITY;
1343 let neg_inf: f64 = NEG_INFINITY;
1345 assert_eq!(inf, inf.exp());
1346 assert_eq!(0.0, neg_inf.exp());
1347 assert!(nan.exp().is_nan());
1352 assert_eq!(32.0, 5.0f64.exp2());
1353 assert_eq!(1.0, 0.0f64.exp2());
1355 let inf: f64 = INFINITY;
1356 let neg_inf: f64 = NEG_INFINITY;
1358 assert_eq!(inf, inf.exp2());
1359 assert_eq!(0.0, neg_inf.exp2());
1360 assert!(nan.exp2().is_nan());
1366 let inf: f64 = INFINITY;
1367 let neg_inf: f64 = NEG_INFINITY;
1368 assert_approx_eq!(1.0f64.exp().ln(), 1.0);
1369 assert!(nan.ln().is_nan());
1370 assert_eq!(inf.ln(), inf);
1371 assert!(neg_inf.ln().is_nan());
1372 assert!((-2.3f64).ln().is_nan());
1373 assert_eq!((-0.0f64).ln(), neg_inf);
1374 assert_eq!(0.0f64.ln(), neg_inf);
1375 assert_approx_eq!(4.0f64.ln(), 1.386294);
1381 let inf: f64 = INFINITY;
1382 let neg_inf: f64 = NEG_INFINITY;
1383 assert_eq!(10.0f64.log(10.0), 1.0);
1384 assert_approx_eq!(2.3f64.log(3.5), 0.664858);
1385 assert_eq!(1.0f64.exp().log(1.0f64.exp()), 1.0);
1386 assert!(1.0f64.log(1.0).is_nan());
1387 assert!(1.0f64.log(-13.9).is_nan());
1388 assert!(nan.log(2.3).is_nan());
1389 assert_eq!(inf.log(10.0), inf);
1390 assert!(neg_inf.log(8.8).is_nan());
1391 assert!((-2.3f64).log(0.1).is_nan());
1392 assert_eq!((-0.0f64).log(2.0), neg_inf);
1393 assert_eq!(0.0f64.log(7.0), neg_inf);
1399 let inf: f64 = INFINITY;
1400 let neg_inf: f64 = NEG_INFINITY;
1401 assert_approx_eq!(10.0f64.log2(), 3.321928);
1402 assert_approx_eq!(2.3f64.log2(), 1.201634);
1403 assert_approx_eq!(1.0f64.exp().log2(), 1.442695);
1404 assert!(nan.log2().is_nan());
1405 assert_eq!(inf.log2(), inf);
1406 assert!(neg_inf.log2().is_nan());
1407 assert!((-2.3f64).log2().is_nan());
1408 assert_eq!((-0.0f64).log2(), neg_inf);
1409 assert_eq!(0.0f64.log2(), neg_inf);
1415 let inf: f64 = INFINITY;
1416 let neg_inf: f64 = NEG_INFINITY;
1417 assert_eq!(10.0f64.log10(), 1.0);
1418 assert_approx_eq!(2.3f64.log10(), 0.361728);
1419 assert_approx_eq!(1.0f64.exp().log10(), 0.434294);
1420 assert_eq!(1.0f64.log10(), 0.0);
1421 assert!(nan.log10().is_nan());
1422 assert_eq!(inf.log10(), inf);
1423 assert!(neg_inf.log10().is_nan());
1424 assert!((-2.3f64).log10().is_nan());
1425 assert_eq!((-0.0f64).log10(), neg_inf);
1426 assert_eq!(0.0f64.log10(), neg_inf);
1430 fn test_to_degrees() {
1431 let pi: f64 = consts::PI;
1433 let inf: f64 = INFINITY;
1434 let neg_inf: f64 = NEG_INFINITY;
1435 assert_eq!(0.0f64.to_degrees(), 0.0);
1436 assert_approx_eq!((-5.8f64).to_degrees(), -332.315521);
1437 assert_eq!(pi.to_degrees(), 180.0);
1438 assert!(nan.to_degrees().is_nan());
1439 assert_eq!(inf.to_degrees(), inf);
1440 assert_eq!(neg_inf.to_degrees(), neg_inf);
1444 fn test_to_radians() {
1445 let pi: f64 = consts::PI;
1447 let inf: f64 = INFINITY;
1448 let neg_inf: f64 = NEG_INFINITY;
1449 assert_eq!(0.0f64.to_radians(), 0.0);
1450 assert_approx_eq!(154.6f64.to_radians(), 2.698279);
1451 assert_approx_eq!((-332.31f64).to_radians(), -5.799903);
1452 assert_eq!(180.0f64.to_radians(), pi);
1453 assert!(nan.to_radians().is_nan());
1454 assert_eq!(inf.to_radians(), inf);
1455 assert_eq!(neg_inf.to_radians(), neg_inf);
1460 assert_eq!(0.0f64.asinh(), 0.0f64);
1461 assert_eq!((-0.0f64).asinh(), -0.0f64);
1463 let inf: f64 = INFINITY;
1464 let neg_inf: f64 = NEG_INFINITY;
1466 assert_eq!(inf.asinh(), inf);
1467 assert_eq!(neg_inf.asinh(), neg_inf);
1468 assert!(nan.asinh().is_nan());
1469 assert!((-0.0f64).asinh().is_sign_negative());
1471 assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64);
1472 assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
1477 assert_eq!(1.0f64.acosh(), 0.0f64);
1478 assert!(0.999f64.acosh().is_nan());
1480 let inf: f64 = INFINITY;
1481 let neg_inf: f64 = NEG_INFINITY;
1483 assert_eq!(inf.acosh(), inf);
1484 assert!(neg_inf.acosh().is_nan());
1485 assert!(nan.acosh().is_nan());
1486 assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
1487 assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
1492 assert_eq!(0.0f64.atanh(), 0.0f64);
1493 assert_eq!((-0.0f64).atanh(), -0.0f64);
1495 let inf: f64 = INFINITY;
1496 let neg_inf: f64 = NEG_INFINITY;
1498 assert_eq!(1.0f64.atanh(), inf);
1499 assert_eq!((-1.0f64).atanh(), neg_inf);
1500 assert!(2f64.atanh().atanh().is_nan());
1501 assert!((-2f64).atanh().atanh().is_nan());
1502 assert!(inf.atanh().is_nan());
1503 assert!(neg_inf.atanh().is_nan());
1504 assert!(nan.atanh().is_nan());
1505 assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64);
1506 assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64);
1510 fn test_real_consts() {
1512 let pi: f64 = consts::PI;
1513 let frac_pi_2: f64 = consts::FRAC_PI_2;
1514 let frac_pi_3: f64 = consts::FRAC_PI_3;
1515 let frac_pi_4: f64 = consts::FRAC_PI_4;
1516 let frac_pi_6: f64 = consts::FRAC_PI_6;
1517 let frac_pi_8: f64 = consts::FRAC_PI_8;
1518 let frac_1_pi: f64 = consts::FRAC_1_PI;
1519 let frac_2_pi: f64 = consts::FRAC_2_PI;
1520 let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRT_PI;
1521 let sqrt2: f64 = consts::SQRT_2;
1522 let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT_2;
1523 let e: f64 = consts::E;
1524 let log2_e: f64 = consts::LOG2_E;
1525 let log10_e: f64 = consts::LOG10_E;
1526 let ln_2: f64 = consts::LN_2;
1527 let ln_10: f64 = consts::LN_10;
1529 assert_approx_eq!(frac_pi_2, pi / 2f64);
1530 assert_approx_eq!(frac_pi_3, pi / 3f64);
1531 assert_approx_eq!(frac_pi_4, pi / 4f64);
1532 assert_approx_eq!(frac_pi_6, pi / 6f64);
1533 assert_approx_eq!(frac_pi_8, pi / 8f64);
1534 assert_approx_eq!(frac_1_pi, 1f64 / pi);
1535 assert_approx_eq!(frac_2_pi, 2f64 / pi);
1536 assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt());
1537 assert_approx_eq!(sqrt2, 2f64.sqrt());
1538 assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt());
1539 assert_approx_eq!(log2_e, e.log2());
1540 assert_approx_eq!(log10_e, e.log10());
1541 assert_approx_eq!(ln_2, 2f64.ln());
1542 assert_approx_eq!(ln_10, 10f64.ln());
1546 fn test_float_bits_conv() {
1547 assert_eq!((1f64).to_bits(), 0x3ff0000000000000);
1548 assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
1549 assert_eq!((1337f64).to_bits(), 0x4094e40000000000);
1550 assert_eq!((-14.25f64).to_bits(), 0xc02c800000000000);
1551 assert_approx_eq!(f64::from_bits(0x3ff0000000000000), 1.0);
1552 assert_approx_eq!(f64::from_bits(0x4029000000000000), 12.5);
1553 assert_approx_eq!(f64::from_bits(0x4094e40000000000), 1337.0);
1554 assert_approx_eq!(f64::from_bits(0xc02c800000000000), -14.25);
1556 // Check that NaNs roundtrip their bits regardless of signalingness
1557 // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits
1558 let masked_nan1 = f64::NAN.to_bits() ^ 0x000A_AAAA_AAAA_AAAA;
1559 let masked_nan2 = f64::NAN.to_bits() ^ 0x0005_5555_5555_5555;
1560 assert!(f64::from_bits(masked_nan1).is_nan());
1561 assert!(f64::from_bits(masked_nan2).is_nan());
1563 assert_eq!(f64::from_bits(masked_nan1).to_bits(), masked_nan1);
1564 assert_eq!(f64::from_bits(masked_nan2).to_bits(), masked_nan2);
1569 fn test_clamp_min_greater_than_max() {
1570 let _ = 1.0f64.clamp(3.0, 1.0);
1575 fn test_clamp_min_is_nan() {
1576 let _ = 1.0f64.clamp(NAN, 1.0);
1581 fn test_clamp_max_is_nan() {
1582 let _ = 1.0f64.clamp(3.0, NAN);