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
139 /// let y = -3.5_f64;
141 /// let abs_difference_x = (x.abs() - x).abs();
142 /// let abs_difference_y = (y.abs() - (-y)).abs();
144 /// assert!(abs_difference_x < 1e-10);
145 /// assert!(abs_difference_y < 1e-10);
147 /// assert!(f64::NAN.abs().is_nan());
149 #[must_use = "method returns a new number and does not mutate the original value"]
150 #[stable(feature = "rust1", since = "1.0.0")]
152 pub fn abs(self) -> f64 {
153 unsafe { intrinsics::fabsf64(self) }
156 /// Returns a number that represents the sign of `self`.
158 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
159 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
160 /// - `NAN` if the number is `NAN`
169 /// assert_eq!(f.signum(), 1.0);
170 /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
172 /// assert!(f64::NAN.signum().is_nan());
174 #[must_use = "method returns a new number and does not mutate the original value"]
175 #[stable(feature = "rust1", since = "1.0.0")]
177 pub fn signum(self) -> f64 {
178 if self.is_nan() { NAN } else { 1.0_f64.copysign(self) }
181 /// Returns a number composed of the magnitude of `self` and the sign of
184 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
185 /// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of
186 /// `sign` is returned.
195 /// assert_eq!(f.copysign(0.42), 3.5_f64);
196 /// assert_eq!(f.copysign(-0.42), -3.5_f64);
197 /// assert_eq!((-f).copysign(0.42), 3.5_f64);
198 /// assert_eq!((-f).copysign(-0.42), -3.5_f64);
200 /// assert!(f64::NAN.copysign(1.0).is_nan());
202 #[must_use = "method returns a new number and does not mutate the original value"]
203 #[stable(feature = "copysign", since = "1.35.0")]
205 pub fn copysign(self, sign: f64) -> f64 {
206 unsafe { intrinsics::copysignf64(self, sign) }
209 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
210 /// error, yielding a more accurate result than an unfused multiply-add.
212 /// Using `mul_add` can be more performant than an unfused multiply-add if
213 /// the target architecture has a dedicated `fma` CPU instruction.
218 /// let m = 10.0_f64;
220 /// let b = 60.0_f64;
223 /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs();
225 /// assert!(abs_difference < 1e-10);
227 #[must_use = "method returns a new number and does not mutate the original value"]
228 #[stable(feature = "rust1", since = "1.0.0")]
230 pub fn mul_add(self, a: f64, b: f64) -> f64 {
231 unsafe { intrinsics::fmaf64(self, a, b) }
234 /// Calculates Euclidean division, the matching method for `rem_euclid`.
236 /// This computes the integer `n` such that
237 /// `self = n * rhs + self.rem_euclid(rhs)`.
238 /// In other words, the result is `self / rhs` rounded to the integer `n`
239 /// such that `self >= n * rhs`.
244 /// let a: f64 = 7.0;
246 /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
247 /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
248 /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
249 /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0
251 #[must_use = "method returns a new number and does not mutate the original value"]
253 #[stable(feature = "euclidean_division", since = "1.38.0")]
254 pub fn div_euclid(self, rhs: f64) -> f64 {
255 let q = (self / rhs).trunc();
256 if self % rhs < 0.0 {
257 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
262 /// Calculates the least nonnegative remainder of `self (mod rhs)`.
264 /// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
265 /// most cases. However, due to a floating point round-off error it can
266 /// result in `r == rhs.abs()`, violating the mathematical definition, if
267 /// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
268 /// This result is not an element of the function's codomain, but it is the
269 /// closest floating point number in the real numbers and thus fulfills the
270 /// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
276 /// let a: f64 = 7.0;
278 /// assert_eq!(a.rem_euclid(b), 3.0);
279 /// assert_eq!((-a).rem_euclid(b), 1.0);
280 /// assert_eq!(a.rem_euclid(-b), 3.0);
281 /// assert_eq!((-a).rem_euclid(-b), 1.0);
282 /// // limitation due to round-off error
283 /// assert!((-std::f64::EPSILON).rem_euclid(3.0) != 0.0);
285 #[must_use = "method returns a new number and does not mutate the original value"]
287 #[stable(feature = "euclidean_division", since = "1.38.0")]
288 pub fn rem_euclid(self, rhs: f64) -> f64 {
290 if r < 0.0 { r + rhs.abs() } else { r }
293 /// Raises a number to an integer power.
295 /// Using this function is generally faster than using `powf`
301 /// let abs_difference = (x.powi(2) - (x * x)).abs();
303 /// assert!(abs_difference < 1e-10);
305 #[must_use = "method returns a new number and does not mutate the original value"]
306 #[stable(feature = "rust1", since = "1.0.0")]
308 pub fn powi(self, n: i32) -> f64 {
309 unsafe { intrinsics::powif64(self, n) }
312 /// Raises a number to a floating point power.
318 /// let abs_difference = (x.powf(2.0) - (x * x)).abs();
320 /// assert!(abs_difference < 1e-10);
322 #[must_use = "method returns a new number and does not mutate the original value"]
323 #[stable(feature = "rust1", since = "1.0.0")]
325 pub fn powf(self, n: f64) -> f64 {
326 unsafe { intrinsics::powf64(self, n) }
329 /// Returns the square root of a number.
331 /// Returns NaN if `self` is a negative number.
336 /// let positive = 4.0_f64;
337 /// let negative = -4.0_f64;
339 /// let abs_difference = (positive.sqrt() - 2.0).abs();
341 /// assert!(abs_difference < 1e-10);
342 /// assert!(negative.sqrt().is_nan());
344 #[must_use = "method returns a new number and does not mutate the original value"]
345 #[stable(feature = "rust1", since = "1.0.0")]
347 pub fn sqrt(self) -> f64 {
348 unsafe { intrinsics::sqrtf64(self) }
351 /// Returns `e^(self)`, (the exponential function).
356 /// let one = 1.0_f64;
358 /// let e = one.exp();
360 /// // ln(e) - 1 == 0
361 /// let abs_difference = (e.ln() - 1.0).abs();
363 /// assert!(abs_difference < 1e-10);
365 #[must_use = "method returns a new number and does not mutate the original value"]
366 #[stable(feature = "rust1", since = "1.0.0")]
368 pub fn exp(self) -> f64 {
369 unsafe { intrinsics::expf64(self) }
372 /// Returns `2^(self)`.
380 /// let abs_difference = (f.exp2() - 4.0).abs();
382 /// assert!(abs_difference < 1e-10);
384 #[must_use = "method returns a new number and does not mutate the original value"]
385 #[stable(feature = "rust1", since = "1.0.0")]
387 pub fn exp2(self) -> f64 {
388 unsafe { intrinsics::exp2f64(self) }
391 /// Returns the natural logarithm of the number.
396 /// let one = 1.0_f64;
398 /// let e = one.exp();
400 /// // ln(e) - 1 == 0
401 /// let abs_difference = (e.ln() - 1.0).abs();
403 /// assert!(abs_difference < 1e-10);
405 #[must_use = "method returns a new number and does not mutate the original value"]
406 #[stable(feature = "rust1", since = "1.0.0")]
408 pub fn ln(self) -> f64 {
409 self.log_wrapper(|n| unsafe { intrinsics::logf64(n) })
412 /// Returns the logarithm of the number with respect to an arbitrary base.
414 /// The result may not be correctly rounded owing to implementation details;
415 /// `self.log2()` can produce more accurate results for base 2, and
416 /// `self.log10()` can produce more accurate results for base 10.
421 /// let twenty_five = 25.0_f64;
423 /// // log5(25) - 2 == 0
424 /// let abs_difference = (twenty_five.log(5.0) - 2.0).abs();
426 /// assert!(abs_difference < 1e-10);
428 #[must_use = "method returns a new number and does not mutate the original value"]
429 #[stable(feature = "rust1", since = "1.0.0")]
431 pub fn log(self, base: f64) -> f64 {
432 self.ln() / base.ln()
435 /// Returns the base 2 logarithm of the number.
440 /// let four = 4.0_f64;
442 /// // log2(4) - 2 == 0
443 /// let abs_difference = (four.log2() - 2.0).abs();
445 /// assert!(abs_difference < 1e-10);
447 #[must_use = "method returns a new number and does not mutate the original value"]
448 #[stable(feature = "rust1", since = "1.0.0")]
450 pub fn log2(self) -> f64 {
451 self.log_wrapper(|n| {
452 #[cfg(target_os = "android")]
453 return crate::sys::android::log2f64(n);
454 #[cfg(not(target_os = "android"))]
455 return unsafe { intrinsics::log2f64(n) };
459 /// Returns the base 10 logarithm of the number.
464 /// let hundred = 100.0_f64;
466 /// // log10(100) - 2 == 0
467 /// let abs_difference = (hundred.log10() - 2.0).abs();
469 /// assert!(abs_difference < 1e-10);
471 #[must_use = "method returns a new number and does not mutate the original value"]
472 #[stable(feature = "rust1", since = "1.0.0")]
474 pub fn log10(self) -> f64 {
475 self.log_wrapper(|n| unsafe { intrinsics::log10f64(n) })
478 /// The positive difference of two numbers.
480 /// * If `self <= other`: `0:0`
481 /// * Else: `self - other`
487 /// let y = -3.0_f64;
489 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
490 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
492 /// assert!(abs_difference_x < 1e-10);
493 /// assert!(abs_difference_y < 1e-10);
495 #[must_use = "method returns a new number and does not mutate the original value"]
496 #[stable(feature = "rust1", since = "1.0.0")]
500 reason = "you probably meant `(self - other).abs()`: \
501 this operation is `(self - other).max(0.0)` \
502 except that `abs_sub` also propagates NaNs (also \
503 known as `fdim` in C). If you truly need the positive \
504 difference, consider using that expression or the C function \
505 `fdim`, depending on how you wish to handle NaN (please consider \
506 filing an issue describing your use-case too)."
508 pub fn abs_sub(self, other: f64) -> f64 {
509 unsafe { cmath::fdim(self, other) }
512 /// Returns the cubic root of a number.
519 /// // x^(1/3) - 2 == 0
520 /// let abs_difference = (x.cbrt() - 2.0).abs();
522 /// assert!(abs_difference < 1e-10);
524 #[must_use = "method returns a new number and does not mutate the original value"]
525 #[stable(feature = "rust1", since = "1.0.0")]
527 pub fn cbrt(self) -> f64 {
528 unsafe { cmath::cbrt(self) }
531 /// Calculates the length of the hypotenuse of a right-angle triangle given
532 /// legs of length `x` and `y`.
540 /// // sqrt(x^2 + y^2)
541 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
543 /// assert!(abs_difference < 1e-10);
545 #[must_use = "method returns a new number and does not mutate the original value"]
546 #[stable(feature = "rust1", since = "1.0.0")]
548 pub fn hypot(self, other: f64) -> f64 {
549 unsafe { cmath::hypot(self, other) }
552 /// Computes the sine of a number (in radians).
559 /// let x = f64::consts::FRAC_PI_2;
561 /// let abs_difference = (x.sin() - 1.0).abs();
563 /// assert!(abs_difference < 1e-10);
565 #[must_use = "method returns a new number and does not mutate the original value"]
566 #[stable(feature = "rust1", since = "1.0.0")]
568 pub fn sin(self) -> f64 {
569 unsafe { intrinsics::sinf64(self) }
572 /// Computes the cosine of a number (in radians).
579 /// let x = 2.0 * f64::consts::PI;
581 /// let abs_difference = (x.cos() - 1.0).abs();
583 /// assert!(abs_difference < 1e-10);
585 #[must_use = "method returns a new number and does not mutate the original value"]
586 #[stable(feature = "rust1", since = "1.0.0")]
588 pub fn cos(self) -> f64 {
589 unsafe { intrinsics::cosf64(self) }
592 /// Computes the tangent of a number (in radians).
599 /// let x = f64::consts::FRAC_PI_4;
600 /// let abs_difference = (x.tan() - 1.0).abs();
602 /// assert!(abs_difference < 1e-14);
604 #[must_use = "method returns a new number and does not mutate the original value"]
605 #[stable(feature = "rust1", since = "1.0.0")]
607 pub fn tan(self) -> f64 {
608 unsafe { cmath::tan(self) }
611 /// Computes the arcsine of a number. Return value is in radians in
612 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
620 /// let f = f64::consts::FRAC_PI_2;
622 /// // asin(sin(pi/2))
623 /// let abs_difference = (f.sin().asin() - f64::consts::FRAC_PI_2).abs();
625 /// assert!(abs_difference < 1e-10);
627 #[must_use = "method returns a new number and does not mutate the original value"]
628 #[stable(feature = "rust1", since = "1.0.0")]
630 pub fn asin(self) -> f64 {
631 unsafe { cmath::asin(self) }
634 /// Computes the arccosine of a number. Return value is in radians in
635 /// the range [0, pi] or NaN if the number is outside the range
643 /// let f = f64::consts::FRAC_PI_4;
645 /// // acos(cos(pi/4))
646 /// let abs_difference = (f.cos().acos() - f64::consts::FRAC_PI_4).abs();
648 /// assert!(abs_difference < 1e-10);
650 #[must_use = "method returns a new number and does not mutate the original value"]
651 #[stable(feature = "rust1", since = "1.0.0")]
653 pub fn acos(self) -> f64 {
654 unsafe { cmath::acos(self) }
657 /// Computes the arctangent of a number. Return value is in radians in the
658 /// range [-pi/2, pi/2];
666 /// let abs_difference = (f.tan().atan() - 1.0).abs();
668 /// assert!(abs_difference < 1e-10);
670 #[must_use = "method returns a new number and does not mutate the original value"]
671 #[stable(feature = "rust1", since = "1.0.0")]
673 pub fn atan(self) -> f64 {
674 unsafe { cmath::atan(self) }
677 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
679 /// * `x = 0`, `y = 0`: `0`
680 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
681 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
682 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
689 /// // Positive angles measured counter-clockwise
690 /// // from positive x axis
691 /// // -pi/4 radians (45 deg clockwise)
692 /// let x1 = 3.0_f64;
693 /// let y1 = -3.0_f64;
695 /// // 3pi/4 radians (135 deg counter-clockwise)
696 /// let x2 = -3.0_f64;
697 /// let y2 = 3.0_f64;
699 /// let abs_difference_1 = (y1.atan2(x1) - (-f64::consts::FRAC_PI_4)).abs();
700 /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * f64::consts::FRAC_PI_4)).abs();
702 /// assert!(abs_difference_1 < 1e-10);
703 /// assert!(abs_difference_2 < 1e-10);
705 #[must_use = "method returns a new number and does not mutate the original value"]
706 #[stable(feature = "rust1", since = "1.0.0")]
708 pub fn atan2(self, other: f64) -> f64 {
709 unsafe { cmath::atan2(self, other) }
712 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
713 /// `(sin(x), cos(x))`.
720 /// let x = f64::consts::FRAC_PI_4;
721 /// let f = x.sin_cos();
723 /// let abs_difference_0 = (f.0 - x.sin()).abs();
724 /// let abs_difference_1 = (f.1 - x.cos()).abs();
726 /// assert!(abs_difference_0 < 1e-10);
727 /// assert!(abs_difference_1 < 1e-10);
729 #[stable(feature = "rust1", since = "1.0.0")]
731 pub fn sin_cos(self) -> (f64, f64) {
732 (self.sin(), self.cos())
735 /// Returns `e^(self) - 1` in a way that is accurate even if the
736 /// number is close to zero.
744 /// let abs_difference = (x.ln().exp_m1() - 6.0).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 exp_m1(self) -> f64 {
752 unsafe { cmath::expm1(self) }
755 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
756 /// the operations were performed separately.
763 /// let x = f64::consts::E - 1.0;
765 /// // ln(1 + (e - 1)) == ln(e) == 1
766 /// let abs_difference = (x.ln_1p() - 1.0).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 ln_1p(self) -> f64 {
774 unsafe { cmath::log1p(self) }
777 /// Hyperbolic sine function.
784 /// let e = f64::consts::E;
787 /// let f = x.sinh();
788 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
789 /// let g = ((e * e) - 1.0) / (2.0 * e);
790 /// let abs_difference = (f - g).abs();
792 /// assert!(abs_difference < 1e-10);
794 #[must_use = "method returns a new number and does not mutate the original value"]
795 #[stable(feature = "rust1", since = "1.0.0")]
797 pub fn sinh(self) -> f64 {
798 unsafe { cmath::sinh(self) }
801 /// Hyperbolic cosine function.
808 /// let e = f64::consts::E;
810 /// let f = x.cosh();
811 /// // Solving cosh() at 1 gives this result
812 /// let g = ((e * e) + 1.0) / (2.0 * e);
813 /// let abs_difference = (f - g).abs();
816 /// assert!(abs_difference < 1.0e-10);
818 #[must_use = "method returns a new number and does not mutate the original value"]
819 #[stable(feature = "rust1", since = "1.0.0")]
821 pub fn cosh(self) -> f64 {
822 unsafe { cmath::cosh(self) }
825 /// Hyperbolic tangent function.
832 /// let e = f64::consts::E;
835 /// let f = x.tanh();
836 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
837 /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
838 /// let abs_difference = (f - g).abs();
840 /// assert!(abs_difference < 1.0e-10);
842 #[must_use = "method returns a new number and does not mutate the original value"]
843 #[stable(feature = "rust1", since = "1.0.0")]
845 pub fn tanh(self) -> f64 {
846 unsafe { cmath::tanh(self) }
849 /// Inverse hyperbolic sine function.
855 /// let f = x.sinh().asinh();
857 /// let abs_difference = (f - x).abs();
859 /// assert!(abs_difference < 1.0e-10);
861 #[must_use = "method returns a new number and does not mutate the original value"]
862 #[stable(feature = "rust1", since = "1.0.0")]
864 pub fn asinh(self) -> f64 {
865 if self == NEG_INFINITY {
868 (self + ((self * self) + 1.0).sqrt()).ln().copysign(self)
872 /// Inverse hyperbolic cosine function.
878 /// let f = x.cosh().acosh();
880 /// let abs_difference = (f - x).abs();
882 /// assert!(abs_difference < 1.0e-10);
884 #[must_use = "method returns a new number and does not mutate the original value"]
885 #[stable(feature = "rust1", since = "1.0.0")]
887 pub fn acosh(self) -> f64 {
888 if self < 1.0 { NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() }
891 /// Inverse hyperbolic tangent function.
898 /// let e = f64::consts::E;
899 /// let f = e.tanh().atanh();
901 /// let abs_difference = (f - e).abs();
903 /// assert!(abs_difference < 1.0e-10);
905 #[must_use = "method returns a new number and does not mutate the original value"]
906 #[stable(feature = "rust1", since = "1.0.0")]
908 pub fn atanh(self) -> f64 {
909 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
912 /// Restrict a value to a certain interval unless it is NaN.
914 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
915 /// less than `min`. Otherwise this returns `self`.
917 /// Not that this function returns NaN if the initial value was NaN as
922 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
927 /// #![feature(clamp)]
928 /// assert!((-3.0f64).clamp(-2.0, 1.0) == -2.0);
929 /// assert!((0.0f64).clamp(-2.0, 1.0) == 0.0);
930 /// assert!((2.0f64).clamp(-2.0, 1.0) == 1.0);
931 /// assert!((std::f64::NAN).clamp(-2.0, 1.0).is_nan());
933 #[must_use = "method returns a new number and does not mutate the original value"]
934 #[unstable(feature = "clamp", issue = "44095")]
936 pub fn clamp(self, min: f64, max: f64) -> f64 {
948 // Solaris/Illumos requires a wrapper around log, log2, and log10 functions
949 // because of their non-standard behavior (e.g., log(-n) returns -Inf instead
951 fn log_wrapper<F: Fn(f64) -> f64>(self, log_fn: F) -> f64 {
952 if !cfg!(target_os = "solaris") {
955 if self.is_finite() {
958 } else if self == 0.0 {
959 NEG_INFINITY // log(0) = -Inf
963 } else if self.is_nan() {
964 self // log(NaN) = NaN
965 } else if self > 0.0 {
966 self // log(Inf) = Inf
968 NAN // log(-Inf) = NaN
978 use crate::num::FpCategory as Fp;
983 test_num(10f64, 2f64);
988 assert_eq!(NAN.min(2.0), 2.0);
989 assert_eq!(2.0f64.min(NAN), 2.0);
994 assert_eq!(NAN.max(2.0), 2.0);
995 assert_eq!(2.0f64.max(NAN), 2.0);
1001 assert!(nan.is_nan());
1002 assert!(!nan.is_infinite());
1003 assert!(!nan.is_finite());
1004 assert!(!nan.is_normal());
1005 assert!(nan.is_sign_positive());
1006 assert!(!nan.is_sign_negative());
1007 assert_eq!(Fp::Nan, nan.classify());
1011 fn test_infinity() {
1012 let inf: f64 = INFINITY;
1013 assert!(inf.is_infinite());
1014 assert!(!inf.is_finite());
1015 assert!(inf.is_sign_positive());
1016 assert!(!inf.is_sign_negative());
1017 assert!(!inf.is_nan());
1018 assert!(!inf.is_normal());
1019 assert_eq!(Fp::Infinite, inf.classify());
1023 fn test_neg_infinity() {
1024 let neg_inf: f64 = NEG_INFINITY;
1025 assert!(neg_inf.is_infinite());
1026 assert!(!neg_inf.is_finite());
1027 assert!(!neg_inf.is_sign_positive());
1028 assert!(neg_inf.is_sign_negative());
1029 assert!(!neg_inf.is_nan());
1030 assert!(!neg_inf.is_normal());
1031 assert_eq!(Fp::Infinite, neg_inf.classify());
1036 let zero: f64 = 0.0f64;
1037 assert_eq!(0.0, zero);
1038 assert!(!zero.is_infinite());
1039 assert!(zero.is_finite());
1040 assert!(zero.is_sign_positive());
1041 assert!(!zero.is_sign_negative());
1042 assert!(!zero.is_nan());
1043 assert!(!zero.is_normal());
1044 assert_eq!(Fp::Zero, zero.classify());
1048 fn test_neg_zero() {
1049 let neg_zero: f64 = -0.0;
1050 assert_eq!(0.0, neg_zero);
1051 assert!(!neg_zero.is_infinite());
1052 assert!(neg_zero.is_finite());
1053 assert!(!neg_zero.is_sign_positive());
1054 assert!(neg_zero.is_sign_negative());
1055 assert!(!neg_zero.is_nan());
1056 assert!(!neg_zero.is_normal());
1057 assert_eq!(Fp::Zero, neg_zero.classify());
1060 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1063 let one: f64 = 1.0f64;
1064 assert_eq!(1.0, one);
1065 assert!(!one.is_infinite());
1066 assert!(one.is_finite());
1067 assert!(one.is_sign_positive());
1068 assert!(!one.is_sign_negative());
1069 assert!(!one.is_nan());
1070 assert!(one.is_normal());
1071 assert_eq!(Fp::Normal, one.classify());
1077 let inf: f64 = INFINITY;
1078 let neg_inf: f64 = NEG_INFINITY;
1079 assert!(nan.is_nan());
1080 assert!(!0.0f64.is_nan());
1081 assert!(!5.3f64.is_nan());
1082 assert!(!(-10.732f64).is_nan());
1083 assert!(!inf.is_nan());
1084 assert!(!neg_inf.is_nan());
1088 fn test_is_infinite() {
1090 let inf: f64 = INFINITY;
1091 let neg_inf: f64 = NEG_INFINITY;
1092 assert!(!nan.is_infinite());
1093 assert!(inf.is_infinite());
1094 assert!(neg_inf.is_infinite());
1095 assert!(!0.0f64.is_infinite());
1096 assert!(!42.8f64.is_infinite());
1097 assert!(!(-109.2f64).is_infinite());
1101 fn test_is_finite() {
1103 let inf: f64 = INFINITY;
1104 let neg_inf: f64 = NEG_INFINITY;
1105 assert!(!nan.is_finite());
1106 assert!(!inf.is_finite());
1107 assert!(!neg_inf.is_finite());
1108 assert!(0.0f64.is_finite());
1109 assert!(42.8f64.is_finite());
1110 assert!((-109.2f64).is_finite());
1113 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1115 fn test_is_normal() {
1117 let inf: f64 = INFINITY;
1118 let neg_inf: f64 = NEG_INFINITY;
1119 let zero: f64 = 0.0f64;
1120 let neg_zero: f64 = -0.0;
1121 assert!(!nan.is_normal());
1122 assert!(!inf.is_normal());
1123 assert!(!neg_inf.is_normal());
1124 assert!(!zero.is_normal());
1125 assert!(!neg_zero.is_normal());
1126 assert!(1f64.is_normal());
1127 assert!(1e-307f64.is_normal());
1128 assert!(!1e-308f64.is_normal());
1131 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1133 fn test_classify() {
1135 let inf: f64 = INFINITY;
1136 let neg_inf: f64 = NEG_INFINITY;
1137 let zero: f64 = 0.0f64;
1138 let neg_zero: f64 = -0.0;
1139 assert_eq!(nan.classify(), Fp::Nan);
1140 assert_eq!(inf.classify(), Fp::Infinite);
1141 assert_eq!(neg_inf.classify(), Fp::Infinite);
1142 assert_eq!(zero.classify(), Fp::Zero);
1143 assert_eq!(neg_zero.classify(), Fp::Zero);
1144 assert_eq!(1e-307f64.classify(), Fp::Normal);
1145 assert_eq!(1e-308f64.classify(), Fp::Subnormal);
1150 assert_approx_eq!(1.0f64.floor(), 1.0f64);
1151 assert_approx_eq!(1.3f64.floor(), 1.0f64);
1152 assert_approx_eq!(1.5f64.floor(), 1.0f64);
1153 assert_approx_eq!(1.7f64.floor(), 1.0f64);
1154 assert_approx_eq!(0.0f64.floor(), 0.0f64);
1155 assert_approx_eq!((-0.0f64).floor(), -0.0f64);
1156 assert_approx_eq!((-1.0f64).floor(), -1.0f64);
1157 assert_approx_eq!((-1.3f64).floor(), -2.0f64);
1158 assert_approx_eq!((-1.5f64).floor(), -2.0f64);
1159 assert_approx_eq!((-1.7f64).floor(), -2.0f64);
1164 assert_approx_eq!(1.0f64.ceil(), 1.0f64);
1165 assert_approx_eq!(1.3f64.ceil(), 2.0f64);
1166 assert_approx_eq!(1.5f64.ceil(), 2.0f64);
1167 assert_approx_eq!(1.7f64.ceil(), 2.0f64);
1168 assert_approx_eq!(0.0f64.ceil(), 0.0f64);
1169 assert_approx_eq!((-0.0f64).ceil(), -0.0f64);
1170 assert_approx_eq!((-1.0f64).ceil(), -1.0f64);
1171 assert_approx_eq!((-1.3f64).ceil(), -1.0f64);
1172 assert_approx_eq!((-1.5f64).ceil(), -1.0f64);
1173 assert_approx_eq!((-1.7f64).ceil(), -1.0f64);
1178 assert_approx_eq!(1.0f64.round(), 1.0f64);
1179 assert_approx_eq!(1.3f64.round(), 1.0f64);
1180 assert_approx_eq!(1.5f64.round(), 2.0f64);
1181 assert_approx_eq!(1.7f64.round(), 2.0f64);
1182 assert_approx_eq!(0.0f64.round(), 0.0f64);
1183 assert_approx_eq!((-0.0f64).round(), -0.0f64);
1184 assert_approx_eq!((-1.0f64).round(), -1.0f64);
1185 assert_approx_eq!((-1.3f64).round(), -1.0f64);
1186 assert_approx_eq!((-1.5f64).round(), -2.0f64);
1187 assert_approx_eq!((-1.7f64).round(), -2.0f64);
1192 assert_approx_eq!(1.0f64.trunc(), 1.0f64);
1193 assert_approx_eq!(1.3f64.trunc(), 1.0f64);
1194 assert_approx_eq!(1.5f64.trunc(), 1.0f64);
1195 assert_approx_eq!(1.7f64.trunc(), 1.0f64);
1196 assert_approx_eq!(0.0f64.trunc(), 0.0f64);
1197 assert_approx_eq!((-0.0f64).trunc(), -0.0f64);
1198 assert_approx_eq!((-1.0f64).trunc(), -1.0f64);
1199 assert_approx_eq!((-1.3f64).trunc(), -1.0f64);
1200 assert_approx_eq!((-1.5f64).trunc(), -1.0f64);
1201 assert_approx_eq!((-1.7f64).trunc(), -1.0f64);
1206 assert_approx_eq!(1.0f64.fract(), 0.0f64);
1207 assert_approx_eq!(1.3f64.fract(), 0.3f64);
1208 assert_approx_eq!(1.5f64.fract(), 0.5f64);
1209 assert_approx_eq!(1.7f64.fract(), 0.7f64);
1210 assert_approx_eq!(0.0f64.fract(), 0.0f64);
1211 assert_approx_eq!((-0.0f64).fract(), -0.0f64);
1212 assert_approx_eq!((-1.0f64).fract(), -0.0f64);
1213 assert_approx_eq!((-1.3f64).fract(), -0.3f64);
1214 assert_approx_eq!((-1.5f64).fract(), -0.5f64);
1215 assert_approx_eq!((-1.7f64).fract(), -0.7f64);
1220 assert_eq!(INFINITY.abs(), INFINITY);
1221 assert_eq!(1f64.abs(), 1f64);
1222 assert_eq!(0f64.abs(), 0f64);
1223 assert_eq!((-0f64).abs(), 0f64);
1224 assert_eq!((-1f64).abs(), 1f64);
1225 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1226 assert_eq!((1f64 / NEG_INFINITY).abs(), 0f64);
1227 assert!(NAN.abs().is_nan());
1232 assert_eq!(INFINITY.signum(), 1f64);
1233 assert_eq!(1f64.signum(), 1f64);
1234 assert_eq!(0f64.signum(), 1f64);
1235 assert_eq!((-0f64).signum(), -1f64);
1236 assert_eq!((-1f64).signum(), -1f64);
1237 assert_eq!(NEG_INFINITY.signum(), -1f64);
1238 assert_eq!((1f64 / NEG_INFINITY).signum(), -1f64);
1239 assert!(NAN.signum().is_nan());
1243 fn test_is_sign_positive() {
1244 assert!(INFINITY.is_sign_positive());
1245 assert!(1f64.is_sign_positive());
1246 assert!(0f64.is_sign_positive());
1247 assert!(!(-0f64).is_sign_positive());
1248 assert!(!(-1f64).is_sign_positive());
1249 assert!(!NEG_INFINITY.is_sign_positive());
1250 assert!(!(1f64 / NEG_INFINITY).is_sign_positive());
1251 assert!(NAN.is_sign_positive());
1252 assert!(!(-NAN).is_sign_positive());
1256 fn test_is_sign_negative() {
1257 assert!(!INFINITY.is_sign_negative());
1258 assert!(!1f64.is_sign_negative());
1259 assert!(!0f64.is_sign_negative());
1260 assert!((-0f64).is_sign_negative());
1261 assert!((-1f64).is_sign_negative());
1262 assert!(NEG_INFINITY.is_sign_negative());
1263 assert!((1f64 / NEG_INFINITY).is_sign_negative());
1264 assert!(!NAN.is_sign_negative());
1265 assert!((-NAN).is_sign_negative());
1271 let inf: f64 = INFINITY;
1272 let neg_inf: f64 = NEG_INFINITY;
1273 assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05);
1274 assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65);
1275 assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2);
1276 assert_approx_eq!(3.4f64.mul_add(-0.0, 5.6), 5.6);
1277 assert!(nan.mul_add(7.8, 9.0).is_nan());
1278 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1279 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1280 assert_eq!(8.9f64.mul_add(inf, 3.2), inf);
1281 assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf);
1287 let inf: f64 = INFINITY;
1288 let neg_inf: f64 = NEG_INFINITY;
1289 assert_eq!(1.0f64.recip(), 1.0);
1290 assert_eq!(2.0f64.recip(), 0.5);
1291 assert_eq!((-0.4f64).recip(), -2.5);
1292 assert_eq!(0.0f64.recip(), inf);
1293 assert!(nan.recip().is_nan());
1294 assert_eq!(inf.recip(), 0.0);
1295 assert_eq!(neg_inf.recip(), 0.0);
1301 let inf: f64 = INFINITY;
1302 let neg_inf: f64 = NEG_INFINITY;
1303 assert_eq!(1.0f64.powi(1), 1.0);
1304 assert_approx_eq!((-3.1f64).powi(2), 9.61);
1305 assert_approx_eq!(5.9f64.powi(-2), 0.028727);
1306 assert_eq!(8.3f64.powi(0), 1.0);
1307 assert!(nan.powi(2).is_nan());
1308 assert_eq!(inf.powi(3), inf);
1309 assert_eq!(neg_inf.powi(2), inf);
1315 let inf: f64 = INFINITY;
1316 let neg_inf: f64 = NEG_INFINITY;
1317 assert_eq!(1.0f64.powf(1.0), 1.0);
1318 assert_approx_eq!(3.4f64.powf(4.5), 246.408183);
1319 assert_approx_eq!(2.7f64.powf(-3.2), 0.041652);
1320 assert_approx_eq!((-3.1f64).powf(2.0), 9.61);
1321 assert_approx_eq!(5.9f64.powf(-2.0), 0.028727);
1322 assert_eq!(8.3f64.powf(0.0), 1.0);
1323 assert!(nan.powf(2.0).is_nan());
1324 assert_eq!(inf.powf(2.0), inf);
1325 assert_eq!(neg_inf.powf(3.0), neg_inf);
1329 fn test_sqrt_domain() {
1330 assert!(NAN.sqrt().is_nan());
1331 assert!(NEG_INFINITY.sqrt().is_nan());
1332 assert!((-1.0f64).sqrt().is_nan());
1333 assert_eq!((-0.0f64).sqrt(), -0.0);
1334 assert_eq!(0.0f64.sqrt(), 0.0);
1335 assert_eq!(1.0f64.sqrt(), 1.0);
1336 assert_eq!(INFINITY.sqrt(), INFINITY);
1341 assert_eq!(1.0, 0.0f64.exp());
1342 assert_approx_eq!(2.718282, 1.0f64.exp());
1343 assert_approx_eq!(148.413159, 5.0f64.exp());
1345 let inf: f64 = INFINITY;
1346 let neg_inf: f64 = NEG_INFINITY;
1348 assert_eq!(inf, inf.exp());
1349 assert_eq!(0.0, neg_inf.exp());
1350 assert!(nan.exp().is_nan());
1355 assert_eq!(32.0, 5.0f64.exp2());
1356 assert_eq!(1.0, 0.0f64.exp2());
1358 let inf: f64 = INFINITY;
1359 let neg_inf: f64 = NEG_INFINITY;
1361 assert_eq!(inf, inf.exp2());
1362 assert_eq!(0.0, neg_inf.exp2());
1363 assert!(nan.exp2().is_nan());
1369 let inf: f64 = INFINITY;
1370 let neg_inf: f64 = NEG_INFINITY;
1371 assert_approx_eq!(1.0f64.exp().ln(), 1.0);
1372 assert!(nan.ln().is_nan());
1373 assert_eq!(inf.ln(), inf);
1374 assert!(neg_inf.ln().is_nan());
1375 assert!((-2.3f64).ln().is_nan());
1376 assert_eq!((-0.0f64).ln(), neg_inf);
1377 assert_eq!(0.0f64.ln(), neg_inf);
1378 assert_approx_eq!(4.0f64.ln(), 1.386294);
1384 let inf: f64 = INFINITY;
1385 let neg_inf: f64 = NEG_INFINITY;
1386 assert_eq!(10.0f64.log(10.0), 1.0);
1387 assert_approx_eq!(2.3f64.log(3.5), 0.664858);
1388 assert_eq!(1.0f64.exp().log(1.0f64.exp()), 1.0);
1389 assert!(1.0f64.log(1.0).is_nan());
1390 assert!(1.0f64.log(-13.9).is_nan());
1391 assert!(nan.log(2.3).is_nan());
1392 assert_eq!(inf.log(10.0), inf);
1393 assert!(neg_inf.log(8.8).is_nan());
1394 assert!((-2.3f64).log(0.1).is_nan());
1395 assert_eq!((-0.0f64).log(2.0), neg_inf);
1396 assert_eq!(0.0f64.log(7.0), neg_inf);
1402 let inf: f64 = INFINITY;
1403 let neg_inf: f64 = NEG_INFINITY;
1404 assert_approx_eq!(10.0f64.log2(), 3.321928);
1405 assert_approx_eq!(2.3f64.log2(), 1.201634);
1406 assert_approx_eq!(1.0f64.exp().log2(), 1.442695);
1407 assert!(nan.log2().is_nan());
1408 assert_eq!(inf.log2(), inf);
1409 assert!(neg_inf.log2().is_nan());
1410 assert!((-2.3f64).log2().is_nan());
1411 assert_eq!((-0.0f64).log2(), neg_inf);
1412 assert_eq!(0.0f64.log2(), neg_inf);
1418 let inf: f64 = INFINITY;
1419 let neg_inf: f64 = NEG_INFINITY;
1420 assert_eq!(10.0f64.log10(), 1.0);
1421 assert_approx_eq!(2.3f64.log10(), 0.361728);
1422 assert_approx_eq!(1.0f64.exp().log10(), 0.434294);
1423 assert_eq!(1.0f64.log10(), 0.0);
1424 assert!(nan.log10().is_nan());
1425 assert_eq!(inf.log10(), inf);
1426 assert!(neg_inf.log10().is_nan());
1427 assert!((-2.3f64).log10().is_nan());
1428 assert_eq!((-0.0f64).log10(), neg_inf);
1429 assert_eq!(0.0f64.log10(), neg_inf);
1433 fn test_to_degrees() {
1434 let pi: f64 = consts::PI;
1436 let inf: f64 = INFINITY;
1437 let neg_inf: f64 = NEG_INFINITY;
1438 assert_eq!(0.0f64.to_degrees(), 0.0);
1439 assert_approx_eq!((-5.8f64).to_degrees(), -332.315521);
1440 assert_eq!(pi.to_degrees(), 180.0);
1441 assert!(nan.to_degrees().is_nan());
1442 assert_eq!(inf.to_degrees(), inf);
1443 assert_eq!(neg_inf.to_degrees(), neg_inf);
1447 fn test_to_radians() {
1448 let pi: f64 = consts::PI;
1450 let inf: f64 = INFINITY;
1451 let neg_inf: f64 = NEG_INFINITY;
1452 assert_eq!(0.0f64.to_radians(), 0.0);
1453 assert_approx_eq!(154.6f64.to_radians(), 2.698279);
1454 assert_approx_eq!((-332.31f64).to_radians(), -5.799903);
1455 assert_eq!(180.0f64.to_radians(), pi);
1456 assert!(nan.to_radians().is_nan());
1457 assert_eq!(inf.to_radians(), inf);
1458 assert_eq!(neg_inf.to_radians(), neg_inf);
1463 assert_eq!(0.0f64.asinh(), 0.0f64);
1464 assert_eq!((-0.0f64).asinh(), -0.0f64);
1466 let inf: f64 = INFINITY;
1467 let neg_inf: f64 = NEG_INFINITY;
1469 assert_eq!(inf.asinh(), inf);
1470 assert_eq!(neg_inf.asinh(), neg_inf);
1471 assert!(nan.asinh().is_nan());
1472 assert!((-0.0f64).asinh().is_sign_negative());
1474 assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64);
1475 assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
1480 assert_eq!(1.0f64.acosh(), 0.0f64);
1481 assert!(0.999f64.acosh().is_nan());
1483 let inf: f64 = INFINITY;
1484 let neg_inf: f64 = NEG_INFINITY;
1486 assert_eq!(inf.acosh(), inf);
1487 assert!(neg_inf.acosh().is_nan());
1488 assert!(nan.acosh().is_nan());
1489 assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
1490 assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
1495 assert_eq!(0.0f64.atanh(), 0.0f64);
1496 assert_eq!((-0.0f64).atanh(), -0.0f64);
1498 let inf: f64 = INFINITY;
1499 let neg_inf: f64 = NEG_INFINITY;
1501 assert_eq!(1.0f64.atanh(), inf);
1502 assert_eq!((-1.0f64).atanh(), neg_inf);
1503 assert!(2f64.atanh().atanh().is_nan());
1504 assert!((-2f64).atanh().atanh().is_nan());
1505 assert!(inf.atanh().is_nan());
1506 assert!(neg_inf.atanh().is_nan());
1507 assert!(nan.atanh().is_nan());
1508 assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64);
1509 assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64);
1513 fn test_real_consts() {
1515 let pi: f64 = consts::PI;
1516 let frac_pi_2: f64 = consts::FRAC_PI_2;
1517 let frac_pi_3: f64 = consts::FRAC_PI_3;
1518 let frac_pi_4: f64 = consts::FRAC_PI_4;
1519 let frac_pi_6: f64 = consts::FRAC_PI_6;
1520 let frac_pi_8: f64 = consts::FRAC_PI_8;
1521 let frac_1_pi: f64 = consts::FRAC_1_PI;
1522 let frac_2_pi: f64 = consts::FRAC_2_PI;
1523 let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRT_PI;
1524 let sqrt2: f64 = consts::SQRT_2;
1525 let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT_2;
1526 let e: f64 = consts::E;
1527 let log2_e: f64 = consts::LOG2_E;
1528 let log10_e: f64 = consts::LOG10_E;
1529 let ln_2: f64 = consts::LN_2;
1530 let ln_10: f64 = consts::LN_10;
1532 assert_approx_eq!(frac_pi_2, pi / 2f64);
1533 assert_approx_eq!(frac_pi_3, pi / 3f64);
1534 assert_approx_eq!(frac_pi_4, pi / 4f64);
1535 assert_approx_eq!(frac_pi_6, pi / 6f64);
1536 assert_approx_eq!(frac_pi_8, pi / 8f64);
1537 assert_approx_eq!(frac_1_pi, 1f64 / pi);
1538 assert_approx_eq!(frac_2_pi, 2f64 / pi);
1539 assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt());
1540 assert_approx_eq!(sqrt2, 2f64.sqrt());
1541 assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt());
1542 assert_approx_eq!(log2_e, e.log2());
1543 assert_approx_eq!(log10_e, e.log10());
1544 assert_approx_eq!(ln_2, 2f64.ln());
1545 assert_approx_eq!(ln_10, 10f64.ln());
1549 fn test_float_bits_conv() {
1550 assert_eq!((1f64).to_bits(), 0x3ff0000000000000);
1551 assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
1552 assert_eq!((1337f64).to_bits(), 0x4094e40000000000);
1553 assert_eq!((-14.25f64).to_bits(), 0xc02c800000000000);
1554 assert_approx_eq!(f64::from_bits(0x3ff0000000000000), 1.0);
1555 assert_approx_eq!(f64::from_bits(0x4029000000000000), 12.5);
1556 assert_approx_eq!(f64::from_bits(0x4094e40000000000), 1337.0);
1557 assert_approx_eq!(f64::from_bits(0xc02c800000000000), -14.25);
1559 // Check that NaNs roundtrip their bits regardless of signalingness
1560 // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits
1561 let masked_nan1 = f64::NAN.to_bits() ^ 0x000A_AAAA_AAAA_AAAA;
1562 let masked_nan2 = f64::NAN.to_bits() ^ 0x0005_5555_5555_5555;
1563 assert!(f64::from_bits(masked_nan1).is_nan());
1564 assert!(f64::from_bits(masked_nan2).is_nan());
1566 assert_eq!(f64::from_bits(masked_nan1).to_bits(), masked_nan1);
1567 assert_eq!(f64::from_bits(masked_nan2).to_bits(), masked_nan2);
1572 fn test_clamp_min_greater_than_max() {
1573 let _ = 1.0f64.clamp(3.0, 1.0);
1578 fn test_clamp_min_is_nan() {
1579 let _ = 1.0f64.clamp(NAN, 1.0);
1584 fn test_clamp_max_is_nan() {
1585 let _ = 1.0f64.clamp(3.0, NAN);