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::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON};
18 #[stable(feature = "rust1", since = "1.0.0")]
19 pub use core::f64::{MIN_EXP, MAX_EXP, MIN_10_EXP};
20 #[stable(feature = "rust1", since = "1.0.0")]
21 pub use core::f64::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
22 #[stable(feature = "rust1", since = "1.0.0")]
23 pub use core::f64::{MIN, MIN_POSITIVE, MAX};
24 #[stable(feature = "rust1", since = "1.0.0")]
25 pub use core::f64::consts;
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 #[stable(feature = "rust1", since = "1.0.0")]
45 pub fn floor(self) -> f64 {
46 unsafe { intrinsics::floorf64(self) }
49 /// Returns the smallest integer greater than or equal to a number.
57 /// assert_eq!(f.ceil(), 4.0);
58 /// assert_eq!(g.ceil(), 4.0);
60 #[stable(feature = "rust1", since = "1.0.0")]
62 pub fn ceil(self) -> f64 {
63 unsafe { intrinsics::ceilf64(self) }
66 /// Returns the nearest integer to a number. Round half-way cases away from
75 /// assert_eq!(f.round(), 3.0);
76 /// assert_eq!(g.round(), -3.0);
78 #[stable(feature = "rust1", since = "1.0.0")]
80 pub fn round(self) -> f64 {
81 unsafe { intrinsics::roundf64(self) }
84 /// Returns the integer part of a number.
93 /// assert_eq!(f.trunc(), 3.0);
94 /// assert_eq!(g.trunc(), 3.0);
95 /// assert_eq!(h.trunc(), -3.0);
97 #[stable(feature = "rust1", since = "1.0.0")]
99 pub fn trunc(self) -> f64 {
100 unsafe { intrinsics::truncf64(self) }
103 /// Returns the fractional part of a number.
109 /// let y = -3.5_f64;
110 /// let abs_difference_x = (x.fract() - 0.5).abs();
111 /// let abs_difference_y = (y.fract() - (-0.5)).abs();
113 /// assert!(abs_difference_x < 1e-10);
114 /// assert!(abs_difference_y < 1e-10);
116 #[stable(feature = "rust1", since = "1.0.0")]
118 pub fn fract(self) -> f64 { self - self.trunc() }
120 /// Computes the absolute value of `self`. Returns `NAN` if the
129 /// let y = -3.5_f64;
131 /// let abs_difference_x = (x.abs() - x).abs();
132 /// let abs_difference_y = (y.abs() - (-y)).abs();
134 /// assert!(abs_difference_x < 1e-10);
135 /// assert!(abs_difference_y < 1e-10);
137 /// assert!(f64::NAN.abs().is_nan());
139 #[stable(feature = "rust1", since = "1.0.0")]
141 pub fn abs(self) -> f64 {
142 unsafe { intrinsics::fabsf64(self) }
145 /// Returns a number that represents the sign of `self`.
147 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
148 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
149 /// - `NAN` if the number is `NAN`
158 /// assert_eq!(f.signum(), 1.0);
159 /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
161 /// assert!(f64::NAN.signum().is_nan());
163 #[stable(feature = "rust1", since = "1.0.0")]
165 pub fn signum(self) -> f64 {
169 1.0_f64.copysign(self)
173 /// Returns a number composed of the magnitude of `self` and the sign of
176 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
177 /// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of
178 /// `sign` is returned.
187 /// assert_eq!(f.copysign(0.42), 3.5_f64);
188 /// assert_eq!(f.copysign(-0.42), -3.5_f64);
189 /// assert_eq!((-f).copysign(0.42), 3.5_f64);
190 /// assert_eq!((-f).copysign(-0.42), -3.5_f64);
192 /// assert!(f64::NAN.copysign(1.0).is_nan());
196 #[stable(feature = "copysign", since = "1.35.0")]
197 pub fn copysign(self, sign: f64) -> f64 {
198 unsafe { intrinsics::copysignf64(self, sign) }
201 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
202 /// error, yielding a more accurate result than an unfused multiply-add.
204 /// Using `mul_add` can be more performant than an unfused multiply-add if
205 /// the target architecture has a dedicated `fma` CPU instruction.
210 /// let m = 10.0_f64;
212 /// let b = 60.0_f64;
215 /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs();
217 /// assert!(abs_difference < 1e-10);
219 #[stable(feature = "rust1", since = "1.0.0")]
221 pub fn mul_add(self, a: f64, b: f64) -> f64 {
222 unsafe { intrinsics::fmaf64(self, a, b) }
225 /// Calculates Euclidean division, the matching method for `rem_euclid`.
227 /// This computes the integer `n` such that
228 /// `self = n * rhs + self.rem_euclid(rhs)`.
229 /// In other words, the result is `self / rhs` rounded to the integer `n`
230 /// such that `self >= n * rhs`.
235 /// let a: f64 = 7.0;
237 /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
238 /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
239 /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
240 /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0
243 #[stable(feature = "euclidean_division", since = "1.38.0")]
244 pub fn div_euclid(self, rhs: f64) -> f64 {
245 let q = (self / rhs).trunc();
246 if self % rhs < 0.0 {
247 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
252 /// Calculates the least nonnegative remainder of `self (mod rhs)`.
254 /// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
255 /// most cases. However, due to a floating point round-off error it can
256 /// result in `r == rhs.abs()`, violating the mathematical definition, if
257 /// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
258 /// This result is not an element of the function's codomain, but it is the
259 /// closest floating point number in the real numbers and thus fulfills the
260 /// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
266 /// let a: f64 = 7.0;
268 /// assert_eq!(a.rem_euclid(b), 3.0);
269 /// assert_eq!((-a).rem_euclid(b), 1.0);
270 /// assert_eq!(a.rem_euclid(-b), 3.0);
271 /// assert_eq!((-a).rem_euclid(-b), 1.0);
272 /// // limitation due to round-off error
273 /// assert!((-std::f64::EPSILON).rem_euclid(3.0) != 0.0);
276 #[stable(feature = "euclidean_division", since = "1.38.0")]
277 pub fn rem_euclid(self, rhs: f64) -> f64 {
286 /// Raises a number to an integer power.
288 /// Using this function is generally faster than using `powf`
294 /// let abs_difference = (x.powi(2) - (x * x)).abs();
296 /// assert!(abs_difference < 1e-10);
298 #[stable(feature = "rust1", since = "1.0.0")]
300 pub fn powi(self, n: i32) -> f64 {
301 unsafe { intrinsics::powif64(self, n) }
304 /// Raises a number to a floating point power.
310 /// let abs_difference = (x.powf(2.0) - (x * x)).abs();
312 /// assert!(abs_difference < 1e-10);
314 #[stable(feature = "rust1", since = "1.0.0")]
316 pub fn powf(self, n: f64) -> f64 {
317 unsafe { intrinsics::powf64(self, n) }
320 /// Takes the square root of a number.
322 /// Returns NaN if `self` is a negative number.
327 /// let positive = 4.0_f64;
328 /// let negative = -4.0_f64;
330 /// let abs_difference = (positive.sqrt() - 2.0).abs();
332 /// assert!(abs_difference < 1e-10);
333 /// assert!(negative.sqrt().is_nan());
335 #[stable(feature = "rust1", since = "1.0.0")]
337 pub fn sqrt(self) -> f64 {
341 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 #[stable(feature = "rust1", since = "1.0.0")]
361 pub fn exp(self) -> f64 {
362 unsafe { intrinsics::expf64(self) }
365 /// Returns `2^(self)`.
373 /// let abs_difference = (f.exp2() - 4.0).abs();
375 /// assert!(abs_difference < 1e-10);
377 #[stable(feature = "rust1", since = "1.0.0")]
379 pub fn exp2(self) -> f64 {
380 unsafe { intrinsics::exp2f64(self) }
383 /// Returns the natural logarithm of the number.
388 /// let one = 1.0_f64;
390 /// let e = one.exp();
392 /// // ln(e) - 1 == 0
393 /// let abs_difference = (e.ln() - 1.0).abs();
395 /// assert!(abs_difference < 1e-10);
397 #[stable(feature = "rust1", since = "1.0.0")]
399 pub fn ln(self) -> f64 {
400 self.log_wrapper(|n| { unsafe { intrinsics::logf64(n) } })
403 /// Returns the logarithm of the number with respect to an arbitrary base.
405 /// The result may not be correctly rounded owing to implementation details;
406 /// `self.log2()` can produce more accurate results for base 2, and
407 /// `self.log10()` can produce more accurate results for base 10.
412 /// let five = 5.0_f64;
414 /// // log5(5) - 1 == 0
415 /// let abs_difference = (five.log(5.0) - 1.0).abs();
417 /// assert!(abs_difference < 1e-10);
419 #[stable(feature = "rust1", since = "1.0.0")]
421 pub fn log(self, base: f64) -> f64 { self.ln() / base.ln() }
423 /// Returns the base 2 logarithm of the number.
428 /// let two = 2.0_f64;
430 /// // log2(2) - 1 == 0
431 /// let abs_difference = (two.log2() - 1.0).abs();
433 /// assert!(abs_difference < 1e-10);
435 #[stable(feature = "rust1", since = "1.0.0")]
437 pub fn log2(self) -> f64 {
438 self.log_wrapper(|n| {
439 #[cfg(target_os = "android")]
440 return crate::sys::android::log2f64(n);
441 #[cfg(not(target_os = "android"))]
442 return unsafe { intrinsics::log2f64(n) };
446 /// Returns the base 10 logarithm of the number.
451 /// let ten = 10.0_f64;
453 /// // log10(10) - 1 == 0
454 /// let abs_difference = (ten.log10() - 1.0).abs();
456 /// assert!(abs_difference < 1e-10);
458 #[stable(feature = "rust1", since = "1.0.0")]
460 pub fn log10(self) -> f64 {
461 self.log_wrapper(|n| { unsafe { intrinsics::log10f64(n) } })
464 /// The positive difference of two numbers.
466 /// * If `self <= other`: `0:0`
467 /// * Else: `self - other`
473 /// let y = -3.0_f64;
475 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
476 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
478 /// assert!(abs_difference_x < 1e-10);
479 /// assert!(abs_difference_y < 1e-10);
481 #[stable(feature = "rust1", since = "1.0.0")]
483 #[rustc_deprecated(since = "1.10.0",
484 reason = "you probably meant `(self - other).abs()`: \
485 this operation is `(self - other).max(0.0)` \
486 except that `abs_sub` also propagates NaNs (also \
487 known as `fdim` in C). If you truly need the positive \
488 difference, consider using that expression or the C function \
489 `fdim`, depending on how you wish to handle NaN (please consider \
490 filing an issue describing your use-case too).")]
491 pub fn abs_sub(self, other: f64) -> f64 {
492 unsafe { cmath::fdim(self, other) }
495 /// Takes the cubic root of a number.
502 /// // x^(1/3) - 2 == 0
503 /// let abs_difference = (x.cbrt() - 2.0).abs();
505 /// assert!(abs_difference < 1e-10);
507 #[stable(feature = "rust1", since = "1.0.0")]
509 pub fn cbrt(self) -> f64 {
510 unsafe { cmath::cbrt(self) }
513 /// Calculates the length of the hypotenuse of a right-angle triangle given
514 /// legs of length `x` and `y`.
522 /// // sqrt(x^2 + y^2)
523 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
525 /// assert!(abs_difference < 1e-10);
527 #[stable(feature = "rust1", since = "1.0.0")]
529 pub fn hypot(self, other: f64) -> f64 {
530 unsafe { cmath::hypot(self, other) }
533 /// Computes the sine of a number (in radians).
540 /// let x = f64::consts::FRAC_PI_2;
542 /// let abs_difference = (x.sin() - 1.0).abs();
544 /// assert!(abs_difference < 1e-10);
546 #[stable(feature = "rust1", since = "1.0.0")]
548 pub fn sin(self) -> f64 {
549 unsafe { intrinsics::sinf64(self) }
552 /// Computes the cosine of a number (in radians).
559 /// let x = 2.0 * f64::consts::PI;
561 /// let abs_difference = (x.cos() - 1.0).abs();
563 /// assert!(abs_difference < 1e-10);
565 #[stable(feature = "rust1", since = "1.0.0")]
567 pub fn cos(self) -> f64 {
568 unsafe { intrinsics::cosf64(self) }
571 /// Computes the tangent of a number (in radians).
578 /// let x = f64::consts::FRAC_PI_4;
579 /// let abs_difference = (x.tan() - 1.0).abs();
581 /// assert!(abs_difference < 1e-14);
583 #[stable(feature = "rust1", since = "1.0.0")]
585 pub fn tan(self) -> f64 {
586 unsafe { cmath::tan(self) }
589 /// Computes the arcsine of a number. Return value is in radians in
590 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
598 /// let f = f64::consts::FRAC_PI_2;
600 /// // asin(sin(pi/2))
601 /// let abs_difference = (f.sin().asin() - f64::consts::FRAC_PI_2).abs();
603 /// assert!(abs_difference < 1e-10);
605 #[stable(feature = "rust1", since = "1.0.0")]
607 pub fn asin(self) -> f64 {
608 unsafe { cmath::asin(self) }
611 /// Computes the arccosine of a number. Return value is in radians in
612 /// the range [0, pi] or NaN if the number is outside the range
620 /// let f = f64::consts::FRAC_PI_4;
622 /// // acos(cos(pi/4))
623 /// let abs_difference = (f.cos().acos() - f64::consts::FRAC_PI_4).abs();
625 /// assert!(abs_difference < 1e-10);
627 #[stable(feature = "rust1", since = "1.0.0")]
629 pub fn acos(self) -> f64 {
630 unsafe { cmath::acos(self) }
633 /// Computes the arctangent of a number. Return value is in radians in the
634 /// range [-pi/2, pi/2];
642 /// let abs_difference = (f.tan().atan() - 1.0).abs();
644 /// assert!(abs_difference < 1e-10);
646 #[stable(feature = "rust1", since = "1.0.0")]
648 pub fn atan(self) -> f64 {
649 unsafe { cmath::atan(self) }
652 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
654 /// * `x = 0`, `y = 0`: `0`
655 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
656 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
657 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
664 /// // Positive angles measured counter-clockwise
665 /// // from positive x axis
666 /// // -pi/4 radians (45 deg clockwise)
667 /// let x1 = 3.0_f64;
668 /// let y1 = -3.0_f64;
670 /// // 3pi/4 radians (135 deg counter-clockwise)
671 /// let x2 = -3.0_f64;
672 /// let y2 = 3.0_f64;
674 /// let abs_difference_1 = (y1.atan2(x1) - (-f64::consts::FRAC_PI_4)).abs();
675 /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * f64::consts::FRAC_PI_4)).abs();
677 /// assert!(abs_difference_1 < 1e-10);
678 /// assert!(abs_difference_2 < 1e-10);
680 #[stable(feature = "rust1", since = "1.0.0")]
682 pub fn atan2(self, other: f64) -> f64 {
683 unsafe { cmath::atan2(self, other) }
686 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
687 /// `(sin(x), cos(x))`.
694 /// let x = f64::consts::FRAC_PI_4;
695 /// let f = x.sin_cos();
697 /// let abs_difference_0 = (f.0 - x.sin()).abs();
698 /// let abs_difference_1 = (f.1 - x.cos()).abs();
700 /// assert!(abs_difference_0 < 1e-10);
701 /// assert!(abs_difference_1 < 1e-10);
703 #[stable(feature = "rust1", since = "1.0.0")]
705 pub fn sin_cos(self) -> (f64, f64) {
706 (self.sin(), self.cos())
709 /// Returns `e^(self) - 1` in a way that is accurate even if the
710 /// number is close to zero.
718 /// let abs_difference = (x.ln().exp_m1() - 6.0).abs();
720 /// assert!(abs_difference < 1e-10);
722 #[stable(feature = "rust1", since = "1.0.0")]
724 pub fn exp_m1(self) -> f64 {
725 unsafe { cmath::expm1(self) }
728 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
729 /// the operations were performed separately.
736 /// let x = f64::consts::E - 1.0;
738 /// // ln(1 + (e - 1)) == ln(e) == 1
739 /// let abs_difference = (x.ln_1p() - 1.0).abs();
741 /// assert!(abs_difference < 1e-10);
743 #[stable(feature = "rust1", since = "1.0.0")]
745 pub fn ln_1p(self) -> f64 {
746 unsafe { cmath::log1p(self) }
749 /// Hyperbolic sine function.
756 /// let e = f64::consts::E;
759 /// let f = x.sinh();
760 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
761 /// let g = ((e * e) - 1.0) / (2.0 * e);
762 /// let abs_difference = (f - g).abs();
764 /// assert!(abs_difference < 1e-10);
766 #[stable(feature = "rust1", since = "1.0.0")]
768 pub fn sinh(self) -> f64 {
769 unsafe { cmath::sinh(self) }
772 /// Hyperbolic cosine function.
779 /// let e = f64::consts::E;
781 /// let f = x.cosh();
782 /// // Solving cosh() at 1 gives this result
783 /// let g = ((e * e) + 1.0) / (2.0 * e);
784 /// let abs_difference = (f - g).abs();
787 /// assert!(abs_difference < 1.0e-10);
789 #[stable(feature = "rust1", since = "1.0.0")]
791 pub fn cosh(self) -> f64 {
792 unsafe { cmath::cosh(self) }
795 /// Hyperbolic tangent function.
802 /// let e = f64::consts::E;
805 /// let f = x.tanh();
806 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
807 /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
808 /// let abs_difference = (f - g).abs();
810 /// assert!(abs_difference < 1.0e-10);
812 #[stable(feature = "rust1", since = "1.0.0")]
814 pub fn tanh(self) -> f64 {
815 unsafe { cmath::tanh(self) }
818 /// Inverse hyperbolic sine function.
824 /// let f = x.sinh().asinh();
826 /// let abs_difference = (f - x).abs();
828 /// assert!(abs_difference < 1.0e-10);
830 #[stable(feature = "rust1", since = "1.0.0")]
832 pub fn asinh(self) -> f64 {
833 if self == NEG_INFINITY {
836 (self + ((self * self) + 1.0).sqrt()).ln().copysign(self)
840 /// Inverse hyperbolic cosine function.
846 /// let f = x.cosh().acosh();
848 /// let abs_difference = (f - x).abs();
850 /// assert!(abs_difference < 1.0e-10);
852 #[stable(feature = "rust1", since = "1.0.0")]
854 pub fn acosh(self) -> f64 {
858 (self + ((self * self) - 1.0).sqrt()).ln()
862 /// Inverse hyperbolic tangent function.
869 /// let e = f64::consts::E;
870 /// let f = e.tanh().atanh();
872 /// let abs_difference = (f - e).abs();
874 /// assert!(abs_difference < 1.0e-10);
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 /// Not 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!((std::f64::NAN).clamp(-2.0, 1.0).is_nan());
903 #[unstable(feature = "clamp", issue = "44095")]
905 pub fn clamp(self, min: f64, max: f64) -> f64 {
908 if x < min { x = min; }
909 if x > max { x = max; }
913 // Solaris/Illumos requires a wrapper around log, log2, and log10 functions
914 // because of their non-standard behavior (e.g., log(-n) returns -Inf instead
916 fn log_wrapper<F: Fn(f64) -> f64>(self, log_fn: F) -> f64 {
917 if !cfg!(target_os = "solaris") {
920 if self.is_finite() {
923 } else if self == 0.0 {
924 NEG_INFINITY // log(0) = -Inf
928 } else if self.is_nan() {
929 self // log(NaN) = NaN
930 } else if self > 0.0 {
931 self // log(Inf) = Inf
933 NAN // log(-Inf) = NaN
944 use crate::num::FpCategory as Fp;
948 test_num(10f64, 2f64);
953 assert_eq!(NAN.min(2.0), 2.0);
954 assert_eq!(2.0f64.min(NAN), 2.0);
959 assert_eq!(NAN.max(2.0), 2.0);
960 assert_eq!(2.0f64.max(NAN), 2.0);
966 assert!(nan.is_nan());
967 assert!(!nan.is_infinite());
968 assert!(!nan.is_finite());
969 assert!(!nan.is_normal());
970 assert!(nan.is_sign_positive());
971 assert!(!nan.is_sign_negative());
972 assert_eq!(Fp::Nan, nan.classify());
977 let inf: f64 = INFINITY;
978 assert!(inf.is_infinite());
979 assert!(!inf.is_finite());
980 assert!(inf.is_sign_positive());
981 assert!(!inf.is_sign_negative());
982 assert!(!inf.is_nan());
983 assert!(!inf.is_normal());
984 assert_eq!(Fp::Infinite, inf.classify());
988 fn test_neg_infinity() {
989 let neg_inf: f64 = NEG_INFINITY;
990 assert!(neg_inf.is_infinite());
991 assert!(!neg_inf.is_finite());
992 assert!(!neg_inf.is_sign_positive());
993 assert!(neg_inf.is_sign_negative());
994 assert!(!neg_inf.is_nan());
995 assert!(!neg_inf.is_normal());
996 assert_eq!(Fp::Infinite, neg_inf.classify());
1001 let zero: f64 = 0.0f64;
1002 assert_eq!(0.0, zero);
1003 assert!(!zero.is_infinite());
1004 assert!(zero.is_finite());
1005 assert!(zero.is_sign_positive());
1006 assert!(!zero.is_sign_negative());
1007 assert!(!zero.is_nan());
1008 assert!(!zero.is_normal());
1009 assert_eq!(Fp::Zero, zero.classify());
1013 fn test_neg_zero() {
1014 let neg_zero: f64 = -0.0;
1015 assert_eq!(0.0, neg_zero);
1016 assert!(!neg_zero.is_infinite());
1017 assert!(neg_zero.is_finite());
1018 assert!(!neg_zero.is_sign_positive());
1019 assert!(neg_zero.is_sign_negative());
1020 assert!(!neg_zero.is_nan());
1021 assert!(!neg_zero.is_normal());
1022 assert_eq!(Fp::Zero, neg_zero.classify());
1025 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1028 let one: f64 = 1.0f64;
1029 assert_eq!(1.0, one);
1030 assert!(!one.is_infinite());
1031 assert!(one.is_finite());
1032 assert!(one.is_sign_positive());
1033 assert!(!one.is_sign_negative());
1034 assert!(!one.is_nan());
1035 assert!(one.is_normal());
1036 assert_eq!(Fp::Normal, one.classify());
1042 let inf: f64 = INFINITY;
1043 let neg_inf: f64 = NEG_INFINITY;
1044 assert!(nan.is_nan());
1045 assert!(!0.0f64.is_nan());
1046 assert!(!5.3f64.is_nan());
1047 assert!(!(-10.732f64).is_nan());
1048 assert!(!inf.is_nan());
1049 assert!(!neg_inf.is_nan());
1053 fn test_is_infinite() {
1055 let inf: f64 = INFINITY;
1056 let neg_inf: f64 = NEG_INFINITY;
1057 assert!(!nan.is_infinite());
1058 assert!(inf.is_infinite());
1059 assert!(neg_inf.is_infinite());
1060 assert!(!0.0f64.is_infinite());
1061 assert!(!42.8f64.is_infinite());
1062 assert!(!(-109.2f64).is_infinite());
1066 fn test_is_finite() {
1068 let inf: f64 = INFINITY;
1069 let neg_inf: f64 = NEG_INFINITY;
1070 assert!(!nan.is_finite());
1071 assert!(!inf.is_finite());
1072 assert!(!neg_inf.is_finite());
1073 assert!(0.0f64.is_finite());
1074 assert!(42.8f64.is_finite());
1075 assert!((-109.2f64).is_finite());
1078 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1080 fn test_is_normal() {
1082 let inf: f64 = INFINITY;
1083 let neg_inf: f64 = NEG_INFINITY;
1084 let zero: f64 = 0.0f64;
1085 let neg_zero: f64 = -0.0;
1086 assert!(!nan.is_normal());
1087 assert!(!inf.is_normal());
1088 assert!(!neg_inf.is_normal());
1089 assert!(!zero.is_normal());
1090 assert!(!neg_zero.is_normal());
1091 assert!(1f64.is_normal());
1092 assert!(1e-307f64.is_normal());
1093 assert!(!1e-308f64.is_normal());
1096 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1098 fn test_classify() {
1100 let inf: f64 = INFINITY;
1101 let neg_inf: f64 = NEG_INFINITY;
1102 let zero: f64 = 0.0f64;
1103 let neg_zero: f64 = -0.0;
1104 assert_eq!(nan.classify(), Fp::Nan);
1105 assert_eq!(inf.classify(), Fp::Infinite);
1106 assert_eq!(neg_inf.classify(), Fp::Infinite);
1107 assert_eq!(zero.classify(), Fp::Zero);
1108 assert_eq!(neg_zero.classify(), Fp::Zero);
1109 assert_eq!(1e-307f64.classify(), Fp::Normal);
1110 assert_eq!(1e-308f64.classify(), Fp::Subnormal);
1115 assert_approx_eq!(1.0f64.floor(), 1.0f64);
1116 assert_approx_eq!(1.3f64.floor(), 1.0f64);
1117 assert_approx_eq!(1.5f64.floor(), 1.0f64);
1118 assert_approx_eq!(1.7f64.floor(), 1.0f64);
1119 assert_approx_eq!(0.0f64.floor(), 0.0f64);
1120 assert_approx_eq!((-0.0f64).floor(), -0.0f64);
1121 assert_approx_eq!((-1.0f64).floor(), -1.0f64);
1122 assert_approx_eq!((-1.3f64).floor(), -2.0f64);
1123 assert_approx_eq!((-1.5f64).floor(), -2.0f64);
1124 assert_approx_eq!((-1.7f64).floor(), -2.0f64);
1129 assert_approx_eq!(1.0f64.ceil(), 1.0f64);
1130 assert_approx_eq!(1.3f64.ceil(), 2.0f64);
1131 assert_approx_eq!(1.5f64.ceil(), 2.0f64);
1132 assert_approx_eq!(1.7f64.ceil(), 2.0f64);
1133 assert_approx_eq!(0.0f64.ceil(), 0.0f64);
1134 assert_approx_eq!((-0.0f64).ceil(), -0.0f64);
1135 assert_approx_eq!((-1.0f64).ceil(), -1.0f64);
1136 assert_approx_eq!((-1.3f64).ceil(), -1.0f64);
1137 assert_approx_eq!((-1.5f64).ceil(), -1.0f64);
1138 assert_approx_eq!((-1.7f64).ceil(), -1.0f64);
1143 assert_approx_eq!(1.0f64.round(), 1.0f64);
1144 assert_approx_eq!(1.3f64.round(), 1.0f64);
1145 assert_approx_eq!(1.5f64.round(), 2.0f64);
1146 assert_approx_eq!(1.7f64.round(), 2.0f64);
1147 assert_approx_eq!(0.0f64.round(), 0.0f64);
1148 assert_approx_eq!((-0.0f64).round(), -0.0f64);
1149 assert_approx_eq!((-1.0f64).round(), -1.0f64);
1150 assert_approx_eq!((-1.3f64).round(), -1.0f64);
1151 assert_approx_eq!((-1.5f64).round(), -2.0f64);
1152 assert_approx_eq!((-1.7f64).round(), -2.0f64);
1157 assert_approx_eq!(1.0f64.trunc(), 1.0f64);
1158 assert_approx_eq!(1.3f64.trunc(), 1.0f64);
1159 assert_approx_eq!(1.5f64.trunc(), 1.0f64);
1160 assert_approx_eq!(1.7f64.trunc(), 1.0f64);
1161 assert_approx_eq!(0.0f64.trunc(), 0.0f64);
1162 assert_approx_eq!((-0.0f64).trunc(), -0.0f64);
1163 assert_approx_eq!((-1.0f64).trunc(), -1.0f64);
1164 assert_approx_eq!((-1.3f64).trunc(), -1.0f64);
1165 assert_approx_eq!((-1.5f64).trunc(), -1.0f64);
1166 assert_approx_eq!((-1.7f64).trunc(), -1.0f64);
1171 assert_approx_eq!(1.0f64.fract(), 0.0f64);
1172 assert_approx_eq!(1.3f64.fract(), 0.3f64);
1173 assert_approx_eq!(1.5f64.fract(), 0.5f64);
1174 assert_approx_eq!(1.7f64.fract(), 0.7f64);
1175 assert_approx_eq!(0.0f64.fract(), 0.0f64);
1176 assert_approx_eq!((-0.0f64).fract(), -0.0f64);
1177 assert_approx_eq!((-1.0f64).fract(), -0.0f64);
1178 assert_approx_eq!((-1.3f64).fract(), -0.3f64);
1179 assert_approx_eq!((-1.5f64).fract(), -0.5f64);
1180 assert_approx_eq!((-1.7f64).fract(), -0.7f64);
1185 assert_eq!(INFINITY.abs(), INFINITY);
1186 assert_eq!(1f64.abs(), 1f64);
1187 assert_eq!(0f64.abs(), 0f64);
1188 assert_eq!((-0f64).abs(), 0f64);
1189 assert_eq!((-1f64).abs(), 1f64);
1190 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1191 assert_eq!((1f64 / NEG_INFINITY).abs(), 0f64);
1192 assert!(NAN.abs().is_nan());
1197 assert_eq!(INFINITY.signum(), 1f64);
1198 assert_eq!(1f64.signum(), 1f64);
1199 assert_eq!(0f64.signum(), 1f64);
1200 assert_eq!((-0f64).signum(), -1f64);
1201 assert_eq!((-1f64).signum(), -1f64);
1202 assert_eq!(NEG_INFINITY.signum(), -1f64);
1203 assert_eq!((1f64 / NEG_INFINITY).signum(), -1f64);
1204 assert!(NAN.signum().is_nan());
1208 fn test_is_sign_positive() {
1209 assert!(INFINITY.is_sign_positive());
1210 assert!(1f64.is_sign_positive());
1211 assert!(0f64.is_sign_positive());
1212 assert!(!(-0f64).is_sign_positive());
1213 assert!(!(-1f64).is_sign_positive());
1214 assert!(!NEG_INFINITY.is_sign_positive());
1215 assert!(!(1f64 / NEG_INFINITY).is_sign_positive());
1216 assert!(NAN.is_sign_positive());
1217 assert!(!(-NAN).is_sign_positive());
1221 fn test_is_sign_negative() {
1222 assert!(!INFINITY.is_sign_negative());
1223 assert!(!1f64.is_sign_negative());
1224 assert!(!0f64.is_sign_negative());
1225 assert!((-0f64).is_sign_negative());
1226 assert!((-1f64).is_sign_negative());
1227 assert!(NEG_INFINITY.is_sign_negative());
1228 assert!((1f64 / NEG_INFINITY).is_sign_negative());
1229 assert!(!NAN.is_sign_negative());
1230 assert!((-NAN).is_sign_negative());
1236 let inf: f64 = INFINITY;
1237 let neg_inf: f64 = NEG_INFINITY;
1238 assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05);
1239 assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65);
1240 assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2);
1241 assert_approx_eq!(3.4f64.mul_add(-0.0, 5.6), 5.6);
1242 assert!(nan.mul_add(7.8, 9.0).is_nan());
1243 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1244 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1245 assert_eq!(8.9f64.mul_add(inf, 3.2), inf);
1246 assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf);
1252 let inf: f64 = INFINITY;
1253 let neg_inf: f64 = NEG_INFINITY;
1254 assert_eq!(1.0f64.recip(), 1.0);
1255 assert_eq!(2.0f64.recip(), 0.5);
1256 assert_eq!((-0.4f64).recip(), -2.5);
1257 assert_eq!(0.0f64.recip(), inf);
1258 assert!(nan.recip().is_nan());
1259 assert_eq!(inf.recip(), 0.0);
1260 assert_eq!(neg_inf.recip(), 0.0);
1266 let inf: f64 = INFINITY;
1267 let neg_inf: f64 = NEG_INFINITY;
1268 assert_eq!(1.0f64.powi(1), 1.0);
1269 assert_approx_eq!((-3.1f64).powi(2), 9.61);
1270 assert_approx_eq!(5.9f64.powi(-2), 0.028727);
1271 assert_eq!(8.3f64.powi(0), 1.0);
1272 assert!(nan.powi(2).is_nan());
1273 assert_eq!(inf.powi(3), inf);
1274 assert_eq!(neg_inf.powi(2), inf);
1280 let inf: f64 = INFINITY;
1281 let neg_inf: f64 = NEG_INFINITY;
1282 assert_eq!(1.0f64.powf(1.0), 1.0);
1283 assert_approx_eq!(3.4f64.powf(4.5), 246.408183);
1284 assert_approx_eq!(2.7f64.powf(-3.2), 0.041652);
1285 assert_approx_eq!((-3.1f64).powf(2.0), 9.61);
1286 assert_approx_eq!(5.9f64.powf(-2.0), 0.028727);
1287 assert_eq!(8.3f64.powf(0.0), 1.0);
1288 assert!(nan.powf(2.0).is_nan());
1289 assert_eq!(inf.powf(2.0), inf);
1290 assert_eq!(neg_inf.powf(3.0), neg_inf);
1294 fn test_sqrt_domain() {
1295 assert!(NAN.sqrt().is_nan());
1296 assert!(NEG_INFINITY.sqrt().is_nan());
1297 assert!((-1.0f64).sqrt().is_nan());
1298 assert_eq!((-0.0f64).sqrt(), -0.0);
1299 assert_eq!(0.0f64.sqrt(), 0.0);
1300 assert_eq!(1.0f64.sqrt(), 1.0);
1301 assert_eq!(INFINITY.sqrt(), INFINITY);
1306 assert_eq!(1.0, 0.0f64.exp());
1307 assert_approx_eq!(2.718282, 1.0f64.exp());
1308 assert_approx_eq!(148.413159, 5.0f64.exp());
1310 let inf: f64 = INFINITY;
1311 let neg_inf: f64 = NEG_INFINITY;
1313 assert_eq!(inf, inf.exp());
1314 assert_eq!(0.0, neg_inf.exp());
1315 assert!(nan.exp().is_nan());
1320 assert_eq!(32.0, 5.0f64.exp2());
1321 assert_eq!(1.0, 0.0f64.exp2());
1323 let inf: f64 = INFINITY;
1324 let neg_inf: f64 = NEG_INFINITY;
1326 assert_eq!(inf, inf.exp2());
1327 assert_eq!(0.0, neg_inf.exp2());
1328 assert!(nan.exp2().is_nan());
1334 let inf: f64 = INFINITY;
1335 let neg_inf: f64 = NEG_INFINITY;
1336 assert_approx_eq!(1.0f64.exp().ln(), 1.0);
1337 assert!(nan.ln().is_nan());
1338 assert_eq!(inf.ln(), inf);
1339 assert!(neg_inf.ln().is_nan());
1340 assert!((-2.3f64).ln().is_nan());
1341 assert_eq!((-0.0f64).ln(), neg_inf);
1342 assert_eq!(0.0f64.ln(), neg_inf);
1343 assert_approx_eq!(4.0f64.ln(), 1.386294);
1349 let inf: f64 = INFINITY;
1350 let neg_inf: f64 = NEG_INFINITY;
1351 assert_eq!(10.0f64.log(10.0), 1.0);
1352 assert_approx_eq!(2.3f64.log(3.5), 0.664858);
1353 assert_eq!(1.0f64.exp().log(1.0f64.exp()), 1.0);
1354 assert!(1.0f64.log(1.0).is_nan());
1355 assert!(1.0f64.log(-13.9).is_nan());
1356 assert!(nan.log(2.3).is_nan());
1357 assert_eq!(inf.log(10.0), inf);
1358 assert!(neg_inf.log(8.8).is_nan());
1359 assert!((-2.3f64).log(0.1).is_nan());
1360 assert_eq!((-0.0f64).log(2.0), neg_inf);
1361 assert_eq!(0.0f64.log(7.0), neg_inf);
1367 let inf: f64 = INFINITY;
1368 let neg_inf: f64 = NEG_INFINITY;
1369 assert_approx_eq!(10.0f64.log2(), 3.321928);
1370 assert_approx_eq!(2.3f64.log2(), 1.201634);
1371 assert_approx_eq!(1.0f64.exp().log2(), 1.442695);
1372 assert!(nan.log2().is_nan());
1373 assert_eq!(inf.log2(), inf);
1374 assert!(neg_inf.log2().is_nan());
1375 assert!((-2.3f64).log2().is_nan());
1376 assert_eq!((-0.0f64).log2(), neg_inf);
1377 assert_eq!(0.0f64.log2(), neg_inf);
1383 let inf: f64 = INFINITY;
1384 let neg_inf: f64 = NEG_INFINITY;
1385 assert_eq!(10.0f64.log10(), 1.0);
1386 assert_approx_eq!(2.3f64.log10(), 0.361728);
1387 assert_approx_eq!(1.0f64.exp().log10(), 0.434294);
1388 assert_eq!(1.0f64.log10(), 0.0);
1389 assert!(nan.log10().is_nan());
1390 assert_eq!(inf.log10(), inf);
1391 assert!(neg_inf.log10().is_nan());
1392 assert!((-2.3f64).log10().is_nan());
1393 assert_eq!((-0.0f64).log10(), neg_inf);
1394 assert_eq!(0.0f64.log10(), neg_inf);
1398 fn test_to_degrees() {
1399 let pi: f64 = consts::PI;
1401 let inf: f64 = INFINITY;
1402 let neg_inf: f64 = NEG_INFINITY;
1403 assert_eq!(0.0f64.to_degrees(), 0.0);
1404 assert_approx_eq!((-5.8f64).to_degrees(), -332.315521);
1405 assert_eq!(pi.to_degrees(), 180.0);
1406 assert!(nan.to_degrees().is_nan());
1407 assert_eq!(inf.to_degrees(), inf);
1408 assert_eq!(neg_inf.to_degrees(), neg_inf);
1412 fn test_to_radians() {
1413 let pi: f64 = consts::PI;
1415 let inf: f64 = INFINITY;
1416 let neg_inf: f64 = NEG_INFINITY;
1417 assert_eq!(0.0f64.to_radians(), 0.0);
1418 assert_approx_eq!(154.6f64.to_radians(), 2.698279);
1419 assert_approx_eq!((-332.31f64).to_radians(), -5.799903);
1420 assert_eq!(180.0f64.to_radians(), pi);
1421 assert!(nan.to_radians().is_nan());
1422 assert_eq!(inf.to_radians(), inf);
1423 assert_eq!(neg_inf.to_radians(), neg_inf);
1428 assert_eq!(0.0f64.asinh(), 0.0f64);
1429 assert_eq!((-0.0f64).asinh(), -0.0f64);
1431 let inf: f64 = INFINITY;
1432 let neg_inf: f64 = NEG_INFINITY;
1434 assert_eq!(inf.asinh(), inf);
1435 assert_eq!(neg_inf.asinh(), neg_inf);
1436 assert!(nan.asinh().is_nan());
1437 assert!((-0.0f64).asinh().is_sign_negative());
1439 assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64);
1440 assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
1445 assert_eq!(1.0f64.acosh(), 0.0f64);
1446 assert!(0.999f64.acosh().is_nan());
1448 let inf: f64 = INFINITY;
1449 let neg_inf: f64 = NEG_INFINITY;
1451 assert_eq!(inf.acosh(), inf);
1452 assert!(neg_inf.acosh().is_nan());
1453 assert!(nan.acosh().is_nan());
1454 assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
1455 assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
1460 assert_eq!(0.0f64.atanh(), 0.0f64);
1461 assert_eq!((-0.0f64).atanh(), -0.0f64);
1463 let inf: f64 = INFINITY;
1464 let neg_inf: f64 = NEG_INFINITY;
1466 assert_eq!(1.0f64.atanh(), inf);
1467 assert_eq!((-1.0f64).atanh(), neg_inf);
1468 assert!(2f64.atanh().atanh().is_nan());
1469 assert!((-2f64).atanh().atanh().is_nan());
1470 assert!(inf.atanh().is_nan());
1471 assert!(neg_inf.atanh().is_nan());
1472 assert!(nan.atanh().is_nan());
1473 assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64);
1474 assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64);
1478 fn test_real_consts() {
1480 let pi: f64 = consts::PI;
1481 let frac_pi_2: f64 = consts::FRAC_PI_2;
1482 let frac_pi_3: f64 = consts::FRAC_PI_3;
1483 let frac_pi_4: f64 = consts::FRAC_PI_4;
1484 let frac_pi_6: f64 = consts::FRAC_PI_6;
1485 let frac_pi_8: f64 = consts::FRAC_PI_8;
1486 let frac_1_pi: f64 = consts::FRAC_1_PI;
1487 let frac_2_pi: f64 = consts::FRAC_2_PI;
1488 let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRT_PI;
1489 let sqrt2: f64 = consts::SQRT_2;
1490 let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT_2;
1491 let e: f64 = consts::E;
1492 let log2_e: f64 = consts::LOG2_E;
1493 let log10_e: f64 = consts::LOG10_E;
1494 let ln_2: f64 = consts::LN_2;
1495 let ln_10: f64 = consts::LN_10;
1497 assert_approx_eq!(frac_pi_2, pi / 2f64);
1498 assert_approx_eq!(frac_pi_3, pi / 3f64);
1499 assert_approx_eq!(frac_pi_4, pi / 4f64);
1500 assert_approx_eq!(frac_pi_6, pi / 6f64);
1501 assert_approx_eq!(frac_pi_8, pi / 8f64);
1502 assert_approx_eq!(frac_1_pi, 1f64 / pi);
1503 assert_approx_eq!(frac_2_pi, 2f64 / pi);
1504 assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt());
1505 assert_approx_eq!(sqrt2, 2f64.sqrt());
1506 assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt());
1507 assert_approx_eq!(log2_e, e.log2());
1508 assert_approx_eq!(log10_e, e.log10());
1509 assert_approx_eq!(ln_2, 2f64.ln());
1510 assert_approx_eq!(ln_10, 10f64.ln());
1514 fn test_float_bits_conv() {
1515 assert_eq!((1f64).to_bits(), 0x3ff0000000000000);
1516 assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
1517 assert_eq!((1337f64).to_bits(), 0x4094e40000000000);
1518 assert_eq!((-14.25f64).to_bits(), 0xc02c800000000000);
1519 assert_approx_eq!(f64::from_bits(0x3ff0000000000000), 1.0);
1520 assert_approx_eq!(f64::from_bits(0x4029000000000000), 12.5);
1521 assert_approx_eq!(f64::from_bits(0x4094e40000000000), 1337.0);
1522 assert_approx_eq!(f64::from_bits(0xc02c800000000000), -14.25);
1524 // Check that NaNs roundtrip their bits regardless of signalingness
1525 // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits
1526 let masked_nan1 = f64::NAN.to_bits() ^ 0x000A_AAAA_AAAA_AAAA;
1527 let masked_nan2 = f64::NAN.to_bits() ^ 0x0005_5555_5555_5555;
1528 assert!(f64::from_bits(masked_nan1).is_nan());
1529 assert!(f64::from_bits(masked_nan2).is_nan());
1531 assert_eq!(f64::from_bits(masked_nan1).to_bits(), masked_nan1);
1532 assert_eq!(f64::from_bits(masked_nan2).to_bits(), masked_nan2);
1537 fn test_clamp_min_greater_than_max() {
1538 1.0f64.clamp(3.0, 1.0);
1543 fn test_clamp_min_is_nan() {
1544 1.0f64.clamp(NAN, 1.0);
1549 fn test_clamp_max_is_nan() {
1550 1.0f64.clamp(3.0, NAN);