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)]
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.
38 /// assert_eq!(f.floor(), 3.0);
39 /// assert_eq!(g.floor(), 3.0);
41 #[stable(feature = "rust1", since = "1.0.0")]
43 pub fn floor(self) -> f64 {
44 unsafe { intrinsics::floorf64(self) }
47 /// Returns the smallest integer greater than or equal to a number.
55 /// assert_eq!(f.ceil(), 4.0);
56 /// assert_eq!(g.ceil(), 4.0);
58 #[stable(feature = "rust1", since = "1.0.0")]
60 pub fn ceil(self) -> f64 {
61 unsafe { intrinsics::ceilf64(self) }
64 /// Returns the nearest integer to a number. Round half-way cases away from
73 /// assert_eq!(f.round(), 3.0);
74 /// assert_eq!(g.round(), -3.0);
76 #[stable(feature = "rust1", since = "1.0.0")]
78 pub fn round(self) -> f64 {
79 unsafe { intrinsics::roundf64(self) }
82 /// Returns the integer part of a number.
90 /// assert_eq!(f.trunc(), 3.0);
91 /// assert_eq!(g.trunc(), -3.0);
93 #[stable(feature = "rust1", since = "1.0.0")]
95 pub fn trunc(self) -> f64 {
96 unsafe { intrinsics::truncf64(self) }
99 /// Returns the fractional part of a number.
105 /// let y = -3.5_f64;
106 /// let abs_difference_x = (x.fract() - 0.5).abs();
107 /// let abs_difference_y = (y.fract() - (-0.5)).abs();
109 /// assert!(abs_difference_x < 1e-10);
110 /// assert!(abs_difference_y < 1e-10);
112 #[stable(feature = "rust1", since = "1.0.0")]
114 pub fn fract(self) -> f64 { self - self.trunc() }
116 /// Computes the absolute value of `self`. Returns `NAN` if the
125 /// let y = -3.5_f64;
127 /// let abs_difference_x = (x.abs() - x).abs();
128 /// let abs_difference_y = (y.abs() - (-y)).abs();
130 /// assert!(abs_difference_x < 1e-10);
131 /// assert!(abs_difference_y < 1e-10);
133 /// assert!(f64::NAN.abs().is_nan());
135 #[stable(feature = "rust1", since = "1.0.0")]
137 pub fn abs(self) -> f64 {
138 unsafe { intrinsics::fabsf64(self) }
141 /// Returns a number that represents the sign of `self`.
143 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
144 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
145 /// - `NAN` if the number is `NAN`
154 /// assert_eq!(f.signum(), 1.0);
155 /// assert_eq!(f64::NEG_INFINITY.signum(), -1.0);
157 /// assert!(f64::NAN.signum().is_nan());
159 #[stable(feature = "rust1", since = "1.0.0")]
161 pub fn signum(self) -> f64 {
165 unsafe { intrinsics::copysignf64(1.0, self) }
169 /// Returns a number composed of the magnitude of `self` and the sign of
172 /// Equal to `self` if the sign of `self` and `y` are the same, otherwise
173 /// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of
179 /// #![feature(copysign)]
184 /// assert_eq!(f.copysign(0.42), 3.5_f64);
185 /// assert_eq!(f.copysign(-0.42), -3.5_f64);
186 /// assert_eq!((-f).copysign(0.42), 3.5_f64);
187 /// assert_eq!((-f).copysign(-0.42), -3.5_f64);
189 /// assert!(f64::NAN.copysign(1.0).is_nan());
193 #[unstable(feature="copysign", issue="55169")]
194 pub fn copysign(self, y: f64) -> f64 {
195 unsafe { intrinsics::copysignf64(self, y) }
198 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
199 /// error, yielding a more accurate result than an unfused multiply-add.
201 /// Using `mul_add` can be more performant than an unfused multiply-add if
202 /// the target architecture has a dedicated `fma` CPU instruction.
207 /// let m = 10.0_f64;
209 /// let b = 60.0_f64;
212 /// let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs();
214 /// assert!(abs_difference < 1e-10);
216 #[stable(feature = "rust1", since = "1.0.0")]
218 pub fn mul_add(self, a: f64, b: f64) -> f64 {
219 unsafe { intrinsics::fmaf64(self, a, b) }
222 /// Calculates Euclidean division, the matching method for `rem_euclid`.
224 /// This computes the integer `n` such that
225 /// `self = n * rhs + self.rem_euclid(rhs)`.
226 /// In other words, the result is `self / rhs` rounded to the integer `n`
227 /// such that `self >= n * rhs`.
232 /// #![feature(euclidean_division)]
233 /// let a: f64 = 7.0;
235 /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
236 /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
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
241 #[unstable(feature = "euclidean_division", issue = "49048")]
242 pub fn div_euclid(self, rhs: f64) -> f64 {
243 let q = (self / rhs).trunc();
244 if self % rhs < 0.0 {
245 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 }
250 /// Calculates the least nonnegative remainder of `self (mod rhs)`.
252 /// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
253 /// most cases. However, due to a floating point round-off error it can
254 /// result in `r == rhs.abs()`, violating the mathematical definition, if
255 /// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
256 /// This result is not an element of the function's codomain, but it is the
257 /// closest floating point number in the real numbers and thus fulfills the
258 /// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
264 /// #![feature(euclidean_division)]
265 /// let a: f64 = 7.0;
267 /// assert_eq!(a.rem_euclid(b), 3.0);
268 /// assert_eq!((-a).rem_euclid(b), 1.0);
269 /// assert_eq!(a.rem_euclid(-b), 3.0);
270 /// assert_eq!((-a).rem_euclid(-b), 1.0);
271 /// // limitation due to round-off error
272 /// assert!((-std::f64::EPSILON).rem_euclid(3.0) != 0.0);
275 #[unstable(feature = "euclidean_division", issue = "49048")]
276 pub fn rem_euclid(self, rhs: f64) -> f64 {
285 /// Raises a number to an integer power.
287 /// Using this function is generally faster than using `powf`
293 /// let abs_difference = (x.powi(2) - x*x).abs();
295 /// assert!(abs_difference < 1e-10);
297 #[stable(feature = "rust1", since = "1.0.0")]
299 pub fn powi(self, n: i32) -> f64 {
300 unsafe { intrinsics::powif64(self, n) }
303 /// Raises a number to a floating point power.
309 /// let abs_difference = (x.powf(2.0) - x*x).abs();
311 /// assert!(abs_difference < 1e-10);
313 #[stable(feature = "rust1", since = "1.0.0")]
315 pub fn powf(self, n: f64) -> f64 {
316 unsafe { intrinsics::powf64(self, n) }
319 /// Takes the square root of a number.
321 /// Returns NaN if `self` is a negative number.
326 /// let positive = 4.0_f64;
327 /// let negative = -4.0_f64;
329 /// let abs_difference = (positive.sqrt() - 2.0).abs();
331 /// assert!(abs_difference < 1e-10);
332 /// assert!(negative.sqrt().is_nan());
334 #[stable(feature = "rust1", since = "1.0.0")]
336 pub fn sqrt(self) -> f64 {
340 unsafe { intrinsics::sqrtf64(self) }
344 /// Returns `e^(self)`, (the exponential function).
349 /// let one = 1.0_f64;
351 /// let e = one.exp();
353 /// // ln(e) - 1 == 0
354 /// let abs_difference = (e.ln() - 1.0).abs();
356 /// assert!(abs_difference < 1e-10);
358 #[stable(feature = "rust1", since = "1.0.0")]
360 pub fn exp(self) -> f64 {
361 unsafe { intrinsics::expf64(self) }
364 /// Returns `2^(self)`.
372 /// let abs_difference = (f.exp2() - 4.0).abs();
374 /// assert!(abs_difference < 1e-10);
376 #[stable(feature = "rust1", since = "1.0.0")]
378 pub fn exp2(self) -> f64 {
379 unsafe { intrinsics::exp2f64(self) }
382 /// Returns the natural logarithm of the number.
387 /// let one = 1.0_f64;
389 /// let e = one.exp();
391 /// // ln(e) - 1 == 0
392 /// let abs_difference = (e.ln() - 1.0).abs();
394 /// assert!(abs_difference < 1e-10);
396 #[stable(feature = "rust1", since = "1.0.0")]
398 pub fn ln(self) -> f64 {
399 self.log_wrapper(|n| { unsafe { intrinsics::logf64(n) } })
402 /// Returns the logarithm of the number with respect to an arbitrary base.
404 /// The result may not be correctly rounded owing to implementation details;
405 /// `self.log2()` can produce more accurate results for base 2, and
406 /// `self.log10()` can produce more accurate results for base 10.
411 /// let five = 5.0_f64;
413 /// // log5(5) - 1 == 0
414 /// let abs_difference = (five.log(5.0) - 1.0).abs();
416 /// assert!(abs_difference < 1e-10);
418 #[stable(feature = "rust1", since = "1.0.0")]
420 pub fn log(self, base: f64) -> f64 { self.ln() / base.ln() }
422 /// Returns the base 2 logarithm of the number.
427 /// let two = 2.0_f64;
429 /// // log2(2) - 1 == 0
430 /// let abs_difference = (two.log2() - 1.0).abs();
432 /// assert!(abs_difference < 1e-10);
434 #[stable(feature = "rust1", since = "1.0.0")]
436 pub fn log2(self) -> f64 {
437 self.log_wrapper(|n| {
438 #[cfg(target_os = "android")]
439 return ::sys::android::log2f64(n);
440 #[cfg(not(target_os = "android"))]
441 return unsafe { intrinsics::log2f64(n) };
445 /// Returns the base 10 logarithm of the number.
450 /// let ten = 10.0_f64;
452 /// // log10(10) - 1 == 0
453 /// let abs_difference = (ten.log10() - 1.0).abs();
455 /// assert!(abs_difference < 1e-10);
457 #[stable(feature = "rust1", since = "1.0.0")]
459 pub fn log10(self) -> f64 {
460 self.log_wrapper(|n| { unsafe { intrinsics::log10f64(n) } })
463 /// The positive difference of two numbers.
465 /// * If `self <= other`: `0:0`
466 /// * Else: `self - other`
472 /// let y = -3.0_f64;
474 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
475 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
477 /// assert!(abs_difference_x < 1e-10);
478 /// assert!(abs_difference_y < 1e-10);
480 #[stable(feature = "rust1", since = "1.0.0")]
482 #[rustc_deprecated(since = "1.10.0",
483 reason = "you probably meant `(self - other).abs()`: \
484 this operation is `(self - other).max(0.0)` \
485 except that `abs_sub` also propagates NaNs (also \
486 known as `fdim` in C). If you truly need the positive \
487 difference, consider using that expression or the C function \
488 `fdim`, depending on how you wish to handle NaN (please consider \
489 filing an issue describing your use-case too).")]
490 pub fn abs_sub(self, other: f64) -> f64 {
491 unsafe { cmath::fdim(self, other) }
494 /// Takes the cubic root of a number.
501 /// // x^(1/3) - 2 == 0
502 /// let abs_difference = (x.cbrt() - 2.0).abs();
504 /// assert!(abs_difference < 1e-10);
506 #[stable(feature = "rust1", since = "1.0.0")]
508 pub fn cbrt(self) -> f64 {
509 unsafe { cmath::cbrt(self) }
512 /// Calculates the length of the hypotenuse of a right-angle triangle given
513 /// legs of length `x` and `y`.
521 /// // sqrt(x^2 + y^2)
522 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
524 /// assert!(abs_difference < 1e-10);
526 #[stable(feature = "rust1", since = "1.0.0")]
528 pub fn hypot(self, other: f64) -> f64 {
529 unsafe { cmath::hypot(self, other) }
532 /// Computes the sine of a number (in radians).
539 /// let x = f64::consts::PI/2.0;
541 /// let abs_difference = (x.sin() - 1.0).abs();
543 /// assert!(abs_difference < 1e-10);
545 #[stable(feature = "rust1", since = "1.0.0")]
547 pub fn sin(self) -> f64 {
548 unsafe { intrinsics::sinf64(self) }
551 /// Computes the cosine of a number (in radians).
558 /// let x = 2.0*f64::consts::PI;
560 /// let abs_difference = (x.cos() - 1.0).abs();
562 /// assert!(abs_difference < 1e-10);
564 #[stable(feature = "rust1", since = "1.0.0")]
566 pub fn cos(self) -> f64 {
567 unsafe { intrinsics::cosf64(self) }
570 /// Computes the tangent of a number (in radians).
577 /// let x = f64::consts::PI/4.0;
578 /// let abs_difference = (x.tan() - 1.0).abs();
580 /// assert!(abs_difference < 1e-14);
582 #[stable(feature = "rust1", since = "1.0.0")]
584 pub fn tan(self) -> f64 {
585 unsafe { cmath::tan(self) }
588 /// Computes the arcsine of a number. Return value is in radians in
589 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
597 /// let f = f64::consts::PI / 2.0;
599 /// // asin(sin(pi/2))
600 /// let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs();
602 /// assert!(abs_difference < 1e-10);
604 #[stable(feature = "rust1", since = "1.0.0")]
606 pub fn asin(self) -> f64 {
607 unsafe { cmath::asin(self) }
610 /// Computes the arccosine of a number. Return value is in radians in
611 /// the range [0, pi] or NaN if the number is outside the range
619 /// let f = f64::consts::PI / 4.0;
621 /// // acos(cos(pi/4))
622 /// let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs();
624 /// assert!(abs_difference < 1e-10);
626 #[stable(feature = "rust1", since = "1.0.0")]
628 pub fn acos(self) -> f64 {
629 unsafe { cmath::acos(self) }
632 /// Computes the arctangent of a number. Return value is in radians in the
633 /// range [-pi/2, pi/2];
641 /// let abs_difference = (f.tan().atan() - 1.0).abs();
643 /// assert!(abs_difference < 1e-10);
645 #[stable(feature = "rust1", since = "1.0.0")]
647 pub fn atan(self) -> f64 {
648 unsafe { cmath::atan(self) }
651 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
653 /// * `x = 0`, `y = 0`: `0`
654 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
655 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
656 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
663 /// let pi = f64::consts::PI;
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) - (-pi/4.0)).abs();
675 /// let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).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::PI/4.0;
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()
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 {
857 x => (x + ((x * x) - 1.0).sqrt()).ln(),
861 /// Inverse hyperbolic tangent function.
868 /// let e = f64::consts::E;
869 /// let f = e.tanh().atanh();
871 /// let abs_difference = (f - e).abs();
873 /// assert!(abs_difference < 1.0e-10);
875 #[stable(feature = "rust1", since = "1.0.0")]
877 pub fn atanh(self) -> f64 {
878 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
881 // Solaris/Illumos requires a wrapper around log, log2, and log10 functions
882 // because of their non-standard behavior (e.g., log(-n) returns -Inf instead
884 fn log_wrapper<F: Fn(f64) -> f64>(self, log_fn: F) -> f64 {
885 if !cfg!(target_os = "solaris") {
888 if self.is_finite() {
891 } else if self == 0.0 {
892 NEG_INFINITY // log(0) = -Inf
896 } else if self.is_nan() {
897 self // log(NaN) = NaN
898 } else if self > 0.0 {
899 self // log(Inf) = Inf
901 NAN // log(-Inf) = NaN
912 use num::FpCategory as Fp;
916 test_num(10f64, 2f64);
921 assert_eq!(NAN.min(2.0), 2.0);
922 assert_eq!(2.0f64.min(NAN), 2.0);
927 assert_eq!(NAN.max(2.0), 2.0);
928 assert_eq!(2.0f64.max(NAN), 2.0);
934 assert!(nan.is_nan());
935 assert!(!nan.is_infinite());
936 assert!(!nan.is_finite());
937 assert!(!nan.is_normal());
938 assert!(nan.is_sign_positive());
939 assert!(!nan.is_sign_negative());
940 assert_eq!(Fp::Nan, nan.classify());
945 let inf: f64 = INFINITY;
946 assert!(inf.is_infinite());
947 assert!(!inf.is_finite());
948 assert!(inf.is_sign_positive());
949 assert!(!inf.is_sign_negative());
950 assert!(!inf.is_nan());
951 assert!(!inf.is_normal());
952 assert_eq!(Fp::Infinite, inf.classify());
956 fn test_neg_infinity() {
957 let neg_inf: f64 = NEG_INFINITY;
958 assert!(neg_inf.is_infinite());
959 assert!(!neg_inf.is_finite());
960 assert!(!neg_inf.is_sign_positive());
961 assert!(neg_inf.is_sign_negative());
962 assert!(!neg_inf.is_nan());
963 assert!(!neg_inf.is_normal());
964 assert_eq!(Fp::Infinite, neg_inf.classify());
969 let zero: f64 = 0.0f64;
970 assert_eq!(0.0, zero);
971 assert!(!zero.is_infinite());
972 assert!(zero.is_finite());
973 assert!(zero.is_sign_positive());
974 assert!(!zero.is_sign_negative());
975 assert!(!zero.is_nan());
976 assert!(!zero.is_normal());
977 assert_eq!(Fp::Zero, zero.classify());
982 let neg_zero: f64 = -0.0;
983 assert_eq!(0.0, neg_zero);
984 assert!(!neg_zero.is_infinite());
985 assert!(neg_zero.is_finite());
986 assert!(!neg_zero.is_sign_positive());
987 assert!(neg_zero.is_sign_negative());
988 assert!(!neg_zero.is_nan());
989 assert!(!neg_zero.is_normal());
990 assert_eq!(Fp::Zero, neg_zero.classify());
993 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
996 let one: f64 = 1.0f64;
997 assert_eq!(1.0, one);
998 assert!(!one.is_infinite());
999 assert!(one.is_finite());
1000 assert!(one.is_sign_positive());
1001 assert!(!one.is_sign_negative());
1002 assert!(!one.is_nan());
1003 assert!(one.is_normal());
1004 assert_eq!(Fp::Normal, one.classify());
1010 let inf: f64 = INFINITY;
1011 let neg_inf: f64 = NEG_INFINITY;
1012 assert!(nan.is_nan());
1013 assert!(!0.0f64.is_nan());
1014 assert!(!5.3f64.is_nan());
1015 assert!(!(-10.732f64).is_nan());
1016 assert!(!inf.is_nan());
1017 assert!(!neg_inf.is_nan());
1021 fn test_is_infinite() {
1023 let inf: f64 = INFINITY;
1024 let neg_inf: f64 = NEG_INFINITY;
1025 assert!(!nan.is_infinite());
1026 assert!(inf.is_infinite());
1027 assert!(neg_inf.is_infinite());
1028 assert!(!0.0f64.is_infinite());
1029 assert!(!42.8f64.is_infinite());
1030 assert!(!(-109.2f64).is_infinite());
1034 fn test_is_finite() {
1036 let inf: f64 = INFINITY;
1037 let neg_inf: f64 = NEG_INFINITY;
1038 assert!(!nan.is_finite());
1039 assert!(!inf.is_finite());
1040 assert!(!neg_inf.is_finite());
1041 assert!(0.0f64.is_finite());
1042 assert!(42.8f64.is_finite());
1043 assert!((-109.2f64).is_finite());
1046 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1048 fn test_is_normal() {
1050 let inf: f64 = INFINITY;
1051 let neg_inf: f64 = NEG_INFINITY;
1052 let zero: f64 = 0.0f64;
1053 let neg_zero: f64 = -0.0;
1054 assert!(!nan.is_normal());
1055 assert!(!inf.is_normal());
1056 assert!(!neg_inf.is_normal());
1057 assert!(!zero.is_normal());
1058 assert!(!neg_zero.is_normal());
1059 assert!(1f64.is_normal());
1060 assert!(1e-307f64.is_normal());
1061 assert!(!1e-308f64.is_normal());
1064 #[cfg_attr(all(target_arch = "wasm32", target_os = "emscripten"), ignore)] // issue 42630
1066 fn test_classify() {
1068 let inf: f64 = INFINITY;
1069 let neg_inf: f64 = NEG_INFINITY;
1070 let zero: f64 = 0.0f64;
1071 let neg_zero: f64 = -0.0;
1072 assert_eq!(nan.classify(), Fp::Nan);
1073 assert_eq!(inf.classify(), Fp::Infinite);
1074 assert_eq!(neg_inf.classify(), Fp::Infinite);
1075 assert_eq!(zero.classify(), Fp::Zero);
1076 assert_eq!(neg_zero.classify(), Fp::Zero);
1077 assert_eq!(1e-307f64.classify(), Fp::Normal);
1078 assert_eq!(1e-308f64.classify(), Fp::Subnormal);
1083 assert_approx_eq!(1.0f64.floor(), 1.0f64);
1084 assert_approx_eq!(1.3f64.floor(), 1.0f64);
1085 assert_approx_eq!(1.5f64.floor(), 1.0f64);
1086 assert_approx_eq!(1.7f64.floor(), 1.0f64);
1087 assert_approx_eq!(0.0f64.floor(), 0.0f64);
1088 assert_approx_eq!((-0.0f64).floor(), -0.0f64);
1089 assert_approx_eq!((-1.0f64).floor(), -1.0f64);
1090 assert_approx_eq!((-1.3f64).floor(), -2.0f64);
1091 assert_approx_eq!((-1.5f64).floor(), -2.0f64);
1092 assert_approx_eq!((-1.7f64).floor(), -2.0f64);
1097 assert_approx_eq!(1.0f64.ceil(), 1.0f64);
1098 assert_approx_eq!(1.3f64.ceil(), 2.0f64);
1099 assert_approx_eq!(1.5f64.ceil(), 2.0f64);
1100 assert_approx_eq!(1.7f64.ceil(), 2.0f64);
1101 assert_approx_eq!(0.0f64.ceil(), 0.0f64);
1102 assert_approx_eq!((-0.0f64).ceil(), -0.0f64);
1103 assert_approx_eq!((-1.0f64).ceil(), -1.0f64);
1104 assert_approx_eq!((-1.3f64).ceil(), -1.0f64);
1105 assert_approx_eq!((-1.5f64).ceil(), -1.0f64);
1106 assert_approx_eq!((-1.7f64).ceil(), -1.0f64);
1111 assert_approx_eq!(1.0f64.round(), 1.0f64);
1112 assert_approx_eq!(1.3f64.round(), 1.0f64);
1113 assert_approx_eq!(1.5f64.round(), 2.0f64);
1114 assert_approx_eq!(1.7f64.round(), 2.0f64);
1115 assert_approx_eq!(0.0f64.round(), 0.0f64);
1116 assert_approx_eq!((-0.0f64).round(), -0.0f64);
1117 assert_approx_eq!((-1.0f64).round(), -1.0f64);
1118 assert_approx_eq!((-1.3f64).round(), -1.0f64);
1119 assert_approx_eq!((-1.5f64).round(), -2.0f64);
1120 assert_approx_eq!((-1.7f64).round(), -2.0f64);
1125 assert_approx_eq!(1.0f64.trunc(), 1.0f64);
1126 assert_approx_eq!(1.3f64.trunc(), 1.0f64);
1127 assert_approx_eq!(1.5f64.trunc(), 1.0f64);
1128 assert_approx_eq!(1.7f64.trunc(), 1.0f64);
1129 assert_approx_eq!(0.0f64.trunc(), 0.0f64);
1130 assert_approx_eq!((-0.0f64).trunc(), -0.0f64);
1131 assert_approx_eq!((-1.0f64).trunc(), -1.0f64);
1132 assert_approx_eq!((-1.3f64).trunc(), -1.0f64);
1133 assert_approx_eq!((-1.5f64).trunc(), -1.0f64);
1134 assert_approx_eq!((-1.7f64).trunc(), -1.0f64);
1139 assert_approx_eq!(1.0f64.fract(), 0.0f64);
1140 assert_approx_eq!(1.3f64.fract(), 0.3f64);
1141 assert_approx_eq!(1.5f64.fract(), 0.5f64);
1142 assert_approx_eq!(1.7f64.fract(), 0.7f64);
1143 assert_approx_eq!(0.0f64.fract(), 0.0f64);
1144 assert_approx_eq!((-0.0f64).fract(), -0.0f64);
1145 assert_approx_eq!((-1.0f64).fract(), -0.0f64);
1146 assert_approx_eq!((-1.3f64).fract(), -0.3f64);
1147 assert_approx_eq!((-1.5f64).fract(), -0.5f64);
1148 assert_approx_eq!((-1.7f64).fract(), -0.7f64);
1153 assert_eq!(INFINITY.abs(), INFINITY);
1154 assert_eq!(1f64.abs(), 1f64);
1155 assert_eq!(0f64.abs(), 0f64);
1156 assert_eq!((-0f64).abs(), 0f64);
1157 assert_eq!((-1f64).abs(), 1f64);
1158 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1159 assert_eq!((1f64/NEG_INFINITY).abs(), 0f64);
1160 assert!(NAN.abs().is_nan());
1165 assert_eq!(INFINITY.signum(), 1f64);
1166 assert_eq!(1f64.signum(), 1f64);
1167 assert_eq!(0f64.signum(), 1f64);
1168 assert_eq!((-0f64).signum(), -1f64);
1169 assert_eq!((-1f64).signum(), -1f64);
1170 assert_eq!(NEG_INFINITY.signum(), -1f64);
1171 assert_eq!((1f64/NEG_INFINITY).signum(), -1f64);
1172 assert!(NAN.signum().is_nan());
1176 fn test_is_sign_positive() {
1177 assert!(INFINITY.is_sign_positive());
1178 assert!(1f64.is_sign_positive());
1179 assert!(0f64.is_sign_positive());
1180 assert!(!(-0f64).is_sign_positive());
1181 assert!(!(-1f64).is_sign_positive());
1182 assert!(!NEG_INFINITY.is_sign_positive());
1183 assert!(!(1f64/NEG_INFINITY).is_sign_positive());
1184 assert!(NAN.is_sign_positive());
1185 assert!(!(-NAN).is_sign_positive());
1189 fn test_is_sign_negative() {
1190 assert!(!INFINITY.is_sign_negative());
1191 assert!(!1f64.is_sign_negative());
1192 assert!(!0f64.is_sign_negative());
1193 assert!((-0f64).is_sign_negative());
1194 assert!((-1f64).is_sign_negative());
1195 assert!(NEG_INFINITY.is_sign_negative());
1196 assert!((1f64/NEG_INFINITY).is_sign_negative());
1197 assert!(!NAN.is_sign_negative());
1198 assert!((-NAN).is_sign_negative());
1204 let inf: f64 = INFINITY;
1205 let neg_inf: f64 = NEG_INFINITY;
1206 assert_approx_eq!(12.3f64.mul_add(4.5, 6.7), 62.05);
1207 assert_approx_eq!((-12.3f64).mul_add(-4.5, -6.7), 48.65);
1208 assert_approx_eq!(0.0f64.mul_add(8.9, 1.2), 1.2);
1209 assert_approx_eq!(3.4f64.mul_add(-0.0, 5.6), 5.6);
1210 assert!(nan.mul_add(7.8, 9.0).is_nan());
1211 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1212 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1213 assert_eq!(8.9f64.mul_add(inf, 3.2), inf);
1214 assert_eq!((-3.2f64).mul_add(2.4, neg_inf), neg_inf);
1220 let inf: f64 = INFINITY;
1221 let neg_inf: f64 = NEG_INFINITY;
1222 assert_eq!(1.0f64.recip(), 1.0);
1223 assert_eq!(2.0f64.recip(), 0.5);
1224 assert_eq!((-0.4f64).recip(), -2.5);
1225 assert_eq!(0.0f64.recip(), inf);
1226 assert!(nan.recip().is_nan());
1227 assert_eq!(inf.recip(), 0.0);
1228 assert_eq!(neg_inf.recip(), 0.0);
1234 let inf: f64 = INFINITY;
1235 let neg_inf: f64 = NEG_INFINITY;
1236 assert_eq!(1.0f64.powi(1), 1.0);
1237 assert_approx_eq!((-3.1f64).powi(2), 9.61);
1238 assert_approx_eq!(5.9f64.powi(-2), 0.028727);
1239 assert_eq!(8.3f64.powi(0), 1.0);
1240 assert!(nan.powi(2).is_nan());
1241 assert_eq!(inf.powi(3), inf);
1242 assert_eq!(neg_inf.powi(2), inf);
1248 let inf: f64 = INFINITY;
1249 let neg_inf: f64 = NEG_INFINITY;
1250 assert_eq!(1.0f64.powf(1.0), 1.0);
1251 assert_approx_eq!(3.4f64.powf(4.5), 246.408183);
1252 assert_approx_eq!(2.7f64.powf(-3.2), 0.041652);
1253 assert_approx_eq!((-3.1f64).powf(2.0), 9.61);
1254 assert_approx_eq!(5.9f64.powf(-2.0), 0.028727);
1255 assert_eq!(8.3f64.powf(0.0), 1.0);
1256 assert!(nan.powf(2.0).is_nan());
1257 assert_eq!(inf.powf(2.0), inf);
1258 assert_eq!(neg_inf.powf(3.0), neg_inf);
1262 fn test_sqrt_domain() {
1263 assert!(NAN.sqrt().is_nan());
1264 assert!(NEG_INFINITY.sqrt().is_nan());
1265 assert!((-1.0f64).sqrt().is_nan());
1266 assert_eq!((-0.0f64).sqrt(), -0.0);
1267 assert_eq!(0.0f64.sqrt(), 0.0);
1268 assert_eq!(1.0f64.sqrt(), 1.0);
1269 assert_eq!(INFINITY.sqrt(), INFINITY);
1274 assert_eq!(1.0, 0.0f64.exp());
1275 assert_approx_eq!(2.718282, 1.0f64.exp());
1276 assert_approx_eq!(148.413159, 5.0f64.exp());
1278 let inf: f64 = INFINITY;
1279 let neg_inf: f64 = NEG_INFINITY;
1281 assert_eq!(inf, inf.exp());
1282 assert_eq!(0.0, neg_inf.exp());
1283 assert!(nan.exp().is_nan());
1288 assert_eq!(32.0, 5.0f64.exp2());
1289 assert_eq!(1.0, 0.0f64.exp2());
1291 let inf: f64 = INFINITY;
1292 let neg_inf: f64 = NEG_INFINITY;
1294 assert_eq!(inf, inf.exp2());
1295 assert_eq!(0.0, neg_inf.exp2());
1296 assert!(nan.exp2().is_nan());
1302 let inf: f64 = INFINITY;
1303 let neg_inf: f64 = NEG_INFINITY;
1304 assert_approx_eq!(1.0f64.exp().ln(), 1.0);
1305 assert!(nan.ln().is_nan());
1306 assert_eq!(inf.ln(), inf);
1307 assert!(neg_inf.ln().is_nan());
1308 assert!((-2.3f64).ln().is_nan());
1309 assert_eq!((-0.0f64).ln(), neg_inf);
1310 assert_eq!(0.0f64.ln(), neg_inf);
1311 assert_approx_eq!(4.0f64.ln(), 1.386294);
1317 let inf: f64 = INFINITY;
1318 let neg_inf: f64 = NEG_INFINITY;
1319 assert_eq!(10.0f64.log(10.0), 1.0);
1320 assert_approx_eq!(2.3f64.log(3.5), 0.664858);
1321 assert_eq!(1.0f64.exp().log(1.0f64.exp()), 1.0);
1322 assert!(1.0f64.log(1.0).is_nan());
1323 assert!(1.0f64.log(-13.9).is_nan());
1324 assert!(nan.log(2.3).is_nan());
1325 assert_eq!(inf.log(10.0), inf);
1326 assert!(neg_inf.log(8.8).is_nan());
1327 assert!((-2.3f64).log(0.1).is_nan());
1328 assert_eq!((-0.0f64).log(2.0), neg_inf);
1329 assert_eq!(0.0f64.log(7.0), neg_inf);
1335 let inf: f64 = INFINITY;
1336 let neg_inf: f64 = NEG_INFINITY;
1337 assert_approx_eq!(10.0f64.log2(), 3.321928);
1338 assert_approx_eq!(2.3f64.log2(), 1.201634);
1339 assert_approx_eq!(1.0f64.exp().log2(), 1.442695);
1340 assert!(nan.log2().is_nan());
1341 assert_eq!(inf.log2(), inf);
1342 assert!(neg_inf.log2().is_nan());
1343 assert!((-2.3f64).log2().is_nan());
1344 assert_eq!((-0.0f64).log2(), neg_inf);
1345 assert_eq!(0.0f64.log2(), neg_inf);
1351 let inf: f64 = INFINITY;
1352 let neg_inf: f64 = NEG_INFINITY;
1353 assert_eq!(10.0f64.log10(), 1.0);
1354 assert_approx_eq!(2.3f64.log10(), 0.361728);
1355 assert_approx_eq!(1.0f64.exp().log10(), 0.434294);
1356 assert_eq!(1.0f64.log10(), 0.0);
1357 assert!(nan.log10().is_nan());
1358 assert_eq!(inf.log10(), inf);
1359 assert!(neg_inf.log10().is_nan());
1360 assert!((-2.3f64).log10().is_nan());
1361 assert_eq!((-0.0f64).log10(), neg_inf);
1362 assert_eq!(0.0f64.log10(), neg_inf);
1366 fn test_to_degrees() {
1367 let pi: f64 = consts::PI;
1369 let inf: f64 = INFINITY;
1370 let neg_inf: f64 = NEG_INFINITY;
1371 assert_eq!(0.0f64.to_degrees(), 0.0);
1372 assert_approx_eq!((-5.8f64).to_degrees(), -332.315521);
1373 assert_eq!(pi.to_degrees(), 180.0);
1374 assert!(nan.to_degrees().is_nan());
1375 assert_eq!(inf.to_degrees(), inf);
1376 assert_eq!(neg_inf.to_degrees(), neg_inf);
1380 fn test_to_radians() {
1381 let pi: f64 = consts::PI;
1383 let inf: f64 = INFINITY;
1384 let neg_inf: f64 = NEG_INFINITY;
1385 assert_eq!(0.0f64.to_radians(), 0.0);
1386 assert_approx_eq!(154.6f64.to_radians(), 2.698279);
1387 assert_approx_eq!((-332.31f64).to_radians(), -5.799903);
1388 assert_eq!(180.0f64.to_radians(), pi);
1389 assert!(nan.to_radians().is_nan());
1390 assert_eq!(inf.to_radians(), inf);
1391 assert_eq!(neg_inf.to_radians(), neg_inf);
1396 assert_eq!(0.0f64.asinh(), 0.0f64);
1397 assert_eq!((-0.0f64).asinh(), -0.0f64);
1399 let inf: f64 = INFINITY;
1400 let neg_inf: f64 = NEG_INFINITY;
1402 assert_eq!(inf.asinh(), inf);
1403 assert_eq!(neg_inf.asinh(), neg_inf);
1404 assert!(nan.asinh().is_nan());
1405 assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64);
1406 assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
1411 assert_eq!(1.0f64.acosh(), 0.0f64);
1412 assert!(0.999f64.acosh().is_nan());
1414 let inf: f64 = INFINITY;
1415 let neg_inf: f64 = NEG_INFINITY;
1417 assert_eq!(inf.acosh(), inf);
1418 assert!(neg_inf.acosh().is_nan());
1419 assert!(nan.acosh().is_nan());
1420 assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
1421 assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
1426 assert_eq!(0.0f64.atanh(), 0.0f64);
1427 assert_eq!((-0.0f64).atanh(), -0.0f64);
1429 let inf: f64 = INFINITY;
1430 let neg_inf: f64 = NEG_INFINITY;
1432 assert_eq!(1.0f64.atanh(), inf);
1433 assert_eq!((-1.0f64).atanh(), neg_inf);
1434 assert!(2f64.atanh().atanh().is_nan());
1435 assert!((-2f64).atanh().atanh().is_nan());
1436 assert!(inf.atanh().is_nan());
1437 assert!(neg_inf.atanh().is_nan());
1438 assert!(nan.atanh().is_nan());
1439 assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64);
1440 assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64);
1444 fn test_real_consts() {
1446 let pi: f64 = consts::PI;
1447 let frac_pi_2: f64 = consts::FRAC_PI_2;
1448 let frac_pi_3: f64 = consts::FRAC_PI_3;
1449 let frac_pi_4: f64 = consts::FRAC_PI_4;
1450 let frac_pi_6: f64 = consts::FRAC_PI_6;
1451 let frac_pi_8: f64 = consts::FRAC_PI_8;
1452 let frac_1_pi: f64 = consts::FRAC_1_PI;
1453 let frac_2_pi: f64 = consts::FRAC_2_PI;
1454 let frac_2_sqrtpi: f64 = consts::FRAC_2_SQRT_PI;
1455 let sqrt2: f64 = consts::SQRT_2;
1456 let frac_1_sqrt2: f64 = consts::FRAC_1_SQRT_2;
1457 let e: f64 = consts::E;
1458 let log2_e: f64 = consts::LOG2_E;
1459 let log10_e: f64 = consts::LOG10_E;
1460 let ln_2: f64 = consts::LN_2;
1461 let ln_10: f64 = consts::LN_10;
1463 assert_approx_eq!(frac_pi_2, pi / 2f64);
1464 assert_approx_eq!(frac_pi_3, pi / 3f64);
1465 assert_approx_eq!(frac_pi_4, pi / 4f64);
1466 assert_approx_eq!(frac_pi_6, pi / 6f64);
1467 assert_approx_eq!(frac_pi_8, pi / 8f64);
1468 assert_approx_eq!(frac_1_pi, 1f64 / pi);
1469 assert_approx_eq!(frac_2_pi, 2f64 / pi);
1470 assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt());
1471 assert_approx_eq!(sqrt2, 2f64.sqrt());
1472 assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt());
1473 assert_approx_eq!(log2_e, e.log2());
1474 assert_approx_eq!(log10_e, e.log10());
1475 assert_approx_eq!(ln_2, 2f64.ln());
1476 assert_approx_eq!(ln_10, 10f64.ln());
1480 fn test_float_bits_conv() {
1481 assert_eq!((1f64).to_bits(), 0x3ff0000000000000);
1482 assert_eq!((12.5f64).to_bits(), 0x4029000000000000);
1483 assert_eq!((1337f64).to_bits(), 0x4094e40000000000);
1484 assert_eq!((-14.25f64).to_bits(), 0xc02c800000000000);
1485 assert_approx_eq!(f64::from_bits(0x3ff0000000000000), 1.0);
1486 assert_approx_eq!(f64::from_bits(0x4029000000000000), 12.5);
1487 assert_approx_eq!(f64::from_bits(0x4094e40000000000), 1337.0);
1488 assert_approx_eq!(f64::from_bits(0xc02c800000000000), -14.25);
1490 // Check that NaNs roundtrip their bits regardless of signalingness
1491 // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits
1492 let masked_nan1 = f64::NAN.to_bits() ^ 0x000A_AAAA_AAAA_AAAA;
1493 let masked_nan2 = f64::NAN.to_bits() ^ 0x0005_5555_5555_5555;
1494 assert!(f64::from_bits(masked_nan1).is_nan());
1495 assert!(f64::from_bits(masked_nan2).is_nan());
1497 assert_eq!(f64::from_bits(masked_nan1).to_bits(), masked_nan1);
1498 assert_eq!(f64::from_bits(masked_nan2).to_bits(), masked_nan2);