1 //! This module provides constants which are specific to the implementation
2 //! of the `f32` floating point data type.
4 //! *[See also the `f32` primitive type](../../std/primitive.f32.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::f32::{RADIX, MANTISSA_DIGITS, DIGITS, EPSILON};
18 #[stable(feature = "rust1", since = "1.0.0")]
19 pub use core::f32::{MIN_EXP, MAX_EXP, MIN_10_EXP};
20 #[stable(feature = "rust1", since = "1.0.0")]
21 pub use core::f32::{MAX_10_EXP, NAN, INFINITY, NEG_INFINITY};
22 #[stable(feature = "rust1", since = "1.0.0")]
23 pub use core::f32::{MIN, MIN_POSITIVE, MAX};
24 #[stable(feature = "rust1", since = "1.0.0")]
25 pub use core::f32::consts;
28 #[lang = "f32_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) -> f32 {
46 // On MSVC LLVM will lower many math intrinsics to a call to the
47 // corresponding function. On MSVC, however, many of these functions
48 // aren't actually available as symbols to call, but rather they are all
49 // `static inline` functions in header files. This means that from a C
50 // perspective it's "compatible", but not so much from an ABI
51 // perspective (which we're worried about).
53 // The inline header functions always just cast to a f64 and do their
54 // operation, so we do that here as well, but only for MSVC targets.
56 // Note that there are many MSVC-specific float operations which
57 // redirect to this comment, so `floorf` is just one case of a missing
58 // function on MSVC, but there are many others elsewhere.
59 #[cfg(target_env = "msvc")]
60 return (self as f64).floor() as f32;
61 #[cfg(not(target_env = "msvc"))]
62 return unsafe { intrinsics::floorf32(self) };
65 /// Returns the smallest integer greater than or equal to a number.
73 /// assert_eq!(f.ceil(), 4.0);
74 /// assert_eq!(g.ceil(), 4.0);
76 #[stable(feature = "rust1", since = "1.0.0")]
78 pub fn ceil(self) -> f32 {
79 // see notes above in `floor`
80 #[cfg(target_env = "msvc")]
81 return (self as f64).ceil() as f32;
82 #[cfg(not(target_env = "msvc"))]
83 return unsafe { intrinsics::ceilf32(self) };
86 /// Returns the nearest integer to a number. Round half-way cases away from
95 /// assert_eq!(f.round(), 3.0);
96 /// assert_eq!(g.round(), -3.0);
98 #[stable(feature = "rust1", since = "1.0.0")]
100 pub fn round(self) -> f32 {
101 unsafe { intrinsics::roundf32(self) }
104 /// Returns the integer part of a number.
111 /// let h = -3.7_f32;
113 /// assert_eq!(f.trunc(), 3.0);
114 /// assert_eq!(g.trunc(), 3.0);
115 /// assert_eq!(h.trunc(), -3.0);
117 #[stable(feature = "rust1", since = "1.0.0")]
119 pub fn trunc(self) -> f32 {
120 unsafe { intrinsics::truncf32(self) }
123 /// Returns the fractional part of a number.
131 /// let y = -3.5_f32;
132 /// let abs_difference_x = (x.fract() - 0.5).abs();
133 /// let abs_difference_y = (y.fract() - (-0.5)).abs();
135 /// assert!(abs_difference_x <= f32::EPSILON);
136 /// assert!(abs_difference_y <= f32::EPSILON);
138 #[stable(feature = "rust1", since = "1.0.0")]
140 pub fn fract(self) -> f32 { self - self.trunc() }
142 /// Computes the absolute value of `self`. Returns `NAN` if the
151 /// let y = -3.5_f32;
153 /// let abs_difference_x = (x.abs() - x).abs();
154 /// let abs_difference_y = (y.abs() - (-y)).abs();
156 /// assert!(abs_difference_x <= f32::EPSILON);
157 /// assert!(abs_difference_y <= f32::EPSILON);
159 /// assert!(f32::NAN.abs().is_nan());
161 #[stable(feature = "rust1", since = "1.0.0")]
163 pub fn abs(self) -> f32 {
164 unsafe { intrinsics::fabsf32(self) }
167 /// Returns a number that represents the sign of `self`.
169 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
170 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
171 /// - `NAN` if the number is `NAN`
180 /// assert_eq!(f.signum(), 1.0);
181 /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
183 /// assert!(f32::NAN.signum().is_nan());
185 #[stable(feature = "rust1", since = "1.0.0")]
187 pub fn signum(self) -> f32 {
191 1.0_f32.copysign(self)
195 /// Returns a number composed of the magnitude of `self` and the sign of
198 /// Equal to `self` if the sign of `self` and `sign` are the same, otherwise
199 /// equal to `-self`. If `self` is a `NAN`, then a `NAN` with the sign of
200 /// `sign` is returned.
209 /// assert_eq!(f.copysign(0.42), 3.5_f32);
210 /// assert_eq!(f.copysign(-0.42), -3.5_f32);
211 /// assert_eq!((-f).copysign(0.42), 3.5_f32);
212 /// assert_eq!((-f).copysign(-0.42), -3.5_f32);
214 /// assert!(f32::NAN.copysign(1.0).is_nan());
218 #[stable(feature = "copysign", since = "1.35.0")]
219 pub fn copysign(self, sign: f32) -> f32 {
220 unsafe { intrinsics::copysignf32(self, sign) }
223 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding
224 /// error, yielding a more accurate result than an unfused multiply-add.
226 /// Using `mul_add` can be more performant than an unfused multiply-add if
227 /// the target architecture has a dedicated `fma` CPU instruction.
234 /// let m = 10.0_f32;
236 /// let b = 60.0_f32;
239 /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs();
241 /// assert!(abs_difference <= f32::EPSILON);
243 #[stable(feature = "rust1", since = "1.0.0")]
245 pub fn mul_add(self, a: f32, b: f32) -> f32 {
246 unsafe { intrinsics::fmaf32(self, a, b) }
249 /// Calculates Euclidean division, the matching method for `rem_euclid`.
251 /// This computes the integer `n` such that
252 /// `self = n * rhs + self.rem_euclid(rhs)`.
253 /// In other words, the result is `self / rhs` rounded to the integer `n`
254 /// such that `self >= n * rhs`.
259 /// let a: f32 = 7.0;
261 /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
262 /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
263 /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
264 /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0
267 #[stable(feature = "euclidean_division", since = "1.38.0")]
268 pub fn div_euclid(self, rhs: f32) -> f32 {
269 let q = (self / rhs).trunc();
270 if self % rhs < 0.0 {
271 return if rhs > 0.0 { q - 1.0 } else { q + 1.0 }
276 /// Calculates the least nonnegative remainder of `self (mod rhs)`.
278 /// In particular, the return value `r` satisfies `0.0 <= r < rhs.abs()` in
279 /// most cases. However, due to a floating point round-off error it can
280 /// result in `r == rhs.abs()`, violating the mathematical definition, if
281 /// `self` is much smaller than `rhs.abs()` in magnitude and `self < 0.0`.
282 /// This result is not an element of the function's codomain, but it is the
283 /// closest floating point number in the real numbers and thus fulfills the
284 /// property `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`
290 /// let a: f32 = 7.0;
292 /// assert_eq!(a.rem_euclid(b), 3.0);
293 /// assert_eq!((-a).rem_euclid(b), 1.0);
294 /// assert_eq!(a.rem_euclid(-b), 3.0);
295 /// assert_eq!((-a).rem_euclid(-b), 1.0);
296 /// // limitation due to round-off error
297 /// assert!((-std::f32::EPSILON).rem_euclid(3.0) != 0.0);
300 #[stable(feature = "euclidean_division", since = "1.38.0")]
301 pub fn rem_euclid(self, rhs: f32) -> f32 {
311 /// Raises a number to an integer power.
313 /// Using this function is generally faster than using `powf`
321 /// let abs_difference = (x.powi(2) - (x * x)).abs();
323 /// assert!(abs_difference <= f32::EPSILON);
325 #[stable(feature = "rust1", since = "1.0.0")]
327 pub fn powi(self, n: i32) -> f32 {
328 unsafe { intrinsics::powif32(self, n) }
331 /// Raises a number to a floating point power.
339 /// let abs_difference = (x.powf(2.0) - (x * x)).abs();
341 /// assert!(abs_difference <= f32::EPSILON);
343 #[stable(feature = "rust1", since = "1.0.0")]
345 pub fn powf(self, n: f32) -> f32 {
346 // see notes above in `floor`
347 #[cfg(target_env = "msvc")]
348 return (self as f64).powf(n as f64) as f32;
349 #[cfg(not(target_env = "msvc"))]
350 return unsafe { intrinsics::powf32(self, n) };
353 /// Takes the square root of a number.
355 /// Returns NaN if `self` is a negative number.
362 /// let positive = 4.0_f32;
363 /// let negative = -4.0_f32;
365 /// let abs_difference = (positive.sqrt() - 2.0).abs();
367 /// assert!(abs_difference <= f32::EPSILON);
368 /// assert!(negative.sqrt().is_nan());
370 #[stable(feature = "rust1", since = "1.0.0")]
372 pub fn sqrt(self) -> f32 {
376 unsafe { intrinsics::sqrtf32(self) }
380 /// Returns `e^(self)`, (the exponential function).
387 /// let one = 1.0f32;
389 /// let e = one.exp();
391 /// // ln(e) - 1 == 0
392 /// let abs_difference = (e.ln() - 1.0).abs();
394 /// assert!(abs_difference <= f32::EPSILON);
396 #[stable(feature = "rust1", since = "1.0.0")]
398 pub fn exp(self) -> f32 {
399 // see notes above in `floor`
400 #[cfg(target_env = "msvc")]
401 return (self as f64).exp() as f32;
402 #[cfg(not(target_env = "msvc"))]
403 return unsafe { intrinsics::expf32(self) };
406 /// Returns `2^(self)`.
416 /// let abs_difference = (f.exp2() - 4.0).abs();
418 /// assert!(abs_difference <= f32::EPSILON);
420 #[stable(feature = "rust1", since = "1.0.0")]
422 pub fn exp2(self) -> f32 {
423 unsafe { intrinsics::exp2f32(self) }
426 /// Returns the natural logarithm of the number.
433 /// let one = 1.0f32;
435 /// let e = one.exp();
437 /// // ln(e) - 1 == 0
438 /// let abs_difference = (e.ln() - 1.0).abs();
440 /// assert!(abs_difference <= f32::EPSILON);
442 #[stable(feature = "rust1", since = "1.0.0")]
444 pub fn ln(self) -> f32 {
445 // see notes above in `floor`
446 #[cfg(target_env = "msvc")]
447 return (self as f64).ln() as f32;
448 #[cfg(not(target_env = "msvc"))]
449 return unsafe { intrinsics::logf32(self) };
452 /// Returns the logarithm of the number with respect to an arbitrary base.
454 /// The result may not be correctly rounded owing to implementation details;
455 /// `self.log2()` can produce more accurate results for base 2, and
456 /// `self.log10()` can produce more accurate results for base 10.
463 /// let five = 5.0f32;
465 /// // log5(5) - 1 == 0
466 /// let abs_difference = (five.log(5.0) - 1.0).abs();
468 /// assert!(abs_difference <= f32::EPSILON);
470 #[stable(feature = "rust1", since = "1.0.0")]
472 pub fn log(self, base: f32) -> f32 { self.ln() / base.ln() }
474 /// Returns the base 2 logarithm of the number.
481 /// let two = 2.0f32;
483 /// // log2(2) - 1 == 0
484 /// let abs_difference = (two.log2() - 1.0).abs();
486 /// assert!(abs_difference <= f32::EPSILON);
488 #[stable(feature = "rust1", since = "1.0.0")]
490 pub fn log2(self) -> f32 {
491 #[cfg(target_os = "android")]
492 return crate::sys::android::log2f32(self);
493 #[cfg(not(target_os = "android"))]
494 return unsafe { intrinsics::log2f32(self) };
497 /// Returns the base 10 logarithm of the number.
504 /// let ten = 10.0f32;
506 /// // log10(10) - 1 == 0
507 /// let abs_difference = (ten.log10() - 1.0).abs();
509 /// assert!(abs_difference <= f32::EPSILON);
511 #[stable(feature = "rust1", since = "1.0.0")]
513 pub fn log10(self) -> f32 {
514 // see notes above in `floor`
515 #[cfg(target_env = "msvc")]
516 return (self as f64).log10() as f32;
517 #[cfg(not(target_env = "msvc"))]
518 return unsafe { intrinsics::log10f32(self) };
521 /// The positive difference of two numbers.
523 /// * If `self <= other`: `0:0`
524 /// * Else: `self - other`
534 /// let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs();
535 /// let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs();
537 /// assert!(abs_difference_x <= f32::EPSILON);
538 /// assert!(abs_difference_y <= f32::EPSILON);
540 #[stable(feature = "rust1", since = "1.0.0")]
542 #[rustc_deprecated(since = "1.10.0",
543 reason = "you probably meant `(self - other).abs()`: \
544 this operation is `(self - other).max(0.0)` \
545 except that `abs_sub` also propagates NaNs (also \
546 known as `fdimf` in C). If you truly need the positive \
547 difference, consider using that expression or the C function \
548 `fdimf`, depending on how you wish to handle NaN (please consider \
549 filing an issue describing your use-case too).")]
550 pub fn abs_sub(self, other: f32) -> f32 {
551 unsafe { cmath::fdimf(self, other) }
554 /// Takes the cubic root of a number.
563 /// // x^(1/3) - 2 == 0
564 /// let abs_difference = (x.cbrt() - 2.0).abs();
566 /// assert!(abs_difference <= f32::EPSILON);
568 #[stable(feature = "rust1", since = "1.0.0")]
570 pub fn cbrt(self) -> f32 {
571 unsafe { cmath::cbrtf(self) }
574 /// Calculates the length of the hypotenuse of a right-angle triangle given
575 /// legs of length `x` and `y`.
585 /// // sqrt(x^2 + y^2)
586 /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
588 /// assert!(abs_difference <= f32::EPSILON);
590 #[stable(feature = "rust1", since = "1.0.0")]
592 pub fn hypot(self, other: f32) -> f32 {
593 unsafe { cmath::hypotf(self, other) }
596 /// Computes the sine of a number (in radians).
603 /// let x = f32::consts::FRAC_PI_2;
605 /// let abs_difference = (x.sin() - 1.0).abs();
607 /// assert!(abs_difference <= f32::EPSILON);
609 #[stable(feature = "rust1", since = "1.0.0")]
611 pub fn sin(self) -> f32 {
612 // see notes in `core::f32::Float::floor`
613 #[cfg(target_env = "msvc")]
614 return (self as f64).sin() as f32;
615 #[cfg(not(target_env = "msvc"))]
616 return unsafe { intrinsics::sinf32(self) };
619 /// Computes the cosine of a number (in radians).
626 /// let x = 2.0 * f32::consts::PI;
628 /// let abs_difference = (x.cos() - 1.0).abs();
630 /// assert!(abs_difference <= f32::EPSILON);
632 #[stable(feature = "rust1", since = "1.0.0")]
634 pub fn cos(self) -> f32 {
635 // see notes in `core::f32::Float::floor`
636 #[cfg(target_env = "msvc")]
637 return (self as f64).cos() as f32;
638 #[cfg(not(target_env = "msvc"))]
639 return unsafe { intrinsics::cosf32(self) };
642 /// Computes the tangent of a number (in radians).
649 /// let x = f32::consts::FRAC_PI_4;
650 /// let abs_difference = (x.tan() - 1.0).abs();
652 /// assert!(abs_difference <= f32::EPSILON);
654 #[stable(feature = "rust1", since = "1.0.0")]
656 pub fn tan(self) -> f32 {
657 unsafe { cmath::tanf(self) }
660 /// Computes the arcsine of a number. Return value is in radians in
661 /// the range [-pi/2, pi/2] or NaN if the number is outside the range
669 /// let f = f32::consts::FRAC_PI_2;
671 /// // asin(sin(pi/2))
672 /// let abs_difference = (f.sin().asin() - f32::consts::FRAC_PI_2).abs();
674 /// assert!(abs_difference <= f32::EPSILON);
676 #[stable(feature = "rust1", since = "1.0.0")]
678 pub fn asin(self) -> f32 {
679 unsafe { cmath::asinf(self) }
682 /// Computes the arccosine of a number. Return value is in radians in
683 /// the range [0, pi] or NaN if the number is outside the range
691 /// let f = f32::consts::FRAC_PI_4;
693 /// // acos(cos(pi/4))
694 /// let abs_difference = (f.cos().acos() - f32::consts::FRAC_PI_4).abs();
696 /// assert!(abs_difference <= f32::EPSILON);
698 #[stable(feature = "rust1", since = "1.0.0")]
700 pub fn acos(self) -> f32 {
701 unsafe { cmath::acosf(self) }
704 /// Computes the arctangent of a number. Return value is in radians in the
705 /// range [-pi/2, pi/2];
715 /// let abs_difference = (f.tan().atan() - 1.0).abs();
717 /// assert!(abs_difference <= f32::EPSILON);
719 #[stable(feature = "rust1", since = "1.0.0")]
721 pub fn atan(self) -> f32 {
722 unsafe { cmath::atanf(self) }
725 /// Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`) in radians.
727 /// * `x = 0`, `y = 0`: `0`
728 /// * `x >= 0`: `arctan(y/x)` -> `[-pi/2, pi/2]`
729 /// * `y >= 0`: `arctan(y/x) + pi` -> `(pi/2, pi]`
730 /// * `y < 0`: `arctan(y/x) - pi` -> `(-pi, -pi/2)`
737 /// // Positive angles measured counter-clockwise
738 /// // from positive x axis
739 /// // -pi/4 radians (45 deg clockwise)
741 /// let y1 = -3.0f32;
743 /// // 3pi/4 radians (135 deg counter-clockwise)
744 /// let x2 = -3.0f32;
747 /// let abs_difference_1 = (y1.atan2(x1) - (-f32::consts::FRAC_PI_4)).abs();
748 /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * f32::consts::FRAC_PI_4)).abs();
750 /// assert!(abs_difference_1 <= f32::EPSILON);
751 /// assert!(abs_difference_2 <= f32::EPSILON);
753 #[stable(feature = "rust1", since = "1.0.0")]
755 pub fn atan2(self, other: f32) -> f32 {
756 unsafe { cmath::atan2f(self, other) }
759 /// Simultaneously computes the sine and cosine of the number, `x`. Returns
760 /// `(sin(x), cos(x))`.
767 /// let x = f32::consts::FRAC_PI_4;
768 /// let f = x.sin_cos();
770 /// let abs_difference_0 = (f.0 - x.sin()).abs();
771 /// let abs_difference_1 = (f.1 - x.cos()).abs();
773 /// assert!(abs_difference_0 <= f32::EPSILON);
774 /// assert!(abs_difference_1 <= f32::EPSILON);
776 #[stable(feature = "rust1", since = "1.0.0")]
778 pub fn sin_cos(self) -> (f32, f32) {
779 (self.sin(), self.cos())
782 /// Returns `e^(self) - 1` in a way that is accurate even if the
783 /// number is close to zero.
793 /// let abs_difference = (x.ln().exp_m1() - 5.0).abs();
795 /// assert!(abs_difference <= f32::EPSILON);
797 #[stable(feature = "rust1", since = "1.0.0")]
799 pub fn exp_m1(self) -> f32 {
800 unsafe { cmath::expm1f(self) }
803 /// Returns `ln(1+n)` (natural logarithm) more accurately than if
804 /// the operations were performed separately.
811 /// let x = f32::consts::E - 1.0;
813 /// // ln(1 + (e - 1)) == ln(e) == 1
814 /// let abs_difference = (x.ln_1p() - 1.0).abs();
816 /// assert!(abs_difference <= f32::EPSILON);
818 #[stable(feature = "rust1", since = "1.0.0")]
820 pub fn ln_1p(self) -> f32 {
821 unsafe { cmath::log1pf(self) }
824 /// Hyperbolic sine function.
831 /// let e = f32::consts::E;
834 /// let f = x.sinh();
835 /// // Solving sinh() at 1 gives `(e^2-1)/(2e)`
836 /// let g = ((e * e) - 1.0) / (2.0 * e);
837 /// let abs_difference = (f - g).abs();
839 /// assert!(abs_difference <= f32::EPSILON);
841 #[stable(feature = "rust1", since = "1.0.0")]
843 pub fn sinh(self) -> f32 {
844 unsafe { cmath::sinhf(self) }
847 /// Hyperbolic cosine function.
854 /// let e = f32::consts::E;
856 /// let f = x.cosh();
857 /// // Solving cosh() at 1 gives this result
858 /// let g = ((e * e) + 1.0) / (2.0 * e);
859 /// let abs_difference = (f - g).abs();
862 /// assert!(abs_difference <= f32::EPSILON);
864 #[stable(feature = "rust1", since = "1.0.0")]
866 pub fn cosh(self) -> f32 {
867 unsafe { cmath::coshf(self) }
870 /// Hyperbolic tangent function.
877 /// let e = f32::consts::E;
880 /// let f = x.tanh();
881 /// // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))`
882 /// let g = (1.0 - e.powi(-2)) / (1.0 + e.powi(-2));
883 /// let abs_difference = (f - g).abs();
885 /// assert!(abs_difference <= f32::EPSILON);
887 #[stable(feature = "rust1", since = "1.0.0")]
889 pub fn tanh(self) -> f32 {
890 unsafe { cmath::tanhf(self) }
893 /// Inverse hyperbolic sine function.
901 /// let f = x.sinh().asinh();
903 /// let abs_difference = (f - x).abs();
905 /// assert!(abs_difference <= f32::EPSILON);
907 #[stable(feature = "rust1", since = "1.0.0")]
909 pub fn asinh(self) -> f32 {
910 if self == NEG_INFINITY {
913 (self + ((self * self) + 1.0).sqrt()).ln()
917 /// Inverse hyperbolic cosine function.
925 /// let f = x.cosh().acosh();
927 /// let abs_difference = (f - x).abs();
929 /// assert!(abs_difference <= f32::EPSILON);
931 #[stable(feature = "rust1", since = "1.0.0")]
933 pub fn acosh(self) -> f32 {
935 x if x < 1.0 => crate::f32::NAN,
936 x => (x + ((x * x) - 1.0).sqrt()).ln(),
940 /// Inverse hyperbolic tangent function.
947 /// let e = f32::consts::E;
948 /// let f = e.tanh().atanh();
950 /// let abs_difference = (f - e).abs();
952 /// assert!(abs_difference <= 1e-5);
954 #[stable(feature = "rust1", since = "1.0.0")]
956 pub fn atanh(self) -> f32 {
957 0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
960 /// Restrict a value to a certain interval unless it is NaN.
962 /// Returns `max` if `self` is greater than `max`, and `min` if `self` is
963 /// less than `min`. Otherwise this returns `self`.
965 /// Not that this function returns NaN if the initial value was NaN as
970 /// Panics if `min > max`, `min` is NaN, or `max` is NaN.
975 /// #![feature(clamp)]
976 /// assert!((-3.0f32).clamp(-2.0, 1.0) == -2.0);
977 /// assert!((0.0f32).clamp(-2.0, 1.0) == 0.0);
978 /// assert!((2.0f32).clamp(-2.0, 1.0) == 1.0);
979 /// assert!((std::f32::NAN).clamp(-2.0, 1.0).is_nan());
981 #[unstable(feature = "clamp", issue = "44095")]
983 pub fn clamp(self, min: f32, max: f32) -> f32 {
986 if x < min { x = min; }
987 if x > max { x = max; }
998 use crate::num::FpCategory as Fp;
1002 test_num(10f32, 2f32);
1007 assert_eq!(NAN.min(2.0), 2.0);
1008 assert_eq!(2.0f32.min(NAN), 2.0);
1013 assert_eq!(NAN.max(2.0), 2.0);
1014 assert_eq!(2.0f32.max(NAN), 2.0);
1019 let nan: f32 = f32::NAN;
1020 assert!(nan.is_nan());
1021 assert!(!nan.is_infinite());
1022 assert!(!nan.is_finite());
1023 assert!(!nan.is_normal());
1024 assert!(nan.is_sign_positive());
1025 assert!(!nan.is_sign_negative());
1026 assert_eq!(Fp::Nan, nan.classify());
1030 fn test_infinity() {
1031 let inf: f32 = f32::INFINITY;
1032 assert!(inf.is_infinite());
1033 assert!(!inf.is_finite());
1034 assert!(inf.is_sign_positive());
1035 assert!(!inf.is_sign_negative());
1036 assert!(!inf.is_nan());
1037 assert!(!inf.is_normal());
1038 assert_eq!(Fp::Infinite, inf.classify());
1042 fn test_neg_infinity() {
1043 let neg_inf: f32 = f32::NEG_INFINITY;
1044 assert!(neg_inf.is_infinite());
1045 assert!(!neg_inf.is_finite());
1046 assert!(!neg_inf.is_sign_positive());
1047 assert!(neg_inf.is_sign_negative());
1048 assert!(!neg_inf.is_nan());
1049 assert!(!neg_inf.is_normal());
1050 assert_eq!(Fp::Infinite, neg_inf.classify());
1055 let zero: f32 = 0.0f32;
1056 assert_eq!(0.0, zero);
1057 assert!(!zero.is_infinite());
1058 assert!(zero.is_finite());
1059 assert!(zero.is_sign_positive());
1060 assert!(!zero.is_sign_negative());
1061 assert!(!zero.is_nan());
1062 assert!(!zero.is_normal());
1063 assert_eq!(Fp::Zero, zero.classify());
1067 fn test_neg_zero() {
1068 let neg_zero: f32 = -0.0;
1069 assert_eq!(0.0, neg_zero);
1070 assert!(!neg_zero.is_infinite());
1071 assert!(neg_zero.is_finite());
1072 assert!(!neg_zero.is_sign_positive());
1073 assert!(neg_zero.is_sign_negative());
1074 assert!(!neg_zero.is_nan());
1075 assert!(!neg_zero.is_normal());
1076 assert_eq!(Fp::Zero, neg_zero.classify());
1081 let one: f32 = 1.0f32;
1082 assert_eq!(1.0, one);
1083 assert!(!one.is_infinite());
1084 assert!(one.is_finite());
1085 assert!(one.is_sign_positive());
1086 assert!(!one.is_sign_negative());
1087 assert!(!one.is_nan());
1088 assert!(one.is_normal());
1089 assert_eq!(Fp::Normal, one.classify());
1094 let nan: f32 = f32::NAN;
1095 let inf: f32 = f32::INFINITY;
1096 let neg_inf: f32 = f32::NEG_INFINITY;
1097 assert!(nan.is_nan());
1098 assert!(!0.0f32.is_nan());
1099 assert!(!5.3f32.is_nan());
1100 assert!(!(-10.732f32).is_nan());
1101 assert!(!inf.is_nan());
1102 assert!(!neg_inf.is_nan());
1106 fn test_is_infinite() {
1107 let nan: f32 = f32::NAN;
1108 let inf: f32 = f32::INFINITY;
1109 let neg_inf: f32 = f32::NEG_INFINITY;
1110 assert!(!nan.is_infinite());
1111 assert!(inf.is_infinite());
1112 assert!(neg_inf.is_infinite());
1113 assert!(!0.0f32.is_infinite());
1114 assert!(!42.8f32.is_infinite());
1115 assert!(!(-109.2f32).is_infinite());
1119 fn test_is_finite() {
1120 let nan: f32 = f32::NAN;
1121 let inf: f32 = f32::INFINITY;
1122 let neg_inf: f32 = f32::NEG_INFINITY;
1123 assert!(!nan.is_finite());
1124 assert!(!inf.is_finite());
1125 assert!(!neg_inf.is_finite());
1126 assert!(0.0f32.is_finite());
1127 assert!(42.8f32.is_finite());
1128 assert!((-109.2f32).is_finite());
1132 fn test_is_normal() {
1133 let nan: f32 = f32::NAN;
1134 let inf: f32 = f32::INFINITY;
1135 let neg_inf: f32 = f32::NEG_INFINITY;
1136 let zero: f32 = 0.0f32;
1137 let neg_zero: f32 = -0.0;
1138 assert!(!nan.is_normal());
1139 assert!(!inf.is_normal());
1140 assert!(!neg_inf.is_normal());
1141 assert!(!zero.is_normal());
1142 assert!(!neg_zero.is_normal());
1143 assert!(1f32.is_normal());
1144 assert!(1e-37f32.is_normal());
1145 assert!(!1e-38f32.is_normal());
1149 fn test_classify() {
1150 let nan: f32 = f32::NAN;
1151 let inf: f32 = f32::INFINITY;
1152 let neg_inf: f32 = f32::NEG_INFINITY;
1153 let zero: f32 = 0.0f32;
1154 let neg_zero: f32 = -0.0;
1155 assert_eq!(nan.classify(), Fp::Nan);
1156 assert_eq!(inf.classify(), Fp::Infinite);
1157 assert_eq!(neg_inf.classify(), Fp::Infinite);
1158 assert_eq!(zero.classify(), Fp::Zero);
1159 assert_eq!(neg_zero.classify(), Fp::Zero);
1160 assert_eq!(1f32.classify(), Fp::Normal);
1161 assert_eq!(1e-37f32.classify(), Fp::Normal);
1162 assert_eq!(1e-38f32.classify(), Fp::Subnormal);
1167 assert_approx_eq!(1.0f32.floor(), 1.0f32);
1168 assert_approx_eq!(1.3f32.floor(), 1.0f32);
1169 assert_approx_eq!(1.5f32.floor(), 1.0f32);
1170 assert_approx_eq!(1.7f32.floor(), 1.0f32);
1171 assert_approx_eq!(0.0f32.floor(), 0.0f32);
1172 assert_approx_eq!((-0.0f32).floor(), -0.0f32);
1173 assert_approx_eq!((-1.0f32).floor(), -1.0f32);
1174 assert_approx_eq!((-1.3f32).floor(), -2.0f32);
1175 assert_approx_eq!((-1.5f32).floor(), -2.0f32);
1176 assert_approx_eq!((-1.7f32).floor(), -2.0f32);
1181 assert_approx_eq!(1.0f32.ceil(), 1.0f32);
1182 assert_approx_eq!(1.3f32.ceil(), 2.0f32);
1183 assert_approx_eq!(1.5f32.ceil(), 2.0f32);
1184 assert_approx_eq!(1.7f32.ceil(), 2.0f32);
1185 assert_approx_eq!(0.0f32.ceil(), 0.0f32);
1186 assert_approx_eq!((-0.0f32).ceil(), -0.0f32);
1187 assert_approx_eq!((-1.0f32).ceil(), -1.0f32);
1188 assert_approx_eq!((-1.3f32).ceil(), -1.0f32);
1189 assert_approx_eq!((-1.5f32).ceil(), -1.0f32);
1190 assert_approx_eq!((-1.7f32).ceil(), -1.0f32);
1195 assert_approx_eq!(1.0f32.round(), 1.0f32);
1196 assert_approx_eq!(1.3f32.round(), 1.0f32);
1197 assert_approx_eq!(1.5f32.round(), 2.0f32);
1198 assert_approx_eq!(1.7f32.round(), 2.0f32);
1199 assert_approx_eq!(0.0f32.round(), 0.0f32);
1200 assert_approx_eq!((-0.0f32).round(), -0.0f32);
1201 assert_approx_eq!((-1.0f32).round(), -1.0f32);
1202 assert_approx_eq!((-1.3f32).round(), -1.0f32);
1203 assert_approx_eq!((-1.5f32).round(), -2.0f32);
1204 assert_approx_eq!((-1.7f32).round(), -2.0f32);
1209 assert_approx_eq!(1.0f32.trunc(), 1.0f32);
1210 assert_approx_eq!(1.3f32.trunc(), 1.0f32);
1211 assert_approx_eq!(1.5f32.trunc(), 1.0f32);
1212 assert_approx_eq!(1.7f32.trunc(), 1.0f32);
1213 assert_approx_eq!(0.0f32.trunc(), 0.0f32);
1214 assert_approx_eq!((-0.0f32).trunc(), -0.0f32);
1215 assert_approx_eq!((-1.0f32).trunc(), -1.0f32);
1216 assert_approx_eq!((-1.3f32).trunc(), -1.0f32);
1217 assert_approx_eq!((-1.5f32).trunc(), -1.0f32);
1218 assert_approx_eq!((-1.7f32).trunc(), -1.0f32);
1223 assert_approx_eq!(1.0f32.fract(), 0.0f32);
1224 assert_approx_eq!(1.3f32.fract(), 0.3f32);
1225 assert_approx_eq!(1.5f32.fract(), 0.5f32);
1226 assert_approx_eq!(1.7f32.fract(), 0.7f32);
1227 assert_approx_eq!(0.0f32.fract(), 0.0f32);
1228 assert_approx_eq!((-0.0f32).fract(), -0.0f32);
1229 assert_approx_eq!((-1.0f32).fract(), -0.0f32);
1230 assert_approx_eq!((-1.3f32).fract(), -0.3f32);
1231 assert_approx_eq!((-1.5f32).fract(), -0.5f32);
1232 assert_approx_eq!((-1.7f32).fract(), -0.7f32);
1237 assert_eq!(INFINITY.abs(), INFINITY);
1238 assert_eq!(1f32.abs(), 1f32);
1239 assert_eq!(0f32.abs(), 0f32);
1240 assert_eq!((-0f32).abs(), 0f32);
1241 assert_eq!((-1f32).abs(), 1f32);
1242 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1243 assert_eq!((1f32/NEG_INFINITY).abs(), 0f32);
1244 assert!(NAN.abs().is_nan());
1249 assert_eq!(INFINITY.signum(), 1f32);
1250 assert_eq!(1f32.signum(), 1f32);
1251 assert_eq!(0f32.signum(), 1f32);
1252 assert_eq!((-0f32).signum(), -1f32);
1253 assert_eq!((-1f32).signum(), -1f32);
1254 assert_eq!(NEG_INFINITY.signum(), -1f32);
1255 assert_eq!((1f32/NEG_INFINITY).signum(), -1f32);
1256 assert!(NAN.signum().is_nan());
1260 fn test_is_sign_positive() {
1261 assert!(INFINITY.is_sign_positive());
1262 assert!(1f32.is_sign_positive());
1263 assert!(0f32.is_sign_positive());
1264 assert!(!(-0f32).is_sign_positive());
1265 assert!(!(-1f32).is_sign_positive());
1266 assert!(!NEG_INFINITY.is_sign_positive());
1267 assert!(!(1f32/NEG_INFINITY).is_sign_positive());
1268 assert!(NAN.is_sign_positive());
1269 assert!(!(-NAN).is_sign_positive());
1273 fn test_is_sign_negative() {
1274 assert!(!INFINITY.is_sign_negative());
1275 assert!(!1f32.is_sign_negative());
1276 assert!(!0f32.is_sign_negative());
1277 assert!((-0f32).is_sign_negative());
1278 assert!((-1f32).is_sign_negative());
1279 assert!(NEG_INFINITY.is_sign_negative());
1280 assert!((1f32/NEG_INFINITY).is_sign_negative());
1281 assert!(!NAN.is_sign_negative());
1282 assert!((-NAN).is_sign_negative());
1287 let nan: f32 = f32::NAN;
1288 let inf: f32 = f32::INFINITY;
1289 let neg_inf: f32 = f32::NEG_INFINITY;
1290 assert_approx_eq!(12.3f32.mul_add(4.5, 6.7), 62.05);
1291 assert_approx_eq!((-12.3f32).mul_add(-4.5, -6.7), 48.65);
1292 assert_approx_eq!(0.0f32.mul_add(8.9, 1.2), 1.2);
1293 assert_approx_eq!(3.4f32.mul_add(-0.0, 5.6), 5.6);
1294 assert!(nan.mul_add(7.8, 9.0).is_nan());
1295 assert_eq!(inf.mul_add(7.8, 9.0), inf);
1296 assert_eq!(neg_inf.mul_add(7.8, 9.0), neg_inf);
1297 assert_eq!(8.9f32.mul_add(inf, 3.2), inf);
1298 assert_eq!((-3.2f32).mul_add(2.4, neg_inf), neg_inf);
1303 let nan: f32 = f32::NAN;
1304 let inf: f32 = f32::INFINITY;
1305 let neg_inf: f32 = f32::NEG_INFINITY;
1306 assert_eq!(1.0f32.recip(), 1.0);
1307 assert_eq!(2.0f32.recip(), 0.5);
1308 assert_eq!((-0.4f32).recip(), -2.5);
1309 assert_eq!(0.0f32.recip(), inf);
1310 assert!(nan.recip().is_nan());
1311 assert_eq!(inf.recip(), 0.0);
1312 assert_eq!(neg_inf.recip(), 0.0);
1317 let nan: f32 = f32::NAN;
1318 let inf: f32 = f32::INFINITY;
1319 let neg_inf: f32 = f32::NEG_INFINITY;
1320 assert_eq!(1.0f32.powi(1), 1.0);
1321 assert_approx_eq!((-3.1f32).powi(2), 9.61);
1322 assert_approx_eq!(5.9f32.powi(-2), 0.028727);
1323 assert_eq!(8.3f32.powi(0), 1.0);
1324 assert!(nan.powi(2).is_nan());
1325 assert_eq!(inf.powi(3), inf);
1326 assert_eq!(neg_inf.powi(2), inf);
1331 let nan: f32 = f32::NAN;
1332 let inf: f32 = f32::INFINITY;
1333 let neg_inf: f32 = f32::NEG_INFINITY;
1334 assert_eq!(1.0f32.powf(1.0), 1.0);
1335 assert_approx_eq!(3.4f32.powf(4.5), 246.408218);
1336 assert_approx_eq!(2.7f32.powf(-3.2), 0.041652);
1337 assert_approx_eq!((-3.1f32).powf(2.0), 9.61);
1338 assert_approx_eq!(5.9f32.powf(-2.0), 0.028727);
1339 assert_eq!(8.3f32.powf(0.0), 1.0);
1340 assert!(nan.powf(2.0).is_nan());
1341 assert_eq!(inf.powf(2.0), inf);
1342 assert_eq!(neg_inf.powf(3.0), neg_inf);
1346 fn test_sqrt_domain() {
1347 assert!(NAN.sqrt().is_nan());
1348 assert!(NEG_INFINITY.sqrt().is_nan());
1349 assert!((-1.0f32).sqrt().is_nan());
1350 assert_eq!((-0.0f32).sqrt(), -0.0);
1351 assert_eq!(0.0f32.sqrt(), 0.0);
1352 assert_eq!(1.0f32.sqrt(), 1.0);
1353 assert_eq!(INFINITY.sqrt(), INFINITY);
1358 assert_eq!(1.0, 0.0f32.exp());
1359 assert_approx_eq!(2.718282, 1.0f32.exp());
1360 assert_approx_eq!(148.413162, 5.0f32.exp());
1362 let inf: f32 = f32::INFINITY;
1363 let neg_inf: f32 = f32::NEG_INFINITY;
1364 let nan: f32 = f32::NAN;
1365 assert_eq!(inf, inf.exp());
1366 assert_eq!(0.0, neg_inf.exp());
1367 assert!(nan.exp().is_nan());
1372 assert_eq!(32.0, 5.0f32.exp2());
1373 assert_eq!(1.0, 0.0f32.exp2());
1375 let inf: f32 = f32::INFINITY;
1376 let neg_inf: f32 = f32::NEG_INFINITY;
1377 let nan: f32 = f32::NAN;
1378 assert_eq!(inf, inf.exp2());
1379 assert_eq!(0.0, neg_inf.exp2());
1380 assert!(nan.exp2().is_nan());
1385 let nan: f32 = f32::NAN;
1386 let inf: f32 = f32::INFINITY;
1387 let neg_inf: f32 = f32::NEG_INFINITY;
1388 assert_approx_eq!(1.0f32.exp().ln(), 1.0);
1389 assert!(nan.ln().is_nan());
1390 assert_eq!(inf.ln(), inf);
1391 assert!(neg_inf.ln().is_nan());
1392 assert!((-2.3f32).ln().is_nan());
1393 assert_eq!((-0.0f32).ln(), neg_inf);
1394 assert_eq!(0.0f32.ln(), neg_inf);
1395 assert_approx_eq!(4.0f32.ln(), 1.386294);
1400 let nan: f32 = f32::NAN;
1401 let inf: f32 = f32::INFINITY;
1402 let neg_inf: f32 = f32::NEG_INFINITY;
1403 assert_eq!(10.0f32.log(10.0), 1.0);
1404 assert_approx_eq!(2.3f32.log(3.5), 0.664858);
1405 assert_eq!(1.0f32.exp().log(1.0f32.exp()), 1.0);
1406 assert!(1.0f32.log(1.0).is_nan());
1407 assert!(1.0f32.log(-13.9).is_nan());
1408 assert!(nan.log(2.3).is_nan());
1409 assert_eq!(inf.log(10.0), inf);
1410 assert!(neg_inf.log(8.8).is_nan());
1411 assert!((-2.3f32).log(0.1).is_nan());
1412 assert_eq!((-0.0f32).log(2.0), neg_inf);
1413 assert_eq!(0.0f32.log(7.0), neg_inf);
1418 let nan: f32 = f32::NAN;
1419 let inf: f32 = f32::INFINITY;
1420 let neg_inf: f32 = f32::NEG_INFINITY;
1421 assert_approx_eq!(10.0f32.log2(), 3.321928);
1422 assert_approx_eq!(2.3f32.log2(), 1.201634);
1423 assert_approx_eq!(1.0f32.exp().log2(), 1.442695);
1424 assert!(nan.log2().is_nan());
1425 assert_eq!(inf.log2(), inf);
1426 assert!(neg_inf.log2().is_nan());
1427 assert!((-2.3f32).log2().is_nan());
1428 assert_eq!((-0.0f32).log2(), neg_inf);
1429 assert_eq!(0.0f32.log2(), neg_inf);
1434 let nan: f32 = f32::NAN;
1435 let inf: f32 = f32::INFINITY;
1436 let neg_inf: f32 = f32::NEG_INFINITY;
1437 assert_eq!(10.0f32.log10(), 1.0);
1438 assert_approx_eq!(2.3f32.log10(), 0.361728);
1439 assert_approx_eq!(1.0f32.exp().log10(), 0.434294);
1440 assert_eq!(1.0f32.log10(), 0.0);
1441 assert!(nan.log10().is_nan());
1442 assert_eq!(inf.log10(), inf);
1443 assert!(neg_inf.log10().is_nan());
1444 assert!((-2.3f32).log10().is_nan());
1445 assert_eq!((-0.0f32).log10(), neg_inf);
1446 assert_eq!(0.0f32.log10(), neg_inf);
1450 fn test_to_degrees() {
1451 let pi: f32 = consts::PI;
1452 let nan: f32 = f32::NAN;
1453 let inf: f32 = f32::INFINITY;
1454 let neg_inf: f32 = f32::NEG_INFINITY;
1455 assert_eq!(0.0f32.to_degrees(), 0.0);
1456 assert_approx_eq!((-5.8f32).to_degrees(), -332.315521);
1457 assert_eq!(pi.to_degrees(), 180.0);
1458 assert!(nan.to_degrees().is_nan());
1459 assert_eq!(inf.to_degrees(), inf);
1460 assert_eq!(neg_inf.to_degrees(), neg_inf);
1461 assert_eq!(1_f32.to_degrees(), 57.2957795130823208767981548141051703);
1465 fn test_to_radians() {
1466 let pi: f32 = consts::PI;
1467 let nan: f32 = f32::NAN;
1468 let inf: f32 = f32::INFINITY;
1469 let neg_inf: f32 = f32::NEG_INFINITY;
1470 assert_eq!(0.0f32.to_radians(), 0.0);
1471 assert_approx_eq!(154.6f32.to_radians(), 2.698279);
1472 assert_approx_eq!((-332.31f32).to_radians(), -5.799903);
1473 assert_eq!(180.0f32.to_radians(), pi);
1474 assert!(nan.to_radians().is_nan());
1475 assert_eq!(inf.to_radians(), inf);
1476 assert_eq!(neg_inf.to_radians(), neg_inf);
1481 assert_eq!(0.0f32.asinh(), 0.0f32);
1482 assert_eq!((-0.0f32).asinh(), -0.0f32);
1484 let inf: f32 = f32::INFINITY;
1485 let neg_inf: f32 = f32::NEG_INFINITY;
1486 let nan: f32 = f32::NAN;
1487 assert_eq!(inf.asinh(), inf);
1488 assert_eq!(neg_inf.asinh(), neg_inf);
1489 assert!(nan.asinh().is_nan());
1490 assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32);
1491 assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32);
1496 assert_eq!(1.0f32.acosh(), 0.0f32);
1497 assert!(0.999f32.acosh().is_nan());
1499 let inf: f32 = f32::INFINITY;
1500 let neg_inf: f32 = f32::NEG_INFINITY;
1501 let nan: f32 = f32::NAN;
1502 assert_eq!(inf.acosh(), inf);
1503 assert!(neg_inf.acosh().is_nan());
1504 assert!(nan.acosh().is_nan());
1505 assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32);
1506 assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32);
1511 assert_eq!(0.0f32.atanh(), 0.0f32);
1512 assert_eq!((-0.0f32).atanh(), -0.0f32);
1514 let inf32: f32 = f32::INFINITY;
1515 let neg_inf32: f32 = f32::NEG_INFINITY;
1516 assert_eq!(1.0f32.atanh(), inf32);
1517 assert_eq!((-1.0f32).atanh(), neg_inf32);
1519 assert!(2f64.atanh().atanh().is_nan());
1520 assert!((-2f64).atanh().atanh().is_nan());
1522 let inf64: f32 = f32::INFINITY;
1523 let neg_inf64: f32 = f32::NEG_INFINITY;
1524 let nan32: f32 = f32::NAN;
1525 assert!(inf64.atanh().is_nan());
1526 assert!(neg_inf64.atanh().is_nan());
1527 assert!(nan32.atanh().is_nan());
1529 assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32);
1530 assert_approx_eq!((-0.5f32).atanh(), -0.54930614433405484569762261846126285f32);
1534 fn test_real_consts() {
1537 let pi: f32 = consts::PI;
1538 let frac_pi_2: f32 = consts::FRAC_PI_2;
1539 let frac_pi_3: f32 = consts::FRAC_PI_3;
1540 let frac_pi_4: f32 = consts::FRAC_PI_4;
1541 let frac_pi_6: f32 = consts::FRAC_PI_6;
1542 let frac_pi_8: f32 = consts::FRAC_PI_8;
1543 let frac_1_pi: f32 = consts::FRAC_1_PI;
1544 let frac_2_pi: f32 = consts::FRAC_2_PI;
1545 let frac_2_sqrtpi: f32 = consts::FRAC_2_SQRT_PI;
1546 let sqrt2: f32 = consts::SQRT_2;
1547 let frac_1_sqrt2: f32 = consts::FRAC_1_SQRT_2;
1548 let e: f32 = consts::E;
1549 let log2_e: f32 = consts::LOG2_E;
1550 let log10_e: f32 = consts::LOG10_E;
1551 let ln_2: f32 = consts::LN_2;
1552 let ln_10: f32 = consts::LN_10;
1554 assert_approx_eq!(frac_pi_2, pi / 2f32);
1555 assert_approx_eq!(frac_pi_3, pi / 3f32);
1556 assert_approx_eq!(frac_pi_4, pi / 4f32);
1557 assert_approx_eq!(frac_pi_6, pi / 6f32);
1558 assert_approx_eq!(frac_pi_8, pi / 8f32);
1559 assert_approx_eq!(frac_1_pi, 1f32 / pi);
1560 assert_approx_eq!(frac_2_pi, 2f32 / pi);
1561 assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt());
1562 assert_approx_eq!(sqrt2, 2f32.sqrt());
1563 assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt());
1564 assert_approx_eq!(log2_e, e.log2());
1565 assert_approx_eq!(log10_e, e.log10());
1566 assert_approx_eq!(ln_2, 2f32.ln());
1567 assert_approx_eq!(ln_10, 10f32.ln());
1571 fn test_float_bits_conv() {
1572 assert_eq!((1f32).to_bits(), 0x3f800000);
1573 assert_eq!((12.5f32).to_bits(), 0x41480000);
1574 assert_eq!((1337f32).to_bits(), 0x44a72000);
1575 assert_eq!((-14.25f32).to_bits(), 0xc1640000);
1576 assert_approx_eq!(f32::from_bits(0x3f800000), 1.0);
1577 assert_approx_eq!(f32::from_bits(0x41480000), 12.5);
1578 assert_approx_eq!(f32::from_bits(0x44a72000), 1337.0);
1579 assert_approx_eq!(f32::from_bits(0xc1640000), -14.25);
1581 // Check that NaNs roundtrip their bits regardless of signalingness
1582 // 0xA is 0b1010; 0x5 is 0b0101 -- so these two together clobbers all the mantissa bits
1583 let masked_nan1 = f32::NAN.to_bits() ^ 0x002A_AAAA;
1584 let masked_nan2 = f32::NAN.to_bits() ^ 0x0055_5555;
1585 assert!(f32::from_bits(masked_nan1).is_nan());
1586 assert!(f32::from_bits(masked_nan2).is_nan());
1588 assert_eq!(f32::from_bits(masked_nan1).to_bits(), masked_nan1);
1589 assert_eq!(f32::from_bits(masked_nan2).to_bits(), masked_nan2);
1594 fn test_clamp_min_greater_than_max() {
1595 1.0f32.clamp(3.0, 1.0);
1600 fn test_clamp_min_is_nan() {
1601 1.0f32.clamp(NAN, 1.0);
1606 fn test_clamp_max_is_nan() {
1607 1.0f32.clamp(3.0, NAN);