1 // Copyright 2012-2014 The Rust Project Developers. See the COPYRIGHT
2 // file at the top-level directory of this distribution and at
3 // http://rust-lang.org/COPYRIGHT.
5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
8 // option. This file may not be copied, modified, or distributed
9 // except according to those terms.
11 //! Operations and constants for 32-bits floats (`f32` type)
13 #![allow(missing_doc)]
18 use from_str::FromStr;
20 use num::{FPCategory, FPNaN, FPInfinite , FPZero, FPSubnormal, FPNormal};
21 use num::{Zero, One, Bounded, strconv};
27 use libc::{c_float, c_int};
31 pub fn acosf(n: c_float) -> c_float;
32 pub fn asinf(n: c_float) -> c_float;
33 pub fn atanf(n: c_float) -> c_float;
34 pub fn atan2f(a: c_float, b: c_float) -> c_float;
35 pub fn cbrtf(n: c_float) -> c_float;
36 pub fn coshf(n: c_float) -> c_float;
37 pub fn erff(n: c_float) -> c_float;
38 pub fn erfcf(n: c_float) -> c_float;
39 pub fn expm1f(n: c_float) -> c_float;
40 pub fn fdimf(a: c_float, b: c_float) -> c_float;
41 pub fn frexpf(n: c_float, value: &mut c_int) -> c_float;
42 pub fn fmaxf(a: c_float, b: c_float) -> c_float;
43 pub fn fminf(a: c_float, b: c_float) -> c_float;
44 pub fn nextafterf(x: c_float, y: c_float) -> c_float;
45 pub fn hypotf(x: c_float, y: c_float) -> c_float;
46 pub fn ldexpf(x: c_float, n: c_int) -> c_float;
47 pub fn logbf(n: c_float) -> c_float;
48 pub fn log1pf(n: c_float) -> c_float;
49 pub fn ilogbf(n: c_float) -> c_int;
50 pub fn modff(n: c_float, iptr: &mut c_float) -> c_float;
51 pub fn sinhf(n: c_float) -> c_float;
52 pub fn tanf(n: c_float) -> c_float;
53 pub fn tanhf(n: c_float) -> c_float;
54 pub fn tgammaf(n: c_float) -> c_float;
57 pub fn lgammaf_r(n: c_float, sign: &mut c_int) -> c_float;
60 #[link_name="__lgammaf_r"]
61 pub fn lgammaf_r(n: c_float, sign: &mut c_int) -> c_float;
65 // FIXME(#11621): These constants should be deprecated once CTFE is implemented
66 // in favour of calling their respective functions in `Bounded` and `Float`.
68 pub static RADIX: uint = 2u;
70 pub static MANTISSA_DIGITS: uint = 53u;
71 pub static DIGITS: uint = 15u;
73 pub static EPSILON: f64 = 2.220446e-16_f64;
75 // FIXME (#1433): this is wrong, replace with hexadecimal (%a) statics
77 pub static MIN_VALUE: f64 = 2.225074e-308_f64;
78 pub static MAX_VALUE: f64 = 1.797693e+308_f64;
80 pub static MIN_EXP: uint = -1021u;
81 pub static MAX_EXP: uint = 1024u;
83 pub static MIN_10_EXP: int = -307;
84 pub static MAX_10_EXP: int = 308;
86 pub static NAN: f32 = 0.0_f32/0.0_f32;
87 pub static INFINITY: f32 = 1.0_f32/0.0_f32;
88 pub static NEG_INFINITY: f32 = -1.0_f32/0.0_f32;
90 /// Various useful constants.
92 // FIXME (requires Issue #1433 to fix): replace with mathematical
93 // staticants from cmath.
95 // FIXME(#11621): These constants should be deprecated once CTFE is
96 // implemented in favour of calling their respective functions in `Float`.
98 /// Archimedes' constant
99 pub static PI: f32 = 3.14159265358979323846264338327950288_f32;
102 pub static FRAC_PI_2: f32 = 1.57079632679489661923132169163975144_f32;
105 pub static FRAC_PI_4: f32 = 0.785398163397448309615660845819875721_f32;
108 pub static FRAC_1_PI: f32 = 0.318309886183790671537767526745028724_f32;
111 pub static FRAC_2_PI: f32 = 0.636619772367581343075535053490057448_f32;
114 pub static FRAC_2_SQRTPI: f32 = 1.12837916709551257389615890312154517_f32;
117 pub static SQRT2: f32 = 1.41421356237309504880168872420969808_f32;
120 pub static FRAC_1_SQRT2: f32 = 0.707106781186547524400844362104849039_f32;
123 pub static E: f32 = 2.71828182845904523536028747135266250_f32;
126 pub static LOG2_E: f32 = 1.44269504088896340735992468100189214_f32;
129 pub static LOG10_E: f32 = 0.434294481903251827651128918916605082_f32;
132 pub static LN_2: f32 = 0.693147180559945309417232121458176568_f32;
135 pub static LN_10: f32 = 2.30258509299404568401799145468436421_f32;
143 fn eq(&self, other: &f32) -> bool { (*self) == (*other) }
149 fn lt(&self, other: &f32) -> bool { (*self) < (*other) }
151 fn le(&self, other: &f32) -> bool { (*self) <= (*other) }
153 fn ge(&self, other: &f32) -> bool { (*self) >= (*other) }
155 fn gt(&self, other: &f32) -> bool { (*self) > (*other) }
158 impl Default for f32 {
160 fn default() -> f32 { 0.0 }
165 fn zero() -> f32 { 0.0 }
167 /// Returns true if the number is equal to either `0.0` or `-0.0`
169 fn is_zero(&self) -> bool { *self == 0.0 || *self == -0.0 }
174 fn one() -> f32 { 1.0 }
178 impl Add<f32,f32> for f32 {
180 fn add(&self, other: &f32) -> f32 { *self + *other }
184 impl Sub<f32,f32> for f32 {
186 fn sub(&self, other: &f32) -> f32 { *self - *other }
190 impl Mul<f32,f32> for f32 {
192 fn mul(&self, other: &f32) -> f32 { *self * *other }
196 impl Div<f32,f32> for f32 {
198 fn div(&self, other: &f32) -> f32 { *self / *other }
202 impl Rem<f32,f32> for f32 {
204 fn rem(&self, other: &f32) -> f32 { *self % *other }
208 impl Neg<f32> for f32 {
210 fn neg(&self) -> f32 { -*self }
213 impl Signed for f32 {
214 /// Computes the absolute value. Returns `NAN` if the number is `NAN`.
216 fn abs(&self) -> f32 { unsafe{intrinsics::fabsf32(*self)} }
218 /// The positive difference of two numbers. Returns `0.0` if the number is less than or
219 /// equal to `other`, otherwise the difference between`self` and `other` is returned.
221 fn abs_sub(&self, other: &f32) -> f32 { unsafe{cmath::fdimf(*self, *other)} }
225 /// - `1.0` if the number is positive, `+0.0` or `INFINITY`
226 /// - `-1.0` if the number is negative, `-0.0` or `NEG_INFINITY`
227 /// - `NAN` if the number is NaN
229 fn signum(&self) -> f32 {
230 if self.is_nan() { NAN } else { unsafe{intrinsics::copysignf32(1.0, *self)} }
233 /// Returns `true` if the number is positive, including `+0.0` and `INFINITY`
235 fn is_positive(&self) -> bool { *self > 0.0 || (1.0 / *self) == INFINITY }
237 /// Returns `true` if the number is negative, including `-0.0` and `NEG_INFINITY`
239 fn is_negative(&self) -> bool { *self < 0.0 || (1.0 / *self) == NEG_INFINITY }
242 impl Bounded for f32 {
244 fn min_value() -> f32 { 1.17549435e-38 }
247 fn max_value() -> f32 { 3.40282347e+38 }
250 impl Primitive for f32 {}
253 fn powi(&self, n: i32) -> f32 { unsafe{intrinsics::powif32(*self, n)} }
256 fn max(self, other: f32) -> f32 {
257 unsafe { cmath::fmaxf(self, other) }
261 fn min(self, other: f32) -> f32 {
262 unsafe { cmath::fminf(self, other) }
266 fn nan() -> f32 { 0.0 / 0.0 }
269 fn infinity() -> f32 { 1.0 / 0.0 }
272 fn neg_infinity() -> f32 { -1.0 / 0.0 }
275 fn neg_zero() -> f32 { -0.0 }
277 /// Returns `true` if the number is NaN
279 fn is_nan(&self) -> bool { *self != *self }
281 /// Returns `true` if the number is infinite
283 fn is_infinite(&self) -> bool {
284 *self == Float::infinity() || *self == Float::neg_infinity()
287 /// Returns `true` if the number is neither infinite or NaN
289 fn is_finite(&self) -> bool {
290 !(self.is_nan() || self.is_infinite())
293 /// Returns `true` if the number is neither zero, infinite, subnormal or NaN
295 fn is_normal(&self) -> bool {
296 self.classify() == FPNormal
299 /// Returns the floating point category of the number. If only one property is going to
300 /// be tested, it is generally faster to use the specific predicate instead.
301 fn classify(&self) -> FPCategory {
302 static EXP_MASK: u32 = 0x7f800000;
303 static MAN_MASK: u32 = 0x007fffff;
305 let bits: u32 = unsafe {::cast::transmute(*self)};
306 match (bits & MAN_MASK, bits & EXP_MASK) {
308 (_, 0) => FPSubnormal,
309 (0, EXP_MASK) => FPInfinite,
310 (_, EXP_MASK) => FPNaN,
316 fn mantissa_digits(_: Option<f32>) -> uint { 24 }
319 fn digits(_: Option<f32>) -> uint { 6 }
322 fn epsilon() -> f32 { 1.19209290e-07 }
325 fn min_exp(_: Option<f32>) -> int { -125 }
328 fn max_exp(_: Option<f32>) -> int { 128 }
331 fn min_10_exp(_: Option<f32>) -> int { -37 }
334 fn max_10_exp(_: Option<f32>) -> int { 38 }
336 /// Constructs a floating point number by multiplying `x` by 2 raised to the power of `exp`
338 fn ldexp(x: f32, exp: int) -> f32 { unsafe{cmath::ldexpf(x, exp as c_int)} }
340 /// Breaks the number into a normalized fraction and a base-2 exponent, satisfying:
342 /// - `self = x * pow(2, exp)`
343 /// - `0.5 <= abs(x) < 1.0`
345 fn frexp(&self) -> (f32, int) {
348 let x = cmath::frexpf(*self, &mut exp);
353 /// Returns the exponential of the number, minus `1`, in a way that is accurate
354 /// even if the number is close to zero
356 fn exp_m1(&self) -> f32 { unsafe{cmath::expm1f(*self)} }
358 /// Returns the natural logarithm of the number plus `1` (`ln(1+n)`) more accurately
359 /// than if the operations were performed separately
361 fn ln_1p(&self) -> f32 { unsafe{cmath::log1pf(*self)} }
363 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding error. This
364 /// produces a more accurate result with better performance than a separate multiplication
365 /// operation followed by an add.
367 fn mul_add(&self, a: f32, b: f32) -> f32 { unsafe{intrinsics::fmaf32(*self, a, b)} }
369 /// Returns the next representable floating-point value in the direction of `other`
371 fn next_after(&self, other: f32) -> f32 { unsafe{cmath::nextafterf(*self, other)} }
373 /// Returns the mantissa, exponent and sign as integers.
374 fn integer_decode(&self) -> (u64, i16, i8) {
375 let bits: u32 = unsafe {
376 ::cast::transmute(*self)
378 let sign: i8 = if bits >> 31 == 0 { 1 } else { -1 };
379 let mut exponent: i16 = ((bits >> 23) & 0xff) as i16;
380 let mantissa = if exponent == 0 {
381 (bits & 0x7fffff) << 1
383 (bits & 0x7fffff) | 0x800000
385 // Exponent bias + mantissa shift
386 exponent -= 127 + 23;
387 (mantissa as u64, exponent, sign)
390 /// Round half-way cases toward `NEG_INFINITY`
392 fn floor(&self) -> f32 { unsafe{intrinsics::floorf32(*self)} }
394 /// Round half-way cases toward `INFINITY`
396 fn ceil(&self) -> f32 { unsafe{intrinsics::ceilf32(*self)} }
398 /// Round half-way cases away from `0.0`
400 fn round(&self) -> f32 { unsafe{intrinsics::roundf32(*self)} }
402 /// The integer part of the number (rounds towards `0.0`)
404 fn trunc(&self) -> f32 { unsafe{intrinsics::truncf32(*self)} }
406 /// The fractional part of the number, satisfying:
410 /// assert!(x == x.trunc() + x.fract())
413 fn fract(&self) -> f32 { *self - self.trunc() }
415 /// Archimedes' constant
417 fn pi() -> f32 { 3.14159265358979323846264338327950288 }
421 fn two_pi() -> f32 { 6.28318530717958647692528676655900576 }
425 fn frac_pi_2() -> f32 { 1.57079632679489661923132169163975144 }
429 fn frac_pi_3() -> f32 { 1.04719755119659774615421446109316763 }
433 fn frac_pi_4() -> f32 { 0.785398163397448309615660845819875721 }
437 fn frac_pi_6() -> f32 { 0.52359877559829887307710723054658381 }
441 fn frac_pi_8() -> f32 { 0.39269908169872415480783042290993786 }
445 fn frac_1_pi() -> f32 { 0.318309886183790671537767526745028724 }
449 fn frac_2_pi() -> f32 { 0.636619772367581343075535053490057448 }
453 fn frac_2_sqrtpi() -> f32 { 1.12837916709551257389615890312154517 }
457 fn sqrt2() -> f32 { 1.41421356237309504880168872420969808 }
461 fn frac_1_sqrt2() -> f32 { 0.707106781186547524400844362104849039 }
465 fn e() -> f32 { 2.71828182845904523536028747135266250 }
469 fn log2_e() -> f32 { 1.44269504088896340735992468100189214 }
473 fn log10_e() -> f32 { 0.434294481903251827651128918916605082 }
477 fn ln_2() -> f32 { 0.693147180559945309417232121458176568 }
481 fn ln_10() -> f32 { 2.30258509299404568401799145468436421 }
483 /// The reciprocal (multiplicative inverse) of the number
485 fn recip(&self) -> f32 { 1.0 / *self }
488 fn powf(&self, n: &f32) -> f32 { unsafe{intrinsics::powf32(*self, *n)} }
491 fn sqrt(&self) -> f32 { unsafe{intrinsics::sqrtf32(*self)} }
494 fn rsqrt(&self) -> f32 { self.sqrt().recip() }
497 fn cbrt(&self) -> f32 { unsafe{cmath::cbrtf(*self)} }
500 fn hypot(&self, other: &f32) -> f32 { unsafe{cmath::hypotf(*self, *other)} }
503 fn sin(&self) -> f32 { unsafe{intrinsics::sinf32(*self)} }
506 fn cos(&self) -> f32 { unsafe{intrinsics::cosf32(*self)} }
509 fn tan(&self) -> f32 { unsafe{cmath::tanf(*self)} }
512 fn asin(&self) -> f32 { unsafe{cmath::asinf(*self)} }
515 fn acos(&self) -> f32 { unsafe{cmath::acosf(*self)} }
518 fn atan(&self) -> f32 { unsafe{cmath::atanf(*self)} }
521 fn atan2(&self, other: &f32) -> f32 { unsafe{cmath::atan2f(*self, *other)} }
523 /// Simultaneously computes the sine and cosine of the number
525 fn sin_cos(&self) -> (f32, f32) {
526 (self.sin(), self.cos())
529 /// Returns the exponential of the number
531 fn exp(&self) -> f32 { unsafe{intrinsics::expf32(*self)} }
533 /// Returns 2 raised to the power of the number
535 fn exp2(&self) -> f32 { unsafe{intrinsics::exp2f32(*self)} }
537 /// Returns the natural logarithm of the number
539 fn ln(&self) -> f32 { unsafe{intrinsics::logf32(*self)} }
541 /// Returns the logarithm of the number with respect to an arbitrary base
543 fn log(&self, base: &f32) -> f32 { self.ln() / base.ln() }
545 /// Returns the base 2 logarithm of the number
547 fn log2(&self) -> f32 { unsafe{intrinsics::log2f32(*self)} }
549 /// Returns the base 10 logarithm of the number
551 fn log10(&self) -> f32 { unsafe{intrinsics::log10f32(*self)} }
554 fn sinh(&self) -> f32 { unsafe{cmath::sinhf(*self)} }
557 fn cosh(&self) -> f32 { unsafe{cmath::coshf(*self)} }
560 fn tanh(&self) -> f32 { unsafe{cmath::tanhf(*self)} }
562 /// Inverse hyperbolic sine
566 /// - on success, the inverse hyperbolic sine of `self` will be returned
567 /// - `self` if `self` is `0.0`, `-0.0`, `INFINITY`, or `NEG_INFINITY`
568 /// - `NAN` if `self` is `NAN`
570 fn asinh(&self) -> f32 {
572 NEG_INFINITY => NEG_INFINITY,
573 x => (x + ((x * x) + 1.0).sqrt()).ln(),
577 /// Inverse hyperbolic cosine
581 /// - on success, the inverse hyperbolic cosine of `self` will be returned
582 /// - `INFINITY` if `self` is `INFINITY`
583 /// - `NAN` if `self` is `NAN` or `self < 1.0` (including `NEG_INFINITY`)
585 fn acosh(&self) -> f32 {
587 x if x < 1.0 => Float::nan(),
588 x => (x + ((x * x) - 1.0).sqrt()).ln(),
592 /// Inverse hyperbolic tangent
596 /// - on success, the inverse hyperbolic tangent of `self` will be returned
597 /// - `self` if `self` is `0.0` or `-0.0`
598 /// - `INFINITY` if `self` is `1.0`
599 /// - `NEG_INFINITY` if `self` is `-1.0`
600 /// - `NAN` if the `self` is `NAN` or outside the domain of `-1.0 <= self <= 1.0`
601 /// (including `INFINITY` and `NEG_INFINITY`)
603 fn atanh(&self) -> f32 {
604 0.5 * ((2.0 * *self) / (1.0 - *self)).ln_1p()
607 /// Converts to degrees, assuming the number is in radians
609 fn to_degrees(&self) -> f32 { *self * (180.0f32 / Float::pi()) }
611 /// Converts to radians, assuming the number is in degrees
613 fn to_radians(&self) -> f32 {
614 let value: f32 = Float::pi();
615 *self * (value / 180.0f32)
620 // Section: String Conversions
623 /// Converts a float to a string
627 /// * num - The float value
629 pub fn to_str(num: f32) -> ~str {
630 let (r, _) = strconv::float_to_str_common(
631 num, 10u, true, strconv::SignNeg, strconv::DigAll, strconv::ExpNone, false);
635 /// Converts a float to a string in hexadecimal format
639 /// * num - The float value
641 pub fn to_str_hex(num: f32) -> ~str {
642 let (r, _) = strconv::float_to_str_common(
643 num, 16u, true, strconv::SignNeg, strconv::DigAll, strconv::ExpNone, false);
647 /// Converts a float to a string in a given radix, and a flag indicating
648 /// whether it's a special value
652 /// * num - The float value
653 /// * radix - The base to use
655 pub fn to_str_radix_special(num: f32, rdx: uint) -> (~str, bool) {
656 strconv::float_to_str_common(num, rdx, true,
657 strconv::SignNeg, strconv::DigAll, strconv::ExpNone, false)
660 /// Converts a float to a string with exactly the number of
661 /// provided significant digits
665 /// * num - The float value
666 /// * digits - The number of significant digits
668 pub fn to_str_exact(num: f32, dig: uint) -> ~str {
669 let (r, _) = strconv::float_to_str_common(
670 num, 10u, true, strconv::SignNeg, strconv::DigExact(dig), strconv::ExpNone, false);
674 /// Converts a float to a string with a maximum number of
675 /// significant digits
679 /// * num - The float value
680 /// * digits - The number of significant digits
682 pub fn to_str_digits(num: f32, dig: uint) -> ~str {
683 let (r, _) = strconv::float_to_str_common(
684 num, 10u, true, strconv::SignNeg, strconv::DigMax(dig), strconv::ExpNone, false);
688 /// Converts a float to a string using the exponential notation with exactly the number of
689 /// provided digits after the decimal point in the significand
693 /// * num - The float value
694 /// * digits - The number of digits after the decimal point
695 /// * upper - Use `E` instead of `e` for the exponent sign
697 pub fn to_str_exp_exact(num: f32, dig: uint, upper: bool) -> ~str {
698 let (r, _) = strconv::float_to_str_common(
699 num, 10u, true, strconv::SignNeg, strconv::DigExact(dig), strconv::ExpDec, upper);
703 /// Converts a float to a string using the exponential notation with the maximum number of
704 /// digits after the decimal point in the significand
708 /// * num - The float value
709 /// * digits - The number of digits after the decimal point
710 /// * upper - Use `E` instead of `e` for the exponent sign
712 pub fn to_str_exp_digits(num: f32, dig: uint, upper: bool) -> ~str {
713 let (r, _) = strconv::float_to_str_common(
714 num, 10u, true, strconv::SignNeg, strconv::DigMax(dig), strconv::ExpDec, upper);
718 impl num::ToStrRadix for f32 {
719 /// Converts a float to a string in a given radix
723 /// * num - The float value
724 /// * radix - The base to use
728 /// Fails if called on a special value like `inf`, `-inf` or `NaN` due to
729 /// possible misinterpretation of the result at higher bases. If those values
730 /// are expected, use `to_str_radix_special()` instead.
732 fn to_str_radix(&self, rdx: uint) -> ~str {
733 let (r, special) = strconv::float_to_str_common(
734 *self, rdx, true, strconv::SignNeg, strconv::DigAll, strconv::ExpNone, false);
735 if special { fail!("number has a special value, \
736 try to_str_radix_special() if those are expected") }
741 /// Convert a string in base 16 to a float.
742 /// Accepts an optional binary exponent.
744 /// This function accepts strings such as
747 /// * '+a4.fe', equivalent to 'a4.fe'
749 /// * '2b.aP128', or equivalently, '2b.ap128'
751 /// * '.' (understood as 0)
753 /// * '.c', or, equivalently, '0.c'
754 /// * '+inf', 'inf', '-inf', 'NaN'
756 /// Leading and trailing whitespace represent an error.
764 /// `None` if the string did not represent a valid number. Otherwise,
765 /// `Some(n)` where `n` is the floating-point number represented by `[num]`.
767 pub fn from_str_hex(num: &str) -> Option<f32> {
768 strconv::from_str_common(num, 16u, true, true, true,
769 strconv::ExpBin, false, false)
772 impl FromStr for f32 {
773 /// Convert a string in base 10 to a float.
774 /// Accepts an optional decimal exponent.
776 /// This function accepts strings such as
779 /// * '+3.14', equivalent to '3.14'
781 /// * '2.5E10', or equivalently, '2.5e10'
783 /// * '.' (understood as 0)
785 /// * '.5', or, equivalently, '0.5'
786 /// * '+inf', 'inf', '-inf', 'NaN'
788 /// Leading and trailing whitespace represent an error.
796 /// `None` if the string did not represent a valid number. Otherwise,
797 /// `Some(n)` where `n` is the floating-point number represented by `num`.
799 fn from_str(val: &str) -> Option<f32> {
800 strconv::from_str_common(val, 10u, true, true, true,
801 strconv::ExpDec, false, false)
805 impl num::FromStrRadix for f32 {
806 /// Convert a string in a given base to a float.
808 /// Due to possible conflicts, this function does **not** accept
809 /// the special values `inf`, `-inf`, `+inf` and `NaN`, **nor**
810 /// does it recognize exponents of any kind.
812 /// Leading and trailing whitespace represent an error.
817 /// * radix - The base to use. Must lie in the range [2 .. 36]
821 /// `None` if the string did not represent a valid number. Otherwise,
822 /// `Some(n)` where `n` is the floating-point number represented by `num`.
824 fn from_str_radix(val: &str, rdx: uint) -> Option<f32> {
825 strconv::from_str_common(val, rdx, true, true, false,
826 strconv::ExpNone, false, false)
838 assert_eq!(NAN.min(2.0), 2.0);
839 assert_eq!(2.0f32.min(NAN), 2.0);
844 assert_eq!(NAN.max(2.0), 2.0);
845 assert_eq!(2.0f32.max(NAN), 2.0);
850 num::test_num(10f32, 2f32);
855 assert_approx_eq!(1.0f32.floor(), 1.0f32);
856 assert_approx_eq!(1.3f32.floor(), 1.0f32);
857 assert_approx_eq!(1.5f32.floor(), 1.0f32);
858 assert_approx_eq!(1.7f32.floor(), 1.0f32);
859 assert_approx_eq!(0.0f32.floor(), 0.0f32);
860 assert_approx_eq!((-0.0f32).floor(), -0.0f32);
861 assert_approx_eq!((-1.0f32).floor(), -1.0f32);
862 assert_approx_eq!((-1.3f32).floor(), -2.0f32);
863 assert_approx_eq!((-1.5f32).floor(), -2.0f32);
864 assert_approx_eq!((-1.7f32).floor(), -2.0f32);
869 assert_approx_eq!(1.0f32.ceil(), 1.0f32);
870 assert_approx_eq!(1.3f32.ceil(), 2.0f32);
871 assert_approx_eq!(1.5f32.ceil(), 2.0f32);
872 assert_approx_eq!(1.7f32.ceil(), 2.0f32);
873 assert_approx_eq!(0.0f32.ceil(), 0.0f32);
874 assert_approx_eq!((-0.0f32).ceil(), -0.0f32);
875 assert_approx_eq!((-1.0f32).ceil(), -1.0f32);
876 assert_approx_eq!((-1.3f32).ceil(), -1.0f32);
877 assert_approx_eq!((-1.5f32).ceil(), -1.0f32);
878 assert_approx_eq!((-1.7f32).ceil(), -1.0f32);
883 assert_approx_eq!(1.0f32.round(), 1.0f32);
884 assert_approx_eq!(1.3f32.round(), 1.0f32);
885 assert_approx_eq!(1.5f32.round(), 2.0f32);
886 assert_approx_eq!(1.7f32.round(), 2.0f32);
887 assert_approx_eq!(0.0f32.round(), 0.0f32);
888 assert_approx_eq!((-0.0f32).round(), -0.0f32);
889 assert_approx_eq!((-1.0f32).round(), -1.0f32);
890 assert_approx_eq!((-1.3f32).round(), -1.0f32);
891 assert_approx_eq!((-1.5f32).round(), -2.0f32);
892 assert_approx_eq!((-1.7f32).round(), -2.0f32);
897 assert_approx_eq!(1.0f32.trunc(), 1.0f32);
898 assert_approx_eq!(1.3f32.trunc(), 1.0f32);
899 assert_approx_eq!(1.5f32.trunc(), 1.0f32);
900 assert_approx_eq!(1.7f32.trunc(), 1.0f32);
901 assert_approx_eq!(0.0f32.trunc(), 0.0f32);
902 assert_approx_eq!((-0.0f32).trunc(), -0.0f32);
903 assert_approx_eq!((-1.0f32).trunc(), -1.0f32);
904 assert_approx_eq!((-1.3f32).trunc(), -1.0f32);
905 assert_approx_eq!((-1.5f32).trunc(), -1.0f32);
906 assert_approx_eq!((-1.7f32).trunc(), -1.0f32);
911 assert_approx_eq!(1.0f32.fract(), 0.0f32);
912 assert_approx_eq!(1.3f32.fract(), 0.3f32);
913 assert_approx_eq!(1.5f32.fract(), 0.5f32);
914 assert_approx_eq!(1.7f32.fract(), 0.7f32);
915 assert_approx_eq!(0.0f32.fract(), 0.0f32);
916 assert_approx_eq!((-0.0f32).fract(), -0.0f32);
917 assert_approx_eq!((-1.0f32).fract(), -0.0f32);
918 assert_approx_eq!((-1.3f32).fract(), -0.3f32);
919 assert_approx_eq!((-1.5f32).fract(), -0.5f32);
920 assert_approx_eq!((-1.7f32).fract(), -0.7f32);
925 assert_eq!(0.0f32.asinh(), 0.0f32);
926 assert_eq!((-0.0f32).asinh(), -0.0f32);
928 let inf: f32 = Float::infinity();
929 let neg_inf: f32 = Float::neg_infinity();
930 let nan: f32 = Float::nan();
931 assert_eq!(inf.asinh(), inf);
932 assert_eq!(neg_inf.asinh(), neg_inf);
933 assert!(nan.asinh().is_nan());
934 assert_approx_eq!(2.0f32.asinh(), 1.443635475178810342493276740273105f32);
935 assert_approx_eq!((-2.0f32).asinh(), -1.443635475178810342493276740273105f32);
940 assert_eq!(1.0f32.acosh(), 0.0f32);
941 assert!(0.999f32.acosh().is_nan());
943 let inf: f32 = Float::infinity();
944 let neg_inf: f32 = Float::neg_infinity();
945 let nan: f32 = Float::nan();
946 assert_eq!(inf.acosh(), inf);
947 assert!(neg_inf.acosh().is_nan());
948 assert!(nan.acosh().is_nan());
949 assert_approx_eq!(2.0f32.acosh(), 1.31695789692481670862504634730796844f32);
950 assert_approx_eq!(3.0f32.acosh(), 1.76274717403908605046521864995958461f32);
955 assert_eq!(0.0f32.atanh(), 0.0f32);
956 assert_eq!((-0.0f32).atanh(), -0.0f32);
958 let inf32: f32 = Float::infinity();
959 let neg_inf32: f32 = Float::neg_infinity();
960 assert_eq!(1.0f32.atanh(), inf32);
961 assert_eq!((-1.0f32).atanh(), neg_inf32);
963 assert!(2f64.atanh().atanh().is_nan());
964 assert!((-2f64).atanh().atanh().is_nan());
966 let inf64: f32 = Float::infinity();
967 let neg_inf64: f32 = Float::neg_infinity();
968 let nan32: f32 = Float::nan();
969 assert!(inf64.atanh().is_nan());
970 assert!(neg_inf64.atanh().is_nan());
971 assert!(nan32.atanh().is_nan());
973 assert_approx_eq!(0.5f32.atanh(), 0.54930614433405484569762261846126285f32);
974 assert_approx_eq!((-0.5f32).atanh(), -0.54930614433405484569762261846126285f32);
978 fn test_real_consts() {
979 let pi: f32 = Float::pi();
980 let two_pi: f32 = Float::two_pi();
981 let frac_pi_2: f32 = Float::frac_pi_2();
982 let frac_pi_3: f32 = Float::frac_pi_3();
983 let frac_pi_4: f32 = Float::frac_pi_4();
984 let frac_pi_6: f32 = Float::frac_pi_6();
985 let frac_pi_8: f32 = Float::frac_pi_8();
986 let frac_1_pi: f32 = Float::frac_1_pi();
987 let frac_2_pi: f32 = Float::frac_2_pi();
988 let frac_2_sqrtpi: f32 = Float::frac_2_sqrtpi();
989 let sqrt2: f32 = Float::sqrt2();
990 let frac_1_sqrt2: f32 = Float::frac_1_sqrt2();
991 let e: f32 = Float::e();
992 let log2_e: f32 = Float::log2_e();
993 let log10_e: f32 = Float::log10_e();
994 let ln_2: f32 = Float::ln_2();
995 let ln_10: f32 = Float::ln_10();
997 assert_approx_eq!(two_pi, 2f32 * pi);
998 assert_approx_eq!(frac_pi_2, pi / 2f32);
999 assert_approx_eq!(frac_pi_3, pi / 3f32);
1000 assert_approx_eq!(frac_pi_4, pi / 4f32);
1001 assert_approx_eq!(frac_pi_6, pi / 6f32);
1002 assert_approx_eq!(frac_pi_8, pi / 8f32);
1003 assert_approx_eq!(frac_1_pi, 1f32 / pi);
1004 assert_approx_eq!(frac_2_pi, 2f32 / pi);
1005 assert_approx_eq!(frac_2_sqrtpi, 2f32 / pi.sqrt());
1006 assert_approx_eq!(sqrt2, 2f32.sqrt());
1007 assert_approx_eq!(frac_1_sqrt2, 1f32 / 2f32.sqrt());
1008 assert_approx_eq!(log2_e, e.log2());
1009 assert_approx_eq!(log10_e, e.log10());
1010 assert_approx_eq!(ln_2, 2f32.ln());
1011 assert_approx_eq!(ln_10, 10f32.ln());
1016 assert_eq!(INFINITY.abs(), INFINITY);
1017 assert_eq!(1f32.abs(), 1f32);
1018 assert_eq!(0f32.abs(), 0f32);
1019 assert_eq!((-0f32).abs(), 0f32);
1020 assert_eq!((-1f32).abs(), 1f32);
1021 assert_eq!(NEG_INFINITY.abs(), INFINITY);
1022 assert_eq!((1f32/NEG_INFINITY).abs(), 0f32);
1023 assert!(NAN.abs().is_nan());
1028 assert_eq!((-1f32).abs_sub(&1f32), 0f32);
1029 assert_eq!(1f32.abs_sub(&1f32), 0f32);
1030 assert_eq!(1f32.abs_sub(&0f32), 1f32);
1031 assert_eq!(1f32.abs_sub(&-1f32), 2f32);
1032 assert_eq!(NEG_INFINITY.abs_sub(&0f32), 0f32);
1033 assert_eq!(INFINITY.abs_sub(&1f32), INFINITY);
1034 assert_eq!(0f32.abs_sub(&NEG_INFINITY), INFINITY);
1035 assert_eq!(0f32.abs_sub(&INFINITY), 0f32);
1039 fn test_abs_sub_nowin() {
1040 assert!(NAN.abs_sub(&-1f32).is_nan());
1041 assert!(1f32.abs_sub(&NAN).is_nan());
1046 assert_eq!(INFINITY.signum(), 1f32);
1047 assert_eq!(1f32.signum(), 1f32);
1048 assert_eq!(0f32.signum(), 1f32);
1049 assert_eq!((-0f32).signum(), -1f32);
1050 assert_eq!((-1f32).signum(), -1f32);
1051 assert_eq!(NEG_INFINITY.signum(), -1f32);
1052 assert_eq!((1f32/NEG_INFINITY).signum(), -1f32);
1053 assert!(NAN.signum().is_nan());
1057 fn test_is_positive() {
1058 assert!(INFINITY.is_positive());
1059 assert!(1f32.is_positive());
1060 assert!(0f32.is_positive());
1061 assert!(!(-0f32).is_positive());
1062 assert!(!(-1f32).is_positive());
1063 assert!(!NEG_INFINITY.is_positive());
1064 assert!(!(1f32/NEG_INFINITY).is_positive());
1065 assert!(!NAN.is_positive());
1069 fn test_is_negative() {
1070 assert!(!INFINITY.is_negative());
1071 assert!(!1f32.is_negative());
1072 assert!(!0f32.is_negative());
1073 assert!((-0f32).is_negative());
1074 assert!((-1f32).is_negative());
1075 assert!(NEG_INFINITY.is_negative());
1076 assert!((1f32/NEG_INFINITY).is_negative());
1077 assert!(!NAN.is_negative());
1081 fn test_is_normal() {
1082 let nan: f32 = Float::nan();
1083 let inf: f32 = Float::infinity();
1084 let neg_inf: f32 = Float::neg_infinity();
1085 let zero: f32 = Zero::zero();
1086 let neg_zero: f32 = Float::neg_zero();
1087 assert!(!nan.is_normal());
1088 assert!(!inf.is_normal());
1089 assert!(!neg_inf.is_normal());
1090 assert!(!zero.is_normal());
1091 assert!(!neg_zero.is_normal());
1092 assert!(1f32.is_normal());
1093 assert!(1e-37f32.is_normal());
1094 assert!(!1e-38f32.is_normal());
1098 fn test_classify() {
1099 let nan: f32 = Float::nan();
1100 let inf: f32 = Float::infinity();
1101 let neg_inf: f32 = Float::neg_infinity();
1102 let zero: f32 = Zero::zero();
1103 let neg_zero: f32 = Float::neg_zero();
1104 assert_eq!(nan.classify(), FPNaN);
1105 assert_eq!(inf.classify(), FPInfinite);
1106 assert_eq!(neg_inf.classify(), FPInfinite);
1107 assert_eq!(zero.classify(), FPZero);
1108 assert_eq!(neg_zero.classify(), FPZero);
1109 assert_eq!(1f32.classify(), FPNormal);
1110 assert_eq!(1e-37f32.classify(), FPNormal);
1111 assert_eq!(1e-38f32.classify(), FPSubnormal);
1116 // We have to use from_str until base-2 exponents
1117 // are supported in floating-point literals
1118 let f1: f32 = from_str_hex("1p-123").unwrap();
1119 let f2: f32 = from_str_hex("1p-111").unwrap();
1120 assert_eq!(Float::ldexp(1f32, -123), f1);
1121 assert_eq!(Float::ldexp(1f32, -111), f2);
1123 assert_eq!(Float::ldexp(0f32, -123), 0f32);
1124 assert_eq!(Float::ldexp(-0f32, -123), -0f32);
1126 let inf: f32 = Float::infinity();
1127 let neg_inf: f32 = Float::neg_infinity();
1128 let nan: f32 = Float::nan();
1129 assert_eq!(Float::ldexp(inf, -123), inf);
1130 assert_eq!(Float::ldexp(neg_inf, -123), neg_inf);
1131 assert!(Float::ldexp(nan, -123).is_nan());
1136 // We have to use from_str until base-2 exponents
1137 // are supported in floating-point literals
1138 let f1: f32 = from_str_hex("1p-123").unwrap();
1139 let f2: f32 = from_str_hex("1p-111").unwrap();
1140 let (x1, exp1) = f1.frexp();
1141 let (x2, exp2) = f2.frexp();
1142 assert_eq!((x1, exp1), (0.5f32, -122));
1143 assert_eq!((x2, exp2), (0.5f32, -110));
1144 assert_eq!(Float::ldexp(x1, exp1), f1);
1145 assert_eq!(Float::ldexp(x2, exp2), f2);
1147 assert_eq!(0f32.frexp(), (0f32, 0));
1148 assert_eq!((-0f32).frexp(), (-0f32, 0));
1151 #[test] #[ignore(cfg(windows))] // FIXME #8755
1152 fn test_frexp_nowin() {
1153 let inf: f32 = Float::infinity();
1154 let neg_inf: f32 = Float::neg_infinity();
1155 let nan: f32 = Float::nan();
1156 assert_eq!(match inf.frexp() { (x, _) => x }, inf)
1157 assert_eq!(match neg_inf.frexp() { (x, _) => x }, neg_inf)
1158 assert!(match nan.frexp() { (x, _) => x.is_nan() })
1162 fn test_integer_decode() {
1163 assert_eq!(3.14159265359f32.integer_decode(), (13176795u64, -22i16, 1i8));
1164 assert_eq!((-8573.5918555f32).integer_decode(), (8779358u64, -10i16, -1i8));
1165 assert_eq!(2f32.powf(&100.0).integer_decode(), (8388608u64, 77i16, 1i8));
1166 assert_eq!(0f32.integer_decode(), (0u64, -150i16, 1i8));
1167 assert_eq!((-0f32).integer_decode(), (0u64, -150i16, -1i8));
1168 assert_eq!(INFINITY.integer_decode(), (8388608u64, 105i16, 1i8));
1169 assert_eq!(NEG_INFINITY.integer_decode(), (8388608u64, 105i16, -1i8));
1170 assert_eq!(NAN.integer_decode(), (12582912u64, 105i16, 1i8));