1 // Copyright 2012 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 `f64`
14 use num::{Zero, One, strconv};
15 use num::{FPCategory, FPNaN, FPInfinite , FPZero, FPSubnormal, FPNormal};
18 pub use cmath::c_double_targ_consts::*;
19 pub use cmp::{min, max};
21 // An inner module is required to get the #[inline(always)] attribute on the
23 pub use self::delegated::*;
25 macro_rules! delegate(
30 $arg:ident : $arg_ty:ty
32 ) -> $rv:ty = $bound_name:path
36 use cmath::c_double_utils;
37 use libc::{c_double, c_int};
38 use unstable::intrinsics;
42 pub fn $name($( $arg : $arg_ty ),*) -> $rv {
44 $bound_name($( $arg ),*)
54 fn abs(n: f64) -> f64 = intrinsics::fabsf64,
55 fn cos(n: f64) -> f64 = intrinsics::cosf64,
56 fn exp(n: f64) -> f64 = intrinsics::expf64,
57 fn exp2(n: f64) -> f64 = intrinsics::exp2f64,
58 fn floor(x: f64) -> f64 = intrinsics::floorf64,
59 fn ln(n: f64) -> f64 = intrinsics::logf64,
60 fn log10(n: f64) -> f64 = intrinsics::log10f64,
61 fn log2(n: f64) -> f64 = intrinsics::log2f64,
62 fn mul_add(a: f64, b: f64, c: f64) -> f64 = intrinsics::fmaf64,
63 fn pow(n: f64, e: f64) -> f64 = intrinsics::powf64,
64 fn powi(n: f64, e: c_int) -> f64 = intrinsics::powif64,
65 fn sin(n: f64) -> f64 = intrinsics::sinf64,
66 fn sqrt(n: f64) -> f64 = intrinsics::sqrtf64,
68 // LLVM 3.3 required to use intrinsics for these four
69 fn ceil(n: c_double) -> c_double = c_double_utils::ceil,
70 fn trunc(n: c_double) -> c_double = c_double_utils::trunc,
72 fn ceil(n: f64) -> f64 = intrinsics::ceilf64,
73 fn trunc(n: f64) -> f64 = intrinsics::truncf64,
74 fn rint(n: c_double) -> c_double = intrinsics::rintf64,
75 fn nearbyint(n: c_double) -> c_double = intrinsics::nearbyintf64,
79 fn acos(n: c_double) -> c_double = c_double_utils::acos,
80 fn asin(n: c_double) -> c_double = c_double_utils::asin,
81 fn atan(n: c_double) -> c_double = c_double_utils::atan,
82 fn atan2(a: c_double, b: c_double) -> c_double = c_double_utils::atan2,
83 fn cbrt(n: c_double) -> c_double = c_double_utils::cbrt,
84 fn copysign(x: c_double, y: c_double) -> c_double = c_double_utils::copysign,
85 fn cosh(n: c_double) -> c_double = c_double_utils::cosh,
86 fn erf(n: c_double) -> c_double = c_double_utils::erf,
87 fn erfc(n: c_double) -> c_double = c_double_utils::erfc,
88 fn exp_m1(n: c_double) -> c_double = c_double_utils::exp_m1,
89 fn abs_sub(a: c_double, b: c_double) -> c_double = c_double_utils::abs_sub,
90 fn fmax(a: c_double, b: c_double) -> c_double = c_double_utils::fmax,
91 fn fmin(a: c_double, b: c_double) -> c_double = c_double_utils::fmin,
92 fn next_after(x: c_double, y: c_double) -> c_double = c_double_utils::next_after,
93 fn frexp(n: c_double, value: &mut c_int) -> c_double = c_double_utils::frexp,
94 fn hypot(x: c_double, y: c_double) -> c_double = c_double_utils::hypot,
95 fn ldexp(x: c_double, n: c_int) -> c_double = c_double_utils::ldexp,
96 fn lgamma(n: c_double, sign: &mut c_int) -> c_double = c_double_utils::lgamma,
97 fn log_radix(n: c_double) -> c_double = c_double_utils::log_radix,
98 fn ln_1p(n: c_double) -> c_double = c_double_utils::ln_1p,
99 fn ilog_radix(n: c_double) -> c_int = c_double_utils::ilog_radix,
100 fn modf(n: c_double, iptr: &mut c_double) -> c_double = c_double_utils::modf,
101 fn round(n: c_double) -> c_double = c_double_utils::round,
102 fn ldexp_radix(n: c_double, i: c_int) -> c_double = c_double_utils::ldexp_radix,
103 fn sinh(n: c_double) -> c_double = c_double_utils::sinh,
104 fn tan(n: c_double) -> c_double = c_double_utils::tan,
105 fn tanh(n: c_double) -> c_double = c_double_utils::tanh,
106 fn tgamma(n: c_double) -> c_double = c_double_utils::tgamma,
107 fn j0(n: c_double) -> c_double = c_double_utils::j0,
108 fn j1(n: c_double) -> c_double = c_double_utils::j1,
109 fn jn(i: c_int, n: c_double) -> c_double = c_double_utils::jn,
110 fn y0(n: c_double) -> c_double = c_double_utils::y0,
111 fn y1(n: c_double) -> c_double = c_double_utils::y1,
112 fn yn(i: c_int, n: c_double) -> c_double = c_double_utils::yn
115 // FIXME (#1433): obtain these in a different way
117 // These are not defined inside consts:: for consistency with
120 pub static radix: uint = 2u;
122 pub static mantissa_digits: uint = 53u;
123 pub static digits: uint = 15u;
125 pub static epsilon: f64 = 2.2204460492503131e-16_f64;
127 pub static min_value: f64 = 2.2250738585072014e-308_f64;
128 pub static max_value: f64 = 1.7976931348623157e+308_f64;
130 pub static min_exp: int = -1021;
131 pub static max_exp: int = 1024;
133 pub static min_10_exp: int = -307;
134 pub static max_10_exp: int = 308;
136 pub static NaN: f64 = 0.0_f64/0.0_f64;
138 pub static infinity: f64 = 1.0_f64/0.0_f64;
140 pub static neg_infinity: f64 = -1.0_f64/0.0_f64;
143 pub fn add(x: f64, y: f64) -> f64 { return x + y; }
146 pub fn sub(x: f64, y: f64) -> f64 { return x - y; }
149 pub fn mul(x: f64, y: f64) -> f64 { return x * y; }
152 pub fn div(x: f64, y: f64) -> f64 { return x / y; }
155 pub fn rem(x: f64, y: f64) -> f64 { return x % y; }
158 pub fn lt(x: f64, y: f64) -> bool { return x < y; }
161 pub fn le(x: f64, y: f64) -> bool { return x <= y; }
164 pub fn eq(x: f64, y: f64) -> bool { return x == y; }
167 pub fn ne(x: f64, y: f64) -> bool { return x != y; }
170 pub fn ge(x: f64, y: f64) -> bool { return x >= y; }
173 pub fn gt(x: f64, y: f64) -> bool { return x > y; }
176 // FIXME (#1999): add is_normal, is_subnormal, and fpclassify
180 // FIXME (requires Issue #1433 to fix): replace with mathematical
181 // constants from cmath.
182 /// Archimedes' constant
183 pub static pi: f64 = 3.14159265358979323846264338327950288_f64;
186 pub static frac_pi_2: f64 = 1.57079632679489661923132169163975144_f64;
189 pub static frac_pi_4: f64 = 0.785398163397448309615660845819875721_f64;
192 pub static frac_1_pi: f64 = 0.318309886183790671537767526745028724_f64;
195 pub static frac_2_pi: f64 = 0.636619772367581343075535053490057448_f64;
198 pub static frac_2_sqrtpi: f64 = 1.12837916709551257389615890312154517_f64;
201 pub static sqrt2: f64 = 1.41421356237309504880168872420969808_f64;
204 pub static frac_1_sqrt2: f64 = 0.707106781186547524400844362104849039_f64;
207 pub static e: f64 = 2.71828182845904523536028747135266250_f64;
210 pub static log2_e: f64 = 1.44269504088896340735992468100189214_f64;
213 pub static log10_e: f64 = 0.434294481903251827651128918916605082_f64;
216 pub static ln_2: f64 = 0.693147180559945309417232121458176568_f64;
219 pub static ln_10: f64 = 2.30258509299404568401799145468436421_f64;
227 fn eq(&self, other: &f64) -> bool { (*self) == (*other) }
229 fn ne(&self, other: &f64) -> bool { (*self) != (*other) }
233 impl ApproxEq<f64> for f64 {
235 fn approx_epsilon() -> f64 { 1.0e-6 }
238 fn approx_eq(&self, other: &f64) -> bool {
239 self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<f64, f64>())
243 fn approx_eq_eps(&self, other: &f64, approx_epsilon: &f64) -> bool {
244 (*self - *other).abs() < *approx_epsilon
251 fn lt(&self, other: &f64) -> bool { (*self) < (*other) }
253 fn le(&self, other: &f64) -> bool { (*self) <= (*other) }
255 fn ge(&self, other: &f64) -> bool { (*self) >= (*other) }
257 fn gt(&self, other: &f64) -> bool { (*self) > (*other) }
260 impl Orderable for f64 {
261 /// Returns `NaN` if either of the numbers are `NaN`.
263 fn min(&self, other: &f64) -> f64 {
264 if self.is_NaN() || other.is_NaN() { Float::NaN() } else { fmin(*self, *other) }
267 /// Returns `NaN` if either of the numbers are `NaN`.
269 fn max(&self, other: &f64) -> f64 {
270 if self.is_NaN() || other.is_NaN() { Float::NaN() } else { fmax(*self, *other) }
273 /// Returns the number constrained within the range `mn <= self <= mx`.
274 /// If any of the numbers are `NaN` then `NaN` is returned.
276 fn clamp(&self, mn: &f64, mx: &f64) -> f64 {
278 (self.is_NaN()) { *self }
279 (!(*self <= *mx)) { *mx }
280 (!(*self >= *mn)) { *mn }
288 fn zero() -> f64 { 0.0 }
290 /// Returns true if the number is equal to either `0.0` or `-0.0`
292 fn is_zero(&self) -> bool { *self == 0.0 || *self == -0.0 }
297 fn one() -> f64 { 1.0 }
301 impl Add<f64,f64> for f64 {
302 fn add(&self, other: &f64) -> f64 { *self + *other }
305 impl Sub<f64,f64> for f64 {
306 fn sub(&self, other: &f64) -> f64 { *self - *other }
309 impl Mul<f64,f64> for f64 {
310 fn mul(&self, other: &f64) -> f64 { *self * *other }
313 impl Div<f64,f64> for f64 {
314 fn div(&self, other: &f64) -> f64 { *self / *other }
317 impl Rem<f64,f64> for f64 {
319 fn rem(&self, other: &f64) -> f64 { *self % *other }
322 impl Neg<f64> for f64 {
323 fn neg(&self) -> f64 { -*self }
326 impl Signed for f64 {
327 /// Computes the absolute value. Returns `NaN` if the number is `NaN`.
329 fn abs(&self) -> f64 { abs(*self) }
332 /// The positive difference of two numbers. Returns `0.0` if the number is less than or
333 /// equal to `other`, otherwise the difference between`self` and `other` is returned.
336 fn abs_sub(&self, other: &f64) -> f64 { abs_sub(*self, *other) }
341 /// - `1.0` if the number is positive, `+0.0` or `infinity`
342 /// - `-1.0` if the number is negative, `-0.0` or `neg_infinity`
343 /// - `NaN` if the number is NaN
346 fn signum(&self) -> f64 {
347 if self.is_NaN() { NaN } else { copysign(1.0, *self) }
350 /// Returns `true` if the number is positive, including `+0.0` and `infinity`
352 fn is_positive(&self) -> bool { *self > 0.0 || (1.0 / *self) == infinity }
354 /// Returns `true` if the number is negative, including `-0.0` and `neg_infinity`
356 fn is_negative(&self) -> bool { *self < 0.0 || (1.0 / *self) == neg_infinity }
360 /// Round half-way cases toward `neg_infinity`
362 fn floor(&self) -> f64 { floor(*self) }
364 /// Round half-way cases toward `infinity`
366 fn ceil(&self) -> f64 { ceil(*self) }
368 /// Round half-way cases away from `0.0`
370 fn round(&self) -> f64 { round(*self) }
372 /// The integer part of the number (rounds towards `0.0`)
374 fn trunc(&self) -> f64 { trunc(*self) }
377 /// The fractional part of the number, satisfying:
380 /// assert!(x == trunc(x) + fract(x))
384 fn fract(&self) -> f64 { *self - self.trunc() }
387 impl Fractional for f64 {
388 /// The reciprocal (multiplicative inverse) of the number
390 fn recip(&self) -> f64 { 1.0 / *self }
393 impl Algebraic for f64 {
395 fn pow(&self, n: f64) -> f64 { pow(*self, n) }
398 fn sqrt(&self) -> f64 { sqrt(*self) }
401 fn rsqrt(&self) -> f64 { self.sqrt().recip() }
404 fn cbrt(&self) -> f64 { cbrt(*self) }
407 fn hypot(&self, other: f64) -> f64 { hypot(*self, other) }
410 impl Trigonometric for f64 {
412 fn sin(&self) -> f64 { sin(*self) }
415 fn cos(&self) -> f64 { cos(*self) }
418 fn tan(&self) -> f64 { tan(*self) }
421 fn asin(&self) -> f64 { asin(*self) }
424 fn acos(&self) -> f64 { acos(*self) }
427 fn atan(&self) -> f64 { atan(*self) }
430 fn atan2(&self, other: f64) -> f64 { atan2(*self, other) }
432 /// Simultaneously computes the sine and cosine of the number
434 fn sin_cos(&self) -> (f64, f64) {
435 (self.sin(), self.cos())
439 impl Exponential for f64 {
440 /// Returns the exponential of the number
442 fn exp(&self) -> f64 { exp(*self) }
444 /// Returns 2 raised to the power of the number
446 fn exp2(&self) -> f64 { exp2(*self) }
448 /// Returns the natural logarithm of the number
450 fn ln(&self) -> f64 { ln(*self) }
452 /// Returns the logarithm of the number with respect to an arbitrary base
454 fn log(&self, base: f64) -> f64 { self.ln() / base.ln() }
456 /// Returns the base 2 logarithm of the number
458 fn log2(&self) -> f64 { log2(*self) }
460 /// Returns the base 10 logarithm of the number
462 fn log10(&self) -> f64 { log10(*self) }
465 impl Hyperbolic for f64 {
467 fn sinh(&self) -> f64 { sinh(*self) }
470 fn cosh(&self) -> f64 { cosh(*self) }
473 fn tanh(&self) -> f64 { tanh(*self) }
476 /// Inverse hyperbolic sine
480 /// - on success, the inverse hyperbolic sine of `self` will be returned
481 /// - `self` if `self` is `0.0`, `-0.0`, `infinity`, or `neg_infinity`
482 /// - `NaN` if `self` is `NaN`
485 fn asinh(&self) -> f64 {
487 neg_infinity => neg_infinity,
488 x => (x + ((x * x) + 1.0).sqrt()).ln(),
493 /// Inverse hyperbolic cosine
497 /// - on success, the inverse hyperbolic cosine of `self` will be returned
498 /// - `infinity` if `self` is `infinity`
499 /// - `NaN` if `self` is `NaN` or `self < 1.0` (including `neg_infinity`)
502 fn acosh(&self) -> f64 {
504 x if x < 1.0 => Float::NaN(),
505 x => (x + ((x * x) - 1.0).sqrt()).ln(),
510 /// Inverse hyperbolic tangent
514 /// - on success, the inverse hyperbolic tangent of `self` will be returned
515 /// - `self` if `self` is `0.0` or `-0.0`
516 /// - `infinity` if `self` is `1.0`
517 /// - `neg_infinity` if `self` is `-1.0`
518 /// - `NaN` if the `self` is `NaN` or outside the domain of `-1.0 <= self <= 1.0`
519 /// (including `infinity` and `neg_infinity`)
522 fn atanh(&self) -> f64 {
523 0.5 * ((2.0 * *self) / (1.0 - *self)).ln_1p()
528 /// Archimedes' constant
530 fn pi() -> f64 { 3.14159265358979323846264338327950288 }
534 fn two_pi() -> f64 { 6.28318530717958647692528676655900576 }
538 fn frac_pi_2() -> f64 { 1.57079632679489661923132169163975144 }
542 fn frac_pi_3() -> f64 { 1.04719755119659774615421446109316763 }
546 fn frac_pi_4() -> f64 { 0.785398163397448309615660845819875721 }
550 fn frac_pi_6() -> f64 { 0.52359877559829887307710723054658381 }
554 fn frac_pi_8() -> f64 { 0.39269908169872415480783042290993786 }
558 fn frac_1_pi() -> f64 { 0.318309886183790671537767526745028724 }
562 fn frac_2_pi() -> f64 { 0.636619772367581343075535053490057448 }
566 fn frac_2_sqrtpi() -> f64 { 1.12837916709551257389615890312154517 }
570 fn sqrt2() -> f64 { 1.41421356237309504880168872420969808 }
574 fn frac_1_sqrt2() -> f64 { 0.707106781186547524400844362104849039 }
578 fn e() -> f64 { 2.71828182845904523536028747135266250 }
582 fn log2_e() -> f64 { 1.44269504088896340735992468100189214 }
586 fn log10_e() -> f64 { 0.434294481903251827651128918916605082 }
590 fn ln_2() -> f64 { 0.693147180559945309417232121458176568 }
594 fn ln_10() -> f64 { 2.30258509299404568401799145468436421 }
596 /// Converts to degrees, assuming the number is in radians
598 fn to_degrees(&self) -> f64 { *self * (180.0 / Real::pi::<f64>()) }
600 /// Converts to radians, assuming the number is in degrees
602 fn to_radians(&self) -> f64 { *self * (Real::pi::<f64>() / 180.0) }
605 impl RealExt for f64 {
607 fn lgamma(&self) -> (int, f64) {
609 let result = lgamma(*self, &mut sign);
610 (sign as int, result)
614 fn tgamma(&self) -> f64 { tgamma(*self) }
617 fn j0(&self) -> f64 { j0(*self) }
620 fn j1(&self) -> f64 { j1(*self) }
623 fn jn(&self, n: int) -> f64 { jn(n as c_int, *self) }
626 fn y0(&self) -> f64 { y0(*self) }
629 fn y1(&self) -> f64 { y1(*self) }
632 fn yn(&self, n: int) -> f64 { yn(n as c_int, *self) }
635 impl Bounded for f64 {
637 fn min_value() -> f64 { 2.2250738585072014e-308 }
640 fn max_value() -> f64 { 1.7976931348623157e+308 }
643 impl Primitive for f64 {
645 fn bits() -> uint { 64 }
648 fn bytes() -> uint { Primitive::bits::<f64>() / 8 }
653 fn NaN() -> f64 { 0.0 / 0.0 }
656 fn infinity() -> f64 { 1.0 / 0.0 }
659 fn neg_infinity() -> f64 { -1.0 / 0.0 }
662 fn neg_zero() -> f64 { -0.0 }
664 /// Returns `true` if the number is NaN
666 fn is_NaN(&self) -> bool { *self != *self }
668 /// Returns `true` if the number is infinite
670 fn is_infinite(&self) -> bool {
671 *self == Float::infinity() || *self == Float::neg_infinity()
674 /// Returns `true` if the number is neither infinite or NaN
676 fn is_finite(&self) -> bool {
677 !(self.is_NaN() || self.is_infinite())
680 /// Returns `true` if the number is neither zero, infinite, subnormal or NaN
682 fn is_normal(&self) -> bool {
683 self.classify() == FPNormal
686 /// Returns the floating point category of the number. If only one property is going to
687 /// be tested, it is generally faster to use the specific predicate instead.
688 fn classify(&self) -> FPCategory {
689 static EXP_MASK: u64 = 0x7ff0000000000000;
690 static MAN_MASK: u64 = 0x000fffffffffffff;
693 unsafe { ::cast::transmute::<f64,u64>(*self) } & MAN_MASK,
694 unsafe { ::cast::transmute::<f64,u64>(*self) } & EXP_MASK,
697 (_, 0) => FPSubnormal,
698 (0, EXP_MASK) => FPInfinite,
699 (_, EXP_MASK) => FPNaN,
705 fn mantissa_digits() -> uint { 53 }
708 fn digits() -> uint { 15 }
711 fn epsilon() -> f64 { 2.2204460492503131e-16 }
714 fn min_exp() -> int { -1021 }
717 fn max_exp() -> int { 1024 }
720 fn min_10_exp() -> int { -307 }
723 fn max_10_exp() -> int { 308 }
725 /// Constructs a floating point number by multiplying `x` by 2 raised to the power of `exp`
727 fn ldexp(x: f64, exp: int) -> f64 {
728 ldexp(x, exp as c_int)
732 /// Breaks the number into a normalized fraction and a base-2 exponent, satisfying:
734 /// - `self = x * pow(2, exp)`
735 /// - `0.5 <= abs(x) < 1.0`
738 fn frexp(&self) -> (f64, int) {
740 let x = frexp(*self, &mut exp);
745 /// Returns the exponential of the number, minus `1`, in a way that is accurate
746 /// even if the number is close to zero
749 fn exp_m1(&self) -> f64 { exp_m1(*self) }
752 /// Returns the natural logarithm of the number plus `1` (`ln(1+n)`) more accurately
753 /// than if the operations were performed separately
756 fn ln_1p(&self) -> f64 { ln_1p(*self) }
759 /// Fused multiply-add. Computes `(self * a) + b` with only one rounding error. This
760 /// produces a more accurate result with better performance than a separate multiplication
761 /// operation followed by an add.
764 fn mul_add(&self, a: f64, b: f64) -> f64 {
768 /// Returns the next representable floating-point value in the direction of `other`
770 fn next_after(&self, other: f64) -> f64 {
771 next_after(*self, other)
776 // Section: String Conversions
780 /// Converts a float to a string
784 /// * num - The float value
787 pub fn to_str(num: f64) -> ~str {
788 let (r, _) = strconv::to_str_common(
789 &num, 10u, true, strconv::SignNeg, strconv::DigAll);
794 /// Converts a float to a string in hexadecimal format
798 /// * num - The float value
801 pub fn to_str_hex(num: f64) -> ~str {
802 let (r, _) = strconv::to_str_common(
803 &num, 16u, true, strconv::SignNeg, strconv::DigAll);
808 /// Converts a float to a string in a given radix
812 /// * num - The float value
813 /// * radix - The base to use
817 /// Fails if called on a special value like `inf`, `-inf` or `NaN` due to
818 /// possible misinterpretation of the result at higher bases. If those values
819 /// are expected, use `to_str_radix_special()` instead.
822 pub fn to_str_radix(num: f64, rdx: uint) -> ~str {
823 let (r, special) = strconv::to_str_common(
824 &num, rdx, true, strconv::SignNeg, strconv::DigAll);
825 if special { fail!("number has a special value, \
826 try to_str_radix_special() if those are expected") }
831 /// Converts a float to a string in a given radix, and a flag indicating
832 /// whether it's a special value
836 /// * num - The float value
837 /// * radix - The base to use
840 pub fn to_str_radix_special(num: f64, rdx: uint) -> (~str, bool) {
841 strconv::to_str_common(&num, rdx, true,
842 strconv::SignNeg, strconv::DigAll)
846 /// Converts a float to a string with exactly the number of
847 /// provided significant digits
851 /// * num - The float value
852 /// * digits - The number of significant digits
855 pub fn to_str_exact(num: f64, dig: uint) -> ~str {
856 let (r, _) = strconv::to_str_common(
857 &num, 10u, true, strconv::SignNeg, strconv::DigExact(dig));
862 /// Converts a float to a string with a maximum number of
863 /// significant digits
867 /// * num - The float value
868 /// * digits - The number of significant digits
871 pub fn to_str_digits(num: f64, dig: uint) -> ~str {
872 let (r, _) = strconv::to_str_common(
873 &num, 10u, true, strconv::SignNeg, strconv::DigMax(dig));
877 impl to_str::ToStr for f64 {
879 fn to_str(&self) -> ~str { to_str_digits(*self, 8) }
882 impl num::ToStrRadix for f64 {
884 fn to_str_radix(&self, rdx: uint) -> ~str {
885 to_str_radix(*self, rdx)
890 /// Convert a string in base 10 to a float.
891 /// Accepts a optional decimal exponent.
893 /// This function accepts strings such as
896 /// * '+3.14', equivalent to '3.14'
898 /// * '2.5E10', or equivalently, '2.5e10'
900 /// * '.' (understood as 0)
902 /// * '.5', or, equivalently, '0.5'
903 /// * '+inf', 'inf', '-inf', 'NaN'
905 /// Leading and trailing whitespace represent an error.
913 /// `none` if the string did not represent a valid number. Otherwise,
914 /// `Some(n)` where `n` is the floating-point number represented by `num`.
917 pub fn from_str(num: &str) -> Option<f64> {
918 strconv::from_str_common(num, 10u, true, true, true,
919 strconv::ExpDec, false, false)
923 /// Convert a string in base 16 to a float.
924 /// Accepts a optional binary exponent.
926 /// This function accepts strings such as
929 /// * '+a4.fe', equivalent to 'a4.fe'
931 /// * '2b.aP128', or equivalently, '2b.ap128'
933 /// * '.' (understood as 0)
935 /// * '.c', or, equivalently, '0.c'
936 /// * '+inf', 'inf', '-inf', 'NaN'
938 /// Leading and trailing whitespace represent an error.
946 /// `none` if the string did not represent a valid number. Otherwise,
947 /// `Some(n)` where `n` is the floating-point number represented by `[num]`.
950 pub fn from_str_hex(num: &str) -> Option<f64> {
951 strconv::from_str_common(num, 16u, true, true, true,
952 strconv::ExpBin, false, false)
956 /// Convert a string in an given base to a float.
958 /// Due to possible conflicts, this function does **not** accept
959 /// the special values `inf`, `-inf`, `+inf` and `NaN`, **nor**
960 /// does it recognize exponents of any kind.
962 /// Leading and trailing whitespace represent an error.
967 /// * radix - The base to use. Must lie in the range [2 .. 36]
971 /// `none` if the string did not represent a valid number. Otherwise,
972 /// `Some(n)` where `n` is the floating-point number represented by `num`.
975 pub fn from_str_radix(num: &str, rdx: uint) -> Option<f64> {
976 strconv::from_str_common(num, rdx, true, true, false,
977 strconv::ExpNone, false, false)
980 impl FromStr for f64 {
982 fn from_str(val: &str) -> Option<f64> { from_str(val) }
985 impl num::FromStrRadix for f64 {
987 fn from_str_radix(val: &str, rdx: uint) -> Option<f64> {
988 from_str_radix(val, rdx)
1001 num::test_num(10f64, 2f64);
1006 assert_eq!(1f64.min(&2f64), 1f64);
1007 assert_eq!(2f64.min(&1f64), 1f64);
1008 assert!(1f64.min(&Float::NaN::<f64>()).is_NaN());
1009 assert!(Float::NaN::<f64>().min(&1f64).is_NaN());
1014 assert_eq!(1f64.max(&2f64), 2f64);
1015 assert_eq!(2f64.max(&1f64), 2f64);
1016 assert!(1f64.max(&Float::NaN::<f64>()).is_NaN());
1017 assert!(Float::NaN::<f64>().max(&1f64).is_NaN());
1022 assert_eq!(1f64.clamp(&2f64, &4f64), 2f64);
1023 assert_eq!(8f64.clamp(&2f64, &4f64), 4f64);
1024 assert_eq!(3f64.clamp(&2f64, &4f64), 3f64);
1025 assert!(3f64.clamp(&Float::NaN::<f64>(), &4f64).is_NaN());
1026 assert!(3f64.clamp(&2f64, &Float::NaN::<f64>()).is_NaN());
1027 assert!(Float::NaN::<f64>().clamp(&2f64, &4f64).is_NaN());
1032 assert_approx_eq!(1.0f64.floor(), 1.0f64);
1033 assert_approx_eq!(1.3f64.floor(), 1.0f64);
1034 assert_approx_eq!(1.5f64.floor(), 1.0f64);
1035 assert_approx_eq!(1.7f64.floor(), 1.0f64);
1036 assert_approx_eq!(0.0f64.floor(), 0.0f64);
1037 assert_approx_eq!((-0.0f64).floor(), -0.0f64);
1038 assert_approx_eq!((-1.0f64).floor(), -1.0f64);
1039 assert_approx_eq!((-1.3f64).floor(), -2.0f64);
1040 assert_approx_eq!((-1.5f64).floor(), -2.0f64);
1041 assert_approx_eq!((-1.7f64).floor(), -2.0f64);
1046 assert_approx_eq!(1.0f64.ceil(), 1.0f64);
1047 assert_approx_eq!(1.3f64.ceil(), 2.0f64);
1048 assert_approx_eq!(1.5f64.ceil(), 2.0f64);
1049 assert_approx_eq!(1.7f64.ceil(), 2.0f64);
1050 assert_approx_eq!(0.0f64.ceil(), 0.0f64);
1051 assert_approx_eq!((-0.0f64).ceil(), -0.0f64);
1052 assert_approx_eq!((-1.0f64).ceil(), -1.0f64);
1053 assert_approx_eq!((-1.3f64).ceil(), -1.0f64);
1054 assert_approx_eq!((-1.5f64).ceil(), -1.0f64);
1055 assert_approx_eq!((-1.7f64).ceil(), -1.0f64);
1060 assert_approx_eq!(1.0f64.round(), 1.0f64);
1061 assert_approx_eq!(1.3f64.round(), 1.0f64);
1062 assert_approx_eq!(1.5f64.round(), 2.0f64);
1063 assert_approx_eq!(1.7f64.round(), 2.0f64);
1064 assert_approx_eq!(0.0f64.round(), 0.0f64);
1065 assert_approx_eq!((-0.0f64).round(), -0.0f64);
1066 assert_approx_eq!((-1.0f64).round(), -1.0f64);
1067 assert_approx_eq!((-1.3f64).round(), -1.0f64);
1068 assert_approx_eq!((-1.5f64).round(), -2.0f64);
1069 assert_approx_eq!((-1.7f64).round(), -2.0f64);
1074 assert_approx_eq!(1.0f64.trunc(), 1.0f64);
1075 assert_approx_eq!(1.3f64.trunc(), 1.0f64);
1076 assert_approx_eq!(1.5f64.trunc(), 1.0f64);
1077 assert_approx_eq!(1.7f64.trunc(), 1.0f64);
1078 assert_approx_eq!(0.0f64.trunc(), 0.0f64);
1079 assert_approx_eq!((-0.0f64).trunc(), -0.0f64);
1080 assert_approx_eq!((-1.0f64).trunc(), -1.0f64);
1081 assert_approx_eq!((-1.3f64).trunc(), -1.0f64);
1082 assert_approx_eq!((-1.5f64).trunc(), -1.0f64);
1083 assert_approx_eq!((-1.7f64).trunc(), -1.0f64);
1088 assert_approx_eq!(1.0f64.fract(), 0.0f64);
1089 assert_approx_eq!(1.3f64.fract(), 0.3f64);
1090 assert_approx_eq!(1.5f64.fract(), 0.5f64);
1091 assert_approx_eq!(1.7f64.fract(), 0.7f64);
1092 assert_approx_eq!(0.0f64.fract(), 0.0f64);
1093 assert_approx_eq!((-0.0f64).fract(), -0.0f64);
1094 assert_approx_eq!((-1.0f64).fract(), -0.0f64);
1095 assert_approx_eq!((-1.3f64).fract(), -0.3f64);
1096 assert_approx_eq!((-1.5f64).fract(), -0.5f64);
1097 assert_approx_eq!((-1.7f64).fract(), -0.7f64);
1102 assert_eq!(0.0f64.asinh(), 0.0f64);
1103 assert_eq!((-0.0f64).asinh(), -0.0f64);
1104 assert_eq!(Float::infinity::<f64>().asinh(), Float::infinity::<f64>());
1105 assert_eq!(Float::neg_infinity::<f64>().asinh(), Float::neg_infinity::<f64>());
1106 assert!(Float::NaN::<f64>().asinh().is_NaN());
1107 assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64);
1108 assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64);
1113 assert_eq!(1.0f64.acosh(), 0.0f64);
1114 assert!(0.999f64.acosh().is_NaN());
1115 assert_eq!(Float::infinity::<f64>().acosh(), Float::infinity::<f64>());
1116 assert!(Float::neg_infinity::<f64>().acosh().is_NaN());
1117 assert!(Float::NaN::<f64>().acosh().is_NaN());
1118 assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64);
1119 assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64);
1124 assert_eq!(0.0f64.atanh(), 0.0f64);
1125 assert_eq!((-0.0f64).atanh(), -0.0f64);
1126 assert_eq!(1.0f64.atanh(), Float::infinity::<f64>());
1127 assert_eq!((-1.0f64).atanh(), Float::neg_infinity::<f64>());
1128 assert!(2f64.atanh().atanh().is_NaN());
1129 assert!((-2f64).atanh().atanh().is_NaN());
1130 assert!(Float::infinity::<f64>().atanh().is_NaN());
1131 assert!(Float::neg_infinity::<f64>().atanh().is_NaN());
1132 assert!(Float::NaN::<f64>().atanh().is_NaN());
1133 assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64);
1134 assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64);
1138 fn test_real_consts() {
1139 assert_approx_eq!(Real::two_pi::<f64>(), 2.0 * Real::pi::<f64>());
1140 assert_approx_eq!(Real::frac_pi_2::<f64>(), Real::pi::<f64>() / 2f64);
1141 assert_approx_eq!(Real::frac_pi_3::<f64>(), Real::pi::<f64>() / 3f64);
1142 assert_approx_eq!(Real::frac_pi_4::<f64>(), Real::pi::<f64>() / 4f64);
1143 assert_approx_eq!(Real::frac_pi_6::<f64>(), Real::pi::<f64>() / 6f64);
1144 assert_approx_eq!(Real::frac_pi_8::<f64>(), Real::pi::<f64>() / 8f64);
1145 assert_approx_eq!(Real::frac_1_pi::<f64>(), 1f64 / Real::pi::<f64>());
1146 assert_approx_eq!(Real::frac_2_pi::<f64>(), 2f64 / Real::pi::<f64>());
1147 assert_approx_eq!(Real::frac_2_sqrtpi::<f64>(), 2f64 / Real::pi::<f64>().sqrt());
1148 assert_approx_eq!(Real::sqrt2::<f64>(), 2f64.sqrt());
1149 assert_approx_eq!(Real::frac_1_sqrt2::<f64>(), 1f64 / 2f64.sqrt());
1150 assert_approx_eq!(Real::log2_e::<f64>(), Real::e::<f64>().log2());
1151 assert_approx_eq!(Real::log10_e::<f64>(), Real::e::<f64>().log10());
1152 assert_approx_eq!(Real::ln_2::<f64>(), 2f64.ln());
1153 assert_approx_eq!(Real::ln_10::<f64>(), 10f64.ln());
1158 assert_eq!(infinity.abs(), infinity);
1159 assert_eq!(1f64.abs(), 1f64);
1160 assert_eq!(0f64.abs(), 0f64);
1161 assert_eq!((-0f64).abs(), 0f64);
1162 assert_eq!((-1f64).abs(), 1f64);
1163 assert_eq!(neg_infinity.abs(), infinity);
1164 assert_eq!((1f64/neg_infinity).abs(), 0f64);
1165 assert!(NaN.abs().is_NaN());
1170 assert_eq!((-1f64).abs_sub(&1f64), 0f64);
1171 assert_eq!(1f64.abs_sub(&1f64), 0f64);
1172 assert_eq!(1f64.abs_sub(&0f64), 1f64);
1173 assert_eq!(1f64.abs_sub(&-1f64), 2f64);
1174 assert_eq!(neg_infinity.abs_sub(&0f64), 0f64);
1175 assert_eq!(infinity.abs_sub(&1f64), infinity);
1176 assert_eq!(0f64.abs_sub(&neg_infinity), infinity);
1177 assert_eq!(0f64.abs_sub(&infinity), 0f64);
1178 assert!(NaN.abs_sub(&-1f64).is_NaN());
1179 assert!(1f64.abs_sub(&NaN).is_NaN());
1184 assert_eq!(infinity.signum(), 1f64);
1185 assert_eq!(1f64.signum(), 1f64);
1186 assert_eq!(0f64.signum(), 1f64);
1187 assert_eq!((-0f64).signum(), -1f64);
1188 assert_eq!((-1f64).signum(), -1f64);
1189 assert_eq!(neg_infinity.signum(), -1f64);
1190 assert_eq!((1f64/neg_infinity).signum(), -1f64);
1191 assert!(NaN.signum().is_NaN());
1195 fn test_is_positive() {
1196 assert!(infinity.is_positive());
1197 assert!(1f64.is_positive());
1198 assert!(0f64.is_positive());
1199 assert!(!(-0f64).is_positive());
1200 assert!(!(-1f64).is_positive());
1201 assert!(!neg_infinity.is_positive());
1202 assert!(!(1f64/neg_infinity).is_positive());
1203 assert!(!NaN.is_positive());
1207 fn test_is_negative() {
1208 assert!(!infinity.is_negative());
1209 assert!(!1f64.is_negative());
1210 assert!(!0f64.is_negative());
1211 assert!((-0f64).is_negative());
1212 assert!((-1f64).is_negative());
1213 assert!(neg_infinity.is_negative());
1214 assert!((1f64/neg_infinity).is_negative());
1215 assert!(!NaN.is_negative());
1219 fn test_approx_eq() {
1220 assert!(1.0f64.approx_eq(&1f64));
1221 assert!(0.9999999f64.approx_eq(&1f64));
1222 assert!(1.000001f64.approx_eq_eps(&1f64, &1.0e-5));
1223 assert!(1.0000001f64.approx_eq_eps(&1f64, &1.0e-6));
1224 assert!(!1.0000001f64.approx_eq_eps(&1f64, &1.0e-7));
1228 fn test_primitive() {
1229 assert_eq!(Primitive::bits::<f64>(), sys::size_of::<f64>() * 8);
1230 assert_eq!(Primitive::bytes::<f64>(), sys::size_of::<f64>());
1234 fn test_is_normal() {
1235 assert!(!Float::NaN::<f64>().is_normal());
1236 assert!(!Float::infinity::<f64>().is_normal());
1237 assert!(!Float::neg_infinity::<f64>().is_normal());
1238 assert!(!Zero::zero::<f64>().is_normal());
1239 assert!(!Float::neg_zero::<f64>().is_normal());
1240 assert!(1f64.is_normal());
1241 assert!(1e-307f64.is_normal());
1242 assert!(!1e-308f64.is_normal());
1246 fn test_classify() {
1247 assert_eq!(Float::NaN::<f64>().classify(), FPNaN);
1248 assert_eq!(Float::infinity::<f64>().classify(), FPInfinite);
1249 assert_eq!(Float::neg_infinity::<f64>().classify(), FPInfinite);
1250 assert_eq!(Zero::zero::<f64>().classify(), FPZero);
1251 assert_eq!(Float::neg_zero::<f64>().classify(), FPZero);
1252 assert_eq!(1e-307f64.classify(), FPNormal);
1253 assert_eq!(1e-308f64.classify(), FPSubnormal);
1258 // We have to use from_str until base-2 exponents
1259 // are supported in floating-point literals
1260 let f1: f64 = from_str_hex("1p-123").unwrap();
1261 let f2: f64 = from_str_hex("1p-111").unwrap();
1262 assert_eq!(Float::ldexp(1f64, -123), f1);
1263 assert_eq!(Float::ldexp(1f64, -111), f2);
1265 assert_eq!(Float::ldexp(0f64, -123), 0f64);
1266 assert_eq!(Float::ldexp(-0f64, -123), -0f64);
1267 assert_eq!(Float::ldexp(Float::infinity::<f64>(), -123),
1268 Float::infinity::<f64>());
1269 assert_eq!(Float::ldexp(Float::neg_infinity::<f64>(), -123),
1270 Float::neg_infinity::<f64>());
1271 assert!(Float::ldexp(Float::NaN::<f64>(), -123).is_NaN());
1276 // We have to use from_str until base-2 exponents
1277 // are supported in floating-point literals
1278 let f1: f64 = from_str_hex("1p-123").unwrap();
1279 let f2: f64 = from_str_hex("1p-111").unwrap();
1280 let (x1, exp1) = f1.frexp();
1281 let (x2, exp2) = f2.frexp();
1282 assert_eq!((x1, exp1), (0.5f64, -122));
1283 assert_eq!((x2, exp2), (0.5f64, -110));
1284 assert_eq!(Float::ldexp(x1, exp1), f1);
1285 assert_eq!(Float::ldexp(x2, exp2), f2);
1287 assert_eq!(0f64.frexp(), (0f64, 0));
1288 assert_eq!((-0f64).frexp(), (-0f64, 0));
1289 assert_eq!(match Float::infinity::<f64>().frexp() { (x, _) => x },
1290 Float::infinity::<f64>())
1291 assert_eq!(match Float::neg_infinity::<f64>().frexp() { (x, _) => x },
1292 Float::neg_infinity::<f64>())
1293 assert!(match Float::NaN::<f64>().frexp() { (x, _) => x.is_NaN() })