// Copyright 2012 The Rust Project Developers. See the COPYRIGHT // file at the top-level directory of this distribution and at // http://rust-lang.org/COPYRIGHT. // // Licensed under the Apache License, Version 2.0 or the MIT license // , at your // option. This file may not be copied, modified, or distributed // except according to those terms. //! Operations and constants for `f64` #[allow(missing_doc)]; #[allow(non_uppercase_statics)]; use libc::c_int; use num::{Zero, One, strconv}; use num::{FPCategory, FPNaN, FPInfinite , FPZero, FPSubnormal, FPNormal}; use num; use prelude::*; use to_str; pub use cmath::c_double_targ_consts::*; pub use cmp::{min, max}; use self::delegated::*; macro_rules! delegate( ( $( fn $name:ident( $( $arg:ident : $arg_ty:ty ),* ) -> $rv:ty = $bound_name:path ),* ) => ( // An inner module is required to get the #[inline] attribute on the // functions. mod delegated { use cmath::c_double_utils; use libc::{c_double, c_int}; use unstable::intrinsics; $( #[inline] #[fixed_stack_segment] #[inline(never)] pub fn $name($( $arg : $arg_ty ),*) -> $rv { unsafe { $bound_name($( $arg ),*) } } )* } ) ) delegate!( // intrinsics fn abs(n: f64) -> f64 = intrinsics::fabsf64, fn cos(n: f64) -> f64 = intrinsics::cosf64, fn exp(n: f64) -> f64 = intrinsics::expf64, fn exp2(n: f64) -> f64 = intrinsics::exp2f64, fn floor(x: f64) -> f64 = intrinsics::floorf64, fn ln(n: f64) -> f64 = intrinsics::logf64, fn log10(n: f64) -> f64 = intrinsics::log10f64, fn log2(n: f64) -> f64 = intrinsics::log2f64, fn mul_add(a: f64, b: f64, c: f64) -> f64 = intrinsics::fmaf64, fn pow(n: f64, e: f64) -> f64 = intrinsics::powf64, fn powi(n: f64, e: c_int) -> f64 = intrinsics::powif64, fn sin(n: f64) -> f64 = intrinsics::sinf64, fn sqrt(n: f64) -> f64 = intrinsics::sqrtf64, // LLVM 3.3 required to use intrinsics for these four fn ceil(n: c_double) -> c_double = c_double_utils::ceil, fn trunc(n: c_double) -> c_double = c_double_utils::trunc, /* fn ceil(n: f64) -> f64 = intrinsics::ceilf64, fn trunc(n: f64) -> f64 = intrinsics::truncf64, fn rint(n: c_double) -> c_double = intrinsics::rintf64, fn nearbyint(n: c_double) -> c_double = intrinsics::nearbyintf64, */ // cmath fn acos(n: c_double) -> c_double = c_double_utils::acos, fn asin(n: c_double) -> c_double = c_double_utils::asin, fn atan(n: c_double) -> c_double = c_double_utils::atan, fn atan2(a: c_double, b: c_double) -> c_double = c_double_utils::atan2, fn cbrt(n: c_double) -> c_double = c_double_utils::cbrt, fn copysign(x: c_double, y: c_double) -> c_double = c_double_utils::copysign, fn cosh(n: c_double) -> c_double = c_double_utils::cosh, fn erf(n: c_double) -> c_double = c_double_utils::erf, fn erfc(n: c_double) -> c_double = c_double_utils::erfc, fn exp_m1(n: c_double) -> c_double = c_double_utils::exp_m1, fn abs_sub(a: c_double, b: c_double) -> c_double = c_double_utils::abs_sub, fn next_after(x: c_double, y: c_double) -> c_double = c_double_utils::next_after, fn frexp(n: c_double, value: &mut c_int) -> c_double = c_double_utils::frexp, fn hypot(x: c_double, y: c_double) -> c_double = c_double_utils::hypot, fn ldexp(x: c_double, n: c_int) -> c_double = c_double_utils::ldexp, fn lgamma(n: c_double, sign: &mut c_int) -> c_double = c_double_utils::lgamma, fn log_radix(n: c_double) -> c_double = c_double_utils::log_radix, fn ln_1p(n: c_double) -> c_double = c_double_utils::ln_1p, fn ilog_radix(n: c_double) -> c_int = c_double_utils::ilog_radix, fn modf(n: c_double, iptr: &mut c_double) -> c_double = c_double_utils::modf, fn round(n: c_double) -> c_double = c_double_utils::round, fn ldexp_radix(n: c_double, i: c_int) -> c_double = c_double_utils::ldexp_radix, fn sinh(n: c_double) -> c_double = c_double_utils::sinh, fn tan(n: c_double) -> c_double = c_double_utils::tan, fn tanh(n: c_double) -> c_double = c_double_utils::tanh, fn tgamma(n: c_double) -> c_double = c_double_utils::tgamma, fn j0(n: c_double) -> c_double = c_double_utils::j0, fn j1(n: c_double) -> c_double = c_double_utils::j1, fn jn(i: c_int, n: c_double) -> c_double = c_double_utils::jn, fn y0(n: c_double) -> c_double = c_double_utils::y0, fn y1(n: c_double) -> c_double = c_double_utils::y1, fn yn(i: c_int, n: c_double) -> c_double = c_double_utils::yn ) // FIXME (#1433): obtain these in a different way // These are not defined inside consts:: for consistency with // the integer types pub static radix: uint = 2u; pub static mantissa_digits: uint = 53u; pub static digits: uint = 15u; pub static epsilon: f64 = 2.2204460492503131e-16_f64; pub static min_value: f64 = 2.2250738585072014e-308_f64; pub static max_value: f64 = 1.7976931348623157e+308_f64; pub static min_exp: int = -1021; pub static max_exp: int = 1024; pub static min_10_exp: int = -307; pub static max_10_exp: int = 308; pub static NaN: f64 = 0.0_f64/0.0_f64; pub static infinity: f64 = 1.0_f64/0.0_f64; pub static neg_infinity: f64 = -1.0_f64/0.0_f64; // FIXME (#1999): add is_normal, is_subnormal, and fpclassify /* Module: consts */ pub mod consts { // FIXME (requires Issue #1433 to fix): replace with mathematical // constants from cmath. /// Archimedes' constant pub static pi: f64 = 3.14159265358979323846264338327950288_f64; /// pi/2.0 pub static frac_pi_2: f64 = 1.57079632679489661923132169163975144_f64; /// pi/4.0 pub static frac_pi_4: f64 = 0.785398163397448309615660845819875721_f64; /// 1.0/pi pub static frac_1_pi: f64 = 0.318309886183790671537767526745028724_f64; /// 2.0/pi pub static frac_2_pi: f64 = 0.636619772367581343075535053490057448_f64; /// 2.0/sqrt(pi) pub static frac_2_sqrtpi: f64 = 1.12837916709551257389615890312154517_f64; /// sqrt(2.0) pub static sqrt2: f64 = 1.41421356237309504880168872420969808_f64; /// 1.0/sqrt(2.0) pub static frac_1_sqrt2: f64 = 0.707106781186547524400844362104849039_f64; /// Euler's number pub static e: f64 = 2.71828182845904523536028747135266250_f64; /// log2(e) pub static log2_e: f64 = 1.44269504088896340735992468100189214_f64; /// log10(e) pub static log10_e: f64 = 0.434294481903251827651128918916605082_f64; /// ln(2.0) pub static ln_2: f64 = 0.693147180559945309417232121458176568_f64; /// ln(10.0) pub static ln_10: f64 = 2.30258509299404568401799145468436421_f64; } impl Num for f64 {} #[cfg(not(test))] impl Eq for f64 { #[inline] fn eq(&self, other: &f64) -> bool { (*self) == (*other) } } #[cfg(not(test))] impl ApproxEq for f64 { #[inline] fn approx_epsilon() -> f64 { 1.0e-6 } #[inline] fn approx_eq(&self, other: &f64) -> bool { self.approx_eq_eps(other, &1.0e-6) } #[inline] fn approx_eq_eps(&self, other: &f64, approx_epsilon: &f64) -> bool { (*self - *other).abs() < *approx_epsilon } } #[cfg(not(test))] impl Ord for f64 { #[inline] fn lt(&self, other: &f64) -> bool { (*self) < (*other) } #[inline] fn le(&self, other: &f64) -> bool { (*self) <= (*other) } #[inline] fn ge(&self, other: &f64) -> bool { (*self) >= (*other) } #[inline] fn gt(&self, other: &f64) -> bool { (*self) > (*other) } } impl Orderable for f64 { /// Returns `NaN` if either of the numbers are `NaN`. #[inline] fn min(&self, other: &f64) -> f64 { cond!( (self.is_NaN()) { *self } (other.is_NaN()) { *other } (*self < *other) { *self } _ { *other } ) } /// Returns `NaN` if either of the numbers are `NaN`. #[inline] fn max(&self, other: &f64) -> f64 { cond!( (self.is_NaN()) { *self } (other.is_NaN()) { *other } (*self > *other) { *self } _ { *other } ) } /// Returns the number constrained within the range `mn <= self <= mx`. /// If any of the numbers are `NaN` then `NaN` is returned. #[inline] fn clamp(&self, mn: &f64, mx: &f64) -> f64 { cond!( (self.is_NaN()) { *self } (!(*self <= *mx)) { *mx } (!(*self >= *mn)) { *mn } _ { *self } ) } } impl Zero for f64 { #[inline] fn zero() -> f64 { 0.0 } /// Returns true if the number is equal to either `0.0` or `-0.0` #[inline] fn is_zero(&self) -> bool { *self == 0.0 || *self == -0.0 } } impl One for f64 { #[inline] fn one() -> f64 { 1.0 } } #[cfg(not(test))] impl Add for f64 { #[inline] fn add(&self, other: &f64) -> f64 { *self + *other } } #[cfg(not(test))] impl Sub for f64 { #[inline] fn sub(&self, other: &f64) -> f64 { *self - *other } } #[cfg(not(test))] impl Mul for f64 { #[inline] fn mul(&self, other: &f64) -> f64 { *self * *other } } #[cfg(not(test))] impl Div for f64 { #[inline] fn div(&self, other: &f64) -> f64 { *self / *other } } #[cfg(not(test))] impl Rem for f64 { #[inline] fn rem(&self, other: &f64) -> f64 { *self % *other } } #[cfg(not(test))] impl Neg for f64 { fn neg(&self) -> f64 { -*self } } impl Signed for f64 { /// Computes the absolute value. Returns `NaN` if the number is `NaN`. #[inline] fn abs(&self) -> f64 { abs(*self) } /// /// The positive difference of two numbers. Returns `0.0` if the number is less than or /// equal to `other`, otherwise the difference between`self` and `other` is returned. /// #[inline] fn abs_sub(&self, other: &f64) -> f64 { abs_sub(*self, *other) } /// /// # Returns /// /// - `1.0` if the number is positive, `+0.0` or `infinity` /// - `-1.0` if the number is negative, `-0.0` or `neg_infinity` /// - `NaN` if the number is NaN /// #[inline] fn signum(&self) -> f64 { if self.is_NaN() { NaN } else { copysign(1.0, *self) } } /// Returns `true` if the number is positive, including `+0.0` and `infinity` #[inline] fn is_positive(&self) -> bool { *self > 0.0 || (1.0 / *self) == infinity } /// Returns `true` if the number is negative, including `-0.0` and `neg_infinity` #[inline] fn is_negative(&self) -> bool { *self < 0.0 || (1.0 / *self) == neg_infinity } } impl Round for f64 { /// Round half-way cases toward `neg_infinity` #[inline] fn floor(&self) -> f64 { floor(*self) } /// Round half-way cases toward `infinity` #[inline] fn ceil(&self) -> f64 { ceil(*self) } /// Round half-way cases away from `0.0` #[inline] fn round(&self) -> f64 { round(*self) } /// The integer part of the number (rounds towards `0.0`) #[inline] fn trunc(&self) -> f64 { trunc(*self) } /// /// The fractional part of the number, satisfying: /// /// ~~~ {.rust} /// assert!(x == trunc(x) + fract(x)) /// ~~~ /// #[inline] fn fract(&self) -> f64 { *self - self.trunc() } } impl Fractional for f64 { /// The reciprocal (multiplicative inverse) of the number #[inline] fn recip(&self) -> f64 { 1.0 / *self } } impl Algebraic for f64 { #[inline] fn pow(&self, n: &f64) -> f64 { pow(*self, *n) } #[inline] fn sqrt(&self) -> f64 { sqrt(*self) } #[inline] fn rsqrt(&self) -> f64 { self.sqrt().recip() } #[inline] fn cbrt(&self) -> f64 { cbrt(*self) } #[inline] fn hypot(&self, other: &f64) -> f64 { hypot(*self, *other) } } impl Trigonometric for f64 { #[inline] fn sin(&self) -> f64 { sin(*self) } #[inline] fn cos(&self) -> f64 { cos(*self) } #[inline] fn tan(&self) -> f64 { tan(*self) } #[inline] fn asin(&self) -> f64 { asin(*self) } #[inline] fn acos(&self) -> f64 { acos(*self) } #[inline] fn atan(&self) -> f64 { atan(*self) } #[inline] fn atan2(&self, other: &f64) -> f64 { atan2(*self, *other) } /// Simultaneously computes the sine and cosine of the number #[inline] fn sin_cos(&self) -> (f64, f64) { (self.sin(), self.cos()) } } impl Exponential for f64 { /// Returns the exponential of the number #[inline] fn exp(&self) -> f64 { exp(*self) } /// Returns 2 raised to the power of the number #[inline] fn exp2(&self) -> f64 { exp2(*self) } /// Returns the natural logarithm of the number #[inline] fn ln(&self) -> f64 { ln(*self) } /// Returns the logarithm of the number with respect to an arbitrary base #[inline] fn log(&self, base: &f64) -> f64 { self.ln() / base.ln() } /// Returns the base 2 logarithm of the number #[inline] fn log2(&self) -> f64 { log2(*self) } /// Returns the base 10 logarithm of the number #[inline] fn log10(&self) -> f64 { log10(*self) } } impl Hyperbolic for f64 { #[inline] fn sinh(&self) -> f64 { sinh(*self) } #[inline] fn cosh(&self) -> f64 { cosh(*self) } #[inline] fn tanh(&self) -> f64 { tanh(*self) } /// /// Inverse hyperbolic sine /// /// # Returns /// /// - on success, the inverse hyperbolic sine of `self` will be returned /// - `self` if `self` is `0.0`, `-0.0`, `infinity`, or `neg_infinity` /// - `NaN` if `self` is `NaN` /// #[inline] fn asinh(&self) -> f64 { match *self { neg_infinity => neg_infinity, x => (x + ((x * x) + 1.0).sqrt()).ln(), } } /// /// Inverse hyperbolic cosine /// /// # Returns /// /// - on success, the inverse hyperbolic cosine of `self` will be returned /// - `infinity` if `self` is `infinity` /// - `NaN` if `self` is `NaN` or `self < 1.0` (including `neg_infinity`) /// #[inline] fn acosh(&self) -> f64 { match *self { x if x < 1.0 => Float::NaN(), x => (x + ((x * x) - 1.0).sqrt()).ln(), } } /// /// Inverse hyperbolic tangent /// /// # Returns /// /// - on success, the inverse hyperbolic tangent of `self` will be returned /// - `self` if `self` is `0.0` or `-0.0` /// - `infinity` if `self` is `1.0` /// - `neg_infinity` if `self` is `-1.0` /// - `NaN` if the `self` is `NaN` or outside the domain of `-1.0 <= self <= 1.0` /// (including `infinity` and `neg_infinity`) /// #[inline] fn atanh(&self) -> f64 { 0.5 * ((2.0 * *self) / (1.0 - *self)).ln_1p() } } impl Real for f64 { /// Archimedes' constant #[inline] fn pi() -> f64 { 3.14159265358979323846264338327950288 } /// 2.0 * pi #[inline] fn two_pi() -> f64 { 6.28318530717958647692528676655900576 } /// pi / 2.0 #[inline] fn frac_pi_2() -> f64 { 1.57079632679489661923132169163975144 } /// pi / 3.0 #[inline] fn frac_pi_3() -> f64 { 1.04719755119659774615421446109316763 } /// pi / 4.0 #[inline] fn frac_pi_4() -> f64 { 0.785398163397448309615660845819875721 } /// pi / 6.0 #[inline] fn frac_pi_6() -> f64 { 0.52359877559829887307710723054658381 } /// pi / 8.0 #[inline] fn frac_pi_8() -> f64 { 0.39269908169872415480783042290993786 } /// 1.0 / pi #[inline] fn frac_1_pi() -> f64 { 0.318309886183790671537767526745028724 } /// 2.0 / pi #[inline] fn frac_2_pi() -> f64 { 0.636619772367581343075535053490057448 } /// 2.0 / sqrt(pi) #[inline] fn frac_2_sqrtpi() -> f64 { 1.12837916709551257389615890312154517 } /// sqrt(2.0) #[inline] fn sqrt2() -> f64 { 1.41421356237309504880168872420969808 } /// 1.0 / sqrt(2.0) #[inline] fn frac_1_sqrt2() -> f64 { 0.707106781186547524400844362104849039 } /// Euler's number #[inline] fn e() -> f64 { 2.71828182845904523536028747135266250 } /// log2(e) #[inline] fn log2_e() -> f64 { 1.44269504088896340735992468100189214 } /// log10(e) #[inline] fn log10_e() -> f64 { 0.434294481903251827651128918916605082 } /// ln(2.0) #[inline] fn ln_2() -> f64 { 0.693147180559945309417232121458176568 } /// ln(10.0) #[inline] fn ln_10() -> f64 { 2.30258509299404568401799145468436421 } /// Converts to degrees, assuming the number is in radians #[inline] fn to_degrees(&self) -> f64 { *self * (180.0f64 / Real::pi()) } /// Converts to radians, assuming the number is in degrees #[inline] fn to_radians(&self) -> f64 { let value: f64 = Real::pi(); *self * (value / 180.0) } } impl RealExt for f64 { #[inline] fn lgamma(&self) -> (int, f64) { let mut sign = 0; let result = lgamma(*self, &mut sign); (sign as int, result) } #[inline] fn tgamma(&self) -> f64 { tgamma(*self) } #[inline] fn j0(&self) -> f64 { j0(*self) } #[inline] fn j1(&self) -> f64 { j1(*self) } #[inline] fn jn(&self, n: int) -> f64 { jn(n as c_int, *self) } #[inline] fn y0(&self) -> f64 { y0(*self) } #[inline] fn y1(&self) -> f64 { y1(*self) } #[inline] fn yn(&self, n: int) -> f64 { yn(n as c_int, *self) } } impl Bounded for f64 { #[inline] fn min_value() -> f64 { 2.2250738585072014e-308 } #[inline] fn max_value() -> f64 { 1.7976931348623157e+308 } } impl Primitive for f64 { #[inline] fn bits(_: Option) -> uint { 64 } #[inline] fn bytes(_: Option) -> uint { Primitive::bits(Some(0f64)) / 8 } } impl Float for f64 { #[inline] fn NaN() -> f64 { 0.0 / 0.0 } #[inline] fn infinity() -> f64 { 1.0 / 0.0 } #[inline] fn neg_infinity() -> f64 { -1.0 / 0.0 } #[inline] fn neg_zero() -> f64 { -0.0 } /// Returns `true` if the number is NaN #[inline] fn is_NaN(&self) -> bool { *self != *self } /// Returns `true` if the number is infinite #[inline] fn is_infinite(&self) -> bool { *self == Float::infinity() || *self == Float::neg_infinity() } /// Returns `true` if the number is neither infinite or NaN #[inline] fn is_finite(&self) -> bool { !(self.is_NaN() || self.is_infinite()) } /// Returns `true` if the number is neither zero, infinite, subnormal or NaN #[inline] fn is_normal(&self) -> bool { self.classify() == FPNormal } /// Returns the floating point category of the number. If only one property is going to /// be tested, it is generally faster to use the specific predicate instead. fn classify(&self) -> FPCategory { static EXP_MASK: u64 = 0x7ff0000000000000; static MAN_MASK: u64 = 0x000fffffffffffff; match ( unsafe { ::cast::transmute::(*self) } & MAN_MASK, unsafe { ::cast::transmute::(*self) } & EXP_MASK, ) { (0, 0) => FPZero, (_, 0) => FPSubnormal, (0, EXP_MASK) => FPInfinite, (_, EXP_MASK) => FPNaN, _ => FPNormal, } } #[inline] fn mantissa_digits(_: Option) -> uint { 53 } #[inline] fn digits(_: Option) -> uint { 15 } #[inline] fn epsilon() -> f64 { 2.2204460492503131e-16 } #[inline] fn min_exp(_: Option) -> int { -1021 } #[inline] fn max_exp(_: Option) -> int { 1024 } #[inline] fn min_10_exp(_: Option) -> int { -307 } #[inline] fn max_10_exp(_: Option) -> int { 308 } /// Constructs a floating point number by multiplying `x` by 2 raised to the power of `exp` #[inline] fn ldexp(x: f64, exp: int) -> f64 { ldexp(x, exp as c_int) } /// /// Breaks the number into a normalized fraction and a base-2 exponent, satisfying: /// /// - `self = x * pow(2, exp)` /// - `0.5 <= abs(x) < 1.0` /// #[inline] fn frexp(&self) -> (f64, int) { let mut exp = 0; let x = frexp(*self, &mut exp); (x, exp as int) } /// /// Returns the exponential of the number, minus `1`, in a way that is accurate /// even if the number is close to zero /// #[inline] fn exp_m1(&self) -> f64 { exp_m1(*self) } /// /// Returns the natural logarithm of the number plus `1` (`ln(1+n)`) more accurately /// than if the operations were performed separately /// #[inline] fn ln_1p(&self) -> f64 { ln_1p(*self) } /// /// Fused multiply-add. Computes `(self * a) + b` with only one rounding error. This /// produces a more accurate result with better performance than a separate multiplication /// operation followed by an add. /// #[inline] fn mul_add(&self, a: f64, b: f64) -> f64 { mul_add(*self, a, b) } /// Returns the next representable floating-point value in the direction of `other` #[inline] fn next_after(&self, other: f64) -> f64 { next_after(*self, other) } } // // Section: String Conversions // /// /// Converts a float to a string /// /// # Arguments /// /// * num - The float value /// #[inline] pub fn to_str(num: f64) -> ~str { let (r, _) = strconv::float_to_str_common( num, 10u, true, strconv::SignNeg, strconv::DigAll); r } /// /// Converts a float to a string in hexadecimal format /// /// # Arguments /// /// * num - The float value /// #[inline] pub fn to_str_hex(num: f64) -> ~str { let (r, _) = strconv::float_to_str_common( num, 16u, true, strconv::SignNeg, strconv::DigAll); r } /// /// Converts a float to a string in a given radix, and a flag indicating /// whether it's a special value /// /// # Arguments /// /// * num - The float value /// * radix - The base to use /// #[inline] pub fn to_str_radix_special(num: f64, rdx: uint) -> (~str, bool) { strconv::float_to_str_common(num, rdx, true, strconv::SignNeg, strconv::DigAll) } /// /// Converts a float to a string with exactly the number of /// provided significant digits /// /// # Arguments /// /// * num - The float value /// * digits - The number of significant digits /// #[inline] pub fn to_str_exact(num: f64, dig: uint) -> ~str { let (r, _) = strconv::float_to_str_common( num, 10u, true, strconv::SignNeg, strconv::DigExact(dig)); r } /// /// Converts a float to a string with a maximum number of /// significant digits /// /// # Arguments /// /// * num - The float value /// * digits - The number of significant digits /// #[inline] pub fn to_str_digits(num: f64, dig: uint) -> ~str { let (r, _) = strconv::float_to_str_common( num, 10u, true, strconv::SignNeg, strconv::DigMax(dig)); r } impl to_str::ToStr for f64 { #[inline] fn to_str(&self) -> ~str { to_str_digits(*self, 8) } } impl num::ToStrRadix for f64 { /// Converts a float to a string in a given radix /// /// # Arguments /// /// * num - The float value /// * radix - The base to use /// /// # Failure /// /// Fails if called on a special value like `inf`, `-inf` or `NaN` due to /// possible misinterpretation of the result at higher bases. If those values /// are expected, use `to_str_radix_special()` instead. #[inline] fn to_str_radix(&self, rdx: uint) -> ~str { let (r, special) = strconv::float_to_str_common( *self, rdx, true, strconv::SignNeg, strconv::DigAll); if special { fail!("number has a special value, \ try to_str_radix_special() if those are expected") } r } } /// /// Convert a string in base 10 to a float. /// Accepts a optional decimal exponent. /// /// This function accepts strings such as /// /// * '3.14' /// * '+3.14', equivalent to '3.14' /// * '-3.14' /// * '2.5E10', or equivalently, '2.5e10' /// * '2.5E-10' /// * '.' (understood as 0) /// * '5.' /// * '.5', or, equivalently, '0.5' /// * '+inf', 'inf', '-inf', 'NaN' /// /// Leading and trailing whitespace represent an error. /// /// # Arguments /// /// * num - A string /// /// # Return value /// /// `none` if the string did not represent a valid number. Otherwise, /// `Some(n)` where `n` is the floating-point number represented by `num`. /// #[inline] pub fn from_str(num: &str) -> Option { strconv::from_str_common(num, 10u, true, true, true, strconv::ExpDec, false, false) } /// /// Convert a string in base 16 to a float. /// Accepts a optional binary exponent. /// /// This function accepts strings such as /// /// * 'a4.fe' /// * '+a4.fe', equivalent to 'a4.fe' /// * '-a4.fe' /// * '2b.aP128', or equivalently, '2b.ap128' /// * '2b.aP-128' /// * '.' (understood as 0) /// * 'c.' /// * '.c', or, equivalently, '0.c' /// * '+inf', 'inf', '-inf', 'NaN' /// /// Leading and trailing whitespace represent an error. /// /// # Arguments /// /// * num - A string /// /// # Return value /// /// `none` if the string did not represent a valid number. Otherwise, /// `Some(n)` where `n` is the floating-point number represented by `[num]`. /// #[inline] pub fn from_str_hex(num: &str) -> Option { strconv::from_str_common(num, 16u, true, true, true, strconv::ExpBin, false, false) } /// /// Convert a string in an given base to a float. /// /// Due to possible conflicts, this function does **not** accept /// the special values `inf`, `-inf`, `+inf` and `NaN`, **nor** /// does it recognize exponents of any kind. /// /// Leading and trailing whitespace represent an error. /// /// # Arguments /// /// * num - A string /// * radix - The base to use. Must lie in the range [2 .. 36] /// /// # Return value /// /// `none` if the string did not represent a valid number. Otherwise, /// `Some(n)` where `n` is the floating-point number represented by `num`. /// #[inline] pub fn from_str_radix(num: &str, rdx: uint) -> Option { strconv::from_str_common(num, rdx, true, true, false, strconv::ExpNone, false, false) } impl FromStr for f64 { #[inline] fn from_str(val: &str) -> Option { from_str(val) } } impl num::FromStrRadix for f64 { #[inline] fn from_str_radix(val: &str, rdx: uint) -> Option { from_str_radix(val, rdx) } } #[cfg(test)] mod tests { use f64::*; use prelude::*; use num::*; use num; use sys; #[test] fn test_num() { num::test_num(10f64, 2f64); } #[test] fn test_min() { assert_eq!(1f64.min(&2f64), 1f64); assert_eq!(2f64.min(&1f64), 1f64); let nan: f64 = Float::NaN(); assert!(1f64.min(&nan).is_NaN()); assert!(nan.min(&1f64).is_NaN()); } #[test] fn test_max() { assert_eq!(1f64.max(&2f64), 2f64); assert_eq!(2f64.max(&1f64), 2f64); let nan: f64 = Float::NaN(); assert!(1f64.max(&nan).is_NaN()); assert!(nan.max(&1f64).is_NaN()); } #[test] fn test_clamp() { assert_eq!(1f64.clamp(&2f64, &4f64), 2f64); assert_eq!(8f64.clamp(&2f64, &4f64), 4f64); assert_eq!(3f64.clamp(&2f64, &4f64), 3f64); let nan: f64 = Float::NaN(); assert!(3f64.clamp(&nan, &4f64).is_NaN()); assert!(3f64.clamp(&2f64, &nan).is_NaN()); assert!(nan.clamp(&2f64, &4f64).is_NaN()); } #[test] fn test_floor() { assert_approx_eq!(1.0f64.floor(), 1.0f64); assert_approx_eq!(1.3f64.floor(), 1.0f64); assert_approx_eq!(1.5f64.floor(), 1.0f64); assert_approx_eq!(1.7f64.floor(), 1.0f64); assert_approx_eq!(0.0f64.floor(), 0.0f64); assert_approx_eq!((-0.0f64).floor(), -0.0f64); assert_approx_eq!((-1.0f64).floor(), -1.0f64); assert_approx_eq!((-1.3f64).floor(), -2.0f64); assert_approx_eq!((-1.5f64).floor(), -2.0f64); assert_approx_eq!((-1.7f64).floor(), -2.0f64); } #[test] fn test_ceil() { assert_approx_eq!(1.0f64.ceil(), 1.0f64); assert_approx_eq!(1.3f64.ceil(), 2.0f64); assert_approx_eq!(1.5f64.ceil(), 2.0f64); assert_approx_eq!(1.7f64.ceil(), 2.0f64); assert_approx_eq!(0.0f64.ceil(), 0.0f64); assert_approx_eq!((-0.0f64).ceil(), -0.0f64); assert_approx_eq!((-1.0f64).ceil(), -1.0f64); assert_approx_eq!((-1.3f64).ceil(), -1.0f64); assert_approx_eq!((-1.5f64).ceil(), -1.0f64); assert_approx_eq!((-1.7f64).ceil(), -1.0f64); } #[test] fn test_round() { assert_approx_eq!(1.0f64.round(), 1.0f64); assert_approx_eq!(1.3f64.round(), 1.0f64); assert_approx_eq!(1.5f64.round(), 2.0f64); assert_approx_eq!(1.7f64.round(), 2.0f64); assert_approx_eq!(0.0f64.round(), 0.0f64); assert_approx_eq!((-0.0f64).round(), -0.0f64); assert_approx_eq!((-1.0f64).round(), -1.0f64); assert_approx_eq!((-1.3f64).round(), -1.0f64); assert_approx_eq!((-1.5f64).round(), -2.0f64); assert_approx_eq!((-1.7f64).round(), -2.0f64); } #[test] fn test_trunc() { assert_approx_eq!(1.0f64.trunc(), 1.0f64); assert_approx_eq!(1.3f64.trunc(), 1.0f64); assert_approx_eq!(1.5f64.trunc(), 1.0f64); assert_approx_eq!(1.7f64.trunc(), 1.0f64); assert_approx_eq!(0.0f64.trunc(), 0.0f64); assert_approx_eq!((-0.0f64).trunc(), -0.0f64); assert_approx_eq!((-1.0f64).trunc(), -1.0f64); assert_approx_eq!((-1.3f64).trunc(), -1.0f64); assert_approx_eq!((-1.5f64).trunc(), -1.0f64); assert_approx_eq!((-1.7f64).trunc(), -1.0f64); } #[test] fn test_fract() { assert_approx_eq!(1.0f64.fract(), 0.0f64); assert_approx_eq!(1.3f64.fract(), 0.3f64); assert_approx_eq!(1.5f64.fract(), 0.5f64); assert_approx_eq!(1.7f64.fract(), 0.7f64); assert_approx_eq!(0.0f64.fract(), 0.0f64); assert_approx_eq!((-0.0f64).fract(), -0.0f64); assert_approx_eq!((-1.0f64).fract(), -0.0f64); assert_approx_eq!((-1.3f64).fract(), -0.3f64); assert_approx_eq!((-1.5f64).fract(), -0.5f64); assert_approx_eq!((-1.7f64).fract(), -0.7f64); } #[test] fn test_asinh() { assert_eq!(0.0f64.asinh(), 0.0f64); assert_eq!((-0.0f64).asinh(), -0.0f64); let inf: f64 = Float::infinity(); let neg_inf: f64 = Float::neg_infinity(); let nan: f64 = Float::NaN(); assert_eq!(inf.asinh(), inf); assert_eq!(neg_inf.asinh(), neg_inf); assert!(nan.asinh().is_NaN()); assert_approx_eq!(2.0f64.asinh(), 1.443635475178810342493276740273105f64); assert_approx_eq!((-2.0f64).asinh(), -1.443635475178810342493276740273105f64); } #[test] fn test_acosh() { assert_eq!(1.0f64.acosh(), 0.0f64); assert!(0.999f64.acosh().is_NaN()); let inf: f64 = Float::infinity(); let neg_inf: f64 = Float::neg_infinity(); let nan: f64 = Float::NaN(); assert_eq!(inf.acosh(), inf); assert!(neg_inf.acosh().is_NaN()); assert!(nan.acosh().is_NaN()); assert_approx_eq!(2.0f64.acosh(), 1.31695789692481670862504634730796844f64); assert_approx_eq!(3.0f64.acosh(), 1.76274717403908605046521864995958461f64); } #[test] fn test_atanh() { assert_eq!(0.0f64.atanh(), 0.0f64); assert_eq!((-0.0f64).atanh(), -0.0f64); let inf: f64 = Float::infinity(); let neg_inf: f64 = Float::neg_infinity(); let nan: f64 = Float::NaN(); assert_eq!(1.0f64.atanh(), inf); assert_eq!((-1.0f64).atanh(), neg_inf); assert!(2f64.atanh().atanh().is_NaN()); assert!((-2f64).atanh().atanh().is_NaN()); assert!(inf.atanh().is_NaN()); assert!(neg_inf.atanh().is_NaN()); assert!(nan.atanh().is_NaN()); assert_approx_eq!(0.5f64.atanh(), 0.54930614433405484569762261846126285f64); assert_approx_eq!((-0.5f64).atanh(), -0.54930614433405484569762261846126285f64); } #[test] fn test_real_consts() { let pi: f64 = Real::pi(); let two_pi: f64 = Real::two_pi(); let frac_pi_2: f64 = Real::frac_pi_2(); let frac_pi_3: f64 = Real::frac_pi_3(); let frac_pi_4: f64 = Real::frac_pi_4(); let frac_pi_6: f64 = Real::frac_pi_6(); let frac_pi_8: f64 = Real::frac_pi_8(); let frac_1_pi: f64 = Real::frac_1_pi(); let frac_2_pi: f64 = Real::frac_2_pi(); let frac_2_sqrtpi: f64 = Real::frac_2_sqrtpi(); let sqrt2: f64 = Real::sqrt2(); let frac_1_sqrt2: f64 = Real::frac_1_sqrt2(); let e: f64 = Real::e(); let log2_e: f64 = Real::log2_e(); let log10_e: f64 = Real::log10_e(); let ln_2: f64 = Real::ln_2(); let ln_10: f64 = Real::ln_10(); assert_approx_eq!(two_pi, 2.0 * pi); assert_approx_eq!(frac_pi_2, pi / 2f64); assert_approx_eq!(frac_pi_3, pi / 3f64); assert_approx_eq!(frac_pi_4, pi / 4f64); assert_approx_eq!(frac_pi_6, pi / 6f64); assert_approx_eq!(frac_pi_8, pi / 8f64); assert_approx_eq!(frac_1_pi, 1f64 / pi); assert_approx_eq!(frac_2_pi, 2f64 / pi); assert_approx_eq!(frac_2_sqrtpi, 2f64 / pi.sqrt()); assert_approx_eq!(sqrt2, 2f64.sqrt()); assert_approx_eq!(frac_1_sqrt2, 1f64 / 2f64.sqrt()); assert_approx_eq!(log2_e, e.log2()); assert_approx_eq!(log10_e, e.log10()); assert_approx_eq!(ln_2, 2f64.ln()); assert_approx_eq!(ln_10, 10f64.ln()); } #[test] pub fn test_abs() { assert_eq!(infinity.abs(), infinity); assert_eq!(1f64.abs(), 1f64); assert_eq!(0f64.abs(), 0f64); assert_eq!((-0f64).abs(), 0f64); assert_eq!((-1f64).abs(), 1f64); assert_eq!(neg_infinity.abs(), infinity); assert_eq!((1f64/neg_infinity).abs(), 0f64); assert!(NaN.abs().is_NaN()); } #[test] fn test_abs_sub() { assert_eq!((-1f64).abs_sub(&1f64), 0f64); assert_eq!(1f64.abs_sub(&1f64), 0f64); assert_eq!(1f64.abs_sub(&0f64), 1f64); assert_eq!(1f64.abs_sub(&-1f64), 2f64); assert_eq!(neg_infinity.abs_sub(&0f64), 0f64); assert_eq!(infinity.abs_sub(&1f64), infinity); assert_eq!(0f64.abs_sub(&neg_infinity), infinity); assert_eq!(0f64.abs_sub(&infinity), 0f64); } #[test] #[ignore(cfg(windows))] // FIXME #8663 fn test_abs_sub_nowin() { assert!(NaN.abs_sub(&-1f64).is_NaN()); assert!(1f64.abs_sub(&NaN).is_NaN()); } #[test] fn test_signum() { assert_eq!(infinity.signum(), 1f64); assert_eq!(1f64.signum(), 1f64); assert_eq!(0f64.signum(), 1f64); assert_eq!((-0f64).signum(), -1f64); assert_eq!((-1f64).signum(), -1f64); assert_eq!(neg_infinity.signum(), -1f64); assert_eq!((1f64/neg_infinity).signum(), -1f64); assert!(NaN.signum().is_NaN()); } #[test] fn test_is_positive() { assert!(infinity.is_positive()); assert!(1f64.is_positive()); assert!(0f64.is_positive()); assert!(!(-0f64).is_positive()); assert!(!(-1f64).is_positive()); assert!(!neg_infinity.is_positive()); assert!(!(1f64/neg_infinity).is_positive()); assert!(!NaN.is_positive()); } #[test] fn test_is_negative() { assert!(!infinity.is_negative()); assert!(!1f64.is_negative()); assert!(!0f64.is_negative()); assert!((-0f64).is_negative()); assert!((-1f64).is_negative()); assert!(neg_infinity.is_negative()); assert!((1f64/neg_infinity).is_negative()); assert!(!NaN.is_negative()); } #[test] fn test_approx_eq() { assert!(1.0f64.approx_eq(&1f64)); assert!(0.9999999f64.approx_eq(&1f64)); assert!(1.000001f64.approx_eq_eps(&1f64, &1.0e-5)); assert!(1.0000001f64.approx_eq_eps(&1f64, &1.0e-6)); assert!(!1.0000001f64.approx_eq_eps(&1f64, &1.0e-7)); } #[test] fn test_primitive() { let none: Option = None; assert_eq!(Primitive::bits(none), sys::size_of::() * 8); assert_eq!(Primitive::bytes(none), sys::size_of::()); } #[test] fn test_is_normal() { let nan: f64 = Float::NaN(); let inf: f64 = Float::infinity(); let neg_inf: f64 = Float::neg_infinity(); let zero: f64 = Zero::zero(); let neg_zero: f64 = Float::neg_zero(); assert!(!nan.is_normal()); assert!(!inf.is_normal()); assert!(!neg_inf.is_normal()); assert!(!zero.is_normal()); assert!(!neg_zero.is_normal()); assert!(1f64.is_normal()); assert!(1e-307f64.is_normal()); assert!(!1e-308f64.is_normal()); } #[test] fn test_classify() { let nan: f64 = Float::NaN(); let inf: f64 = Float::infinity(); let neg_inf: f64 = Float::neg_infinity(); let zero: f64 = Zero::zero(); let neg_zero: f64 = Float::neg_zero(); assert_eq!(nan.classify(), FPNaN); assert_eq!(inf.classify(), FPInfinite); assert_eq!(neg_inf.classify(), FPInfinite); assert_eq!(zero.classify(), FPZero); assert_eq!(neg_zero.classify(), FPZero); assert_eq!(1e-307f64.classify(), FPNormal); assert_eq!(1e-308f64.classify(), FPSubnormal); } #[test] fn test_ldexp() { // We have to use from_str until base-2 exponents // are supported in floating-point literals let f1: f64 = from_str_hex("1p-123").unwrap(); let f2: f64 = from_str_hex("1p-111").unwrap(); assert_eq!(Float::ldexp(1f64, -123), f1); assert_eq!(Float::ldexp(1f64, -111), f2); assert_eq!(Float::ldexp(0f64, -123), 0f64); assert_eq!(Float::ldexp(-0f64, -123), -0f64); let inf: f64 = Float::infinity(); let neg_inf: f64 = Float::neg_infinity(); let nan: f64 = Float::NaN(); assert_eq!(Float::ldexp(inf, -123), inf); assert_eq!(Float::ldexp(neg_inf, -123), neg_inf); assert!(Float::ldexp(nan, -123).is_NaN()); } #[test] fn test_frexp() { // We have to use from_str until base-2 exponents // are supported in floating-point literals let f1: f64 = from_str_hex("1p-123").unwrap(); let f2: f64 = from_str_hex("1p-111").unwrap(); let (x1, exp1) = f1.frexp(); let (x2, exp2) = f2.frexp(); assert_eq!((x1, exp1), (0.5f64, -122)); assert_eq!((x2, exp2), (0.5f64, -110)); assert_eq!(Float::ldexp(x1, exp1), f1); assert_eq!(Float::ldexp(x2, exp2), f2); assert_eq!(0f64.frexp(), (0f64, 0)); assert_eq!((-0f64).frexp(), (-0f64, 0)); } #[test] #[ignore(cfg(windows))] // FIXME #8755 fn test_frexp_nowin() { let inf: f64 = Float::infinity(); let neg_inf: f64 = Float::neg_infinity(); let nan: f64 = Float::NaN(); assert_eq!(match inf.frexp() { (x, _) => x }, inf) assert_eq!(match neg_inf.frexp() { (x, _) => x }, neg_inf) assert!(match nan.frexp() { (x, _) => x.is_NaN() }) } }