// Copyright 2012-2014 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 64-bits floats (`f64` type) #![allow(missing_doc)] use prelude::*; use cast; use default::Default; use from_str::FromStr; use libc::{c_int}; use num::{FPCategory, FPNaN, FPInfinite , FPZero, FPSubnormal, FPNormal}; use num::{Zero, One, Bounded, strconv}; use num; use intrinsics; #[allow(dead_code)] mod cmath { use libc::{c_double, c_int}; #[link_name = "m"] extern { pub fn acos(n: c_double) -> c_double; pub fn asin(n: c_double) -> c_double; pub fn atan(n: c_double) -> c_double; pub fn atan2(a: c_double, b: c_double) -> c_double; pub fn cbrt(n: c_double) -> c_double; pub fn cosh(n: c_double) -> c_double; pub fn erf(n: c_double) -> c_double; pub fn erfc(n: c_double) -> c_double; pub fn expm1(n: c_double) -> c_double; pub fn fdim(a: c_double, b: c_double) -> c_double; pub fn fmax(a: c_double, b: c_double) -> c_double; pub fn fmin(a: c_double, b: c_double) -> c_double; pub fn fmod(a: c_double, b: c_double) -> c_double; pub fn nextafter(x: c_double, y: c_double) -> c_double; pub fn frexp(n: c_double, value: &mut c_int) -> c_double; pub fn hypot(x: c_double, y: c_double) -> c_double; pub fn ldexp(x: c_double, n: c_int) -> c_double; pub fn logb(n: c_double) -> c_double; pub fn log1p(n: c_double) -> c_double; pub fn ilogb(n: c_double) -> c_int; pub fn modf(n: c_double, iptr: &mut c_double) -> c_double; pub fn sinh(n: c_double) -> c_double; pub fn tan(n: c_double) -> c_double; pub fn tanh(n: c_double) -> c_double; pub fn tgamma(n: c_double) -> c_double; // These are commonly only available for doubles pub fn j0(n: c_double) -> c_double; pub fn j1(n: c_double) -> c_double; pub fn jn(i: c_int, n: c_double) -> c_double; pub fn y0(n: c_double) -> c_double; pub fn y1(n: c_double) -> c_double; pub fn yn(i: c_int, n: c_double) -> c_double; #[cfg(unix)] pub fn lgamma_r(n: c_double, sign: &mut c_int) -> c_double; #[cfg(windows)] #[link_name="__lgamma_r"] pub fn lgamma_r(n: c_double, sign: &mut c_int) -> c_double; } } // FIXME(#5527): These constants should be deprecated once associated // constants are implemented in favour of referencing the respective // members of `Bounded` and `Float`. pub static RADIX: uint = 2u; pub static MANTISSA_DIGITS: uint = 53u; pub static DIGITS: uint = 15u; pub static EPSILON: f64 = 2.2204460492503131e-16_f64; /// Smallest finite f64 value pub static MIN_VALUE: f64 = -1.7976931348623157e+308_f64; /// Smallest positive, normalized f64 value pub static MIN_POS_VALUE: f64 = 2.2250738585072014e-308_f64; /// Largest finite f64 value 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; /// Various useful constants. pub mod consts { // FIXME: replace with mathematical constants from cmath. // FIXME(#5527): These constants should be deprecated once associated // constants are implemented in favour of referencing the respective members // of `Float`. /// Archimedes' constant pub static PI: f64 = 3.14159265358979323846264338327950288_f64; /// pi * 2.0 pub static PI_2: f64 = 6.28318530717958647692528676655900576_f64; /// pi/2.0 pub static FRAC_PI_2: f64 = 1.57079632679489661923132169163975144_f64; /// pi/3.0 pub static FRAC_PI_3: f64 = 1.04719755119659774615421446109316763_f64; /// pi/4.0 pub static FRAC_PI_4: f64 = 0.785398163397448309615660845819875721_f64; /// pi/6.0 pub static FRAC_PI_6: f64 = 0.52359877559829887307710723054658381_f64; /// pi/8.0 pub static FRAC_PI_8: f64 = 0.39269908169872415480783042290993786_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 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 Default for f64 { #[inline] fn default() -> f64 { 0.0 } } 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 { unsafe { cmath::fmod(*self, *other) } } } #[cfg(not(test))] impl Neg for f64 { #[inline] 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 { unsafe { intrinsics::fabsf64(*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 { unsafe { cmath::fdim(*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 { unsafe { intrinsics::copysignf64(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 Bounded for f64 { // NOTE: this is the smallest non-infinite f32 value, *not* MIN_VALUE #[inline] fn min_value() -> f64 { -MAX_VALUE } #[inline] fn max_value() -> f64 { MAX_VALUE } } impl Primitive for f64 {} impl Float for f64 { #[inline] fn nan() -> f64 { NAN } #[inline] fn infinity() -> f64 { INFINITY } #[inline] fn neg_infinity() -> f64 { NEG_INFINITY } #[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; let bits: u64 = unsafe { cast::transmute(self) }; match (bits & MAN_MASK, bits & EXP_MASK) { (0, 0) => FPZero, (_, 0) => FPSubnormal, (0, EXP_MASK) => FPInfinite, (_, EXP_MASK) => FPNaN, _ => FPNormal, } } #[inline] fn mantissa_digits(_: Option) -> uint { MANTISSA_DIGITS } #[inline] fn digits(_: Option) -> uint { DIGITS } #[inline] fn epsilon() -> f64 { EPSILON } #[inline] fn min_exp(_: Option) -> int { MIN_EXP } #[inline] fn max_exp(_: Option) -> int { MAX_EXP } #[inline] fn min_10_exp(_: Option) -> int { MIN_10_EXP } #[inline] fn max_10_exp(_: Option) -> int { MAX_10_EXP } #[inline] fn min_pos_value(_: Option) -> f64 { MIN_POS_VALUE } /// Constructs a floating point number by multiplying `x` by 2 raised to the /// power of `exp` #[inline] fn ldexp(x: f64, exp: int) -> f64 { unsafe { cmath::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) { unsafe { let mut exp = 0; let x = cmath::frexp(self, &mut exp); (x, exp as int) } } /// Returns the mantissa, exponent and sign as integers. fn integer_decode(self) -> (u64, i16, i8) { let bits: u64 = unsafe { cast::transmute(self) }; let sign: i8 = if bits >> 63 == 0 { 1 } else { -1 }; let mut exponent: i16 = ((bits >> 52) & 0x7ff) as i16; let mantissa = if exponent == 0 { (bits & 0xfffffffffffff) << 1 } else { (bits & 0xfffffffffffff) | 0x10000000000000 }; // Exponent bias + mantissa shift exponent -= 1023 + 52; (mantissa, exponent, sign) } /// Returns the next representable floating-point value in the direction of /// `other`. #[inline] fn next_after(self, other: f64) -> f64 { unsafe { cmath::nextafter(self, other) } } /// Round half-way cases toward `NEG_INFINITY` #[inline] fn floor(self) -> f64 { unsafe { intrinsics::floorf64(self) } } /// Round half-way cases toward `INFINITY` #[inline] fn ceil(self) -> f64 { unsafe { intrinsics::ceilf64(self) } } /// Round half-way cases away from `0.0` #[inline] fn round(self) -> f64 { unsafe { intrinsics::roundf64(self) } } /// The integer part of the number (rounds towards `0.0`) #[inline] fn trunc(self) -> f64 { unsafe { intrinsics::truncf64(self) } } /// The fractional part of the number, satisfying: /// /// ```rust /// let x = 1.65f64; /// assert!(x == x.trunc() + x.fract()) /// ``` #[inline] fn fract(self) -> f64 { self - self.trunc() } #[inline] fn max(self, other: f64) -> f64 { unsafe { cmath::fmax(self, other) } } #[inline] fn min(self, other: f64) -> f64 { unsafe { cmath::fmin(self, other) } } /// 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 { unsafe { intrinsics::fmaf64(self, a, b) } } /// The reciprocal (multiplicative inverse) of the number #[inline] fn recip(self) -> f64 { 1.0 / self } #[inline] fn powf(self, n: f64) -> f64 { unsafe { intrinsics::powf64(self, n) } } #[inline] fn powi(self, n: i32) -> f64 { unsafe { intrinsics::powif64(self, n) } } /// sqrt(2.0) #[inline] fn sqrt2() -> f64 { consts::SQRT2 } /// 1.0 / sqrt(2.0) #[inline] fn frac_1_sqrt2() -> f64 { consts::FRAC_1_SQRT2 } #[inline] fn sqrt(self) -> f64 { unsafe { intrinsics::sqrtf64(self) } } #[inline] fn rsqrt(self) -> f64 { self.sqrt().recip() } #[inline] fn cbrt(self) -> f64 { unsafe { cmath::cbrt(self) } } #[inline] fn hypot(self, other: f64) -> f64 { unsafe { cmath::hypot(self, other) } } /// Archimedes' constant #[inline] fn pi() -> f64 { consts::PI } /// 2.0 * pi #[inline] fn two_pi() -> f64 { consts::PI_2 } /// pi / 2.0 #[inline] fn frac_pi_2() -> f64 { consts::FRAC_PI_2 } /// pi / 3.0 #[inline] fn frac_pi_3() -> f64 { consts::FRAC_PI_3 } /// pi / 4.0 #[inline] fn frac_pi_4() -> f64 { consts::FRAC_PI_4 } /// pi / 6.0 #[inline] fn frac_pi_6() -> f64 { consts::FRAC_PI_6 } /// pi / 8.0 #[inline] fn frac_pi_8() -> f64 { consts::FRAC_PI_8 } /// 1.0 / pi #[inline] fn frac_1_pi() -> f64 { consts::FRAC_1_PI } /// 2.0 / pi #[inline] fn frac_2_pi() -> f64 { consts::FRAC_2_PI } /// 2.0 / sqrt(pi) #[inline] fn frac_2_sqrtpi() -> f64 { consts::FRAC_2_SQRTPI } #[inline] fn sin(self) -> f64 { unsafe { intrinsics::sinf64(self) } } #[inline] fn cos(self) -> f64 { unsafe { intrinsics::cosf64(self) } } #[inline] fn tan(self) -> f64 { unsafe { cmath::tan(self) } } #[inline] fn asin(self) -> f64 { unsafe { cmath::asin(self) } } #[inline] fn acos(self) -> f64 { unsafe { cmath::acos(self) } } #[inline] fn atan(self) -> f64 { unsafe { cmath::atan(self) } } #[inline] fn atan2(self, other: f64) -> f64 { unsafe { cmath::atan2(self, other) } } /// Simultaneously computes the sine and cosine of the number #[inline] fn sin_cos(self) -> (f64, f64) { (self.sin(), self.cos()) } /// Euler's number #[inline] fn e() -> f64 { consts::E } /// log2(e) #[inline] fn log2_e() -> f64 { consts::LOG2_E } /// log10(e) #[inline] fn log10_e() -> f64 { consts::LOG10_E } /// ln(2.0) #[inline] fn ln_2() -> f64 { consts::LN_2 } /// ln(10.0) #[inline] fn ln_10() -> f64 { consts::LN_10 } /// Returns the exponential of the number #[inline] fn exp(self) -> f64 { unsafe { intrinsics::expf64(self) } } /// Returns 2 raised to the power of the number #[inline] fn exp2(self) -> f64 { unsafe { intrinsics::exp2f64(self) } } /// 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 { unsafe { cmath::expm1(self) } } /// Returns the natural logarithm of the number #[inline] fn ln(self) -> f64 { unsafe { intrinsics::logf64(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 { unsafe { intrinsics::log2f64(self) } } /// Returns the base 10 logarithm of the number #[inline] fn log10(self) -> f64 { unsafe { intrinsics::log10f64(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 { unsafe { cmath::log1p(self) } } #[inline] fn sinh(self) -> f64 { unsafe { cmath::sinh(self) } } #[inline] fn cosh(self) -> f64 { unsafe { cmath::cosh(self) } } #[inline] fn tanh(self) -> f64 { unsafe { cmath::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() } /// Converts to degrees, assuming the number is in radians #[inline] fn to_degrees(self) -> f64 { self * (180.0f64 / Float::pi()) } /// Converts to radians, assuming the number is in degrees #[inline] fn to_radians(self) -> f64 { let value: f64 = Float::pi(); self * (value / 180.0) } } // // 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, strconv::ExpNone, false); 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, strconv::ExpNone, false); 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, strconv::ExpNone, false) } /// 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), strconv::ExpNone, false); 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), strconv::ExpNone, false); r } /// Converts a float to a string using the exponential notation with exactly the number of /// provided digits after the decimal point in the significand /// /// # Arguments /// /// * num - The float value /// * digits - The number of digits after the decimal point /// * upper - Use `E` instead of `e` for the exponent sign #[inline] pub fn to_str_exp_exact(num: f64, dig: uint, upper: bool) -> ~str { let (r, _) = strconv::float_to_str_common( num, 10u, true, strconv::SignNeg, strconv::DigExact(dig), strconv::ExpDec, upper); r } /// Converts a float to a string using the exponential notation with the maximum number of /// digits after the decimal point in the significand /// /// # Arguments /// /// * num - The float value /// * digits - The number of digits after the decimal point /// * upper - Use `E` instead of `e` for the exponent sign #[inline] pub fn to_str_exp_digits(num: f64, dig: uint, upper: bool) -> ~str { let (r, _) = strconv::float_to_str_common( num, 10u, true, strconv::SignNeg, strconv::DigMax(dig), strconv::ExpDec, upper); r } 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, strconv::ExpNone, false); if special { fail!("number has a special value, \ try to_str_radix_special() if those are expected") } r } } /// Convert a string in base 16 to a float. /// Accepts an 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) } impl FromStr for f64 { /// Convert a string in base 10 to a float. /// Accepts an 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] fn from_str(val: &str) -> Option { strconv::from_str_common(val, 10u, true, true, true, strconv::ExpDec, false, false) } } impl num::FromStrRadix for f64 { /// Convert a string in a 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] fn from_str_radix(val: &str, rdx: uint) -> Option { strconv::from_str_common(val, rdx, true, true, false, strconv::ExpNone, false, false) } } #[cfg(test)] mod tests { use f64::*; use num::*; use num; #[test] fn test_min_nan() { assert_eq!(NAN.min(2.0), 2.0); assert_eq!(2.0f64.min(NAN), 2.0); } #[test] fn test_max_nan() { assert_eq!(NAN.max(2.0), 2.0); assert_eq!(2.0f64.max(NAN), 2.0); } #[test] fn test_num() { num::test_num(10f64, 2f64); } #[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 = Float::pi(); let two_pi: f64 = Float::two_pi(); let frac_pi_2: f64 = Float::frac_pi_2(); let frac_pi_3: f64 = Float::frac_pi_3(); let frac_pi_4: f64 = Float::frac_pi_4(); let frac_pi_6: f64 = Float::frac_pi_6(); let frac_pi_8: f64 = Float::frac_pi_8(); let frac_1_pi: f64 = Float::frac_1_pi(); let frac_2_pi: f64 = Float::frac_2_pi(); let frac_2_sqrtpi: f64 = Float::frac_2_sqrtpi(); let sqrt2: f64 = Float::sqrt2(); let frac_1_sqrt2: f64 = Float::frac_1_sqrt2(); let e: f64 = Float::e(); let log2_e: f64 = Float::log2_e(); let log10_e: f64 = Float::log10_e(); let ln_2: f64 = Float::ln_2(); let ln_10: f64 = Float::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] 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_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() }) } #[test] fn test_integer_decode() { assert_eq!(3.14159265359f64.integer_decode(), (7074237752028906u64, -51i16, 1i8)); assert_eq!((-8573.5918555f64).integer_decode(), (4713381968463931u64, -39i16, -1i8)); assert_eq!(2f64.powf(100.0).integer_decode(), (4503599627370496u64, 48i16, 1i8)); assert_eq!(0f64.integer_decode(), (0u64, -1075i16, 1i8)); assert_eq!((-0f64).integer_decode(), (0u64, -1075i16, -1i8)); assert_eq!(INFINITY.integer_decode(), (4503599627370496u64, 972i16, 1i8)); assert_eq!(NEG_INFINITY.integer_decode(), (4503599627370496, 972, -1)); assert_eq!(NAN.integer_decode(), (6755399441055744u64, 972i16, 1i8)); } }