// 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 `float` // Even though this module exports everything defined in it, // because it contains re-exports, we also have to explicitly // export locally defined things. That's a bit annoying. // export when m_float == c_double // PORT this must match in width according to architecture use f64; use num::NumCast; use num::strconv; use num; use option::{None, Option, Some}; use to_str; use from_str; #[cfg(notest)] use cmp::{Eq, Ord}; #[cfg(notest)] use ops; pub use f64::{add, sub, mul, div, rem, lt, le, eq, ne, ge, gt}; pub use f64::logarithm; pub use f64::{acos, asin, atan2, cbrt, ceil, copysign, cosh, floor}; pub use f64::{erf, erfc, exp, expm1, exp2, abs_sub}; pub use f64::{mul_add, fmax, fmin, nextafter, frexp, hypot, ldexp}; pub use f64::{lgamma, ln, log_radix, ln1p, log10, log2, ilog_radix}; pub use f64::{modf, pow, round, sinh, tanh, tgamma, trunc}; pub use f64::signbit; pub use f64::{j0, j1, jn, y0, y1, yn}; pub const NaN: float = 0.0/0.0; pub const infinity: float = 1.0/0.0; pub const neg_infinity: float = -1.0/0.0; /* Module: consts */ pub mod consts { // FIXME (requires Issue #1433 to fix): replace with mathematical // constants from cmath. /// Archimedes' constant pub const pi: float = 3.14159265358979323846264338327950288; /// pi/2.0 pub const frac_pi_2: float = 1.57079632679489661923132169163975144; /// pi/4.0 pub const frac_pi_4: float = 0.785398163397448309615660845819875721; /// 1.0/pi pub const frac_1_pi: float = 0.318309886183790671537767526745028724; /// 2.0/pi pub const frac_2_pi: float = 0.636619772367581343075535053490057448; /// 2.0/sqrt(pi) pub const frac_2_sqrtpi: float = 1.12837916709551257389615890312154517; /// sqrt(2.0) pub const sqrt2: float = 1.41421356237309504880168872420969808; /// 1.0/sqrt(2.0) pub const frac_1_sqrt2: float = 0.707106781186547524400844362104849039; /// Euler's number pub const e: float = 2.71828182845904523536028747135266250; /// log2(e) pub const log2_e: float = 1.44269504088896340735992468100189214; /// log10(e) pub const log10_e: float = 0.434294481903251827651128918916605082; /// ln(2.0) pub const ln_2: float = 0.693147180559945309417232121458176568; /// ln(10.0) pub const ln_10: float = 2.30258509299404568401799145468436421; } /* * Section: String Conversions */ /** * Converts a float to a string * * # Arguments * * * num - The float value */ #[inline(always)] pub fn to_str(num: float) -> ~str { let (r, _) = strconv::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(always)] pub fn to_str_hex(num: float) -> ~str { let (r, _) = strconv::to_str_common( &num, 16u, true, strconv::SignNeg, strconv::DigAll); r } /** * 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(always)] pub fn to_str_radix(num: float, radix: uint) -> ~str { let (r, special) = strconv::to_str_common( &num, radix, true, strconv::SignNeg, strconv::DigAll); if special { fail!(~"number has a special value, \ try to_str_radix_special() if those are expected") } 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(always)] pub fn to_str_radix_special(num: float, radix: uint) -> (~str, bool) { strconv::to_str_common(&num, radix, 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(always)] pub fn to_str_exact(num: float, digits: uint) -> ~str { let (r, _) = strconv::to_str_common( &num, 10u, true, strconv::SignNeg, strconv::DigExact(digits)); r } #[test] pub fn test_to_str_exact_do_decimal() { let s = to_str_exact(5.0, 4u); fail_unless!(s == ~"5.0000"); } /** * 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(always)] pub fn to_str_digits(num: float, digits: uint) -> ~str { let (r, _) = strconv::to_str_common( &num, 10u, true, strconv::SignNeg, strconv::DigMax(digits)); r } impl to_str::ToStr for float { #[inline(always)] fn to_str(&self) -> ~str { to_str_digits(*self, 8) } } impl num::ToStrRadix for float { #[inline(always)] fn to_str_radix(&self, radix: uint) -> ~str { to_str_radix(*self, radix) } } /** * 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(always)] pub fn from_str(num: &str) -> Option { strconv::from_str_common(num, 10u, true, true, true, strconv::ExpDec, 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(always)] pub fn from_str_hex(num: &str) -> Option { strconv::from_str_common(num, 16u, true, true, true, strconv::ExpBin, 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(always)] pub fn from_str_radix(num: &str, radix: uint) -> Option { strconv::from_str_common(num, radix, true, true, false, strconv::ExpNone, false) } impl from_str::FromStr for float { #[inline(always)] fn from_str(val: &str) -> Option { from_str(val) } } impl num::FromStrRadix for float { #[inline(always)] fn from_str_radix(val: &str, radix: uint) -> Option { from_str_radix(val, radix) } } /** * Section: Arithmetics */ /** * Compute the exponentiation of an integer by another integer as a float * * # Arguments * * * x - The base * * pow - The exponent * * # Return value * * `NaN` if both `x` and `pow` are `0u`, otherwise `x^pow` */ pub fn pow_with_uint(base: uint, pow: uint) -> float { if base == 0u { if pow == 0u { return NaN as float; } return 0.; } let mut my_pow = pow; let mut total = 1f; let mut multiplier = base as float; while (my_pow > 0u) { if my_pow % 2u == 1u { total = total * multiplier; } my_pow /= 2u; multiplier *= multiplier; } return total; } #[inline(always)] pub fn is_positive(x: float) -> bool { f64::is_positive(x as f64) } #[inline(always)] pub fn is_negative(x: float) -> bool { f64::is_negative(x as f64) } #[inline(always)] pub fn is_nonpositive(x: float) -> bool { f64::is_nonpositive(x as f64) } #[inline(always)] pub fn is_nonnegative(x: float) -> bool { f64::is_nonnegative(x as f64) } #[inline(always)] pub fn is_zero(x: float) -> bool { f64::is_zero(x as f64) } #[inline(always)] pub fn is_infinite(x: float) -> bool { f64::is_infinite(x as f64) } #[inline(always)] pub fn is_finite(x: float) -> bool { f64::is_finite(x as f64) } #[inline(always)] pub fn is_NaN(x: float) -> bool { f64::is_NaN(x as f64) } #[inline(always)] pub fn abs(x: float) -> float { unsafe { f64::abs(x as f64) as float } } #[inline(always)] pub fn sqrt(x: float) -> float { unsafe { f64::sqrt(x as f64) as float } } #[inline(always)] pub fn atan(x: float) -> float { unsafe { f64::atan(x as f64) as float } } #[inline(always)] pub fn sin(x: float) -> float { unsafe { f64::sin(x as f64) as float } } #[inline(always)] pub fn cos(x: float) -> float { unsafe { f64::cos(x as f64) as float } } #[inline(always)] pub fn tan(x: float) -> float { unsafe { f64::tan(x as f64) as float } } #[cfg(notest)] impl Eq for float { fn eq(&self, other: &float) -> bool { (*self) == (*other) } fn ne(&self, other: &float) -> bool { (*self) != (*other) } } #[cfg(notest)] impl Ord for float { fn lt(&self, other: &float) -> bool { (*self) < (*other) } fn le(&self, other: &float) -> bool { (*self) <= (*other) } fn ge(&self, other: &float) -> bool { (*self) >= (*other) } fn gt(&self, other: &float) -> bool { (*self) > (*other) } } impl num::Zero for float { #[inline(always)] fn zero() -> float { 0.0 } } impl num::One for float { #[inline(always)] fn one() -> float { 1.0 } } impl NumCast for float { /** * Cast `n` to a `float` */ #[inline(always)] fn from(n: N) -> float { n.to_float() } #[inline(always)] fn to_u8(&self) -> u8 { *self as u8 } #[inline(always)] fn to_u16(&self) -> u16 { *self as u16 } #[inline(always)] fn to_u32(&self) -> u32 { *self as u32 } #[inline(always)] fn to_u64(&self) -> u64 { *self as u64 } #[inline(always)] fn to_uint(&self) -> uint { *self as uint } #[inline(always)] fn to_i8(&self) -> i8 { *self as i8 } #[inline(always)] fn to_i16(&self) -> i16 { *self as i16 } #[inline(always)] fn to_i32(&self) -> i32 { *self as i32 } #[inline(always)] fn to_i64(&self) -> i64 { *self as i64 } #[inline(always)] fn to_int(&self) -> int { *self as int } #[inline(always)] fn to_f32(&self) -> f32 { *self as f32 } #[inline(always)] fn to_f64(&self) -> f64 { *self as f64 } #[inline(always)] fn to_float(&self) -> float { *self } } impl num::Round for float { #[inline(always)] fn round(&self, mode: num::RoundMode) -> float { match mode { num::RoundDown => f64::floor(*self as f64) as float, num::RoundUp => f64::ceil(*self as f64) as float, num::RoundToZero if is_negative(*self) => f64::ceil(*self as f64) as float, num::RoundToZero => f64::floor(*self as f64) as float, num::RoundFromZero if is_negative(*self) => f64::floor(*self as f64) as float, num::RoundFromZero => f64::ceil(*self as f64) as float } } #[inline(always)] fn floor(&self) -> float { f64::floor(*self as f64) as float} #[inline(always)] fn ceil(&self) -> float { f64::ceil(*self as f64) as float} #[inline(always)] fn fract(&self) -> float { if is_negative(*self) { (*self) - (f64::ceil(*self as f64) as float) } else { (*self) - (f64::floor(*self as f64) as float) } } } #[cfg(notest)] impl ops::Add for float { fn add(&self, other: &float) -> float { *self + *other } } #[cfg(notest)] impl ops::Sub for float { fn sub(&self, other: &float) -> float { *self - *other } } #[cfg(notest)] impl ops::Mul for float { fn mul(&self, other: &float) -> float { *self * *other } } #[cfg(notest)] impl ops::Div for float { fn div(&self, other: &float) -> float { *self / *other } } #[cfg(notest)] impl ops::Modulo for float { fn modulo(&self, other: &float) -> float { *self % *other } } #[cfg(notest)] impl ops::Neg for float { fn neg(&self) -> float { -*self } } #[test] pub fn test_from_str() { fail_unless!(from_str(~"3") == Some(3.)); fail_unless!(from_str(~"3.14") == Some(3.14)); fail_unless!(from_str(~"+3.14") == Some(3.14)); fail_unless!(from_str(~"-3.14") == Some(-3.14)); fail_unless!(from_str(~"2.5E10") == Some(25000000000.)); fail_unless!(from_str(~"2.5e10") == Some(25000000000.)); fail_unless!(from_str(~"25000000000.E-10") == Some(2.5)); fail_unless!(from_str(~".") == Some(0.)); fail_unless!(from_str(~".e1") == Some(0.)); fail_unless!(from_str(~".e-1") == Some(0.)); fail_unless!(from_str(~"5.") == Some(5.)); fail_unless!(from_str(~".5") == Some(0.5)); fail_unless!(from_str(~"0.5") == Some(0.5)); fail_unless!(from_str(~"-.5") == Some(-0.5)); fail_unless!(from_str(~"-5") == Some(-5.)); fail_unless!(from_str(~"inf") == Some(infinity)); fail_unless!(from_str(~"+inf") == Some(infinity)); fail_unless!(from_str(~"-inf") == Some(neg_infinity)); // note: NaN != NaN, hence this slightly complex test match from_str(~"NaN") { Some(f) => fail_unless!(is_NaN(f)), None => fail!() } // note: -0 == 0, hence these slightly more complex tests match from_str(~"-0") { Some(v) if is_zero(v) => fail_unless!(is_negative(v)), _ => fail!() } match from_str(~"0") { Some(v) if is_zero(v) => fail_unless!(is_positive(v)), _ => fail!() } fail_unless!(from_str(~"").is_none()); fail_unless!(from_str(~"x").is_none()); fail_unless!(from_str(~" ").is_none()); fail_unless!(from_str(~" ").is_none()); fail_unless!(from_str(~"e").is_none()); fail_unless!(from_str(~"E").is_none()); fail_unless!(from_str(~"E1").is_none()); fail_unless!(from_str(~"1e1e1").is_none()); fail_unless!(from_str(~"1e1.1").is_none()); fail_unless!(from_str(~"1e1-1").is_none()); } #[test] pub fn test_from_str_hex() { fail_unless!(from_str_hex(~"a4") == Some(164.)); fail_unless!(from_str_hex(~"a4.fe") == Some(164.9921875)); fail_unless!(from_str_hex(~"-a4.fe") == Some(-164.9921875)); fail_unless!(from_str_hex(~"+a4.fe") == Some(164.9921875)); fail_unless!(from_str_hex(~"ff0P4") == Some(0xff00 as float)); fail_unless!(from_str_hex(~"ff0p4") == Some(0xff00 as float)); fail_unless!(from_str_hex(~"ff0p-4") == Some(0xff as float)); fail_unless!(from_str_hex(~".") == Some(0.)); fail_unless!(from_str_hex(~".p1") == Some(0.)); fail_unless!(from_str_hex(~".p-1") == Some(0.)); fail_unless!(from_str_hex(~"f.") == Some(15.)); fail_unless!(from_str_hex(~".f") == Some(0.9375)); fail_unless!(from_str_hex(~"0.f") == Some(0.9375)); fail_unless!(from_str_hex(~"-.f") == Some(-0.9375)); fail_unless!(from_str_hex(~"-f") == Some(-15.)); fail_unless!(from_str_hex(~"inf") == Some(infinity)); fail_unless!(from_str_hex(~"+inf") == Some(infinity)); fail_unless!(from_str_hex(~"-inf") == Some(neg_infinity)); // note: NaN != NaN, hence this slightly complex test match from_str_hex(~"NaN") { Some(f) => fail_unless!(is_NaN(f)), None => fail!() } // note: -0 == 0, hence these slightly more complex tests match from_str_hex(~"-0") { Some(v) if is_zero(v) => fail_unless!(is_negative(v)), _ => fail!() } match from_str_hex(~"0") { Some(v) if is_zero(v) => fail_unless!(is_positive(v)), _ => fail!() } fail_unless!(from_str_hex(~"e") == Some(14.)); fail_unless!(from_str_hex(~"E") == Some(14.)); fail_unless!(from_str_hex(~"E1") == Some(225.)); fail_unless!(from_str_hex(~"1e1e1") == Some(123361.)); fail_unless!(from_str_hex(~"1e1.1") == Some(481.0625)); fail_unless!(from_str_hex(~"").is_none()); fail_unless!(from_str_hex(~"x").is_none()); fail_unless!(from_str_hex(~" ").is_none()); fail_unless!(from_str_hex(~" ").is_none()); fail_unless!(from_str_hex(~"p").is_none()); fail_unless!(from_str_hex(~"P").is_none()); fail_unless!(from_str_hex(~"P1").is_none()); fail_unless!(from_str_hex(~"1p1p1").is_none()); fail_unless!(from_str_hex(~"1p1.1").is_none()); fail_unless!(from_str_hex(~"1p1-1").is_none()); } #[test] pub fn test_to_str_hex() { fail_unless!(to_str_hex(164.) == ~"a4"); fail_unless!(to_str_hex(164.9921875) == ~"a4.fe"); fail_unless!(to_str_hex(-164.9921875) == ~"-a4.fe"); fail_unless!(to_str_hex(0xff00 as float) == ~"ff00"); fail_unless!(to_str_hex(-(0xff00 as float)) == ~"-ff00"); fail_unless!(to_str_hex(0.) == ~"0"); fail_unless!(to_str_hex(15.) == ~"f"); fail_unless!(to_str_hex(-15.) == ~"-f"); fail_unless!(to_str_hex(0.9375) == ~"0.f"); fail_unless!(to_str_hex(-0.9375) == ~"-0.f"); fail_unless!(to_str_hex(infinity) == ~"inf"); fail_unless!(to_str_hex(neg_infinity) == ~"-inf"); fail_unless!(to_str_hex(NaN) == ~"NaN"); fail_unless!(to_str_hex(0.) == ~"0"); fail_unless!(to_str_hex(-0.) == ~"-0"); } #[test] pub fn test_to_str_radix() { fail_unless!(to_str_radix(36., 36u) == ~"10"); fail_unless!(to_str_radix(8.125, 2u) == ~"1000.001"); } #[test] pub fn test_from_str_radix() { fail_unless!(from_str_radix(~"10", 36u) == Some(36.)); fail_unless!(from_str_radix(~"1000.001", 2u) == Some(8.125)); } #[test] pub fn test_positive() { fail_unless!((is_positive(infinity))); fail_unless!((is_positive(1.))); fail_unless!((is_positive(0.))); fail_unless!((!is_positive(-1.))); fail_unless!((!is_positive(neg_infinity))); fail_unless!((!is_positive(1./neg_infinity))); fail_unless!((!is_positive(NaN))); } #[test] pub fn test_negative() { fail_unless!((!is_negative(infinity))); fail_unless!((!is_negative(1.))); fail_unless!((!is_negative(0.))); fail_unless!((is_negative(-1.))); fail_unless!((is_negative(neg_infinity))); fail_unless!((is_negative(1./neg_infinity))); fail_unless!((!is_negative(NaN))); } #[test] pub fn test_nonpositive() { fail_unless!((!is_nonpositive(infinity))); fail_unless!((!is_nonpositive(1.))); fail_unless!((!is_nonpositive(0.))); fail_unless!((is_nonpositive(-1.))); fail_unless!((is_nonpositive(neg_infinity))); fail_unless!((is_nonpositive(1./neg_infinity))); fail_unless!((!is_nonpositive(NaN))); } #[test] pub fn test_nonnegative() { fail_unless!((is_nonnegative(infinity))); fail_unless!((is_nonnegative(1.))); fail_unless!((is_nonnegative(0.))); fail_unless!((!is_nonnegative(-1.))); fail_unless!((!is_nonnegative(neg_infinity))); fail_unless!((!is_nonnegative(1./neg_infinity))); fail_unless!((!is_nonnegative(NaN))); } #[test] pub fn test_to_str_inf() { fail_unless!(to_str_digits(infinity, 10u) == ~"inf"); fail_unless!(to_str_digits(-infinity, 10u) == ~"-inf"); } #[test] pub fn test_round() { fail_unless!(round(5.8) == 6.0); fail_unless!(round(5.2) == 5.0); fail_unless!(round(3.0) == 3.0); fail_unless!(round(2.5) == 3.0); fail_unless!(round(-3.5) == -4.0); } #[test] pub fn test_num() { let ten: float = num::cast(10); let two: float = num::cast(2); fail_unless!((ten.add(&two) == num::cast(12))); fail_unless!((ten.sub(&two) == num::cast(8))); fail_unless!((ten.mul(&two) == num::cast(20))); fail_unless!((ten.div(&two) == num::cast(5))); fail_unless!((ten.modulo(&two) == num::cast(0))); } #[test] fn test_numcast() { fail_unless!((20u == 20f.to_uint())); fail_unless!((20u8 == 20f.to_u8())); fail_unless!((20u16 == 20f.to_u16())); fail_unless!((20u32 == 20f.to_u32())); fail_unless!((20u64 == 20f.to_u64())); fail_unless!((20i == 20f.to_int())); fail_unless!((20i8 == 20f.to_i8())); fail_unless!((20i16 == 20f.to_i16())); fail_unless!((20i32 == 20f.to_i32())); fail_unless!((20i64 == 20f.to_i64())); fail_unless!((20f == 20f.to_float())); fail_unless!((20f32 == 20f.to_f32())); fail_unless!((20f64 == 20f.to_f64())); fail_unless!((20f == NumCast::from(20u))); fail_unless!((20f == NumCast::from(20u8))); fail_unless!((20f == NumCast::from(20u16))); fail_unless!((20f == NumCast::from(20u32))); fail_unless!((20f == NumCast::from(20u64))); fail_unless!((20f == NumCast::from(20i))); fail_unless!((20f == NumCast::from(20i8))); fail_unless!((20f == NumCast::from(20i16))); fail_unless!((20f == NumCast::from(20i32))); fail_unless!((20f == NumCast::from(20i64))); fail_unless!((20f == NumCast::from(20f))); fail_unless!((20f == NumCast::from(20f32))); fail_unless!((20f == NumCast::from(20f64))); fail_unless!((20f == num::cast(20u))); fail_unless!((20f == num::cast(20u8))); fail_unless!((20f == num::cast(20u16))); fail_unless!((20f == num::cast(20u32))); fail_unless!((20f == num::cast(20u64))); fail_unless!((20f == num::cast(20i))); fail_unless!((20f == num::cast(20i8))); fail_unless!((20f == num::cast(20i16))); fail_unless!((20f == num::cast(20i32))); fail_unless!((20f == num::cast(20i64))); fail_unless!((20f == num::cast(20f))); fail_unless!((20f == num::cast(20f32))); fail_unless!((20f == num::cast(20f64))); } // // Local Variables: // mode: rust // fill-column: 78; // indent-tabs-mode: nil // c-basic-offset: 4 // buffer-file-coding-system: utf-8-unix // End: //