// 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` use num::strconv; use num; use option::Option; use to_str; use from_str; #[cfg(notest)] use cmp; #[cfg(notest)] use ops; pub use cmath::c_double_targ_consts::*; pub use cmp::{min, max}; // An inner module is required to get the #[inline(always)] attribute on the // functions. pub use self::delegated::*; macro_rules! delegate( ( $( fn $name:ident( $( $arg:ident : $arg_ty:ty ),* ) -> $rv:ty = $bound_name:path ),* ) => ( mod delegated { use cmath::c_double_utils; use libc::{c_double, c_int}; use unstable::intrinsics; $( #[inline(always)] 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 expm1(n: c_double) -> c_double = c_double_utils::expm1, fn abs_sub(a: c_double, b: c_double) -> c_double = c_double_utils::abs_sub, fn fmax(a: c_double, b: c_double) -> c_double = c_double_utils::fmax, fn fmin(a: c_double, b: c_double) -> c_double = c_double_utils::fmin, fn nextafter(x: c_double, y: c_double) -> c_double = c_double_utils::nextafter, 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 ln1p(n: c_double) -> c_double = c_double_utils::ln1p, 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; #[inline(always)] pub fn is_NaN(f: f64) -> bool { f != f } #[inline(always)] pub fn add(x: f64, y: f64) -> f64 { return x + y; } #[inline(always)] pub fn sub(x: f64, y: f64) -> f64 { return x - y; } #[inline(always)] pub fn mul(x: f64, y: f64) -> f64 { return x * y; } #[inline(always)] pub fn div(x: f64, y: f64) -> f64 { return x / y; } #[inline(always)] pub fn rem(x: f64, y: f64) -> f64 { return x % y; } #[inline(always)] pub fn lt(x: f64, y: f64) -> bool { return x < y; } #[inline(always)] pub fn le(x: f64, y: f64) -> bool { return x <= y; } #[inline(always)] pub fn eq(x: f64, y: f64) -> bool { return x == y; } #[inline(always)] pub fn ne(x: f64, y: f64) -> bool { return x != y; } #[inline(always)] pub fn ge(x: f64, y: f64) -> bool { return x >= y; } #[inline(always)] pub fn gt(x: f64, y: f64) -> bool { return x > y; } /// Returns true if `x` is a positive number, including +0.0f640 and +Infinity #[inline(always)] pub fn is_positive(x: f64) -> bool { return x > 0.0f64 || (1.0f64/x) == infinity; } /// Returns true if `x` is a negative number, including -0.0f640 and -Infinity #[inline(always)] pub fn is_negative(x: f64) -> bool { return x < 0.0f64 || (1.0f64/x) == neg_infinity; } /** * Returns true if `x` is a negative number, including -0.0f640 and -Infinity * * This is the same as `f64::is_negative`. */ #[inline(always)] pub fn is_nonpositive(x: f64) -> bool { return x < 0.0f64 || (1.0f64/x) == neg_infinity; } /** * Returns true if `x` is a positive number, including +0.0f640 and +Infinity * * This is the same as `f64::positive`. */ #[inline(always)] pub fn is_nonnegative(x: f64) -> bool { return x > 0.0f64 || (1.0f64/x) == infinity; } /// Returns true if `x` is a zero number (positive or negative zero) #[inline(always)] pub fn is_zero(x: f64) -> bool { return x == 0.0f64 || x == -0.0f64; } /// Returns true if `x`is an infinite number #[inline(always)] pub fn is_infinite(x: f64) -> bool { return x == infinity || x == neg_infinity; } /// Returns true if `x` is a finite number #[inline(always)] pub fn is_finite(x: f64) -> bool { return !(is_NaN(x) || is_infinite(x)); } // 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; } #[inline(always)] pub fn signbit(x: f64) -> int { if is_negative(x) { return 1; } else { return 0; } } #[inline(always)] pub fn logarithm(n: f64, b: f64) -> f64 { return log2(n) / log2(b); } #[cfg(notest)] impl cmp::Eq for f64 { #[inline(always)] fn eq(&self, other: &f64) -> bool { (*self) == (*other) } #[inline(always)] fn ne(&self, other: &f64) -> bool { (*self) != (*other) } } #[cfg(notest)] impl cmp::Ord for f64 { #[inline(always)] fn lt(&self, other: &f64) -> bool { (*self) < (*other) } #[inline(always)] fn le(&self, other: &f64) -> bool { (*self) <= (*other) } #[inline(always)] fn ge(&self, other: &f64) -> bool { (*self) >= (*other) } #[inline(always)] fn gt(&self, other: &f64) -> bool { (*self) > (*other) } } impl num::Zero for f64 { #[inline(always)] fn zero() -> f64 { 0.0 } } impl num::One for f64 { #[inline(always)] fn one() -> f64 { 1.0 } } #[cfg(notest)] impl ops::Add for f64 { #[inline(always)] fn add(&self, other: &f64) -> f64 { *self + *other } } #[cfg(notest)] impl ops::Sub for f64 { #[inline(always)] fn sub(&self, other: &f64) -> f64 { *self - *other } } #[cfg(notest)] impl ops::Mul for f64 { #[inline(always)] fn mul(&self, other: &f64) -> f64 { *self * *other } } #[cfg(notest)] impl ops::Div for f64 { #[inline(always)] fn div(&self, other: &f64) -> f64 { *self / *other } } #[cfg(notest)] impl ops::Modulo for f64 { #[inline(always)] fn modulo(&self, other: &f64) -> f64 { *self % *other } } #[cfg(notest)] impl ops::Neg for f64 { #[inline(always)] fn neg(&self) -> f64 { -*self } } impl num::Round for f64 { #[inline(always)] fn round(&self, mode: num::RoundMode) -> f64 { match mode { num::RoundDown => floor(*self), num::RoundUp => ceil(*self), num::RoundToZero if is_negative(*self) => ceil(*self), num::RoundToZero => floor(*self), num::RoundFromZero if is_negative(*self) => floor(*self), num::RoundFromZero => ceil(*self) } } #[inline(always)] fn floor(&self) -> f64 { floor(*self) } #[inline(always)] fn ceil(&self) -> f64 { ceil(*self) } #[inline(always)] fn fract(&self) -> f64 { if is_negative(*self) { (*self) - ceil(*self) } else { (*self) - floor(*self) } } } /** * Section: String Conversions */ /** * Converts a float to a string * * # Arguments * * * num - The float value */ #[inline(always)] pub fn to_str(num: f64) -> ~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: f64) -> ~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: f64, rdx: uint) -> ~str { let (r, special) = strconv::to_str_common( &num, rdx, 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: f64, rdx: uint) -> (~str, bool) { strconv::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(always)] pub fn to_str_exact(num: f64, dig: uint) -> ~str { let (r, _) = strconv::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(always)] pub fn to_str_digits(num: f64, dig: uint) -> ~str { let (r, _) = strconv::to_str_common( &num, 10u, true, strconv::SignNeg, strconv::DigMax(dig)); r } impl to_str::ToStr for f64 { #[inline(always)] fn to_str(&self) -> ~str { to_str_digits(*self, 8) } } impl num::ToStrRadix for f64 { #[inline(always)] fn to_str_radix(&self, rdx: uint) -> ~str { to_str_radix(*self, rdx) } } /** * 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, 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, 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, rdx: uint) -> Option { strconv::from_str_common(num, rdx, true, true, false, strconv::ExpNone, false, false) } impl from_str::FromStr for f64 { #[inline(always)] fn from_str(val: &str) -> Option { from_str(val) } } impl num::FromStrRadix for f64 { #[inline(always)] fn from_str_radix(val: &str, rdx: uint) -> Option { from_str_radix(val, rdx) } } // // Local Variables: // mode: rust // fill-column: 78; // indent-tabs-mode: nil // c-basic-offset: 4 // buffer-file-coding-system: utf-8-unix // End: //