679 lines
20 KiB
Rust
679 lines
20 KiB
Rust
// Copyright 2012 The Rust Project Developers. See the COPYRIGHT
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// file at the top-level directory of this distribution and at
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// http://rust-lang.org/COPYRIGHT.
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//
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// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
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// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
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// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
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// option. This file may not be copied, modified, or distributed
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// except according to those terms.
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//! Operations and constants for `float`
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// Even though this module exports everything defined in it,
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// because it contains re-exports, we also have to explicitly
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// export locally defined things. That's a bit annoying.
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// export when m_float == c_double
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// PORT this must match in width according to architecture
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use f64;
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use num::strconv;
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use num;
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use option::Option;
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use to_str;
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use from_str;
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#[cfg(notest)] use cmp::{Eq, Ord};
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#[cfg(notest)] use ops;
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pub use f64::{add, sub, mul, div, rem, lt, le, eq, ne, ge, gt};
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pub use f64::logarithm;
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pub use f64::{acos, asin, atan2, cbrt, ceil, copysign, cosh, floor};
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pub use f64::{erf, erfc, exp, expm1, exp2, abs_sub};
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pub use f64::{mul_add, fmax, fmin, nextafter, frexp, hypot, ldexp};
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pub use f64::{lgamma, ln, log_radix, ln1p, log10, log2, ilog_radix};
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pub use f64::{modf, pow, round, sinh, tanh, tgamma, trunc};
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pub use f64::signbit;
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pub use f64::{j0, j1, jn, y0, y1, yn};
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pub static NaN: float = 0.0/0.0;
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pub static infinity: float = 1.0/0.0;
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pub static neg_infinity: float = -1.0/0.0;
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/* Module: consts */
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pub mod consts {
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// FIXME (requires Issue #1433 to fix): replace with mathematical
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// staticants from cmath.
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/// Archimedes' staticant
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pub static pi: float = 3.14159265358979323846264338327950288;
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/// pi/2.0
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pub static frac_pi_2: float = 1.57079632679489661923132169163975144;
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/// pi/4.0
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pub static frac_pi_4: float = 0.785398163397448309615660845819875721;
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/// 1.0/pi
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pub static frac_1_pi: float = 0.318309886183790671537767526745028724;
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/// 2.0/pi
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pub static frac_2_pi: float = 0.636619772367581343075535053490057448;
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/// 2.0/sqrt(pi)
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pub static frac_2_sqrtpi: float = 1.12837916709551257389615890312154517;
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/// sqrt(2.0)
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pub static sqrt2: float = 1.41421356237309504880168872420969808;
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/// 1.0/sqrt(2.0)
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pub static frac_1_sqrt2: float = 0.707106781186547524400844362104849039;
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/// Euler's number
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pub static e: float = 2.71828182845904523536028747135266250;
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/// log2(e)
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pub static log2_e: float = 1.44269504088896340735992468100189214;
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/// log10(e)
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pub static log10_e: float = 0.434294481903251827651128918916605082;
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/// ln(2.0)
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pub static ln_2: float = 0.693147180559945309417232121458176568;
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/// ln(10.0)
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pub static ln_10: float = 2.30258509299404568401799145468436421;
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}
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/*
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* Section: String Conversions
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*/
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/**
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* Converts a float to a string
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*
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* # Arguments
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*
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* * num - The float value
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*/
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#[inline(always)]
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pub fn to_str(num: float) -> ~str {
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let (r, _) = strconv::to_str_common(
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&num, 10u, true, strconv::SignNeg, strconv::DigAll);
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r
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}
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/**
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* Converts a float to a string in hexadecimal format
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*
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* # Arguments
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*
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* * num - The float value
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*/
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#[inline(always)]
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pub fn to_str_hex(num: float) -> ~str {
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let (r, _) = strconv::to_str_common(
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&num, 16u, true, strconv::SignNeg, strconv::DigAll);
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r
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}
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/**
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* Converts a float to a string in a given radix
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*
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* # Arguments
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*
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* * num - The float value
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* * radix - The base to use
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*
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* # Failure
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*
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* Fails if called on a special value like `inf`, `-inf` or `NaN` due to
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* possible misinterpretation of the result at higher bases. If those values
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* are expected, use `to_str_radix_special()` instead.
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*/
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#[inline(always)]
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pub fn to_str_radix(num: float, radix: uint) -> ~str {
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let (r, special) = strconv::to_str_common(
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&num, radix, true, strconv::SignNeg, strconv::DigAll);
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if special { fail!(~"number has a special value, \
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try to_str_radix_special() if those are expected") }
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r
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}
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/**
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* Converts a float to a string in a given radix, and a flag indicating
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* whether it's a special value
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*
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* # Arguments
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*
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* * num - The float value
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* * radix - The base to use
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*/
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#[inline(always)]
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pub fn to_str_radix_special(num: float, radix: uint) -> (~str, bool) {
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strconv::to_str_common(&num, radix, true,
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strconv::SignNeg, strconv::DigAll)
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}
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/**
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* Converts a float to a string with exactly the number of
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* provided significant digits
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*
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* # Arguments
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*
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* * num - The float value
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* * digits - The number of significant digits
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*/
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#[inline(always)]
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pub fn to_str_exact(num: float, digits: uint) -> ~str {
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let (r, _) = strconv::to_str_common(
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&num, 10u, true, strconv::SignNeg, strconv::DigExact(digits));
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r
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}
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/**
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* Converts a float to a string with a maximum number of
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* significant digits
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*
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* # Arguments
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*
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* * num - The float value
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* * digits - The number of significant digits
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*/
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#[inline(always)]
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pub fn to_str_digits(num: float, digits: uint) -> ~str {
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let (r, _) = strconv::to_str_common(
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&num, 10u, true, strconv::SignNeg, strconv::DigMax(digits));
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r
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}
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impl to_str::ToStr for float {
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#[inline(always)]
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fn to_str(&self) -> ~str { to_str_digits(*self, 8) }
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}
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impl num::ToStrRadix for float {
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#[inline(always)]
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fn to_str_radix(&self, radix: uint) -> ~str {
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to_str_radix(*self, radix)
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}
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}
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/**
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* Convert a string in base 10 to a float.
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* Accepts a optional decimal exponent.
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*
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* This function accepts strings such as
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*
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* * '3.14'
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* * '+3.14', equivalent to '3.14'
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* * '-3.14'
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* * '2.5E10', or equivalently, '2.5e10'
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* * '2.5E-10'
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* * '.' (understood as 0)
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* * '5.'
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* * '.5', or, equivalently, '0.5'
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* * '+inf', 'inf', '-inf', 'NaN'
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*
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* Leading and trailing whitespace represent an error.
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*
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* # Arguments
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*
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* * num - A string
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*
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* # Return value
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*
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* `none` if the string did not represent a valid number. Otherwise,
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* `Some(n)` where `n` is the floating-point number represented by `num`.
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*/
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#[inline(always)]
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pub fn from_str(num: &str) -> Option<float> {
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strconv::from_str_common(num, 10u, true, true, true,
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strconv::ExpDec, false, false)
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}
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/**
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* Convert a string in base 16 to a float.
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* Accepts a optional binary exponent.
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*
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* This function accepts strings such as
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*
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* * 'a4.fe'
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* * '+a4.fe', equivalent to 'a4.fe'
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* * '-a4.fe'
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* * '2b.aP128', or equivalently, '2b.ap128'
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* * '2b.aP-128'
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* * '.' (understood as 0)
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* * 'c.'
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* * '.c', or, equivalently, '0.c'
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* * '+inf', 'inf', '-inf', 'NaN'
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*
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* Leading and trailing whitespace represent an error.
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*
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* # Arguments
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*
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* * num - A string
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*
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* # Return value
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*
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* `none` if the string did not represent a valid number. Otherwise,
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* `Some(n)` where `n` is the floating-point number represented by `[num]`.
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*/
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#[inline(always)]
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pub fn from_str_hex(num: &str) -> Option<float> {
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strconv::from_str_common(num, 16u, true, true, true,
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strconv::ExpBin, false, false)
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}
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/**
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* Convert a string in an given base to a float.
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*
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* Due to possible conflicts, this function does **not** accept
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* the special values `inf`, `-inf`, `+inf` and `NaN`, **nor**
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* does it recognize exponents of any kind.
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*
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* Leading and trailing whitespace represent an error.
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*
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* # Arguments
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*
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* * num - A string
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* * radix - The base to use. Must lie in the range [2 .. 36]
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*
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* # Return value
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*
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* `none` if the string did not represent a valid number. Otherwise,
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* `Some(n)` where `n` is the floating-point number represented by `num`.
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*/
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#[inline(always)]
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pub fn from_str_radix(num: &str, radix: uint) -> Option<float> {
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strconv::from_str_common(num, radix, true, true, false,
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strconv::ExpNone, false, false)
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}
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impl from_str::FromStr for float {
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#[inline(always)]
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fn from_str(val: &str) -> Option<float> { from_str(val) }
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}
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impl num::FromStrRadix for float {
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#[inline(always)]
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fn from_str_radix(val: &str, radix: uint) -> Option<float> {
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from_str_radix(val, radix)
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}
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}
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/**
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* Section: Arithmetics
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*/
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/**
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* Compute the exponentiation of an integer by another integer as a float
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*
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* # Arguments
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*
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* * x - The base
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* * pow - The exponent
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*
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* # Return value
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*
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* `NaN` if both `x` and `pow` are `0u`, otherwise `x^pow`
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*/
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pub fn pow_with_uint(base: uint, pow: uint) -> float {
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if base == 0u {
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if pow == 0u {
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return NaN as float;
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}
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return 0.;
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}
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let mut my_pow = pow;
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let mut total = 1f;
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let mut multiplier = base as float;
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while (my_pow > 0u) {
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if my_pow % 2u == 1u {
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total = total * multiplier;
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}
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my_pow /= 2u;
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multiplier *= multiplier;
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}
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return total;
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}
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#[inline(always)]
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pub fn is_positive(x: float) -> bool { f64::is_positive(x as f64) }
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#[inline(always)]
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pub fn is_negative(x: float) -> bool { f64::is_negative(x as f64) }
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#[inline(always)]
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pub fn is_nonpositive(x: float) -> bool { f64::is_nonpositive(x as f64) }
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#[inline(always)]
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pub fn is_nonnegative(x: float) -> bool { f64::is_nonnegative(x as f64) }
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#[inline(always)]
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pub fn is_zero(x: float) -> bool { f64::is_zero(x as f64) }
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#[inline(always)]
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pub fn is_infinite(x: float) -> bool { f64::is_infinite(x as f64) }
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#[inline(always)]
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pub fn is_finite(x: float) -> bool { f64::is_finite(x as f64) }
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#[inline(always)]
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pub fn is_NaN(x: float) -> bool { f64::is_NaN(x as f64) }
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#[inline(always)]
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pub fn abs(x: float) -> float {
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f64::abs(x as f64) as float
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}
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#[inline(always)]
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pub fn sqrt(x: float) -> float {
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f64::sqrt(x as f64) as float
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}
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#[inline(always)]
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pub fn atan(x: float) -> float {
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f64::atan(x as f64) as float
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}
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#[inline(always)]
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pub fn sin(x: float) -> float {
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f64::sin(x as f64) as float
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}
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#[inline(always)]
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pub fn cos(x: float) -> float {
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f64::cos(x as f64) as float
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}
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#[inline(always)]
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pub fn tan(x: float) -> float {
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f64::tan(x as f64) as float
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}
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#[cfg(notest)]
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impl Eq for float {
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fn eq(&self, other: &float) -> bool { (*self) == (*other) }
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fn ne(&self, other: &float) -> bool { (*self) != (*other) }
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}
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#[cfg(notest)]
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impl Ord for float {
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fn lt(&self, other: &float) -> bool { (*self) < (*other) }
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fn le(&self, other: &float) -> bool { (*self) <= (*other) }
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fn ge(&self, other: &float) -> bool { (*self) >= (*other) }
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fn gt(&self, other: &float) -> bool { (*self) > (*other) }
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}
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impl num::Zero for float {
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#[inline(always)]
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fn zero() -> float { 0.0 }
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}
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impl num::One for float {
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#[inline(always)]
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fn one() -> float { 1.0 }
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}
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impl num::Round for float {
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#[inline(always)]
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fn round(&self, mode: num::RoundMode) -> float {
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match mode {
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num::RoundDown
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=> f64::floor(*self as f64) as float,
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num::RoundUp
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=> f64::ceil(*self as f64) as float,
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num::RoundToZero if is_negative(*self)
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=> f64::ceil(*self as f64) as float,
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num::RoundToZero
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=> f64::floor(*self as f64) as float,
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num::RoundFromZero if is_negative(*self)
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=> f64::floor(*self as f64) as float,
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num::RoundFromZero
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=> f64::ceil(*self as f64) as float
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}
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}
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#[inline(always)]
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fn floor(&self) -> float { f64::floor(*self as f64) as float}
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#[inline(always)]
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fn ceil(&self) -> float { f64::ceil(*self as f64) as float}
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#[inline(always)]
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fn fract(&self) -> float {
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if is_negative(*self) {
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(*self) - (f64::ceil(*self as f64) as float)
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} else {
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(*self) - (f64::floor(*self as f64) as float)
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}
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}
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}
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#[cfg(notest)]
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impl ops::Add<float,float> for float {
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fn add(&self, other: &float) -> float { *self + *other }
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}
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#[cfg(notest)]
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impl ops::Sub<float,float> for float {
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fn sub(&self, other: &float) -> float { *self - *other }
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}
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#[cfg(notest)]
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impl ops::Mul<float,float> for float {
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fn mul(&self, other: &float) -> float { *self * *other }
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}
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#[cfg(notest)]
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impl ops::Div<float,float> for float {
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fn div(&self, other: &float) -> float { *self / *other }
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}
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#[cfg(notest)]
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impl ops::Modulo<float,float> for float {
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fn modulo(&self, other: &float) -> float { *self % *other }
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}
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#[cfg(notest)]
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impl ops::Neg<float> for float {
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fn neg(&self) -> float { -*self }
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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use prelude::*;
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#[test]
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pub fn test_to_str_exact_do_decimal() {
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let s = to_str_exact(5.0, 4u);
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assert!(s == ~"5.0000");
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}
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#[test]
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pub fn test_from_str() {
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assert!(from_str(~"3") == Some(3.));
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assert!(from_str(~"3.14") == Some(3.14));
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assert!(from_str(~"+3.14") == Some(3.14));
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assert!(from_str(~"-3.14") == Some(-3.14));
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assert!(from_str(~"2.5E10") == Some(25000000000.));
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assert!(from_str(~"2.5e10") == Some(25000000000.));
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assert!(from_str(~"25000000000.E-10") == Some(2.5));
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assert!(from_str(~".") == Some(0.));
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assert!(from_str(~".e1") == Some(0.));
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assert!(from_str(~".e-1") == Some(0.));
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assert!(from_str(~"5.") == Some(5.));
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assert!(from_str(~".5") == Some(0.5));
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assert!(from_str(~"0.5") == Some(0.5));
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assert!(from_str(~"-.5") == Some(-0.5));
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assert!(from_str(~"-5") == Some(-5.));
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assert!(from_str(~"inf") == Some(infinity));
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assert!(from_str(~"+inf") == Some(infinity));
|
|
assert!(from_str(~"-inf") == Some(neg_infinity));
|
|
// note: NaN != NaN, hence this slightly complex test
|
|
match from_str(~"NaN") {
|
|
Some(f) => assert!(is_NaN(f)),
|
|
None => fail!()
|
|
}
|
|
// note: -0 == 0, hence these slightly more complex tests
|
|
match from_str(~"-0") {
|
|
Some(v) if is_zero(v) => assert!(is_negative(v)),
|
|
_ => fail!()
|
|
}
|
|
match from_str(~"0") {
|
|
Some(v) if is_zero(v) => assert!(is_positive(v)),
|
|
_ => fail!()
|
|
}
|
|
|
|
assert!(from_str(~"").is_none());
|
|
assert!(from_str(~"x").is_none());
|
|
assert!(from_str(~" ").is_none());
|
|
assert!(from_str(~" ").is_none());
|
|
assert!(from_str(~"e").is_none());
|
|
assert!(from_str(~"E").is_none());
|
|
assert!(from_str(~"E1").is_none());
|
|
assert!(from_str(~"1e1e1").is_none());
|
|
assert!(from_str(~"1e1.1").is_none());
|
|
assert!(from_str(~"1e1-1").is_none());
|
|
}
|
|
|
|
#[test]
|
|
pub fn test_from_str_hex() {
|
|
assert!(from_str_hex(~"a4") == Some(164.));
|
|
assert!(from_str_hex(~"a4.fe") == Some(164.9921875));
|
|
assert!(from_str_hex(~"-a4.fe") == Some(-164.9921875));
|
|
assert!(from_str_hex(~"+a4.fe") == Some(164.9921875));
|
|
assert!(from_str_hex(~"ff0P4") == Some(0xff00 as float));
|
|
assert!(from_str_hex(~"ff0p4") == Some(0xff00 as float));
|
|
assert!(from_str_hex(~"ff0p-4") == Some(0xff as float));
|
|
assert!(from_str_hex(~".") == Some(0.));
|
|
assert!(from_str_hex(~".p1") == Some(0.));
|
|
assert!(from_str_hex(~".p-1") == Some(0.));
|
|
assert!(from_str_hex(~"f.") == Some(15.));
|
|
assert!(from_str_hex(~".f") == Some(0.9375));
|
|
assert!(from_str_hex(~"0.f") == Some(0.9375));
|
|
assert!(from_str_hex(~"-.f") == Some(-0.9375));
|
|
assert!(from_str_hex(~"-f") == Some(-15.));
|
|
assert!(from_str_hex(~"inf") == Some(infinity));
|
|
assert!(from_str_hex(~"+inf") == Some(infinity));
|
|
assert!(from_str_hex(~"-inf") == Some(neg_infinity));
|
|
// note: NaN != NaN, hence this slightly complex test
|
|
match from_str_hex(~"NaN") {
|
|
Some(f) => assert!(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) => assert!(is_negative(v)),
|
|
_ => fail!()
|
|
}
|
|
match from_str_hex(~"0") {
|
|
Some(v) if is_zero(v) => assert!(is_positive(v)),
|
|
_ => fail!()
|
|
}
|
|
assert!(from_str_hex(~"e") == Some(14.));
|
|
assert!(from_str_hex(~"E") == Some(14.));
|
|
assert!(from_str_hex(~"E1") == Some(225.));
|
|
assert!(from_str_hex(~"1e1e1") == Some(123361.));
|
|
assert!(from_str_hex(~"1e1.1") == Some(481.0625));
|
|
|
|
assert!(from_str_hex(~"").is_none());
|
|
assert!(from_str_hex(~"x").is_none());
|
|
assert!(from_str_hex(~" ").is_none());
|
|
assert!(from_str_hex(~" ").is_none());
|
|
assert!(from_str_hex(~"p").is_none());
|
|
assert!(from_str_hex(~"P").is_none());
|
|
assert!(from_str_hex(~"P1").is_none());
|
|
assert!(from_str_hex(~"1p1p1").is_none());
|
|
assert!(from_str_hex(~"1p1.1").is_none());
|
|
assert!(from_str_hex(~"1p1-1").is_none());
|
|
}
|
|
|
|
#[test]
|
|
pub fn test_to_str_hex() {
|
|
assert!(to_str_hex(164.) == ~"a4");
|
|
assert!(to_str_hex(164.9921875) == ~"a4.fe");
|
|
assert!(to_str_hex(-164.9921875) == ~"-a4.fe");
|
|
assert!(to_str_hex(0xff00 as float) == ~"ff00");
|
|
assert!(to_str_hex(-(0xff00 as float)) == ~"-ff00");
|
|
assert!(to_str_hex(0.) == ~"0");
|
|
assert!(to_str_hex(15.) == ~"f");
|
|
assert!(to_str_hex(-15.) == ~"-f");
|
|
assert!(to_str_hex(0.9375) == ~"0.f");
|
|
assert!(to_str_hex(-0.9375) == ~"-0.f");
|
|
assert!(to_str_hex(infinity) == ~"inf");
|
|
assert!(to_str_hex(neg_infinity) == ~"-inf");
|
|
assert!(to_str_hex(NaN) == ~"NaN");
|
|
assert!(to_str_hex(0.) == ~"0");
|
|
assert!(to_str_hex(-0.) == ~"-0");
|
|
}
|
|
|
|
#[test]
|
|
pub fn test_to_str_radix() {
|
|
assert!(to_str_radix(36., 36u) == ~"10");
|
|
assert!(to_str_radix(8.125, 2u) == ~"1000.001");
|
|
}
|
|
|
|
#[test]
|
|
pub fn test_from_str_radix() {
|
|
assert!(from_str_radix(~"10", 36u) == Some(36.));
|
|
assert!(from_str_radix(~"1000.001", 2u) == Some(8.125));
|
|
}
|
|
|
|
#[test]
|
|
pub fn test_positive() {
|
|
assert!((is_positive(infinity)));
|
|
assert!((is_positive(1.)));
|
|
assert!((is_positive(0.)));
|
|
assert!((!is_positive(-1.)));
|
|
assert!((!is_positive(neg_infinity)));
|
|
assert!((!is_positive(1./neg_infinity)));
|
|
assert!((!is_positive(NaN)));
|
|
}
|
|
|
|
#[test]
|
|
pub fn test_negative() {
|
|
assert!((!is_negative(infinity)));
|
|
assert!((!is_negative(1.)));
|
|
assert!((!is_negative(0.)));
|
|
assert!((is_negative(-1.)));
|
|
assert!((is_negative(neg_infinity)));
|
|
assert!((is_negative(1./neg_infinity)));
|
|
assert!((!is_negative(NaN)));
|
|
}
|
|
|
|
#[test]
|
|
pub fn test_nonpositive() {
|
|
assert!((!is_nonpositive(infinity)));
|
|
assert!((!is_nonpositive(1.)));
|
|
assert!((!is_nonpositive(0.)));
|
|
assert!((is_nonpositive(-1.)));
|
|
assert!((is_nonpositive(neg_infinity)));
|
|
assert!((is_nonpositive(1./neg_infinity)));
|
|
assert!((!is_nonpositive(NaN)));
|
|
}
|
|
|
|
#[test]
|
|
pub fn test_nonnegative() {
|
|
assert!((is_nonnegative(infinity)));
|
|
assert!((is_nonnegative(1.)));
|
|
assert!((is_nonnegative(0.)));
|
|
assert!((!is_nonnegative(-1.)));
|
|
assert!((!is_nonnegative(neg_infinity)));
|
|
assert!((!is_nonnegative(1./neg_infinity)));
|
|
assert!((!is_nonnegative(NaN)));
|
|
}
|
|
|
|
#[test]
|
|
pub fn test_to_str_inf() {
|
|
assert!(to_str_digits(infinity, 10u) == ~"inf");
|
|
assert!(to_str_digits(-infinity, 10u) == ~"-inf");
|
|
}
|
|
|
|
#[test]
|
|
pub fn test_round() {
|
|
assert!(round(5.8) == 6.0);
|
|
assert!(round(5.2) == 5.0);
|
|
assert!(round(3.0) == 3.0);
|
|
assert!(round(2.5) == 3.0);
|
|
assert!(round(-3.5) == -4.0);
|
|
}
|
|
}
|
|
|
|
//
|
|
// Local Variables:
|
|
// mode: rust
|
|
// fill-column: 78;
|
|
// indent-tabs-mode: nil
|
|
// c-basic-offset: 4
|
|
// buffer-file-coding-system: utf-8-unix
|
|
// End:
|
|
//
|