rust/src/libcore/num/float.rs

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// 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 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, 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.
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// export when m_float == c_double
// PORT this must match in width according to architecture
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use m_float = f64;
use cmp::{Eq, Ord};
use cmp;
use f64;
use num;
use num::NumCast;
use option::{None, Option, Some};
use str;
use uint;
use to_str;
use from_str;
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};
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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 pure fn to_str(num: float) -> ~str {
let (r, _) = num::to_str_common(
&num, 10u, true, true, num::SignNeg, num::DigAll);
r
}
/**
* Converts a float to a string in hexadecimal format
*
* # Arguments
*
* * num - The float value
*/
#[inline(always)]
pub pure fn to_str_hex(num: float) -> ~str {
let (r, _) = num::to_str_common(
&num, 16u, true, true, num::SignNeg, num::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 pure fn to_str_radix(num: float, radix: uint) -> ~str {
let (r, special) = num::to_str_common(
&num, radix, true, true, num::SignNeg, num::DigAll);
if special { die!(~"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 pure fn to_str_radix_special(num: float, radix: uint) -> (~str, bool) {
num::to_str_common(&num, radix, true, true, num::SignNeg, num::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)]
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pub pure fn to_str_exact(num: float, digits: uint) -> ~str {
let (r, _) = num::to_str_common(
&num, 10u, true, true, num::SignNeg, num::DigExact(digits));
r
}
#[test]
pub fn test_to_str_exact_do_decimal() {
let s = to_str_exact(5.0, 4u);
assert 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 pure fn to_str_digits(num: float, digits: uint) -> ~str {
let (r, _) = num::to_str_common(
&num, 10u, true, true, num::SignNeg, num::DigMax(digits));
r
}
impl float: to_str::ToStr {
#[inline(always)]
pure fn to_str(&self) -> ~str { to_str_digits(*self, 8) }
}
impl float: num::ToStrRadix {
#[inline(always)]
pure 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)]
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pub pure fn from_str(num: &str) -> Option<float> {
num::from_str_common(num, 10u, true, true, true, num::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 pure fn from_str_hex(num: &str) -> Option<float> {
num::from_str_common(num, 16u, true, true, true, num::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 pure fn from_str_radix(num: &str, radix: uint) -> Option<float> {
num::from_str_common(num, radix, true, true, false, num::ExpNone, false)
}
impl float: from_str::FromStr {
#[inline(always)]
static pure fn from_str(val: &str) -> Option<float> { from_str(val) }
}
impl float: num::FromStrRadix {
#[inline(always)]
static pure fn from_str_radix(val: &str, radix: uint) -> Option<float> {
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 pure fn pow_with_uint(base: uint, pow: uint) -> float {
if base == 0u {
if pow == 0u {
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return NaN as float;
}
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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;
}
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return total;
}
#[inline(always)]
pub pure fn is_positive(x: float) -> bool { f64::is_positive(x as f64) }
#[inline(always)]
pub pure fn is_negative(x: float) -> bool { f64::is_negative(x as f64) }
#[inline(always)]
pub pure fn is_nonpositive(x: float) -> bool { f64::is_nonpositive(x as f64) }
#[inline(always)]
pub pure fn is_nonnegative(x: float) -> bool { f64::is_nonnegative(x as f64) }
#[inline(always)]
pub pure fn is_zero(x: float) -> bool { f64::is_zero(x as f64) }
#[inline(always)]
pub pure fn is_infinite(x: float) -> bool { f64::is_infinite(x as f64) }
#[inline(always)]
pub pure fn is_finite(x: float) -> bool { f64::is_finite(x as f64) }
#[inline(always)]
pub pure fn is_NaN(x: float) -> bool { f64::is_NaN(x as f64) }
#[inline(always)]
pub pure fn abs(x: float) -> float {
unsafe { f64::abs(x as f64) as float }
}
#[inline(always)]
pub pure fn sqrt(x: float) -> float {
unsafe { f64::sqrt(x as f64) as float }
}
#[inline(always)]
pub pure fn atan(x: float) -> float {
unsafe { f64::atan(x as f64) as float }
}
#[inline(always)]
pub pure fn sin(x: float) -> float {
unsafe { f64::sin(x as f64) as float }
}
#[inline(always)]
pub pure fn cos(x: float) -> float {
unsafe { f64::cos(x as f64) as float }
}
#[inline(always)]
pub pure fn tan(x: float) -> float {
unsafe { f64::tan(x as f64) as float }
}
#[cfg(notest)]
impl float : Eq {
pure fn eq(&self, other: &float) -> bool { (*self) == (*other) }
pure fn ne(&self, other: &float) -> bool { (*self) != (*other) }
}
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#[cfg(notest)]
impl float : Ord {
pure fn lt(&self, other: &float) -> bool { (*self) < (*other) }
pure fn le(&self, other: &float) -> bool { (*self) <= (*other) }
pure fn ge(&self, other: &float) -> bool { (*self) >= (*other) }
pure fn gt(&self, other: &float) -> bool { (*self) > (*other) }
}
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impl float: num::Num {
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#[inline(always)]
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pub pure fn add(&self, other: &float) -> float { return *self + *other; }
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#[inline(always)]
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pub pure fn sub(&self, other: &float) -> float { return *self - *other; }
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#[inline(always)]
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pub pure fn mul(&self, other: &float) -> float { return *self * *other; }
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#[inline(always)]
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pub pure fn div(&self, other: &float) -> float { return *self / *other; }
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#[inline(always)]
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pure fn modulo(&self, other: &float) -> float { return *self % *other; }
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#[inline(always)]
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pure fn neg(&self) -> float { return -*self; }
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}
impl float: num::Zero {
#[inline(always)]
static pure fn zero() -> float { 0.0 }
}
impl float: num::One {
#[inline(always)]
static pure fn one() -> float { 1.0 }
}
pub impl float: NumCast {
/**
* Cast `n` to a `float`
*/
#[inline(always)]
static pure fn from<N:NumCast>(n: N) -> float { n.to_float() }
#[inline(always)] pure fn to_u8(&self) -> u8 { *self as u8 }
#[inline(always)] pure fn to_u16(&self) -> u16 { *self as u16 }
#[inline(always)] pure fn to_u32(&self) -> u32 { *self as u32 }
#[inline(always)] pure fn to_u64(&self) -> u64 { *self as u64 }
#[inline(always)] pure fn to_uint(&self) -> uint { *self as uint }
#[inline(always)] pure fn to_i8(&self) -> i8 { *self as i8 }
#[inline(always)] pure fn to_i16(&self) -> i16 { *self as i16 }
#[inline(always)] pure fn to_i32(&self) -> i32 { *self as i32 }
#[inline(always)] pure fn to_i64(&self) -> i64 { *self as i64 }
#[inline(always)] pure fn to_int(&self) -> int { *self as int }
#[inline(always)] pure fn to_f32(&self) -> f32 { *self as f32 }
#[inline(always)] pure fn to_f64(&self) -> f64 { *self as f64 }
#[inline(always)] pure fn to_float(&self) -> float { *self }
}
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impl float: num::Round {
#[inline(always)]
pure 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)]
pure fn floor(&self) -> float { f64::floor(*self as f64) as float}
#[inline(always)]
pure fn ceil(&self) -> float { f64::ceil(*self as f64) as float}
#[inline(always)]
pure 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)
}
}
}
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#[test]
pub fn test_from_str() {
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assert from_str(~"3") == Some(3.);
assert from_str(~"3.14") == Some(3.14);
assert from_str(~"+3.14") == Some(3.14);
assert from_str(~"-3.14") == Some(-3.14);
assert from_str(~"2.5E10") == Some(25000000000.);
assert from_str(~"2.5e10") == Some(25000000000.);
assert from_str(~"25000000000.E-10") == Some(2.5);
assert from_str(~".") == Some(0.);
assert from_str(~".e1") == Some(0.);
assert from_str(~".e-1") == Some(0.);
assert from_str(~"5.") == Some(5.);
assert from_str(~".5") == Some(0.5);
assert from_str(~"0.5") == Some(0.5);
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assert from_str(~"-.5") == Some(-0.5);
assert from_str(~"-5") == Some(-5.);
assert from_str(~"inf") == Some(infinity);
assert from_str(~"+inf") == Some(infinity);
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assert from_str(~"-inf") == Some(neg_infinity);
// note: NaN != NaN, hence this slightly complex test
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match from_str(~"NaN") {
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Some(f) => assert is_NaN(f),
None => die!()
}
// note: -0 == 0, hence these slightly more complex tests
match from_str(~"-0") {
Some(v) if is_zero(v) => assert is_negative(v),
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_ => die!()
}
match from_str(~"0") {
Some(v) if is_zero(v) => assert is_positive(v),
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_ => die!()
}
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();
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}
#[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),
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None => die!()
}
// note: -0 == 0, hence these slightly more complex tests
match from_str_hex(~"-0") {
Some(v) if is_zero(v) => assert is_negative(v),
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_ => die!()
}
match from_str_hex(~"0") {
Some(v) if is_zero(v) => assert is_positive(v),
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_ => die!()
}
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);
}
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#[test]
pub fn test_positive() {
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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() {
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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() {
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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() {
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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";
}
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#[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;
}
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#[test]
pub fn test_num() {
let ten: float = num::cast(10);
let two: float = num::cast(2);
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assert (ten.add(&two) == num::cast(12));
assert (ten.sub(&two) == num::cast(8));
assert (ten.mul(&two) == num::cast(20));
assert (ten.div(&two) == num::cast(5));
assert (ten.modulo(&two) == num::cast(0));
}
#[test]
fn test_numcast() {
assert (20u == 20f.to_uint());
assert (20u8 == 20f.to_u8());
assert (20u16 == 20f.to_u16());
assert (20u32 == 20f.to_u32());
assert (20u64 == 20f.to_u64());
assert (20i == 20f.to_int());
assert (20i8 == 20f.to_i8());
assert (20i16 == 20f.to_i16());
assert (20i32 == 20f.to_i32());
assert (20i64 == 20f.to_i64());
assert (20f == 20f.to_float());
assert (20f32 == 20f.to_f32());
assert (20f64 == 20f.to_f64());
assert (20f == NumCast::from(20u));
assert (20f == NumCast::from(20u8));
assert (20f == NumCast::from(20u16));
assert (20f == NumCast::from(20u32));
assert (20f == NumCast::from(20u64));
assert (20f == NumCast::from(20i));
assert (20f == NumCast::from(20i8));
assert (20f == NumCast::from(20i16));
assert (20f == NumCast::from(20i32));
assert (20f == NumCast::from(20i64));
assert (20f == NumCast::from(20f));
assert (20f == NumCast::from(20f32));
assert (20f == NumCast::from(20f64));
assert (20f == num::cast(20u));
assert (20f == num::cast(20u8));
assert (20f == num::cast(20u16));
assert (20f == num::cast(20u32));
assert (20f == num::cast(20u64));
assert (20f == num::cast(20i));
assert (20f == num::cast(20i8));
assert (20f == num::cast(20i16));
assert (20f == num::cast(20i32));
assert (20f == num::cast(20i64));
assert (20f == num::cast(20f));
assert (20f == num::cast(20f32));
assert (20f == num::cast(20f64));
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}
//
// Local Variables:
// mode: rust
// fill-column: 78;
// indent-tabs-mode: nil
// c-basic-offset: 4
// buffer-file-coding-system: utf-8-unix
// End:
//