567 lines
16 KiB
Rust
567 lines
16 KiB
Rust
// NB: transitionary, de-mode-ing.
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#[forbid(deprecated_mode)];
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#[forbid(deprecated_pattern)];
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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 to_str_common, to_str_exact, to_str, from_str;
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export add, sub, mul, div, rem, lt, le, eq, ne, ge, gt;
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export is_positive, is_negative, is_nonpositive, is_nonnegative;
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export is_zero, is_infinite, is_finite;
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export NaN, is_NaN, infinity, neg_infinity;
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export consts;
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export logarithm;
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export acos, asin, atan, atan2, cbrt, ceil, copysign, cos, cosh, floor;
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export erf, erfc, exp, expm1, exp2, abs, abs_sub;
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export mul_add, fmax, fmin, nextafter, frexp, hypot, ldexp;
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export lgamma, ln, log_radix, ln1p, log10, log2, ilog_radix;
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export modf, pow, round, sin, sinh, sqrt, tan, tanh, tgamma, trunc;
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export signbit;
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export pow_with_uint;
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export num;
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// export when m_float == c_double
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export j0, j1, jn, y0, y1, yn;
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// PORT this must match in width according to architecture
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use m_float = f64;
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use f64::{add, sub, mul, div, rem, lt, le, eq, ne, ge, gt};
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use f64::logarithm;
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use f64::{acos, asin, atan2, cbrt, ceil, copysign, cosh, floor};
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use f64::{erf, erfc, exp, expm1, exp2, abs_sub};
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use f64::{mul_add, fmax, fmin, nextafter, frexp, hypot, ldexp};
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use f64::{lgamma, ln, log_radix, ln1p, log10, log2, ilog_radix};
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use f64::{modf, pow, round, sinh, tanh, tgamma, trunc};
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use f64::signbit;
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use f64::{j0, j1, jn, y0, y1, yn};
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use cmp::{Eq, Ord};
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use num::from_int;
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const NaN: float = 0.0/0.0;
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const infinity: float = 1.0/0.0;
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const neg_infinity: float = -1.0/0.0;
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/* Module: consts */
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mod consts {
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// FIXME (requires Issue #1433 to fix): replace with mathematical
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// constants from cmath.
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/// Archimedes' constant
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const pi: float = 3.14159265358979323846264338327950288;
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/// pi/2.0
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const frac_pi_2: float = 1.57079632679489661923132169163975144;
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/// pi/4.0
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const frac_pi_4: float = 0.785398163397448309615660845819875721;
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/// 1.0/pi
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const frac_1_pi: float = 0.318309886183790671537767526745028724;
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/// 2.0/pi
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const frac_2_pi: float = 0.636619772367581343075535053490057448;
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/// 2.0/sqrt(pi)
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const frac_2_sqrtpi: float = 1.12837916709551257389615890312154517;
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/// sqrt(2.0)
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const sqrt2: float = 1.41421356237309504880168872420969808;
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/// 1.0/sqrt(2.0)
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const frac_1_sqrt2: float = 0.707106781186547524400844362104849039;
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/// Euler's number
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const e: float = 2.71828182845904523536028747135266250;
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/// log2(e)
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const log2_e: float = 1.44269504088896340735992468100189214;
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/// log10(e)
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const log10_e: float = 0.434294481903251827651128918916605082;
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/// ln(2.0)
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const ln_2: float = 0.693147180559945309417232121458176568;
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/// ln(10.0)
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const 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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* * digits - The number of significant digits
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* * exact - Whether to enforce the exact number of significant digits
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*/
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fn to_str_common(num: float, digits: uint, exact: bool) -> ~str {
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if is_NaN(num) { return ~"NaN"; }
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if num == infinity { return ~"inf"; }
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if num == neg_infinity { return ~"-inf"; }
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let mut (num, sign) = if num < 0.0 { (-num, ~"-") } else { (num, ~"") };
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// truncated integer
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let trunc = num as uint;
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// decimal remainder
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let mut frac = num - (trunc as float);
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// stack of digits
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let mut fractionalParts = ~[];
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// FIXME: (#2608)
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// This used to return right away without rounding, as "~[-]num",
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// but given epsilon like in f64.rs, I don't see how the comparison
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// to epsilon did much when only used there.
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// if (frac < epsilon && !exact) || digits == 0u { return accum; }
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//
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// With something better, possibly weird results like this can be avoided:
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// assert "3.14158999999999988262" == my_to_str_exact(3.14159, 20u);
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let mut ii = digits;
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let mut epsilon_prime = 1.0 / pow_with_uint(10u, ii);
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// while we still need digits
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// build stack of digits
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while ii > 0u && (frac >= epsilon_prime || exact) {
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// store the next digit
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frac *= 10.0;
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let digit = frac as uint;
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vec::push(fractionalParts, digit);
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// calculate the next frac
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frac -= digit as float;
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epsilon_prime *= 10.0;
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ii -= 1u;
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}
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let mut acc;
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let mut racc = ~"";
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let mut carry = if frac * 10.0 as uint >= 5u { 1u } else { 0u };
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// turn digits into string
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// using stack of digits
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while vec::len(fractionalParts) > 0u {
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let mut adjusted_digit = carry + vec::pop(fractionalParts);
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if adjusted_digit == 10u {
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carry = 1u;
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adjusted_digit %= 10u
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} else {
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carry = 0u
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};
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racc = uint::str(adjusted_digit) + racc;
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}
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// pad decimals with trailing zeroes
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while str::len(racc) < digits && exact {
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racc += ~"0"
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}
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// combine ints and decimals
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let mut ones = uint::str(trunc + carry);
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if racc == ~"" {
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acc = sign + ones;
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} else {
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acc = sign + ones + ~"." + racc;
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}
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move acc
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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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fn to_str_exact(num: float, digits: uint) -> ~str {
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to_str_common(num, digits, true)
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}
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#[test]
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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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/**
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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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fn to_str(num: float, digits: uint) -> ~str {
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to_str_common(num, digits, false)
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}
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/**
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* Convert a string to a float
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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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* * '', or, equivalently, '.' (understood as 0)
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* * '5.'
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* * '.5', or, equivalently, '0.5'
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* * 'inf', '-inf', 'NaN'
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*
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* Leading and trailing whitespace are ignored.
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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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fn from_str(num: &str) -> Option<float> {
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if num == "inf" {
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return Some(infinity as float);
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} else if num == "-inf" {
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return Some(neg_infinity as float);
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} else if num == "NaN" {
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return Some(NaN as float);
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}
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let mut pos = 0u; //Current byte position in the string.
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//Used to walk the string in O(n).
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let len = str::len(num); //Length of the string, in bytes.
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if len == 0u { return None; }
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let mut total = 0f; //Accumulated result
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let mut c = 'z'; //Latest char.
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//The string must start with one of the following characters.
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match str::char_at(num, 0u) {
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'-' | '+' | '0' .. '9' | '.' => (),
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_ => return None
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}
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//Determine if first char is '-'/'+'. Set [pos] and [neg] accordingly.
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let mut neg = false; //Sign of the result
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match str::char_at(num, 0u) {
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'-' => {
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neg = true;
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pos = 1u;
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}
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'+' => {
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pos = 1u;
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}
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_ => ()
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}
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//Examine the following chars until '.', 'e', 'E'
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while(pos < len) {
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let char_range = str::char_range_at(num, pos);
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c = char_range.ch;
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pos = char_range.next;
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match c {
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'0' .. '9' => {
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total = total * 10f;
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total += ((c as int) - ('0' as int)) as float;
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}
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'.' | 'e' | 'E' => break,
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_ => return None
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}
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}
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if c == '.' {//Examine decimal part
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let mut decimal = 1f;
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while(pos < len) {
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let char_range = str::char_range_at(num, pos);
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c = char_range.ch;
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pos = char_range.next;
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match c {
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'0' | '1' | '2' | '3' | '4' | '5' | '6'| '7' | '8' | '9' => {
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decimal /= 10f;
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total += (((c as int) - ('0' as int)) as float)*decimal;
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}
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'e' | 'E' => break,
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_ => return None
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}
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}
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}
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if (c == 'e') || (c == 'E') { //Examine exponent
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let mut exponent = 0u;
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let mut neg_exponent = false;
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if(pos < len) {
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let char_range = str::char_range_at(num, pos);
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c = char_range.ch;
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match c {
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'+' => {
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pos = char_range.next;
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}
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'-' => {
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pos = char_range.next;
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neg_exponent = true;
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}
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_ => ()
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}
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while(pos < len) {
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let char_range = str::char_range_at(num, pos);
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c = char_range.ch;
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match c {
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'0' | '1' | '2' | '3' | '4' | '5' | '6'| '7' | '8' | '9' => {
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exponent *= 10u;
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exponent += ((c as uint) - ('0' as uint));
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}
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_ => break
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}
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pos = char_range.next;
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}
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let multiplier = pow_with_uint(10u, exponent);
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//Note: not ~[int::pow], otherwise, we'll quickly
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//end up with a nice overflow
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if neg_exponent {
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total = total / multiplier;
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} else {
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total = total * multiplier;
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}
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} else {
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return None;
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}
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}
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if(pos < len) {
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return None;
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} else {
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if(neg) {
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total *= -1f;
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}
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return Some(total);
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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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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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pure fn is_positive(x: float) -> bool { f64::is_positive(x as f64) }
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pure fn is_negative(x: float) -> bool { f64::is_negative(x as f64) }
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pure fn is_nonpositive(x: float) -> bool { f64::is_nonpositive(x as f64) }
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pure fn is_nonnegative(x: float) -> bool { f64::is_nonnegative(x as f64) }
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pure fn is_zero(x: float) -> bool { f64::is_zero(x as f64) }
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pure fn is_infinite(x: float) -> bool { f64::is_infinite(x as f64) }
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pure fn is_finite(x: float) -> bool { f64::is_finite(x as f64) }
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pure fn is_NaN(x: float) -> bool { f64::is_NaN(x as f64) }
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pure fn abs(x: float) -> float { f64::abs(x as f64) as float }
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pure fn sqrt(x: float) -> float { f64::sqrt(x as f64) as float }
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pure fn atan(x: float) -> float { f64::atan(x as f64) as float }
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pure fn sin(x: float) -> float { f64::sin(x as f64) as float }
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pure fn cos(x: float) -> float { f64::cos(x as f64) as float }
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pure fn tan(x: float) -> float { f64::tan(x as f64) as float }
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impl float: Eq {
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pure fn eq(&&other: float) -> bool { self == other }
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pure fn ne(&&other: float) -> bool { self != other }
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}
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impl float: Ord {
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pure fn lt(&&other: float) -> bool { self < other }
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pure fn le(&&other: float) -> bool { self <= other }
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pure fn ge(&&other: float) -> bool { self >= other }
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pure fn gt(&&other: float) -> bool { self > other }
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}
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impl float: num::Num {
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pure fn add(&&other: float) -> float { return self + other; }
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pure fn sub(&&other: float) -> float { return self - other; }
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pure fn mul(&&other: float) -> float { return self * other; }
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pure fn div(&&other: float) -> float { return self / other; }
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pure fn modulo(&&other: float) -> float { return self % other; }
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pure fn neg() -> float { return -self; }
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pure fn to_int() -> int { return self as int; }
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static pure fn from_int(n: int) -> float { return n as float; }
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}
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#[test]
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fn test_from_str() {
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assert from_str(~"3") == Some(3.);
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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(~"0.5") == 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(-0.5);
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assert from_str(~"-5") == Some(-5.);
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assert from_str(~"-0") == Some(-0.);
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assert from_str(~"0") == Some(0.);
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assert from_str(~"inf") == Some(infinity);
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assert from_str(~"-inf") == Some(neg_infinity);
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// 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),
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None => fail
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}
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assert from_str(~"").is_none();
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assert from_str(~"x").is_none();
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assert from_str(~" ").is_none();
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assert from_str(~" ").is_none();
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assert from_str(~"e").is_none();
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assert from_str(~"E").is_none();
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assert from_str(~"E1").is_none();
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assert from_str(~"1e1e1").is_none();
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assert from_str(~"1e1.1").is_none();
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assert from_str(~"1e1-1").is_none();
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}
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#[test]
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fn test_positive() {
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assert(is_positive(infinity));
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assert(is_positive(1.));
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assert(is_positive(0.));
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assert(!is_positive(-1.));
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assert(!is_positive(neg_infinity));
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assert(!is_positive(1./neg_infinity));
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assert(!is_positive(NaN));
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}
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|
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#[test]
|
|
fn test_negative() {
|
|
assert(!is_negative(infinity));
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|
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));
|
|
}
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|
|
|
#[test]
|
|
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]
|
|
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]
|
|
fn test_to_str_inf() {
|
|
assert to_str(infinity, 10u) == ~"inf";
|
|
assert to_str(-infinity, 10u) == ~"-inf";
|
|
}
|
|
|
|
#[test]
|
|
fn test_traits() {
|
|
fn test<U:num::Num cmp::Eq>(ten: &U) {
|
|
assert (ten.to_int() == 10);
|
|
|
|
let two: U = from_int(2);
|
|
assert (two.to_int() == 2);
|
|
|
|
assert (ten.add(two) == from_int(12));
|
|
assert (ten.sub(two) == from_int(8));
|
|
assert (ten.mul(two) == from_int(20));
|
|
assert (ten.div(two) == from_int(5));
|
|
assert (ten.modulo(two) == from_int(0));
|
|
}
|
|
|
|
test(&10.0);
|
|
}
|
|
|
|
|
|
//
|
|
// Local Variables:
|
|
// mode: rust
|
|
// fill-column: 78;
|
|
// indent-tabs-mode: nil
|
|
// c-basic-offset: 4
|
|
// buffer-file-coding-system: utf-8-unix
|
|
// End:
|
|
//
|
|
|
|
|
|
|
|
|
|
|