rust/src/libcore/float.rs

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#[doc = "Operations and constants for `float`"];
// Even though this module exports everything defined in it,
// because it contains re-exports, we also have to explicitly
// export locally defined things. That's a bit annoying.
export to_str_common, to_str_exact, to_str, from_str;
export add, sub, mul, div, rem, lt, le, gt, eq, ne;
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export is_positive, is_negative, is_nonpositive, is_nonnegative;
export is_zero, is_infinite, is_finite;
export NaN, is_NaN, infinity, neg_infinity;
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;
export mul_add, fmax, fmin, nextafter, frexp, hypot, ldexp;
export lgamma, ln, log_radix, ln1p, log10, log2, ilog_radix;
export modf, pow, round, sin, sinh, sqrt, tan, tanh, tgamma, trunc;
export signbit;
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export pow_with_uint;
export num;
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// export when m_float == c_double
export j0, j1, jn, y0, y1, yn;
// PORT this must match in width according to architecture
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import m_float = f64;
import f64::{add, sub, mul, div, rem, lt, le, gt, eq, ne};
import f64::logarithm;
import f64::{acos, asin, atan2, cbrt, ceil, copysign, cosh, floor};
import f64::{erf, erfc, exp, expm1, exp2, abs_sub};
import f64::{mul_add, fmax, fmin, nextafter, frexp, hypot, ldexp};
import f64::{lgamma, ln, log_radix, ln1p, log10, log2, ilog_radix};
import f64::{modf, pow, round, sinh, tanh, tgamma, trunc};
import f64::signbit;
import f64::{j0, j1, jn, y0, y1, yn};
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const NaN: float = 0.0/0.0;
const infinity: float = 1.0/0.0;
const neg_infinity: float = -1.0/0.0;
/* Module: consts */
mod consts {
// FIXME (requires Issue #1433 to fix): replace with mathematical
// constants from cmath.
#[doc = "Archimedes' constant"]
const pi: float = 3.14159265358979323846264338327950288;
#[doc = "pi/2.0"]
const frac_pi_2: float = 1.57079632679489661923132169163975144;
#[doc = "pi/4.0"]
const frac_pi_4: float = 0.785398163397448309615660845819875721;
#[doc = "1.0/pi"]
const frac_1_pi: float = 0.318309886183790671537767526745028724;
#[doc = "2.0/pi"]
const frac_2_pi: float = 0.636619772367581343075535053490057448;
#[doc = "2.0/sqrt(pi)"]
const frac_2_sqrtpi: float = 1.12837916709551257389615890312154517;
#[doc = "sqrt(2.0)"]
const sqrt2: float = 1.41421356237309504880168872420969808;
#[doc = "1.0/sqrt(2.0)"]
const frac_1_sqrt2: float = 0.707106781186547524400844362104849039;
#[doc = "Euler's number"]
const e: float = 2.71828182845904523536028747135266250;
#[doc = "log2(e)"]
const log2_e: float = 1.44269504088896340735992468100189214;
#[doc = "log10(e)"]
const log10_e: float = 0.434294481903251827651128918916605082;
#[doc = "ln(2.0)"]
const ln_2: float = 0.693147180559945309417232121458176568;
#[doc = "ln(10.0)"]
const ln_10: float = 2.30258509299404568401799145468436421;
}
/**
* Section: String Conversions
*/
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#[doc = "
Converts a float to a string
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# Arguments
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* num - The float value
* digits - The number of significant digits
* exact - Whether to enforce the exact number of significant digits
"]
fn to_str_common(num: float, digits: uint, exact: bool) -> str {
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if is_NaN(num) { ret "NaN"; }
if num == infinity { ret "inf"; }
if num == neg_infinity { ret "-inf"; }
let mut (num, sign) = if num < 0.0 { (-num, "-") } else { (num, "") };
// truncated integer
let trunc = num as uint;
// decimal remainder
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let mut frac = num - (trunc as float);
// stack of digits
let mut fractionalParts = ~[];
// FIXME: (#2608)
// This used to return right away without rounding, as "~[-]num",
// but given epsilon like in f64.rs, I don't see how the comparison
// to epsilon did much when only used there.
// if (frac < epsilon && !exact) || digits == 0u { ret accum; }
//
// With something better, possibly weird results like this can be avoided:
// assert "3.14158999999999988262" == my_to_str_exact(3.14159, 20u);
let mut ii = digits;
let mut epsilon_prime = 1.0 / pow_with_uint(10u, ii);
// while we still need digits
// build stack of digits
while ii > 0u && (frac >= epsilon_prime || exact) {
// store the next digit
frac *= 10.0;
let digit = frac as uint;
vec::push(fractionalParts, digit);
// calculate the next frac
frac -= digit as float;
epsilon_prime *= 10.0;
ii -= 1u;
}
let mut acc;
let mut racc = "";
let mut carry = if frac * 10.0 as uint >= 5u { 1u } else { 0u };
// turn digits into string
// using stack of digits
while vec::len(fractionalParts) > 0u {
let mut adjusted_digit = carry + vec::pop(fractionalParts);
if adjusted_digit == 10u {
carry = 1u;
adjusted_digit %= 10u
} else {
carry = 0u
};
racc = uint::str(adjusted_digit) + racc;
}
// pad decimals with trailing zeroes
while str::len(racc) < digits && exact {
racc += "0"
}
// combine ints and decimals
let mut ones = uint::str(trunc + carry);
if racc == "" {
acc = sign + ones;
} else {
acc = sign + ones + "." + racc;
}
ret acc;
}
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#[doc = "
Converts a float to a string with exactly the number of
provided significant digits
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# Arguments
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* num - The float value
* digits - The number of significant digits
"]
fn to_str_exact(num: float, digits: uint) -> str {
to_str_common(num, digits, true)
}
#[test]
fn test_to_str_exact_do_decimal() {
let s = to_str_exact(5.0, 4u);
assert s == "5.0000";
}
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#[doc = "
Converts a float to a string with a maximum number of
significant digits
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# Arguments
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* num - The float value
* digits - The number of significant digits
"]
fn to_str(num: float, digits: uint) -> str {
to_str_common(num, digits, false)
}
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#[doc = "
Convert a string to a float
This function accepts strings such as
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* '3.14'
* '+3.14', equivalent to '3.14'
* '-3.14'
* '2.5E10', or equivalently, '2.5e10'
* '2.5E-10'
* '', or, equivalently, '.' (understood as 0)
* '5.'
* '.5', or, equivalently, '0.5'
* 'inf', '-inf', 'NaN'
Leading and trailing whitespace are ignored.
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# Arguments
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* num - A string
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# Return value
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`none` if the string did not represent a valid number. Otherwise, `some(n)`
where `n` is the floating-point number represented by `[num]/~`.
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"]
fn from_str(num: str) -> option<float> {
if num == "inf" {
ret some(infinity as float);
} else if num == "-inf" {
ret some(neg_infinity as float);
} else if num == "NaN" {
ret some(NaN as float);
}
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let mut pos = 0u; //Current byte position in the string.
//Used to walk the string in O(n).
let len = str::len(num); //Length of the string, in bytes.
if len == 0u { ret none; }
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let mut total = 0f; //Accumulated result
let mut c = 'z'; //Latest char.
//The string must start with one of the following characters.
alt str::char_at(num, 0u) {
'-' | '+' | '0' to '9' | '.' {}
_ { ret none; }
}
//Determine if first char is '-'/'+'. Set ~[pos] and ~[neg] accordingly.
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let mut neg = false; //Sign of the result
alt str::char_at(num, 0u) {
'-' {
neg = true;
pos = 1u;
}
'+' {
pos = 1u;
}
_ {}
}
//Examine the following chars until '.', 'e', 'E'
while(pos < len) {
let char_range = str::char_range_at(num, pos);
c = char_range.ch;
pos = char_range.next;
alt c {
'0' to '9' {
total = total * 10f;
total += ((c as int) - ('0' as int)) as float;
}
'.' | 'e' | 'E' {
break;
}
_ {
ret none;
}
}
}
if c == '.' {//Examine decimal part
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let mut decimal = 1f;
while(pos < len) {
let char_range = str::char_range_at(num, pos);
c = char_range.ch;
pos = char_range.next;
alt c {
'0' | '1' | '2' | '3' | '4' | '5' | '6'| '7' | '8' | '9' {
decimal /= 10f;
total += (((c as int) - ('0' as int)) as float)*decimal;
}
'e' | 'E' {
break;
}
_ {
ret none;
}
}
}
}
if (c == 'e') | (c == 'E') {//Examine exponent
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let mut exponent = 0u;
let mut neg_exponent = false;
if(pos < len) {
let char_range = str::char_range_at(num, pos);
c = char_range.ch;
alt c {
'+' {
pos = char_range.next;
}
'-' {
pos = char_range.next;
neg_exponent = true;
}
_ {}
}
while(pos < len) {
let char_range = str::char_range_at(num, pos);
c = char_range.ch;
alt c {
'0' | '1' | '2' | '3' | '4' | '5' | '6'| '7' | '8' | '9' {
exponent *= 10u;
exponent += ((c as uint) - ('0' as uint));
}
_ {
break;
}
}
pos = char_range.next;
}
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let multiplier = pow_with_uint(10u, exponent);
//Note: not ~[int::pow], otherwise, we'll quickly
//end up with a nice overflow
if neg_exponent {
total = total / multiplier;
} else {
total = total * multiplier;
}
} else {
ret none;
}
}
if(pos < len) {
ret none;
} else {
if(neg) {
total *= -1f;
}
ret some(total);
}
}
/**
* Section: Arithmetics
*/
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#[doc = "
Compute the exponentiation of an integer by another integer as a float
# Arguments
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* x - The base
* pow - The exponent
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# Return value
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`NaN` if both `x` and `pow` are `0u`, otherwise `x^pow`
"]
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fn pow_with_uint(base: uint, pow: uint) -> float {
if base == 0u {
if pow == 0u {
ret NaN as float;
}
ret 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;
}
ret total;
}
fn is_positive(x: float) -> bool { f64::is_positive(x as f64) }
fn is_negative(x: float) -> bool { f64::is_negative(x as f64) }
fn is_nonpositive(x: float) -> bool { f64::is_nonpositive(x as f64) }
fn is_nonnegative(x: float) -> bool { f64::is_nonnegative(x as f64) }
fn is_zero(x: float) -> bool { f64::is_zero(x as f64) }
fn is_infinite(x: float) -> bool { f64::is_infinite(x as f64) }
fn is_finite(x: float) -> bool { f64::is_finite(x as f64) }
fn is_NaN(x: float) -> bool { f64::is_NaN(x as f64) }
fn abs(x: float) -> float { f64::abs(x as f64) as float }
fn sqrt(x: float) -> float { f64::sqrt(x as f64) as float }
fn atan(x: float) -> float { f64::atan(x as f64) as float }
fn sin(x: float) -> float { f64::sin(x as f64) as float }
fn cos(x: float) -> float { f64::cos(x as f64) as float }
fn tan(x: float) -> float { f64::tan(x as f64) as float }
impl num of num::num for float {
fn add(&&other: float) -> float { ret self + other; }
fn sub(&&other: float) -> float { ret self - other; }
fn mul(&&other: float) -> float { ret self * other; }
fn div(&&other: float) -> float { ret self / other; }
fn modulo(&&other: float) -> float { ret self % other; }
fn neg() -> float { ret -self; }
fn to_int() -> int { ret self as int; }
fn from_int(n: int) -> float { ret n as float; }
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}
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#[test]
fn test_from_str() {
assert from_str("3") == some(3.);
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);
assert from_str("0.5") == some(0.5);
assert from_str("0.5") == some(0.5);
assert from_str("-.5") == some(-0.5);
assert from_str("-.5") == some(-0.5);
assert from_str("-5") == some(-5.);
assert from_str("-0") == some(-0.);
assert from_str("0") == some(0.);
assert from_str("inf") == some(infinity);
assert from_str("-inf") == some(neg_infinity);
// note: NaN != NaN, hence this slightly complex test
alt from_str("NaN") {
some(f) { assert is_NaN(f); }
none { fail; }
}
assert from_str("") == none;
assert from_str("x") == none;
assert from_str(" ") == none;
assert from_str(" ") == none;
assert from_str("e") == none;
assert from_str("E") == none;
assert from_str("E1") == none;
assert from_str("1e1e1") == none;
assert from_str("1e1.1") == none;
assert from_str("1e1-1") == none;
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}
#[test]
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]
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]
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";
}
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#[test]
fn test_ifaces() {
fn test<U:num::num>(ten: U) {
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assert (ten.to_int() == 10);
let two = ten.from_int(2);
assert (two.to_int() == 2);
assert (ten.add(two) == ten.from_int(12));
assert (ten.sub(two) == ten.from_int(8));
assert (ten.mul(two) == ten.from_int(20));
assert (ten.div(two) == ten.from_int(5));
assert (ten.modulo(two) == ten.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:
//
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