discourse/app/assets/stylesheets/common/foundation/math.scss

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// This file:
// Copyright (c) 2013 Takeru Suzuki
// Licensed under the MIT license.
// https://github.com/terkel/mathsass
// Constants
$E: 2.718281828459045;
$PI: 3.141592653589793;
$LN2: 0.6931471805599453;
$SQRT2: 1.4142135623730951;
@function error($message) {
@warn "#{_error("The direction used does not exist")}";
@return null;
}
// Returns the factorial of a non-negative integer.
// @param {Number} $x A non-negative integer.
// @return {Number}
// @example
// fact(0) // 1
// fact(8) // 40320
@function fact($x) {
@if $x < 0 or $x != floor($x) {
@warn "Argument for `fact()` must be a positive integer.";
@return null;
}
$ret: 1;
@while $x > 0 {
$ret: $ret * $x;
$x: $x - 1;
}
@return $ret;
}
// Returns a two-element list containing the normalized fraction and exponent of number.
// @param {Number} $x
// @return {List} fraction, exponent
@function frexp($x) {
$exp: 0;
@if $x < 0 {
$x: $x * -1;
}
@if $x < 0.5 {
@while $x < 0.5 {
$x: $x * 2;
$exp: $exp - 1;
}
} @else if $x >= 1 {
@while $x >= 1 {
$x: $x / 2;
$exp: $exp + 1;
}
}
@return $x, $exp;
}
// Returns $x * 2^$exp
// @param {Number} $x
// @param {Number} $exp
@function ldexp($x, $exp) {
$b: if($exp >= 0, 2, 1 / 2);
@if $exp < 0 {
$exp: $exp * -1;
}
@while $exp > 0 {
@if $exp % 2 == 1 {
$x: $x * $b;
}
$b: $b * $b;
$exp: floor($exp * 0.5);
}
@return $x;
}
// Returns the natural logarithm of a number.
// @param {Number} $x
// @example
// log(2) // 0.69315
// log(10) // 2.30259
@function log($x) {
@if $x <= 0 {
@return 0 / 0;
}
$k: nth(frexp($x / $SQRT2), 2);
$x: $x / ldexp(1, $k);
$x: ($x - 1) / ($x + 1);
$x2: $x * $x;
$i: 1;
$s: $x;
$sp: null;
@while $sp != $s {
$x: $x * $x2;
$i: $i + 2;
$sp: $s;
$s: $s + $x / $i;
}
@return $LN2 * $k + 2 * $s;
}
@function ipow($base, $exp) {
@if $exp != floor($exp) {
@return error("Exponent for `ipow()` must be an integer.");
}
$r: 1;
$s: 0;
@if $exp < 0 {
$exp: $exp * -1;
$s: 1;
}
@while $exp > 0 {
@if $exp % 2 == 1 {
$r: $r * $base;
}
$exp: floor($exp * 0.5);
$base: $base * $base;
}
@return if($s != 0, 1 / $r, $r);
}
// Returns E^x, where x is the argument, and E is Euler's constant, the base of the natural logarithms.
// @param {Number} $x
// @example
// exp(1) // 2.71828
// exp(-1) // 0.36788
@function exp($x) {
$ret: 0;
@for $n from 0 to 24 {
$ret: $ret + ipow($x, $n) / fact($n);
}
@return $ret;
}
// Returns base to the exponent power.
// @param {Number} $base The base number
// @param {Number} $exp The exponent to which to raise base
// @return {Number}
// @example
// pow(4, 2) // 16
// pow(4, -2) // 0.0625
// pow(4, 0.2) // 1.31951
@function pow($base, $exp) {
@if $exp == floor($exp) {
@return ipow($base, $exp);
} @else {
@return exp(log($base) * $exp);
}
}
// Returns the square root of a number.
// @param {Number} $x
// @example
// sqrt(2) // 1.41421
// sqrt(5) // 2.23607
@function sqrt($x) {
@if $x < 0 {
@return error("Argument for `sqrt()` must be a positive number.");
}
$ret: 1;
@for $i from 1 through 24 {
$ret: $ret - (pow($ret, 2) - $x) / (2 * $ret);
}
@return $ret;
}