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