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// ---- | |
// Sass (v3.3.0.rc.1) | |
// Compass (v0.13.alpha.10) | |
// ---- | |
$E: 2.718281828459045; | |
$PI: 3.141592653589793; | |
$LN2: 0.6931471805599453; | |
$SQRT2: 1.4142135623730951; | |
// 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 * $s; | |
} | |
@function pow ($base, $exp) { | |
@if $exp == floor($exp) { | |
$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, $r); | |
} @else { | |
@return exp(log($base) * $exp); | |
} | |
} | |
// 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: $ret + pow($x, $n) / fact($n); | |
} | |
@return $ret; | |
} | |
// 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; | |
} | |
test { | |
test: pow(14, 3.3); | |
test2: pow(4, 0.2); | |
} |
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test { | |
test: 6056.42238; | |
test2: 1.31951; | |
} |
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