// ==========================================================================
// Tools / Maths
// ==========================================================================

// Removes the unit from the given number.
//
// @param  {number} $number The number to strip.
// @return {number}

@function strip-units($number) {
    @return math.div($number, ($number * 0 + 1));
}

// Returns the square root of the given number.
//
// @param  {number} $number The number to calculate.
// @return {number}

@function sqrt($number) {
    $x: 1;
    $value: $x;

    @for $i from 1 through 10 {
        $value: $x - math.div(($x * $x - abs($number)), (2 * $x));
        $x: $value;
    }

    @return $value;
}

// Returns a number raised to the power of an exponent.
//
// @param  {number} $number The base number.
// @param  {number} $exp    The exponent.
// @return {number}

@function pow($number, $exp) {
    $value: 1;

    @if $exp > 0 {
        @for $i from 1 through $exp {
            $value: $value * $number;
        }
    } @else if $exp < 0 {
        @for $i from 1 through -$exp {
            $value: math.div($value, $number);
        }
    }

    @return $value;
}

// Returns the factorial of the given number.
//
// @param  {number} $number The number to calculate.
// @return {number}

@function fact($number) {
    $value: 1;

    @if $number > 0 {
        @for $i from 1 through $number {
            $value: $value * $i;
        }
    }

    @return $value;
}

// Returns an approximation of pi, with 11 decimals.
//
// @return {number}

@function pi() {
    @return 3.14159265359;
}

// Converts the number in degrees to the radian equivalent .
//
// @param  {number} $angle  The angular value to calculate.
// @return {number}         If $angle has the `deg` unit,
//                          the radian equivalent is returned.
//                          Otherwise, the unitless value of $angle is returned.

@function rad($angle) {
    $unit: unit($angle);
    $angle: strip-units($angle);

    // If the angle has `deg` as unit, convert to radians.
    @if ($unit == deg) {
        @return math.div($angle, 180) * pi();
    }

    @return $angle;
}

// Returns the sine of the given number.
//
// @param  {number} $angle The angle to calculate.
// @return {number}

@function sin($angle) {
    $sin: 0;
    $angle: rad($angle);

    @for $i from 0 through 10 {
        $sin: $sin + pow(-1, $i) * math.div(pow($angle, (2 * $i + 1)), fact(2 * $i + 1));
    }

    @return $sin;
}

// Returns the cosine of the given number.
//
// @param  {string} $angle The angle to calculate.
// @return {number}

@function cos($angle) {
    $cos: 0;
    $angle: rad($angle);

    @for $i from 0 through 10 {
        $cos: $cos + pow(-1, $i) * math.div(pow($angle, 2 * $i), fact(2 * $i));
    }

    @return $cos;
}

// Returns the tangent of the given number.
//
// @param  {string} $angle The angle to calculate.
// @return {number}

@function tan($angle) {
    @return math.div(sin($angle), cos($angle));
}