#define PI 3.14159265
#define RECIPROCAL_PI 0.31830988618
#define EPSILON 1e-6

#define saturate(a) clamp(a, 0.0, 1.0)

float intDiv(const in float a, const in float b) { return float(int(a) / int(b)); }
float intMod(const in float a, const in float b) { return a - b * float(int(a) / int(b)); }

float pow2(const in float x) { return x*x; }

const float maxFloat = 10000.0; // NOTE constant also set in TypeScript
const float floatLogFactor = log(maxFloat + 1.0);
float encodeFloatLog(const in float value) { return log(value + 1.0) / floatLogFactor; }
float decodeFloatLog(const in float value) { return exp(value * floatLogFactor) - 1.0; }

vec3 encodeFloatRGB(in float value) {
    value = clamp(value, 0.0, 16777216.0 - 1.0) + 1.0;
    vec3 c = vec3(0.0);
    c.b = mod(value, 256.0);
    value = floor(value / 256.0);
    c.g = mod(value, 256.0);
    value = floor(value / 256.0);
    c.r = mod(value, 256.0);
    return c / 255.0;
}
float decodeFloatRGB(const in vec3 rgb) {
    return (rgb.r * 256.0 * 256.0 * 255.0 + rgb.g * 256.0 * 255.0 + rgb.b * 255.0) - 1.0;
}

#if __VERSION__ != 300
    // transpose

    float transpose(const in float m) {
        return m;
    }

    mat2 transpose(const in mat2 m) {
        return mat2(
            m[0][0], m[1][0],
            m[0][1], m[1][1]
        );
    }

    mat3 transpose(const in mat3 m) {
        return mat3(
            m[0][0], m[1][0], m[2][0],
            m[0][1], m[1][1], m[2][1],
            m[0][2], m[1][2], m[2][2]
        );
    }

    mat4 transpose(const in mat4 m) {
        return mat4(
            m[0][0], m[1][0], m[2][0], m[3][0],
            m[0][1], m[1][1], m[2][1], m[3][1],
            m[0][2], m[1][2], m[2][2], m[3][2],
            m[0][3], m[1][3], m[2][3], m[3][3]
        );
    }

    float inverse(const in float m) {
        return 1.0 / m;
    }

    // inverse

    mat2 inverse(const in mat2 m) {
        return mat2(m[1][1],-m[0][1],
                -m[1][0], m[0][0]) / (m[0][0]*m[1][1] - m[0][1]*m[1][0]);
    }

    mat3 inverse(const in mat3 m) {
        float a00 = m[0][0], a01 = m[0][1], a02 = m[0][2];
        float a10 = m[1][0], a11 = m[1][1], a12 = m[1][2];
        float a20 = m[2][0], a21 = m[2][1], a22 = m[2][2];

        float b01 = a22 * a11 - a12 * a21;
        float b11 = -a22 * a10 + a12 * a20;
        float b21 = a21 * a10 - a11 * a20;

        float det = a00 * b01 + a01 * b11 + a02 * b21;

        return mat3(b01, (-a22 * a01 + a02 * a21), (a12 * a01 - a02 * a11),
                    b11, (a22 * a00 - a02 * a20), (-a12 * a00 + a02 * a10),
                    b21, (-a21 * a00 + a01 * a20), (a11 * a00 - a01 * a10)) / det;
    }

    mat4 inverse(const in mat4 m) {
        float
            a00 = m[0][0], a01 = m[0][1], a02 = m[0][2], a03 = m[0][3],
            a10 = m[1][0], a11 = m[1][1], a12 = m[1][2], a13 = m[1][3],
            a20 = m[2][0], a21 = m[2][1], a22 = m[2][2], a23 = m[2][3],
            a30 = m[3][0], a31 = m[3][1], a32 = m[3][2], a33 = m[3][3],

            b00 = a00 * a11 - a01 * a10,
            b01 = a00 * a12 - a02 * a10,
            b02 = a00 * a13 - a03 * a10,
            b03 = a01 * a12 - a02 * a11,
            b04 = a01 * a13 - a03 * a11,
            b05 = a02 * a13 - a03 * a12,
            b06 = a20 * a31 - a21 * a30,
            b07 = a20 * a32 - a22 * a30,
            b08 = a20 * a33 - a23 * a30,
            b09 = a21 * a32 - a22 * a31,
            b10 = a21 * a33 - a23 * a31,
            b11 = a22 * a33 - a23 * a32,

            det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;

        return mat4(
            a11 * b11 - a12 * b10 + a13 * b09,
            a02 * b10 - a01 * b11 - a03 * b09,
            a31 * b05 - a32 * b04 + a33 * b03,
            a22 * b04 - a21 * b05 - a23 * b03,
            a12 * b08 - a10 * b11 - a13 * b07,
            a00 * b11 - a02 * b08 + a03 * b07,
            a32 * b02 - a30 * b05 - a33 * b01,
            a20 * b05 - a22 * b02 + a23 * b01,
            a10 * b10 - a11 * b08 + a13 * b06,
            a01 * b08 - a00 * b10 - a03 * b06,
            a30 * b04 - a31 * b02 + a33 * b00,
            a21 * b02 - a20 * b04 - a23 * b00,
            a11 * b07 - a10 * b09 - a12 * b06,
            a00 * b09 - a01 * b07 + a02 * b06,
            a31 * b01 - a30 * b03 - a32 * b00,
            a20 * b03 - a21 * b01 + a22 * b00) / det;
    }
#endif