export default /* glsl */`
#define PI 3.141592653589793
#define PI2 6.283185307179586
#define PI_HALF 1.5707963267948966
#define RECIPROCAL_PI 0.3183098861837907
#define RECIPROCAL_PI2 0.15915494309189535
#define EPSILON 1e-6

#ifndef saturate
// <tonemapping_pars_fragment> may have defined saturate() already
#define saturate( a ) clamp( a, 0.0, 1.0 )
#endif
#define whiteComplement( a ) ( 1.0 - saturate( a ) )

float pow2( const in float x ) { return x*x; }
vec3 pow2( const in vec3 x ) { return x*x; }
float pow3( const in float x ) { return x*x*x; }
float pow4( const in float x ) { float x2 = x*x; return x2*x2; }
float max3( const in vec3 v ) { return max( max( v.x, v.y ), v.z ); }
float average( const in vec3 v ) { return dot( v, vec3( 0.3333333 ) ); }

// expects values in the range of [0,1]x[0,1], returns values in the [0,1] range.
// do not collapse into a single function per: http://byteblacksmith.com/improvements-to-the-canonical-one-liner-glsl-rand-for-opengl-es-2-0/
highp float rand( const in vec2 uv ) {

	const highp float a = 12.9898, b = 78.233, c = 43758.5453;
	highp float dt = dot( uv.xy, vec2( a,b ) ), sn = mod( dt, PI );

	return fract( sin( sn ) * c );

}

#ifdef HIGH_PRECISION
	float precisionSafeLength( vec3 v ) { return length( v ); }
#else
	float precisionSafeLength( vec3 v ) {
		float maxComponent = max3( abs( v ) );
		return length( v / maxComponent ) * maxComponent;
	}
#endif

struct IncidentLight {
	vec3 color;
	vec3 direction;
	bool visible;
};

struct ReflectedLight {
	vec3 directDiffuse;
	vec3 directSpecular;
	vec3 indirectDiffuse;
	vec3 indirectSpecular;
};

#ifdef USE_ALPHAHASH

	varying vec3 vPosition;

#endif

vec3 transformDirection( in vec3 dir, in mat4 matrix ) {

	return normalize( ( matrix * vec4( dir, 0.0 ) ).xyz );

}

vec3 inverseTransformDirection( in vec3 dir, in mat4 matrix ) {

	// dir can be either a direction vector or a normal vector
	// upper-left 3x3 of matrix is assumed to be orthogonal

	return normalize( ( vec4( dir, 0.0 ) * matrix ).xyz );

}

mat3 transposeMat3( const in mat3 m ) {

	mat3 tmp;

	tmp[ 0 ] = vec3( m[ 0 ].x, m[ 1 ].x, m[ 2 ].x );
	tmp[ 1 ] = vec3( m[ 0 ].y, m[ 1 ].y, m[ 2 ].y );
	tmp[ 2 ] = vec3( m[ 0 ].z, m[ 1 ].z, m[ 2 ].z );

	return tmp;

}

float luminance( const in vec3 rgb ) {

	// assumes rgb is in linear color space with sRGB primaries and D65 white point

	const vec3 weights = vec3( 0.2126729, 0.7151522, 0.0721750 );

	return dot( weights, rgb );

}

bool isPerspectiveMatrix( mat4 m ) {

	return m[ 2 ][ 3 ] == - 1.0;

}

vec2 equirectUv( in vec3 dir ) {

	// dir is assumed to be unit length

	float u = atan( dir.z, dir.x ) * RECIPROCAL_PI2 + 0.5;

	float v = asin( clamp( dir.y, - 1.0, 1.0 ) ) * RECIPROCAL_PI + 0.5;

	return vec2( u, v );

}

vec3 BRDF_Lambert( const in vec3 diffuseColor ) {

	return RECIPROCAL_PI * diffuseColor;

} // validated

vec3 F_Schlick( const in vec3 f0, const in float f90, const in float dotVH ) {

	// Original approximation by Christophe Schlick '94
	// float fresnel = pow( 1.0 - dotVH, 5.0 );

	// Optimized variant (presented by Epic at SIGGRAPH '13)
	// https://cdn2.unrealengine.com/Resources/files/2013SiggraphPresentationsNotes-26915738.pdf
	float fresnel = exp2( ( - 5.55473 * dotVH - 6.98316 ) * dotVH );

	return f0 * ( 1.0 - fresnel ) + ( f90 * fresnel );

} // validated

float F_Schlick( const in float f0, const in float f90, const in float dotVH ) {

	// Original approximation by Christophe Schlick '94
	// float fresnel = pow( 1.0 - dotVH, 5.0 );

	// Optimized variant (presented by Epic at SIGGRAPH '13)
	// https://cdn2.unrealengine.com/Resources/files/2013SiggraphPresentationsNotes-26915738.pdf
	float fresnel = exp2( ( - 5.55473 * dotVH - 6.98316 ) * dotVH );

	return f0 * ( 1.0 - fresnel ) + ( f90 * fresnel );

} // validated
`;