12.4 - GLSL Operators (Mathematical and Logical)¶

GLSL is designed for efficient vector and matrix processing. Therefore almost all of its operators are overloaded to perform standard vector and matrix operations as defined in linear algebra. In cases where an operation is not defined in linear algebra, the operation is typically done component-wise, where the operation is performed on each individual element of the vector or matrix.

Almost all math operators work on both float and int data types, but not in the same expression. GLSL does not perform any automatic casting of data types. Therefore, make sure all of the operands in an expression are of the same data type. Here are some examples of invalid mixed mode expressions:

float a = 3 * 0.7;            // Error. The 3 is an integer. Make it 3.0
int b = 10.0 * 0.7;           // Error. You can't assign a float to an integer.
b = int(10.0 * 0.7);          // Valid
vec3 c = vec3(1.0, 2.0, 3.0);
ivec3 d = ivec3(1,2,3);
vec3 e = c + d;               // Error. You can't add floats and integers.

Vector algebra operations require that the operands be of the same size. For example, you can add two vec3‘s together, but not a vec3 and a vec4. The result of a vector operation is always the same size as the original operands (except in the cases where a scalar and a vector are used.)

GLSL only supports square matrices, so the size of two matrices must be equal to multiply them together. A vector is treated as either a row or column vector whenever it is multiplied by a matrix, whichever makes the operation correct. You do not have to transpose a vector as you would in normal matrix algebra.

The GLSL compiler optimizes your code for execution. Therefore, don’t make overly complex equations and think you are somehow making the code faster. A series of well documented equations is preferable over a single, hard to understand, equation.

bool  b;  // scalar
int   i;  // scalar
float f;  // scalar
bvec2 bv; // Or bvec3, bvec4 (Boolean vector)
ivec2 iv; // Or ivec3, ivec4 (integer vector)
vec2  v;  // Or vec3, vec4   (floating point vector)
mat2  m;  // Or mat3, mat4   (floating point matrix)