High Level Shading Language - Practical Rendering and Computation with Direct3D 11 - page 333

provides HLSL shader programs with full access to the functionality provided by the as-
sembly instruction set. In a few cases, intrinsic functions also provide an optimized set of
common mathematical operations, which spares the programmer from implementing them
manually. The following sections contain tables listing intrinsic functions grouped by cat-
egory, with a brief description for each. For a full description (including return types and
parameters), consult the SDK documentation

6.7.1 Mathematical Functions

Vector/Matrix Operations
Table 6.5 contains a list of all vector and matrix math intrinsics supported by HLSL. These
intrinsics implement mathematical operations that can be performed on vector and matrix
data types.

Intrinsic Description

mul Matrix/Matrix, Matrix/Vector, or Vector/Vector multiplication

dot Vector dot product

cross Vector cross product

Matrix transpose

transpose

determinant Matrix determinant

Vector length/magnitude

length

normalize Geometric vector normalize

distance Computes the distance between two points

Flips a surface normal direction such that it points in a direction op-
posite to an incident vector

faceforward

reflect Computes a reflection vector, given normal and incident vectors

Computes a refraction vector, given an entering direction, normal vec-
tor, and refraction index

refract

Table 6.5. Vector/matrix math intrinsics.

General Math Functions
Table 6.6 contains a listing of HLSL's general math intrinsics. These instrinsics are mostly
scalar math operations, similar to those found in the C Standard Library.