stillwwater/mathlib

C++ vector math

mathf

Small C++ library with vector math routines, Xorshift random number generator, and simplex noise.

Misc math

• rsqrt(x) Returns 1 / sqrtf(x)
• fast_rsqrt(x) Returns the approximate reciprocal square root using SSE intrinsics when available
• floortoi(x) Floor a float converting it to an int. This is faster than static_cast<int>(floorf(x))
• clamp(x, a, b) Clamp a value to be in the the range [a, b]
• clampi(x, a, b) Same as clamp but for integers instead of floats
• clamp01(x) The saturate function, clamps a value to be in [0, 1]
• lerp(a, b, t) Linearly interpolate between vector a and b at time t where t is in [0, 1]
• unlerp(a, b, x) The opposite of lerp, returns the position in the curve t for a given value x.
• remap(a, b, c, d, x) Maps a value x in the range [a, b] to be in the range [c, d]
• signf(x) returns 1 if x is positive, -1 if x is negative, 0 otherwise.
• next_pow2(x) Returns the next power of two given a unsigned integer x.

Vector operators

• -vec
• vec + vec, vec - vec
• vec * vec, vec / vec Component-wise multiply and divide
• vec * scalar scalar * vec, vec / scalar
• +=, -=, *=, /=
• vec(scalar) Initializes all components to a scalar value, can be used to represent the zero vector as float3(0) for example. This is an explicit constructor, so scalars will not implicitly convert to vector types. Similar constructors exist to convert between vectors of different types/dimensions.

For 4D vectors, most operators map to their equivalent SSE instructions.

Vector member functions

• length() Returns length / magnitude / norm of the vector.
• length_sqr() Returns the length of the vector squared.

Float vectors (float2, float3, float4)

Functions defined for all floating point vector types.

• dot(a, b)
• normalize(v)
• normalize_safe(v) Returns a normalized vector without producing NaN when v is the zero vector.
• clamp(v, a, b) Clamps each vector component to be in the range [a, b]
• clamp01(v) Saturate function, clamps the vector have all components in [0, 1]
• lerp(a, b, t) Linearly interpolate between vector a and b at time t where t is in [0, 1]
• frac(v) Returns 1 - vfloor(v)
• vstep(edge, v) Returns a vector with each component equal to v[i] >= edge[i]
• vmin(a, b) Component-wise fminf
• vmax(a, b) Component-wise fmaxf
• vabs(a, b) Component-wise fabsf
• vfloor(a, b) Component-wise floorf
• vceil(a, b) Component-wise ceilf
• vsqrt(a, b) Component-wise ceilf
• vrsqrt(a, b) Component-wise rsqrt, for float4 the rsqrt SSE instrinsic is used.
• pprint(v) Print a vector

float2 specific functions

• vangle(a, b) Returns the angle between two vectors in degrees
• vangle_rad(a, b) Returns the angle between two vectors in radians
• reflect(v, normal)

float3 specific functions

• cross(a, b)
• reflect(v, normal)
• refract(v, normal, eta)

Integer vectors (int2, int3, int4)

• clampi(v, a, b)
• vabs(v)
• vmin(a, b)
• vmax(a, b)

Vector shuffles (swizzle)

Constructs a new vector by selecting elements from a given vector.

shuffle<0, 0, 1, 1>(float2(1, 2)) // float4(1, 1, 2, 2)
shuffle<3, 2, 1, 0>(float4(1, 2, 3, 4)) // float4(4, 3, 2, 1)
shuffle<1, 2>(float3(1, 2, 3)) // float2(2, 3)

Vector SIMD

The 4D vector types (int4 and float4) use sse instructions when available for most operators. To use vec.m128 and vec.m128i to use with float and integer sse instructions respectively. __m128 can be implicitly be converted to float4 and __m128i to int4.

mathlib's Issues

Documentation for Noise code