Foundation::Math Namespace Reference

Mathematical utilities and types. More...

Classes
union	FloatBits

Typedefs
using	float4 = vec4
using	float3 = vec3
using	float2 = vec2
using	float4x4 = mat4

Functions
unsigned short	quantizeFP16 (float v)
float	quantizeFP32 (float v, int N)
float	dequantizeFP16 (unsigned short h)
float	quantizeFP32 (float v, int32_t N)
float	dequantizeFP16 (uint16_t h)
uint32_t	quantizeUnorm (float v, int32_t N)
float	dequantizeUnorm (int32_t q, int32_t Nbits)
int32_t	quantizeSnorm (float v, int32_t N)
float	dequantizeSnorm (int32_t q, int32_t Nbits)
uint32_t	quantizeSnormShifted (float v, int32_t Nbits)
float	dequantizeSnormShifted (uint32_t q, int32_t Nbits)
vec2	packUnitOctahedral (vec3 v)
vec3	unpackUnitOctahedral (vec2 v)

Variables
constexpr float	EPS = 1e-6

Detailed Description

Mathematical utilities and types.

Float (de)quantization code taken from meshoptimizer (https://github.com/zeux/meshoptimizer)

All rights reserved by the original author, see license in meshoptimizer.h

Typedef Documentation

float2

using Foundation::Math::float2 = typedef vec2

float3

using Foundation::Math::float3 = typedef vec3

float4

using Foundation::Math::float4 = typedef vec4

float4x4

using Foundation::Math::float4x4 = typedef mat4

Function Documentation

dequantizeFP16() [1/2]

float Foundation::Math::dequantizeFP16

(

uint16_t

h

)

Reverse quantization of a half-precision (as defined by IEEE-754 fp16) floating point value Preserves Inf/NaN, flushes denormals to zero

dequantizeFP16() [2/2]

float Foundation::Math::dequantizeFP16

(

unsigned short

h

)

dequantizeSnorm()

float Foundation::Math::dequantizeSnorm ( int32_t  q, int32_t  Nbits  )

inline

dequantizeSnormShifted()

float Foundation::Math::dequantizeSnormShifted ( uint32_t  q, int32_t  Nbits  )

inline

dequantizeUnorm()

float Foundation::Math::dequantizeUnorm ( int32_t  q, int32_t  Nbits  )

inline

packUnitOctahedral()

vec2 Foundation::Math::packUnitOctahedral

(

vec3

v

)

Unit Vector Packing See also:

• https://aras-p.info/texts/CompactNormalStorage.html
• https://www.shadertoy.com/view/Mtfyzl

quantizeFP16()

uint16_t Foundation::Math::quantizeFP16

(

float

v

)

Quantize a float into half-precision (as defined by IEEE-754 fp16) floating point value Generates +-inf for overflow, preserves NaN, flushes denormals to zero, rounds to nearest Representable magnitude range: [6e-5; 65504] Maximum relative reconstruction error: 5e-4

quantizeFP32() [1/2]

float Foundation::Math::quantizeFP32	(	float	v,
		int	N
	)

quantizeFP32() [2/2]

float Foundation::Math::quantizeFP32	(	float	v,
		int32_t	N
	)

Quantize a float into a floating point value with a limited number of significant mantissa bits, preserving the IEEE-754 fp32 binary representation Generates +-inf for overflow, preserves NaN, flushes denormals to zero, rounds to nearest Assumes N is in a valid mantissa precision range, which is 1..23

quantizeSnorm()

int32_t Foundation::Math::quantizeSnorm ( float  v, int32_t  N  )

inline

[-1, 1] range -> [-(1<< (Nbits - 1)) - 1, (1 << (Nbits - 1))] \in N e.g. Nbits = 10 -> [-511, 512] In transport you may want to add 1 << (Nbits - 1) to the quantized value to shift it to [0, 1 << NBits) range since you'd be packing complement int32 bits - truncation would result in a loss of precision To do this, use QuantizeSnormShifted and DequantizeSnormShifted

quantizeSnormShifted()

uint32_t Foundation::Math::quantizeSnormShifted ( float  v, int32_t  Nbits  )

inline

quantizeUnorm()

uint32_t Foundation::Math::quantizeUnorm ( float  v, int32_t  N  )

inline

unpackUnitOctahedral()

vec3 Foundation::Math::unpackUnitOctahedral

(

vec2

v

)

Variable Documentation

EPS

constexpr float Foundation::Math::EPS = 1e-6

constexpr