A reimplementation of Mario Kart Wii's physics engine in C++
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Classes | Functions | Variables
EGG::Mathf Namespace Reference

Detailed Description

Math functions and constants used in the base game.

Classes

struct  AtanEntry
 
struct  BaseAndDec32
 
struct  BaseAndDec64
 
union  c32
 
union  c64
 
struct  SinCosEntry
 

Functions

f32 frsqrt (f32 x)
 
f32 SinFIdx (f32 fidx)
 
f32 CosFIdx (f32 fidx)
 
std::pair< f32, f32 > SinCosFIdx (f32 fidx)
 
f32 AtanFIdx_ (f32 x)
 
f32 Atan2FIdx (f32 y, f32 x)
 
u32 FindRootsQuadratic (f32 a, f32 b, f32 c, f32 &root1, f32 &root2)
 
f32 Hermite (f32 p0, f32 m0, f32 p1, f32 m1, f32 t)
 Evaluates a cubic Hermite curve at a given parameter t.
 
static f32 sqrt (f32 x)
 
static f32 sin (f32 x)
 
static f32 cos (f32 x)
 
static f32 asin (f32 x)
 
static f32 acos (f32 x)
 
static f32 atan2 (f32 y, f32 x)
 
static f32 abs (f32 x)
 
static f64 force25Bit (f64 x)
 This is used to mimic the Wii's floating-point unit.
 
static f32 fma (f32 x, f32 y, f32 z)
 Fused multiply-add operation.
 
static f32 fms (f32 x, f32 y, f32 z)
 Fused multiply-subtract operation.
 
static f64 frsqrte (const f64 val)
 
static f32 fres (const f32 val)
 
static f32 finv (f32 x)
 Fused Newton-Raphson operation.
 

Variables

static constexpr SinCosEntry sSinCosTbl [256+1]
 
static constexpr AtanEntry sArcTanTbl [32+1]
 
static constexpr u64 EXPONENT_SHIFT_F64 = 52
 
static constexpr u64 MANTISSA_MASK_F64 = 0x000fffffffffffffULL
 
static constexpr u64 EXPONENT_MASK_F64 = 0x7ff0000000000000ULL
 
static constexpr u64 SIGN_MASK_F64 = 0x8000000000000000ULL
 
static constexpr std::array< BaseAndDec64, 32 > RSQRTE_TABLE
 
static constexpr std::array< BaseAndDec32, 32 > FRES_TABLE
 

Function Documentation

◆ abs()

static f32 EGG::Mathf::abs ( f32 x)
inlinestaticnodiscard

Definition at line 62 of file Math.hh.

◆ acos()

static f32 EGG::Mathf::acos ( f32 x)
inlinestaticnodiscard0x8022F8C0

Definition at line 53 of file Math.hh.

◆ asin()

static f32 EGG::Mathf::asin ( f32 x)
inlinestaticnodiscard0x8022F89C

Definition at line 48 of file Math.hh.

◆ atan2()

static f32 EGG::Mathf::atan2 ( f32 y,
f32 x )
inlinestaticnodiscard0x8022F8E4

Definition at line 58 of file Math.hh.

◆ Atan2FIdx()

f32 EGG::Mathf::Atan2FIdx ( f32 y,
f32 x )
nodiscard0x800853C0

Definition at line 387 of file Math.cc.

◆ AtanFIdx_()

f32 EGG::Mathf::AtanFIdx_ ( f32 x)
nodiscard

Definition at line 379 of file Math.cc.

◆ cos()

static f32 EGG::Mathf::cos ( f32 x)
inlinestaticnodiscard0x8022F86C

Takes in radians

Definition at line 43 of file Math.hh.

◆ CosFIdx()

f32 EGG::Mathf::CosFIdx ( f32 fidx)
nodiscard0x80085180

Definition at line 343 of file Math.cc.

◆ FindRootsQuadratic()

u32 EGG::Mathf::FindRootsQuadratic ( f32 a,
f32 b,
f32 c,
f32 & root1,
f32 & root2 )
0x800867C0

Definition at line 424 of file Math.cc.

◆ finv()

static f32 EGG::Mathf::finv ( f32 x)
inlinestaticnodiscard

Fused Newton-Raphson operation.

Definition at line 324 of file Math.hh.

◆ fma()

static f32 EGG::Mathf::fma ( f32 x,
f32 y,
f32 z )
inlinestaticnodiscard

Fused multiply-add operation.

We cannot use std::fma due to the Wii computing at 64-bit precision.

Definition at line 77 of file Math.hh.

◆ fms()

static f32 EGG::Mathf::fms ( f32 x,
f32 y,
f32 z )
inlinestaticnodiscard

Fused multiply-subtract operation.

We cannot use std::fms due to the Wii computing at 64-bit precision.

Definition at line 84 of file Math.hh.

◆ force25Bit()

static f64 EGG::Mathf::force25Bit ( f64 x)
inlinestaticnodiscard

This is used to mimic the Wii's floating-point unit.

This handles the edgecase where double-precision floating-point numbers are passed into single-precision floating-point operands in assembly.

Definition at line 69 of file Math.hh.

◆ fres()

static f32 EGG::Mathf::fres ( const f32 val)
inlinestaticnodiscard

Definition at line 258 of file Math.hh.

◆ frsqrt()

f32 EGG::Mathf::frsqrt ( f32 x)
nodiscard0x80085040

CREDIT: Hanachan

Definition at line 315 of file Math.cc.

◆ frsqrte()

static f64 EGG::Mathf::frsqrte ( const f64 val)
inlinestaticnodiscard

Definition at line 167 of file Math.hh.

◆ Hermite()

f32 EGG::Mathf::Hermite ( f32 p0,
f32 m0,
f32 p1,
f32 m1,
f32 t )
nodiscard0x80085070

Evaluates a cubic Hermite curve at a given parameter t.

Computes

\[H(t) = h_0(t)\,p_0 + h_1(t)\,p_1 + h_2(t)\,m_0 + h_3(t)\,m_1\]

where the cubic Hermite basis functions are:

\[h_0(\theta) = 2\theta^3 - 3\theta^2 + 1\]

\[h_1(\theta) = -2\theta^3 + 3\theta^2\]

\[h_2(\theta) = \theta^3 - 2\theta^2 + \theta\]

\[h_3(\theta) = \theta^3 - \theta^2\]

Parameters
p0Start value.
m0Start tangent.
p1End value.
m1End tangent.
tInterpolation parameter in the domain [0, 1]
Returns
Interpolated value at t.

Definition at line 479 of file Math.cc.

◆ sin()

static f32 EGG::Mathf::sin ( f32 x)
inlinestaticnodiscard0x8022F860

Takes in radians

Definition at line 37 of file Math.hh.

◆ SinCosFIdx()

std::pair< f32, f32 > EGG::Mathf::SinCosFIdx ( f32 fidx)
nodiscard0x800851E0

Definition at line 358 of file Math.cc.

◆ SinFIdx()

f32 EGG::Mathf::SinFIdx ( f32 fidx)
nodiscard0x80085110

Definition at line 328 of file Math.cc.

◆ sqrt()

static f32 EGG::Mathf::sqrt ( f32 x)
inlinestaticnodiscard0x8022F80C

Definition at line 23 of file Math.hh.

Variable Documentation

◆ EXPONENT_MASK_F64

u64 EGG::Mathf::EXPONENT_MASK_F64 = 0x7ff0000000000000ULL
staticconstexpr

Definition at line 129 of file Math.hh.

◆ EXPONENT_SHIFT_F64

u64 EGG::Mathf::EXPONENT_SHIFT_F64 = 52
staticconstexpr

Definition at line 127 of file Math.hh.

◆ FRES_TABLE

std::array<BaseAndDec32, 32> EGG::Mathf::FRES_TABLE
staticconstexpr

Definition at line 223 of file Math.hh.

◆ MANTISSA_MASK_F64

u64 EGG::Mathf::MANTISSA_MASK_F64 = 0x000fffffffffffffULL
staticconstexpr

Definition at line 128 of file Math.hh.

◆ RSQRTE_TABLE

std::array<BaseAndDec64, 32> EGG::Mathf::RSQRTE_TABLE
staticconstexpr

Definition at line 132 of file Math.hh.

◆ sArcTanTbl

AtanEntry EGG::Mathf::sArcTanTbl[32+1]
staticconstexpr0x80274148

Definition at line 277 of file Math.cc.

◆ SIGN_MASK_F64

u64 EGG::Mathf::SIGN_MASK_F64 = 0x8000000000000000ULL
staticconstexpr

Definition at line 130 of file Math.hh.

◆ sSinCosTbl

SinCosEntry EGG::Mathf::sSinCosTbl[256+1]
staticconstexpr0x80248010

Definition at line 16 of file Math.cc.