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
static constexpr f64	force25Bit (f64 x)
	This is used to mimic the Wii's floating-point unit.

static constexpr f32	fma (f32 x, f32 y, f32 z)
	Fused multiply-add operation.

static constexpr f32	fms (f32 x, f32 y, f32 z)
	Fused multiply-subtract operation.

static constexpr f32	SinFIdx (f32 fidx)

static constexpr f32	CosFIdx (f32 fidx)

static constexpr std::pair< f32, f32 >	SinCosFIdx (f32 fidx)

static constexpr f32	AtanFIdx_ (f32 x)

static constexpr f32	Atan2FIdx (f32 y, f32 x)

static constexpr f32	sin (f32 x)

static constexpr f32	cos (f32 x)

static constexpr f32	asin (f32 x)

static constexpr f32	acos (f32 x)

static constexpr f32	atan2 (f32 y, f32 x)

static constexpr f32	abs (f32 x)

static constexpr f64	frsqrte (const f64 val)

static constexpr f32	fres (const f32 val)

static constexpr f32	frsqrt (f32 x)

static constexpr f32	sqrt (f32 x)

static constexpr u32	FindRootsQuadratic (f32 a, f32 b, f32 c, f32 &root1, f32 &root2)

static constexpr f32	finv (f32 x)
	Fused Newton-Raphson operation.

static constexpr f32	Hermite (f32 p0, f32 m0, f32 p1, f32 m1, f32 t)
	Evaluates a cubic Hermite curve at a given parameter `t`.

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 constexpr f32 Kinoko::EGG::Mathf::abs ( f32 x )

inlinestaticnodiscardconstexpr

Definition at line 476 of file Math.hh.

◆ acos()

static constexpr f32 Kinoko::EGG::Mathf::acos ( f32 x )

inlinestaticnodiscardconstexpr0x8022F8C0

Definition at line 467 of file Math.hh.

◆ asin()

static constexpr f32 Kinoko::EGG::Mathf::asin ( f32 x )

inlinestaticnodiscardconstexpr0x8022F89C

Definition at line 462 of file Math.hh.

◆ atan2()

static constexpr f32 Kinoko::EGG::Mathf::atan2	(	f32	y,
		f32	x )

inlinestaticnodiscardconstexpr0x8022F8E4

Definition at line 472 of file Math.hh.

◆ Atan2FIdx()

static constexpr f32 Kinoko::EGG::Mathf::Atan2FIdx	(	f32	y,
		f32	x )

inlinestaticnodiscardconstexpr0x800853C0

Definition at line 413 of file Math.hh.

◆ AtanFIdx_()

static constexpr f32 Kinoko::EGG::Mathf::AtanFIdx_ ( f32 x )

inlinestaticnodiscardconstexpr

Definition at line 405 of file Math.hh.

◆ cos()

static constexpr f32 Kinoko::EGG::Mathf::cos ( f32 x )

inlinestaticnodiscardconstexpr0x8022F86C

Takes in radians

Definition at line 457 of file Math.hh.

◆ CosFIdx()

static constexpr f32 Kinoko::EGG::Mathf::CosFIdx ( f32 fidx )

inlinestaticnodiscardconstexpr0x80085180

Definition at line 369 of file Math.hh.

◆ FindRootsQuadratic()

static constexpr u32 Kinoko::EGG::Mathf::FindRootsQuadratic	(	f32	a,
		f32	b,
		f32	c,
		f32 &	root1,
		f32 &	root2 )

inlinestaticconstexpr0x800867C0

Definition at line 734 of file Math.hh.

◆ finv()

static constexpr f32 Kinoko::EGG::Mathf::finv ( f32 x )

inlinestaticnodiscardconstexpr

Fused Newton-Raphson operation.

Definition at line 775 of file Math.hh.

◆ fma()

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

inlinestaticnodiscardconstexpr

Fused multiply-add operation.

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

Definition at line 33 of file Math.hh.

◆ fms()

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

inlinestaticnodiscardconstexpr

Fused multiply-subtract operation.

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

Definition at line 40 of file Math.hh.

◆ force25Bit()

static constexpr f64 Kinoko::EGG::Mathf::force25Bit ( f64 x )

inlinestaticnodiscardconstexpr

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 25 of file Math.hh.

◆ fres()

static constexpr f32 Kinoko::EGG::Mathf::fres ( const f32 val )

inlinestaticnodiscardconstexpr

Definition at line 649 of file Math.hh.

◆ frsqrt()

static constexpr f32 Kinoko::EGG::Mathf::frsqrt ( f32 x )

inlinestaticnodiscardconstexpr0x80085040

CREDIT: Hanachan

Definition at line 716 of file Math.hh.

◆ frsqrte()

static constexpr f64 Kinoko::EGG::Mathf::frsqrte ( const f64 val )

inlinestaticnodiscardconstexpr

Definition at line 558 of file Math.hh.

◆ Hermite()

static constexpr f32 Kinoko::EGG::Mathf::Hermite	(	f32	p0,
		f32	m0,
		f32	p1,
		f32	m1,
		f32	t )

inlinestaticnodiscardconstexpr0x80085070

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

p0	Start value.
m0	Start tangent.
p1	End value.
m1	End tangent.
t	Interpolation parameter in the domain [0, 1]

Returns: Interpolated value at t.

Definition at line 797 of file Math.hh.

◆ sin()

static constexpr f32 Kinoko::EGG::Mathf::sin ( f32 x )

inlinestaticnodiscardconstexpr0x8022F860

Takes in radians

Definition at line 451 of file Math.hh.

◆ SinCosFIdx()

static constexpr std::pair< f32, f32 > Kinoko::EGG::Mathf::SinCosFIdx ( f32 fidx )

inlinestaticnodiscardconstexpr0x800851E0

Definition at line 384 of file Math.hh.

◆ SinFIdx()

static constexpr f32 Kinoko::EGG::Mathf::SinFIdx ( f32 fidx )

inlinestaticnodiscardconstexpr0x80085110

Definition at line 354 of file Math.hh.

◆ sqrt()

static constexpr f32 Kinoko::EGG::Mathf::sqrt ( f32 x )

inlinestaticnodiscardconstexpr0x8022F80C

Definition at line 729 of file Math.hh.

Variable Documentation

◆ EXPONENT_MASK_F64

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

staticconstexpr

Definition at line 520 of file Math.hh.

◆ EXPONENT_SHIFT_F64

u64 Kinoko::EGG::Mathf::EXPONENT_SHIFT_F64 = 52

staticconstexpr

Definition at line 518 of file Math.hh.

◆ FRES_TABLE

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

staticconstexpr

Definition at line 614 of file Math.hh.

◆ MANTISSA_MASK_F64

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

staticconstexpr

Definition at line 519 of file Math.hh.

◆ RSQRTE_TABLE

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

staticconstexpr

Definition at line 523 of file Math.hh.

◆ sArcTanTbl

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

staticconstexpr0x80274148

Definition at line 317 of file Math.hh.

◆ SIGN_MASK_F64

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

staticconstexpr

Definition at line 521 of file Math.hh.

◆ sSinCosTbl

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

staticconstexpr0x80248010

Definition at line 56 of file Math.hh.

Detailed Description

Classes

Functions

Variables

Function Documentation

◆ abs()

◆ acos()

◆ asin()

◆ atan2()

◆ Atan2FIdx()

◆ AtanFIdx_()

◆ cos()

◆ CosFIdx()

◆ FindRootsQuadratic()

◆ finv()

◆ fma()

◆ fms()

◆ force25Bit()

◆ fres()

◆ frsqrt()

◆ frsqrte()

◆ Hermite()

◆ sin()

◆ SinCosFIdx()

◆ SinFIdx()

◆ sqrt()

Variable Documentation

◆ EXPONENT_MASK_F64

◆ EXPONENT_SHIFT_F64

◆ FRES_TABLE

◆ MANTISSA_MASK_F64

◆ RSQRTE_TABLE

◆ sArcTanTbl

◆ SIGN_MASK_F64

◆ sSinCosTbl