DoomRTX/neo/engine/idlib/math/Math.cpp

/*
===========================================================================

IceTech GPL Source Code
Copyright (C) 2026 Justin Marshall

This file is part of the IceTech GPL Source Code (?IceTech Source Code?).

IceTech Source Code is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

IceTech Source Code is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with IceTech Source Code.  If not, see <http://www.gnu.org/licenses/>.

In addition, the IceTech Source Code is also subject to certain additional terms. You should have received a copy of these additional terms immediately following the terms and conditions of the GNU General Public License which accompanied the IceTech Source Code.  If not, please request a copy in writing from id Software at the address below.

If you have questions concerning this license or the applicable additional terms, you may contact in writing Justin Marshall, justinmarshall20@gmail.com

===========================================================================
*/

#include "precompiled.h"
#pragma hdrstop


const float	idMath::PI = 3.14159265358979323846f;
const float	idMath::TWO_PI = 2.0f * PI;
const float	idMath::HALF_PI = 0.5f * PI;
const float	idMath::ONEFOURTH_PI = 0.25f * PI;
const float idMath::E = 2.71828182845904523536f;
const float idMath::SQRT_TWO = 1.41421356237309504880f;
const float idMath::SQRT_THREE = 1.73205080756887729352f;
#ifdef QUAKE4
// RAVEN BEGIN
const float	idMath::THREEFOURTHS_PI = 0.75f * PI;
// RAVEN END
#endif
const float	idMath::SQRT_1OVER2 = 0.70710678118654752440f;
const float	idMath::SQRT_1OVER3 = 0.57735026918962576450f;
const float	idMath::M_DEG2RAD = PI / 180.0f;
const float	idMath::M_RAD2DEG = 180.0f / PI;
const float	idMath::M_SEC2MS = 1000.0f;
const float	idMath::M_MS2SEC = 0.001f;
const float	idMath::INFINITY = 1e30f;
const float idMath::FLT_EPSILON = 1.192092896e-07f;
#ifdef QUAKE4
// RAVEN BEGIN
// jscott: renamed to prevent name clash
const float idMath::FLOAT_EPSILON = 1.192092896e-07f;
// RAVEN END
#endif
const int idMath::INT_MIN = (-2147483647 - 1);
const int idMath::INT_MAX = 2147483647;

bool		idMath::initialized = false;
dword		idMath::iSqrt[SQRT_TABLE_SIZE];		// inverse square root lookup table

#ifdef QUAKE4
#ifdef ID_WIN_X86_SSE
const float idMath::SSE_FLOAT_ZERO = 0.0f;
const float idMath::SSE_FLOAT_255 = 255.0f;
#endif
#endif

/*
===============
idMath::Init
===============
*/
void idMath::Init(void) {
	union _flint fi, fo;

	for (int i = 0; i < SQRT_TABLE_SIZE; i++) {
		fi.i = ((EXP_BIAS - 1) << EXP_POS) | (i << LOOKUP_POS);
		fo.f = (float)(1.0 / sqrt(fi.f));
		iSqrt[i] = ((dword)(((fo.i + (1 << (SEED_POS - 2))) >> SEED_POS) & 0xFF)) << SEED_POS;
	}

	iSqrt[SQRT_TABLE_SIZE / 2] = ((dword)(0xFF)) << (SEED_POS);

	initialized = true;
}

/*
================
idMath::FloatToBits
================
*/
int idMath::FloatToBits(float f, int exponentBits, int mantissaBits) {
	int i, sign, exponent, mantissa, value;

	assert(exponentBits >= 2 && exponentBits <= 8);
	assert(mantissaBits >= 2 && mantissaBits <= 23);

	int maxBits = (((1 << (exponentBits - 1)) - 1) << mantissaBits) | ((1 << mantissaBits) - 1);
	int minBits = (((1 << exponentBits) - 2) << mantissaBits) | 1;

	float max = BitsToFloat(maxBits, exponentBits, mantissaBits);
	float min = BitsToFloat(minBits, exponentBits, mantissaBits);

	if (f >= 0.0f) {
		if (f >= max) {
			return maxBits;
		}
		else if (f <= min) {
			return minBits;
		}
	}
	else {
		if (f <= -max) {
			return (maxBits | (1 << (exponentBits + mantissaBits)));
		}
		else if (f >= -min) {
			return (minBits | (1 << (exponentBits + mantissaBits)));
		}
	}

	exponentBits--;
	i = *reinterpret_cast<int*>(&f);
	sign = (i >> IEEE_FLT_SIGN_BIT) & 1;
	exponent = ((i >> IEEE_FLT_MANTISSA_BITS) & ((1 << IEEE_FLT_EXPONENT_BITS) - 1)) - IEEE_FLT_EXPONENT_BIAS;
	mantissa = i & ((1 << IEEE_FLT_MANTISSA_BITS) - 1);
	value = sign << (1 + exponentBits + mantissaBits);
	value |= ((INTSIGNBITSET(exponent) << exponentBits) | (abs(exponent) & ((1 << exponentBits) - 1))) << mantissaBits;
	value |= mantissa >> (IEEE_FLT_MANTISSA_BITS - mantissaBits);
	return value;
}

/*
================
idMath::BitsToFloat
================
*/
float idMath::BitsToFloat(int i, int exponentBits, int mantissaBits) {
	static int exponentSign[2] = { 1, -1 };
	int sign, exponent, mantissa, value;

	assert(exponentBits >= 2 && exponentBits <= 8);
	assert(mantissaBits >= 2 && mantissaBits <= 23);

	exponentBits--;
	sign = i >> (1 + exponentBits + mantissaBits);
	exponent = ((i >> mantissaBits) & ((1 << exponentBits) - 1)) * exponentSign[(i >> (exponentBits + mantissaBits)) & 1];
	mantissa = (i & ((1 << mantissaBits) - 1)) << (IEEE_FLT_MANTISSA_BITS - mantissaBits);
	value = sign << IEEE_FLT_SIGN_BIT | (exponent + IEEE_FLT_EXPONENT_BIAS) << IEEE_FLT_MANTISSA_BITS | mantissa;
	return *reinterpret_cast<float*>(&value);
}


#ifdef QUAKE4
// RAVEN BEGIN
// bdube: added block

void idMath::ArtesianFromPolar(idVec3& result, idVec3 view)
{
	float	s1, c1, s2, c2;

	idMath::SinCos(view[1], s1, c1);
	idMath::SinCos(view[2], s2, c2);

	result[0] = c1 * s2 * view[0];
	result[1] = s1 * s2 * view[0];
	result[2] = c2 * view[0];
}

void idMath::PolarFromArtesian(idVec3& view, idVec3 artesian)
{
	float	length;
	view[0] = artesian.Length();
	view[1] = idMath::ATan(artesian[1], artesian[0]);
	length = sqrtf((artesian[0] * artesian[0]) + (artesian[1] * artesian[1]));
	view[2] = idMath::ATan(length, artesian[2]);
}
#endif
// ================================================================================================
// jscott: fast and reliable random routines
// ================================================================================================

unsigned long rvRandom::mSeed;

float rvRandom::flrand(float min, float max)
{
	float	result;

	mSeed = (mSeed * 214013L) + 2531011;
	// Note: the shift and divide cannot be combined as this breaks the routine
	result = (float)(mSeed >> 17);						// 0 - 32767 range
	result = ((result * (max - min)) * (1.0f / 32768.0f)) + min;
	return(result);
}

float rvRandom::flrand() {
	return flrand(0.0f, 1.0f);
}

float rvRandom::flrand(const idVec2& v) {
	return flrand(v[0], v[1]);
}

int rvRandom::irand(int min, int max)
{
	int		result;

	max++;
	mSeed = (mSeed * 214013L) + 2531011;
	result = mSeed >> 17;
	result = ((result * (max - min)) >> 15) + min;
	return(result);
}

// Try to get a seed independent of the random number system

int rvRandom::Init(void)
{
	mSeed *= (unsigned long)sys->Milliseconds();

	return(mSeed);
}

#ifdef QUAKE4
// RAVEN BEGIN
// bdube: added block

// ================================================================================================
// Barycentric texture coordinate functions
// Get the *SIGNED* area of a triangle required for barycentric
// ================================================================================================
float idMath::BarycentricTriangleArea(const idVec3& normal, const idVec3& a, const idVec3& b, const idVec3& c)
{
	idVec3	v1, v2;
	idVec3	cross;
	float	area;

	v1 = b - a;
	v2 = c - a;
	cross = v1.Cross(v2);
	area = 0.5f * DotProduct(cross, normal);

	return(area);
}

void idMath::BarycentricEvaluate(idVec2& result, const idVec3& point, const idVec3& normal, const float area, const idVec3 t[3], const idVec2 tc[3])
{
	float	b1, b2, b3;

	b1 = idMath::BarycentricTriangleArea(normal, point, t[1], t[2]) / area;
	b2 = idMath::BarycentricTriangleArea(normal, t[0], point, t[2]) / area;
	b3 = idMath::BarycentricTriangleArea(normal, t[0], t[1], point) / area;

	result[0] = (b1 * tc[0][0]) + (b2 * tc[1][0]) + (b3 * tc[2][0]);
	result[1] = (b1 * tc[0][1]) + (b2 * tc[1][1]) + (b3 * tc[2][1]);
}

// abahr:
float idMath::Lerp(const idVec2& range, float frac) {
	return Lerp(range[0], range[1], frac);
}

// abahr:
float idMath::Lerp(float start, float end, float frac) {
	if (frac >= 1.0f) {
		return end;
	}

	if (frac <= 0.0f) {
		return start;
	}

	return start + (end - start) * frac;
}

// abahr:
float idMath::MidPointLerp(float start, float mid, float end, float frac) {
	if (frac < 0.5f) {
		return Lerp(start, mid, 2.0f * frac);
	}

	return Lerp(mid, end, 2.0f * (frac - 0.5f));
}

float idMath::dBToScale(float db) {

	if (db < -60.0f) {

		return(0.0f);

	}
	else {

		return(powf(2.0f, db * (1.0f / 6.0f)));
	}
}

float idMath::ScaleToDb(float scale) {

	if (scale <= 0.0f) {

		return(-60.0f);

	}
	else {

		return(6.0f * idMath::Log(scale) / idMath::Log(2));
	}
}

// RAVEN END
#endif

float idMath::Distance(idVec3 p1, idVec3 p2)
{
	idVec3 v = p2 - p1;
	return v.Length();
}