Math.cpp

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

Doom 3 GPL Source Code
Copyright (C) 1999-2011 id Software LLC, a ZeniMax Media company. 

This file is part of the Doom 3 GPL Source Code (?Doom 3 Source Code?).  

Doom 3 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.

Doom 3 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 Doom 3 Source Code.  If not, see <http://www.gnu.org/licenses/>.

In addition, the Doom 3 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 Doom 3 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 id Software LLC, c/o ZeniMax Media Inc., Suite 120, Rockville, Maryland 20850 USA.

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

#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;
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;

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

/*
===============
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);
}