/*
===========================================================================
Doom 3 BFG Edition GPL Source Code
Copyright (C) 1993-2012 id Software LLC, a ZeniMax Media company.
This file is part of the Doom 3 BFG Edition GPL Source Code ("Doom 3 BFG Edition Source Code").
Doom 3 BFG Edition 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 BFG Edition 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 BFG Edition Source Code. If not, see .
In addition, the Doom 3 BFG Edition 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 BFG Edition 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.
===========================================================================
*/
#pragma hdrstop
#include "precompiled.h"
const int SMALLEST_NON_DENORMAL = 1 << IEEE_FLT_MANTISSA_BITS;
const int NAN_VALUE = 0x7f800000;
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::ONEOVER_PI = 1.0f / idMath::PI;
const float idMath::ONEOVER_TWOPI = 1.0f / idMath::TWO_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;
const float idMath::FLT_SMALLEST_NON_DENORMAL = * reinterpret_cast< const float* >( & SMALLEST_NON_DENORMAL ); // 1.1754944e-038f
const __m128 idMath::SIMD_SP_zero = { 0.0f, 0.0f, 0.0f, 0.0f };
const __m128 idMath::SIMD_SP_255 = { 255.0f, 255.0f, 255.0f, 255.0f };
const __m128 idMath::SIMD_SP_min_char = { -128.0f, -128.0f, -128.0f, -128.0f };
const __m128 idMath::SIMD_SP_max_char = { 127.0f, 127.0f, 127.0f, 127.0f };
const __m128 idMath::SIMD_SP_min_short = { -32768.0f, -32768.0f, -32768.0f, -32768.0f };
const __m128 idMath::SIMD_SP_max_short = { 32767.0f, 32767.0f, 32767.0f, 32767.0f };
const __m128 idMath::SIMD_SP_smallestNonDenorm = { FLT_SMALLEST_NON_DENORMAL, FLT_SMALLEST_NON_DENORMAL, FLT_SMALLEST_NON_DENORMAL, FLT_SMALLEST_NON_DENORMAL };
const __m128 idMath::SIMD_SP_tiny = { 1e-4f, 1e-4f, 1e-4f, 1e-4f };
const __m128 idMath::SIMD_SP_rsqrt_c0 = { 3.0f, 3.0f, 3.0f, 3.0f };
const __m128 idMath::SIMD_SP_rsqrt_c1 = { -0.5f, -0.5f, -0.5f, -0.5f };
bool idMath::initialized = false;
dword idMath::iSqrt[SQRT_TABLE_SIZE]; // inverse square root lookup table
/*
===============
idMath::Init
===============
*/
void idMath::Init()
{
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( &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 |= ( ( INT32_SIGNBITSET( 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( &value );
}