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neo/idlib/math/Math.cpp

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+/*
+===========================================================================
+
+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 <http://www.gnu.org/licenses/>.
+
+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<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 |= ( ( 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<float *>(&value);
+}