316 lines
9.7 KiB
C++
316 lines
9.7 KiB
C++
// Copyright (C) 2007 Id Software, Inc.
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//
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#include "../precompiled.h"
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#pragma hdrstop
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const float idMath::PI = 3.14159265358979323846f;
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const float idMath::TWO_PI = 2.0f * PI;
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const float idMath::HALF_PI = 0.5f * PI;
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const float idMath::ONEFOURTH_PI = 0.25f * PI;
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const float idMath::THREEFOURTHS_PI = 0.75f * PI;
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const float idMath::E = 2.71828182845904523536f;
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const float idMath::SQRT_TWO = 1.41421356237309504880f;
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const float idMath::SQRT_THREE = 1.73205080756887729352f;
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const float idMath::SQRT_1OVER2 = 0.70710678118654752440f;
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const float idMath::SQRT_1OVER3 = 0.57735026918962576450f;
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const float idMath::M_DEG2RAD = PI / 180.0f;
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const float idMath::M_RAD2DEG = 180.0f / PI;
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const float idMath::M_SEC2MS = 1000.0f;
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const float idMath::M_MS2SEC = 0.001f;
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const float idMath::INFINITY = 1e30f;
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const float idMath::FLT_EPSILON = 1.192092896e-07f;
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bool idMath::initialized = false;
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dword idMath::iSqrt[SQRT_TABLE_SIZE]; // inverse square root lookup table
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#ifdef ID_WIN_X86_SSE
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const float idMath::SSE_FLOAT_ZERO = 0.0f;
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const float idMath::SSE_FLOAT_255 = 255.0f;
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#endif
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/*
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===============
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idMath::Init
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===============
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*/
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void idMath::Init( void ) {
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union _flint fi, fo;
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for ( int i = 0; i < SQRT_TABLE_SIZE; i++ ) {
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fi.i = ((EXP_BIAS-1) << EXP_POS) | (i << LOOKUP_POS);
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fo.f = (float)( 1.0 / sqrt( fi.f ) );
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iSqrt[i] = ((dword)(((fo.i + (1<<(SEED_POS-2))) >> SEED_POS) & 0xFF))<<SEED_POS;
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}
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iSqrt[SQRT_TABLE_SIZE / 2] = ((dword)(0xFF))<<(SEED_POS);
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initialized = true;
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}
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/*
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================
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idMath::FloatToBits
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================
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*/
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int idMath::FloatToBits( float f, int exponentBits, int mantissaBits ) {
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int i, sign, exponent, mantissa, value;
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assert( exponentBits >= 2 && exponentBits <= 8 );
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assert( mantissaBits >= 2 && mantissaBits <= 23 );
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int maxBits = ( 1 << ( exponentBits + mantissaBits ) ) - 1;
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int minBits = 1;
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float max = BitsToFloat( maxBits, exponentBits, mantissaBits );
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float min = BitsToFloat( minBits, exponentBits, mantissaBits );
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if ( f >= 0.0f ) {
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if ( f >= max ) {
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return maxBits;
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} else if ( f == min ) {
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return minBits;
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} else if ( f < min ) {
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return 0;
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}
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} else {
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if ( f <= -max ) {
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return ( maxBits | ( 1 << ( exponentBits + mantissaBits ) ) );
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} else if ( f == -min ) {
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return ( minBits | ( 1 << ( exponentBits + mantissaBits ) ) );
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} else if ( f > -min ) {
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return 0;
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}
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}
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i = *reinterpret_cast<int *>(&f);
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sign = ( i >> IEEE_FLT_SIGN_BIT ) & 1;
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exponent = ( ( i >> IEEE_FLT_MANTISSA_BITS ) & ( ( 1 << IEEE_FLT_EXPONENT_BITS ) - 1 ) ) - IEEE_FLT_EXPONENT_BIAS;
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mantissa = i & ( ( 1 << IEEE_FLT_MANTISSA_BITS ) - 1 );
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value = sign << ( exponentBits + mantissaBits );
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value |= ( exponent + ( ( 1 << ( exponentBits - 1 ) ) - 1 ) ) << mantissaBits;
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value |= mantissa >> ( IEEE_FLT_MANTISSA_BITS - mantissaBits );
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return value;
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}
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/*
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================
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idMath::BitsToFloat
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================
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*/
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float idMath::BitsToFloat( int i, int exponentBits, int mantissaBits ) {
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int sign, exponent, mantissa, value;
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assert( exponentBits >= 2 && exponentBits <= 8 );
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assert( mantissaBits >= 2 && mantissaBits <= 23 );
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if ( ( i & ( ( 1 << ( exponentBits + mantissaBits ) ) - 1 ) ) == 0 ) {
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// if exponent & mantissa are zero, value is plus or minus zero
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return 0.0f;
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}
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sign = i >> ( exponentBits + mantissaBits );
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exponent = ( ( i >> mantissaBits ) & ( ( 1 << exponentBits ) - 1 ) ) - ( ( 1 << ( exponentBits - 1 ) ) - 1 );
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mantissa = ( i & ( ( 1 << mantissaBits ) - 1 ) ) << ( IEEE_FLT_MANTISSA_BITS - mantissaBits );
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value = sign << IEEE_FLT_SIGN_BIT | ( exponent + IEEE_FLT_EXPONENT_BIAS ) << IEEE_FLT_MANTISSA_BITS | mantissa;
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return *reinterpret_cast<float *>(&value);
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}
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/*
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================
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idMath::TestFloatBitConversions
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================
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*/
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void idMath::TestFloatBitConversions() {
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//
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// test every value that can be represented within the valid ranges of bits
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char testBuf[ 512 ];
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int numFails = 0;
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for ( int exponentBits = 2; exponentBits <= 8; exponentBits++ ) {
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for ( int mantissaBits = 2; mantissaBits <= 23; mantissaBits++ ) {
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sprintf( testBuf, "Float Testing: exp %i mant %i ...... ", exponentBits, mantissaBits );
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#ifdef _WIN32
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OutputDebugString( testBuf );
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#else
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printf( "%s", testBuf );
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#endif
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int maxBits = ( 1 << ( exponentBits + mantissaBits ) ) - 1;
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int minBits = 1;
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float max = idMath::BitsToFloat( maxBits, exponentBits, mantissaBits );
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float min = idMath::BitsToFloat( minBits, exponentBits, mantissaBits );
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bool failed = false;
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// test that all representable values convert to & from a float & maintain value
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unsigned int totalNumbersRepresentable = 1 << ( exponentBits + mantissaBits + 1 );
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for ( unsigned int i = 0; i < totalNumbersRepresentable; i++ ) {
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// skip anything with zero mantissa & exponent
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float testFloat = idMath::BitsToFloat( *( ( int* )&i ), exponentBits, mantissaBits );
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unsigned int testBits = idMath::FloatToBits( testFloat, exponentBits, mantissaBits );
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#pragma warning( push )
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#pragma warning( disable: 4389 )
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if ( i == 1 << ( exponentBits + mantissaBits ) ) {
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#pragma warning( pop )
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// negative zero should be the same as positive zero (not IEEE-754, but simple)
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if ( testBits != 0 ) {
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failed = true;
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break;
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}
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} else if ( testBits != i ) {
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failed = true;
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break;
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}
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}
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for ( float i = -max * 2.0f; i < max * 2.0f; ) {
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unsigned int testBits = idMath::FloatToBits( i, exponentBits, mantissaBits );
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float testFloat = idMath::BitsToFloat( testBits, exponentBits, mantissaBits );
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// it will have already passed the test of bit->float for this value, if
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// FloatToBits has returned anything in the valid range
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unsigned int minForThisExp = testBits - ( testBits & mantissaBits ) + 1;
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float minError = idMath::Fabs( idMath::BitsToFloat( minForThisExp, exponentBits, mantissaBits ) );
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if ( i < -max ) {
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if ( testFloat != -max ) {
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failed = true;
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break;
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}
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} else if ( i > max ) {
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if ( testFloat != max ) {
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failed = true;
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break;
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}
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} else if ( i > -min && i < min ) {
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if ( testFloat != 0.0f ) {
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failed = true;
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break;
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}
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} else {
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float error = idMath::Fabs( i - testFloat );
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if ( error > minError ) {
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failed = true;
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break;
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}
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}
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i += minError;
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}
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if ( failed ) {
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numFails++;
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sprintf( testBuf, "FAILED\n" );
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} else {
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sprintf( testBuf, "PASSED\n" );
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}
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#ifdef _WIN32
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OutputDebugString( testBuf );
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#else
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printf( "%s", testBuf );
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#endif
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}
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}
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sprintf( testBuf, "%i tests failed\n", numFails );
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#ifdef _WIN32
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OutputDebugString( testBuf );
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#else
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printf( "%s", testBuf );
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#endif
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}
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// ================================================================================================
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// jscott: fast and reliable random routines
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// ================================================================================================
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unsigned long rvRandom::mSeed;
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float rvRandom::flrand( float min, float max )
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{
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float result;
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mSeed = ( mSeed * 214013L ) + 2531011;
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// Note: the shift and divide cannot be combined as this breaks the routine
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result = ( float )( mSeed >> 17 ); // 0 - 32767 range
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result = ( ( result * ( max - min ) ) * ( 1.0f / 32768.0f ) ) + min;
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return( result );
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}
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float rvRandom::flrand() {
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return flrand( 0.0f, 1.0f );
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}
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float rvRandom::flrand( const idVec2& v ) {
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return flrand( v[0], v[1] );
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}
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int rvRandom::irand( int min, int max )
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{
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int result;
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max++;
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mSeed = ( mSeed * 214013L ) + 2531011;
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result = mSeed >> 17;
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result = ( ( result * ( max - min ) ) >> 15 ) + min;
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return( result );
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}
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// Try to get a seed independent of the random number system
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int rvRandom::Init( void )
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{
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mSeed *= ( unsigned long )sys->Milliseconds();
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return( mSeed );
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}
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// ================================================================================================
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// Barycentric texture coordinate functions
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// Get the *SIGNED* area of a triangle required for barycentric
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// ================================================================================================
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float idMath::BarycentricTriangleArea( const idVec3 &normal, const idVec3 &a, const idVec3 &b, const idVec3 &c )
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{
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idVec3 v1, v2;
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idVec3 cross;
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float area;
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v1 = b - a;
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v2 = c - a;
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cross = v1.Cross( v2 );
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area = 0.5f * ( cross * normal );
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return( area );
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}
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void idMath::BarycentricEvaluate( idVec2 &result, const idVec3 &point, const idVec3 &normal, const float area, const idVec3 t[3], const idVec2 tc[3] )
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{
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float b1, b2, b3;
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float scale = 1.f;
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scale /= area;
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b1 = idMath::BarycentricTriangleArea( normal, point, t[1], t[2] );
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b2 = idMath::BarycentricTriangleArea( normal, t[0], point, t[2] );
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b3 = idMath::BarycentricTriangleArea( normal, t[0], t[1], point );
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result[0] = ( ( b1 * tc[0][0] ) + ( b2 * tc[1][0] ) + ( b3 * tc[2][0] ) ) * scale;
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result[1] = ( ( b1 * tc[0][1] ) + ( b2 * tc[1][1] ) + ( b3 * tc[2][1] ) ) * scale;
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}
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void idMath::BarycentricEvaluate( idVec2 &result, const idVec3 &point, const idVec3 &normal, const float area, const idVec3 t[3], const short tc[ 3 ][ 2 ], float scale ) {
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float b1, b2, b3;
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scale /= area;
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b1 = idMath::BarycentricTriangleArea( normal, point, t[1], t[2] );
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b2 = idMath::BarycentricTriangleArea( normal, t[0], point, t[2] );
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b3 = idMath::BarycentricTriangleArea( normal, t[0], t[1], point );
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result[0] = ( ( b1 * tc[0][0] ) + ( b2 * tc[1][0] ) + ( b3 * tc[2][0] ) ) * scale;
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result[1] = ( ( b1 * tc[0][1] ) + ( b2 * tc[1][1] ) + ( b3 * tc[2][1] ) ) * scale;
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}
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