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/*
* Copyright 2009, Google Inc.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
*
* * Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* * Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following disclaimer
* in the documentation and/or other materials provided with the
* distribution.
* * Neither the name of Google Inc. nor the names of its
* contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
// The file contains defintions of various math related functions.
#include <math.h>
#include "core/cross/precompile.h"
#include "core/cross/math_utilities.h"
static const float kEpsilon = 0.00001f;
namespace Vectormath {
namespace Aos {
// Creates a perspective projection matrix.
Matrix4 CreatePerspectiveMatrix(float vertical_field_of_view_radians,
float aspect,
float z_near,
float z_far) {
float dz = z_near - z_far;
if (aspect > kEpsilon && fabsf(dz) > kEpsilon) {
float vertical_scale = 1.0f / tanf(vertical_field_of_view_radians / 2.0f);
float horizontal_scale = vertical_scale / aspect;
return Matrix4(Vector4(horizontal_scale, 0.0f, 0.0f, 0.0f),
Vector4(0.0f, vertical_scale, 0.0f, 0.0f),
Vector4(0.0f, 0.0f, z_far / dz, -1.0f),
Vector4(0.0f, 0.0f, z_near * z_far / dz, 0.0f));
}
return Matrix4::identity();
}
// Creates an arbitrary frustum projection matrix.
Matrix4 CreateFrustumMatrix(float left,
float right,
float bottom,
float top,
float z_near,
float z_far) {
float dx = (right - left);
float dy = (top - bottom);
float dz = (z_near - z_far);
if (fabsf(dx) > kEpsilon && fabsf(dy) > kEpsilon && fabsf(dz) > kEpsilon) {
return Matrix4(
Vector4(2.0f * z_near / dx, 0.0f, 0.0f, 0.0f),
Vector4(0.0f, 2.0f * z_near / dy, 0.0f, 0.0f),
Vector4((left + right) / dx, (top + bottom) / dy, z_far / dz, -1.0f),
Vector4(0.0f, 0.0f, z_near * z_far / dz, 0.0f));
}
return Matrix4::identity();
}
// Creates an orthographic projection matrix.
Matrix4 CreateOrthographicMatrix(float left,
float right,
float bottom,
float top,
float z_near,
float z_far) {
if (fabsf(left - right) > kEpsilon &&
fabsf(top - bottom) > kEpsilon &&
fabsf(z_near - z_far) > kEpsilon) {
return Matrix4(
Vector4(2.0f / (right - left), 0.0f, 0.0f, 0.0f),
Vector4(0.0f, 2.0f / (top - bottom), 0.0f, 0.0f),
Vector4(0.0f, 0.0f, 1.0f / (z_near - z_far), 0.0f),
Vector4((left + right) / (left - right),
(top + bottom) / (bottom - top),
z_near / (z_near - z_far),
1.0f));
}
return Matrix4::identity();
}
namespace {
// -15 stored using a single precision bias of 127
const unsigned kHalfFloatMinBiasedExpAsSingleFpExponent = 0x38000000u;
// max exponent value in single precision that will be converted
// to Inf or Nan when stored as a half-float
const unsigned kHalfFloatMaxBiasedExpAsSingleFpExponent = 0x47800000u;
// 255 is the max exponent biased value
const unsigned kFloatMaxBiasedExponent = (0xFFu << 23);
const unsigned kHalfFloatMaxBiasedExponent = (0x1Fu << 10);
} // anonymous namespace
uint16 FloatToHalf(float value) {
union FloatAndUInt {
float f;
unsigned u;
} temp;
temp.f = value;
unsigned v = temp.u;
unsigned sign = static_cast<uint16>(v >> 31);
unsigned mantissa;
unsigned exponent;
uint16 half;
// get mantissa
mantissa = v & ((1 << 23) - 1);
// get exponent bits
exponent = v & kFloatMaxBiasedExponent;
if (exponent >= kHalfFloatMaxBiasedExpAsSingleFpExponent) {
// check if the original single precision float number is a NaN
if (mantissa && (exponent == kFloatMaxBiasedExponent)) {
// we have a single precision NaN
mantissa = (1 << 23) - 1;
} else {
// 16-bit half-float representation stores number as Inf
mantissa = 0;
}
half = (static_cast<uint16>(sign) << 15) |
static_cast<uint16>(kHalfFloatMaxBiasedExponent) |
static_cast<uint16>(mantissa >> 13);
// check if exponent is <= -15
} else if (exponent <= kHalfFloatMinBiasedExpAsSingleFpExponent) {
// store a denorm half-float value or zero
exponent = (kHalfFloatMinBiasedExpAsSingleFpExponent -
exponent) >> 23;
mantissa >>= (14 + exponent);
half = (static_cast<uint16>(sign) << 15) |
static_cast<uint16>(mantissa);
} else {
half =
(static_cast<uint16>(sign) << 15) |
static_cast<uint16>(
(exponent - kHalfFloatMinBiasedExpAsSingleFpExponent) >> 13) |
static_cast<uint16>(mantissa >> 13);
}
return half;
}
float HalfToFloat(uint16 half) {
unsigned int value;
unsigned int sign = static_cast<unsigned int>(half >> 15);
unsigned int mantissa = static_cast<unsigned int>(half & ((1 << 10) - 1));
unsigned int exponent = static_cast<unsigned int>(
half & kHalfFloatMaxBiasedExponent);
if (exponent == kHalfFloatMaxBiasedExponent) {
// we have a half-float NaN or Inf
// half-float NaNs will be converted to a single precision NaN
// half-float Infs will be converted to a single precision Inf
exponent = kFloatMaxBiasedExponent;
if (mantissa)
mantissa = (1 << 23) - 1; // set all bits to indicate a NaN
} else if (exponent == 0x0) {
// convert half-float zero/denorm to single precision value
if (mantissa) {
mantissa <<= 1;
exponent = kHalfFloatMinBiasedExpAsSingleFpExponent;
// check for leading 1 in denorm mantissa
while ((mantissa & (1 << 10)) == 0) {
// for every leading 0, decrement single precision exponent by 1
// and shift half-float mantissa value to the left
mantissa <<= 1;
exponent -= (1 << 23);
}
// clamp the mantissa to 10-bits
mantissa &= ((1 << 10) - 1);
// shift left to generate single-precision mantissa of 23-bits
mantissa <<= 13;
}
} else {
// shift left to generate single-precision mantissa of 23-bits
mantissa <<= 13;
// generate single precision biased exponent value
exponent = (exponent << 13) + kHalfFloatMinBiasedExpAsSingleFpExponent;
}
value = (sign << 31) | exponent | mantissa;
return *((float *)&value);
}
} // namespace Vectormath
} // namespace Aos
namespace o3d {
float FrobeniusNorm(const Matrix3& matrix) {
Matrix3 elementsSquared = mulPerElem(matrix, matrix);
Vector3 ones(1, 1, 1);
float sumOfElementsSquared = 0.0f;
for (int i = 0; i < 3; ++i) {
sumOfElementsSquared += dot(ones, elementsSquared.getCol(i));
}
return sqrtf(sumOfElementsSquared);
}
float FrobeniusNorm(const Matrix4& matrix) {
Matrix4 elementsSquared = mulPerElem(matrix, matrix);
Vector4 ones(1, 1, 1, 1);
float sumOfElementsSquared = 0.0f;
for (int i = 0; i < 4; ++i) {
sumOfElementsSquared += dot(ones, elementsSquared.getCol(i));
}
return sqrtf(sumOfElementsSquared);
}
} // namespace o3d
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