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+//
+// Copyright (c) 2002-2013 The ANGLE Project Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+//
+
+// mathutil.h: Math and bit manipulation functions.
+
+#ifndef COMMON_MATHUTIL_H_
+#define COMMON_MATHUTIL_H_
+
+#include <limits>
+#include <algorithm>
+#include <math.h>
+#include <string.h>
+#include <stdint.h>
+#include <stdlib.h>
+
+#include <base/numerics/safe_math.h>
+
+#include "common/debug.h"
+#include "common/platform.h"
+
+namespace angle
+{
+using base::CheckedNumeric;
+using base::IsValueInRangeForNumericType;
+}
+
+namespace gl
+{
+
+const unsigned int Float32One = 0x3F800000;
+const unsigned short Float16One = 0x3C00;
+
+struct Vector4
+{
+ Vector4() {}
+ Vector4(float x, float y, float z, float w) : x(x), y(y), z(z), w(w) {}
+
+ float x;
+ float y;
+ float z;
+ float w;
+};
+
+struct Vector2
+{
+ Vector2() {}
+ Vector2(float x, float y) : x(x), y(y) {}
+
+ float x;
+ float y;
+};
+
+inline bool isPow2(int x)
+{
+ return (x & (x - 1)) == 0 && (x != 0);
+}
+
+inline int log2(int x)
+{
+ int r = 0;
+ while ((x >> r) > 1) r++;
+ return r;
+}
+
+inline unsigned int ceilPow2(unsigned int x)
+{
+ if (x != 0) x--;
+ x |= x >> 1;
+ x |= x >> 2;
+ x |= x >> 4;
+ x |= x >> 8;
+ x |= x >> 16;
+ x++;
+
+ return x;
+}
+
+inline int clampToInt(unsigned int x)
+{
+ return static_cast<int>(std::min(x, static_cast<unsigned int>(std::numeric_limits<int>::max())));
+}
+
+template <typename DestT, typename SrcT>
+inline DestT clampCast(SrcT value)
+{
+ static const DestT destLo = std::numeric_limits<DestT>::min();
+ static const DestT destHi = std::numeric_limits<DestT>::max();
+ static const SrcT srcLo = static_cast<SrcT>(destLo);
+ static const SrcT srcHi = static_cast<SrcT>(destHi);
+
+ // When value is outside of or equal to the limits for DestT we use the DestT limit directly.
+ // This avoids undefined behaviors due to loss of precision when converting from floats to
+ // integers:
+ // destHi for ints is 2147483647 but the closest float number is around 2147483648, so when
+ // doing a conversion from float to int we run into an UB because the float is outside of the
+ // range representable by the int.
+ if (value <= srcLo)
+ {
+ return destLo;
+ }
+ else if (value >= srcHi)
+ {
+ return destHi;
+ }
+ else
+ {
+ return static_cast<DestT>(value);
+ }
+}
+
+template<typename T, typename MIN, typename MAX>
+inline T clamp(T x, MIN min, MAX max)
+{
+ // Since NaNs fail all comparison tests, a NaN value will default to min
+ return x > min ? (x > max ? max : x) : min;
+}
+
+inline float clamp01(float x)
+{
+ return clamp(x, 0.0f, 1.0f);
+}
+
+template<const int n>
+inline unsigned int unorm(float x)
+{
+ const unsigned int max = 0xFFFFFFFF >> (32 - n);
+
+ if (x > 1)
+ {
+ return max;
+ }
+ else if (x < 0)
+ {
+ return 0;
+ }
+ else
+ {
+ return (unsigned int)(max * x + 0.5f);
+ }
+}
+
+inline bool supportsSSE2()
+{
+#if defined(ANGLE_USE_SSE)
+ static bool checked = false;
+ static bool supports = false;
+
+ if (checked)
+ {
+ return supports;
+ }
+
+#if defined(ANGLE_PLATFORM_WINDOWS) && !defined(_M_ARM)
+ {
+ int info[4];
+ __cpuid(info, 0);
+
+ if (info[0] >= 1)
+ {
+ __cpuid(info, 1);
+
+ supports = (info[3] >> 26) & 1;
+ }
+ }
+#endif // defined(ANGLE_PLATFORM_WINDOWS) && !defined(_M_ARM)
+ checked = true;
+ return supports;
+#else // defined(ANGLE_USE_SSE)
+ return false;
+#endif
+}
+
+template <typename destType, typename sourceType>
+destType bitCast(const sourceType &source)
+{
+ size_t copySize = std::min(sizeof(destType), sizeof(sourceType));
+ destType output;
+ memcpy(&output, &source, copySize);
+ return output;
+}
+
+inline unsigned short float32ToFloat16(float fp32)
+{
+ unsigned int fp32i = bitCast<unsigned int>(fp32);
+ unsigned int sign = (fp32i & 0x80000000) >> 16;
+ unsigned int abs = fp32i & 0x7FFFFFFF;
+
+ if(abs > 0x47FFEFFF) // Infinity
+ {
+ return static_cast<unsigned short>(sign | 0x7FFF);
+ }
+ else if(abs < 0x38800000) // Denormal
+ {
+ unsigned int mantissa = (abs & 0x007FFFFF) | 0x00800000;
+ int e = 113 - (abs >> 23);
+
+ if(e < 24)
+ {
+ abs = mantissa >> e;
+ }
+ else
+ {
+ abs = 0;
+ }
+
+ return static_cast<unsigned short>(sign | (abs + 0x00000FFF + ((abs >> 13) & 1)) >> 13);
+ }
+ else
+ {
+ return static_cast<unsigned short>(sign | (abs + 0xC8000000 + 0x00000FFF + ((abs >> 13) & 1)) >> 13);
+ }
+}
+
+float float16ToFloat32(unsigned short h);
+
+unsigned int convertRGBFloatsTo999E5(float red, float green, float blue);
+void convert999E5toRGBFloats(unsigned int input, float *red, float *green, float *blue);
+
+inline unsigned short float32ToFloat11(float fp32)
+{
+ const unsigned int float32MantissaMask = 0x7FFFFF;
+ const unsigned int float32ExponentMask = 0x7F800000;
+ const unsigned int float32SignMask = 0x80000000;
+ const unsigned int float32ValueMask = ~float32SignMask;
+ const unsigned int float32ExponentFirstBit = 23;
+ const unsigned int float32ExponentBias = 127;
+
+ const unsigned short float11Max = 0x7BF;
+ const unsigned short float11MantissaMask = 0x3F;
+ const unsigned short float11ExponentMask = 0x7C0;
+ const unsigned short float11BitMask = 0x7FF;
+ const unsigned int float11ExponentBias = 14;
+
+ const unsigned int float32Maxfloat11 = 0x477E0000;
+ const unsigned int float32Minfloat11 = 0x38800000;
+
+ const unsigned int float32Bits = bitCast<unsigned int>(fp32);
+ const bool float32Sign = (float32Bits & float32SignMask) == float32SignMask;
+
+ unsigned int float32Val = float32Bits & float32ValueMask;
+
+ if ((float32Val & float32ExponentMask) == float32ExponentMask)
+ {
+ // INF or NAN
+ if ((float32Val & float32MantissaMask) != 0)
+ {
+ return float11ExponentMask | (((float32Val >> 17) | (float32Val >> 11) | (float32Val >> 6) | (float32Val)) & float11MantissaMask);
+ }
+ else if (float32Sign)
+ {
+ // -INF is clamped to 0 since float11 is positive only
+ return 0;
+ }
+ else
+ {
+ return float11ExponentMask;
+ }
+ }
+ else if (float32Sign)
+ {
+ // float11 is positive only, so clamp to zero
+ return 0;
+ }
+ else if (float32Val > float32Maxfloat11)
+ {
+ // The number is too large to be represented as a float11, set to max
+ return float11Max;
+ }
+ else
+ {
+ if (float32Val < float32Minfloat11)
+ {
+ // The number is too small to be represented as a normalized float11
+ // Convert it to a denormalized value.
+ const unsigned int shift = (float32ExponentBias - float11ExponentBias) - (float32Val >> float32ExponentFirstBit);
+ float32Val = ((1 << float32ExponentFirstBit) | (float32Val & float32MantissaMask)) >> shift;
+ }
+ else
+ {
+ // Rebias the exponent to represent the value as a normalized float11
+ float32Val += 0xC8000000;
+ }
+
+ return ((float32Val + 0xFFFF + ((float32Val >> 17) & 1)) >> 17) & float11BitMask;
+ }
+}
+
+inline unsigned short float32ToFloat10(float fp32)
+{
+ const unsigned int float32MantissaMask = 0x7FFFFF;
+ const unsigned int float32ExponentMask = 0x7F800000;
+ const unsigned int float32SignMask = 0x80000000;
+ const unsigned int float32ValueMask = ~float32SignMask;
+ const unsigned int float32ExponentFirstBit = 23;
+ const unsigned int float32ExponentBias = 127;
+
+ const unsigned short float10Max = 0x3DF;
+ const unsigned short float10MantissaMask = 0x1F;
+ const unsigned short float10ExponentMask = 0x3E0;
+ const unsigned short float10BitMask = 0x3FF;
+ const unsigned int float10ExponentBias = 14;
+
+ const unsigned int float32Maxfloat10 = 0x477C0000;
+ const unsigned int float32Minfloat10 = 0x38800000;
+
+ const unsigned int float32Bits = bitCast<unsigned int>(fp32);
+ const bool float32Sign = (float32Bits & float32SignMask) == float32SignMask;
+
+ unsigned int float32Val = float32Bits & float32ValueMask;
+
+ if ((float32Val & float32ExponentMask) == float32ExponentMask)
+ {
+ // INF or NAN
+ if ((float32Val & float32MantissaMask) != 0)
+ {
+ return float10ExponentMask | (((float32Val >> 18) | (float32Val >> 13) | (float32Val >> 3) | (float32Val)) & float10MantissaMask);
+ }
+ else if (float32Sign)
+ {
+ // -INF is clamped to 0 since float11 is positive only
+ return 0;
+ }
+ else
+ {
+ return float10ExponentMask;
+ }
+ }
+ else if (float32Sign)
+ {
+ // float10 is positive only, so clamp to zero
+ return 0;
+ }
+ else if (float32Val > float32Maxfloat10)
+ {
+ // The number is too large to be represented as a float11, set to max
+ return float10Max;
+ }
+ else
+ {
+ if (float32Val < float32Minfloat10)
+ {
+ // The number is too small to be represented as a normalized float11
+ // Convert it to a denormalized value.
+ const unsigned int shift = (float32ExponentBias - float10ExponentBias) - (float32Val >> float32ExponentFirstBit);
+ float32Val = ((1 << float32ExponentFirstBit) | (float32Val & float32MantissaMask)) >> shift;
+ }
+ else
+ {
+ // Rebias the exponent to represent the value as a normalized float11
+ float32Val += 0xC8000000;
+ }
+
+ return ((float32Val + 0x1FFFF + ((float32Val >> 18) & 1)) >> 18) & float10BitMask;
+ }
+}
+
+inline float float11ToFloat32(unsigned short fp11)
+{
+ unsigned short exponent = (fp11 >> 6) & 0x1F;
+ unsigned short mantissa = fp11 & 0x3F;
+
+ if (exponent == 0x1F)
+ {
+ // INF or NAN
+ return bitCast<float>(0x7f800000 | (mantissa << 17));
+ }
+ else
+ {
+ if (exponent != 0)
+ {
+ // normalized
+ }
+ else if (mantissa != 0)
+ {
+ // The value is denormalized
+ exponent = 1;
+
+ do
+ {
+ exponent--;
+ mantissa <<= 1;
+ }
+ while ((mantissa & 0x40) == 0);
+
+ mantissa = mantissa & 0x3F;
+ }
+ else // The value is zero
+ {
+ exponent = static_cast<unsigned short>(-112);
+ }
+
+ return bitCast<float>(((exponent + 112) << 23) | (mantissa << 17));
+ }
+}
+
+inline float float10ToFloat32(unsigned short fp11)
+{
+ unsigned short exponent = (fp11 >> 5) & 0x1F;
+ unsigned short mantissa = fp11 & 0x1F;
+
+ if (exponent == 0x1F)
+ {
+ // INF or NAN
+ return bitCast<float>(0x7f800000 | (mantissa << 17));
+ }
+ else
+ {
+ if (exponent != 0)
+ {
+ // normalized
+ }
+ else if (mantissa != 0)
+ {
+ // The value is denormalized
+ exponent = 1;
+
+ do
+ {
+ exponent--;
+ mantissa <<= 1;
+ }
+ while ((mantissa & 0x20) == 0);
+
+ mantissa = mantissa & 0x1F;
+ }
+ else // The value is zero
+ {
+ exponent = static_cast<unsigned short>(-112);
+ }
+
+ return bitCast<float>(((exponent + 112) << 23) | (mantissa << 18));
+ }
+}
+
+template <typename T>
+inline float normalizedToFloat(T input)
+{
+ static_assert(std::numeric_limits<T>::is_integer, "T must be an integer.");
+
+ const float inverseMax = 1.0f / std::numeric_limits<T>::max();
+ return input * inverseMax;
+}
+
+template <unsigned int inputBitCount, typename T>
+inline float normalizedToFloat(T input)
+{
+ static_assert(std::numeric_limits<T>::is_integer, "T must be an integer.");
+ static_assert(inputBitCount < (sizeof(T) * 8), "T must have more bits than inputBitCount.");
+
+ const float inverseMax = 1.0f / ((1 << inputBitCount) - 1);
+ return input * inverseMax;
+}
+
+template <typename T>
+inline T floatToNormalized(float input)
+{
+ return static_cast<T>(std::numeric_limits<T>::max() * input + 0.5f);
+}
+
+template <unsigned int outputBitCount, typename T>
+inline T floatToNormalized(float input)
+{
+ static_assert(outputBitCount < (sizeof(T) * 8), "T must have more bits than outputBitCount.");
+ return static_cast<T>(((1 << outputBitCount) - 1) * input + 0.5f);
+}
+
+template <unsigned int inputBitCount, unsigned int inputBitStart, typename T>
+inline T getShiftedData(T input)
+{
+ static_assert(inputBitCount + inputBitStart <= (sizeof(T) * 8),
+ "T must have at least as many bits as inputBitCount + inputBitStart.");
+ const T mask = (1 << inputBitCount) - 1;
+ return (input >> inputBitStart) & mask;
+}
+
+template <unsigned int inputBitCount, unsigned int inputBitStart, typename T>
+inline T shiftData(T input)
+{
+ static_assert(inputBitCount + inputBitStart <= (sizeof(T) * 8),
+ "T must have at least as many bits as inputBitCount + inputBitStart.");
+ const T mask = (1 << inputBitCount) - 1;
+ return (input & mask) << inputBitStart;
+}
+
+inline unsigned int CountLeadingZeros(uint32_t x)
+{
+ // Use binary search to find the amount of leading zeros.
+ unsigned int zeros = 32u;
+ uint32_t y;
+
+ y = x >> 16u;
+ if (y != 0)
+ {
+ zeros = zeros - 16u;
+ x = y;
+ }
+ y = x >> 8u;
+ if (y != 0)
+ {
+ zeros = zeros - 8u;
+ x = y;
+ }
+ y = x >> 4u;
+ if (y != 0)
+ {
+ zeros = zeros - 4u;
+ x = y;
+ }
+ y = x >> 2u;
+ if (y != 0)
+ {
+ zeros = zeros - 2u;
+ x = y;
+ }
+ y = x >> 1u;
+ if (y != 0)
+ {
+ return zeros - 2u;
+ }
+ return zeros - x;
+}
+
+inline unsigned char average(unsigned char a, unsigned char b)
+{
+ return ((a ^ b) >> 1) + (a & b);
+}
+
+inline signed char average(signed char a, signed char b)
+{
+ return ((short)a + (short)b) / 2;
+}
+
+inline unsigned short average(unsigned short a, unsigned short b)
+{
+ return ((a ^ b) >> 1) + (a & b);
+}
+
+inline signed short average(signed short a, signed short b)
+{
+ return ((int)a + (int)b) / 2;
+}
+
+inline unsigned int average(unsigned int a, unsigned int b)
+{
+ return ((a ^ b) >> 1) + (a & b);
+}
+
+inline int average(int a, int b)
+{
+ long long average = (static_cast<long long>(a) + static_cast<long long>(b)) / 2ll;
+ return static_cast<int>(average);
+}
+
+inline float average(float a, float b)
+{
+ return (a + b) * 0.5f;
+}
+
+inline unsigned short averageHalfFloat(unsigned short a, unsigned short b)
+{
+ return float32ToFloat16((float16ToFloat32(a) + float16ToFloat32(b)) * 0.5f);
+}
+
+inline unsigned int averageFloat11(unsigned int a, unsigned int b)
+{
+ return float32ToFloat11((float11ToFloat32(static_cast<unsigned short>(a)) + float11ToFloat32(static_cast<unsigned short>(b))) * 0.5f);
+}
+
+inline unsigned int averageFloat10(unsigned int a, unsigned int b)
+{
+ return float32ToFloat10((float10ToFloat32(static_cast<unsigned short>(a)) + float10ToFloat32(static_cast<unsigned short>(b))) * 0.5f);
+}
+
+template <typename T>
+struct Range
+{
+ Range() {}
+ Range(T lo, T hi) : start(lo), end(hi) { ASSERT(lo <= hi); }
+
+ T start;
+ T end;
+
+ T length() const { return end - start; }
+
+ bool intersects(Range<T> other)
+ {
+ if (start <= other.start)
+ {
+ return other.start < end;
+ }
+ else
+ {
+ return start < other.end;
+ }
+ }
+
+ void extend(T value)
+ {
+ start = value > start ? value : start;
+ end = value < end ? value : end;
+ }
+
+ bool empty() const
+ {
+ return end <= start;
+ }
+};
+
+typedef Range<int> RangeI;
+typedef Range<unsigned int> RangeUI;
+
+struct IndexRange
+{
+ IndexRange() : IndexRange(0, 0, 0) {}
+ IndexRange(size_t start_, size_t end_, size_t vertexIndexCount_)
+ : start(start_), end(end_), vertexIndexCount(vertexIndexCount_)
+ {
+ ASSERT(start <= end);
+ }
+
+ // Number of vertices in the range.
+ size_t vertexCount() const { return (end - start) + 1; }
+
+ // Inclusive range of indices that are not primitive restart
+ size_t start;
+ size_t end;
+
+ // Number of non-primitive restart indices
+ size_t vertexIndexCount;
+};
+
+// First, both normalized floating-point values are converted into 16-bit integer values.
+// Then, the results are packed into the returned 32-bit unsigned integer.
+// The first float value will be written to the least significant bits of the output;
+// the last float value will be written to the most significant bits.
+// The conversion of each value to fixed point is done as follows :
+// packSnorm2x16 : round(clamp(c, -1, +1) * 32767.0)
+inline uint32_t packSnorm2x16(float f1, float f2)
+{
+ int16_t leastSignificantBits = static_cast<int16_t>(roundf(clamp(f1, -1.0f, 1.0f) * 32767.0f));
+ int16_t mostSignificantBits = static_cast<int16_t>(roundf(clamp(f2, -1.0f, 1.0f) * 32767.0f));
+ return static_cast<uint32_t>(mostSignificantBits) << 16 |
+ (static_cast<uint32_t>(leastSignificantBits) & 0xFFFF);
+}
+
+// First, unpacks a single 32-bit unsigned integer u into a pair of 16-bit unsigned integers. Then, each
+// component is converted to a normalized floating-point value to generate the returned two float values.
+// The first float value will be extracted from the least significant bits of the input;
+// the last float value will be extracted from the most-significant bits.
+// The conversion for unpacked fixed-point value to floating point is done as follows:
+// unpackSnorm2x16 : clamp(f / 32767.0, -1, +1)
+inline void unpackSnorm2x16(uint32_t u, float *f1, float *f2)
+{
+ int16_t leastSignificantBits = static_cast<int16_t>(u & 0xFFFF);
+ int16_t mostSignificantBits = static_cast<int16_t>(u >> 16);
+ *f1 = clamp(static_cast<float>(leastSignificantBits) / 32767.0f, -1.0f, 1.0f);
+ *f2 = clamp(static_cast<float>(mostSignificantBits) / 32767.0f, -1.0f, 1.0f);
+}
+
+// First, both normalized floating-point values are converted into 16-bit integer values.
+// Then, the results are packed into the returned 32-bit unsigned integer.
+// The first float value will be written to the least significant bits of the output;
+// the last float value will be written to the most significant bits.
+// The conversion of each value to fixed point is done as follows:
+// packUnorm2x16 : round(clamp(c, 0, +1) * 65535.0)
+inline uint32_t packUnorm2x16(float f1, float f2)
+{
+ uint16_t leastSignificantBits = static_cast<uint16_t>(roundf(clamp(f1, 0.0f, 1.0f) * 65535.0f));
+ uint16_t mostSignificantBits = static_cast<uint16_t>(roundf(clamp(f2, 0.0f, 1.0f) * 65535.0f));
+ return static_cast<uint32_t>(mostSignificantBits) << 16 | static_cast<uint32_t>(leastSignificantBits);
+}
+
+// First, unpacks a single 32-bit unsigned integer u into a pair of 16-bit unsigned integers. Then, each
+// component is converted to a normalized floating-point value to generate the returned two float values.
+// The first float value will be extracted from the least significant bits of the input;
+// the last float value will be extracted from the most-significant bits.
+// The conversion for unpacked fixed-point value to floating point is done as follows:
+// unpackUnorm2x16 : f / 65535.0
+inline void unpackUnorm2x16(uint32_t u, float *f1, float *f2)
+{
+ uint16_t leastSignificantBits = static_cast<uint16_t>(u & 0xFFFF);
+ uint16_t mostSignificantBits = static_cast<uint16_t>(u >> 16);
+ *f1 = static_cast<float>(leastSignificantBits) / 65535.0f;
+ *f2 = static_cast<float>(mostSignificantBits) / 65535.0f;
+}
+
+// Returns an unsigned integer obtained by converting the two floating-point values to the 16-bit
+// floating-point representation found in the OpenGL ES Specification, and then packing these
+// two 16-bit integers into a 32-bit unsigned integer.
+// f1: The 16 least-significant bits of the result;
+// f2: The 16 most-significant bits.
+inline uint32_t packHalf2x16(float f1, float f2)
+{
+ uint16_t leastSignificantBits = static_cast<uint16_t>(float32ToFloat16(f1));
+ uint16_t mostSignificantBits = static_cast<uint16_t>(float32ToFloat16(f2));
+ return static_cast<uint32_t>(mostSignificantBits) << 16 | static_cast<uint32_t>(leastSignificantBits);
+}
+
+// Returns two floating-point values obtained by unpacking a 32-bit unsigned integer into a pair of 16-bit values,
+// interpreting those values as 16-bit floating-point numbers according to the OpenGL ES Specification,
+// and converting them to 32-bit floating-point values.
+// The first float value is obtained from the 16 least-significant bits of u;
+// the second component is obtained from the 16 most-significant bits of u.
+inline void unpackHalf2x16(uint32_t u, float *f1, float *f2)
+{
+ uint16_t leastSignificantBits = static_cast<uint16_t>(u & 0xFFFF);
+ uint16_t mostSignificantBits = static_cast<uint16_t>(u >> 16);
+
+ *f1 = float16ToFloat32(leastSignificantBits);
+ *f2 = float16ToFloat32(mostSignificantBits);
+}
+
+// Returns whether the argument is Not a Number.
+// IEEE 754 single precision NaN representation: Exponent(8 bits) - 255, Mantissa(23 bits) - non-zero.
+inline bool isNaN(float f)
+{
+ // Exponent mask: ((1u << 8) - 1u) << 23 = 0x7f800000u
+ // Mantissa mask: ((1u << 23) - 1u) = 0x7fffffu
+ return ((bitCast<uint32_t>(f) & 0x7f800000u) == 0x7f800000u) && (bitCast<uint32_t>(f) & 0x7fffffu);
+}
+
+// Returns whether the argument is infinity.
+// IEEE 754 single precision infinity representation: Exponent(8 bits) - 255, Mantissa(23 bits) - zero.
+inline bool isInf(float f)
+{
+ // Exponent mask: ((1u << 8) - 1u) << 23 = 0x7f800000u
+ // Mantissa mask: ((1u << 23) - 1u) = 0x7fffffu
+ return ((bitCast<uint32_t>(f) & 0x7f800000u) == 0x7f800000u) && !(bitCast<uint32_t>(f) & 0x7fffffu);
+}
+
+namespace priv
+{
+template <unsigned int N, unsigned int R>
+struct iSquareRoot
+{
+ static constexpr unsigned int solve()
+ {
+ return (R * R > N)
+ ? 0
+ : ((R * R == N) ? R : static_cast<unsigned int>(iSquareRoot<N, R + 1>::value));
+ }
+ enum Result
+ {
+ value = iSquareRoot::solve()
+ };
+};
+
+template <unsigned int N>
+struct iSquareRoot<N, N>
+{
+ enum result
+ {
+ value = N
+ };
+};
+
+} // namespace priv
+
+template <unsigned int N>
+constexpr unsigned int iSquareRoot()
+{
+ return priv::iSquareRoot<N, 1>::value;
+}
+
+// Sum, difference and multiplication operations for signed ints that wrap on 32-bit overflow.
+//
+// Unsigned types are defined to do arithmetic modulo 2^n in C++. For signed types, overflow
+// behavior is undefined.
+
+template <typename T>
+inline T WrappingSum(T lhs, T rhs)
+{
+ uint32_t lhsUnsigned = static_cast<uint32_t>(lhs);
+ uint32_t rhsUnsigned = static_cast<uint32_t>(rhs);
+ return static_cast<T>(lhsUnsigned + rhsUnsigned);
+}
+
+template <typename T>
+inline T WrappingDiff(T lhs, T rhs)
+{
+ uint32_t lhsUnsigned = static_cast<uint32_t>(lhs);
+ uint32_t rhsUnsigned = static_cast<uint32_t>(rhs);
+ return static_cast<T>(lhsUnsigned - rhsUnsigned);
+}
+
+inline int32_t WrappingMul(int32_t lhs, int32_t rhs)
+{
+ int64_t lhsWide = static_cast<int64_t>(lhs);
+ int64_t rhsWide = static_cast<int64_t>(rhs);
+ // The multiplication is guaranteed not to overflow.
+ int64_t resultWide = lhsWide * rhsWide;
+ // Implement the desired wrapping behavior by masking out the high-order 32 bits.
+ resultWide = resultWide & 0xffffffffll;
+ // Casting to a narrower signed type is fine since the casted value is representable in the
+ // narrower type.
+ return static_cast<int32_t>(resultWide);
+}
+
+} // namespace gl
+
+namespace rx
+{
+
+template <typename T>
+T roundUp(const T value, const T alignment)
+{
+ auto temp = value + alignment - static_cast<T>(1);
+ return temp - temp % alignment;
+}
+
+template <typename T>
+angle::CheckedNumeric<T> CheckedRoundUp(const T value, const T alignment)
+{
+ angle::CheckedNumeric<T> checkedValue(value);
+ angle::CheckedNumeric<T> checkedAlignment(alignment);
+ return roundUp(checkedValue, checkedAlignment);
+}
+
+inline unsigned int UnsignedCeilDivide(unsigned int value, unsigned int divisor)
+{
+ unsigned int divided = value / divisor;
+ return (divided + ((value % divisor == 0) ? 0 : 1));
+}
+
+#if defined(_MSC_VER)
+
+#define ANGLE_ROTL(x,y) _rotl(x,y)
+#define ANGLE_ROTR16(x,y) _rotr16(x,y)
+
+#else
+
+inline uint32_t RotL(uint32_t x, int8_t r)
+{
+ return (x << r) | (x >> (32 - r));
+}
+
+inline uint16_t RotR16(uint16_t x, int8_t r)
+{
+ return (x >> r) | (x << (16 - r));
+}
+
+#define ANGLE_ROTL(x, y) ::rx::RotL(x, y)
+#define ANGLE_ROTR16(x, y) ::rx::RotR16(x, y)
+
+#endif // namespace rx
+
+}
+
+#endif // COMMON_MATHUTIL_H_
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