/*
* Copyright 2012 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#ifndef SkFloatUtils_DEFINED
#define SkFloatUtils_DEFINED
#include "include/core/SkTypes.h"
#include <limits.h>
#include <
float.h>
template <size_t size>
class SkTypeWithSize {
public:
// Prevents using SkTypeWithSize<N> with non-specialized N.
typedef void UInt;
};
template <>
class SkTypeWithSize<32> {
public:
typedef uint32_t UInt;
};
template <>
class SkTypeWithSize<64> {
public:
typedef uint64_t UInt;
};
template <
typename RawType>
struct SkNumericLimits {
static const int digits = 0;
};
template <>
struct SkNumericLimits<
double> {
static const int digits = DBL_MANT_DIG;
};
template <>
struct SkNumericLimits<
float> {
static const int digits = FLT_MANT_DIG;
};
//See
//http://stackoverflow.com/questions/17333/most-effective-way-for-float-and-double-comparison/3423299#3423299
//http://code.google.com/p/googletest/source/browse/trunk/include/gtest/internal/gtest-internal.h
//http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm
template <
typename RawType,
unsigned int ULPs>
class SkFloatingPoint {
public:
/** Bits is a unsigned integer the same size as the floating point number. */
typedef typename SkTypeWithSize<
sizeof(RawType) * CHAR_BIT>::UInt Bits;
/** # of bits in a number. */
static const size_t kBitCount = CHAR_BIT *
sizeof(RawType);
/** # of fraction bits in a number. */
static const size_t kFractionBitCount = SkNumericLimits<RawType>::digits - 1;
/** # of exponent bits in a number. */
static const size_t kExponentBitCount = kBitCount - 1 - kFractionBitCount;
/** The mask for the sign bit. */
static const Bits kSignBitMask =
static_cast<Bits>(1) << (kBitCount - 1);
/** The mask for the fraction bits. */
static const Bits kFractionBitMask =
~
static_cast<Bits>(0) >> (kExponentBitCount + 1);
/** The mask for the exponent bits. */
static const Bits kExponentBitMask = ~(kSignBitMask | kFractionBitMask);
/** How many ULP's (Units in the Last Place) to tolerate when comparing. */
static const size_t kMaxUlps = ULPs;
/**
* Constructs a FloatingPoint from a raw floating-point number.
*
* On an Intel CPU, passing a non-normalized NAN (Not a Number)
* around may change its bits, although the new value is guaranteed
* to be also a NAN. Therefore, don't expect this constructor to
* preserve the bits in x when x is a NAN.
*/
explicit SkFloatingPoint(
const RawType& x) { fU.value = x; }
/** Returns the exponent bits of this number. */
Bits exponent_bits()
const {
return kExponentBitMask & fU.bits; }
/** Returns the fraction bits of this number. */
Bits fraction_bits()
const {
return kFractionBitMask & fU.bits; }
/** Returns true iff this is NAN (not a number). */
bool is_nan()
const {
// It's a NAN if both of the folloowing are true:
// * the exponent bits are all ones
// * the fraction bits are not all zero.
return (exponent_bits() == kExponentBitMask) && (fraction_bits() != 0);
}
/**
* Returns true iff this number is at most kMaxUlps ULP's away from ths.
* In particular, this function:
* - returns false if either number is (or both are) NAN.
* - treats really large numbers as almost equal to infinity.
* - thinks +0.0 and -0.0 are 0 DLP's apart.
*/
bool AlmostEquals(
const SkFloatingPoint& rhs)
const {
// Any comparison operation involving a NAN must return false.
if (is_nan() || rhs.is_nan())
return false;
const Bits dist = DistanceBetweenSignAndMagnitudeNumbers(fU.bits,
rhs.fU.bits);
//SkDEBUGF("(%f, %f, %d) ", u_.value_, rhs.u_.value_, dist);
return dist <= kMaxUlps;
}
private:
/** The data type used to store the actual floating-point number. */
union FloatingPointUnion {
/** The raw floating-point number. */
RawType value;
/** The bits that represent the number. */
Bits bits;
};
/**
* Converts an integer from the sign-and-magnitude representation to
* the biased representation. More precisely, let N be 2 to the
* power of (kBitCount - 1), an integer x is represented by the
* unsigned number x + N.
*
* For instance,
*
* -N + 1 (the most negative number representable using
* sign-and-magnitude) is represented by 1;
* 0 is represented by N; and
* N - 1 (the biggest number representable using
* sign-and-magnitude) is represented by 2N - 1.
*
* Read http://en.wikipedia.org/wiki/Signed_number_representations
* for more details on signed number representations.
*/
static Bits SignAndMagnitudeToBiased(
const Bits &sam) {
if (kSignBitMask & sam) {
// sam represents a negative number.
return ~sam + 1;
}
else {
// sam represents a positive number.
return kSignBitMask | sam;
}
}
/**
* Given two numbers in the sign-and-magnitude representation,
* returns the distance between them as an unsigned number.
*/
static Bits DistanceBetweenSignAndMagnitudeNumbers(
const Bits &sam1,
const Bits &sam2) {
const Bits biased1 = SignAndMagnitudeToBiased(sam1);
const Bits biased2 = SignAndMagnitudeToBiased(sam2);
return (biased1 >= biased2) ? (biased1 - biased2) : (biased2 - biased1);
}
FloatingPointUnion fU;
};
#endif
