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 /*

  * 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 "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