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0001 // Copyright 2010 the V8 project authors. All rights reserved.
0002 // Redistribution and use in source and binary forms, with or without
0003 // modification, are permitted provided that the following conditions are
0004 // met:
0005 //
0006 //     * Redistributions of source code must retain the above copyright
0007 //       notice, this list of conditions and the following disclaimer.
0008 //     * Redistributions in binary form must reproduce the above
0009 //       copyright notice, this list of conditions and the following
0010 //       disclaimer in the documentation and/or other materials provided
0011 //       with the distribution.
0012 //     * Neither the name of Google Inc. nor the names of its
0013 //       contributors may be used to endorse or promote products derived
0014 //       from this software without specific prior written permission.
0015 //
0016 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
0017 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
0018 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
0019 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
0020 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
0021 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
0022 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
0023 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
0024 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
0025 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
0026 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
0027 
0028 #ifndef DOUBLE_CONVERSION_DIY_FP_H_
0029 #define DOUBLE_CONVERSION_DIY_FP_H_
0030 
0031 #include "utils.h"
0032 
0033 namespace arrow_vendored {
0034 namespace double_conversion {
0035 
0036 // This "Do It Yourself Floating Point" class implements a floating-point number
0037 // with a uint64 significand and an int exponent. Normalized DiyFp numbers will
0038 // have the most significant bit of the significand set.
0039 // Multiplication and Subtraction do not normalize their results.
0040 // DiyFp store only non-negative numbers and are not designed to contain special
0041 // doubles (NaN and Infinity).
0042 class DiyFp {
0043  public:
0044   static const int kSignificandSize = 64;
0045 
0046   DiyFp() : f_(0), e_(0) {}
0047   DiyFp(const uint64_t significand, const int32_t exponent) : f_(significand), e_(exponent) {}
0048 
0049   // this -= other.
0050   // The exponents of both numbers must be the same and the significand of this
0051   // must be greater or equal than the significand of other.
0052   // The result will not be normalized.
0053   void Subtract(const DiyFp& other) {
0054     DOUBLE_CONVERSION_ASSERT(e_ == other.e_);
0055     DOUBLE_CONVERSION_ASSERT(f_ >= other.f_);
0056     f_ -= other.f_;
0057   }
0058 
0059   // Returns a - b.
0060   // The exponents of both numbers must be the same and a must be greater
0061   // or equal than b. The result will not be normalized.
0062   static DiyFp Minus(const DiyFp& a, const DiyFp& b) {
0063     DiyFp result = a;
0064     result.Subtract(b);
0065     return result;
0066   }
0067 
0068   // this *= other.
0069   void Multiply(const DiyFp& other) {
0070     // Simply "emulates" a 128 bit multiplication.
0071     // However: the resulting number only contains 64 bits. The least
0072     // significant 64 bits are only used for rounding the most significant 64
0073     // bits.
0074     const uint64_t kM32 = 0xFFFFFFFFU;
0075     const uint64_t a = f_ >> 32;
0076     const uint64_t b = f_ & kM32;
0077     const uint64_t c = other.f_ >> 32;
0078     const uint64_t d = other.f_ & kM32;
0079     const uint64_t ac = a * c;
0080     const uint64_t bc = b * c;
0081     const uint64_t ad = a * d;
0082     const uint64_t bd = b * d;
0083     // By adding 1U << 31 to tmp we round the final result.
0084     // Halfway cases will be rounded up.
0085     const uint64_t tmp = (bd >> 32) + (ad & kM32) + (bc & kM32) + (1U << 31);
0086     e_ += other.e_ + 64;
0087     f_ = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
0088   }
0089 
0090   // returns a * b;
0091   static DiyFp Times(const DiyFp& a, const DiyFp& b) {
0092     DiyFp result = a;
0093     result.Multiply(b);
0094     return result;
0095   }
0096 
0097   void Normalize() {
0098     DOUBLE_CONVERSION_ASSERT(f_ != 0);
0099     uint64_t significand = f_;
0100     int32_t exponent = e_;
0101 
0102     // This method is mainly called for normalizing boundaries. In general,
0103     // boundaries need to be shifted by 10 bits, and we optimize for this case.
0104     const uint64_t k10MSBits = DOUBLE_CONVERSION_UINT64_2PART_C(0xFFC00000, 00000000);
0105     while ((significand & k10MSBits) == 0) {
0106       significand <<= 10;
0107       exponent -= 10;
0108     }
0109     while ((significand & kUint64MSB) == 0) {
0110       significand <<= 1;
0111       exponent--;
0112     }
0113     f_ = significand;
0114     e_ = exponent;
0115   }
0116 
0117   static DiyFp Normalize(const DiyFp& a) {
0118     DiyFp result = a;
0119     result.Normalize();
0120     return result;
0121   }
0122 
0123   uint64_t f() const { return f_; }
0124   int32_t e() const { return e_; }
0125 
0126   void set_f(uint64_t new_value) { f_ = new_value; }
0127   void set_e(int32_t new_value) { e_ = new_value; }
0128 
0129  private:
0130   static const uint64_t kUint64MSB = DOUBLE_CONVERSION_UINT64_2PART_C(0x80000000, 00000000);
0131 
0132   uint64_t f_;
0133   int32_t e_;
0134 };
0135 
0136 }  // namespace double_conversion
0137 }  // namespace arrow_vendored
0138 
0139 #endif  // DOUBLE_CONVERSION_DIY_FP_H_