1 // Copyright 2010 the V8 project authors. All rights reserved. 2 // Redistribution and use in source and binary forms, with or without 3 // modification, are permitted provided that the following conditions are 4 // met: 5 // 6 // * Redistributions of source code must retain the above copyright 7 // notice, this list of conditions and the following disclaimer. 8 // * Redistributions in binary form must reproduce the above 9 // copyright notice, this list of conditions and the following 10 // disclaimer in the documentation and/or other materials provided 11 // with the distribution. 12 // * Neither the name of Google Inc. nor the names of its 13 // contributors may be used to endorse or promote products derived 14 // from this software without specific prior written permission. 15 // 16 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 17 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 18 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 19 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT 20 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, 21 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT 22 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, 23 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY 24 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT 25 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE 26 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 27 28 #ifndef DOUBLE_CONVERSION_DIY_FP_H_ 29 #define DOUBLE_CONVERSION_DIY_FP_H_ 30 31 #include "utils.h" 32 33 namespace double_conversion { 34 35 // This "Do It Yourself Floating Point" class implements a floating-point number 36 // with a uint64 significand and an int exponent. Normalized DiyFp numbers will 37 // have the most significant bit of the significand set. 38 // Multiplication and Subtraction do not normalize their results. 39 // DiyFp store only non-negative numbers and are not designed to contain special 40 // doubles (NaN and Infinity). 41 class DiyFp { 42 public: 43 static const int kSignificandSize = 64; 44 DiyFp()45 DiyFp() : f_(0), e_(0) {} DiyFp(const uint64_t significand,const int32_t exponent)46 DiyFp(const uint64_t significand, const int32_t exponent) : f_(significand), e_(exponent) {} 47 48 // this -= other. 49 // The exponents of both numbers must be the same and the significand of this 50 // must be greater or equal than the significand of other. 51 // The result will not be normalized. Subtract(const DiyFp & other)52 void Subtract(const DiyFp& other) { 53 DOUBLE_CONVERSION_ASSERT(e_ == other.e_); 54 DOUBLE_CONVERSION_ASSERT(f_ >= other.f_); 55 f_ -= other.f_; 56 } 57 58 // Returns a - b. 59 // The exponents of both numbers must be the same and a must be greater 60 // or equal than b. The result will not be normalized. Minus(const DiyFp & a,const DiyFp & b)61 static DiyFp Minus(const DiyFp& a, const DiyFp& b) { 62 DiyFp result = a; 63 result.Subtract(b); 64 return result; 65 } 66 67 // this *= other. Multiply(const DiyFp & other)68 void Multiply(const DiyFp& other) { 69 // Simply "emulates" a 128 bit multiplication. 70 // However: the resulting number only contains 64 bits. The least 71 // significant 64 bits are only used for rounding the most significant 64 72 // bits. 73 const uint64_t kM32 = 0xFFFFFFFFU; 74 const uint64_t a = f_ >> 32; 75 const uint64_t b = f_ & kM32; 76 const uint64_t c = other.f_ >> 32; 77 const uint64_t d = other.f_ & kM32; 78 const uint64_t ac = a * c; 79 const uint64_t bc = b * c; 80 const uint64_t ad = a * d; 81 const uint64_t bd = b * d; 82 // By adding 1U << 31 to tmp we round the final result. 83 // Halfway cases will be rounded up. 84 const uint64_t tmp = (bd >> 32) + (ad & kM32) + (bc & kM32) + (1U << 31); 85 e_ += other.e_ + 64; 86 f_ = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32); 87 } 88 89 // returns a * b; Times(const DiyFp & a,const DiyFp & b)90 static DiyFp Times(const DiyFp& a, const DiyFp& b) { 91 DiyFp result = a; 92 result.Multiply(b); 93 return result; 94 } 95 Normalize()96 void Normalize() { 97 DOUBLE_CONVERSION_ASSERT(f_ != 0); 98 uint64_t significand = f_; 99 int32_t exponent = e_; 100 101 // This method is mainly called for normalizing boundaries. In general, 102 // boundaries need to be shifted by 10 bits, and we optimize for this case. 103 const uint64_t k10MSBits = DOUBLE_CONVERSION_UINT64_2PART_C(0xFFC00000, 00000000); 104 while ((significand & k10MSBits) == 0) { 105 significand <<= 10; 106 exponent -= 10; 107 } 108 while ((significand & kUint64MSB) == 0) { 109 significand <<= 1; 110 exponent--; 111 } 112 f_ = significand; 113 e_ = exponent; 114 } 115 Normalize(const DiyFp & a)116 static DiyFp Normalize(const DiyFp& a) { 117 DiyFp result = a; 118 result.Normalize(); 119 return result; 120 } 121 f()122 uint64_t f() const { return f_; } e()123 int32_t e() const { return e_; } 124 set_f(uint64_t new_value)125 void set_f(uint64_t new_value) { f_ = new_value; } set_e(int32_t new_value)126 void set_e(int32_t new_value) { e_ = new_value; } 127 128 private: 129 static const uint64_t kUint64MSB = DOUBLE_CONVERSION_UINT64_2PART_C(0x80000000, 00000000); 130 131 uint64_t f_; 132 int32_t e_; 133 }; 134 135 } // namespace double_conversion 136 137 #endif // DOUBLE_CONVERSION_DIY_FP_H_ 138