1 // Copyright 2011 the V8 project authors. All rights reserved.
2 // Use of this source code is governed by a BSD-style license that can be
3 // found in the LICENSE file.
8 #include "src/diy-fp.h"
13 // We assume that doubles and uint64_t have the same endianness.
14 inline uint64_t double_to_uint64(double d) { return bit_cast<uint64_t>(d); }
15 inline double uint64_to_double(uint64_t d64) { return bit_cast<double>(d64); }
17 // Helper functions for doubles.
20 static const uint64_t kSignMask = V8_2PART_UINT64_C(0x80000000, 00000000);
21 static const uint64_t kExponentMask = V8_2PART_UINT64_C(0x7FF00000, 00000000);
22 static const uint64_t kSignificandMask =
23 V8_2PART_UINT64_C(0x000FFFFF, FFFFFFFF);
24 static const uint64_t kHiddenBit = V8_2PART_UINT64_C(0x00100000, 00000000);
25 static const int kPhysicalSignificandSize = 52; // Excludes the hidden bit.
26 static const int kSignificandSize = 53;
29 explicit Double(double d) : d64_(double_to_uint64(d)) {}
30 explicit Double(uint64_t d64) : d64_(d64) {}
31 explicit Double(DiyFp diy_fp)
32 : d64_(DiyFpToUint64(diy_fp)) {}
34 // The value encoded by this Double must be greater or equal to +0.0.
35 // It must not be special (infinity, or NaN).
36 DiyFp AsDiyFp() const {
39 return DiyFp(Significand(), Exponent());
42 // The value encoded by this Double must be strictly greater than 0.
43 DiyFp AsNormalizedDiyFp() const {
44 DCHECK(value() > 0.0);
45 uint64_t f = Significand();
48 // The current double could be a denormal.
49 while ((f & kHiddenBit) == 0) {
53 // Do the final shifts in one go.
54 f <<= DiyFp::kSignificandSize - kSignificandSize;
55 e -= DiyFp::kSignificandSize - kSignificandSize;
59 // Returns the double's bit as uint64.
60 uint64_t AsUint64() const {
64 // Returns the next greater double. Returns +infinity on input +infinity.
65 double NextDouble() const {
66 if (d64_ == kInfinity) return Double(kInfinity).value();
67 if (Sign() < 0 && Significand() == 0) {
72 return Double(d64_ - 1).value();
74 return Double(d64_ + 1).value();
78 int Exponent() const {
79 if (IsDenormal()) return kDenormalExponent;
81 uint64_t d64 = AsUint64();
83 static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
84 return biased_e - kExponentBias;
87 uint64_t Significand() const {
88 uint64_t d64 = AsUint64();
89 uint64_t significand = d64 & kSignificandMask;
91 return significand + kHiddenBit;
97 // Returns true if the double is a denormal.
98 bool IsDenormal() const {
99 uint64_t d64 = AsUint64();
100 return (d64 & kExponentMask) == 0;
103 // We consider denormals not to be special.
104 // Hence only Infinity and NaN are special.
105 bool IsSpecial() const {
106 uint64_t d64 = AsUint64();
107 return (d64 & kExponentMask) == kExponentMask;
110 bool IsInfinite() const {
111 uint64_t d64 = AsUint64();
112 return ((d64 & kExponentMask) == kExponentMask) &&
113 ((d64 & kSignificandMask) == 0);
117 uint64_t d64 = AsUint64();
118 return (d64 & kSignMask) == 0? 1: -1;
121 // Precondition: the value encoded by this Double must be greater or equal
123 DiyFp UpperBoundary() const {
125 return DiyFp(Significand() * 2 + 1, Exponent() - 1);
128 // Returns the two boundaries of this.
129 // The bigger boundary (m_plus) is normalized. The lower boundary has the same
130 // exponent as m_plus.
131 // Precondition: the value encoded by this Double must be greater than 0.
132 void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
133 DCHECK(value() > 0.0);
134 DiyFp v = this->AsDiyFp();
135 bool significand_is_zero = (v.f() == kHiddenBit);
136 DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
138 if (significand_is_zero && v.e() != kDenormalExponent) {
139 // The boundary is closer. Think of v = 1000e10 and v- = 9999e9.
140 // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
141 // at a distance of 1e8.
142 // The only exception is for the smallest normal: the largest denormal is
143 // at the same distance as its successor.
144 // Note: denormals have the same exponent as the smallest normals.
145 m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
147 m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
149 m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
150 m_minus.set_e(m_plus.e());
151 *out_m_plus = m_plus;
152 *out_m_minus = m_minus;
155 double value() const { return uint64_to_double(d64_); }
157 // Returns the significand size for a given order of magnitude.
158 // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
159 // This function returns the number of significant binary digits v will have
160 // once its encoded into a double. In almost all cases this is equal to
161 // kSignificandSize. The only exception are denormals. They start with leading
162 // zeroes and their effective significand-size is hence smaller.
163 static int SignificandSizeForOrderOfMagnitude(int order) {
164 if (order >= (kDenormalExponent + kSignificandSize)) {
165 return kSignificandSize;
167 if (order <= kDenormalExponent) return 0;
168 return order - kDenormalExponent;
172 static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
173 static const int kDenormalExponent = -kExponentBias + 1;
174 static const int kMaxExponent = 0x7FF - kExponentBias;
175 static const uint64_t kInfinity = V8_2PART_UINT64_C(0x7FF00000, 00000000);
179 static uint64_t DiyFpToUint64(DiyFp diy_fp) {
180 uint64_t significand = diy_fp.f();
181 int exponent = diy_fp.e();
182 while (significand > kHiddenBit + kSignificandMask) {
186 if (exponent >= kMaxExponent) {
189 if (exponent < kDenormalExponent) {
192 while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
196 uint64_t biased_exponent;
197 if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
200 biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
202 return (significand & kSignificandMask) |
203 (biased_exponent << kPhysicalSignificandSize);
207 } // namespace internal
210 #endif // V8_DOUBLE_H_