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1 // Copyright 2012 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
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22 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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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_DOUBLE_H_
29 #define DOUBLE_CONVERSION_DOUBLE_H_
30 
31 #include "diy-fp.h"
32 
33 namespace double_conversion {
34 
35 // We assume that doubles and uint64_t have the same endianness.
double_to_uint64(double d)36 static uint64_t double_to_uint64(double d) { return BitCast<uint64_t>(d); }
uint64_to_double(uint64_t d64)37 static double uint64_to_double(uint64_t d64) { return BitCast<double>(d64); }
float_to_uint32(float f)38 static uint32_t float_to_uint32(float f) { return BitCast<uint32_t>(f); }
uint32_to_float(uint32_t d32)39 static float uint32_to_float(uint32_t d32) { return BitCast<float>(d32); }
40 
41 // Helper functions for doubles.
42 class Double {
43  public:
44   static const uint64_t kSignMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x80000000, 00000000);
45   static const uint64_t kExponentMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000);
46   static const uint64_t kSignificandMask = DOUBLE_CONVERSION_UINT64_2PART_C(0x000FFFFF, FFFFFFFF);
47   static const uint64_t kHiddenBit = DOUBLE_CONVERSION_UINT64_2PART_C(0x00100000, 00000000);
48   static const uint64_t kQuietNanBit = DOUBLE_CONVERSION_UINT64_2PART_C(0x00080000, 00000000);
49   static const int kPhysicalSignificandSize = 52;  // Excludes the hidden bit.
50   static const int kSignificandSize = 53;
51   static const int kExponentBias = 0x3FF + kPhysicalSignificandSize;
52   static const int kMaxExponent = 0x7FF - kExponentBias;
53 
Double()54   Double() : d64_(0) {}
Double(double d)55   explicit Double(double d) : d64_(double_to_uint64(d)) {}
Double(uint64_t d64)56   explicit Double(uint64_t d64) : d64_(d64) {}
Double(DiyFp diy_fp)57   explicit Double(DiyFp diy_fp)
58     : d64_(DiyFpToUint64(diy_fp)) {}
59 
60   // The value encoded by this Double must be greater or equal to +0.0.
61   // It must not be special (infinity, or NaN).
AsDiyFp()62   DiyFp AsDiyFp() const {
63     DOUBLE_CONVERSION_ASSERT(Sign() > 0);
64     DOUBLE_CONVERSION_ASSERT(!IsSpecial());
65     return DiyFp(Significand(), Exponent());
66   }
67 
68   // The value encoded by this Double must be strictly greater than 0.
AsNormalizedDiyFp()69   DiyFp AsNormalizedDiyFp() const {
70     DOUBLE_CONVERSION_ASSERT(value() > 0.0);
71     uint64_t f = Significand();
72     int e = Exponent();
73 
74     // The current double could be a denormal.
75     while ((f & kHiddenBit) == 0) {
76       f <<= 1;
77       e--;
78     }
79     // Do the final shifts in one go.
80     f <<= DiyFp::kSignificandSize - kSignificandSize;
81     e -= DiyFp::kSignificandSize - kSignificandSize;
82     return DiyFp(f, e);
83   }
84 
85   // Returns the double's bit as uint64.
AsUint64()86   uint64_t AsUint64() const {
87     return d64_;
88   }
89 
90   // Returns the next greater double. Returns +infinity on input +infinity.
NextDouble()91   double NextDouble() const {
92     if (d64_ == kInfinity) return Double(kInfinity).value();
93     if (Sign() < 0 && Significand() == 0) {
94       // -0.0
95       return 0.0;
96     }
97     if (Sign() < 0) {
98       return Double(d64_ - 1).value();
99     } else {
100       return Double(d64_ + 1).value();
101     }
102   }
103 
PreviousDouble()104   double PreviousDouble() const {
105     if (d64_ == (kInfinity | kSignMask)) return -Infinity();
106     if (Sign() < 0) {
107       return Double(d64_ + 1).value();
108     } else {
109       if (Significand() == 0) return -0.0;
110       return Double(d64_ - 1).value();
111     }
112   }
113 
Exponent()114   int Exponent() const {
115     if (IsDenormal()) return kDenormalExponent;
116 
117     uint64_t d64 = AsUint64();
118     int biased_e =
119         static_cast<int>((d64 & kExponentMask) >> kPhysicalSignificandSize);
120     return biased_e - kExponentBias;
121   }
122 
Significand()123   uint64_t Significand() const {
124     uint64_t d64 = AsUint64();
125     uint64_t significand = d64 & kSignificandMask;
126     if (!IsDenormal()) {
127       return significand + kHiddenBit;
128     } else {
129       return significand;
130     }
131   }
132 
133   // Returns true if the double is a denormal.
IsDenormal()134   bool IsDenormal() const {
135     uint64_t d64 = AsUint64();
136     return (d64 & kExponentMask) == 0;
137   }
138 
139   // We consider denormals not to be special.
140   // Hence only Infinity and NaN are special.
IsSpecial()141   bool IsSpecial() const {
142     uint64_t d64 = AsUint64();
143     return (d64 & kExponentMask) == kExponentMask;
144   }
145 
IsNan()146   bool IsNan() const {
147     uint64_t d64 = AsUint64();
148     return ((d64 & kExponentMask) == kExponentMask) &&
149         ((d64 & kSignificandMask) != 0);
150   }
151 
IsQuietNan()152   bool IsQuietNan() const {
153     return IsNan() && ((AsUint64() & kQuietNanBit) != 0);
154   }
155 
IsSignalingNan()156   bool IsSignalingNan() const {
157     return IsNan() && ((AsUint64() & kQuietNanBit) == 0);
158   }
159 
160 
IsInfinite()161   bool IsInfinite() const {
162     uint64_t d64 = AsUint64();
163     return ((d64 & kExponentMask) == kExponentMask) &&
164         ((d64 & kSignificandMask) == 0);
165   }
166 
Sign()167   int Sign() const {
168     uint64_t d64 = AsUint64();
169     return (d64 & kSignMask) == 0? 1: -1;
170   }
171 
172   // Precondition: the value encoded by this Double must be greater or equal
173   // than +0.0.
UpperBoundary()174   DiyFp UpperBoundary() const {
175     DOUBLE_CONVERSION_ASSERT(Sign() > 0);
176     return DiyFp(Significand() * 2 + 1, Exponent() - 1);
177   }
178 
179   // Computes the two boundaries of this.
180   // The bigger boundary (m_plus) is normalized. The lower boundary has the same
181   // exponent as m_plus.
182   // Precondition: the value encoded by this Double must be greater than 0.
NormalizedBoundaries(DiyFp * out_m_minus,DiyFp * out_m_plus)183   void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
184     DOUBLE_CONVERSION_ASSERT(value() > 0.0);
185     DiyFp v = this->AsDiyFp();
186     DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
187     DiyFp m_minus;
188     if (LowerBoundaryIsCloser()) {
189       m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
190     } else {
191       m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
192     }
193     m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
194     m_minus.set_e(m_plus.e());
195     *out_m_plus = m_plus;
196     *out_m_minus = m_minus;
197   }
198 
LowerBoundaryIsCloser()199   bool LowerBoundaryIsCloser() const {
200     // The boundary is closer if the significand is of the form f == 2^p-1 then
201     // the lower boundary is closer.
202     // Think of v = 1000e10 and v- = 9999e9.
203     // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
204     // at a distance of 1e8.
205     // The only exception is for the smallest normal: the largest denormal is
206     // at the same distance as its successor.
207     // Note: denormals have the same exponent as the smallest normals.
208     bool physical_significand_is_zero = ((AsUint64() & kSignificandMask) == 0);
209     return physical_significand_is_zero && (Exponent() != kDenormalExponent);
210   }
211 
value()212   double value() const { return uint64_to_double(d64_); }
213 
214   // Returns the significand size for a given order of magnitude.
215   // If v = f*2^e with 2^p-1 <= f <= 2^p then p+e is v's order of magnitude.
216   // This function returns the number of significant binary digits v will have
217   // once it's encoded into a double. In almost all cases this is equal to
218   // kSignificandSize. The only exceptions are denormals. They start with
219   // leading zeroes and their effective significand-size is hence smaller.
SignificandSizeForOrderOfMagnitude(int order)220   static int SignificandSizeForOrderOfMagnitude(int order) {
221     if (order >= (kDenormalExponent + kSignificandSize)) {
222       return kSignificandSize;
223     }
224     if (order <= kDenormalExponent) return 0;
225     return order - kDenormalExponent;
226   }
227 
Infinity()228   static double Infinity() {
229     return Double(kInfinity).value();
230   }
231 
NaN()232   static double NaN() {
233     return Double(kNaN).value();
234   }
235 
236  private:
237   static const int kDenormalExponent = -kExponentBias + 1;
238   static const uint64_t kInfinity = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF00000, 00000000);
239   static const uint64_t kNaN = DOUBLE_CONVERSION_UINT64_2PART_C(0x7FF80000, 00000000);
240 
241   const uint64_t d64_;
242 
DiyFpToUint64(DiyFp diy_fp)243   static uint64_t DiyFpToUint64(DiyFp diy_fp) {
244     uint64_t significand = diy_fp.f();
245     int exponent = diy_fp.e();
246     while (significand > kHiddenBit + kSignificandMask) {
247       significand >>= 1;
248       exponent++;
249     }
250     if (exponent >= kMaxExponent) {
251       return kInfinity;
252     }
253     if (exponent < kDenormalExponent) {
254       return 0;
255     }
256     while (exponent > kDenormalExponent && (significand & kHiddenBit) == 0) {
257       significand <<= 1;
258       exponent--;
259     }
260     uint64_t biased_exponent;
261     if (exponent == kDenormalExponent && (significand & kHiddenBit) == 0) {
262       biased_exponent = 0;
263     } else {
264       biased_exponent = static_cast<uint64_t>(exponent + kExponentBias);
265     }
266     return (significand & kSignificandMask) |
267         (biased_exponent << kPhysicalSignificandSize);
268   }
269 
270   DOUBLE_CONVERSION_DISALLOW_COPY_AND_ASSIGN(Double);
271 };
272 
273 class Single {
274  public:
275   static const uint32_t kSignMask = 0x80000000;
276   static const uint32_t kExponentMask = 0x7F800000;
277   static const uint32_t kSignificandMask = 0x007FFFFF;
278   static const uint32_t kHiddenBit = 0x00800000;
279   static const uint32_t kQuietNanBit = 0x00400000;
280   static const int kPhysicalSignificandSize = 23;  // Excludes the hidden bit.
281   static const int kSignificandSize = 24;
282 
Single()283   Single() : d32_(0) {}
Single(float f)284   explicit Single(float f) : d32_(float_to_uint32(f)) {}
Single(uint32_t d32)285   explicit Single(uint32_t d32) : d32_(d32) {}
286 
287   // The value encoded by this Single must be greater or equal to +0.0.
288   // It must not be special (infinity, or NaN).
AsDiyFp()289   DiyFp AsDiyFp() const {
290     DOUBLE_CONVERSION_ASSERT(Sign() > 0);
291     DOUBLE_CONVERSION_ASSERT(!IsSpecial());
292     return DiyFp(Significand(), Exponent());
293   }
294 
295   // Returns the single's bit as uint64.
AsUint32()296   uint32_t AsUint32() const {
297     return d32_;
298   }
299 
Exponent()300   int Exponent() const {
301     if (IsDenormal()) return kDenormalExponent;
302 
303     uint32_t d32 = AsUint32();
304     int biased_e =
305         static_cast<int>((d32 & kExponentMask) >> kPhysicalSignificandSize);
306     return biased_e - kExponentBias;
307   }
308 
Significand()309   uint32_t Significand() const {
310     uint32_t d32 = AsUint32();
311     uint32_t significand = d32 & kSignificandMask;
312     if (!IsDenormal()) {
313       return significand + kHiddenBit;
314     } else {
315       return significand;
316     }
317   }
318 
319   // Returns true if the single is a denormal.
IsDenormal()320   bool IsDenormal() const {
321     uint32_t d32 = AsUint32();
322     return (d32 & kExponentMask) == 0;
323   }
324 
325   // We consider denormals not to be special.
326   // Hence only Infinity and NaN are special.
IsSpecial()327   bool IsSpecial() const {
328     uint32_t d32 = AsUint32();
329     return (d32 & kExponentMask) == kExponentMask;
330   }
331 
IsNan()332   bool IsNan() const {
333     uint32_t d32 = AsUint32();
334     return ((d32 & kExponentMask) == kExponentMask) &&
335         ((d32 & kSignificandMask) != 0);
336   }
337 
IsQuietNan()338   bool IsQuietNan() const {
339     return IsNan() && ((AsUint32() & kQuietNanBit) != 0);
340   }
341 
IsSignalingNan()342   bool IsSignalingNan() const {
343     return IsNan() && ((AsUint32() & kQuietNanBit) == 0);
344   }
345 
346 
IsInfinite()347   bool IsInfinite() const {
348     uint32_t d32 = AsUint32();
349     return ((d32 & kExponentMask) == kExponentMask) &&
350         ((d32 & kSignificandMask) == 0);
351   }
352 
Sign()353   int Sign() const {
354     uint32_t d32 = AsUint32();
355     return (d32 & kSignMask) == 0? 1: -1;
356   }
357 
358   // Computes the two boundaries of this.
359   // The bigger boundary (m_plus) is normalized. The lower boundary has the same
360   // exponent as m_plus.
361   // Precondition: the value encoded by this Single must be greater than 0.
NormalizedBoundaries(DiyFp * out_m_minus,DiyFp * out_m_plus)362   void NormalizedBoundaries(DiyFp* out_m_minus, DiyFp* out_m_plus) const {
363     DOUBLE_CONVERSION_ASSERT(value() > 0.0);
364     DiyFp v = this->AsDiyFp();
365     DiyFp m_plus = DiyFp::Normalize(DiyFp((v.f() << 1) + 1, v.e() - 1));
366     DiyFp m_minus;
367     if (LowerBoundaryIsCloser()) {
368       m_minus = DiyFp((v.f() << 2) - 1, v.e() - 2);
369     } else {
370       m_minus = DiyFp((v.f() << 1) - 1, v.e() - 1);
371     }
372     m_minus.set_f(m_minus.f() << (m_minus.e() - m_plus.e()));
373     m_minus.set_e(m_plus.e());
374     *out_m_plus = m_plus;
375     *out_m_minus = m_minus;
376   }
377 
378   // Precondition: the value encoded by this Single must be greater or equal
379   // than +0.0.
UpperBoundary()380   DiyFp UpperBoundary() const {
381     DOUBLE_CONVERSION_ASSERT(Sign() > 0);
382     return DiyFp(Significand() * 2 + 1, Exponent() - 1);
383   }
384 
LowerBoundaryIsCloser()385   bool LowerBoundaryIsCloser() const {
386     // The boundary is closer if the significand is of the form f == 2^p-1 then
387     // the lower boundary is closer.
388     // Think of v = 1000e10 and v- = 9999e9.
389     // Then the boundary (== (v - v-)/2) is not just at a distance of 1e9 but
390     // at a distance of 1e8.
391     // The only exception is for the smallest normal: the largest denormal is
392     // at the same distance as its successor.
393     // Note: denormals have the same exponent as the smallest normals.
394     bool physical_significand_is_zero = ((AsUint32() & kSignificandMask) == 0);
395     return physical_significand_is_zero && (Exponent() != kDenormalExponent);
396   }
397 
value()398   float value() const { return uint32_to_float(d32_); }
399 
Infinity()400   static float Infinity() {
401     return Single(kInfinity).value();
402   }
403 
NaN()404   static float NaN() {
405     return Single(kNaN).value();
406   }
407 
408  private:
409   static const int kExponentBias = 0x7F + kPhysicalSignificandSize;
410   static const int kDenormalExponent = -kExponentBias + 1;
411   static const int kMaxExponent = 0xFF - kExponentBias;
412   static const uint32_t kInfinity = 0x7F800000;
413   static const uint32_t kNaN = 0x7FC00000;
414 
415   const uint32_t d32_;
416 
417   DOUBLE_CONVERSION_DISALLOW_COPY_AND_ASSIGN(Single);
418 };
419 
420 }  // namespace double_conversion
421 
422 #endif  // DOUBLE_CONVERSION_DOUBLE_H_
423