1 | //===-- APFloat.cpp - Implement APFloat class -----------------------------===// |
2 | // |
3 | // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
4 | // See https://llvm.org/LICENSE.txt for license information. |
5 | // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
6 | // |
7 | //===----------------------------------------------------------------------===// |
8 | // |
9 | // This file implements a class to represent arbitrary precision floating |
10 | // point values and provide a variety of arithmetic operations on them. |
11 | // |
12 | //===----------------------------------------------------------------------===// |
13 | |
14 | #include "llvm/ADT/APFloat.h" |
15 | #include "llvm/ADT/APSInt.h" |
16 | #include "llvm/ADT/ArrayRef.h" |
17 | #include "llvm/ADT/FloatingPointMode.h" |
18 | #include "llvm/ADT/FoldingSet.h" |
19 | #include "llvm/ADT/Hashing.h" |
20 | #include "llvm/ADT/STLExtras.h" |
21 | #include "llvm/ADT/StringExtras.h" |
22 | #include "llvm/ADT/StringRef.h" |
23 | #include "llvm/Config/llvm-config.h" |
24 | #include "llvm/Support/Debug.h" |
25 | #include "llvm/Support/Error.h" |
26 | #include "llvm/Support/MathExtras.h" |
27 | #include "llvm/Support/raw_ostream.h" |
28 | #include <cstring> |
29 | #include <limits.h> |
30 | |
31 | #define APFLOAT_DISPATCH_ON_SEMANTICS(METHOD_CALL) \ |
32 | do { \ |
33 | if (usesLayout<IEEEFloat>(getSemantics())) \ |
34 | return U.IEEE.METHOD_CALL; \ |
35 | if (usesLayout<DoubleAPFloat>(getSemantics())) \ |
36 | return U.Double.METHOD_CALL; \ |
37 | llvm_unreachable("Unexpected semantics"); \ |
38 | } while (false) |
39 | |
40 | using namespace llvm; |
41 | |
42 | /// A macro used to combine two fcCategory enums into one key which can be used |
43 | /// in a switch statement to classify how the interaction of two APFloat's |
44 | /// categories affects an operation. |
45 | /// |
46 | /// TODO: If clang source code is ever allowed to use constexpr in its own |
47 | /// codebase, change this into a static inline function. |
48 | #define PackCategoriesIntoKey(_lhs, _rhs) ((_lhs) * 4 + (_rhs)) |
49 | |
50 | /* Assumed in hexadecimal significand parsing, and conversion to |
51 | hexadecimal strings. */ |
52 | static_assert(APFloatBase::integerPartWidth % 4 == 0, "Part width must be divisible by 4!" ); |
53 | |
54 | namespace llvm { |
55 | |
56 | // How the nonfinite values Inf and NaN are represented. |
57 | enum class fltNonfiniteBehavior { |
58 | // Represents standard IEEE 754 behavior. A value is nonfinite if the |
59 | // exponent field is all 1s. In such cases, a value is Inf if the |
60 | // significand bits are all zero, and NaN otherwise |
61 | IEEE754, |
62 | |
63 | // This behavior is present in the Float8ExMyFN* types (Float8E4M3FN, |
64 | // Float8E5M2FNUZ, Float8E4M3FNUZ, and Float8E4M3B11FNUZ). There is no |
65 | // representation for Inf, and operations that would ordinarily produce Inf |
66 | // produce NaN instead. |
67 | // The details of the NaN representation(s) in this form are determined by the |
68 | // `fltNanEncoding` enum. We treat all NaNs as quiet, as the available |
69 | // encodings do not distinguish between signalling and quiet NaN. |
70 | NanOnly, |
71 | }; |
72 | |
73 | // How NaN values are represented. This is curently only used in combination |
74 | // with fltNonfiniteBehavior::NanOnly, and using a variant other than IEEE |
75 | // while having IEEE non-finite behavior is liable to lead to unexpected |
76 | // results. |
77 | enum class fltNanEncoding { |
78 | // Represents the standard IEEE behavior where a value is NaN if its |
79 | // exponent is all 1s and the significand is non-zero. |
80 | IEEE, |
81 | |
82 | // Represents the behavior in the Float8E4M3 floating point type where NaN is |
83 | // represented by having the exponent and mantissa set to all 1s. |
84 | // This behavior matches the FP8 E4M3 type described in |
85 | // https://arxiv.org/abs/2209.05433. We treat both signed and unsigned NaNs |
86 | // as non-signalling, although the paper does not state whether the NaN |
87 | // values are signalling or not. |
88 | AllOnes, |
89 | |
90 | // Represents the behavior in Float8E{5,4}E{2,3}FNUZ floating point types |
91 | // where NaN is represented by a sign bit of 1 and all 0s in the exponent |
92 | // and mantissa (i.e. the negative zero encoding in a IEEE float). Since |
93 | // there is only one NaN value, it is treated as quiet NaN. This matches the |
94 | // behavior described in https://arxiv.org/abs/2206.02915 . |
95 | NegativeZero, |
96 | }; |
97 | |
98 | /* Represents floating point arithmetic semantics. */ |
99 | struct fltSemantics { |
100 | /* The largest E such that 2^E is representable; this matches the |
101 | definition of IEEE 754. */ |
102 | APFloatBase::ExponentType maxExponent; |
103 | |
104 | /* The smallest E such that 2^E is a normalized number; this |
105 | matches the definition of IEEE 754. */ |
106 | APFloatBase::ExponentType minExponent; |
107 | |
108 | /* Number of bits in the significand. This includes the integer |
109 | bit. */ |
110 | unsigned int precision; |
111 | |
112 | /* Number of bits actually used in the semantics. */ |
113 | unsigned int sizeInBits; |
114 | |
115 | fltNonfiniteBehavior nonFiniteBehavior = fltNonfiniteBehavior::IEEE754; |
116 | |
117 | fltNanEncoding nanEncoding = fltNanEncoding::IEEE; |
118 | // Returns true if any number described by this semantics can be precisely |
119 | // represented by the specified semantics. Does not take into account |
120 | // the value of fltNonfiniteBehavior. |
121 | bool isRepresentableBy(const fltSemantics &S) const { |
122 | return maxExponent <= S.maxExponent && minExponent >= S.minExponent && |
123 | precision <= S.precision; |
124 | } |
125 | }; |
126 | |
127 | static constexpr fltSemantics semIEEEhalf = {.maxExponent: 15, .minExponent: -14, .precision: 11, .sizeInBits: 16}; |
128 | static constexpr fltSemantics semBFloat = {.maxExponent: 127, .minExponent: -126, .precision: 8, .sizeInBits: 16}; |
129 | static constexpr fltSemantics semIEEEsingle = {.maxExponent: 127, .minExponent: -126, .precision: 24, .sizeInBits: 32}; |
130 | static constexpr fltSemantics semIEEEdouble = {.maxExponent: 1023, .minExponent: -1022, .precision: 53, .sizeInBits: 64}; |
131 | static constexpr fltSemantics semIEEEquad = {.maxExponent: 16383, .minExponent: -16382, .precision: 113, .sizeInBits: 128}; |
132 | static constexpr fltSemantics semFloat8E5M2 = {.maxExponent: 15, .minExponent: -14, .precision: 3, .sizeInBits: 8}; |
133 | static constexpr fltSemantics semFloat8E5M2FNUZ = { |
134 | .maxExponent: 15, .minExponent: -15, .precision: 3, .sizeInBits: 8, .nonFiniteBehavior: fltNonfiniteBehavior::NanOnly, .nanEncoding: fltNanEncoding::NegativeZero}; |
135 | static constexpr fltSemantics semFloat8E4M3FN = { |
136 | .maxExponent: 8, .minExponent: -6, .precision: 4, .sizeInBits: 8, .nonFiniteBehavior: fltNonfiniteBehavior::NanOnly, .nanEncoding: fltNanEncoding::AllOnes}; |
137 | static constexpr fltSemantics semFloat8E4M3FNUZ = { |
138 | .maxExponent: 7, .minExponent: -7, .precision: 4, .sizeInBits: 8, .nonFiniteBehavior: fltNonfiniteBehavior::NanOnly, .nanEncoding: fltNanEncoding::NegativeZero}; |
139 | static constexpr fltSemantics semFloat8E4M3B11FNUZ = { |
140 | .maxExponent: 4, .minExponent: -10, .precision: 4, .sizeInBits: 8, .nonFiniteBehavior: fltNonfiniteBehavior::NanOnly, .nanEncoding: fltNanEncoding::NegativeZero}; |
141 | static constexpr fltSemantics semFloatTF32 = {.maxExponent: 127, .minExponent: -126, .precision: 11, .sizeInBits: 19}; |
142 | static constexpr fltSemantics semX87DoubleExtended = {.maxExponent: 16383, .minExponent: -16382, .precision: 64, .sizeInBits: 80}; |
143 | static constexpr fltSemantics semBogus = {.maxExponent: 0, .minExponent: 0, .precision: 0, .sizeInBits: 0}; |
144 | |
145 | /* The IBM double-double semantics. Such a number consists of a pair of IEEE |
146 | 64-bit doubles (Hi, Lo), where |Hi| > |Lo|, and if normal, |
147 | (double)(Hi + Lo) == Hi. The numeric value it's modeling is Hi + Lo. |
148 | Therefore it has two 53-bit mantissa parts that aren't necessarily adjacent |
149 | to each other, and two 11-bit exponents. |
150 | |
151 | Note: we need to make the value different from semBogus as otherwise |
152 | an unsafe optimization may collapse both values to a single address, |
153 | and we heavily rely on them having distinct addresses. */ |
154 | static constexpr fltSemantics semPPCDoubleDouble = {.maxExponent: -1, .minExponent: 0, .precision: 0, .sizeInBits: 128}; |
155 | |
156 | /* These are legacy semantics for the fallback, inaccrurate implementation of |
157 | IBM double-double, if the accurate semPPCDoubleDouble doesn't handle the |
158 | operation. It's equivalent to having an IEEE number with consecutive 106 |
159 | bits of mantissa and 11 bits of exponent. |
160 | |
161 | It's not equivalent to IBM double-double. For example, a legit IBM |
162 | double-double, 1 + epsilon: |
163 | |
164 | 1 + epsilon = 1 + (1 >> 1076) |
165 | |
166 | is not representable by a consecutive 106 bits of mantissa. |
167 | |
168 | Currently, these semantics are used in the following way: |
169 | |
170 | semPPCDoubleDouble -> (IEEEdouble, IEEEdouble) -> |
171 | (64-bit APInt, 64-bit APInt) -> (128-bit APInt) -> |
172 | semPPCDoubleDoubleLegacy -> IEEE operations |
173 | |
174 | We use bitcastToAPInt() to get the bit representation (in APInt) of the |
175 | underlying IEEEdouble, then use the APInt constructor to construct the |
176 | legacy IEEE float. |
177 | |
178 | TODO: Implement all operations in semPPCDoubleDouble, and delete these |
179 | semantics. */ |
180 | static constexpr fltSemantics semPPCDoubleDoubleLegacy = {.maxExponent: 1023, .minExponent: -1022 + 53, |
181 | .precision: 53 + 53, .sizeInBits: 128}; |
182 | |
183 | const llvm::fltSemantics &APFloatBase::EnumToSemantics(Semantics S) { |
184 | switch (S) { |
185 | case S_IEEEhalf: |
186 | return IEEEhalf(); |
187 | case S_BFloat: |
188 | return BFloat(); |
189 | case S_IEEEsingle: |
190 | return IEEEsingle(); |
191 | case S_IEEEdouble: |
192 | return IEEEdouble(); |
193 | case S_IEEEquad: |
194 | return IEEEquad(); |
195 | case S_PPCDoubleDouble: |
196 | return PPCDoubleDouble(); |
197 | case S_Float8E5M2: |
198 | return Float8E5M2(); |
199 | case S_Float8E5M2FNUZ: |
200 | return Float8E5M2FNUZ(); |
201 | case S_Float8E4M3FN: |
202 | return Float8E4M3FN(); |
203 | case S_Float8E4M3FNUZ: |
204 | return Float8E4M3FNUZ(); |
205 | case S_Float8E4M3B11FNUZ: |
206 | return Float8E4M3B11FNUZ(); |
207 | case S_FloatTF32: |
208 | return FloatTF32(); |
209 | case S_x87DoubleExtended: |
210 | return x87DoubleExtended(); |
211 | } |
212 | llvm_unreachable("Unrecognised floating semantics" ); |
213 | } |
214 | |
215 | APFloatBase::Semantics |
216 | APFloatBase::SemanticsToEnum(const llvm::fltSemantics &Sem) { |
217 | if (&Sem == &llvm::APFloat::IEEEhalf()) |
218 | return S_IEEEhalf; |
219 | else if (&Sem == &llvm::APFloat::BFloat()) |
220 | return S_BFloat; |
221 | else if (&Sem == &llvm::APFloat::IEEEsingle()) |
222 | return S_IEEEsingle; |
223 | else if (&Sem == &llvm::APFloat::IEEEdouble()) |
224 | return S_IEEEdouble; |
225 | else if (&Sem == &llvm::APFloat::IEEEquad()) |
226 | return S_IEEEquad; |
227 | else if (&Sem == &llvm::APFloat::PPCDoubleDouble()) |
228 | return S_PPCDoubleDouble; |
229 | else if (&Sem == &llvm::APFloat::Float8E5M2()) |
230 | return S_Float8E5M2; |
231 | else if (&Sem == &llvm::APFloat::Float8E5M2FNUZ()) |
232 | return S_Float8E5M2FNUZ; |
233 | else if (&Sem == &llvm::APFloat::Float8E4M3FN()) |
234 | return S_Float8E4M3FN; |
235 | else if (&Sem == &llvm::APFloat::Float8E4M3FNUZ()) |
236 | return S_Float8E4M3FNUZ; |
237 | else if (&Sem == &llvm::APFloat::Float8E4M3B11FNUZ()) |
238 | return S_Float8E4M3B11FNUZ; |
239 | else if (&Sem == &llvm::APFloat::FloatTF32()) |
240 | return S_FloatTF32; |
241 | else if (&Sem == &llvm::APFloat::x87DoubleExtended()) |
242 | return S_x87DoubleExtended; |
243 | else |
244 | llvm_unreachable("Unknown floating semantics" ); |
245 | } |
246 | |
247 | const fltSemantics &APFloatBase::IEEEhalf() { return semIEEEhalf; } |
248 | const fltSemantics &APFloatBase::BFloat() { return semBFloat; } |
249 | const fltSemantics &APFloatBase::IEEEsingle() { return semIEEEsingle; } |
250 | const fltSemantics &APFloatBase::IEEEdouble() { return semIEEEdouble; } |
251 | const fltSemantics &APFloatBase::IEEEquad() { return semIEEEquad; } |
252 | const fltSemantics &APFloatBase::PPCDoubleDouble() { |
253 | return semPPCDoubleDouble; |
254 | } |
255 | const fltSemantics &APFloatBase::Float8E5M2() { return semFloat8E5M2; } |
256 | const fltSemantics &APFloatBase::Float8E5M2FNUZ() { return semFloat8E5M2FNUZ; } |
257 | const fltSemantics &APFloatBase::Float8E4M3FN() { return semFloat8E4M3FN; } |
258 | const fltSemantics &APFloatBase::Float8E4M3FNUZ() { return semFloat8E4M3FNUZ; } |
259 | const fltSemantics &APFloatBase::Float8E4M3B11FNUZ() { |
260 | return semFloat8E4M3B11FNUZ; |
261 | } |
262 | const fltSemantics &APFloatBase::FloatTF32() { return semFloatTF32; } |
263 | const fltSemantics &APFloatBase::x87DoubleExtended() { |
264 | return semX87DoubleExtended; |
265 | } |
266 | const fltSemantics &APFloatBase::Bogus() { return semBogus; } |
267 | |
268 | constexpr RoundingMode APFloatBase::rmNearestTiesToEven; |
269 | constexpr RoundingMode APFloatBase::rmTowardPositive; |
270 | constexpr RoundingMode APFloatBase::rmTowardNegative; |
271 | constexpr RoundingMode APFloatBase::rmTowardZero; |
272 | constexpr RoundingMode APFloatBase::rmNearestTiesToAway; |
273 | |
274 | /* A tight upper bound on number of parts required to hold the value |
275 | pow(5, power) is |
276 | |
277 | power * 815 / (351 * integerPartWidth) + 1 |
278 | |
279 | However, whilst the result may require only this many parts, |
280 | because we are multiplying two values to get it, the |
281 | multiplication may require an extra part with the excess part |
282 | being zero (consider the trivial case of 1 * 1, tcFullMultiply |
283 | requires two parts to hold the single-part result). So we add an |
284 | extra one to guarantee enough space whilst multiplying. */ |
285 | const unsigned int maxExponent = 16383; |
286 | const unsigned int maxPrecision = 113; |
287 | const unsigned int maxPowerOfFiveExponent = maxExponent + maxPrecision - 1; |
288 | const unsigned int maxPowerOfFiveParts = |
289 | 2 + |
290 | ((maxPowerOfFiveExponent * 815) / (351 * APFloatBase::integerPartWidth)); |
291 | |
292 | unsigned int APFloatBase::semanticsPrecision(const fltSemantics &semantics) { |
293 | return semantics.precision; |
294 | } |
295 | APFloatBase::ExponentType |
296 | APFloatBase::semanticsMaxExponent(const fltSemantics &semantics) { |
297 | return semantics.maxExponent; |
298 | } |
299 | APFloatBase::ExponentType |
300 | APFloatBase::semanticsMinExponent(const fltSemantics &semantics) { |
301 | return semantics.minExponent; |
302 | } |
303 | unsigned int APFloatBase::semanticsSizeInBits(const fltSemantics &semantics) { |
304 | return semantics.sizeInBits; |
305 | } |
306 | unsigned int APFloatBase::semanticsIntSizeInBits(const fltSemantics &semantics, |
307 | bool isSigned) { |
308 | // The max FP value is pow(2, MaxExponent) * (1 + MaxFraction), so we need |
309 | // at least one more bit than the MaxExponent to hold the max FP value. |
310 | unsigned int MinBitWidth = semanticsMaxExponent(semantics) + 1; |
311 | // Extra sign bit needed. |
312 | if (isSigned) |
313 | ++MinBitWidth; |
314 | return MinBitWidth; |
315 | } |
316 | |
317 | bool APFloatBase::isRepresentableAsNormalIn(const fltSemantics &Src, |
318 | const fltSemantics &Dst) { |
319 | // Exponent range must be larger. |
320 | if (Src.maxExponent >= Dst.maxExponent || Src.minExponent <= Dst.minExponent) |
321 | return false; |
322 | |
323 | // If the mantissa is long enough, the result value could still be denormal |
324 | // with a larger exponent range. |
325 | // |
326 | // FIXME: This condition is probably not accurate but also shouldn't be a |
327 | // practical concern with existing types. |
328 | return Dst.precision >= Src.precision; |
329 | } |
330 | |
331 | unsigned APFloatBase::getSizeInBits(const fltSemantics &Sem) { |
332 | return Sem.sizeInBits; |
333 | } |
334 | |
335 | static constexpr APFloatBase::ExponentType |
336 | exponentZero(const fltSemantics &semantics) { |
337 | return semantics.minExponent - 1; |
338 | } |
339 | |
340 | static constexpr APFloatBase::ExponentType |
341 | exponentInf(const fltSemantics &semantics) { |
342 | return semantics.maxExponent + 1; |
343 | } |
344 | |
345 | static constexpr APFloatBase::ExponentType |
346 | exponentNaN(const fltSemantics &semantics) { |
347 | if (semantics.nonFiniteBehavior == fltNonfiniteBehavior::NanOnly) { |
348 | if (semantics.nanEncoding == fltNanEncoding::NegativeZero) |
349 | return exponentZero(semantics); |
350 | return semantics.maxExponent; |
351 | } |
352 | return semantics.maxExponent + 1; |
353 | } |
354 | |
355 | /* A bunch of private, handy routines. */ |
356 | |
357 | static inline Error createError(const Twine &Err) { |
358 | return make_error<StringError>(Args: Err, Args: inconvertibleErrorCode()); |
359 | } |
360 | |
361 | static constexpr inline unsigned int partCountForBits(unsigned int bits) { |
362 | return ((bits) + APFloatBase::integerPartWidth - 1) / APFloatBase::integerPartWidth; |
363 | } |
364 | |
365 | /* Returns 0U-9U. Return values >= 10U are not digits. */ |
366 | static inline unsigned int |
367 | decDigitValue(unsigned int c) |
368 | { |
369 | return c - '0'; |
370 | } |
371 | |
372 | /* Return the value of a decimal exponent of the form |
373 | [+-]ddddddd. |
374 | |
375 | If the exponent overflows, returns a large exponent with the |
376 | appropriate sign. */ |
377 | static Expected<int> readExponent(StringRef::iterator begin, |
378 | StringRef::iterator end) { |
379 | bool isNegative; |
380 | unsigned int absExponent; |
381 | const unsigned int overlargeExponent = 24000; /* FIXME. */ |
382 | StringRef::iterator p = begin; |
383 | |
384 | // Treat no exponent as 0 to match binutils |
385 | if (p == end || ((*p == '-' || *p == '+') && (p + 1) == end)) { |
386 | return 0; |
387 | } |
388 | |
389 | isNegative = (*p == '-'); |
390 | if (*p == '-' || *p == '+') { |
391 | p++; |
392 | if (p == end) |
393 | return createError(Err: "Exponent has no digits" ); |
394 | } |
395 | |
396 | absExponent = decDigitValue(c: *p++); |
397 | if (absExponent >= 10U) |
398 | return createError(Err: "Invalid character in exponent" ); |
399 | |
400 | for (; p != end; ++p) { |
401 | unsigned int value; |
402 | |
403 | value = decDigitValue(c: *p); |
404 | if (value >= 10U) |
405 | return createError(Err: "Invalid character in exponent" ); |
406 | |
407 | absExponent = absExponent * 10U + value; |
408 | if (absExponent >= overlargeExponent) { |
409 | absExponent = overlargeExponent; |
410 | break; |
411 | } |
412 | } |
413 | |
414 | if (isNegative) |
415 | return -(int) absExponent; |
416 | else |
417 | return (int) absExponent; |
418 | } |
419 | |
420 | /* This is ugly and needs cleaning up, but I don't immediately see |
421 | how whilst remaining safe. */ |
422 | static Expected<int> totalExponent(StringRef::iterator p, |
423 | StringRef::iterator end, |
424 | int exponentAdjustment) { |
425 | int unsignedExponent; |
426 | bool negative, overflow; |
427 | int exponent = 0; |
428 | |
429 | if (p == end) |
430 | return createError(Err: "Exponent has no digits" ); |
431 | |
432 | negative = *p == '-'; |
433 | if (*p == '-' || *p == '+') { |
434 | p++; |
435 | if (p == end) |
436 | return createError(Err: "Exponent has no digits" ); |
437 | } |
438 | |
439 | unsignedExponent = 0; |
440 | overflow = false; |
441 | for (; p != end; ++p) { |
442 | unsigned int value; |
443 | |
444 | value = decDigitValue(c: *p); |
445 | if (value >= 10U) |
446 | return createError(Err: "Invalid character in exponent" ); |
447 | |
448 | unsignedExponent = unsignedExponent * 10 + value; |
449 | if (unsignedExponent > 32767) { |
450 | overflow = true; |
451 | break; |
452 | } |
453 | } |
454 | |
455 | if (exponentAdjustment > 32767 || exponentAdjustment < -32768) |
456 | overflow = true; |
457 | |
458 | if (!overflow) { |
459 | exponent = unsignedExponent; |
460 | if (negative) |
461 | exponent = -exponent; |
462 | exponent += exponentAdjustment; |
463 | if (exponent > 32767 || exponent < -32768) |
464 | overflow = true; |
465 | } |
466 | |
467 | if (overflow) |
468 | exponent = negative ? -32768: 32767; |
469 | |
470 | return exponent; |
471 | } |
472 | |
473 | static Expected<StringRef::iterator> |
474 | skipLeadingZeroesAndAnyDot(StringRef::iterator begin, StringRef::iterator end, |
475 | StringRef::iterator *dot) { |
476 | StringRef::iterator p = begin; |
477 | *dot = end; |
478 | while (p != end && *p == '0') |
479 | p++; |
480 | |
481 | if (p != end && *p == '.') { |
482 | *dot = p++; |
483 | |
484 | if (end - begin == 1) |
485 | return createError(Err: "Significand has no digits" ); |
486 | |
487 | while (p != end && *p == '0') |
488 | p++; |
489 | } |
490 | |
491 | return p; |
492 | } |
493 | |
494 | /* Given a normal decimal floating point number of the form |
495 | |
496 | dddd.dddd[eE][+-]ddd |
497 | |
498 | where the decimal point and exponent are optional, fill out the |
499 | structure D. Exponent is appropriate if the significand is |
500 | treated as an integer, and normalizedExponent if the significand |
501 | is taken to have the decimal point after a single leading |
502 | non-zero digit. |
503 | |
504 | If the value is zero, V->firstSigDigit points to a non-digit, and |
505 | the return exponent is zero. |
506 | */ |
507 | struct decimalInfo { |
508 | const char *firstSigDigit; |
509 | const char *lastSigDigit; |
510 | int exponent; |
511 | int normalizedExponent; |
512 | }; |
513 | |
514 | static Error interpretDecimal(StringRef::iterator begin, |
515 | StringRef::iterator end, decimalInfo *D) { |
516 | StringRef::iterator dot = end; |
517 | |
518 | auto PtrOrErr = skipLeadingZeroesAndAnyDot(begin, end, dot: &dot); |
519 | if (!PtrOrErr) |
520 | return PtrOrErr.takeError(); |
521 | StringRef::iterator p = *PtrOrErr; |
522 | |
523 | D->firstSigDigit = p; |
524 | D->exponent = 0; |
525 | D->normalizedExponent = 0; |
526 | |
527 | for (; p != end; ++p) { |
528 | if (*p == '.') { |
529 | if (dot != end) |
530 | return createError(Err: "String contains multiple dots" ); |
531 | dot = p++; |
532 | if (p == end) |
533 | break; |
534 | } |
535 | if (decDigitValue(c: *p) >= 10U) |
536 | break; |
537 | } |
538 | |
539 | if (p != end) { |
540 | if (*p != 'e' && *p != 'E') |
541 | return createError(Err: "Invalid character in significand" ); |
542 | if (p == begin) |
543 | return createError(Err: "Significand has no digits" ); |
544 | if (dot != end && p - begin == 1) |
545 | return createError(Err: "Significand has no digits" ); |
546 | |
547 | /* p points to the first non-digit in the string */ |
548 | auto ExpOrErr = readExponent(begin: p + 1, end); |
549 | if (!ExpOrErr) |
550 | return ExpOrErr.takeError(); |
551 | D->exponent = *ExpOrErr; |
552 | |
553 | /* Implied decimal point? */ |
554 | if (dot == end) |
555 | dot = p; |
556 | } |
557 | |
558 | /* If number is all zeroes accept any exponent. */ |
559 | if (p != D->firstSigDigit) { |
560 | /* Drop insignificant trailing zeroes. */ |
561 | if (p != begin) { |
562 | do |
563 | do |
564 | p--; |
565 | while (p != begin && *p == '0'); |
566 | while (p != begin && *p == '.'); |
567 | } |
568 | |
569 | /* Adjust the exponents for any decimal point. */ |
570 | D->exponent += static_cast<APFloat::ExponentType>((dot - p) - (dot > p)); |
571 | D->normalizedExponent = (D->exponent + |
572 | static_cast<APFloat::ExponentType>((p - D->firstSigDigit) |
573 | - (dot > D->firstSigDigit && dot < p))); |
574 | } |
575 | |
576 | D->lastSigDigit = p; |
577 | return Error::success(); |
578 | } |
579 | |
580 | /* Return the trailing fraction of a hexadecimal number. |
581 | DIGITVALUE is the first hex digit of the fraction, P points to |
582 | the next digit. */ |
583 | static Expected<lostFraction> |
584 | trailingHexadecimalFraction(StringRef::iterator p, StringRef::iterator end, |
585 | unsigned int digitValue) { |
586 | unsigned int hexDigit; |
587 | |
588 | /* If the first trailing digit isn't 0 or 8 we can work out the |
589 | fraction immediately. */ |
590 | if (digitValue > 8) |
591 | return lfMoreThanHalf; |
592 | else if (digitValue < 8 && digitValue > 0) |
593 | return lfLessThanHalf; |
594 | |
595 | // Otherwise we need to find the first non-zero digit. |
596 | while (p != end && (*p == '0' || *p == '.')) |
597 | p++; |
598 | |
599 | if (p == end) |
600 | return createError(Err: "Invalid trailing hexadecimal fraction!" ); |
601 | |
602 | hexDigit = hexDigitValue(C: *p); |
603 | |
604 | /* If we ran off the end it is exactly zero or one-half, otherwise |
605 | a little more. */ |
606 | if (hexDigit == UINT_MAX) |
607 | return digitValue == 0 ? lfExactlyZero: lfExactlyHalf; |
608 | else |
609 | return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf; |
610 | } |
611 | |
612 | /* Return the fraction lost were a bignum truncated losing the least |
613 | significant BITS bits. */ |
614 | static lostFraction |
615 | lostFractionThroughTruncation(const APFloatBase::integerPart *parts, |
616 | unsigned int partCount, |
617 | unsigned int bits) |
618 | { |
619 | unsigned int lsb; |
620 | |
621 | lsb = APInt::tcLSB(parts, n: partCount); |
622 | |
623 | /* Note this is guaranteed true if bits == 0, or LSB == UINT_MAX. */ |
624 | if (bits <= lsb) |
625 | return lfExactlyZero; |
626 | if (bits == lsb + 1) |
627 | return lfExactlyHalf; |
628 | if (bits <= partCount * APFloatBase::integerPartWidth && |
629 | APInt::tcExtractBit(parts, bit: bits - 1)) |
630 | return lfMoreThanHalf; |
631 | |
632 | return lfLessThanHalf; |
633 | } |
634 | |
635 | /* Shift DST right BITS bits noting lost fraction. */ |
636 | static lostFraction |
637 | shiftRight(APFloatBase::integerPart *dst, unsigned int parts, unsigned int bits) |
638 | { |
639 | lostFraction lost_fraction; |
640 | |
641 | lost_fraction = lostFractionThroughTruncation(parts: dst, partCount: parts, bits); |
642 | |
643 | APInt::tcShiftRight(dst, Words: parts, Count: bits); |
644 | |
645 | return lost_fraction; |
646 | } |
647 | |
648 | /* Combine the effect of two lost fractions. */ |
649 | static lostFraction |
650 | combineLostFractions(lostFraction moreSignificant, |
651 | lostFraction lessSignificant) |
652 | { |
653 | if (lessSignificant != lfExactlyZero) { |
654 | if (moreSignificant == lfExactlyZero) |
655 | moreSignificant = lfLessThanHalf; |
656 | else if (moreSignificant == lfExactlyHalf) |
657 | moreSignificant = lfMoreThanHalf; |
658 | } |
659 | |
660 | return moreSignificant; |
661 | } |
662 | |
663 | /* The error from the true value, in half-ulps, on multiplying two |
664 | floating point numbers, which differ from the value they |
665 | approximate by at most HUE1 and HUE2 half-ulps, is strictly less |
666 | than the returned value. |
667 | |
668 | See "How to Read Floating Point Numbers Accurately" by William D |
669 | Clinger. */ |
670 | static unsigned int |
671 | HUerrBound(bool inexactMultiply, unsigned int HUerr1, unsigned int HUerr2) |
672 | { |
673 | assert(HUerr1 < 2 || HUerr2 < 2 || (HUerr1 + HUerr2 < 8)); |
674 | |
675 | if (HUerr1 + HUerr2 == 0) |
676 | return inexactMultiply * 2; /* <= inexactMultiply half-ulps. */ |
677 | else |
678 | return inexactMultiply + 2 * (HUerr1 + HUerr2); |
679 | } |
680 | |
681 | /* The number of ulps from the boundary (zero, or half if ISNEAREST) |
682 | when the least significant BITS are truncated. BITS cannot be |
683 | zero. */ |
684 | static APFloatBase::integerPart |
685 | ulpsFromBoundary(const APFloatBase::integerPart *parts, unsigned int bits, |
686 | bool isNearest) { |
687 | unsigned int count, partBits; |
688 | APFloatBase::integerPart part, boundary; |
689 | |
690 | assert(bits != 0); |
691 | |
692 | bits--; |
693 | count = bits / APFloatBase::integerPartWidth; |
694 | partBits = bits % APFloatBase::integerPartWidth + 1; |
695 | |
696 | part = parts[count] & (~(APFloatBase::integerPart) 0 >> (APFloatBase::integerPartWidth - partBits)); |
697 | |
698 | if (isNearest) |
699 | boundary = (APFloatBase::integerPart) 1 << (partBits - 1); |
700 | else |
701 | boundary = 0; |
702 | |
703 | if (count == 0) { |
704 | if (part - boundary <= boundary - part) |
705 | return part - boundary; |
706 | else |
707 | return boundary - part; |
708 | } |
709 | |
710 | if (part == boundary) { |
711 | while (--count) |
712 | if (parts[count]) |
713 | return ~(APFloatBase::integerPart) 0; /* A lot. */ |
714 | |
715 | return parts[0]; |
716 | } else if (part == boundary - 1) { |
717 | while (--count) |
718 | if (~parts[count]) |
719 | return ~(APFloatBase::integerPart) 0; /* A lot. */ |
720 | |
721 | return -parts[0]; |
722 | } |
723 | |
724 | return ~(APFloatBase::integerPart) 0; /* A lot. */ |
725 | } |
726 | |
727 | /* Place pow(5, power) in DST, and return the number of parts used. |
728 | DST must be at least one part larger than size of the answer. */ |
729 | static unsigned int |
730 | powerOf5(APFloatBase::integerPart *dst, unsigned int power) { |
731 | static const APFloatBase::integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125, 15625, 78125 }; |
732 | APFloatBase::integerPart pow5s[maxPowerOfFiveParts * 2 + 5]; |
733 | pow5s[0] = 78125 * 5; |
734 | |
735 | unsigned int partsCount[16] = { 1 }; |
736 | APFloatBase::integerPart scratch[maxPowerOfFiveParts], *p1, *p2, *pow5; |
737 | unsigned int result; |
738 | assert(power <= maxExponent); |
739 | |
740 | p1 = dst; |
741 | p2 = scratch; |
742 | |
743 | *p1 = firstEightPowers[power & 7]; |
744 | power >>= 3; |
745 | |
746 | result = 1; |
747 | pow5 = pow5s; |
748 | |
749 | for (unsigned int n = 0; power; power >>= 1, n++) { |
750 | unsigned int pc; |
751 | |
752 | pc = partsCount[n]; |
753 | |
754 | /* Calculate pow(5,pow(2,n+3)) if we haven't yet. */ |
755 | if (pc == 0) { |
756 | pc = partsCount[n - 1]; |
757 | APInt::tcFullMultiply(pow5, pow5 - pc, pow5 - pc, pc, pc); |
758 | pc *= 2; |
759 | if (pow5[pc - 1] == 0) |
760 | pc--; |
761 | partsCount[n] = pc; |
762 | } |
763 | |
764 | if (power & 1) { |
765 | APFloatBase::integerPart *tmp; |
766 | |
767 | APInt::tcFullMultiply(p2, p1, pow5, result, pc); |
768 | result += pc; |
769 | if (p2[result - 1] == 0) |
770 | result--; |
771 | |
772 | /* Now result is in p1 with partsCount parts and p2 is scratch |
773 | space. */ |
774 | tmp = p1; |
775 | p1 = p2; |
776 | p2 = tmp; |
777 | } |
778 | |
779 | pow5 += pc; |
780 | } |
781 | |
782 | if (p1 != dst) |
783 | APInt::tcAssign(dst, p1, result); |
784 | |
785 | return result; |
786 | } |
787 | |
788 | /* Zero at the end to avoid modular arithmetic when adding one; used |
789 | when rounding up during hexadecimal output. */ |
790 | static const char hexDigitsLower[] = "0123456789abcdef0" ; |
791 | static const char hexDigitsUpper[] = "0123456789ABCDEF0" ; |
792 | static const char infinityL[] = "infinity" ; |
793 | static const char infinityU[] = "INFINITY" ; |
794 | static const char NaNL[] = "nan" ; |
795 | static const char NaNU[] = "NAN" ; |
796 | |
797 | /* Write out an integerPart in hexadecimal, starting with the most |
798 | significant nibble. Write out exactly COUNT hexdigits, return |
799 | COUNT. */ |
800 | static unsigned int |
801 | partAsHex (char *dst, APFloatBase::integerPart part, unsigned int count, |
802 | const char *hexDigitChars) |
803 | { |
804 | unsigned int result = count; |
805 | |
806 | assert(count != 0 && count <= APFloatBase::integerPartWidth / 4); |
807 | |
808 | part >>= (APFloatBase::integerPartWidth - 4 * count); |
809 | while (count--) { |
810 | dst[count] = hexDigitChars[part & 0xf]; |
811 | part >>= 4; |
812 | } |
813 | |
814 | return result; |
815 | } |
816 | |
817 | /* Write out an unsigned decimal integer. */ |
818 | static char * |
819 | writeUnsignedDecimal (char *dst, unsigned int n) |
820 | { |
821 | char buff[40], *p; |
822 | |
823 | p = buff; |
824 | do |
825 | *p++ = '0' + n % 10; |
826 | while (n /= 10); |
827 | |
828 | do |
829 | *dst++ = *--p; |
830 | while (p != buff); |
831 | |
832 | return dst; |
833 | } |
834 | |
835 | /* Write out a signed decimal integer. */ |
836 | static char * |
837 | writeSignedDecimal (char *dst, int value) |
838 | { |
839 | if (value < 0) { |
840 | *dst++ = '-'; |
841 | dst = writeUnsignedDecimal(dst, n: -(unsigned) value); |
842 | } else |
843 | dst = writeUnsignedDecimal(dst, n: value); |
844 | |
845 | return dst; |
846 | } |
847 | |
848 | namespace detail { |
849 | /* Constructors. */ |
850 | void IEEEFloat::initialize(const fltSemantics *ourSemantics) { |
851 | unsigned int count; |
852 | |
853 | semantics = ourSemantics; |
854 | count = partCount(); |
855 | if (count > 1) |
856 | significand.parts = new integerPart[count]; |
857 | } |
858 | |
859 | void IEEEFloat::freeSignificand() { |
860 | if (needsCleanup()) |
861 | delete [] significand.parts; |
862 | } |
863 | |
864 | void IEEEFloat::assign(const IEEEFloat &rhs) { |
865 | assert(semantics == rhs.semantics); |
866 | |
867 | sign = rhs.sign; |
868 | category = rhs.category; |
869 | exponent = rhs.exponent; |
870 | if (isFiniteNonZero() || category == fcNaN) |
871 | copySignificand(rhs); |
872 | } |
873 | |
874 | void IEEEFloat::copySignificand(const IEEEFloat &rhs) { |
875 | assert(isFiniteNonZero() || category == fcNaN); |
876 | assert(rhs.partCount() >= partCount()); |
877 | |
878 | APInt::tcAssign(significandParts(), rhs.significandParts(), |
879 | partCount()); |
880 | } |
881 | |
882 | /* Make this number a NaN, with an arbitrary but deterministic value |
883 | for the significand. If double or longer, this is a signalling NaN, |
884 | which may not be ideal. If float, this is QNaN(0). */ |
885 | void IEEEFloat::makeNaN(bool SNaN, bool Negative, const APInt *fill) { |
886 | category = fcNaN; |
887 | sign = Negative; |
888 | exponent = exponentNaN(); |
889 | |
890 | integerPart *significand = significandParts(); |
891 | unsigned numParts = partCount(); |
892 | |
893 | APInt fill_storage; |
894 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly) { |
895 | // Finite-only types do not distinguish signalling and quiet NaN, so |
896 | // make them all signalling. |
897 | SNaN = false; |
898 | if (semantics->nanEncoding == fltNanEncoding::NegativeZero) { |
899 | sign = true; |
900 | fill_storage = APInt::getZero(numBits: semantics->precision - 1); |
901 | } else { |
902 | fill_storage = APInt::getAllOnes(numBits: semantics->precision - 1); |
903 | } |
904 | fill = &fill_storage; |
905 | } |
906 | |
907 | // Set the significand bits to the fill. |
908 | if (!fill || fill->getNumWords() < numParts) |
909 | APInt::tcSet(significand, 0, numParts); |
910 | if (fill) { |
911 | APInt::tcAssign(significand, fill->getRawData(), |
912 | std::min(a: fill->getNumWords(), b: numParts)); |
913 | |
914 | // Zero out the excess bits of the significand. |
915 | unsigned bitsToPreserve = semantics->precision - 1; |
916 | unsigned part = bitsToPreserve / 64; |
917 | bitsToPreserve %= 64; |
918 | significand[part] &= ((1ULL << bitsToPreserve) - 1); |
919 | for (part++; part != numParts; ++part) |
920 | significand[part] = 0; |
921 | } |
922 | |
923 | unsigned QNaNBit = semantics->precision - 2; |
924 | |
925 | if (SNaN) { |
926 | // We always have to clear the QNaN bit to make it an SNaN. |
927 | APInt::tcClearBit(significand, bit: QNaNBit); |
928 | |
929 | // If there are no bits set in the payload, we have to set |
930 | // *something* to make it a NaN instead of an infinity; |
931 | // conventionally, this is the next bit down from the QNaN bit. |
932 | if (APInt::tcIsZero(significand, numParts)) |
933 | APInt::tcSetBit(significand, bit: QNaNBit - 1); |
934 | } else if (semantics->nanEncoding == fltNanEncoding::NegativeZero) { |
935 | // The only NaN is a quiet NaN, and it has no bits sets in the significand. |
936 | // Do nothing. |
937 | } else { |
938 | // We always have to set the QNaN bit to make it a QNaN. |
939 | APInt::tcSetBit(significand, bit: QNaNBit); |
940 | } |
941 | |
942 | // For x87 extended precision, we want to make a NaN, not a |
943 | // pseudo-NaN. Maybe we should expose the ability to make |
944 | // pseudo-NaNs? |
945 | if (semantics == &semX87DoubleExtended) |
946 | APInt::tcSetBit(significand, bit: QNaNBit + 1); |
947 | } |
948 | |
949 | IEEEFloat &IEEEFloat::operator=(const IEEEFloat &rhs) { |
950 | if (this != &rhs) { |
951 | if (semantics != rhs.semantics) { |
952 | freeSignificand(); |
953 | initialize(ourSemantics: rhs.semantics); |
954 | } |
955 | assign(rhs); |
956 | } |
957 | |
958 | return *this; |
959 | } |
960 | |
961 | IEEEFloat &IEEEFloat::operator=(IEEEFloat &&rhs) { |
962 | freeSignificand(); |
963 | |
964 | semantics = rhs.semantics; |
965 | significand = rhs.significand; |
966 | exponent = rhs.exponent; |
967 | category = rhs.category; |
968 | sign = rhs.sign; |
969 | |
970 | rhs.semantics = &semBogus; |
971 | return *this; |
972 | } |
973 | |
974 | bool IEEEFloat::isDenormal() const { |
975 | return isFiniteNonZero() && (exponent == semantics->minExponent) && |
976 | (APInt::tcExtractBit(significandParts(), |
977 | bit: semantics->precision - 1) == 0); |
978 | } |
979 | |
980 | bool IEEEFloat::isSmallest() const { |
981 | // The smallest number by magnitude in our format will be the smallest |
982 | // denormal, i.e. the floating point number with exponent being minimum |
983 | // exponent and significand bitwise equal to 1 (i.e. with MSB equal to 0). |
984 | return isFiniteNonZero() && exponent == semantics->minExponent && |
985 | significandMSB() == 0; |
986 | } |
987 | |
988 | bool IEEEFloat::isSmallestNormalized() const { |
989 | return getCategory() == fcNormal && exponent == semantics->minExponent && |
990 | isSignificandAllZerosExceptMSB(); |
991 | } |
992 | |
993 | bool IEEEFloat::isSignificandAllOnes() const { |
994 | // Test if the significand excluding the integral bit is all ones. This allows |
995 | // us to test for binade boundaries. |
996 | const integerPart *Parts = significandParts(); |
997 | const unsigned PartCount = partCountForBits(bits: semantics->precision); |
998 | for (unsigned i = 0; i < PartCount - 1; i++) |
999 | if (~Parts[i]) |
1000 | return false; |
1001 | |
1002 | // Set the unused high bits to all ones when we compare. |
1003 | const unsigned NumHighBits = |
1004 | PartCount*integerPartWidth - semantics->precision + 1; |
1005 | assert(NumHighBits <= integerPartWidth && NumHighBits > 0 && |
1006 | "Can not have more high bits to fill than integerPartWidth" ); |
1007 | const integerPart HighBitFill = |
1008 | ~integerPart(0) << (integerPartWidth - NumHighBits); |
1009 | if (~(Parts[PartCount - 1] | HighBitFill)) |
1010 | return false; |
1011 | |
1012 | return true; |
1013 | } |
1014 | |
1015 | bool IEEEFloat::isSignificandAllOnesExceptLSB() const { |
1016 | // Test if the significand excluding the integral bit is all ones except for |
1017 | // the least significant bit. |
1018 | const integerPart *Parts = significandParts(); |
1019 | |
1020 | if (Parts[0] & 1) |
1021 | return false; |
1022 | |
1023 | const unsigned PartCount = partCountForBits(bits: semantics->precision); |
1024 | for (unsigned i = 0; i < PartCount - 1; i++) { |
1025 | if (~Parts[i] & ~unsigned{!i}) |
1026 | return false; |
1027 | } |
1028 | |
1029 | // Set the unused high bits to all ones when we compare. |
1030 | const unsigned NumHighBits = |
1031 | PartCount * integerPartWidth - semantics->precision + 1; |
1032 | assert(NumHighBits <= integerPartWidth && NumHighBits > 0 && |
1033 | "Can not have more high bits to fill than integerPartWidth" ); |
1034 | const integerPart HighBitFill = ~integerPart(0) |
1035 | << (integerPartWidth - NumHighBits); |
1036 | if (~(Parts[PartCount - 1] | HighBitFill | 0x1)) |
1037 | return false; |
1038 | |
1039 | return true; |
1040 | } |
1041 | |
1042 | bool IEEEFloat::isSignificandAllZeros() const { |
1043 | // Test if the significand excluding the integral bit is all zeros. This |
1044 | // allows us to test for binade boundaries. |
1045 | const integerPart *Parts = significandParts(); |
1046 | const unsigned PartCount = partCountForBits(bits: semantics->precision); |
1047 | |
1048 | for (unsigned i = 0; i < PartCount - 1; i++) |
1049 | if (Parts[i]) |
1050 | return false; |
1051 | |
1052 | // Compute how many bits are used in the final word. |
1053 | const unsigned NumHighBits = |
1054 | PartCount*integerPartWidth - semantics->precision + 1; |
1055 | assert(NumHighBits < integerPartWidth && "Can not have more high bits to " |
1056 | "clear than integerPartWidth" ); |
1057 | const integerPart HighBitMask = ~integerPart(0) >> NumHighBits; |
1058 | |
1059 | if (Parts[PartCount - 1] & HighBitMask) |
1060 | return false; |
1061 | |
1062 | return true; |
1063 | } |
1064 | |
1065 | bool IEEEFloat::isSignificandAllZerosExceptMSB() const { |
1066 | const integerPart *Parts = significandParts(); |
1067 | const unsigned PartCount = partCountForBits(bits: semantics->precision); |
1068 | |
1069 | for (unsigned i = 0; i < PartCount - 1; i++) { |
1070 | if (Parts[i]) |
1071 | return false; |
1072 | } |
1073 | |
1074 | const unsigned NumHighBits = |
1075 | PartCount * integerPartWidth - semantics->precision + 1; |
1076 | return Parts[PartCount - 1] == integerPart(1) |
1077 | << (integerPartWidth - NumHighBits); |
1078 | } |
1079 | |
1080 | bool IEEEFloat::isLargest() const { |
1081 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly && |
1082 | semantics->nanEncoding == fltNanEncoding::AllOnes) { |
1083 | // The largest number by magnitude in our format will be the floating point |
1084 | // number with maximum exponent and with significand that is all ones except |
1085 | // the LSB. |
1086 | return isFiniteNonZero() && exponent == semantics->maxExponent && |
1087 | isSignificandAllOnesExceptLSB(); |
1088 | } else { |
1089 | // The largest number by magnitude in our format will be the floating point |
1090 | // number with maximum exponent and with significand that is all ones. |
1091 | return isFiniteNonZero() && exponent == semantics->maxExponent && |
1092 | isSignificandAllOnes(); |
1093 | } |
1094 | } |
1095 | |
1096 | bool IEEEFloat::isInteger() const { |
1097 | // This could be made more efficient; I'm going for obviously correct. |
1098 | if (!isFinite()) return false; |
1099 | IEEEFloat truncated = *this; |
1100 | truncated.roundToIntegral(rmTowardZero); |
1101 | return compare(truncated) == cmpEqual; |
1102 | } |
1103 | |
1104 | bool IEEEFloat::bitwiseIsEqual(const IEEEFloat &rhs) const { |
1105 | if (this == &rhs) |
1106 | return true; |
1107 | if (semantics != rhs.semantics || |
1108 | category != rhs.category || |
1109 | sign != rhs.sign) |
1110 | return false; |
1111 | if (category==fcZero || category==fcInfinity) |
1112 | return true; |
1113 | |
1114 | if (isFiniteNonZero() && exponent != rhs.exponent) |
1115 | return false; |
1116 | |
1117 | return std::equal(first1: significandParts(), last1: significandParts() + partCount(), |
1118 | first2: rhs.significandParts()); |
1119 | } |
1120 | |
1121 | IEEEFloat::IEEEFloat(const fltSemantics &ourSemantics, integerPart value) { |
1122 | initialize(ourSemantics: &ourSemantics); |
1123 | sign = 0; |
1124 | category = fcNormal; |
1125 | zeroSignificand(); |
1126 | exponent = ourSemantics.precision - 1; |
1127 | significandParts()[0] = value; |
1128 | normalize(rmNearestTiesToEven, lfExactlyZero); |
1129 | } |
1130 | |
1131 | IEEEFloat::IEEEFloat(const fltSemantics &ourSemantics) { |
1132 | initialize(ourSemantics: &ourSemantics); |
1133 | makeZero(Neg: false); |
1134 | } |
1135 | |
1136 | // Delegate to the previous constructor, because later copy constructor may |
1137 | // actually inspects category, which can't be garbage. |
1138 | IEEEFloat::IEEEFloat(const fltSemantics &ourSemantics, uninitializedTag tag) |
1139 | : IEEEFloat(ourSemantics) {} |
1140 | |
1141 | IEEEFloat::IEEEFloat(const IEEEFloat &rhs) { |
1142 | initialize(ourSemantics: rhs.semantics); |
1143 | assign(rhs); |
1144 | } |
1145 | |
1146 | IEEEFloat::IEEEFloat(IEEEFloat &&rhs) : semantics(&semBogus) { |
1147 | *this = std::move(rhs); |
1148 | } |
1149 | |
1150 | IEEEFloat::~IEEEFloat() { freeSignificand(); } |
1151 | |
1152 | unsigned int IEEEFloat::partCount() const { |
1153 | return partCountForBits(bits: semantics->precision + 1); |
1154 | } |
1155 | |
1156 | const IEEEFloat::integerPart *IEEEFloat::significandParts() const { |
1157 | return const_cast<IEEEFloat *>(this)->significandParts(); |
1158 | } |
1159 | |
1160 | IEEEFloat::integerPart *IEEEFloat::significandParts() { |
1161 | if (partCount() > 1) |
1162 | return significand.parts; |
1163 | else |
1164 | return &significand.part; |
1165 | } |
1166 | |
1167 | void IEEEFloat::zeroSignificand() { |
1168 | APInt::tcSet(significandParts(), 0, partCount()); |
1169 | } |
1170 | |
1171 | /* Increment an fcNormal floating point number's significand. */ |
1172 | void IEEEFloat::incrementSignificand() { |
1173 | integerPart carry; |
1174 | |
1175 | carry = APInt::tcIncrement(dst: significandParts(), parts: partCount()); |
1176 | |
1177 | /* Our callers should never cause us to overflow. */ |
1178 | assert(carry == 0); |
1179 | (void)carry; |
1180 | } |
1181 | |
1182 | /* Add the significand of the RHS. Returns the carry flag. */ |
1183 | IEEEFloat::integerPart IEEEFloat::addSignificand(const IEEEFloat &rhs) { |
1184 | integerPart *parts; |
1185 | |
1186 | parts = significandParts(); |
1187 | |
1188 | assert(semantics == rhs.semantics); |
1189 | assert(exponent == rhs.exponent); |
1190 | |
1191 | return APInt::tcAdd(parts, rhs.significandParts(), carry: 0, partCount()); |
1192 | } |
1193 | |
1194 | /* Subtract the significand of the RHS with a borrow flag. Returns |
1195 | the borrow flag. */ |
1196 | IEEEFloat::integerPart IEEEFloat::subtractSignificand(const IEEEFloat &rhs, |
1197 | integerPart borrow) { |
1198 | integerPart *parts; |
1199 | |
1200 | parts = significandParts(); |
1201 | |
1202 | assert(semantics == rhs.semantics); |
1203 | assert(exponent == rhs.exponent); |
1204 | |
1205 | return APInt::tcSubtract(parts, rhs.significandParts(), carry: borrow, |
1206 | partCount()); |
1207 | } |
1208 | |
1209 | /* Multiply the significand of the RHS. If ADDEND is non-NULL, add it |
1210 | on to the full-precision result of the multiplication. Returns the |
1211 | lost fraction. */ |
1212 | lostFraction IEEEFloat::multiplySignificand(const IEEEFloat &rhs, |
1213 | IEEEFloat addend) { |
1214 | unsigned int omsb; // One, not zero, based MSB. |
1215 | unsigned int partsCount, newPartsCount, precision; |
1216 | integerPart *lhsSignificand; |
1217 | integerPart scratch[4]; |
1218 | integerPart *fullSignificand; |
1219 | lostFraction lost_fraction; |
1220 | bool ignored; |
1221 | |
1222 | assert(semantics == rhs.semantics); |
1223 | |
1224 | precision = semantics->precision; |
1225 | |
1226 | // Allocate space for twice as many bits as the original significand, plus one |
1227 | // extra bit for the addition to overflow into. |
1228 | newPartsCount = partCountForBits(bits: precision * 2 + 1); |
1229 | |
1230 | if (newPartsCount > 4) |
1231 | fullSignificand = new integerPart[newPartsCount]; |
1232 | else |
1233 | fullSignificand = scratch; |
1234 | |
1235 | lhsSignificand = significandParts(); |
1236 | partsCount = partCount(); |
1237 | |
1238 | APInt::tcFullMultiply(fullSignificand, lhsSignificand, |
1239 | rhs.significandParts(), partsCount, partsCount); |
1240 | |
1241 | lost_fraction = lfExactlyZero; |
1242 | omsb = APInt::tcMSB(parts: fullSignificand, n: newPartsCount) + 1; |
1243 | exponent += rhs.exponent; |
1244 | |
1245 | // Assume the operands involved in the multiplication are single-precision |
1246 | // FP, and the two multiplicants are: |
1247 | // *this = a23 . a22 ... a0 * 2^e1 |
1248 | // rhs = b23 . b22 ... b0 * 2^e2 |
1249 | // the result of multiplication is: |
1250 | // *this = c48 c47 c46 . c45 ... c0 * 2^(e1+e2) |
1251 | // Note that there are three significant bits at the left-hand side of the |
1252 | // radix point: two for the multiplication, and an overflow bit for the |
1253 | // addition (that will always be zero at this point). Move the radix point |
1254 | // toward left by two bits, and adjust exponent accordingly. |
1255 | exponent += 2; |
1256 | |
1257 | if (addend.isNonZero()) { |
1258 | // The intermediate result of the multiplication has "2 * precision" |
1259 | // signicant bit; adjust the addend to be consistent with mul result. |
1260 | // |
1261 | Significand savedSignificand = significand; |
1262 | const fltSemantics *savedSemantics = semantics; |
1263 | fltSemantics extendedSemantics; |
1264 | opStatus status; |
1265 | unsigned int extendedPrecision; |
1266 | |
1267 | // Normalize our MSB to one below the top bit to allow for overflow. |
1268 | extendedPrecision = 2 * precision + 1; |
1269 | if (omsb != extendedPrecision - 1) { |
1270 | assert(extendedPrecision > omsb); |
1271 | APInt::tcShiftLeft(fullSignificand, Words: newPartsCount, |
1272 | Count: (extendedPrecision - 1) - omsb); |
1273 | exponent -= (extendedPrecision - 1) - omsb; |
1274 | } |
1275 | |
1276 | /* Create new semantics. */ |
1277 | extendedSemantics = *semantics; |
1278 | extendedSemantics.precision = extendedPrecision; |
1279 | |
1280 | if (newPartsCount == 1) |
1281 | significand.part = fullSignificand[0]; |
1282 | else |
1283 | significand.parts = fullSignificand; |
1284 | semantics = &extendedSemantics; |
1285 | |
1286 | // Make a copy so we can convert it to the extended semantics. |
1287 | // Note that we cannot convert the addend directly, as the extendedSemantics |
1288 | // is a local variable (which we take a reference to). |
1289 | IEEEFloat extendedAddend(addend); |
1290 | status = extendedAddend.convert(extendedSemantics, rmTowardZero, &ignored); |
1291 | assert(status == opOK); |
1292 | (void)status; |
1293 | |
1294 | // Shift the significand of the addend right by one bit. This guarantees |
1295 | // that the high bit of the significand is zero (same as fullSignificand), |
1296 | // so the addition will overflow (if it does overflow at all) into the top bit. |
1297 | lost_fraction = extendedAddend.shiftSignificandRight(1); |
1298 | assert(lost_fraction == lfExactlyZero && |
1299 | "Lost precision while shifting addend for fused-multiply-add." ); |
1300 | |
1301 | lost_fraction = addOrSubtractSignificand(extendedAddend, subtract: false); |
1302 | |
1303 | /* Restore our state. */ |
1304 | if (newPartsCount == 1) |
1305 | fullSignificand[0] = significand.part; |
1306 | significand = savedSignificand; |
1307 | semantics = savedSemantics; |
1308 | |
1309 | omsb = APInt::tcMSB(parts: fullSignificand, n: newPartsCount) + 1; |
1310 | } |
1311 | |
1312 | // Convert the result having "2 * precision" significant-bits back to the one |
1313 | // having "precision" significant-bits. First, move the radix point from |
1314 | // poision "2*precision - 1" to "precision - 1". The exponent need to be |
1315 | // adjusted by "2*precision - 1" - "precision - 1" = "precision". |
1316 | exponent -= precision + 1; |
1317 | |
1318 | // In case MSB resides at the left-hand side of radix point, shift the |
1319 | // mantissa right by some amount to make sure the MSB reside right before |
1320 | // the radix point (i.e. "MSB . rest-significant-bits"). |
1321 | // |
1322 | // Note that the result is not normalized when "omsb < precision". So, the |
1323 | // caller needs to call IEEEFloat::normalize() if normalized value is |
1324 | // expected. |
1325 | if (omsb > precision) { |
1326 | unsigned int bits, significantParts; |
1327 | lostFraction lf; |
1328 | |
1329 | bits = omsb - precision; |
1330 | significantParts = partCountForBits(bits: omsb); |
1331 | lf = shiftRight(dst: fullSignificand, parts: significantParts, bits); |
1332 | lost_fraction = combineLostFractions(moreSignificant: lf, lessSignificant: lost_fraction); |
1333 | exponent += bits; |
1334 | } |
1335 | |
1336 | APInt::tcAssign(lhsSignificand, fullSignificand, partsCount); |
1337 | |
1338 | if (newPartsCount > 4) |
1339 | delete [] fullSignificand; |
1340 | |
1341 | return lost_fraction; |
1342 | } |
1343 | |
1344 | lostFraction IEEEFloat::multiplySignificand(const IEEEFloat &rhs) { |
1345 | return multiplySignificand(rhs, addend: IEEEFloat(*semantics)); |
1346 | } |
1347 | |
1348 | /* Multiply the significands of LHS and RHS to DST. */ |
1349 | lostFraction IEEEFloat::divideSignificand(const IEEEFloat &rhs) { |
1350 | unsigned int bit, i, partsCount; |
1351 | const integerPart *rhsSignificand; |
1352 | integerPart *lhsSignificand, *dividend, *divisor; |
1353 | integerPart scratch[4]; |
1354 | lostFraction lost_fraction; |
1355 | |
1356 | assert(semantics == rhs.semantics); |
1357 | |
1358 | lhsSignificand = significandParts(); |
1359 | rhsSignificand = rhs.significandParts(); |
1360 | partsCount = partCount(); |
1361 | |
1362 | if (partsCount > 2) |
1363 | dividend = new integerPart[partsCount * 2]; |
1364 | else |
1365 | dividend = scratch; |
1366 | |
1367 | divisor = dividend + partsCount; |
1368 | |
1369 | /* Copy the dividend and divisor as they will be modified in-place. */ |
1370 | for (i = 0; i < partsCount; i++) { |
1371 | dividend[i] = lhsSignificand[i]; |
1372 | divisor[i] = rhsSignificand[i]; |
1373 | lhsSignificand[i] = 0; |
1374 | } |
1375 | |
1376 | exponent -= rhs.exponent; |
1377 | |
1378 | unsigned int precision = semantics->precision; |
1379 | |
1380 | /* Normalize the divisor. */ |
1381 | bit = precision - APInt::tcMSB(parts: divisor, n: partsCount) - 1; |
1382 | if (bit) { |
1383 | exponent += bit; |
1384 | APInt::tcShiftLeft(divisor, Words: partsCount, Count: bit); |
1385 | } |
1386 | |
1387 | /* Normalize the dividend. */ |
1388 | bit = precision - APInt::tcMSB(parts: dividend, n: partsCount) - 1; |
1389 | if (bit) { |
1390 | exponent -= bit; |
1391 | APInt::tcShiftLeft(dividend, Words: partsCount, Count: bit); |
1392 | } |
1393 | |
1394 | /* Ensure the dividend >= divisor initially for the loop below. |
1395 | Incidentally, this means that the division loop below is |
1396 | guaranteed to set the integer bit to one. */ |
1397 | if (APInt::tcCompare(dividend, divisor, partsCount) < 0) { |
1398 | exponent--; |
1399 | APInt::tcShiftLeft(dividend, Words: partsCount, Count: 1); |
1400 | assert(APInt::tcCompare(dividend, divisor, partsCount) >= 0); |
1401 | } |
1402 | |
1403 | /* Long division. */ |
1404 | for (bit = precision; bit; bit -= 1) { |
1405 | if (APInt::tcCompare(dividend, divisor, partsCount) >= 0) { |
1406 | APInt::tcSubtract(dividend, divisor, carry: 0, partsCount); |
1407 | APInt::tcSetBit(lhsSignificand, bit: bit - 1); |
1408 | } |
1409 | |
1410 | APInt::tcShiftLeft(dividend, Words: partsCount, Count: 1); |
1411 | } |
1412 | |
1413 | /* Figure out the lost fraction. */ |
1414 | int cmp = APInt::tcCompare(dividend, divisor, partsCount); |
1415 | |
1416 | if (cmp > 0) |
1417 | lost_fraction = lfMoreThanHalf; |
1418 | else if (cmp == 0) |
1419 | lost_fraction = lfExactlyHalf; |
1420 | else if (APInt::tcIsZero(dividend, partsCount)) |
1421 | lost_fraction = lfExactlyZero; |
1422 | else |
1423 | lost_fraction = lfLessThanHalf; |
1424 | |
1425 | if (partsCount > 2) |
1426 | delete [] dividend; |
1427 | |
1428 | return lost_fraction; |
1429 | } |
1430 | |
1431 | unsigned int IEEEFloat::significandMSB() const { |
1432 | return APInt::tcMSB(parts: significandParts(), n: partCount()); |
1433 | } |
1434 | |
1435 | unsigned int IEEEFloat::significandLSB() const { |
1436 | return APInt::tcLSB(significandParts(), n: partCount()); |
1437 | } |
1438 | |
1439 | /* Note that a zero result is NOT normalized to fcZero. */ |
1440 | lostFraction IEEEFloat::shiftSignificandRight(unsigned int bits) { |
1441 | /* Our exponent should not overflow. */ |
1442 | assert((ExponentType) (exponent + bits) >= exponent); |
1443 | |
1444 | exponent += bits; |
1445 | |
1446 | return shiftRight(dst: significandParts(), parts: partCount(), bits); |
1447 | } |
1448 | |
1449 | /* Shift the significand left BITS bits, subtract BITS from its exponent. */ |
1450 | void IEEEFloat::shiftSignificandLeft(unsigned int bits) { |
1451 | assert(bits < semantics->precision); |
1452 | |
1453 | if (bits) { |
1454 | unsigned int partsCount = partCount(); |
1455 | |
1456 | APInt::tcShiftLeft(significandParts(), Words: partsCount, Count: bits); |
1457 | exponent -= bits; |
1458 | |
1459 | assert(!APInt::tcIsZero(significandParts(), partsCount)); |
1460 | } |
1461 | } |
1462 | |
1463 | IEEEFloat::cmpResult |
1464 | IEEEFloat::compareAbsoluteValue(const IEEEFloat &rhs) const { |
1465 | int compare; |
1466 | |
1467 | assert(semantics == rhs.semantics); |
1468 | assert(isFiniteNonZero()); |
1469 | assert(rhs.isFiniteNonZero()); |
1470 | |
1471 | compare = exponent - rhs.exponent; |
1472 | |
1473 | /* If exponents are equal, do an unsigned bignum comparison of the |
1474 | significands. */ |
1475 | if (compare == 0) |
1476 | compare = APInt::tcCompare(significandParts(), rhs.significandParts(), |
1477 | partCount()); |
1478 | |
1479 | if (compare > 0) |
1480 | return cmpGreaterThan; |
1481 | else if (compare < 0) |
1482 | return cmpLessThan; |
1483 | else |
1484 | return cmpEqual; |
1485 | } |
1486 | |
1487 | /* Set the least significant BITS bits of a bignum, clear the |
1488 | rest. */ |
1489 | static void tcSetLeastSignificantBits(APInt::WordType *dst, unsigned parts, |
1490 | unsigned bits) { |
1491 | unsigned i = 0; |
1492 | while (bits > APInt::APINT_BITS_PER_WORD) { |
1493 | dst[i++] = ~(APInt::WordType)0; |
1494 | bits -= APInt::APINT_BITS_PER_WORD; |
1495 | } |
1496 | |
1497 | if (bits) |
1498 | dst[i++] = ~(APInt::WordType)0 >> (APInt::APINT_BITS_PER_WORD - bits); |
1499 | |
1500 | while (i < parts) |
1501 | dst[i++] = 0; |
1502 | } |
1503 | |
1504 | /* Handle overflow. Sign is preserved. We either become infinity or |
1505 | the largest finite number. */ |
1506 | IEEEFloat::opStatus IEEEFloat::handleOverflow(roundingMode rounding_mode) { |
1507 | /* Infinity? */ |
1508 | if (rounding_mode == rmNearestTiesToEven || |
1509 | rounding_mode == rmNearestTiesToAway || |
1510 | (rounding_mode == rmTowardPositive && !sign) || |
1511 | (rounding_mode == rmTowardNegative && sign)) { |
1512 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly) |
1513 | makeNaN(SNaN: false, Negative: sign); |
1514 | else |
1515 | category = fcInfinity; |
1516 | return (opStatus) (opOverflow | opInexact); |
1517 | } |
1518 | |
1519 | /* Otherwise we become the largest finite number. */ |
1520 | category = fcNormal; |
1521 | exponent = semantics->maxExponent; |
1522 | tcSetLeastSignificantBits(dst: significandParts(), parts: partCount(), |
1523 | bits: semantics->precision); |
1524 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly && |
1525 | semantics->nanEncoding == fltNanEncoding::AllOnes) |
1526 | APInt::tcClearBit(significandParts(), bit: 0); |
1527 | |
1528 | return opInexact; |
1529 | } |
1530 | |
1531 | /* Returns TRUE if, when truncating the current number, with BIT the |
1532 | new LSB, with the given lost fraction and rounding mode, the result |
1533 | would need to be rounded away from zero (i.e., by increasing the |
1534 | signficand). This routine must work for fcZero of both signs, and |
1535 | fcNormal numbers. */ |
1536 | bool IEEEFloat::roundAwayFromZero(roundingMode rounding_mode, |
1537 | lostFraction lost_fraction, |
1538 | unsigned int bit) const { |
1539 | /* NaNs and infinities should not have lost fractions. */ |
1540 | assert(isFiniteNonZero() || category == fcZero); |
1541 | |
1542 | /* Current callers never pass this so we don't handle it. */ |
1543 | assert(lost_fraction != lfExactlyZero); |
1544 | |
1545 | switch (rounding_mode) { |
1546 | case rmNearestTiesToAway: |
1547 | return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf; |
1548 | |
1549 | case rmNearestTiesToEven: |
1550 | if (lost_fraction == lfMoreThanHalf) |
1551 | return true; |
1552 | |
1553 | /* Our zeroes don't have a significand to test. */ |
1554 | if (lost_fraction == lfExactlyHalf && category != fcZero) |
1555 | return APInt::tcExtractBit(significandParts(), bit); |
1556 | |
1557 | return false; |
1558 | |
1559 | case rmTowardZero: |
1560 | return false; |
1561 | |
1562 | case rmTowardPositive: |
1563 | return !sign; |
1564 | |
1565 | case rmTowardNegative: |
1566 | return sign; |
1567 | |
1568 | default: |
1569 | break; |
1570 | } |
1571 | llvm_unreachable("Invalid rounding mode found" ); |
1572 | } |
1573 | |
1574 | IEEEFloat::opStatus IEEEFloat::normalize(roundingMode rounding_mode, |
1575 | lostFraction lost_fraction) { |
1576 | unsigned int omsb; /* One, not zero, based MSB. */ |
1577 | int exponentChange; |
1578 | |
1579 | if (!isFiniteNonZero()) |
1580 | return opOK; |
1581 | |
1582 | /* Before rounding normalize the exponent of fcNormal numbers. */ |
1583 | omsb = significandMSB() + 1; |
1584 | |
1585 | if (omsb) { |
1586 | /* OMSB is numbered from 1. We want to place it in the integer |
1587 | bit numbered PRECISION if possible, with a compensating change in |
1588 | the exponent. */ |
1589 | exponentChange = omsb - semantics->precision; |
1590 | |
1591 | /* If the resulting exponent is too high, overflow according to |
1592 | the rounding mode. */ |
1593 | if (exponent + exponentChange > semantics->maxExponent) |
1594 | return handleOverflow(rounding_mode); |
1595 | |
1596 | /* Subnormal numbers have exponent minExponent, and their MSB |
1597 | is forced based on that. */ |
1598 | if (exponent + exponentChange < semantics->minExponent) |
1599 | exponentChange = semantics->minExponent - exponent; |
1600 | |
1601 | /* Shifting left is easy as we don't lose precision. */ |
1602 | if (exponentChange < 0) { |
1603 | assert(lost_fraction == lfExactlyZero); |
1604 | |
1605 | shiftSignificandLeft(bits: -exponentChange); |
1606 | |
1607 | return opOK; |
1608 | } |
1609 | |
1610 | if (exponentChange > 0) { |
1611 | lostFraction lf; |
1612 | |
1613 | /* Shift right and capture any new lost fraction. */ |
1614 | lf = shiftSignificandRight(bits: exponentChange); |
1615 | |
1616 | lost_fraction = combineLostFractions(moreSignificant: lf, lessSignificant: lost_fraction); |
1617 | |
1618 | /* Keep OMSB up-to-date. */ |
1619 | if (omsb > (unsigned) exponentChange) |
1620 | omsb -= exponentChange; |
1621 | else |
1622 | omsb = 0; |
1623 | } |
1624 | } |
1625 | |
1626 | // The all-ones values is an overflow if NaN is all ones. If NaN is |
1627 | // represented by negative zero, then it is a valid finite value. |
1628 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly && |
1629 | semantics->nanEncoding == fltNanEncoding::AllOnes && |
1630 | exponent == semantics->maxExponent && isSignificandAllOnes()) |
1631 | return handleOverflow(rounding_mode); |
1632 | |
1633 | /* Now round the number according to rounding_mode given the lost |
1634 | fraction. */ |
1635 | |
1636 | /* As specified in IEEE 754, since we do not trap we do not report |
1637 | underflow for exact results. */ |
1638 | if (lost_fraction == lfExactlyZero) { |
1639 | /* Canonicalize zeroes. */ |
1640 | if (omsb == 0) { |
1641 | category = fcZero; |
1642 | if (semantics->nanEncoding == fltNanEncoding::NegativeZero) |
1643 | sign = false; |
1644 | } |
1645 | |
1646 | return opOK; |
1647 | } |
1648 | |
1649 | /* Increment the significand if we're rounding away from zero. */ |
1650 | if (roundAwayFromZero(rounding_mode, lost_fraction, bit: 0)) { |
1651 | if (omsb == 0) |
1652 | exponent = semantics->minExponent; |
1653 | |
1654 | incrementSignificand(); |
1655 | omsb = significandMSB() + 1; |
1656 | |
1657 | /* Did the significand increment overflow? */ |
1658 | if (omsb == (unsigned) semantics->precision + 1) { |
1659 | /* Renormalize by incrementing the exponent and shifting our |
1660 | significand right one. However if we already have the |
1661 | maximum exponent we overflow to infinity. */ |
1662 | if (exponent == semantics->maxExponent) |
1663 | // Invoke overflow handling with a rounding mode that will guarantee |
1664 | // that the result gets turned into the correct infinity representation. |
1665 | // This is needed instead of just setting the category to infinity to |
1666 | // account for 8-bit floating point types that have no inf, only NaN. |
1667 | return handleOverflow(rounding_mode: sign ? rmTowardNegative : rmTowardPositive); |
1668 | |
1669 | shiftSignificandRight(bits: 1); |
1670 | |
1671 | return opInexact; |
1672 | } |
1673 | |
1674 | // The all-ones values is an overflow if NaN is all ones. If NaN is |
1675 | // represented by negative zero, then it is a valid finite value. |
1676 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly && |
1677 | semantics->nanEncoding == fltNanEncoding::AllOnes && |
1678 | exponent == semantics->maxExponent && isSignificandAllOnes()) |
1679 | return handleOverflow(rounding_mode); |
1680 | } |
1681 | |
1682 | /* The normal case - we were and are not denormal, and any |
1683 | significand increment above didn't overflow. */ |
1684 | if (omsb == semantics->precision) |
1685 | return opInexact; |
1686 | |
1687 | /* We have a non-zero denormal. */ |
1688 | assert(omsb < semantics->precision); |
1689 | |
1690 | /* Canonicalize zeroes. */ |
1691 | if (omsb == 0) { |
1692 | category = fcZero; |
1693 | if (semantics->nanEncoding == fltNanEncoding::NegativeZero) |
1694 | sign = false; |
1695 | } |
1696 | |
1697 | /* The fcZero case is a denormal that underflowed to zero. */ |
1698 | return (opStatus) (opUnderflow | opInexact); |
1699 | } |
1700 | |
1701 | IEEEFloat::opStatus IEEEFloat::addOrSubtractSpecials(const IEEEFloat &rhs, |
1702 | bool subtract) { |
1703 | switch (PackCategoriesIntoKey(category, rhs.category)) { |
1704 | default: |
1705 | llvm_unreachable(nullptr); |
1706 | |
1707 | case PackCategoriesIntoKey(fcZero, fcNaN): |
1708 | case PackCategoriesIntoKey(fcNormal, fcNaN): |
1709 | case PackCategoriesIntoKey(fcInfinity, fcNaN): |
1710 | assign(rhs); |
1711 | [[fallthrough]]; |
1712 | case PackCategoriesIntoKey(fcNaN, fcZero): |
1713 | case PackCategoriesIntoKey(fcNaN, fcNormal): |
1714 | case PackCategoriesIntoKey(fcNaN, fcInfinity): |
1715 | case PackCategoriesIntoKey(fcNaN, fcNaN): |
1716 | if (isSignaling()) { |
1717 | makeQuiet(); |
1718 | return opInvalidOp; |
1719 | } |
1720 | return rhs.isSignaling() ? opInvalidOp : opOK; |
1721 | |
1722 | case PackCategoriesIntoKey(fcNormal, fcZero): |
1723 | case PackCategoriesIntoKey(fcInfinity, fcNormal): |
1724 | case PackCategoriesIntoKey(fcInfinity, fcZero): |
1725 | return opOK; |
1726 | |
1727 | case PackCategoriesIntoKey(fcNormal, fcInfinity): |
1728 | case PackCategoriesIntoKey(fcZero, fcInfinity): |
1729 | category = fcInfinity; |
1730 | sign = rhs.sign ^ subtract; |
1731 | return opOK; |
1732 | |
1733 | case PackCategoriesIntoKey(fcZero, fcNormal): |
1734 | assign(rhs); |
1735 | sign = rhs.sign ^ subtract; |
1736 | return opOK; |
1737 | |
1738 | case PackCategoriesIntoKey(fcZero, fcZero): |
1739 | /* Sign depends on rounding mode; handled by caller. */ |
1740 | return opOK; |
1741 | |
1742 | case PackCategoriesIntoKey(fcInfinity, fcInfinity): |
1743 | /* Differently signed infinities can only be validly |
1744 | subtracted. */ |
1745 | if (((sign ^ rhs.sign)!=0) != subtract) { |
1746 | makeNaN(); |
1747 | return opInvalidOp; |
1748 | } |
1749 | |
1750 | return opOK; |
1751 | |
1752 | case PackCategoriesIntoKey(fcNormal, fcNormal): |
1753 | return opDivByZero; |
1754 | } |
1755 | } |
1756 | |
1757 | /* Add or subtract two normal numbers. */ |
1758 | lostFraction IEEEFloat::addOrSubtractSignificand(const IEEEFloat &rhs, |
1759 | bool subtract) { |
1760 | integerPart carry; |
1761 | lostFraction lost_fraction; |
1762 | int bits; |
1763 | |
1764 | /* Determine if the operation on the absolute values is effectively |
1765 | an addition or subtraction. */ |
1766 | subtract ^= static_cast<bool>(sign ^ rhs.sign); |
1767 | |
1768 | /* Are we bigger exponent-wise than the RHS? */ |
1769 | bits = exponent - rhs.exponent; |
1770 | |
1771 | /* Subtraction is more subtle than one might naively expect. */ |
1772 | if (subtract) { |
1773 | IEEEFloat temp_rhs(rhs); |
1774 | |
1775 | if (bits == 0) |
1776 | lost_fraction = lfExactlyZero; |
1777 | else if (bits > 0) { |
1778 | lost_fraction = temp_rhs.shiftSignificandRight(bits: bits - 1); |
1779 | shiftSignificandLeft(bits: 1); |
1780 | } else { |
1781 | lost_fraction = shiftSignificandRight(bits: -bits - 1); |
1782 | temp_rhs.shiftSignificandLeft(bits: 1); |
1783 | } |
1784 | |
1785 | // Should we reverse the subtraction. |
1786 | if (compareAbsoluteValue(rhs: temp_rhs) == cmpLessThan) { |
1787 | carry = temp_rhs.subtractSignificand |
1788 | (rhs: *this, borrow: lost_fraction != lfExactlyZero); |
1789 | copySignificand(rhs: temp_rhs); |
1790 | sign = !sign; |
1791 | } else { |
1792 | carry = subtractSignificand |
1793 | (rhs: temp_rhs, borrow: lost_fraction != lfExactlyZero); |
1794 | } |
1795 | |
1796 | /* Invert the lost fraction - it was on the RHS and |
1797 | subtracted. */ |
1798 | if (lost_fraction == lfLessThanHalf) |
1799 | lost_fraction = lfMoreThanHalf; |
1800 | else if (lost_fraction == lfMoreThanHalf) |
1801 | lost_fraction = lfLessThanHalf; |
1802 | |
1803 | /* The code above is intended to ensure that no borrow is |
1804 | necessary. */ |
1805 | assert(!carry); |
1806 | (void)carry; |
1807 | } else { |
1808 | if (bits > 0) { |
1809 | IEEEFloat temp_rhs(rhs); |
1810 | |
1811 | lost_fraction = temp_rhs.shiftSignificandRight(bits); |
1812 | carry = addSignificand(rhs: temp_rhs); |
1813 | } else { |
1814 | lost_fraction = shiftSignificandRight(bits: -bits); |
1815 | carry = addSignificand(rhs); |
1816 | } |
1817 | |
1818 | /* We have a guard bit; generating a carry cannot happen. */ |
1819 | assert(!carry); |
1820 | (void)carry; |
1821 | } |
1822 | |
1823 | return lost_fraction; |
1824 | } |
1825 | |
1826 | IEEEFloat::opStatus IEEEFloat::multiplySpecials(const IEEEFloat &rhs) { |
1827 | switch (PackCategoriesIntoKey(category, rhs.category)) { |
1828 | default: |
1829 | llvm_unreachable(nullptr); |
1830 | |
1831 | case PackCategoriesIntoKey(fcZero, fcNaN): |
1832 | case PackCategoriesIntoKey(fcNormal, fcNaN): |
1833 | case PackCategoriesIntoKey(fcInfinity, fcNaN): |
1834 | assign(rhs); |
1835 | sign = false; |
1836 | [[fallthrough]]; |
1837 | case PackCategoriesIntoKey(fcNaN, fcZero): |
1838 | case PackCategoriesIntoKey(fcNaN, fcNormal): |
1839 | case PackCategoriesIntoKey(fcNaN, fcInfinity): |
1840 | case PackCategoriesIntoKey(fcNaN, fcNaN): |
1841 | sign ^= rhs.sign; // restore the original sign |
1842 | if (isSignaling()) { |
1843 | makeQuiet(); |
1844 | return opInvalidOp; |
1845 | } |
1846 | return rhs.isSignaling() ? opInvalidOp : opOK; |
1847 | |
1848 | case PackCategoriesIntoKey(fcNormal, fcInfinity): |
1849 | case PackCategoriesIntoKey(fcInfinity, fcNormal): |
1850 | case PackCategoriesIntoKey(fcInfinity, fcInfinity): |
1851 | category = fcInfinity; |
1852 | return opOK; |
1853 | |
1854 | case PackCategoriesIntoKey(fcZero, fcNormal): |
1855 | case PackCategoriesIntoKey(fcNormal, fcZero): |
1856 | case PackCategoriesIntoKey(fcZero, fcZero): |
1857 | category = fcZero; |
1858 | return opOK; |
1859 | |
1860 | case PackCategoriesIntoKey(fcZero, fcInfinity): |
1861 | case PackCategoriesIntoKey(fcInfinity, fcZero): |
1862 | makeNaN(); |
1863 | return opInvalidOp; |
1864 | |
1865 | case PackCategoriesIntoKey(fcNormal, fcNormal): |
1866 | return opOK; |
1867 | } |
1868 | } |
1869 | |
1870 | IEEEFloat::opStatus IEEEFloat::divideSpecials(const IEEEFloat &rhs) { |
1871 | switch (PackCategoriesIntoKey(category, rhs.category)) { |
1872 | default: |
1873 | llvm_unreachable(nullptr); |
1874 | |
1875 | case PackCategoriesIntoKey(fcZero, fcNaN): |
1876 | case PackCategoriesIntoKey(fcNormal, fcNaN): |
1877 | case PackCategoriesIntoKey(fcInfinity, fcNaN): |
1878 | assign(rhs); |
1879 | sign = false; |
1880 | [[fallthrough]]; |
1881 | case PackCategoriesIntoKey(fcNaN, fcZero): |
1882 | case PackCategoriesIntoKey(fcNaN, fcNormal): |
1883 | case PackCategoriesIntoKey(fcNaN, fcInfinity): |
1884 | case PackCategoriesIntoKey(fcNaN, fcNaN): |
1885 | sign ^= rhs.sign; // restore the original sign |
1886 | if (isSignaling()) { |
1887 | makeQuiet(); |
1888 | return opInvalidOp; |
1889 | } |
1890 | return rhs.isSignaling() ? opInvalidOp : opOK; |
1891 | |
1892 | case PackCategoriesIntoKey(fcInfinity, fcZero): |
1893 | case PackCategoriesIntoKey(fcInfinity, fcNormal): |
1894 | case PackCategoriesIntoKey(fcZero, fcInfinity): |
1895 | case PackCategoriesIntoKey(fcZero, fcNormal): |
1896 | return opOK; |
1897 | |
1898 | case PackCategoriesIntoKey(fcNormal, fcInfinity): |
1899 | category = fcZero; |
1900 | return opOK; |
1901 | |
1902 | case PackCategoriesIntoKey(fcNormal, fcZero): |
1903 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly) |
1904 | makeNaN(SNaN: false, Negative: sign); |
1905 | else |
1906 | category = fcInfinity; |
1907 | return opDivByZero; |
1908 | |
1909 | case PackCategoriesIntoKey(fcInfinity, fcInfinity): |
1910 | case PackCategoriesIntoKey(fcZero, fcZero): |
1911 | makeNaN(); |
1912 | return opInvalidOp; |
1913 | |
1914 | case PackCategoriesIntoKey(fcNormal, fcNormal): |
1915 | return opOK; |
1916 | } |
1917 | } |
1918 | |
1919 | IEEEFloat::opStatus IEEEFloat::modSpecials(const IEEEFloat &rhs) { |
1920 | switch (PackCategoriesIntoKey(category, rhs.category)) { |
1921 | default: |
1922 | llvm_unreachable(nullptr); |
1923 | |
1924 | case PackCategoriesIntoKey(fcZero, fcNaN): |
1925 | case PackCategoriesIntoKey(fcNormal, fcNaN): |
1926 | case PackCategoriesIntoKey(fcInfinity, fcNaN): |
1927 | assign(rhs); |
1928 | [[fallthrough]]; |
1929 | case PackCategoriesIntoKey(fcNaN, fcZero): |
1930 | case PackCategoriesIntoKey(fcNaN, fcNormal): |
1931 | case PackCategoriesIntoKey(fcNaN, fcInfinity): |
1932 | case PackCategoriesIntoKey(fcNaN, fcNaN): |
1933 | if (isSignaling()) { |
1934 | makeQuiet(); |
1935 | return opInvalidOp; |
1936 | } |
1937 | return rhs.isSignaling() ? opInvalidOp : opOK; |
1938 | |
1939 | case PackCategoriesIntoKey(fcZero, fcInfinity): |
1940 | case PackCategoriesIntoKey(fcZero, fcNormal): |
1941 | case PackCategoriesIntoKey(fcNormal, fcInfinity): |
1942 | return opOK; |
1943 | |
1944 | case PackCategoriesIntoKey(fcNormal, fcZero): |
1945 | case PackCategoriesIntoKey(fcInfinity, fcZero): |
1946 | case PackCategoriesIntoKey(fcInfinity, fcNormal): |
1947 | case PackCategoriesIntoKey(fcInfinity, fcInfinity): |
1948 | case PackCategoriesIntoKey(fcZero, fcZero): |
1949 | makeNaN(); |
1950 | return opInvalidOp; |
1951 | |
1952 | case PackCategoriesIntoKey(fcNormal, fcNormal): |
1953 | return opOK; |
1954 | } |
1955 | } |
1956 | |
1957 | IEEEFloat::opStatus IEEEFloat::remainderSpecials(const IEEEFloat &rhs) { |
1958 | switch (PackCategoriesIntoKey(category, rhs.category)) { |
1959 | default: |
1960 | llvm_unreachable(nullptr); |
1961 | |
1962 | case PackCategoriesIntoKey(fcZero, fcNaN): |
1963 | case PackCategoriesIntoKey(fcNormal, fcNaN): |
1964 | case PackCategoriesIntoKey(fcInfinity, fcNaN): |
1965 | assign(rhs); |
1966 | [[fallthrough]]; |
1967 | case PackCategoriesIntoKey(fcNaN, fcZero): |
1968 | case PackCategoriesIntoKey(fcNaN, fcNormal): |
1969 | case PackCategoriesIntoKey(fcNaN, fcInfinity): |
1970 | case PackCategoriesIntoKey(fcNaN, fcNaN): |
1971 | if (isSignaling()) { |
1972 | makeQuiet(); |
1973 | return opInvalidOp; |
1974 | } |
1975 | return rhs.isSignaling() ? opInvalidOp : opOK; |
1976 | |
1977 | case PackCategoriesIntoKey(fcZero, fcInfinity): |
1978 | case PackCategoriesIntoKey(fcZero, fcNormal): |
1979 | case PackCategoriesIntoKey(fcNormal, fcInfinity): |
1980 | return opOK; |
1981 | |
1982 | case PackCategoriesIntoKey(fcNormal, fcZero): |
1983 | case PackCategoriesIntoKey(fcInfinity, fcZero): |
1984 | case PackCategoriesIntoKey(fcInfinity, fcNormal): |
1985 | case PackCategoriesIntoKey(fcInfinity, fcInfinity): |
1986 | case PackCategoriesIntoKey(fcZero, fcZero): |
1987 | makeNaN(); |
1988 | return opInvalidOp; |
1989 | |
1990 | case PackCategoriesIntoKey(fcNormal, fcNormal): |
1991 | return opDivByZero; // fake status, indicating this is not a special case |
1992 | } |
1993 | } |
1994 | |
1995 | /* Change sign. */ |
1996 | void IEEEFloat::changeSign() { |
1997 | // With NaN-as-negative-zero, neither NaN or negative zero can change |
1998 | // their signs. |
1999 | if (semantics->nanEncoding == fltNanEncoding::NegativeZero && |
2000 | (isZero() || isNaN())) |
2001 | return; |
2002 | /* Look mummy, this one's easy. */ |
2003 | sign = !sign; |
2004 | } |
2005 | |
2006 | /* Normalized addition or subtraction. */ |
2007 | IEEEFloat::opStatus IEEEFloat::addOrSubtract(const IEEEFloat &rhs, |
2008 | roundingMode rounding_mode, |
2009 | bool subtract) { |
2010 | opStatus fs; |
2011 | |
2012 | fs = addOrSubtractSpecials(rhs, subtract); |
2013 | |
2014 | /* This return code means it was not a simple case. */ |
2015 | if (fs == opDivByZero) { |
2016 | lostFraction lost_fraction; |
2017 | |
2018 | lost_fraction = addOrSubtractSignificand(rhs, subtract); |
2019 | fs = normalize(rounding_mode, lost_fraction); |
2020 | |
2021 | /* Can only be zero if we lost no fraction. */ |
2022 | assert(category != fcZero || lost_fraction == lfExactlyZero); |
2023 | } |
2024 | |
2025 | /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a |
2026 | positive zero unless rounding to minus infinity, except that |
2027 | adding two like-signed zeroes gives that zero. */ |
2028 | if (category == fcZero) { |
2029 | if (rhs.category != fcZero || (sign == rhs.sign) == subtract) |
2030 | sign = (rounding_mode == rmTowardNegative); |
2031 | // NaN-in-negative-zero means zeros need to be normalized to +0. |
2032 | if (semantics->nanEncoding == fltNanEncoding::NegativeZero) |
2033 | sign = false; |
2034 | } |
2035 | |
2036 | return fs; |
2037 | } |
2038 | |
2039 | /* Normalized addition. */ |
2040 | IEEEFloat::opStatus IEEEFloat::add(const IEEEFloat &rhs, |
2041 | roundingMode rounding_mode) { |
2042 | return addOrSubtract(rhs, rounding_mode, subtract: false); |
2043 | } |
2044 | |
2045 | /* Normalized subtraction. */ |
2046 | IEEEFloat::opStatus IEEEFloat::subtract(const IEEEFloat &rhs, |
2047 | roundingMode rounding_mode) { |
2048 | return addOrSubtract(rhs, rounding_mode, subtract: true); |
2049 | } |
2050 | |
2051 | /* Normalized multiply. */ |
2052 | IEEEFloat::opStatus IEEEFloat::multiply(const IEEEFloat &rhs, |
2053 | roundingMode rounding_mode) { |
2054 | opStatus fs; |
2055 | |
2056 | sign ^= rhs.sign; |
2057 | fs = multiplySpecials(rhs); |
2058 | |
2059 | if (isZero() && semantics->nanEncoding == fltNanEncoding::NegativeZero) |
2060 | sign = false; |
2061 | if (isFiniteNonZero()) { |
2062 | lostFraction lost_fraction = multiplySignificand(rhs); |
2063 | fs = normalize(rounding_mode, lost_fraction); |
2064 | if (lost_fraction != lfExactlyZero) |
2065 | fs = (opStatus) (fs | opInexact); |
2066 | } |
2067 | |
2068 | return fs; |
2069 | } |
2070 | |
2071 | /* Normalized divide. */ |
2072 | IEEEFloat::opStatus IEEEFloat::divide(const IEEEFloat &rhs, |
2073 | roundingMode rounding_mode) { |
2074 | opStatus fs; |
2075 | |
2076 | sign ^= rhs.sign; |
2077 | fs = divideSpecials(rhs); |
2078 | |
2079 | if (isZero() && semantics->nanEncoding == fltNanEncoding::NegativeZero) |
2080 | sign = false; |
2081 | if (isFiniteNonZero()) { |
2082 | lostFraction lost_fraction = divideSignificand(rhs); |
2083 | fs = normalize(rounding_mode, lost_fraction); |
2084 | if (lost_fraction != lfExactlyZero) |
2085 | fs = (opStatus) (fs | opInexact); |
2086 | } |
2087 | |
2088 | return fs; |
2089 | } |
2090 | |
2091 | /* Normalized remainder. */ |
2092 | IEEEFloat::opStatus IEEEFloat::remainder(const IEEEFloat &rhs) { |
2093 | opStatus fs; |
2094 | unsigned int origSign = sign; |
2095 | |
2096 | // First handle the special cases. |
2097 | fs = remainderSpecials(rhs); |
2098 | if (fs != opDivByZero) |
2099 | return fs; |
2100 | |
2101 | fs = opOK; |
2102 | |
2103 | // Make sure the current value is less than twice the denom. If the addition |
2104 | // did not succeed (an overflow has happened), which means that the finite |
2105 | // value we currently posses must be less than twice the denom (as we are |
2106 | // using the same semantics). |
2107 | IEEEFloat P2 = rhs; |
2108 | if (P2.add(rhs, rounding_mode: rmNearestTiesToEven) == opOK) { |
2109 | fs = mod(P2); |
2110 | assert(fs == opOK); |
2111 | } |
2112 | |
2113 | // Lets work with absolute numbers. |
2114 | IEEEFloat P = rhs; |
2115 | P.sign = false; |
2116 | sign = false; |
2117 | |
2118 | // |
2119 | // To calculate the remainder we use the following scheme. |
2120 | // |
2121 | // The remainder is defained as follows: |
2122 | // |
2123 | // remainder = numer - rquot * denom = x - r * p |
2124 | // |
2125 | // Where r is the result of: x/p, rounded toward the nearest integral value |
2126 | // (with halfway cases rounded toward the even number). |
2127 | // |
2128 | // Currently, (after x mod 2p): |
2129 | // r is the number of 2p's present inside x, which is inherently, an even |
2130 | // number of p's. |
2131 | // |
2132 | // We may split the remaining calculation into 4 options: |
2133 | // - if x < 0.5p then we round to the nearest number with is 0, and are done. |
2134 | // - if x == 0.5p then we round to the nearest even number which is 0, and we |
2135 | // are done as well. |
2136 | // - if 0.5p < x < p then we round to nearest number which is 1, and we have |
2137 | // to subtract 1p at least once. |
2138 | // - if x >= p then we must subtract p at least once, as x must be a |
2139 | // remainder. |
2140 | // |
2141 | // By now, we were done, or we added 1 to r, which in turn, now an odd number. |
2142 | // |
2143 | // We can now split the remaining calculation to the following 3 options: |
2144 | // - if x < 0.5p then we round to the nearest number with is 0, and are done. |
2145 | // - if x == 0.5p then we round to the nearest even number. As r is odd, we |
2146 | // must round up to the next even number. so we must subtract p once more. |
2147 | // - if x > 0.5p (and inherently x < p) then we must round r up to the next |
2148 | // integral, and subtract p once more. |
2149 | // |
2150 | |
2151 | // Extend the semantics to prevent an overflow/underflow or inexact result. |
2152 | bool losesInfo; |
2153 | fltSemantics extendedSemantics = *semantics; |
2154 | extendedSemantics.maxExponent++; |
2155 | extendedSemantics.minExponent--; |
2156 | extendedSemantics.precision += 2; |
2157 | |
2158 | IEEEFloat VEx = *this; |
2159 | fs = VEx.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo); |
2160 | assert(fs == opOK && !losesInfo); |
2161 | IEEEFloat PEx = P; |
2162 | fs = PEx.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo); |
2163 | assert(fs == opOK && !losesInfo); |
2164 | |
2165 | // It is simpler to work with 2x instead of 0.5p, and we do not need to lose |
2166 | // any fraction. |
2167 | fs = VEx.add(rhs: VEx, rounding_mode: rmNearestTiesToEven); |
2168 | assert(fs == opOK); |
2169 | |
2170 | if (VEx.compare(PEx) == cmpGreaterThan) { |
2171 | fs = subtract(rhs: P, rounding_mode: rmNearestTiesToEven); |
2172 | assert(fs == opOK); |
2173 | |
2174 | // Make VEx = this.add(this), but because we have different semantics, we do |
2175 | // not want to `convert` again, so we just subtract PEx twice (which equals |
2176 | // to the desired value). |
2177 | fs = VEx.subtract(rhs: PEx, rounding_mode: rmNearestTiesToEven); |
2178 | assert(fs == opOK); |
2179 | fs = VEx.subtract(rhs: PEx, rounding_mode: rmNearestTiesToEven); |
2180 | assert(fs == opOK); |
2181 | |
2182 | cmpResult result = VEx.compare(PEx); |
2183 | if (result == cmpGreaterThan || result == cmpEqual) { |
2184 | fs = subtract(rhs: P, rounding_mode: rmNearestTiesToEven); |
2185 | assert(fs == opOK); |
2186 | } |
2187 | } |
2188 | |
2189 | if (isZero()) { |
2190 | sign = origSign; // IEEE754 requires this |
2191 | if (semantics->nanEncoding == fltNanEncoding::NegativeZero) |
2192 | // But some 8-bit floats only have positive 0. |
2193 | sign = false; |
2194 | } |
2195 | |
2196 | else |
2197 | sign ^= origSign; |
2198 | return fs; |
2199 | } |
2200 | |
2201 | /* Normalized llvm frem (C fmod). */ |
2202 | IEEEFloat::opStatus IEEEFloat::mod(const IEEEFloat &rhs) { |
2203 | opStatus fs; |
2204 | fs = modSpecials(rhs); |
2205 | unsigned int origSign = sign; |
2206 | |
2207 | while (isFiniteNonZero() && rhs.isFiniteNonZero() && |
2208 | compareAbsoluteValue(rhs) != cmpLessThan) { |
2209 | int Exp = ilogb(Arg: *this) - ilogb(Arg: rhs); |
2210 | IEEEFloat V = scalbn(X: rhs, Exp, rmNearestTiesToEven); |
2211 | // V can overflow to NaN with fltNonfiniteBehavior::NanOnly, so explicitly |
2212 | // check for it. |
2213 | if (V.isNaN() || compareAbsoluteValue(rhs: V) == cmpLessThan) |
2214 | V = scalbn(X: rhs, Exp: Exp - 1, rmNearestTiesToEven); |
2215 | V.sign = sign; |
2216 | |
2217 | fs = subtract(rhs: V, rounding_mode: rmNearestTiesToEven); |
2218 | assert(fs==opOK); |
2219 | } |
2220 | if (isZero()) { |
2221 | sign = origSign; // fmod requires this |
2222 | if (semantics->nanEncoding == fltNanEncoding::NegativeZero) |
2223 | sign = false; |
2224 | } |
2225 | return fs; |
2226 | } |
2227 | |
2228 | /* Normalized fused-multiply-add. */ |
2229 | IEEEFloat::opStatus IEEEFloat::fusedMultiplyAdd(const IEEEFloat &multiplicand, |
2230 | const IEEEFloat &addend, |
2231 | roundingMode rounding_mode) { |
2232 | opStatus fs; |
2233 | |
2234 | /* Post-multiplication sign, before addition. */ |
2235 | sign ^= multiplicand.sign; |
2236 | |
2237 | /* If and only if all arguments are normal do we need to do an |
2238 | extended-precision calculation. */ |
2239 | if (isFiniteNonZero() && |
2240 | multiplicand.isFiniteNonZero() && |
2241 | addend.isFinite()) { |
2242 | lostFraction lost_fraction; |
2243 | |
2244 | lost_fraction = multiplySignificand(rhs: multiplicand, addend); |
2245 | fs = normalize(rounding_mode, lost_fraction); |
2246 | if (lost_fraction != lfExactlyZero) |
2247 | fs = (opStatus) (fs | opInexact); |
2248 | |
2249 | /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a |
2250 | positive zero unless rounding to minus infinity, except that |
2251 | adding two like-signed zeroes gives that zero. */ |
2252 | if (category == fcZero && !(fs & opUnderflow) && sign != addend.sign) { |
2253 | sign = (rounding_mode == rmTowardNegative); |
2254 | if (semantics->nanEncoding == fltNanEncoding::NegativeZero) |
2255 | sign = false; |
2256 | } |
2257 | } else { |
2258 | fs = multiplySpecials(rhs: multiplicand); |
2259 | |
2260 | /* FS can only be opOK or opInvalidOp. There is no more work |
2261 | to do in the latter case. The IEEE-754R standard says it is |
2262 | implementation-defined in this case whether, if ADDEND is a |
2263 | quiet NaN, we raise invalid op; this implementation does so. |
2264 | |
2265 | If we need to do the addition we can do so with normal |
2266 | precision. */ |
2267 | if (fs == opOK) |
2268 | fs = addOrSubtract(rhs: addend, rounding_mode, subtract: false); |
2269 | } |
2270 | |
2271 | return fs; |
2272 | } |
2273 | |
2274 | /* Rounding-mode correct round to integral value. */ |
2275 | IEEEFloat::opStatus IEEEFloat::roundToIntegral(roundingMode rounding_mode) { |
2276 | opStatus fs; |
2277 | |
2278 | if (isInfinity()) |
2279 | // [IEEE Std 754-2008 6.1]: |
2280 | // The behavior of infinity in floating-point arithmetic is derived from the |
2281 | // limiting cases of real arithmetic with operands of arbitrarily |
2282 | // large magnitude, when such a limit exists. |
2283 | // ... |
2284 | // Operations on infinite operands are usually exact and therefore signal no |
2285 | // exceptions ... |
2286 | return opOK; |
2287 | |
2288 | if (isNaN()) { |
2289 | if (isSignaling()) { |
2290 | // [IEEE Std 754-2008 6.2]: |
2291 | // Under default exception handling, any operation signaling an invalid |
2292 | // operation exception and for which a floating-point result is to be |
2293 | // delivered shall deliver a quiet NaN. |
2294 | makeQuiet(); |
2295 | // [IEEE Std 754-2008 6.2]: |
2296 | // Signaling NaNs shall be reserved operands that, under default exception |
2297 | // handling, signal the invalid operation exception(see 7.2) for every |
2298 | // general-computational and signaling-computational operation except for |
2299 | // the conversions described in 5.12. |
2300 | return opInvalidOp; |
2301 | } else { |
2302 | // [IEEE Std 754-2008 6.2]: |
2303 | // For an operation with quiet NaN inputs, other than maximum and minimum |
2304 | // operations, if a floating-point result is to be delivered the result |
2305 | // shall be a quiet NaN which should be one of the input NaNs. |
2306 | // ... |
2307 | // Every general-computational and quiet-computational operation involving |
2308 | // one or more input NaNs, none of them signaling, shall signal no |
2309 | // exception, except fusedMultiplyAdd might signal the invalid operation |
2310 | // exception(see 7.2). |
2311 | return opOK; |
2312 | } |
2313 | } |
2314 | |
2315 | if (isZero()) { |
2316 | // [IEEE Std 754-2008 6.3]: |
2317 | // ... the sign of the result of conversions, the quantize operation, the |
2318 | // roundToIntegral operations, and the roundToIntegralExact(see 5.3.1) is |
2319 | // the sign of the first or only operand. |
2320 | return opOK; |
2321 | } |
2322 | |
2323 | // If the exponent is large enough, we know that this value is already |
2324 | // integral, and the arithmetic below would potentially cause it to saturate |
2325 | // to +/-Inf. Bail out early instead. |
2326 | if (exponent+1 >= (int)semanticsPrecision(semantics: *semantics)) |
2327 | return opOK; |
2328 | |
2329 | // The algorithm here is quite simple: we add 2^(p-1), where p is the |
2330 | // precision of our format, and then subtract it back off again. The choice |
2331 | // of rounding modes for the addition/subtraction determines the rounding mode |
2332 | // for our integral rounding as well. |
2333 | // NOTE: When the input value is negative, we do subtraction followed by |
2334 | // addition instead. |
2335 | APInt IntegerConstant(NextPowerOf2(A: semanticsPrecision(semantics: *semantics)), 1); |
2336 | IntegerConstant <<= semanticsPrecision(semantics: *semantics)-1; |
2337 | IEEEFloat MagicConstant(*semantics); |
2338 | fs = MagicConstant.convertFromAPInt(IntegerConstant, false, |
2339 | rmNearestTiesToEven); |
2340 | assert(fs == opOK); |
2341 | MagicConstant.sign = sign; |
2342 | |
2343 | // Preserve the input sign so that we can handle the case of zero result |
2344 | // correctly. |
2345 | bool inputSign = isNegative(); |
2346 | |
2347 | fs = add(rhs: MagicConstant, rounding_mode); |
2348 | |
2349 | // Current value and 'MagicConstant' are both integers, so the result of the |
2350 | // subtraction is always exact according to Sterbenz' lemma. |
2351 | subtract(rhs: MagicConstant, rounding_mode); |
2352 | |
2353 | // Restore the input sign. |
2354 | if (inputSign != isNegative()) |
2355 | changeSign(); |
2356 | |
2357 | return fs; |
2358 | } |
2359 | |
2360 | |
2361 | /* Comparison requires normalized numbers. */ |
2362 | IEEEFloat::cmpResult IEEEFloat::compare(const IEEEFloat &rhs) const { |
2363 | cmpResult result; |
2364 | |
2365 | assert(semantics == rhs.semantics); |
2366 | |
2367 | switch (PackCategoriesIntoKey(category, rhs.category)) { |
2368 | default: |
2369 | llvm_unreachable(nullptr); |
2370 | |
2371 | case PackCategoriesIntoKey(fcNaN, fcZero): |
2372 | case PackCategoriesIntoKey(fcNaN, fcNormal): |
2373 | case PackCategoriesIntoKey(fcNaN, fcInfinity): |
2374 | case PackCategoriesIntoKey(fcNaN, fcNaN): |
2375 | case PackCategoriesIntoKey(fcZero, fcNaN): |
2376 | case PackCategoriesIntoKey(fcNormal, fcNaN): |
2377 | case PackCategoriesIntoKey(fcInfinity, fcNaN): |
2378 | return cmpUnordered; |
2379 | |
2380 | case PackCategoriesIntoKey(fcInfinity, fcNormal): |
2381 | case PackCategoriesIntoKey(fcInfinity, fcZero): |
2382 | case PackCategoriesIntoKey(fcNormal, fcZero): |
2383 | if (sign) |
2384 | return cmpLessThan; |
2385 | else |
2386 | return cmpGreaterThan; |
2387 | |
2388 | case PackCategoriesIntoKey(fcNormal, fcInfinity): |
2389 | case PackCategoriesIntoKey(fcZero, fcInfinity): |
2390 | case PackCategoriesIntoKey(fcZero, fcNormal): |
2391 | if (rhs.sign) |
2392 | return cmpGreaterThan; |
2393 | else |
2394 | return cmpLessThan; |
2395 | |
2396 | case PackCategoriesIntoKey(fcInfinity, fcInfinity): |
2397 | if (sign == rhs.sign) |
2398 | return cmpEqual; |
2399 | else if (sign) |
2400 | return cmpLessThan; |
2401 | else |
2402 | return cmpGreaterThan; |
2403 | |
2404 | case PackCategoriesIntoKey(fcZero, fcZero): |
2405 | return cmpEqual; |
2406 | |
2407 | case PackCategoriesIntoKey(fcNormal, fcNormal): |
2408 | break; |
2409 | } |
2410 | |
2411 | /* Two normal numbers. Do they have the same sign? */ |
2412 | if (sign != rhs.sign) { |
2413 | if (sign) |
2414 | result = cmpLessThan; |
2415 | else |
2416 | result = cmpGreaterThan; |
2417 | } else { |
2418 | /* Compare absolute values; invert result if negative. */ |
2419 | result = compareAbsoluteValue(rhs); |
2420 | |
2421 | if (sign) { |
2422 | if (result == cmpLessThan) |
2423 | result = cmpGreaterThan; |
2424 | else if (result == cmpGreaterThan) |
2425 | result = cmpLessThan; |
2426 | } |
2427 | } |
2428 | |
2429 | return result; |
2430 | } |
2431 | |
2432 | /// IEEEFloat::convert - convert a value of one floating point type to another. |
2433 | /// The return value corresponds to the IEEE754 exceptions. *losesInfo |
2434 | /// records whether the transformation lost information, i.e. whether |
2435 | /// converting the result back to the original type will produce the |
2436 | /// original value (this is almost the same as return value==fsOK, but there |
2437 | /// are edge cases where this is not so). |
2438 | |
2439 | IEEEFloat::opStatus IEEEFloat::convert(const fltSemantics &toSemantics, |
2440 | roundingMode rounding_mode, |
2441 | bool *losesInfo) { |
2442 | lostFraction lostFraction; |
2443 | unsigned int newPartCount, oldPartCount; |
2444 | opStatus fs; |
2445 | int shift; |
2446 | const fltSemantics &fromSemantics = *semantics; |
2447 | bool is_signaling = isSignaling(); |
2448 | |
2449 | lostFraction = lfExactlyZero; |
2450 | newPartCount = partCountForBits(bits: toSemantics.precision + 1); |
2451 | oldPartCount = partCount(); |
2452 | shift = toSemantics.precision - fromSemantics.precision; |
2453 | |
2454 | bool X86SpecialNan = false; |
2455 | if (&fromSemantics == &semX87DoubleExtended && |
2456 | &toSemantics != &semX87DoubleExtended && category == fcNaN && |
2457 | (!(*significandParts() & 0x8000000000000000ULL) || |
2458 | !(*significandParts() & 0x4000000000000000ULL))) { |
2459 | // x86 has some unusual NaNs which cannot be represented in any other |
2460 | // format; note them here. |
2461 | X86SpecialNan = true; |
2462 | } |
2463 | |
2464 | // If this is a truncation of a denormal number, and the target semantics |
2465 | // has larger exponent range than the source semantics (this can happen |
2466 | // when truncating from PowerPC double-double to double format), the |
2467 | // right shift could lose result mantissa bits. Adjust exponent instead |
2468 | // of performing excessive shift. |
2469 | // Also do a similar trick in case shifting denormal would produce zero |
2470 | // significand as this case isn't handled correctly by normalize. |
2471 | if (shift < 0 && isFiniteNonZero()) { |
2472 | int omsb = significandMSB() + 1; |
2473 | int exponentChange = omsb - fromSemantics.precision; |
2474 | if (exponent + exponentChange < toSemantics.minExponent) |
2475 | exponentChange = toSemantics.minExponent - exponent; |
2476 | if (exponentChange < shift) |
2477 | exponentChange = shift; |
2478 | if (exponentChange < 0) { |
2479 | shift -= exponentChange; |
2480 | exponent += exponentChange; |
2481 | } else if (omsb <= -shift) { |
2482 | exponentChange = omsb + shift - 1; // leave at least one bit set |
2483 | shift -= exponentChange; |
2484 | exponent += exponentChange; |
2485 | } |
2486 | } |
2487 | |
2488 | // If this is a truncation, perform the shift before we narrow the storage. |
2489 | if (shift < 0 && (isFiniteNonZero() || |
2490 | (category == fcNaN && semantics->nonFiniteBehavior != |
2491 | fltNonfiniteBehavior::NanOnly))) |
2492 | lostFraction = shiftRight(dst: significandParts(), parts: oldPartCount, bits: -shift); |
2493 | |
2494 | // Fix the storage so it can hold to new value. |
2495 | if (newPartCount > oldPartCount) { |
2496 | // The new type requires more storage; make it available. |
2497 | integerPart *newParts; |
2498 | newParts = new integerPart[newPartCount]; |
2499 | APInt::tcSet(newParts, 0, newPartCount); |
2500 | if (isFiniteNonZero() || category==fcNaN) |
2501 | APInt::tcAssign(newParts, significandParts(), oldPartCount); |
2502 | freeSignificand(); |
2503 | significand.parts = newParts; |
2504 | } else if (newPartCount == 1 && oldPartCount != 1) { |
2505 | // Switch to built-in storage for a single part. |
2506 | integerPart newPart = 0; |
2507 | if (isFiniteNonZero() || category==fcNaN) |
2508 | newPart = significandParts()[0]; |
2509 | freeSignificand(); |
2510 | significand.part = newPart; |
2511 | } |
2512 | |
2513 | // Now that we have the right storage, switch the semantics. |
2514 | semantics = &toSemantics; |
2515 | |
2516 | // If this is an extension, perform the shift now that the storage is |
2517 | // available. |
2518 | if (shift > 0 && (isFiniteNonZero() || category==fcNaN)) |
2519 | APInt::tcShiftLeft(significandParts(), Words: newPartCount, Count: shift); |
2520 | |
2521 | if (isFiniteNonZero()) { |
2522 | fs = normalize(rounding_mode, lost_fraction: lostFraction); |
2523 | *losesInfo = (fs != opOK); |
2524 | } else if (category == fcNaN) { |
2525 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly) { |
2526 | *losesInfo = |
2527 | fromSemantics.nonFiniteBehavior != fltNonfiniteBehavior::NanOnly; |
2528 | makeNaN(SNaN: false, Negative: sign); |
2529 | return is_signaling ? opInvalidOp : opOK; |
2530 | } |
2531 | |
2532 | // If NaN is negative zero, we need to create a new NaN to avoid converting |
2533 | // NaN to -Inf. |
2534 | if (fromSemantics.nanEncoding == fltNanEncoding::NegativeZero && |
2535 | semantics->nanEncoding != fltNanEncoding::NegativeZero) |
2536 | makeNaN(SNaN: false, Negative: false); |
2537 | |
2538 | *losesInfo = lostFraction != lfExactlyZero || X86SpecialNan; |
2539 | |
2540 | // For x87 extended precision, we want to make a NaN, not a special NaN if |
2541 | // the input wasn't special either. |
2542 | if (!X86SpecialNan && semantics == &semX87DoubleExtended) |
2543 | APInt::tcSetBit(significandParts(), bit: semantics->precision - 1); |
2544 | |
2545 | // Convert of sNaN creates qNaN and raises an exception (invalid op). |
2546 | // This also guarantees that a sNaN does not become Inf on a truncation |
2547 | // that loses all payload bits. |
2548 | if (is_signaling) { |
2549 | makeQuiet(); |
2550 | fs = opInvalidOp; |
2551 | } else { |
2552 | fs = opOK; |
2553 | } |
2554 | } else if (category == fcInfinity && |
2555 | semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly) { |
2556 | makeNaN(SNaN: false, Negative: sign); |
2557 | *losesInfo = true; |
2558 | fs = opInexact; |
2559 | } else if (category == fcZero && |
2560 | semantics->nanEncoding == fltNanEncoding::NegativeZero) { |
2561 | // Negative zero loses info, but positive zero doesn't. |
2562 | *losesInfo = |
2563 | fromSemantics.nanEncoding != fltNanEncoding::NegativeZero && sign; |
2564 | fs = *losesInfo ? opInexact : opOK; |
2565 | // NaN is negative zero means -0 -> +0, which can lose information |
2566 | sign = false; |
2567 | } else { |
2568 | *losesInfo = false; |
2569 | fs = opOK; |
2570 | } |
2571 | |
2572 | return fs; |
2573 | } |
2574 | |
2575 | /* Convert a floating point number to an integer according to the |
2576 | rounding mode. If the rounded integer value is out of range this |
2577 | returns an invalid operation exception and the contents of the |
2578 | destination parts are unspecified. If the rounded value is in |
2579 | range but the floating point number is not the exact integer, the C |
2580 | standard doesn't require an inexact exception to be raised. IEEE |
2581 | 854 does require it so we do that. |
2582 | |
2583 | Note that for conversions to integer type the C standard requires |
2584 | round-to-zero to always be used. */ |
2585 | IEEEFloat::opStatus IEEEFloat::convertToSignExtendedInteger( |
2586 | MutableArrayRef<integerPart> parts, unsigned int width, bool isSigned, |
2587 | roundingMode rounding_mode, bool *isExact) const { |
2588 | lostFraction lost_fraction; |
2589 | const integerPart *src; |
2590 | unsigned int dstPartsCount, truncatedBits; |
2591 | |
2592 | *isExact = false; |
2593 | |
2594 | /* Handle the three special cases first. */ |
2595 | if (category == fcInfinity || category == fcNaN) |
2596 | return opInvalidOp; |
2597 | |
2598 | dstPartsCount = partCountForBits(bits: width); |
2599 | assert(dstPartsCount <= parts.size() && "Integer too big" ); |
2600 | |
2601 | if (category == fcZero) { |
2602 | APInt::tcSet(parts.data(), 0, dstPartsCount); |
2603 | // Negative zero can't be represented as an int. |
2604 | *isExact = !sign; |
2605 | return opOK; |
2606 | } |
2607 | |
2608 | src = significandParts(); |
2609 | |
2610 | /* Step 1: place our absolute value, with any fraction truncated, in |
2611 | the destination. */ |
2612 | if (exponent < 0) { |
2613 | /* Our absolute value is less than one; truncate everything. */ |
2614 | APInt::tcSet(parts.data(), 0, dstPartsCount); |
2615 | /* For exponent -1 the integer bit represents .5, look at that. |
2616 | For smaller exponents leftmost truncated bit is 0. */ |
2617 | truncatedBits = semantics->precision -1U - exponent; |
2618 | } else { |
2619 | /* We want the most significant (exponent + 1) bits; the rest are |
2620 | truncated. */ |
2621 | unsigned int bits = exponent + 1U; |
2622 | |
2623 | /* Hopelessly large in magnitude? */ |
2624 | if (bits > width) |
2625 | return opInvalidOp; |
2626 | |
2627 | if (bits < semantics->precision) { |
2628 | /* We truncate (semantics->precision - bits) bits. */ |
2629 | truncatedBits = semantics->precision - bits; |
2630 | APInt::tcExtract(parts.data(), dstCount: dstPartsCount, src, srcBits: bits, srcLSB: truncatedBits); |
2631 | } else { |
2632 | /* We want at least as many bits as are available. */ |
2633 | APInt::tcExtract(parts.data(), dstCount: dstPartsCount, src, srcBits: semantics->precision, |
2634 | srcLSB: 0); |
2635 | APInt::tcShiftLeft(parts.data(), Words: dstPartsCount, |
2636 | Count: bits - semantics->precision); |
2637 | truncatedBits = 0; |
2638 | } |
2639 | } |
2640 | |
2641 | /* Step 2: work out any lost fraction, and increment the absolute |
2642 | value if we would round away from zero. */ |
2643 | if (truncatedBits) { |
2644 | lost_fraction = lostFractionThroughTruncation(parts: src, partCount: partCount(), |
2645 | bits: truncatedBits); |
2646 | if (lost_fraction != lfExactlyZero && |
2647 | roundAwayFromZero(rounding_mode, lost_fraction, bit: truncatedBits)) { |
2648 | if (APInt::tcIncrement(dst: parts.data(), parts: dstPartsCount)) |
2649 | return opInvalidOp; /* Overflow. */ |
2650 | } |
2651 | } else { |
2652 | lost_fraction = lfExactlyZero; |
2653 | } |
2654 | |
2655 | /* Step 3: check if we fit in the destination. */ |
2656 | unsigned int omsb = APInt::tcMSB(parts: parts.data(), n: dstPartsCount) + 1; |
2657 | |
2658 | if (sign) { |
2659 | if (!isSigned) { |
2660 | /* Negative numbers cannot be represented as unsigned. */ |
2661 | if (omsb != 0) |
2662 | return opInvalidOp; |
2663 | } else { |
2664 | /* It takes omsb bits to represent the unsigned integer value. |
2665 | We lose a bit for the sign, but care is needed as the |
2666 | maximally negative integer is a special case. */ |
2667 | if (omsb == width && |
2668 | APInt::tcLSB(parts.data(), n: dstPartsCount) + 1 != omsb) |
2669 | return opInvalidOp; |
2670 | |
2671 | /* This case can happen because of rounding. */ |
2672 | if (omsb > width) |
2673 | return opInvalidOp; |
2674 | } |
2675 | |
2676 | APInt::tcNegate (parts.data(), dstPartsCount); |
2677 | } else { |
2678 | if (omsb >= width + !isSigned) |
2679 | return opInvalidOp; |
2680 | } |
2681 | |
2682 | if (lost_fraction == lfExactlyZero) { |
2683 | *isExact = true; |
2684 | return opOK; |
2685 | } else |
2686 | return opInexact; |
2687 | } |
2688 | |
2689 | /* Same as convertToSignExtendedInteger, except we provide |
2690 | deterministic values in case of an invalid operation exception, |
2691 | namely zero for NaNs and the minimal or maximal value respectively |
2692 | for underflow or overflow. |
2693 | The *isExact output tells whether the result is exact, in the sense |
2694 | that converting it back to the original floating point type produces |
2695 | the original value. This is almost equivalent to result==opOK, |
2696 | except for negative zeroes. |
2697 | */ |
2698 | IEEEFloat::opStatus |
2699 | IEEEFloat::convertToInteger(MutableArrayRef<integerPart> parts, |
2700 | unsigned int width, bool isSigned, |
2701 | roundingMode rounding_mode, bool *isExact) const { |
2702 | opStatus fs; |
2703 | |
2704 | fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode, |
2705 | isExact); |
2706 | |
2707 | if (fs == opInvalidOp) { |
2708 | unsigned int bits, dstPartsCount; |
2709 | |
2710 | dstPartsCount = partCountForBits(bits: width); |
2711 | assert(dstPartsCount <= parts.size() && "Integer too big" ); |
2712 | |
2713 | if (category == fcNaN) |
2714 | bits = 0; |
2715 | else if (sign) |
2716 | bits = isSigned; |
2717 | else |
2718 | bits = width - isSigned; |
2719 | |
2720 | tcSetLeastSignificantBits(dst: parts.data(), parts: dstPartsCount, bits); |
2721 | if (sign && isSigned) |
2722 | APInt::tcShiftLeft(parts.data(), Words: dstPartsCount, Count: width - 1); |
2723 | } |
2724 | |
2725 | return fs; |
2726 | } |
2727 | |
2728 | /* Convert an unsigned integer SRC to a floating point number, |
2729 | rounding according to ROUNDING_MODE. The sign of the floating |
2730 | point number is not modified. */ |
2731 | IEEEFloat::opStatus IEEEFloat::convertFromUnsignedParts( |
2732 | const integerPart *src, unsigned int srcCount, roundingMode rounding_mode) { |
2733 | unsigned int omsb, precision, dstCount; |
2734 | integerPart *dst; |
2735 | lostFraction lost_fraction; |
2736 | |
2737 | category = fcNormal; |
2738 | omsb = APInt::tcMSB(parts: src, n: srcCount) + 1; |
2739 | dst = significandParts(); |
2740 | dstCount = partCount(); |
2741 | precision = semantics->precision; |
2742 | |
2743 | /* We want the most significant PRECISION bits of SRC. There may not |
2744 | be that many; extract what we can. */ |
2745 | if (precision <= omsb) { |
2746 | exponent = omsb - 1; |
2747 | lost_fraction = lostFractionThroughTruncation(parts: src, partCount: srcCount, |
2748 | bits: omsb - precision); |
2749 | APInt::tcExtract(dst, dstCount, src, srcBits: precision, srcLSB: omsb - precision); |
2750 | } else { |
2751 | exponent = precision - 1; |
2752 | lost_fraction = lfExactlyZero; |
2753 | APInt::tcExtract(dst, dstCount, src, srcBits: omsb, srcLSB: 0); |
2754 | } |
2755 | |
2756 | return normalize(rounding_mode, lost_fraction); |
2757 | } |
2758 | |
2759 | IEEEFloat::opStatus IEEEFloat::convertFromAPInt(const APInt &Val, bool isSigned, |
2760 | roundingMode rounding_mode) { |
2761 | unsigned int partCount = Val.getNumWords(); |
2762 | APInt api = Val; |
2763 | |
2764 | sign = false; |
2765 | if (isSigned && api.isNegative()) { |
2766 | sign = true; |
2767 | api = -api; |
2768 | } |
2769 | |
2770 | return convertFromUnsignedParts(src: api.getRawData(), srcCount: partCount, rounding_mode); |
2771 | } |
2772 | |
2773 | /* Convert a two's complement integer SRC to a floating point number, |
2774 | rounding according to ROUNDING_MODE. ISSIGNED is true if the |
2775 | integer is signed, in which case it must be sign-extended. */ |
2776 | IEEEFloat::opStatus |
2777 | IEEEFloat::convertFromSignExtendedInteger(const integerPart *src, |
2778 | unsigned int srcCount, bool isSigned, |
2779 | roundingMode rounding_mode) { |
2780 | opStatus status; |
2781 | |
2782 | if (isSigned && |
2783 | APInt::tcExtractBit(src, bit: srcCount * integerPartWidth - 1)) { |
2784 | integerPart *copy; |
2785 | |
2786 | /* If we're signed and negative negate a copy. */ |
2787 | sign = true; |
2788 | copy = new integerPart[srcCount]; |
2789 | APInt::tcAssign(copy, src, srcCount); |
2790 | APInt::tcNegate(copy, srcCount); |
2791 | status = convertFromUnsignedParts(src: copy, srcCount, rounding_mode); |
2792 | delete [] copy; |
2793 | } else { |
2794 | sign = false; |
2795 | status = convertFromUnsignedParts(src, srcCount, rounding_mode); |
2796 | } |
2797 | |
2798 | return status; |
2799 | } |
2800 | |
2801 | /* FIXME: should this just take a const APInt reference? */ |
2802 | IEEEFloat::opStatus |
2803 | IEEEFloat::convertFromZeroExtendedInteger(const integerPart *parts, |
2804 | unsigned int width, bool isSigned, |
2805 | roundingMode rounding_mode) { |
2806 | unsigned int partCount = partCountForBits(bits: width); |
2807 | APInt api = APInt(width, ArrayRef(parts, partCount)); |
2808 | |
2809 | sign = false; |
2810 | if (isSigned && APInt::tcExtractBit(parts, bit: width - 1)) { |
2811 | sign = true; |
2812 | api = -api; |
2813 | } |
2814 | |
2815 | return convertFromUnsignedParts(src: api.getRawData(), srcCount: partCount, rounding_mode); |
2816 | } |
2817 | |
2818 | Expected<IEEEFloat::opStatus> |
2819 | IEEEFloat::convertFromHexadecimalString(StringRef s, |
2820 | roundingMode rounding_mode) { |
2821 | lostFraction lost_fraction = lfExactlyZero; |
2822 | |
2823 | category = fcNormal; |
2824 | zeroSignificand(); |
2825 | exponent = 0; |
2826 | |
2827 | integerPart *significand = significandParts(); |
2828 | unsigned partsCount = partCount(); |
2829 | unsigned bitPos = partsCount * integerPartWidth; |
2830 | bool computedTrailingFraction = false; |
2831 | |
2832 | // Skip leading zeroes and any (hexa)decimal point. |
2833 | StringRef::iterator begin = s.begin(); |
2834 | StringRef::iterator end = s.end(); |
2835 | StringRef::iterator dot; |
2836 | auto PtrOrErr = skipLeadingZeroesAndAnyDot(begin, end, dot: &dot); |
2837 | if (!PtrOrErr) |
2838 | return PtrOrErr.takeError(); |
2839 | StringRef::iterator p = *PtrOrErr; |
2840 | StringRef::iterator firstSignificantDigit = p; |
2841 | |
2842 | while (p != end) { |
2843 | integerPart hex_value; |
2844 | |
2845 | if (*p == '.') { |
2846 | if (dot != end) |
2847 | return createError(Err: "String contains multiple dots" ); |
2848 | dot = p++; |
2849 | continue; |
2850 | } |
2851 | |
2852 | hex_value = hexDigitValue(C: *p); |
2853 | if (hex_value == UINT_MAX) |
2854 | break; |
2855 | |
2856 | p++; |
2857 | |
2858 | // Store the number while we have space. |
2859 | if (bitPos) { |
2860 | bitPos -= 4; |
2861 | hex_value <<= bitPos % integerPartWidth; |
2862 | significand[bitPos / integerPartWidth] |= hex_value; |
2863 | } else if (!computedTrailingFraction) { |
2864 | auto FractOrErr = trailingHexadecimalFraction(p, end, digitValue: hex_value); |
2865 | if (!FractOrErr) |
2866 | return FractOrErr.takeError(); |
2867 | lost_fraction = *FractOrErr; |
2868 | computedTrailingFraction = true; |
2869 | } |
2870 | } |
2871 | |
2872 | /* Hex floats require an exponent but not a hexadecimal point. */ |
2873 | if (p == end) |
2874 | return createError(Err: "Hex strings require an exponent" ); |
2875 | if (*p != 'p' && *p != 'P') |
2876 | return createError(Err: "Invalid character in significand" ); |
2877 | if (p == begin) |
2878 | return createError(Err: "Significand has no digits" ); |
2879 | if (dot != end && p - begin == 1) |
2880 | return createError(Err: "Significand has no digits" ); |
2881 | |
2882 | /* Ignore the exponent if we are zero. */ |
2883 | if (p != firstSignificantDigit) { |
2884 | int expAdjustment; |
2885 | |
2886 | /* Implicit hexadecimal point? */ |
2887 | if (dot == end) |
2888 | dot = p; |
2889 | |
2890 | /* Calculate the exponent adjustment implicit in the number of |
2891 | significant digits. */ |
2892 | expAdjustment = static_cast<int>(dot - firstSignificantDigit); |
2893 | if (expAdjustment < 0) |
2894 | expAdjustment++; |
2895 | expAdjustment = expAdjustment * 4 - 1; |
2896 | |
2897 | /* Adjust for writing the significand starting at the most |
2898 | significant nibble. */ |
2899 | expAdjustment += semantics->precision; |
2900 | expAdjustment -= partsCount * integerPartWidth; |
2901 | |
2902 | /* Adjust for the given exponent. */ |
2903 | auto ExpOrErr = totalExponent(p: p + 1, end, exponentAdjustment: expAdjustment); |
2904 | if (!ExpOrErr) |
2905 | return ExpOrErr.takeError(); |
2906 | exponent = *ExpOrErr; |
2907 | } |
2908 | |
2909 | return normalize(rounding_mode, lost_fraction); |
2910 | } |
2911 | |
2912 | IEEEFloat::opStatus |
2913 | IEEEFloat::roundSignificandWithExponent(const integerPart *decSigParts, |
2914 | unsigned sigPartCount, int exp, |
2915 | roundingMode rounding_mode) { |
2916 | unsigned int parts, pow5PartCount; |
2917 | fltSemantics calcSemantics = { .maxExponent: 32767, .minExponent: -32767, .precision: 0, .sizeInBits: 0 }; |
2918 | integerPart pow5Parts[maxPowerOfFiveParts]; |
2919 | bool isNearest; |
2920 | |
2921 | isNearest = (rounding_mode == rmNearestTiesToEven || |
2922 | rounding_mode == rmNearestTiesToAway); |
2923 | |
2924 | parts = partCountForBits(bits: semantics->precision + 11); |
2925 | |
2926 | /* Calculate pow(5, abs(exp)). */ |
2927 | pow5PartCount = powerOf5(dst: pow5Parts, power: exp >= 0 ? exp: -exp); |
2928 | |
2929 | for (;; parts *= 2) { |
2930 | opStatus sigStatus, powStatus; |
2931 | unsigned int excessPrecision, truncatedBits; |
2932 | |
2933 | calcSemantics.precision = parts * integerPartWidth - 1; |
2934 | excessPrecision = calcSemantics.precision - semantics->precision; |
2935 | truncatedBits = excessPrecision; |
2936 | |
2937 | IEEEFloat decSig(calcSemantics, uninitialized); |
2938 | decSig.makeZero(Neg: sign); |
2939 | IEEEFloat pow5(calcSemantics); |
2940 | |
2941 | sigStatus = decSig.convertFromUnsignedParts(src: decSigParts, srcCount: sigPartCount, |
2942 | rounding_mode: rmNearestTiesToEven); |
2943 | powStatus = pow5.convertFromUnsignedParts(src: pow5Parts, srcCount: pow5PartCount, |
2944 | rounding_mode: rmNearestTiesToEven); |
2945 | /* Add exp, as 10^n = 5^n * 2^n. */ |
2946 | decSig.exponent += exp; |
2947 | |
2948 | lostFraction calcLostFraction; |
2949 | integerPart HUerr, HUdistance; |
2950 | unsigned int powHUerr; |
2951 | |
2952 | if (exp >= 0) { |
2953 | /* multiplySignificand leaves the precision-th bit set to 1. */ |
2954 | calcLostFraction = decSig.multiplySignificand(rhs: pow5); |
2955 | powHUerr = powStatus != opOK; |
2956 | } else { |
2957 | calcLostFraction = decSig.divideSignificand(rhs: pow5); |
2958 | /* Denormal numbers have less precision. */ |
2959 | if (decSig.exponent < semantics->minExponent) { |
2960 | excessPrecision += (semantics->minExponent - decSig.exponent); |
2961 | truncatedBits = excessPrecision; |
2962 | if (excessPrecision > calcSemantics.precision) |
2963 | excessPrecision = calcSemantics.precision; |
2964 | } |
2965 | /* Extra half-ulp lost in reciprocal of exponent. */ |
2966 | powHUerr = (powStatus == opOK && calcLostFraction == lfExactlyZero) ? 0:2; |
2967 | } |
2968 | |
2969 | /* Both multiplySignificand and divideSignificand return the |
2970 | result with the integer bit set. */ |
2971 | assert(APInt::tcExtractBit |
2972 | (decSig.significandParts(), calcSemantics.precision - 1) == 1); |
2973 | |
2974 | HUerr = HUerrBound(inexactMultiply: calcLostFraction != lfExactlyZero, HUerr1: sigStatus != opOK, |
2975 | HUerr2: powHUerr); |
2976 | HUdistance = 2 * ulpsFromBoundary(parts: decSig.significandParts(), |
2977 | bits: excessPrecision, isNearest); |
2978 | |
2979 | /* Are we guaranteed to round correctly if we truncate? */ |
2980 | if (HUdistance >= HUerr) { |
2981 | APInt::tcExtract(significandParts(), dstCount: partCount(), decSig.significandParts(), |
2982 | srcBits: calcSemantics.precision - excessPrecision, |
2983 | srcLSB: excessPrecision); |
2984 | /* Take the exponent of decSig. If we tcExtract-ed less bits |
2985 | above we must adjust our exponent to compensate for the |
2986 | implicit right shift. */ |
2987 | exponent = (decSig.exponent + semantics->precision |
2988 | - (calcSemantics.precision - excessPrecision)); |
2989 | calcLostFraction = lostFractionThroughTruncation(parts: decSig.significandParts(), |
2990 | partCount: decSig.partCount(), |
2991 | bits: truncatedBits); |
2992 | return normalize(rounding_mode, lost_fraction: calcLostFraction); |
2993 | } |
2994 | } |
2995 | } |
2996 | |
2997 | Expected<IEEEFloat::opStatus> |
2998 | IEEEFloat::convertFromDecimalString(StringRef str, roundingMode rounding_mode) { |
2999 | decimalInfo D; |
3000 | opStatus fs; |
3001 | |
3002 | /* Scan the text. */ |
3003 | StringRef::iterator p = str.begin(); |
3004 | if (Error Err = interpretDecimal(begin: p, end: str.end(), D: &D)) |
3005 | return std::move(Err); |
3006 | |
3007 | /* Handle the quick cases. First the case of no significant digits, |
3008 | i.e. zero, and then exponents that are obviously too large or too |
3009 | small. Writing L for log 10 / log 2, a number d.ddddd*10^exp |
3010 | definitely overflows if |
3011 | |
3012 | (exp - 1) * L >= maxExponent |
3013 | |
3014 | and definitely underflows to zero where |
3015 | |
3016 | (exp + 1) * L <= minExponent - precision |
3017 | |
3018 | With integer arithmetic the tightest bounds for L are |
3019 | |
3020 | 93/28 < L < 196/59 [ numerator <= 256 ] |
3021 | 42039/12655 < L < 28738/8651 [ numerator <= 65536 ] |
3022 | */ |
3023 | |
3024 | // Test if we have a zero number allowing for strings with no null terminators |
3025 | // and zero decimals with non-zero exponents. |
3026 | // |
3027 | // We computed firstSigDigit by ignoring all zeros and dots. Thus if |
3028 | // D->firstSigDigit equals str.end(), every digit must be a zero and there can |
3029 | // be at most one dot. On the other hand, if we have a zero with a non-zero |
3030 | // exponent, then we know that D.firstSigDigit will be non-numeric. |
3031 | if (D.firstSigDigit == str.end() || decDigitValue(c: *D.firstSigDigit) >= 10U) { |
3032 | category = fcZero; |
3033 | fs = opOK; |
3034 | if (semantics->nanEncoding == fltNanEncoding::NegativeZero) |
3035 | sign = false; |
3036 | |
3037 | /* Check whether the normalized exponent is high enough to overflow |
3038 | max during the log-rebasing in the max-exponent check below. */ |
3039 | } else if (D.normalizedExponent - 1 > INT_MAX / 42039) { |
3040 | fs = handleOverflow(rounding_mode); |
3041 | |
3042 | /* If it wasn't, then it also wasn't high enough to overflow max |
3043 | during the log-rebasing in the min-exponent check. Check that it |
3044 | won't overflow min in either check, then perform the min-exponent |
3045 | check. */ |
3046 | } else if (D.normalizedExponent - 1 < INT_MIN / 42039 || |
3047 | (D.normalizedExponent + 1) * 28738 <= |
3048 | 8651 * (semantics->minExponent - (int) semantics->precision)) { |
3049 | /* Underflow to zero and round. */ |
3050 | category = fcNormal; |
3051 | zeroSignificand(); |
3052 | fs = normalize(rounding_mode, lost_fraction: lfLessThanHalf); |
3053 | |
3054 | /* We can finally safely perform the max-exponent check. */ |
3055 | } else if ((D.normalizedExponent - 1) * 42039 |
3056 | >= 12655 * semantics->maxExponent) { |
3057 | /* Overflow and round. */ |
3058 | fs = handleOverflow(rounding_mode); |
3059 | } else { |
3060 | integerPart *decSignificand; |
3061 | unsigned int partCount; |
3062 | |
3063 | /* A tight upper bound on number of bits required to hold an |
3064 | N-digit decimal integer is N * 196 / 59. Allocate enough space |
3065 | to hold the full significand, and an extra part required by |
3066 | tcMultiplyPart. */ |
3067 | partCount = static_cast<unsigned int>(D.lastSigDigit - D.firstSigDigit) + 1; |
3068 | partCount = partCountForBits(bits: 1 + 196 * partCount / 59); |
3069 | decSignificand = new integerPart[partCount + 1]; |
3070 | partCount = 0; |
3071 | |
3072 | /* Convert to binary efficiently - we do almost all multiplication |
3073 | in an integerPart. When this would overflow do we do a single |
3074 | bignum multiplication, and then revert again to multiplication |
3075 | in an integerPart. */ |
3076 | do { |
3077 | integerPart decValue, val, multiplier; |
3078 | |
3079 | val = 0; |
3080 | multiplier = 1; |
3081 | |
3082 | do { |
3083 | if (*p == '.') { |
3084 | p++; |
3085 | if (p == str.end()) { |
3086 | break; |
3087 | } |
3088 | } |
3089 | decValue = decDigitValue(c: *p++); |
3090 | if (decValue >= 10U) { |
3091 | delete[] decSignificand; |
3092 | return createError(Err: "Invalid character in significand" ); |
3093 | } |
3094 | multiplier *= 10; |
3095 | val = val * 10 + decValue; |
3096 | /* The maximum number that can be multiplied by ten with any |
3097 | digit added without overflowing an integerPart. */ |
3098 | } while (p <= D.lastSigDigit && multiplier <= (~ (integerPart) 0 - 9) / 10); |
3099 | |
3100 | /* Multiply out the current part. */ |
3101 | APInt::tcMultiplyPart(dst: decSignificand, src: decSignificand, multiplier, carry: val, |
3102 | srcParts: partCount, dstParts: partCount + 1, add: false); |
3103 | |
3104 | /* If we used another part (likely but not guaranteed), increase |
3105 | the count. */ |
3106 | if (decSignificand[partCount]) |
3107 | partCount++; |
3108 | } while (p <= D.lastSigDigit); |
3109 | |
3110 | category = fcNormal; |
3111 | fs = roundSignificandWithExponent(decSigParts: decSignificand, sigPartCount: partCount, |
3112 | exp: D.exponent, rounding_mode); |
3113 | |
3114 | delete [] decSignificand; |
3115 | } |
3116 | |
3117 | return fs; |
3118 | } |
3119 | |
3120 | bool IEEEFloat::convertFromStringSpecials(StringRef str) { |
3121 | const size_t MIN_NAME_SIZE = 3; |
3122 | |
3123 | if (str.size() < MIN_NAME_SIZE) |
3124 | return false; |
3125 | |
3126 | if (str.equals(RHS: "inf" ) || str.equals(RHS: "INFINITY" ) || str.equals(RHS: "+Inf" )) { |
3127 | makeInf(Neg: false); |
3128 | return true; |
3129 | } |
3130 | |
3131 | bool IsNegative = str.front() == '-'; |
3132 | if (IsNegative) { |
3133 | str = str.drop_front(); |
3134 | if (str.size() < MIN_NAME_SIZE) |
3135 | return false; |
3136 | |
3137 | if (str.equals(RHS: "inf" ) || str.equals(RHS: "INFINITY" ) || str.equals(RHS: "Inf" )) { |
3138 | makeInf(Neg: true); |
3139 | return true; |
3140 | } |
3141 | } |
3142 | |
3143 | // If we have a 's' (or 'S') prefix, then this is a Signaling NaN. |
3144 | bool IsSignaling = str.front() == 's' || str.front() == 'S'; |
3145 | if (IsSignaling) { |
3146 | str = str.drop_front(); |
3147 | if (str.size() < MIN_NAME_SIZE) |
3148 | return false; |
3149 | } |
3150 | |
3151 | if (str.starts_with(Prefix: "nan" ) || str.starts_with(Prefix: "NaN" )) { |
3152 | str = str.drop_front(N: 3); |
3153 | |
3154 | // A NaN without payload. |
3155 | if (str.empty()) { |
3156 | makeNaN(SNaN: IsSignaling, Negative: IsNegative); |
3157 | return true; |
3158 | } |
3159 | |
3160 | // Allow the payload to be inside parentheses. |
3161 | if (str.front() == '(') { |
3162 | // Parentheses should be balanced (and not empty). |
3163 | if (str.size() <= 2 || str.back() != ')') |
3164 | return false; |
3165 | |
3166 | str = str.slice(Start: 1, End: str.size() - 1); |
3167 | } |
3168 | |
3169 | // Determine the payload number's radix. |
3170 | unsigned Radix = 10; |
3171 | if (str[0] == '0') { |
3172 | if (str.size() > 1 && tolower(c: str[1]) == 'x') { |
3173 | str = str.drop_front(N: 2); |
3174 | Radix = 16; |
3175 | } else |
3176 | Radix = 8; |
3177 | } |
3178 | |
3179 | // Parse the payload and make the NaN. |
3180 | APInt Payload; |
3181 | if (!str.getAsInteger(Radix, Result&: Payload)) { |
3182 | makeNaN(SNaN: IsSignaling, Negative: IsNegative, fill: &Payload); |
3183 | return true; |
3184 | } |
3185 | } |
3186 | |
3187 | return false; |
3188 | } |
3189 | |
3190 | Expected<IEEEFloat::opStatus> |
3191 | IEEEFloat::convertFromString(StringRef str, roundingMode rounding_mode) { |
3192 | if (str.empty()) |
3193 | return createError(Err: "Invalid string length" ); |
3194 | |
3195 | // Handle special cases. |
3196 | if (convertFromStringSpecials(str)) |
3197 | return opOK; |
3198 | |
3199 | /* Handle a leading minus sign. */ |
3200 | StringRef::iterator p = str.begin(); |
3201 | size_t slen = str.size(); |
3202 | sign = *p == '-' ? 1 : 0; |
3203 | if (*p == '-' || *p == '+') { |
3204 | p++; |
3205 | slen--; |
3206 | if (!slen) |
3207 | return createError(Err: "String has no digits" ); |
3208 | } |
3209 | |
3210 | if (slen >= 2 && p[0] == '0' && (p[1] == 'x' || p[1] == 'X')) { |
3211 | if (slen == 2) |
3212 | return createError(Err: "Invalid string" ); |
3213 | return convertFromHexadecimalString(s: StringRef(p + 2, slen - 2), |
3214 | rounding_mode); |
3215 | } |
3216 | |
3217 | return convertFromDecimalString(str: StringRef(p, slen), rounding_mode); |
3218 | } |
3219 | |
3220 | /* Write out a hexadecimal representation of the floating point value |
3221 | to DST, which must be of sufficient size, in the C99 form |
3222 | [-]0xh.hhhhp[+-]d. Return the number of characters written, |
3223 | excluding the terminating NUL. |
3224 | |
3225 | If UPPERCASE, the output is in upper case, otherwise in lower case. |
3226 | |
3227 | HEXDIGITS digits appear altogether, rounding the value if |
3228 | necessary. If HEXDIGITS is 0, the minimal precision to display the |
3229 | number precisely is used instead. If nothing would appear after |
3230 | the decimal point it is suppressed. |
3231 | |
3232 | The decimal exponent is always printed and has at least one digit. |
3233 | Zero values display an exponent of zero. Infinities and NaNs |
3234 | appear as "infinity" or "nan" respectively. |
3235 | |
3236 | The above rules are as specified by C99. There is ambiguity about |
3237 | what the leading hexadecimal digit should be. This implementation |
3238 | uses whatever is necessary so that the exponent is displayed as |
3239 | stored. This implies the exponent will fall within the IEEE format |
3240 | range, and the leading hexadecimal digit will be 0 (for denormals), |
3241 | 1 (normal numbers) or 2 (normal numbers rounded-away-from-zero with |
3242 | any other digits zero). |
3243 | */ |
3244 | unsigned int IEEEFloat::convertToHexString(char *dst, unsigned int hexDigits, |
3245 | bool upperCase, |
3246 | roundingMode rounding_mode) const { |
3247 | char *p; |
3248 | |
3249 | p = dst; |
3250 | if (sign) |
3251 | *dst++ = '-'; |
3252 | |
3253 | switch (category) { |
3254 | case fcInfinity: |
3255 | memcpy (dest: dst, src: upperCase ? infinityU: infinityL, n: sizeof infinityU - 1); |
3256 | dst += sizeof infinityL - 1; |
3257 | break; |
3258 | |
3259 | case fcNaN: |
3260 | memcpy (dest: dst, src: upperCase ? NaNU: NaNL, n: sizeof NaNU - 1); |
3261 | dst += sizeof NaNU - 1; |
3262 | break; |
3263 | |
3264 | case fcZero: |
3265 | *dst++ = '0'; |
3266 | *dst++ = upperCase ? 'X': 'x'; |
3267 | *dst++ = '0'; |
3268 | if (hexDigits > 1) { |
3269 | *dst++ = '.'; |
3270 | memset (s: dst, c: '0', n: hexDigits - 1); |
3271 | dst += hexDigits - 1; |
3272 | } |
3273 | *dst++ = upperCase ? 'P': 'p'; |
3274 | *dst++ = '0'; |
3275 | break; |
3276 | |
3277 | case fcNormal: |
3278 | dst = convertNormalToHexString (dst, hexDigits, upperCase, rounding_mode); |
3279 | break; |
3280 | } |
3281 | |
3282 | *dst = 0; |
3283 | |
3284 | return static_cast<unsigned int>(dst - p); |
3285 | } |
3286 | |
3287 | /* Does the hard work of outputting the correctly rounded hexadecimal |
3288 | form of a normal floating point number with the specified number of |
3289 | hexadecimal digits. If HEXDIGITS is zero the minimum number of |
3290 | digits necessary to print the value precisely is output. */ |
3291 | char *IEEEFloat::convertNormalToHexString(char *dst, unsigned int hexDigits, |
3292 | bool upperCase, |
3293 | roundingMode rounding_mode) const { |
3294 | unsigned int count, valueBits, shift, partsCount, outputDigits; |
3295 | const char *hexDigitChars; |
3296 | const integerPart *significand; |
3297 | char *p; |
3298 | bool roundUp; |
3299 | |
3300 | *dst++ = '0'; |
3301 | *dst++ = upperCase ? 'X': 'x'; |
3302 | |
3303 | roundUp = false; |
3304 | hexDigitChars = upperCase ? hexDigitsUpper: hexDigitsLower; |
3305 | |
3306 | significand = significandParts(); |
3307 | partsCount = partCount(); |
3308 | |
3309 | /* +3 because the first digit only uses the single integer bit, so |
3310 | we have 3 virtual zero most-significant-bits. */ |
3311 | valueBits = semantics->precision + 3; |
3312 | shift = integerPartWidth - valueBits % integerPartWidth; |
3313 | |
3314 | /* The natural number of digits required ignoring trailing |
3315 | insignificant zeroes. */ |
3316 | outputDigits = (valueBits - significandLSB () + 3) / 4; |
3317 | |
3318 | /* hexDigits of zero means use the required number for the |
3319 | precision. Otherwise, see if we are truncating. If we are, |
3320 | find out if we need to round away from zero. */ |
3321 | if (hexDigits) { |
3322 | if (hexDigits < outputDigits) { |
3323 | /* We are dropping non-zero bits, so need to check how to round. |
3324 | "bits" is the number of dropped bits. */ |
3325 | unsigned int bits; |
3326 | lostFraction fraction; |
3327 | |
3328 | bits = valueBits - hexDigits * 4; |
3329 | fraction = lostFractionThroughTruncation (parts: significand, partCount: partsCount, bits); |
3330 | roundUp = roundAwayFromZero(rounding_mode, lost_fraction: fraction, bit: bits); |
3331 | } |
3332 | outputDigits = hexDigits; |
3333 | } |
3334 | |
3335 | /* Write the digits consecutively, and start writing in the location |
3336 | of the hexadecimal point. We move the most significant digit |
3337 | left and add the hexadecimal point later. */ |
3338 | p = ++dst; |
3339 | |
3340 | count = (valueBits + integerPartWidth - 1) / integerPartWidth; |
3341 | |
3342 | while (outputDigits && count) { |
3343 | integerPart part; |
3344 | |
3345 | /* Put the most significant integerPartWidth bits in "part". */ |
3346 | if (--count == partsCount) |
3347 | part = 0; /* An imaginary higher zero part. */ |
3348 | else |
3349 | part = significand[count] << shift; |
3350 | |
3351 | if (count && shift) |
3352 | part |= significand[count - 1] >> (integerPartWidth - shift); |
3353 | |
3354 | /* Convert as much of "part" to hexdigits as we can. */ |
3355 | unsigned int curDigits = integerPartWidth / 4; |
3356 | |
3357 | if (curDigits > outputDigits) |
3358 | curDigits = outputDigits; |
3359 | dst += partAsHex (dst, part, count: curDigits, hexDigitChars); |
3360 | outputDigits -= curDigits; |
3361 | } |
3362 | |
3363 | if (roundUp) { |
3364 | char *q = dst; |
3365 | |
3366 | /* Note that hexDigitChars has a trailing '0'. */ |
3367 | do { |
3368 | q--; |
3369 | *q = hexDigitChars[hexDigitValue (C: *q) + 1]; |
3370 | } while (*q == '0'); |
3371 | assert(q >= p); |
3372 | } else { |
3373 | /* Add trailing zeroes. */ |
3374 | memset (s: dst, c: '0', n: outputDigits); |
3375 | dst += outputDigits; |
3376 | } |
3377 | |
3378 | /* Move the most significant digit to before the point, and if there |
3379 | is something after the decimal point add it. This must come |
3380 | after rounding above. */ |
3381 | p[-1] = p[0]; |
3382 | if (dst -1 == p) |
3383 | dst--; |
3384 | else |
3385 | p[0] = '.'; |
3386 | |
3387 | /* Finally output the exponent. */ |
3388 | *dst++ = upperCase ? 'P': 'p'; |
3389 | |
3390 | return writeSignedDecimal (dst, value: exponent); |
3391 | } |
3392 | |
3393 | hash_code hash_value(const IEEEFloat &Arg) { |
3394 | if (!Arg.isFiniteNonZero()) |
3395 | return hash_combine(args: (uint8_t)Arg.category, |
3396 | // NaN has no sign, fix it at zero. |
3397 | args: Arg.isNaN() ? (uint8_t)0 : (uint8_t)Arg.sign, |
3398 | args: Arg.semantics->precision); |
3399 | |
3400 | // Normal floats need their exponent and significand hashed. |
3401 | return hash_combine(args: (uint8_t)Arg.category, args: (uint8_t)Arg.sign, |
3402 | args: Arg.semantics->precision, args: Arg.exponent, |
3403 | args: hash_combine_range( |
3404 | first: Arg.significandParts(), |
3405 | last: Arg.significandParts() + Arg.partCount())); |
3406 | } |
3407 | |
3408 | // Conversion from APFloat to/from host float/double. It may eventually be |
3409 | // possible to eliminate these and have everybody deal with APFloats, but that |
3410 | // will take a while. This approach will not easily extend to long double. |
3411 | // Current implementation requires integerPartWidth==64, which is correct at |
3412 | // the moment but could be made more general. |
3413 | |
3414 | // Denormals have exponent minExponent in APFloat, but minExponent-1 in |
3415 | // the actual IEEE respresentations. We compensate for that here. |
3416 | |
3417 | APInt IEEEFloat::convertF80LongDoubleAPFloatToAPInt() const { |
3418 | assert(semantics == (const llvm::fltSemantics*)&semX87DoubleExtended); |
3419 | assert(partCount()==2); |
3420 | |
3421 | uint64_t myexponent, mysignificand; |
3422 | |
3423 | if (isFiniteNonZero()) { |
3424 | myexponent = exponent+16383; //bias |
3425 | mysignificand = significandParts()[0]; |
3426 | if (myexponent==1 && !(mysignificand & 0x8000000000000000ULL)) |
3427 | myexponent = 0; // denormal |
3428 | } else if (category==fcZero) { |
3429 | myexponent = 0; |
3430 | mysignificand = 0; |
3431 | } else if (category==fcInfinity) { |
3432 | myexponent = 0x7fff; |
3433 | mysignificand = 0x8000000000000000ULL; |
3434 | } else { |
3435 | assert(category == fcNaN && "Unknown category" ); |
3436 | myexponent = 0x7fff; |
3437 | mysignificand = significandParts()[0]; |
3438 | } |
3439 | |
3440 | uint64_t words[2]; |
3441 | words[0] = mysignificand; |
3442 | words[1] = ((uint64_t)(sign & 1) << 15) | |
3443 | (myexponent & 0x7fffLL); |
3444 | return APInt(80, words); |
3445 | } |
3446 | |
3447 | APInt IEEEFloat::convertPPCDoubleDoubleAPFloatToAPInt() const { |
3448 | assert(semantics == (const llvm::fltSemantics *)&semPPCDoubleDoubleLegacy); |
3449 | assert(partCount()==2); |
3450 | |
3451 | uint64_t words[2]; |
3452 | opStatus fs; |
3453 | bool losesInfo; |
3454 | |
3455 | // Convert number to double. To avoid spurious underflows, we re- |
3456 | // normalize against the "double" minExponent first, and only *then* |
3457 | // truncate the mantissa. The result of that second conversion |
3458 | // may be inexact, but should never underflow. |
3459 | // Declare fltSemantics before APFloat that uses it (and |
3460 | // saves pointer to it) to ensure correct destruction order. |
3461 | fltSemantics extendedSemantics = *semantics; |
3462 | extendedSemantics.minExponent = semIEEEdouble.minExponent; |
3463 | IEEEFloat extended(*this); |
3464 | fs = extended.convert(toSemantics: extendedSemantics, rounding_mode: rmNearestTiesToEven, losesInfo: &losesInfo); |
3465 | assert(fs == opOK && !losesInfo); |
3466 | (void)fs; |
3467 | |
3468 | IEEEFloat u(extended); |
3469 | fs = u.convert(toSemantics: semIEEEdouble, rounding_mode: rmNearestTiesToEven, losesInfo: &losesInfo); |
3470 | assert(fs == opOK || fs == opInexact); |
3471 | (void)fs; |
3472 | words[0] = *u.convertDoubleAPFloatToAPInt().getRawData(); |
3473 | |
3474 | // If conversion was exact or resulted in a special case, we're done; |
3475 | // just set the second double to zero. Otherwise, re-convert back to |
3476 | // the extended format and compute the difference. This now should |
3477 | // convert exactly to double. |
3478 | if (u.isFiniteNonZero() && losesInfo) { |
3479 | fs = u.convert(toSemantics: extendedSemantics, rounding_mode: rmNearestTiesToEven, losesInfo: &losesInfo); |
3480 | assert(fs == opOK && !losesInfo); |
3481 | (void)fs; |
3482 | |
3483 | IEEEFloat v(extended); |
3484 | v.subtract(rhs: u, rounding_mode: rmNearestTiesToEven); |
3485 | fs = v.convert(toSemantics: semIEEEdouble, rounding_mode: rmNearestTiesToEven, losesInfo: &losesInfo); |
3486 | assert(fs == opOK && !losesInfo); |
3487 | (void)fs; |
3488 | words[1] = *v.convertDoubleAPFloatToAPInt().getRawData(); |
3489 | } else { |
3490 | words[1] = 0; |
3491 | } |
3492 | |
3493 | return APInt(128, words); |
3494 | } |
3495 | |
3496 | template <const fltSemantics &S> |
3497 | APInt IEEEFloat::convertIEEEFloatToAPInt() const { |
3498 | assert(semantics == &S); |
3499 | |
3500 | constexpr int bias = -(S.minExponent - 1); |
3501 | constexpr unsigned int trailing_significand_bits = S.precision - 1; |
3502 | constexpr int integer_bit_part = trailing_significand_bits / integerPartWidth; |
3503 | constexpr integerPart integer_bit = |
3504 | integerPart{1} << (trailing_significand_bits % integerPartWidth); |
3505 | constexpr uint64_t significand_mask = integer_bit - 1; |
3506 | constexpr unsigned int exponent_bits = |
3507 | S.sizeInBits - 1 - trailing_significand_bits; |
3508 | static_assert(exponent_bits < 64); |
3509 | constexpr uint64_t exponent_mask = (uint64_t{1} << exponent_bits) - 1; |
3510 | |
3511 | uint64_t myexponent; |
3512 | std::array<integerPart, partCountForBits(bits: trailing_significand_bits)> |
3513 | mysignificand; |
3514 | |
3515 | if (isFiniteNonZero()) { |
3516 | myexponent = exponent + bias; |
3517 | std::copy_n(significandParts(), mysignificand.size(), |
3518 | mysignificand.begin()); |
3519 | if (myexponent == 1 && |
3520 | !(significandParts()[integer_bit_part] & integer_bit)) |
3521 | myexponent = 0; // denormal |
3522 | } else if (category == fcZero) { |
3523 | myexponent = ::exponentZero(semantics: S) + bias; |
3524 | mysignificand.fill(0); |
3525 | } else if (category == fcInfinity) { |
3526 | if (S.nonFiniteBehavior == fltNonfiniteBehavior::NanOnly) { |
3527 | llvm_unreachable("semantics don't support inf!" ); |
3528 | } |
3529 | myexponent = ::exponentInf(semantics: S) + bias; |
3530 | mysignificand.fill(0); |
3531 | } else { |
3532 | assert(category == fcNaN && "Unknown category!" ); |
3533 | myexponent = ::exponentNaN(semantics: S) + bias; |
3534 | std::copy_n(significandParts(), mysignificand.size(), |
3535 | mysignificand.begin()); |
3536 | } |
3537 | std::array<uint64_t, (S.sizeInBits + 63) / 64> words; |
3538 | auto words_iter = |
3539 | std::copy_n(mysignificand.begin(), mysignificand.size(), words.begin()); |
3540 | if constexpr (significand_mask != 0) { |
3541 | // Clear the integer bit. |
3542 | words[mysignificand.size() - 1] &= significand_mask; |
3543 | } |
3544 | std::fill(words_iter, words.end(), uint64_t{0}); |
3545 | constexpr size_t last_word = words.size() - 1; |
3546 | uint64_t shifted_sign = static_cast<uint64_t>(sign & 1) |
3547 | << ((S.sizeInBits - 1) % 64); |
3548 | words[last_word] |= shifted_sign; |
3549 | uint64_t shifted_exponent = (myexponent & exponent_mask) |
3550 | << (trailing_significand_bits % 64); |
3551 | words[last_word] |= shifted_exponent; |
3552 | if constexpr (last_word == 0) { |
3553 | return APInt(S.sizeInBits, words[0]); |
3554 | } |
3555 | return APInt(S.sizeInBits, words); |
3556 | } |
3557 | |
3558 | APInt IEEEFloat::convertQuadrupleAPFloatToAPInt() const { |
3559 | assert(partCount() == 2); |
3560 | return convertIEEEFloatToAPInt<semIEEEquad>(); |
3561 | } |
3562 | |
3563 | APInt IEEEFloat::convertDoubleAPFloatToAPInt() const { |
3564 | assert(partCount()==1); |
3565 | return convertIEEEFloatToAPInt<semIEEEdouble>(); |
3566 | } |
3567 | |
3568 | APInt IEEEFloat::convertFloatAPFloatToAPInt() const { |
3569 | assert(partCount()==1); |
3570 | return convertIEEEFloatToAPInt<semIEEEsingle>(); |
3571 | } |
3572 | |
3573 | APInt IEEEFloat::convertBFloatAPFloatToAPInt() const { |
3574 | assert(partCount() == 1); |
3575 | return convertIEEEFloatToAPInt<semBFloat>(); |
3576 | } |
3577 | |
3578 | APInt IEEEFloat::convertHalfAPFloatToAPInt() const { |
3579 | assert(partCount()==1); |
3580 | return convertIEEEFloatToAPInt<semIEEEhalf>(); |
3581 | } |
3582 | |
3583 | APInt IEEEFloat::convertFloat8E5M2APFloatToAPInt() const { |
3584 | assert(partCount() == 1); |
3585 | return convertIEEEFloatToAPInt<semFloat8E5M2>(); |
3586 | } |
3587 | |
3588 | APInt IEEEFloat::convertFloat8E5M2FNUZAPFloatToAPInt() const { |
3589 | assert(partCount() == 1); |
3590 | return convertIEEEFloatToAPInt<semFloat8E5M2FNUZ>(); |
3591 | } |
3592 | |
3593 | APInt IEEEFloat::convertFloat8E4M3FNAPFloatToAPInt() const { |
3594 | assert(partCount() == 1); |
3595 | return convertIEEEFloatToAPInt<semFloat8E4M3FN>(); |
3596 | } |
3597 | |
3598 | APInt IEEEFloat::convertFloat8E4M3FNUZAPFloatToAPInt() const { |
3599 | assert(partCount() == 1); |
3600 | return convertIEEEFloatToAPInt<semFloat8E4M3FNUZ>(); |
3601 | } |
3602 | |
3603 | APInt IEEEFloat::convertFloat8E4M3B11FNUZAPFloatToAPInt() const { |
3604 | assert(partCount() == 1); |
3605 | return convertIEEEFloatToAPInt<semFloat8E4M3B11FNUZ>(); |
3606 | } |
3607 | |
3608 | APInt IEEEFloat::convertFloatTF32APFloatToAPInt() const { |
3609 | assert(partCount() == 1); |
3610 | return convertIEEEFloatToAPInt<semFloatTF32>(); |
3611 | } |
3612 | |
3613 | // This function creates an APInt that is just a bit map of the floating |
3614 | // point constant as it would appear in memory. It is not a conversion, |
3615 | // and treating the result as a normal integer is unlikely to be useful. |
3616 | |
3617 | APInt IEEEFloat::bitcastToAPInt() const { |
3618 | if (semantics == (const llvm::fltSemantics*)&semIEEEhalf) |
3619 | return convertHalfAPFloatToAPInt(); |
3620 | |
3621 | if (semantics == (const llvm::fltSemantics *)&semBFloat) |
3622 | return convertBFloatAPFloatToAPInt(); |
3623 | |
3624 | if (semantics == (const llvm::fltSemantics*)&semIEEEsingle) |
3625 | return convertFloatAPFloatToAPInt(); |
3626 | |
3627 | if (semantics == (const llvm::fltSemantics*)&semIEEEdouble) |
3628 | return convertDoubleAPFloatToAPInt(); |
3629 | |
3630 | if (semantics == (const llvm::fltSemantics*)&semIEEEquad) |
3631 | return convertQuadrupleAPFloatToAPInt(); |
3632 | |
3633 | if (semantics == (const llvm::fltSemantics *)&semPPCDoubleDoubleLegacy) |
3634 | return convertPPCDoubleDoubleAPFloatToAPInt(); |
3635 | |
3636 | if (semantics == (const llvm::fltSemantics *)&semFloat8E5M2) |
3637 | return convertFloat8E5M2APFloatToAPInt(); |
3638 | |
3639 | if (semantics == (const llvm::fltSemantics *)&semFloat8E5M2FNUZ) |
3640 | return convertFloat8E5M2FNUZAPFloatToAPInt(); |
3641 | |
3642 | if (semantics == (const llvm::fltSemantics *)&semFloat8E4M3FN) |
3643 | return convertFloat8E4M3FNAPFloatToAPInt(); |
3644 | |
3645 | if (semantics == (const llvm::fltSemantics *)&semFloat8E4M3FNUZ) |
3646 | return convertFloat8E4M3FNUZAPFloatToAPInt(); |
3647 | |
3648 | if (semantics == (const llvm::fltSemantics *)&semFloat8E4M3B11FNUZ) |
3649 | return convertFloat8E4M3B11FNUZAPFloatToAPInt(); |
3650 | |
3651 | if (semantics == (const llvm::fltSemantics *)&semFloatTF32) |
3652 | return convertFloatTF32APFloatToAPInt(); |
3653 | |
3654 | assert(semantics == (const llvm::fltSemantics*)&semX87DoubleExtended && |
3655 | "unknown format!" ); |
3656 | return convertF80LongDoubleAPFloatToAPInt(); |
3657 | } |
3658 | |
3659 | float IEEEFloat::convertToFloat() const { |
3660 | assert(semantics == (const llvm::fltSemantics*)&semIEEEsingle && |
3661 | "Float semantics are not IEEEsingle" ); |
3662 | APInt api = bitcastToAPInt(); |
3663 | return api.bitsToFloat(); |
3664 | } |
3665 | |
3666 | double IEEEFloat::convertToDouble() const { |
3667 | assert(semantics == (const llvm::fltSemantics*)&semIEEEdouble && |
3668 | "Float semantics are not IEEEdouble" ); |
3669 | APInt api = bitcastToAPInt(); |
3670 | return api.bitsToDouble(); |
3671 | } |
3672 | |
3673 | /// Integer bit is explicit in this format. Intel hardware (387 and later) |
3674 | /// does not support these bit patterns: |
3675 | /// exponent = all 1's, integer bit 0, significand 0 ("pseudoinfinity") |
3676 | /// exponent = all 1's, integer bit 0, significand nonzero ("pseudoNaN") |
3677 | /// exponent!=0 nor all 1's, integer bit 0 ("unnormal") |
3678 | /// exponent = 0, integer bit 1 ("pseudodenormal") |
3679 | /// At the moment, the first three are treated as NaNs, the last one as Normal. |
3680 | void IEEEFloat::initFromF80LongDoubleAPInt(const APInt &api) { |
3681 | uint64_t i1 = api.getRawData()[0]; |
3682 | uint64_t i2 = api.getRawData()[1]; |
3683 | uint64_t myexponent = (i2 & 0x7fff); |
3684 | uint64_t mysignificand = i1; |
3685 | uint8_t myintegerbit = mysignificand >> 63; |
3686 | |
3687 | initialize(ourSemantics: &semX87DoubleExtended); |
3688 | assert(partCount()==2); |
3689 | |
3690 | sign = static_cast<unsigned int>(i2>>15); |
3691 | if (myexponent == 0 && mysignificand == 0) { |
3692 | makeZero(Neg: sign); |
3693 | } else if (myexponent==0x7fff && mysignificand==0x8000000000000000ULL) { |
3694 | makeInf(Neg: sign); |
3695 | } else if ((myexponent == 0x7fff && mysignificand != 0x8000000000000000ULL) || |
3696 | (myexponent != 0x7fff && myexponent != 0 && myintegerbit == 0)) { |
3697 | category = fcNaN; |
3698 | exponent = exponentNaN(); |
3699 | significandParts()[0] = mysignificand; |
3700 | significandParts()[1] = 0; |
3701 | } else { |
3702 | category = fcNormal; |
3703 | exponent = myexponent - 16383; |
3704 | significandParts()[0] = mysignificand; |
3705 | significandParts()[1] = 0; |
3706 | if (myexponent==0) // denormal |
3707 | exponent = -16382; |
3708 | } |
3709 | } |
3710 | |
3711 | void IEEEFloat::initFromPPCDoubleDoubleAPInt(const APInt &api) { |
3712 | uint64_t i1 = api.getRawData()[0]; |
3713 | uint64_t i2 = api.getRawData()[1]; |
3714 | opStatus fs; |
3715 | bool losesInfo; |
3716 | |
3717 | // Get the first double and convert to our format. |
3718 | initFromDoubleAPInt(api: APInt(64, i1)); |
3719 | fs = convert(toSemantics: semPPCDoubleDoubleLegacy, rounding_mode: rmNearestTiesToEven, losesInfo: &losesInfo); |
3720 | assert(fs == opOK && !losesInfo); |
3721 | (void)fs; |
3722 | |
3723 | // Unless we have a special case, add in second double. |
3724 | if (isFiniteNonZero()) { |
3725 | IEEEFloat v(semIEEEdouble, APInt(64, i2)); |
3726 | fs = v.convert(toSemantics: semPPCDoubleDoubleLegacy, rounding_mode: rmNearestTiesToEven, losesInfo: &losesInfo); |
3727 | assert(fs == opOK && !losesInfo); |
3728 | (void)fs; |
3729 | |
3730 | add(rhs: v, rounding_mode: rmNearestTiesToEven); |
3731 | } |
3732 | } |
3733 | |
3734 | template <const fltSemantics &S> |
3735 | void IEEEFloat::initFromIEEEAPInt(const APInt &api) { |
3736 | assert(api.getBitWidth() == S.sizeInBits); |
3737 | constexpr integerPart integer_bit = integerPart{1} |
3738 | << ((S.precision - 1) % integerPartWidth); |
3739 | constexpr uint64_t significand_mask = integer_bit - 1; |
3740 | constexpr unsigned int trailing_significand_bits = S.precision - 1; |
3741 | constexpr unsigned int stored_significand_parts = |
3742 | partCountForBits(bits: trailing_significand_bits); |
3743 | constexpr unsigned int exponent_bits = |
3744 | S.sizeInBits - 1 - trailing_significand_bits; |
3745 | static_assert(exponent_bits < 64); |
3746 | constexpr uint64_t exponent_mask = (uint64_t{1} << exponent_bits) - 1; |
3747 | constexpr int bias = -(S.minExponent - 1); |
3748 | |
3749 | // Copy the bits of the significand. We need to clear out the exponent and |
3750 | // sign bit in the last word. |
3751 | std::array<integerPart, stored_significand_parts> mysignificand; |
3752 | std::copy_n(api.getRawData(), mysignificand.size(), mysignificand.begin()); |
3753 | if constexpr (significand_mask != 0) { |
3754 | mysignificand[mysignificand.size() - 1] &= significand_mask; |
3755 | } |
3756 | |
3757 | // We assume the last word holds the sign bit, the exponent, and potentially |
3758 | // some of the trailing significand field. |
3759 | uint64_t last_word = api.getRawData()[api.getNumWords() - 1]; |
3760 | uint64_t myexponent = |
3761 | (last_word >> (trailing_significand_bits % 64)) & exponent_mask; |
3762 | |
3763 | initialize(ourSemantics: &S); |
3764 | assert(partCount() == mysignificand.size()); |
3765 | |
3766 | sign = static_cast<unsigned int>(last_word >> ((S.sizeInBits - 1) % 64)); |
3767 | |
3768 | bool all_zero_significand = |
3769 | llvm::all_of(mysignificand, [](integerPart bits) { return bits == 0; }); |
3770 | |
3771 | bool is_zero = myexponent == 0 && all_zero_significand; |
3772 | |
3773 | if constexpr (S.nonFiniteBehavior == fltNonfiniteBehavior::IEEE754) { |
3774 | if (myexponent - bias == ::exponentInf(semantics: S) && all_zero_significand) { |
3775 | makeInf(Neg: sign); |
3776 | return; |
3777 | } |
3778 | } |
3779 | |
3780 | bool is_nan = false; |
3781 | |
3782 | if constexpr (S.nanEncoding == fltNanEncoding::IEEE) { |
3783 | is_nan = myexponent - bias == ::exponentNaN(semantics: S) && !all_zero_significand; |
3784 | } else if constexpr (S.nanEncoding == fltNanEncoding::AllOnes) { |
3785 | bool all_ones_significand = |
3786 | std::all_of(mysignificand.begin(), mysignificand.end() - 1, |
3787 | [](integerPart bits) { return bits == ~integerPart{0}; }) && |
3788 | (!significand_mask || |
3789 | mysignificand[mysignificand.size() - 1] == significand_mask); |
3790 | is_nan = myexponent - bias == ::exponentNaN(semantics: S) && all_ones_significand; |
3791 | } else if constexpr (S.nanEncoding == fltNanEncoding::NegativeZero) { |
3792 | is_nan = is_zero && sign; |
3793 | } |
3794 | |
3795 | if (is_nan) { |
3796 | category = fcNaN; |
3797 | exponent = ::exponentNaN(semantics: S); |
3798 | std::copy_n(mysignificand.begin(), mysignificand.size(), |
3799 | significandParts()); |
3800 | return; |
3801 | } |
3802 | |
3803 | if (is_zero) { |
3804 | makeZero(Neg: sign); |
3805 | return; |
3806 | } |
3807 | |
3808 | category = fcNormal; |
3809 | exponent = myexponent - bias; |
3810 | std::copy_n(mysignificand.begin(), mysignificand.size(), significandParts()); |
3811 | if (myexponent == 0) // denormal |
3812 | exponent = S.minExponent; |
3813 | else |
3814 | significandParts()[mysignificand.size()-1] |= integer_bit; // integer bit |
3815 | } |
3816 | |
3817 | void IEEEFloat::initFromQuadrupleAPInt(const APInt &api) { |
3818 | initFromIEEEAPInt<semIEEEquad>(api); |
3819 | } |
3820 | |
3821 | void IEEEFloat::initFromDoubleAPInt(const APInt &api) { |
3822 | initFromIEEEAPInt<semIEEEdouble>(api); |
3823 | } |
3824 | |
3825 | void IEEEFloat::initFromFloatAPInt(const APInt &api) { |
3826 | initFromIEEEAPInt<semIEEEsingle>(api); |
3827 | } |
3828 | |
3829 | void IEEEFloat::initFromBFloatAPInt(const APInt &api) { |
3830 | initFromIEEEAPInt<semBFloat>(api); |
3831 | } |
3832 | |
3833 | void IEEEFloat::initFromHalfAPInt(const APInt &api) { |
3834 | initFromIEEEAPInt<semIEEEhalf>(api); |
3835 | } |
3836 | |
3837 | void IEEEFloat::initFromFloat8E5M2APInt(const APInt &api) { |
3838 | initFromIEEEAPInt<semFloat8E5M2>(api); |
3839 | } |
3840 | |
3841 | void IEEEFloat::initFromFloat8E5M2FNUZAPInt(const APInt &api) { |
3842 | initFromIEEEAPInt<semFloat8E5M2FNUZ>(api); |
3843 | } |
3844 | |
3845 | void IEEEFloat::initFromFloat8E4M3FNAPInt(const APInt &api) { |
3846 | initFromIEEEAPInt<semFloat8E4M3FN>(api); |
3847 | } |
3848 | |
3849 | void IEEEFloat::initFromFloat8E4M3FNUZAPInt(const APInt &api) { |
3850 | initFromIEEEAPInt<semFloat8E4M3FNUZ>(api); |
3851 | } |
3852 | |
3853 | void IEEEFloat::initFromFloat8E4M3B11FNUZAPInt(const APInt &api) { |
3854 | initFromIEEEAPInt<semFloat8E4M3B11FNUZ>(api); |
3855 | } |
3856 | |
3857 | void IEEEFloat::initFromFloatTF32APInt(const APInt &api) { |
3858 | initFromIEEEAPInt<semFloatTF32>(api); |
3859 | } |
3860 | |
3861 | /// Treat api as containing the bits of a floating point number. |
3862 | void IEEEFloat::initFromAPInt(const fltSemantics *Sem, const APInt &api) { |
3863 | assert(api.getBitWidth() == Sem->sizeInBits); |
3864 | if (Sem == &semIEEEhalf) |
3865 | return initFromHalfAPInt(api); |
3866 | if (Sem == &semBFloat) |
3867 | return initFromBFloatAPInt(api); |
3868 | if (Sem == &semIEEEsingle) |
3869 | return initFromFloatAPInt(api); |
3870 | if (Sem == &semIEEEdouble) |
3871 | return initFromDoubleAPInt(api); |
3872 | if (Sem == &semX87DoubleExtended) |
3873 | return initFromF80LongDoubleAPInt(api); |
3874 | if (Sem == &semIEEEquad) |
3875 | return initFromQuadrupleAPInt(api); |
3876 | if (Sem == &semPPCDoubleDoubleLegacy) |
3877 | return initFromPPCDoubleDoubleAPInt(api); |
3878 | if (Sem == &semFloat8E5M2) |
3879 | return initFromFloat8E5M2APInt(api); |
3880 | if (Sem == &semFloat8E5M2FNUZ) |
3881 | return initFromFloat8E5M2FNUZAPInt(api); |
3882 | if (Sem == &semFloat8E4M3FN) |
3883 | return initFromFloat8E4M3FNAPInt(api); |
3884 | if (Sem == &semFloat8E4M3FNUZ) |
3885 | return initFromFloat8E4M3FNUZAPInt(api); |
3886 | if (Sem == &semFloat8E4M3B11FNUZ) |
3887 | return initFromFloat8E4M3B11FNUZAPInt(api); |
3888 | if (Sem == &semFloatTF32) |
3889 | return initFromFloatTF32APInt(api); |
3890 | |
3891 | llvm_unreachable(nullptr); |
3892 | } |
3893 | |
3894 | /// Make this number the largest magnitude normal number in the given |
3895 | /// semantics. |
3896 | void IEEEFloat::makeLargest(bool Negative) { |
3897 | // We want (in interchange format): |
3898 | // sign = {Negative} |
3899 | // exponent = 1..10 |
3900 | // significand = 1..1 |
3901 | category = fcNormal; |
3902 | sign = Negative; |
3903 | exponent = semantics->maxExponent; |
3904 | |
3905 | // Use memset to set all but the highest integerPart to all ones. |
3906 | integerPart *significand = significandParts(); |
3907 | unsigned PartCount = partCount(); |
3908 | memset(s: significand, c: 0xFF, n: sizeof(integerPart)*(PartCount - 1)); |
3909 | |
3910 | // Set the high integerPart especially setting all unused top bits for |
3911 | // internal consistency. |
3912 | const unsigned NumUnusedHighBits = |
3913 | PartCount*integerPartWidth - semantics->precision; |
3914 | significand[PartCount - 1] = (NumUnusedHighBits < integerPartWidth) |
3915 | ? (~integerPart(0) >> NumUnusedHighBits) |
3916 | : 0; |
3917 | |
3918 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly && |
3919 | semantics->nanEncoding == fltNanEncoding::AllOnes) |
3920 | significand[0] &= ~integerPart(1); |
3921 | } |
3922 | |
3923 | /// Make this number the smallest magnitude denormal number in the given |
3924 | /// semantics. |
3925 | void IEEEFloat::makeSmallest(bool Negative) { |
3926 | // We want (in interchange format): |
3927 | // sign = {Negative} |
3928 | // exponent = 0..0 |
3929 | // significand = 0..01 |
3930 | category = fcNormal; |
3931 | sign = Negative; |
3932 | exponent = semantics->minExponent; |
3933 | APInt::tcSet(significandParts(), 1, partCount()); |
3934 | } |
3935 | |
3936 | void IEEEFloat::makeSmallestNormalized(bool Negative) { |
3937 | // We want (in interchange format): |
3938 | // sign = {Negative} |
3939 | // exponent = 0..0 |
3940 | // significand = 10..0 |
3941 | |
3942 | category = fcNormal; |
3943 | zeroSignificand(); |
3944 | sign = Negative; |
3945 | exponent = semantics->minExponent; |
3946 | APInt::tcSetBit(significandParts(), bit: semantics->precision - 1); |
3947 | } |
3948 | |
3949 | IEEEFloat::IEEEFloat(const fltSemantics &Sem, const APInt &API) { |
3950 | initFromAPInt(Sem: &Sem, api: API); |
3951 | } |
3952 | |
3953 | IEEEFloat::IEEEFloat(float f) { |
3954 | initFromAPInt(Sem: &semIEEEsingle, api: APInt::floatToBits(V: f)); |
3955 | } |
3956 | |
3957 | IEEEFloat::IEEEFloat(double d) { |
3958 | initFromAPInt(Sem: &semIEEEdouble, api: APInt::doubleToBits(V: d)); |
3959 | } |
3960 | |
3961 | namespace { |
3962 | void append(SmallVectorImpl<char> &Buffer, StringRef Str) { |
3963 | Buffer.append(in_start: Str.begin(), in_end: Str.end()); |
3964 | } |
3965 | |
3966 | /// Removes data from the given significand until it is no more |
3967 | /// precise than is required for the desired precision. |
3968 | void AdjustToPrecision(APInt &significand, |
3969 | int &exp, unsigned FormatPrecision) { |
3970 | unsigned bits = significand.getActiveBits(); |
3971 | |
3972 | // 196/59 is a very slight overestimate of lg_2(10). |
3973 | unsigned bitsRequired = (FormatPrecision * 196 + 58) / 59; |
3974 | |
3975 | if (bits <= bitsRequired) return; |
3976 | |
3977 | unsigned tensRemovable = (bits - bitsRequired) * 59 / 196; |
3978 | if (!tensRemovable) return; |
3979 | |
3980 | exp += tensRemovable; |
3981 | |
3982 | APInt divisor(significand.getBitWidth(), 1); |
3983 | APInt powten(significand.getBitWidth(), 10); |
3984 | while (true) { |
3985 | if (tensRemovable & 1) |
3986 | divisor *= powten; |
3987 | tensRemovable >>= 1; |
3988 | if (!tensRemovable) break; |
3989 | powten *= powten; |
3990 | } |
3991 | |
3992 | significand = significand.udiv(RHS: divisor); |
3993 | |
3994 | // Truncate the significand down to its active bit count. |
3995 | significand = significand.trunc(width: significand.getActiveBits()); |
3996 | } |
3997 | |
3998 | |
3999 | void AdjustToPrecision(SmallVectorImpl<char> &buffer, |
4000 | int &exp, unsigned FormatPrecision) { |
4001 | unsigned N = buffer.size(); |
4002 | if (N <= FormatPrecision) return; |
4003 | |
4004 | // The most significant figures are the last ones in the buffer. |
4005 | unsigned FirstSignificant = N - FormatPrecision; |
4006 | |
4007 | // Round. |
4008 | // FIXME: this probably shouldn't use 'round half up'. |
4009 | |
4010 | // Rounding down is just a truncation, except we also want to drop |
4011 | // trailing zeros from the new result. |
4012 | if (buffer[FirstSignificant - 1] < '5') { |
4013 | while (FirstSignificant < N && buffer[FirstSignificant] == '0') |
4014 | FirstSignificant++; |
4015 | |
4016 | exp += FirstSignificant; |
4017 | buffer.erase(CS: &buffer[0], CE: &buffer[FirstSignificant]); |
4018 | return; |
4019 | } |
4020 | |
4021 | // Rounding up requires a decimal add-with-carry. If we continue |
4022 | // the carry, the newly-introduced zeros will just be truncated. |
4023 | for (unsigned I = FirstSignificant; I != N; ++I) { |
4024 | if (buffer[I] == '9') { |
4025 | FirstSignificant++; |
4026 | } else { |
4027 | buffer[I]++; |
4028 | break; |
4029 | } |
4030 | } |
4031 | |
4032 | // If we carried through, we have exactly one digit of precision. |
4033 | if (FirstSignificant == N) { |
4034 | exp += FirstSignificant; |
4035 | buffer.clear(); |
4036 | buffer.push_back(Elt: '1'); |
4037 | return; |
4038 | } |
4039 | |
4040 | exp += FirstSignificant; |
4041 | buffer.erase(CS: &buffer[0], CE: &buffer[FirstSignificant]); |
4042 | } |
4043 | } // namespace |
4044 | |
4045 | void IEEEFloat::toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision, |
4046 | unsigned FormatMaxPadding, bool TruncateZero) const { |
4047 | switch (category) { |
4048 | case fcInfinity: |
4049 | if (isNegative()) |
4050 | return append(Buffer&: Str, Str: "-Inf" ); |
4051 | else |
4052 | return append(Buffer&: Str, Str: "+Inf" ); |
4053 | |
4054 | case fcNaN: return append(Buffer&: Str, Str: "NaN" ); |
4055 | |
4056 | case fcZero: |
4057 | if (isNegative()) |
4058 | Str.push_back(Elt: '-'); |
4059 | |
4060 | if (!FormatMaxPadding) { |
4061 | if (TruncateZero) |
4062 | append(Buffer&: Str, Str: "0.0E+0" ); |
4063 | else { |
4064 | append(Buffer&: Str, Str: "0.0" ); |
4065 | if (FormatPrecision > 1) |
4066 | Str.append(NumInputs: FormatPrecision - 1, Elt: '0'); |
4067 | append(Buffer&: Str, Str: "e+00" ); |
4068 | } |
4069 | } else |
4070 | Str.push_back(Elt: '0'); |
4071 | return; |
4072 | |
4073 | case fcNormal: |
4074 | break; |
4075 | } |
4076 | |
4077 | if (isNegative()) |
4078 | Str.push_back(Elt: '-'); |
4079 | |
4080 | // Decompose the number into an APInt and an exponent. |
4081 | int exp = exponent - ((int) semantics->precision - 1); |
4082 | APInt significand( |
4083 | semantics->precision, |
4084 | ArrayRef(significandParts(), partCountForBits(bits: semantics->precision))); |
4085 | |
4086 | // Set FormatPrecision if zero. We want to do this before we |
4087 | // truncate trailing zeros, as those are part of the precision. |
4088 | if (!FormatPrecision) { |
4089 | // We use enough digits so the number can be round-tripped back to an |
4090 | // APFloat. The formula comes from "How to Print Floating-Point Numbers |
4091 | // Accurately" by Steele and White. |
4092 | // FIXME: Using a formula based purely on the precision is conservative; |
4093 | // we can print fewer digits depending on the actual value being printed. |
4094 | |
4095 | // FormatPrecision = 2 + floor(significandBits / lg_2(10)) |
4096 | FormatPrecision = 2 + semantics->precision * 59 / 196; |
4097 | } |
4098 | |
4099 | // Ignore trailing binary zeros. |
4100 | int trailingZeros = significand.countr_zero(); |
4101 | exp += trailingZeros; |
4102 | significand.lshrInPlace(ShiftAmt: trailingZeros); |
4103 | |
4104 | // Change the exponent from 2^e to 10^e. |
4105 | if (exp == 0) { |
4106 | // Nothing to do. |
4107 | } else if (exp > 0) { |
4108 | // Just shift left. |
4109 | significand = significand.zext(width: semantics->precision + exp); |
4110 | significand <<= exp; |
4111 | exp = 0; |
4112 | } else { /* exp < 0 */ |
4113 | int texp = -exp; |
4114 | |
4115 | // We transform this using the identity: |
4116 | // (N)(2^-e) == (N)(5^e)(10^-e) |
4117 | // This means we have to multiply N (the significand) by 5^e. |
4118 | // To avoid overflow, we have to operate on numbers large |
4119 | // enough to store N * 5^e: |
4120 | // log2(N * 5^e) == log2(N) + e * log2(5) |
4121 | // <= semantics->precision + e * 137 / 59 |
4122 | // (log_2(5) ~ 2.321928 < 2.322034 ~ 137/59) |
4123 | |
4124 | unsigned precision = semantics->precision + (137 * texp + 136) / 59; |
4125 | |
4126 | // Multiply significand by 5^e. |
4127 | // N * 5^0101 == N * 5^(1*1) * 5^(0*2) * 5^(1*4) * 5^(0*8) |
4128 | significand = significand.zext(width: precision); |
4129 | APInt five_to_the_i(precision, 5); |
4130 | while (true) { |
4131 | if (texp & 1) significand *= five_to_the_i; |
4132 | |
4133 | texp >>= 1; |
4134 | if (!texp) break; |
4135 | five_to_the_i *= five_to_the_i; |
4136 | } |
4137 | } |
4138 | |
4139 | AdjustToPrecision(significand, exp, FormatPrecision); |
4140 | |
4141 | SmallVector<char, 256> buffer; |
4142 | |
4143 | // Fill the buffer. |
4144 | unsigned precision = significand.getBitWidth(); |
4145 | if (precision < 4) { |
4146 | // We need enough precision to store the value 10. |
4147 | precision = 4; |
4148 | significand = significand.zext(width: precision); |
4149 | } |
4150 | APInt ten(precision, 10); |
4151 | APInt digit(precision, 0); |
4152 | |
4153 | bool inTrail = true; |
4154 | while (significand != 0) { |
4155 | // digit <- significand % 10 |
4156 | // significand <- significand / 10 |
4157 | APInt::udivrem(LHS: significand, RHS: ten, Quotient&: significand, Remainder&: digit); |
4158 | |
4159 | unsigned d = digit.getZExtValue(); |
4160 | |
4161 | // Drop trailing zeros. |
4162 | if (inTrail && !d) exp++; |
4163 | else { |
4164 | buffer.push_back(Elt: (char) ('0' + d)); |
4165 | inTrail = false; |
4166 | } |
4167 | } |
4168 | |
4169 | assert(!buffer.empty() && "no characters in buffer!" ); |
4170 | |
4171 | // Drop down to FormatPrecision. |
4172 | // TODO: don't do more precise calculations above than are required. |
4173 | AdjustToPrecision(buffer, exp, FormatPrecision); |
4174 | |
4175 | unsigned NDigits = buffer.size(); |
4176 | |
4177 | // Check whether we should use scientific notation. |
4178 | bool FormatScientific; |
4179 | if (!FormatMaxPadding) |
4180 | FormatScientific = true; |
4181 | else { |
4182 | if (exp >= 0) { |
4183 | // 765e3 --> 765000 |
4184 | // ^^^ |
4185 | // But we shouldn't make the number look more precise than it is. |
4186 | FormatScientific = ((unsigned) exp > FormatMaxPadding || |
4187 | NDigits + (unsigned) exp > FormatPrecision); |
4188 | } else { |
4189 | // Power of the most significant digit. |
4190 | int MSD = exp + (int) (NDigits - 1); |
4191 | if (MSD >= 0) { |
4192 | // 765e-2 == 7.65 |
4193 | FormatScientific = false; |
4194 | } else { |
4195 | // 765e-5 == 0.00765 |
4196 | // ^ ^^ |
4197 | FormatScientific = ((unsigned) -MSD) > FormatMaxPadding; |
4198 | } |
4199 | } |
4200 | } |
4201 | |
4202 | // Scientific formatting is pretty straightforward. |
4203 | if (FormatScientific) { |
4204 | exp += (NDigits - 1); |
4205 | |
4206 | Str.push_back(Elt: buffer[NDigits-1]); |
4207 | Str.push_back(Elt: '.'); |
4208 | if (NDigits == 1 && TruncateZero) |
4209 | Str.push_back(Elt: '0'); |
4210 | else |
4211 | for (unsigned I = 1; I != NDigits; ++I) |
4212 | Str.push_back(Elt: buffer[NDigits-1-I]); |
4213 | // Fill with zeros up to FormatPrecision. |
4214 | if (!TruncateZero && FormatPrecision > NDigits - 1) |
4215 | Str.append(NumInputs: FormatPrecision - NDigits + 1, Elt: '0'); |
4216 | // For !TruncateZero we use lower 'e'. |
4217 | Str.push_back(Elt: TruncateZero ? 'E' : 'e'); |
4218 | |
4219 | Str.push_back(Elt: exp >= 0 ? '+' : '-'); |
4220 | if (exp < 0) exp = -exp; |
4221 | SmallVector<char, 6> expbuf; |
4222 | do { |
4223 | expbuf.push_back(Elt: (char) ('0' + (exp % 10))); |
4224 | exp /= 10; |
4225 | } while (exp); |
4226 | // Exponent always at least two digits if we do not truncate zeros. |
4227 | if (!TruncateZero && expbuf.size() < 2) |
4228 | expbuf.push_back(Elt: '0'); |
4229 | for (unsigned I = 0, E = expbuf.size(); I != E; ++I) |
4230 | Str.push_back(Elt: expbuf[E-1-I]); |
4231 | return; |
4232 | } |
4233 | |
4234 | // Non-scientific, positive exponents. |
4235 | if (exp >= 0) { |
4236 | for (unsigned I = 0; I != NDigits; ++I) |
4237 | Str.push_back(Elt: buffer[NDigits-1-I]); |
4238 | for (unsigned I = 0; I != (unsigned) exp; ++I) |
4239 | Str.push_back(Elt: '0'); |
4240 | return; |
4241 | } |
4242 | |
4243 | // Non-scientific, negative exponents. |
4244 | |
4245 | // The number of digits to the left of the decimal point. |
4246 | int NWholeDigits = exp + (int) NDigits; |
4247 | |
4248 | unsigned I = 0; |
4249 | if (NWholeDigits > 0) { |
4250 | for (; I != (unsigned) NWholeDigits; ++I) |
4251 | Str.push_back(Elt: buffer[NDigits-I-1]); |
4252 | Str.push_back(Elt: '.'); |
4253 | } else { |
4254 | unsigned NZeros = 1 + (unsigned) -NWholeDigits; |
4255 | |
4256 | Str.push_back(Elt: '0'); |
4257 | Str.push_back(Elt: '.'); |
4258 | for (unsigned Z = 1; Z != NZeros; ++Z) |
4259 | Str.push_back(Elt: '0'); |
4260 | } |
4261 | |
4262 | for (; I != NDigits; ++I) |
4263 | Str.push_back(Elt: buffer[NDigits-I-1]); |
4264 | } |
4265 | |
4266 | bool IEEEFloat::getExactInverse(APFloat *inv) const { |
4267 | // Special floats and denormals have no exact inverse. |
4268 | if (!isFiniteNonZero()) |
4269 | return false; |
4270 | |
4271 | // Check that the number is a power of two by making sure that only the |
4272 | // integer bit is set in the significand. |
4273 | if (significandLSB() != semantics->precision - 1) |
4274 | return false; |
4275 | |
4276 | // Get the inverse. |
4277 | IEEEFloat reciprocal(*semantics, 1ULL); |
4278 | if (reciprocal.divide(rhs: *this, rounding_mode: rmNearestTiesToEven) != opOK) |
4279 | return false; |
4280 | |
4281 | // Avoid multiplication with a denormal, it is not safe on all platforms and |
4282 | // may be slower than a normal division. |
4283 | if (reciprocal.isDenormal()) |
4284 | return false; |
4285 | |
4286 | assert(reciprocal.isFiniteNonZero() && |
4287 | reciprocal.significandLSB() == reciprocal.semantics->precision - 1); |
4288 | |
4289 | if (inv) |
4290 | *inv = APFloat(reciprocal, *semantics); |
4291 | |
4292 | return true; |
4293 | } |
4294 | |
4295 | int IEEEFloat::getExactLog2Abs() const { |
4296 | if (!isFinite() || isZero()) |
4297 | return INT_MIN; |
4298 | |
4299 | const integerPart *Parts = significandParts(); |
4300 | const int PartCount = partCountForBits(bits: semantics->precision); |
4301 | |
4302 | int PopCount = 0; |
4303 | for (int i = 0; i < PartCount; ++i) { |
4304 | PopCount += llvm::popcount(Value: Parts[i]); |
4305 | if (PopCount > 1) |
4306 | return INT_MIN; |
4307 | } |
4308 | |
4309 | if (exponent != semantics->minExponent) |
4310 | return exponent; |
4311 | |
4312 | int CountrParts = 0; |
4313 | for (int i = 0; i < PartCount; |
4314 | ++i, CountrParts += APInt::APINT_BITS_PER_WORD) { |
4315 | if (Parts[i] != 0) { |
4316 | return exponent - semantics->precision + CountrParts + |
4317 | llvm::countr_zero(Val: Parts[i]) + 1; |
4318 | } |
4319 | } |
4320 | |
4321 | llvm_unreachable("didn't find the set bit" ); |
4322 | } |
4323 | |
4324 | bool IEEEFloat::isSignaling() const { |
4325 | if (!isNaN()) |
4326 | return false; |
4327 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly) |
4328 | return false; |
4329 | |
4330 | // IEEE-754R 2008 6.2.1: A signaling NaN bit string should be encoded with the |
4331 | // first bit of the trailing significand being 0. |
4332 | return !APInt::tcExtractBit(significandParts(), bit: semantics->precision - 2); |
4333 | } |
4334 | |
4335 | /// IEEE-754R 2008 5.3.1: nextUp/nextDown. |
4336 | /// |
4337 | /// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with |
4338 | /// appropriate sign switching before/after the computation. |
4339 | IEEEFloat::opStatus IEEEFloat::next(bool nextDown) { |
4340 | // If we are performing nextDown, swap sign so we have -x. |
4341 | if (nextDown) |
4342 | changeSign(); |
4343 | |
4344 | // Compute nextUp(x) |
4345 | opStatus result = opOK; |
4346 | |
4347 | // Handle each float category separately. |
4348 | switch (category) { |
4349 | case fcInfinity: |
4350 | // nextUp(+inf) = +inf |
4351 | if (!isNegative()) |
4352 | break; |
4353 | // nextUp(-inf) = -getLargest() |
4354 | makeLargest(Negative: true); |
4355 | break; |
4356 | case fcNaN: |
4357 | // IEEE-754R 2008 6.2 Par 2: nextUp(sNaN) = qNaN. Set Invalid flag. |
4358 | // IEEE-754R 2008 6.2: nextUp(qNaN) = qNaN. Must be identity so we do not |
4359 | // change the payload. |
4360 | if (isSignaling()) { |
4361 | result = opInvalidOp; |
4362 | // For consistency, propagate the sign of the sNaN to the qNaN. |
4363 | makeNaN(SNaN: false, Negative: isNegative(), fill: nullptr); |
4364 | } |
4365 | break; |
4366 | case fcZero: |
4367 | // nextUp(pm 0) = +getSmallest() |
4368 | makeSmallest(Negative: false); |
4369 | break; |
4370 | case fcNormal: |
4371 | // nextUp(-getSmallest()) = -0 |
4372 | if (isSmallest() && isNegative()) { |
4373 | APInt::tcSet(significandParts(), 0, partCount()); |
4374 | category = fcZero; |
4375 | exponent = 0; |
4376 | if (semantics->nanEncoding == fltNanEncoding::NegativeZero) |
4377 | sign = false; |
4378 | break; |
4379 | } |
4380 | |
4381 | if (isLargest() && !isNegative()) { |
4382 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly) { |
4383 | // nextUp(getLargest()) == NAN |
4384 | makeNaN(); |
4385 | break; |
4386 | } else { |
4387 | // nextUp(getLargest()) == INFINITY |
4388 | APInt::tcSet(significandParts(), 0, partCount()); |
4389 | category = fcInfinity; |
4390 | exponent = semantics->maxExponent + 1; |
4391 | break; |
4392 | } |
4393 | } |
4394 | |
4395 | // nextUp(normal) == normal + inc. |
4396 | if (isNegative()) { |
4397 | // If we are negative, we need to decrement the significand. |
4398 | |
4399 | // We only cross a binade boundary that requires adjusting the exponent |
4400 | // if: |
4401 | // 1. exponent != semantics->minExponent. This implies we are not in the |
4402 | // smallest binade or are dealing with denormals. |
4403 | // 2. Our significand excluding the integral bit is all zeros. |
4404 | bool WillCrossBinadeBoundary = |
4405 | exponent != semantics->minExponent && isSignificandAllZeros(); |
4406 | |
4407 | // Decrement the significand. |
4408 | // |
4409 | // We always do this since: |
4410 | // 1. If we are dealing with a non-binade decrement, by definition we |
4411 | // just decrement the significand. |
4412 | // 2. If we are dealing with a normal -> normal binade decrement, since |
4413 | // we have an explicit integral bit the fact that all bits but the |
4414 | // integral bit are zero implies that subtracting one will yield a |
4415 | // significand with 0 integral bit and 1 in all other spots. Thus we |
4416 | // must just adjust the exponent and set the integral bit to 1. |
4417 | // 3. If we are dealing with a normal -> denormal binade decrement, |
4418 | // since we set the integral bit to 0 when we represent denormals, we |
4419 | // just decrement the significand. |
4420 | integerPart *Parts = significandParts(); |
4421 | APInt::tcDecrement(dst: Parts, parts: partCount()); |
4422 | |
4423 | if (WillCrossBinadeBoundary) { |
4424 | // Our result is a normal number. Do the following: |
4425 | // 1. Set the integral bit to 1. |
4426 | // 2. Decrement the exponent. |
4427 | APInt::tcSetBit(Parts, bit: semantics->precision - 1); |
4428 | exponent--; |
4429 | } |
4430 | } else { |
4431 | // If we are positive, we need to increment the significand. |
4432 | |
4433 | // We only cross a binade boundary that requires adjusting the exponent if |
4434 | // the input is not a denormal and all of said input's significand bits |
4435 | // are set. If all of said conditions are true: clear the significand, set |
4436 | // the integral bit to 1, and increment the exponent. If we have a |
4437 | // denormal always increment since moving denormals and the numbers in the |
4438 | // smallest normal binade have the same exponent in our representation. |
4439 | bool WillCrossBinadeBoundary = !isDenormal() && isSignificandAllOnes(); |
4440 | |
4441 | if (WillCrossBinadeBoundary) { |
4442 | integerPart *Parts = significandParts(); |
4443 | APInt::tcSet(Parts, 0, partCount()); |
4444 | APInt::tcSetBit(Parts, bit: semantics->precision - 1); |
4445 | assert(exponent != semantics->maxExponent && |
4446 | "We can not increment an exponent beyond the maxExponent allowed" |
4447 | " by the given floating point semantics." ); |
4448 | exponent++; |
4449 | } else { |
4450 | incrementSignificand(); |
4451 | } |
4452 | } |
4453 | break; |
4454 | } |
4455 | |
4456 | // If we are performing nextDown, swap sign so we have -nextUp(-x) |
4457 | if (nextDown) |
4458 | changeSign(); |
4459 | |
4460 | return result; |
4461 | } |
4462 | |
4463 | APFloatBase::ExponentType IEEEFloat::exponentNaN() const { |
4464 | return ::exponentNaN(semantics: *semantics); |
4465 | } |
4466 | |
4467 | APFloatBase::ExponentType IEEEFloat::exponentInf() const { |
4468 | return ::exponentInf(semantics: *semantics); |
4469 | } |
4470 | |
4471 | APFloatBase::ExponentType IEEEFloat::exponentZero() const { |
4472 | return ::exponentZero(semantics: *semantics); |
4473 | } |
4474 | |
4475 | void IEEEFloat::makeInf(bool Negative) { |
4476 | if (semantics->nonFiniteBehavior == fltNonfiniteBehavior::NanOnly) { |
4477 | // There is no Inf, so make NaN instead. |
4478 | makeNaN(SNaN: false, Negative); |
4479 | return; |
4480 | } |
4481 | category = fcInfinity; |
4482 | sign = Negative; |
4483 | exponent = exponentInf(); |
4484 | APInt::tcSet(significandParts(), 0, partCount()); |
4485 | } |
4486 | |
4487 | void IEEEFloat::makeZero(bool Negative) { |
4488 | category = fcZero; |
4489 | sign = Negative; |
4490 | if (semantics->nanEncoding == fltNanEncoding::NegativeZero) { |
4491 | // Merge negative zero to positive because 0b10000...000 is used for NaN |
4492 | sign = false; |
4493 | } |
4494 | exponent = exponentZero(); |
4495 | APInt::tcSet(significandParts(), 0, partCount()); |
4496 | } |
4497 | |
4498 | void IEEEFloat::makeQuiet() { |
4499 | assert(isNaN()); |
4500 | if (semantics->nonFiniteBehavior != fltNonfiniteBehavior::NanOnly) |
4501 | APInt::tcSetBit(significandParts(), bit: semantics->precision - 2); |
4502 | } |
4503 | |
4504 | int ilogb(const IEEEFloat &Arg) { |
4505 | if (Arg.isNaN()) |
4506 | return IEEEFloat::IEK_NaN; |
4507 | if (Arg.isZero()) |
4508 | return IEEEFloat::IEK_Zero; |
4509 | if (Arg.isInfinity()) |
4510 | return IEEEFloat::IEK_Inf; |
4511 | if (!Arg.isDenormal()) |
4512 | return Arg.exponent; |
4513 | |
4514 | IEEEFloat Normalized(Arg); |
4515 | int SignificandBits = Arg.getSemantics().precision - 1; |
4516 | |
4517 | Normalized.exponent += SignificandBits; |
4518 | Normalized.normalize(rounding_mode: IEEEFloat::rmNearestTiesToEven, lost_fraction: lfExactlyZero); |
4519 | return Normalized.exponent - SignificandBits; |
4520 | } |
4521 | |
4522 | IEEEFloat scalbn(IEEEFloat X, int Exp, IEEEFloat::roundingMode RoundingMode) { |
4523 | auto MaxExp = X.getSemantics().maxExponent; |
4524 | auto MinExp = X.getSemantics().minExponent; |
4525 | |
4526 | // If Exp is wildly out-of-scale, simply adding it to X.exponent will |
4527 | // overflow; clamp it to a safe range before adding, but ensure that the range |
4528 | // is large enough that the clamp does not change the result. The range we |
4529 | // need to support is the difference between the largest possible exponent and |
4530 | // the normalized exponent of half the smallest denormal. |
4531 | |
4532 | int SignificandBits = X.getSemantics().precision - 1; |
4533 | int MaxIncrement = MaxExp - (MinExp - SignificandBits) + 1; |
4534 | |
4535 | // Clamp to one past the range ends to let normalize handle overlflow. |
4536 | X.exponent += std::clamp(val: Exp, lo: -MaxIncrement - 1, hi: MaxIncrement); |
4537 | X.normalize(rounding_mode: RoundingMode, lost_fraction: lfExactlyZero); |
4538 | if (X.isNaN()) |
4539 | X.makeQuiet(); |
4540 | return X; |
4541 | } |
4542 | |
4543 | IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM) { |
4544 | Exp = ilogb(Arg: Val); |
4545 | |
4546 | // Quiet signalling nans. |
4547 | if (Exp == IEEEFloat::IEK_NaN) { |
4548 | IEEEFloat Quiet(Val); |
4549 | Quiet.makeQuiet(); |
4550 | return Quiet; |
4551 | } |
4552 | |
4553 | if (Exp == IEEEFloat::IEK_Inf) |
4554 | return Val; |
4555 | |
4556 | // 1 is added because frexp is defined to return a normalized fraction in |
4557 | // +/-[0.5, 1.0), rather than the usual +/-[1.0, 2.0). |
4558 | Exp = Exp == IEEEFloat::IEK_Zero ? 0 : Exp + 1; |
4559 | return scalbn(X: Val, Exp: -Exp, RoundingMode: RM); |
4560 | } |
4561 | |
4562 | DoubleAPFloat::DoubleAPFloat(const fltSemantics &S) |
4563 | : Semantics(&S), |
4564 | Floats(new APFloat[2]{APFloat(semIEEEdouble), APFloat(semIEEEdouble)}) { |
4565 | assert(Semantics == &semPPCDoubleDouble); |
4566 | } |
4567 | |
4568 | DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, uninitializedTag) |
4569 | : Semantics(&S), |
4570 | Floats(new APFloat[2]{APFloat(semIEEEdouble, uninitialized), |
4571 | APFloat(semIEEEdouble, uninitialized)}) { |
4572 | assert(Semantics == &semPPCDoubleDouble); |
4573 | } |
4574 | |
4575 | DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, integerPart I) |
4576 | : Semantics(&S), Floats(new APFloat[2]{APFloat(semIEEEdouble, I), |
4577 | APFloat(semIEEEdouble)}) { |
4578 | assert(Semantics == &semPPCDoubleDouble); |
4579 | } |
4580 | |
4581 | DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, const APInt &I) |
4582 | : Semantics(&S), |
4583 | Floats(new APFloat[2]{ |
4584 | APFloat(semIEEEdouble, APInt(64, I.getRawData()[0])), |
4585 | APFloat(semIEEEdouble, APInt(64, I.getRawData()[1]))}) { |
4586 | assert(Semantics == &semPPCDoubleDouble); |
4587 | } |
4588 | |
4589 | DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, APFloat &&First, |
4590 | APFloat &&Second) |
4591 | : Semantics(&S), |
4592 | Floats(new APFloat[2]{std::move(First), std::move(Second)}) { |
4593 | assert(Semantics == &semPPCDoubleDouble); |
4594 | assert(&Floats[0].getSemantics() == &semIEEEdouble); |
4595 | assert(&Floats[1].getSemantics() == &semIEEEdouble); |
4596 | } |
4597 | |
4598 | DoubleAPFloat::DoubleAPFloat(const DoubleAPFloat &RHS) |
4599 | : Semantics(RHS.Semantics), |
4600 | Floats(RHS.Floats ? new APFloat[2]{APFloat(RHS.Floats[0]), |
4601 | APFloat(RHS.Floats[1])} |
4602 | : nullptr) { |
4603 | assert(Semantics == &semPPCDoubleDouble); |
4604 | } |
4605 | |
4606 | DoubleAPFloat::DoubleAPFloat(DoubleAPFloat &&RHS) |
4607 | : Semantics(RHS.Semantics), Floats(std::move(RHS.Floats)) { |
4608 | RHS.Semantics = &semBogus; |
4609 | assert(Semantics == &semPPCDoubleDouble); |
4610 | } |
4611 | |
4612 | DoubleAPFloat &DoubleAPFloat::operator=(const DoubleAPFloat &RHS) { |
4613 | if (Semantics == RHS.Semantics && RHS.Floats) { |
4614 | Floats[0] = RHS.Floats[0]; |
4615 | Floats[1] = RHS.Floats[1]; |
4616 | } else if (this != &RHS) { |
4617 | this->~DoubleAPFloat(); |
4618 | new (this) DoubleAPFloat(RHS); |
4619 | } |
4620 | return *this; |
4621 | } |
4622 | |
4623 | // Implement addition, subtraction, multiplication and division based on: |
4624 | // "Software for Doubled-Precision Floating-Point Computations", |
4625 | // by Seppo Linnainmaa, ACM TOMS vol 7 no 3, September 1981, pages 272-283. |
4626 | APFloat::opStatus DoubleAPFloat::addImpl(const APFloat &a, const APFloat &aa, |
4627 | const APFloat &c, const APFloat &cc, |
4628 | roundingMode RM) { |
4629 | int Status = opOK; |
4630 | APFloat z = a; |
4631 | Status |= z.add(RHS: c, RM); |
4632 | if (!z.isFinite()) { |
4633 | if (!z.isInfinity()) { |
4634 | Floats[0] = std::move(z); |
4635 | Floats[1].makeZero(/* Neg = */ false); |
4636 | return (opStatus)Status; |
4637 | } |
4638 | Status = opOK; |
4639 | auto AComparedToC = a.compareAbsoluteValue(RHS: c); |
4640 | z = cc; |
4641 | Status |= z.add(RHS: aa, RM); |
4642 | if (AComparedToC == APFloat::cmpGreaterThan) { |
4643 | // z = cc + aa + c + a; |
4644 | Status |= z.add(RHS: c, RM); |
4645 | Status |= z.add(RHS: a, RM); |
4646 | } else { |
4647 | // z = cc + aa + a + c; |
4648 | Status |= z.add(RHS: a, RM); |
4649 | Status |= z.add(RHS: c, RM); |
4650 | } |
4651 | if (!z.isFinite()) { |
4652 | Floats[0] = std::move(z); |
4653 | Floats[1].makeZero(/* Neg = */ false); |
4654 | return (opStatus)Status; |
4655 | } |
4656 | Floats[0] = z; |
4657 | APFloat zz = aa; |
4658 | Status |= zz.add(RHS: cc, RM); |
4659 | if (AComparedToC == APFloat::cmpGreaterThan) { |
4660 | // Floats[1] = a - z + c + zz; |
4661 | Floats[1] = a; |
4662 | Status |= Floats[1].subtract(RHS: z, RM); |
4663 | Status |= Floats[1].add(RHS: c, RM); |
4664 | Status |= Floats[1].add(RHS: zz, RM); |
4665 | } else { |
4666 | // Floats[1] = c - z + a + zz; |
4667 | Floats[1] = c; |
4668 | Status |= Floats[1].subtract(RHS: z, RM); |
4669 | Status |= Floats[1].add(RHS: a, RM); |
4670 | Status |= Floats[1].add(RHS: zz, RM); |
4671 | } |
4672 | } else { |
4673 | // q = a - z; |
4674 | APFloat q = a; |
4675 | Status |= q.subtract(RHS: z, RM); |
4676 | |
4677 | // zz = q + c + (a - (q + z)) + aa + cc; |
4678 | // Compute a - (q + z) as -((q + z) - a) to avoid temporary copies. |
4679 | auto zz = q; |
4680 | Status |= zz.add(RHS: c, RM); |
4681 | Status |= q.add(RHS: z, RM); |
4682 | Status |= q.subtract(RHS: a, RM); |
4683 | q.changeSign(); |
4684 | Status |= zz.add(RHS: q, RM); |
4685 | Status |= zz.add(RHS: aa, RM); |
4686 | Status |= zz.add(RHS: cc, RM); |
4687 | if (zz.isZero() && !zz.isNegative()) { |
4688 | Floats[0] = std::move(z); |
4689 | Floats[1].makeZero(/* Neg = */ false); |
4690 | return opOK; |
4691 | } |
4692 | Floats[0] = z; |
4693 | Status |= Floats[0].add(RHS: zz, RM); |
4694 | if (!Floats[0].isFinite()) { |
4695 | Floats[1].makeZero(/* Neg = */ false); |
4696 | return (opStatus)Status; |
4697 | } |
4698 | Floats[1] = std::move(z); |
4699 | Status |= Floats[1].subtract(RHS: Floats[0], RM); |
4700 | Status |= Floats[1].add(RHS: zz, RM); |
4701 | } |
4702 | return (opStatus)Status; |
4703 | } |
4704 | |
4705 | APFloat::opStatus DoubleAPFloat::addWithSpecial(const DoubleAPFloat &LHS, |
4706 | const DoubleAPFloat &RHS, |
4707 | DoubleAPFloat &Out, |
4708 | roundingMode RM) { |
4709 | if (LHS.getCategory() == fcNaN) { |
4710 | Out = LHS; |
4711 | return opOK; |
4712 | } |
4713 | if (RHS.getCategory() == fcNaN) { |
4714 | Out = RHS; |
4715 | return opOK; |
4716 | } |
4717 | if (LHS.getCategory() == fcZero) { |
4718 | Out = RHS; |
4719 | return opOK; |
4720 | } |
4721 | if (RHS.getCategory() == fcZero) { |
4722 | Out = LHS; |
4723 | return opOK; |
4724 | } |
4725 | if (LHS.getCategory() == fcInfinity && RHS.getCategory() == fcInfinity && |
4726 | LHS.isNegative() != RHS.isNegative()) { |
4727 | Out.makeNaN(SNaN: false, Neg: Out.isNegative(), fill: nullptr); |
4728 | return opInvalidOp; |
4729 | } |
4730 | if (LHS.getCategory() == fcInfinity) { |
4731 | Out = LHS; |
4732 | return opOK; |
4733 | } |
4734 | if (RHS.getCategory() == fcInfinity) { |
4735 | Out = RHS; |
4736 | return opOK; |
4737 | } |
4738 | assert(LHS.getCategory() == fcNormal && RHS.getCategory() == fcNormal); |
4739 | |
4740 | APFloat A(LHS.Floats[0]), AA(LHS.Floats[1]), C(RHS.Floats[0]), |
4741 | CC(RHS.Floats[1]); |
4742 | assert(&A.getSemantics() == &semIEEEdouble); |
4743 | assert(&AA.getSemantics() == &semIEEEdouble); |
4744 | assert(&C.getSemantics() == &semIEEEdouble); |
4745 | assert(&CC.getSemantics() == &semIEEEdouble); |
4746 | assert(&Out.Floats[0].getSemantics() == &semIEEEdouble); |
4747 | assert(&Out.Floats[1].getSemantics() == &semIEEEdouble); |
4748 | return Out.addImpl(a: A, aa: AA, c: C, cc: CC, RM); |
4749 | } |
4750 | |
4751 | APFloat::opStatus DoubleAPFloat::add(const DoubleAPFloat &RHS, |
4752 | roundingMode RM) { |
4753 | return addWithSpecial(LHS: *this, RHS, Out&: *this, RM); |
4754 | } |
4755 | |
4756 | APFloat::opStatus DoubleAPFloat::subtract(const DoubleAPFloat &RHS, |
4757 | roundingMode RM) { |
4758 | changeSign(); |
4759 | auto Ret = add(RHS, RM); |
4760 | changeSign(); |
4761 | return Ret; |
4762 | } |
4763 | |
4764 | APFloat::opStatus DoubleAPFloat::multiply(const DoubleAPFloat &RHS, |
4765 | APFloat::roundingMode RM) { |
4766 | const auto &LHS = *this; |
4767 | auto &Out = *this; |
4768 | /* Interesting observation: For special categories, finding the lowest |
4769 | common ancestor of the following layered graph gives the correct |
4770 | return category: |
4771 | |
4772 | NaN |
4773 | / \ |
4774 | Zero Inf |
4775 | \ / |
4776 | Normal |
4777 | |
4778 | e.g. NaN * NaN = NaN |
4779 | Zero * Inf = NaN |
4780 | Normal * Zero = Zero |
4781 | Normal * Inf = Inf |
4782 | */ |
4783 | if (LHS.getCategory() == fcNaN) { |
4784 | Out = LHS; |
4785 | return opOK; |
4786 | } |
4787 | if (RHS.getCategory() == fcNaN) { |
4788 | Out = RHS; |
4789 | return opOK; |
4790 | } |
4791 | if ((LHS.getCategory() == fcZero && RHS.getCategory() == fcInfinity) || |
4792 | (LHS.getCategory() == fcInfinity && RHS.getCategory() == fcZero)) { |
4793 | Out.makeNaN(SNaN: false, Neg: false, fill: nullptr); |
4794 | return opOK; |
4795 | } |
4796 | if (LHS.getCategory() == fcZero || LHS.getCategory() == fcInfinity) { |
4797 | Out = LHS; |
4798 | return opOK; |
4799 | } |
4800 | if (RHS.getCategory() == fcZero || RHS.getCategory() == fcInfinity) { |
4801 | Out = RHS; |
4802 | return opOK; |
4803 | } |
4804 | assert(LHS.getCategory() == fcNormal && RHS.getCategory() == fcNormal && |
4805 | "Special cases not handled exhaustively" ); |
4806 | |
4807 | int Status = opOK; |
4808 | APFloat A = Floats[0], B = Floats[1], C = RHS.Floats[0], D = RHS.Floats[1]; |
4809 | // t = a * c |
4810 | APFloat T = A; |
4811 | Status |= T.multiply(RHS: C, RM); |
4812 | if (!T.isFiniteNonZero()) { |
4813 | Floats[0] = T; |
4814 | Floats[1].makeZero(/* Neg = */ false); |
4815 | return (opStatus)Status; |
4816 | } |
4817 | |
4818 | // tau = fmsub(a, c, t), that is -fmadd(-a, c, t). |
4819 | APFloat Tau = A; |
4820 | T.changeSign(); |
4821 | Status |= Tau.fusedMultiplyAdd(Multiplicand: C, Addend: T, RM); |
4822 | T.changeSign(); |
4823 | { |
4824 | // v = a * d |
4825 | APFloat V = A; |
4826 | Status |= V.multiply(RHS: D, RM); |
4827 | // w = b * c |
4828 | APFloat W = B; |
4829 | Status |= W.multiply(RHS: C, RM); |
4830 | Status |= V.add(RHS: W, RM); |
4831 | // tau += v + w |
4832 | Status |= Tau.add(RHS: V, RM); |
4833 | } |
4834 | // u = t + tau |
4835 | APFloat U = T; |
4836 | Status |= U.add(RHS: Tau, RM); |
4837 | |
4838 | Floats[0] = U; |
4839 | if (!U.isFinite()) { |
4840 | Floats[1].makeZero(/* Neg = */ false); |
4841 | } else { |
4842 | // Floats[1] = (t - u) + tau |
4843 | Status |= T.subtract(RHS: U, RM); |
4844 | Status |= T.add(RHS: Tau, RM); |
4845 | Floats[1] = T; |
4846 | } |
4847 | return (opStatus)Status; |
4848 | } |
4849 | |
4850 | APFloat::opStatus DoubleAPFloat::divide(const DoubleAPFloat &RHS, |
4851 | APFloat::roundingMode RM) { |
4852 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
4853 | APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt()); |
4854 | auto Ret = |
4855 | Tmp.divide(RHS: APFloat(semPPCDoubleDoubleLegacy, RHS.bitcastToAPInt()), RM); |
4856 | *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt()); |
4857 | return Ret; |
4858 | } |
4859 | |
4860 | APFloat::opStatus DoubleAPFloat::remainder(const DoubleAPFloat &RHS) { |
4861 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
4862 | APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt()); |
4863 | auto Ret = |
4864 | Tmp.remainder(RHS: APFloat(semPPCDoubleDoubleLegacy, RHS.bitcastToAPInt())); |
4865 | *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt()); |
4866 | return Ret; |
4867 | } |
4868 | |
4869 | APFloat::opStatus DoubleAPFloat::mod(const DoubleAPFloat &RHS) { |
4870 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
4871 | APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt()); |
4872 | auto Ret = Tmp.mod(RHS: APFloat(semPPCDoubleDoubleLegacy, RHS.bitcastToAPInt())); |
4873 | *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt()); |
4874 | return Ret; |
4875 | } |
4876 | |
4877 | APFloat::opStatus |
4878 | DoubleAPFloat::fusedMultiplyAdd(const DoubleAPFloat &Multiplicand, |
4879 | const DoubleAPFloat &Addend, |
4880 | APFloat::roundingMode RM) { |
4881 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
4882 | APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt()); |
4883 | auto Ret = Tmp.fusedMultiplyAdd( |
4884 | Multiplicand: APFloat(semPPCDoubleDoubleLegacy, Multiplicand.bitcastToAPInt()), |
4885 | Addend: APFloat(semPPCDoubleDoubleLegacy, Addend.bitcastToAPInt()), RM); |
4886 | *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt()); |
4887 | return Ret; |
4888 | } |
4889 | |
4890 | APFloat::opStatus DoubleAPFloat::roundToIntegral(APFloat::roundingMode RM) { |
4891 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
4892 | APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt()); |
4893 | auto Ret = Tmp.roundToIntegral(RM); |
4894 | *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt()); |
4895 | return Ret; |
4896 | } |
4897 | |
4898 | void DoubleAPFloat::changeSign() { |
4899 | Floats[0].changeSign(); |
4900 | Floats[1].changeSign(); |
4901 | } |
4902 | |
4903 | APFloat::cmpResult |
4904 | DoubleAPFloat::compareAbsoluteValue(const DoubleAPFloat &RHS) const { |
4905 | auto Result = Floats[0].compareAbsoluteValue(RHS: RHS.Floats[0]); |
4906 | if (Result != cmpEqual) |
4907 | return Result; |
4908 | Result = Floats[1].compareAbsoluteValue(RHS: RHS.Floats[1]); |
4909 | if (Result == cmpLessThan || Result == cmpGreaterThan) { |
4910 | auto Against = Floats[0].isNegative() ^ Floats[1].isNegative(); |
4911 | auto RHSAgainst = RHS.Floats[0].isNegative() ^ RHS.Floats[1].isNegative(); |
4912 | if (Against && !RHSAgainst) |
4913 | return cmpLessThan; |
4914 | if (!Against && RHSAgainst) |
4915 | return cmpGreaterThan; |
4916 | if (!Against && !RHSAgainst) |
4917 | return Result; |
4918 | if (Against && RHSAgainst) |
4919 | return (cmpResult)(cmpLessThan + cmpGreaterThan - Result); |
4920 | } |
4921 | return Result; |
4922 | } |
4923 | |
4924 | APFloat::fltCategory DoubleAPFloat::getCategory() const { |
4925 | return Floats[0].getCategory(); |
4926 | } |
4927 | |
4928 | bool DoubleAPFloat::isNegative() const { return Floats[0].isNegative(); } |
4929 | |
4930 | void DoubleAPFloat::makeInf(bool Neg) { |
4931 | Floats[0].makeInf(Neg); |
4932 | Floats[1].makeZero(/* Neg = */ false); |
4933 | } |
4934 | |
4935 | void DoubleAPFloat::makeZero(bool Neg) { |
4936 | Floats[0].makeZero(Neg); |
4937 | Floats[1].makeZero(/* Neg = */ false); |
4938 | } |
4939 | |
4940 | void DoubleAPFloat::makeLargest(bool Neg) { |
4941 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
4942 | Floats[0] = APFloat(semIEEEdouble, APInt(64, 0x7fefffffffffffffull)); |
4943 | Floats[1] = APFloat(semIEEEdouble, APInt(64, 0x7c8ffffffffffffeull)); |
4944 | if (Neg) |
4945 | changeSign(); |
4946 | } |
4947 | |
4948 | void DoubleAPFloat::makeSmallest(bool Neg) { |
4949 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
4950 | Floats[0].makeSmallest(Neg); |
4951 | Floats[1].makeZero(/* Neg = */ false); |
4952 | } |
4953 | |
4954 | void DoubleAPFloat::makeSmallestNormalized(bool Neg) { |
4955 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
4956 | Floats[0] = APFloat(semIEEEdouble, APInt(64, 0x0360000000000000ull)); |
4957 | if (Neg) |
4958 | Floats[0].changeSign(); |
4959 | Floats[1].makeZero(/* Neg = */ false); |
4960 | } |
4961 | |
4962 | void DoubleAPFloat::makeNaN(bool SNaN, bool Neg, const APInt *fill) { |
4963 | Floats[0].makeNaN(SNaN, Neg, fill); |
4964 | Floats[1].makeZero(/* Neg = */ false); |
4965 | } |
4966 | |
4967 | APFloat::cmpResult DoubleAPFloat::compare(const DoubleAPFloat &RHS) const { |
4968 | auto Result = Floats[0].compare(RHS: RHS.Floats[0]); |
4969 | // |Float[0]| > |Float[1]| |
4970 | if (Result == APFloat::cmpEqual) |
4971 | return Floats[1].compare(RHS: RHS.Floats[1]); |
4972 | return Result; |
4973 | } |
4974 | |
4975 | bool DoubleAPFloat::bitwiseIsEqual(const DoubleAPFloat &RHS) const { |
4976 | return Floats[0].bitwiseIsEqual(RHS: RHS.Floats[0]) && |
4977 | Floats[1].bitwiseIsEqual(RHS: RHS.Floats[1]); |
4978 | } |
4979 | |
4980 | hash_code hash_value(const DoubleAPFloat &Arg) { |
4981 | if (Arg.Floats) |
4982 | return hash_combine(args: hash_value(Arg: Arg.Floats[0]), args: hash_value(Arg: Arg.Floats[1])); |
4983 | return hash_combine(args: Arg.Semantics); |
4984 | } |
4985 | |
4986 | APInt DoubleAPFloat::bitcastToAPInt() const { |
4987 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
4988 | uint64_t Data[] = { |
4989 | Floats[0].bitcastToAPInt().getRawData()[0], |
4990 | Floats[1].bitcastToAPInt().getRawData()[0], |
4991 | }; |
4992 | return APInt(128, 2, Data); |
4993 | } |
4994 | |
4995 | Expected<APFloat::opStatus> DoubleAPFloat::convertFromString(StringRef S, |
4996 | roundingMode RM) { |
4997 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
4998 | APFloat Tmp(semPPCDoubleDoubleLegacy); |
4999 | auto Ret = Tmp.convertFromString(S, RM); |
5000 | *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt()); |
5001 | return Ret; |
5002 | } |
5003 | |
5004 | APFloat::opStatus DoubleAPFloat::next(bool nextDown) { |
5005 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
5006 | APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt()); |
5007 | auto Ret = Tmp.next(nextDown); |
5008 | *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt()); |
5009 | return Ret; |
5010 | } |
5011 | |
5012 | APFloat::opStatus |
5013 | DoubleAPFloat::convertToInteger(MutableArrayRef<integerPart> Input, |
5014 | unsigned int Width, bool IsSigned, |
5015 | roundingMode RM, bool *IsExact) const { |
5016 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
5017 | return APFloat(semPPCDoubleDoubleLegacy, bitcastToAPInt()) |
5018 | .convertToInteger(Input, Width, IsSigned, RM, IsExact); |
5019 | } |
5020 | |
5021 | APFloat::opStatus DoubleAPFloat::convertFromAPInt(const APInt &Input, |
5022 | bool IsSigned, |
5023 | roundingMode RM) { |
5024 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
5025 | APFloat Tmp(semPPCDoubleDoubleLegacy); |
5026 | auto Ret = Tmp.convertFromAPInt(Input, IsSigned, RM); |
5027 | *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt()); |
5028 | return Ret; |
5029 | } |
5030 | |
5031 | APFloat::opStatus |
5032 | DoubleAPFloat::convertFromSignExtendedInteger(const integerPart *Input, |
5033 | unsigned int InputSize, |
5034 | bool IsSigned, roundingMode RM) { |
5035 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
5036 | APFloat Tmp(semPPCDoubleDoubleLegacy); |
5037 | auto Ret = Tmp.convertFromSignExtendedInteger(Input, InputSize, IsSigned, RM); |
5038 | *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt()); |
5039 | return Ret; |
5040 | } |
5041 | |
5042 | APFloat::opStatus |
5043 | DoubleAPFloat::convertFromZeroExtendedInteger(const integerPart *Input, |
5044 | unsigned int InputSize, |
5045 | bool IsSigned, roundingMode RM) { |
5046 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
5047 | APFloat Tmp(semPPCDoubleDoubleLegacy); |
5048 | auto Ret = Tmp.convertFromZeroExtendedInteger(Input, InputSize, IsSigned, RM); |
5049 | *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt()); |
5050 | return Ret; |
5051 | } |
5052 | |
5053 | unsigned int DoubleAPFloat::convertToHexString(char *DST, |
5054 | unsigned int HexDigits, |
5055 | bool UpperCase, |
5056 | roundingMode RM) const { |
5057 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
5058 | return APFloat(semPPCDoubleDoubleLegacy, bitcastToAPInt()) |
5059 | .convertToHexString(DST, HexDigits, UpperCase, RM); |
5060 | } |
5061 | |
5062 | bool DoubleAPFloat::isDenormal() const { |
5063 | return getCategory() == fcNormal && |
5064 | (Floats[0].isDenormal() || Floats[1].isDenormal() || |
5065 | // (double)(Hi + Lo) == Hi defines a normal number. |
5066 | Floats[0] != Floats[0] + Floats[1]); |
5067 | } |
5068 | |
5069 | bool DoubleAPFloat::isSmallest() const { |
5070 | if (getCategory() != fcNormal) |
5071 | return false; |
5072 | DoubleAPFloat Tmp(*this); |
5073 | Tmp.makeSmallest(Neg: this->isNegative()); |
5074 | return Tmp.compare(RHS: *this) == cmpEqual; |
5075 | } |
5076 | |
5077 | bool DoubleAPFloat::isSmallestNormalized() const { |
5078 | if (getCategory() != fcNormal) |
5079 | return false; |
5080 | |
5081 | DoubleAPFloat Tmp(*this); |
5082 | Tmp.makeSmallestNormalized(Neg: this->isNegative()); |
5083 | return Tmp.compare(RHS: *this) == cmpEqual; |
5084 | } |
5085 | |
5086 | bool DoubleAPFloat::isLargest() const { |
5087 | if (getCategory() != fcNormal) |
5088 | return false; |
5089 | DoubleAPFloat Tmp(*this); |
5090 | Tmp.makeLargest(Neg: this->isNegative()); |
5091 | return Tmp.compare(RHS: *this) == cmpEqual; |
5092 | } |
5093 | |
5094 | bool DoubleAPFloat::isInteger() const { |
5095 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
5096 | return Floats[0].isInteger() && Floats[1].isInteger(); |
5097 | } |
5098 | |
5099 | void DoubleAPFloat::toString(SmallVectorImpl<char> &Str, |
5100 | unsigned FormatPrecision, |
5101 | unsigned FormatMaxPadding, |
5102 | bool TruncateZero) const { |
5103 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
5104 | APFloat(semPPCDoubleDoubleLegacy, bitcastToAPInt()) |
5105 | .toString(Str, FormatPrecision, FormatMaxPadding, TruncateZero); |
5106 | } |
5107 | |
5108 | bool DoubleAPFloat::getExactInverse(APFloat *inv) const { |
5109 | assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
5110 | APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt()); |
5111 | if (!inv) |
5112 | return Tmp.getExactInverse(inv: nullptr); |
5113 | APFloat Inv(semPPCDoubleDoubleLegacy); |
5114 | auto Ret = Tmp.getExactInverse(inv: &Inv); |
5115 | *inv = APFloat(semPPCDoubleDouble, Inv.bitcastToAPInt()); |
5116 | return Ret; |
5117 | } |
5118 | |
5119 | int DoubleAPFloat::getExactLog2() const { |
5120 | // TODO: Implement me |
5121 | return INT_MIN; |
5122 | } |
5123 | |
5124 | int DoubleAPFloat::getExactLog2Abs() const { |
5125 | // TODO: Implement me |
5126 | return INT_MIN; |
5127 | } |
5128 | |
5129 | DoubleAPFloat scalbn(const DoubleAPFloat &Arg, int Exp, |
5130 | APFloat::roundingMode RM) { |
5131 | assert(Arg.Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
5132 | return DoubleAPFloat(semPPCDoubleDouble, scalbn(X: Arg.Floats[0], Exp, RM), |
5133 | scalbn(X: Arg.Floats[1], Exp, RM)); |
5134 | } |
5135 | |
5136 | DoubleAPFloat frexp(const DoubleAPFloat &Arg, int &Exp, |
5137 | APFloat::roundingMode RM) { |
5138 | assert(Arg.Semantics == &semPPCDoubleDouble && "Unexpected Semantics" ); |
5139 | APFloat First = frexp(X: Arg.Floats[0], Exp, RM); |
5140 | APFloat Second = Arg.Floats[1]; |
5141 | if (Arg.getCategory() == APFloat::fcNormal) |
5142 | Second = scalbn(X: Second, Exp: -Exp, RM); |
5143 | return DoubleAPFloat(semPPCDoubleDouble, std::move(First), std::move(Second)); |
5144 | } |
5145 | |
5146 | } // namespace detail |
5147 | |
5148 | APFloat::Storage::Storage(IEEEFloat F, const fltSemantics &Semantics) { |
5149 | if (usesLayout<IEEEFloat>(Semantics)) { |
5150 | new (&IEEE) IEEEFloat(std::move(F)); |
5151 | return; |
5152 | } |
5153 | if (usesLayout<DoubleAPFloat>(Semantics)) { |
5154 | const fltSemantics& S = F.getSemantics(); |
5155 | new (&Double) |
5156 | DoubleAPFloat(Semantics, APFloat(std::move(F), S), |
5157 | APFloat(semIEEEdouble)); |
5158 | return; |
5159 | } |
5160 | llvm_unreachable("Unexpected semantics" ); |
5161 | } |
5162 | |
5163 | Expected<APFloat::opStatus> APFloat::convertFromString(StringRef Str, |
5164 | roundingMode RM) { |
5165 | APFLOAT_DISPATCH_ON_SEMANTICS(convertFromString(Str, RM)); |
5166 | } |
5167 | |
5168 | hash_code hash_value(const APFloat &Arg) { |
5169 | if (APFloat::usesLayout<detail::IEEEFloat>(Semantics: Arg.getSemantics())) |
5170 | return hash_value(Arg: Arg.U.IEEE); |
5171 | if (APFloat::usesLayout<detail::DoubleAPFloat>(Semantics: Arg.getSemantics())) |
5172 | return hash_value(Arg: Arg.U.Double); |
5173 | llvm_unreachable("Unexpected semantics" ); |
5174 | } |
5175 | |
5176 | APFloat::APFloat(const fltSemantics &Semantics, StringRef S) |
5177 | : APFloat(Semantics) { |
5178 | auto StatusOrErr = convertFromString(Str: S, RM: rmNearestTiesToEven); |
5179 | assert(StatusOrErr && "Invalid floating point representation" ); |
5180 | consumeError(Err: StatusOrErr.takeError()); |
5181 | } |
5182 | |
5183 | FPClassTest APFloat::classify() const { |
5184 | if (isZero()) |
5185 | return isNegative() ? fcNegZero : fcPosZero; |
5186 | if (isNormal()) |
5187 | return isNegative() ? fcNegNormal : fcPosNormal; |
5188 | if (isDenormal()) |
5189 | return isNegative() ? fcNegSubnormal : fcPosSubnormal; |
5190 | if (isInfinity()) |
5191 | return isNegative() ? fcNegInf : fcPosInf; |
5192 | assert(isNaN() && "Other class of FP constant" ); |
5193 | return isSignaling() ? fcSNan : fcQNan; |
5194 | } |
5195 | |
5196 | APFloat::opStatus APFloat::convert(const fltSemantics &ToSemantics, |
5197 | roundingMode RM, bool *losesInfo) { |
5198 | if (&getSemantics() == &ToSemantics) { |
5199 | *losesInfo = false; |
5200 | return opOK; |
5201 | } |
5202 | if (usesLayout<IEEEFloat>(Semantics: getSemantics()) && |
5203 | usesLayout<IEEEFloat>(Semantics: ToSemantics)) |
5204 | return U.IEEE.convert(toSemantics: ToSemantics, rounding_mode: RM, losesInfo); |
5205 | if (usesLayout<IEEEFloat>(Semantics: getSemantics()) && |
5206 | usesLayout<DoubleAPFloat>(Semantics: ToSemantics)) { |
5207 | assert(&ToSemantics == &semPPCDoubleDouble); |
5208 | auto Ret = U.IEEE.convert(toSemantics: semPPCDoubleDoubleLegacy, rounding_mode: RM, losesInfo); |
5209 | *this = APFloat(ToSemantics, U.IEEE.bitcastToAPInt()); |
5210 | return Ret; |
5211 | } |
5212 | if (usesLayout<DoubleAPFloat>(Semantics: getSemantics()) && |
5213 | usesLayout<IEEEFloat>(Semantics: ToSemantics)) { |
5214 | auto Ret = getIEEE().convert(toSemantics: ToSemantics, rounding_mode: RM, losesInfo); |
5215 | *this = APFloat(std::move(getIEEE()), ToSemantics); |
5216 | return Ret; |
5217 | } |
5218 | llvm_unreachable("Unexpected semantics" ); |
5219 | } |
5220 | |
5221 | APFloat APFloat::getAllOnesValue(const fltSemantics &Semantics) { |
5222 | return APFloat(Semantics, APInt::getAllOnes(numBits: Semantics.sizeInBits)); |
5223 | } |
5224 | |
5225 | void APFloat::print(raw_ostream &OS) const { |
5226 | SmallVector<char, 16> Buffer; |
5227 | toString(Str&: Buffer); |
5228 | OS << Buffer << "\n" ; |
5229 | } |
5230 | |
5231 | #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP) |
5232 | LLVM_DUMP_METHOD void APFloat::dump() const { print(OS&: dbgs()); } |
5233 | #endif |
5234 | |
5235 | void APFloat::Profile(FoldingSetNodeID &NID) const { |
5236 | NID.Add(x: bitcastToAPInt()); |
5237 | } |
5238 | |
5239 | /* Same as convertToInteger(integerPart*, ...), except the result is returned in |
5240 | an APSInt, whose initial bit-width and signed-ness are used to determine the |
5241 | precision of the conversion. |
5242 | */ |
5243 | APFloat::opStatus APFloat::convertToInteger(APSInt &result, |
5244 | roundingMode rounding_mode, |
5245 | bool *isExact) const { |
5246 | unsigned bitWidth = result.getBitWidth(); |
5247 | SmallVector<uint64_t, 4> parts(result.getNumWords()); |
5248 | opStatus status = convertToInteger(Input: parts, Width: bitWidth, IsSigned: result.isSigned(), |
5249 | RM: rounding_mode, IsExact: isExact); |
5250 | // Keeps the original signed-ness. |
5251 | result = APInt(bitWidth, parts); |
5252 | return status; |
5253 | } |
5254 | |
5255 | double APFloat::convertToDouble() const { |
5256 | if (&getSemantics() == (const llvm::fltSemantics *)&semIEEEdouble) |
5257 | return getIEEE().convertToDouble(); |
5258 | assert(getSemantics().isRepresentableBy(semIEEEdouble) && |
5259 | "Float semantics is not representable by IEEEdouble" ); |
5260 | APFloat Temp = *this; |
5261 | bool LosesInfo; |
5262 | opStatus St = Temp.convert(ToSemantics: semIEEEdouble, RM: rmNearestTiesToEven, losesInfo: &LosesInfo); |
5263 | assert(!(St & opInexact) && !LosesInfo && "Unexpected imprecision" ); |
5264 | (void)St; |
5265 | return Temp.getIEEE().convertToDouble(); |
5266 | } |
5267 | |
5268 | float APFloat::convertToFloat() const { |
5269 | if (&getSemantics() == (const llvm::fltSemantics *)&semIEEEsingle) |
5270 | return getIEEE().convertToFloat(); |
5271 | assert(getSemantics().isRepresentableBy(semIEEEsingle) && |
5272 | "Float semantics is not representable by IEEEsingle" ); |
5273 | APFloat Temp = *this; |
5274 | bool LosesInfo; |
5275 | opStatus St = Temp.convert(ToSemantics: semIEEEsingle, RM: rmNearestTiesToEven, losesInfo: &LosesInfo); |
5276 | assert(!(St & opInexact) && !LosesInfo && "Unexpected imprecision" ); |
5277 | (void)St; |
5278 | return Temp.getIEEE().convertToFloat(); |
5279 | } |
5280 | |
5281 | } // namespace llvm |
5282 | |
5283 | #undef APFLOAT_DISPATCH_ON_SEMANTICS |
5284 | |