Bug Summary

File:src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Support/APFloat.cpp
Warning:line 2229, column 15
Assigned value is garbage or undefined

Annotated Source Code

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clang -cc1 -cc1 -triple amd64-unknown-openbsd7.0 -analyze -disable-free -disable-llvm-verifier -discard-value-names -main-file-name APFloat.cpp -analyzer-store=region -analyzer-opt-analyze-nested-blocks -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=cplusplus -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -setup-static-analyzer -mrelocation-model pic -pic-level 1 -fhalf-no-semantic-interposition -mframe-pointer=all -relaxed-aliasing -fno-rounding-math -mconstructor-aliases -munwind-tables -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -fcoverage-compilation-dir=/usr/src/gnu/usr.bin/clang/libLLVM/obj -resource-dir /usr/local/lib/clang/13.0.0 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/AMDGPU -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Analysis -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ASMParser -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/BinaryFormat -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Bitcode -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Bitcode -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Bitstream -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /include/llvm/CodeGen -I /include/llvm/CodeGen/PBQP -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/IR -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/IR -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/Coroutines -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ProfileData/Coverage -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo/CodeView -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo/DWARF -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo/MSF -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo/PDB -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Demangle -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ExecutionEngine -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ExecutionEngine/JITLink -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ExecutionEngine/Orc -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Frontend -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Frontend/OpenACC -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Frontend -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Frontend/OpenMP -I /include/llvm/CodeGen/GlobalISel -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/IRReader -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/InstCombine -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/Transforms/InstCombine -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/LTO -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Linker -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/MC -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/MC/MCParser -I /include/llvm/CodeGen/MIRParser -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Object -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Option -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Passes -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ProfileData -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/Scalar -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ADT -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Support -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/DebugInfo/Symbolize -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Target -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/Utils -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/Vectorize -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include/llvm/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Target/X86 -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/Transforms/IPO -I /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include -I /usr/src/gnu/usr.bin/clang/libLLVM/../include -I /usr/src/gnu/usr.bin/clang/libLLVM/obj -I /usr/src/gnu/usr.bin/clang/libLLVM/obj/../include -D NDEBUG -D __STDC_LIMIT_MACROS -D __STDC_CONSTANT_MACROS -D __STDC_FORMAT_MACROS -D LLVM_PREFIX="/usr" -D PIC -internal-isystem /usr/include/c++/v1 -internal-isystem /usr/local/lib/clang/13.0.0/include -internal-externc-isystem /usr/include -O2 -Wno-unused-parameter -Wwrite-strings -Wno-missing-field-initializers -Wno-long-long -Wno-comment -std=c++14 -fdeprecated-macro -fdebug-compilation-dir=/usr/src/gnu/usr.bin/clang/libLLVM/obj -ferror-limit 19 -fvisibility-inlines-hidden -fwrapv -D_RET_PROTECTOR -ret-protector -fno-rtti -fgnuc-version=4.2.1 -vectorize-loops -vectorize-slp -fno-builtin-malloc -fno-builtin-calloc -fno-builtin-realloc -fno-builtin-valloc -fno-builtin-free -fno-builtin-strdup -fno-builtin-strndup -analyzer-output=html -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /home/ben/Projects/vmm/scan-build/2022-01-12-194120-40624-1 -x c++ /usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Support/APFloat.cpp

/usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/lib/Support/APFloat.cpp

→
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/FoldingSet.h"
18#include "llvm/ADT/Hashing.h"
19#include "llvm/ADT/StringExtras.h"
20#include "llvm/ADT/StringRef.h"
21#include "llvm/Config/llvm-config.h"
22#include "llvm/Support/Debug.h"
23#include "llvm/Support/Error.h"
24#include "llvm/Support/MathExtras.h"
25#include "llvm/Support/raw_ostream.h"
26#include <cstring>
27#include <limits.h>
28
29#define APFLOAT_DISPATCH_ON_SEMANTICS(METHOD_CALL) \
30 do { \
31 if (usesLayout<IEEEFloat>(getSemantics())) \
32 return U.IEEE.METHOD_CALL; \
33 if (usesLayout<DoubleAPFloat>(getSemantics())) \
34 return U.Double.METHOD_CALL; \
35 llvm_unreachable("Unexpected semantics")__builtin_unreachable(); \
36 } while (false)
37
38using namespace llvm;
39
40/// A macro used to combine two fcCategory enums into one key which can be used
41/// in a switch statement to classify how the interaction of two APFloat's
42/// categories affects an operation.
43///
44/// TODO: If clang source code is ever allowed to use constexpr in its own
45/// codebase, change this into a static inline function.
46#define PackCategoriesIntoKey(_lhs, _rhs)((_lhs) * 4 + (_rhs)) ((_lhs) * 4 + (_rhs))
47
48/* Assumed in hexadecimal significand parsing, and conversion to
49 hexadecimal strings. */
50static_assert(APFloatBase::integerPartWidth % 4 == 0, "Part width must be divisible by 4!");
51
52namespace llvm {
53 /* Represents floating point arithmetic semantics. */
54 struct fltSemantics {
55 /* The largest E such that 2^E is representable; this matches the
56 definition of IEEE 754. */
57 APFloatBase::ExponentType maxExponent;
58
59 /* The smallest E such that 2^E is a normalized number; this
60 matches the definition of IEEE 754. */
61 APFloatBase::ExponentType minExponent;
62
63 /* Number of bits in the significand. This includes the integer
64 bit. */
65 unsigned int precision;
66
67 /* Number of bits actually used in the semantics. */
68 unsigned int sizeInBits;
69
70 // Returns true if any number described by this semantics can be precisely
71 // represented by the specified semantics.
72 bool isRepresentableBy(const fltSemantics &S) const {
73 return maxExponent <= S.maxExponent && minExponent >= S.minExponent &&
74 precision <= S.precision;
75 }
76 };
77
78 static const fltSemantics semIEEEhalf = {15, -14, 11, 16};
79 static const fltSemantics semBFloat = {127, -126, 8, 16};
80 static const fltSemantics semIEEEsingle = {127, -126, 24, 32};
81 static const fltSemantics semIEEEdouble = {1023, -1022, 53, 64};
82 static const fltSemantics semIEEEquad = {16383, -16382, 113, 128};
83 static const fltSemantics semX87DoubleExtended = {16383, -16382, 64, 80};
84 static const fltSemantics semBogus = {0, 0, 0, 0};
85
86 /* The IBM double-double semantics. Such a number consists of a pair of IEEE
87 64-bit doubles (Hi, Lo), where |Hi| > |Lo|, and if normal,
88 (double)(Hi + Lo) == Hi. The numeric value it's modeling is Hi + Lo.
89 Therefore it has two 53-bit mantissa parts that aren't necessarily adjacent
90 to each other, and two 11-bit exponents.
91
92 Note: we need to make the value different from semBogus as otherwise
93 an unsafe optimization may collapse both values to a single address,
94 and we heavily rely on them having distinct addresses. */
95 static const fltSemantics semPPCDoubleDouble = {-1, 0, 0, 0};
96
97 /* These are legacy semantics for the fallback, inaccrurate implementation of
98 IBM double-double, if the accurate semPPCDoubleDouble doesn't handle the
99 operation. It's equivalent to having an IEEE number with consecutive 106
100 bits of mantissa and 11 bits of exponent.
101
102 It's not equivalent to IBM double-double. For example, a legit IBM
103 double-double, 1 + epsilon:
104
105 1 + epsilon = 1 + (1 >> 1076)
106
107 is not representable by a consecutive 106 bits of mantissa.
108
109 Currently, these semantics are used in the following way:
110
111 semPPCDoubleDouble -> (IEEEdouble, IEEEdouble) ->
112 (64-bit APInt, 64-bit APInt) -> (128-bit APInt) ->
113 semPPCDoubleDoubleLegacy -> IEEE operations
114
115 We use bitcastToAPInt() to get the bit representation (in APInt) of the
116 underlying IEEEdouble, then use the APInt constructor to construct the
117 legacy IEEE float.
118
119 TODO: Implement all operations in semPPCDoubleDouble, and delete these
120 semantics. */
121 static const fltSemantics semPPCDoubleDoubleLegacy = {1023, -1022 + 53,
122 53 + 53, 128};
123
124 const llvm::fltSemantics &APFloatBase::EnumToSemantics(Semantics S) {
125 switch (S) {
126 case S_IEEEhalf:
127 return IEEEhalf();
128 case S_BFloat:
129 return BFloat();
130 case S_IEEEsingle:
131 return IEEEsingle();
132 case S_IEEEdouble:
133 return IEEEdouble();
134 case S_x87DoubleExtended:
135 return x87DoubleExtended();
136 case S_IEEEquad:
137 return IEEEquad();
138 case S_PPCDoubleDouble:
139 return PPCDoubleDouble();
140 }
141 llvm_unreachable("Unrecognised floating semantics")__builtin_unreachable();
142 }
143
144 APFloatBase::Semantics
145 APFloatBase::SemanticsToEnum(const llvm::fltSemantics &Sem) {
146 if (&Sem == &llvm::APFloat::IEEEhalf())
147 return S_IEEEhalf;
148 else if (&Sem == &llvm::APFloat::BFloat())
149 return S_BFloat;
150 else if (&Sem == &llvm::APFloat::IEEEsingle())
151 return S_IEEEsingle;
152 else if (&Sem == &llvm::APFloat::IEEEdouble())
153 return S_IEEEdouble;
154 else if (&Sem == &llvm::APFloat::x87DoubleExtended())
155 return S_x87DoubleExtended;
156 else if (&Sem == &llvm::APFloat::IEEEquad())
157 return S_IEEEquad;
158 else if (&Sem == &llvm::APFloat::PPCDoubleDouble())
159 return S_PPCDoubleDouble;
160 else
161 llvm_unreachable("Unknown floating semantics")__builtin_unreachable();
162 }
163
164 const fltSemantics &APFloatBase::IEEEhalf() {
165 return semIEEEhalf;
166 }
167 const fltSemantics &APFloatBase::BFloat() {
168 return semBFloat;
169 }
170 const fltSemantics &APFloatBase::IEEEsingle() {
171 return semIEEEsingle;
172 }
173 const fltSemantics &APFloatBase::IEEEdouble() {
174 return semIEEEdouble;
175 }
176 const fltSemantics &APFloatBase::IEEEquad() {
177 return semIEEEquad;
178 }
179 const fltSemantics &APFloatBase::x87DoubleExtended() {
180 return semX87DoubleExtended;
181 }
182 const fltSemantics &APFloatBase::Bogus() {
183 return semBogus;
184 }
185 const fltSemantics &APFloatBase::PPCDoubleDouble() {
186 return semPPCDoubleDouble;
187 }
188
189 constexpr RoundingMode APFloatBase::rmNearestTiesToEven;
190 constexpr RoundingMode APFloatBase::rmTowardPositive;
191 constexpr RoundingMode APFloatBase::rmTowardNegative;
192 constexpr RoundingMode APFloatBase::rmTowardZero;
193 constexpr RoundingMode APFloatBase::rmNearestTiesToAway;
194
195 /* A tight upper bound on number of parts required to hold the value
196 pow(5, power) is
197
198 power * 815 / (351 * integerPartWidth) + 1
199
200 However, whilst the result may require only this many parts,
201 because we are multiplying two values to get it, the
202 multiplication may require an extra part with the excess part
203 being zero (consider the trivial case of 1 * 1, tcFullMultiply
204 requires two parts to hold the single-part result). So we add an
205 extra one to guarantee enough space whilst multiplying. */
206 const unsigned int maxExponent = 16383;
207 const unsigned int maxPrecision = 113;
208 const unsigned int maxPowerOfFiveExponent = maxExponent + maxPrecision - 1;
209 const unsigned int maxPowerOfFiveParts = 2 + ((maxPowerOfFiveExponent * 815) / (351 * APFloatBase::integerPartWidth));
210
211 unsigned int APFloatBase::semanticsPrecision(const fltSemantics &semantics) {
212 return semantics.precision;
213 }
214 APFloatBase::ExponentType
215 APFloatBase::semanticsMaxExponent(const fltSemantics &semantics) {
216 return semantics.maxExponent;
217 }
218 APFloatBase::ExponentType
219 APFloatBase::semanticsMinExponent(const fltSemantics &semantics) {
220 return semantics.minExponent;
221 }
222 unsigned int APFloatBase::semanticsSizeInBits(const fltSemantics &semantics) {
223 return semantics.sizeInBits;
224 }
225
226 unsigned APFloatBase::getSizeInBits(const fltSemantics &Sem) {
227 return Sem.sizeInBits;
228}
229
230/* A bunch of private, handy routines. */
231
232static inline Error createError(const Twine &Err) {
233 return make_error<StringError>(Err, inconvertibleErrorCode());
234}
235
236static inline unsigned int
237partCountForBits(unsigned int bits)
238{
239 return ((bits) + APFloatBase::integerPartWidth - 1) / APFloatBase::integerPartWidth;
240}
241
242/* Returns 0U-9U. Return values >= 10U are not digits. */
243static inline unsigned int
244decDigitValue(unsigned int c)
245{
246 return c - '0';
247}
248
249/* Return the value of a decimal exponent of the form
250 [+-]ddddddd.
251
252 If the exponent overflows, returns a large exponent with the
253 appropriate sign. */
254static Expected<int> readExponent(StringRef::iterator begin,
255 StringRef::iterator end) {
256 bool isNegative;
257 unsigned int absExponent;
258 const unsigned int overlargeExponent = 24000; /* FIXME. */
259 StringRef::iterator p = begin;
260
261 // Treat no exponent as 0 to match binutils
262 if (p == end || ((*p == '-' || *p == '+') && (p + 1) == end)) {
263 return 0;
264 }
265
266 isNegative = (*p == '-');
267 if (*p == '-' || *p == '+') {
268 p++;
269 if (p == end)
270 return createError("Exponent has no digits");
271 }
272
273 absExponent = decDigitValue(*p++);
274 if (absExponent >= 10U)
275 return createError("Invalid character in exponent");
276
277 for (; p != end; ++p) {
278 unsigned int value;
279
280 value = decDigitValue(*p);
281 if (value >= 10U)
282 return createError("Invalid character in exponent");
283
284 absExponent = absExponent * 10U + value;
285 if (absExponent >= overlargeExponent) {
286 absExponent = overlargeExponent;
287 break;
288 }
289 }
290
291 if (isNegative)
292 return -(int) absExponent;
293 else
294 return (int) absExponent;
295}
296
297/* This is ugly and needs cleaning up, but I don't immediately see
298 how whilst remaining safe. */
299static Expected<int> totalExponent(StringRef::iterator p,
300 StringRef::iterator end,
301 int exponentAdjustment) {
302 int unsignedExponent;
303 bool negative, overflow;
304 int exponent = 0;
305
306 if (p == end)
307 return createError("Exponent has no digits");
308
309 negative = *p == '-';
310 if (*p == '-' || *p == '+') {
311 p++;
312 if (p == end)
313 return createError("Exponent has no digits");
314 }
315
316 unsignedExponent = 0;
317 overflow = false;
318 for (; p != end; ++p) {
319 unsigned int value;
320
321 value = decDigitValue(*p);
322 if (value >= 10U)
323 return createError("Invalid character in exponent");
324
325 unsignedExponent = unsignedExponent * 10 + value;
326 if (unsignedExponent > 32767) {
327 overflow = true;
328 break;
329 }
330 }
331
332 if (exponentAdjustment > 32767 || exponentAdjustment < -32768)
333 overflow = true;
334
335 if (!overflow) {
336 exponent = unsignedExponent;
337 if (negative)
338 exponent = -exponent;
339 exponent += exponentAdjustment;
340 if (exponent > 32767 || exponent < -32768)
341 overflow = true;
342 }
343
344 if (overflow)
345 exponent = negative ? -32768: 32767;
346
347 return exponent;
348}
349
350static Expected<StringRef::iterator>
351skipLeadingZeroesAndAnyDot(StringRef::iterator begin, StringRef::iterator end,
352 StringRef::iterator *dot) {
353 StringRef::iterator p = begin;
354 *dot = end;
355 while (p != end && *p == '0')
356 p++;
357
358 if (p != end && *p == '.') {
359 *dot = p++;
360
361 if (end - begin == 1)
362 return createError("Significand has no digits");
363
364 while (p != end && *p == '0')
365 p++;
366 }
367
368 return p;
369}
370
371/* Given a normal decimal floating point number of the form
372
373 dddd.dddd[eE][+-]ddd
374
375 where the decimal point and exponent are optional, fill out the
376 structure D. Exponent is appropriate if the significand is
377 treated as an integer, and normalizedExponent if the significand
378 is taken to have the decimal point after a single leading
379 non-zero digit.
380
381 If the value is zero, V->firstSigDigit points to a non-digit, and
382 the return exponent is zero.
383*/
384struct decimalInfo {
385 const char *firstSigDigit;
386 const char *lastSigDigit;
387 int exponent;
388 int normalizedExponent;
389};
390
391static Error interpretDecimal(StringRef::iterator begin,
392 StringRef::iterator end, decimalInfo *D) {
393 StringRef::iterator dot = end;
394
395 auto PtrOrErr = skipLeadingZeroesAndAnyDot(begin, end, &dot);
396 if (!PtrOrErr)
397 return PtrOrErr.takeError();
398 StringRef::iterator p = *PtrOrErr;
399
400 D->firstSigDigit = p;
401 D->exponent = 0;
402 D->normalizedExponent = 0;
403
404 for (; p != end; ++p) {
405 if (*p == '.') {
406 if (dot != end)
407 return createError("String contains multiple dots");
408 dot = p++;
409 if (p == end)
410 break;
411 }
412 if (decDigitValue(*p) >= 10U)
413 break;
414 }
415
416 if (p != end) {
417 if (*p != 'e' && *p != 'E')
418 return createError("Invalid character in significand");
419 if (p == begin)
420 return createError("Significand has no digits");
421 if (dot != end && p - begin == 1)
422 return createError("Significand has no digits");
423
424 /* p points to the first non-digit in the string */
425 auto ExpOrErr = readExponent(p + 1, end);
426 if (!ExpOrErr)
427 return ExpOrErr.takeError();
428 D->exponent = *ExpOrErr;
429
430 /* Implied decimal point? */
431 if (dot == end)
432 dot = p;
433 }
434
435 /* If number is all zeroes accept any exponent. */
436 if (p != D->firstSigDigit) {
437 /* Drop insignificant trailing zeroes. */
438 if (p != begin) {
439 do
440 do
441 p--;
442 while (p != begin && *p == '0');
443 while (p != begin && *p == '.');
444 }
445
446 /* Adjust the exponents for any decimal point. */
447 D->exponent += static_cast<APFloat::ExponentType>((dot - p) - (dot > p));
448 D->normalizedExponent = (D->exponent +
449 static_cast<APFloat::ExponentType>((p - D->firstSigDigit)
450 - (dot > D->firstSigDigit && dot < p)));
451 }
452
453 D->lastSigDigit = p;
454 return Error::success();
455}
456
457/* Return the trailing fraction of a hexadecimal number.
458 DIGITVALUE is the first hex digit of the fraction, P points to
459 the next digit. */
460static Expected<lostFraction>
461trailingHexadecimalFraction(StringRef::iterator p, StringRef::iterator end,
462 unsigned int digitValue) {
463 unsigned int hexDigit;
464
465 /* If the first trailing digit isn't 0 or 8 we can work out the
466 fraction immediately. */
467 if (digitValue > 8)
468 return lfMoreThanHalf;
469 else if (digitValue < 8 && digitValue > 0)
470 return lfLessThanHalf;
471
472 // Otherwise we need to find the first non-zero digit.
473 while (p != end && (*p == '0' || *p == '.'))
474 p++;
475
476 if (p == end)
477 return createError("Invalid trailing hexadecimal fraction!");
478
479 hexDigit = hexDigitValue(*p);
480
481 /* If we ran off the end it is exactly zero or one-half, otherwise
482 a little more. */
483 if (hexDigit == -1U)
484 return digitValue == 0 ? lfExactlyZero: lfExactlyHalf;
485 else
486 return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf;
487}
488
489/* Return the fraction lost were a bignum truncated losing the least
490 significant BITS bits. */
491static lostFraction
492lostFractionThroughTruncation(const APFloatBase::integerPart *parts,
493 unsigned int partCount,
494 unsigned int bits)
495{
496 unsigned int lsb;
497
498 lsb = APInt::tcLSB(parts, partCount);
499
500 /* Note this is guaranteed true if bits == 0, or LSB == -1U. */
501 if (bits <= lsb)
502 return lfExactlyZero;
503 if (bits == lsb + 1)
504 return lfExactlyHalf;
505 if (bits <= partCount * APFloatBase::integerPartWidth &&
506 APInt::tcExtractBit(parts, bits - 1))
507 return lfMoreThanHalf;
508
509 return lfLessThanHalf;
510}
511
512/* Shift DST right BITS bits noting lost fraction. */
513static lostFraction
514shiftRight(APFloatBase::integerPart *dst, unsigned int parts, unsigned int bits)
515{
516 lostFraction lost_fraction;
517
518 lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
519
520 APInt::tcShiftRight(dst, parts, bits);
521
522 return lost_fraction;
523}
524
525/* Combine the effect of two lost fractions. */
526static lostFraction
527combineLostFractions(lostFraction moreSignificant,
528 lostFraction lessSignificant)
529{
530 if (lessSignificant != lfExactlyZero) {
531 if (moreSignificant == lfExactlyZero)
532 moreSignificant = lfLessThanHalf;
533 else if (moreSignificant == lfExactlyHalf)
534 moreSignificant = lfMoreThanHalf;
535 }
536
537 return moreSignificant;
538}
539
540/* The error from the true value, in half-ulps, on multiplying two
541 floating point numbers, which differ from the value they
542 approximate by at most HUE1 and HUE2 half-ulps, is strictly less
543 than the returned value.
544
545 See "How to Read Floating Point Numbers Accurately" by William D
546 Clinger. */
547static unsigned int
548HUerrBound(bool inexactMultiply, unsigned int HUerr1, unsigned int HUerr2)
549{
550 assert(HUerr1 < 2 || HUerr2 < 2 || (HUerr1 + HUerr2 < 8))((void)0);
551
552 if (HUerr1 + HUerr2 == 0)
553 return inexactMultiply * 2; /* <= inexactMultiply half-ulps. */
554 else
555 return inexactMultiply + 2 * (HUerr1 + HUerr2);
556}
557
558/* The number of ulps from the boundary (zero, or half if ISNEAREST)
559 when the least significant BITS are truncated. BITS cannot be
560 zero. */
561static APFloatBase::integerPart
562ulpsFromBoundary(const APFloatBase::integerPart *parts, unsigned int bits,
563 bool isNearest) {
564 unsigned int count, partBits;
565 APFloatBase::integerPart part, boundary;
566
567 assert(bits != 0)((void)0);
568
569 bits--;
570 count = bits / APFloatBase::integerPartWidth;
571 partBits = bits % APFloatBase::integerPartWidth + 1;
572
573 part = parts[count] & (~(APFloatBase::integerPart) 0 >> (APFloatBase::integerPartWidth - partBits));
574
575 if (isNearest)
576 boundary = (APFloatBase::integerPart) 1 << (partBits - 1);
577 else
578 boundary = 0;
579
580 if (count == 0) {
581 if (part - boundary <= boundary - part)
582 return part - boundary;
583 else
584 return boundary - part;
585 }
586
587 if (part == boundary) {
588 while (--count)
589 if (parts[count])
590 return ~(APFloatBase::integerPart) 0; /* A lot. */
591
592 return parts[0];
593 } else if (part == boundary - 1) {
594 while (--count)
595 if (~parts[count])
596 return ~(APFloatBase::integerPart) 0; /* A lot. */
597
598 return -parts[0];
599 }
600
601 return ~(APFloatBase::integerPart) 0; /* A lot. */
602}
603
604/* Place pow(5, power) in DST, and return the number of parts used.
605 DST must be at least one part larger than size of the answer. */
606static unsigned int
607powerOf5(APFloatBase::integerPart *dst, unsigned int power) {
608 static const APFloatBase::integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125, 15625, 78125 };
609 APFloatBase::integerPart pow5s[maxPowerOfFiveParts * 2 + 5];
610 pow5s[0] = 78125 * 5;
611
612 unsigned int partsCount[16] = { 1 };
613 APFloatBase::integerPart scratch[maxPowerOfFiveParts], *p1, *p2, *pow5;
614 unsigned int result;
615 assert(power <= maxExponent)((void)0);
616
617 p1 = dst;
618 p2 = scratch;
619
620 *p1 = firstEightPowers[power & 7];
621 power >>= 3;
622
623 result = 1;
624 pow5 = pow5s;
625
626 for (unsigned int n = 0; power; power >>= 1, n++) {
627 unsigned int pc;
628
629 pc = partsCount[n];
630
631 /* Calculate pow(5,pow(2,n+3)) if we haven't yet. */
632 if (pc == 0) {
633 pc = partsCount[n - 1];
634 APInt::tcFullMultiply(pow5, pow5 - pc, pow5 - pc, pc, pc);
635 pc *= 2;
636 if (pow5[pc - 1] == 0)
637 pc--;
638 partsCount[n] = pc;
639 }
640
641 if (power & 1) {
642 APFloatBase::integerPart *tmp;
643
644 APInt::tcFullMultiply(p2, p1, pow5, result, pc);
645 result += pc;
646 if (p2[result - 1] == 0)
647 result--;
648
649 /* Now result is in p1 with partsCount parts and p2 is scratch
650 space. */
651 tmp = p1;
652 p1 = p2;
653 p2 = tmp;
654 }
655
656 pow5 += pc;
657 }
658
659 if (p1 != dst)
660 APInt::tcAssign(dst, p1, result);
661
662 return result;
663}
664
665/* Zero at the end to avoid modular arithmetic when adding one; used
666 when rounding up during hexadecimal output. */
667static const char hexDigitsLower[] = "0123456789abcdef0";
668static const char hexDigitsUpper[] = "0123456789ABCDEF0";
669static const char infinityL[] = "infinity";
670static const char infinityU[] = "INFINITY";
671static const char NaNL[] = "nan";
672static const char NaNU[] = "NAN";
673
674/* Write out an integerPart in hexadecimal, starting with the most
675 significant nibble. Write out exactly COUNT hexdigits, return
676 COUNT. */
677static unsigned int
678partAsHex (char *dst, APFloatBase::integerPart part, unsigned int count,
679 const char *hexDigitChars)
680{
681 unsigned int result = count;
682
683 assert(count != 0 && count <= APFloatBase::integerPartWidth / 4)((void)0);
684
685 part >>= (APFloatBase::integerPartWidth - 4 * count);
686 while (count--) {
687 dst[count] = hexDigitChars[part & 0xf];
688 part >>= 4;
689 }
690
691 return result;
692}
693
694/* Write out an unsigned decimal integer. */
695static char *
696writeUnsignedDecimal (char *dst, unsigned int n)
697{
698 char buff[40], *p;
699
700 p = buff;
701 do
702 *p++ = '0' + n % 10;
703 while (n /= 10);
704
705 do
706 *dst++ = *--p;
707 while (p != buff);
708
709 return dst;
710}
711
712/* Write out a signed decimal integer. */
713static char *
714writeSignedDecimal (char *dst, int value)
715{
716 if (value < 0) {
717 *dst++ = '-';
718 dst = writeUnsignedDecimal(dst, -(unsigned) value);
719 } else
720 dst = writeUnsignedDecimal(dst, value);
721
722 return dst;
723}
724
725namespace detail {
726/* Constructors. */
727void IEEEFloat::initialize(const fltSemantics *ourSemantics) {
728 unsigned int count;
729
730 semantics = ourSemantics;
731 count = partCount();
732 if (count > 1)
733 significand.parts = new integerPart[count];
734}
735
736void IEEEFloat::freeSignificand() {
737 if (needsCleanup())
738 delete [] significand.parts;
739}
740
741void IEEEFloat::assign(const IEEEFloat &rhs) {
742 assert(semantics == rhs.semantics)((void)0);
743
744 sign = rhs.sign;
745 category = rhs.category;
746 exponent = rhs.exponent;
747 if (isFiniteNonZero() || category == fcNaN)
748 copySignificand(rhs);
749}
750
751void IEEEFloat::copySignificand(const IEEEFloat &rhs) {
752 assert(isFiniteNonZero() || category == fcNaN)((void)0);
753 assert(rhs.partCount() >= partCount())((void)0);
754
755 APInt::tcAssign(significandParts(), rhs.significandParts(),
756 partCount());
757}
758
759/* Make this number a NaN, with an arbitrary but deterministic value
760 for the significand. If double or longer, this is a signalling NaN,
761 which may not be ideal. If float, this is QNaN(0). */
762void IEEEFloat::makeNaN(bool SNaN, bool Negative, const APInt *fill) {
763 category = fcNaN;
764 sign = Negative;
765 exponent = exponentNaN();
766
767 integerPart *significand = significandParts();
768 unsigned numParts = partCount();
769
770 // Set the significand bits to the fill.
771 if (!fill || fill->getNumWords() < numParts)
772 APInt::tcSet(significand, 0, numParts);
773 if (fill) {
774 APInt::tcAssign(significand, fill->getRawData(),
775 std::min(fill->getNumWords(), numParts));
776
777 // Zero out the excess bits of the significand.
778 unsigned bitsToPreserve = semantics->precision - 1;
779 unsigned part = bitsToPreserve / 64;
780 bitsToPreserve %= 64;
781 significand[part] &= ((1ULL << bitsToPreserve) - 1);
782 for (part++; part != numParts; ++part)
783 significand[part] = 0;
784 }
785
786 unsigned QNaNBit = semantics->precision - 2;
787
788 if (SNaN) {
789 // We always have to clear the QNaN bit to make it an SNaN.
790 APInt::tcClearBit(significand, QNaNBit);
791
792 // If there are no bits set in the payload, we have to set
793 // *something* to make it a NaN instead of an infinity;
794 // conventionally, this is the next bit down from the QNaN bit.
795 if (APInt::tcIsZero(significand, numParts))
796 APInt::tcSetBit(significand, QNaNBit - 1);
797 } else {
798 // We always have to set the QNaN bit to make it a QNaN.
799 APInt::tcSetBit(significand, QNaNBit);
800 }
801
802 // For x87 extended precision, we want to make a NaN, not a
803 // pseudo-NaN. Maybe we should expose the ability to make
804 // pseudo-NaNs?
805 if (semantics == &semX87DoubleExtended)
806 APInt::tcSetBit(significand, QNaNBit + 1);
807}
808
809IEEEFloat &IEEEFloat::operator=(const IEEEFloat &rhs) {
810 if (this != &rhs) {
811 if (semantics != rhs.semantics) {
812 freeSignificand();
813 initialize(rhs.semantics);
814 }
815 assign(rhs);
816 }
817
818 return *this;
819}
820
821IEEEFloat &IEEEFloat::operator=(IEEEFloat &&rhs) {
822 freeSignificand();
823
824 semantics = rhs.semantics;
825 significand = rhs.significand;
826 exponent = rhs.exponent;
827 category = rhs.category;
828 sign = rhs.sign;
829
830 rhs.semantics = &semBogus;
831 return *this;
832}
833
834bool IEEEFloat::isDenormal() const {
835 return isFiniteNonZero() && (exponent == semantics->minExponent) &&
836 (APInt::tcExtractBit(significandParts(),
837 semantics->precision - 1) == 0);
838}
839
840bool IEEEFloat::isSmallest() const {
841 // The smallest number by magnitude in our format will be the smallest
842 // denormal, i.e. the floating point number with exponent being minimum
843 // exponent and significand bitwise equal to 1 (i.e. with MSB equal to 0).
844 return isFiniteNonZero() && exponent == semantics->minExponent &&
845 significandMSB() == 0;
846}
847
848bool IEEEFloat::isSignificandAllOnes() const {
849 // Test if the significand excluding the integral bit is all ones. This allows
850 // us to test for binade boundaries.
851 const integerPart *Parts = significandParts();
852 const unsigned PartCount = partCountForBits(semantics->precision);
853 for (unsigned i = 0; i < PartCount - 1; i++)
854 if (~Parts[i])
855 return false;
856
857 // Set the unused high bits to all ones when we compare.
858 const unsigned NumHighBits =
859 PartCount*integerPartWidth - semantics->precision + 1;
860 assert(NumHighBits <= integerPartWidth && NumHighBits > 0 &&((void)0)
861 "Can not have more high bits to fill than integerPartWidth")((void)0);
862 const integerPart HighBitFill =
863 ~integerPart(0) << (integerPartWidth - NumHighBits);
864 if (~(Parts[PartCount - 1] | HighBitFill))
865 return false;
866
867 return true;
868}
869
870bool IEEEFloat::isSignificandAllZeros() const {
871 // Test if the significand excluding the integral bit is all zeros. This
872 // allows us to test for binade boundaries.
873 const integerPart *Parts = significandParts();
874 const unsigned PartCount = partCountForBits(semantics->precision);
875
876 for (unsigned i = 0; i < PartCount - 1; i++)
877 if (Parts[i])
878 return false;
879
880 // Compute how many bits are used in the final word.
881 const unsigned NumHighBits =
882 PartCount*integerPartWidth - semantics->precision + 1;
883 assert(NumHighBits < integerPartWidth && "Can not have more high bits to "((void)0)
884 "clear than integerPartWidth")((void)0);
885 const integerPart HighBitMask = ~integerPart(0) >> NumHighBits;
886
887 if (Parts[PartCount - 1] & HighBitMask)
888 return false;
889
890 return true;
891}
892
893bool IEEEFloat::isLargest() const {
894 // The largest number by magnitude in our format will be the floating point
895 // number with maximum exponent and with significand that is all ones.
896 return isFiniteNonZero() && exponent == semantics->maxExponent
897 && isSignificandAllOnes();
898}
899
900bool IEEEFloat::isInteger() const {
901 // This could be made more efficient; I'm going for obviously correct.
902 if (!isFinite()) return false;
903 IEEEFloat truncated = *this;
904 truncated.roundToIntegral(rmTowardZero);
905 return compare(truncated) == cmpEqual;
906}
907
908bool IEEEFloat::bitwiseIsEqual(const IEEEFloat &rhs) const {
909 if (this == &rhs)
910 return true;
911 if (semantics != rhs.semantics ||
912 category != rhs.category ||
913 sign != rhs.sign)
914 return false;
915 if (category==fcZero || category==fcInfinity)
916 return true;
917
918 if (isFiniteNonZero() && exponent != rhs.exponent)
919 return false;
920
921 return std::equal(significandParts(), significandParts() + partCount(),
922 rhs.significandParts());
923}
924
925IEEEFloat::IEEEFloat(const fltSemantics &ourSemantics, integerPart value) {
926 initialize(&ourSemantics);
927 sign = 0;
928 category = fcNormal;
929 zeroSignificand();
930 exponent = ourSemantics.precision - 1;
931 significandParts()[0] = value;
932 normalize(rmNearestTiesToEven, lfExactlyZero);
933}
934
935IEEEFloat::IEEEFloat(const fltSemantics &ourSemantics) {
936 initialize(&ourSemantics);
937 makeZero(false);
938}
939
940// Delegate to the previous constructor, because later copy constructor may
941// actually inspects category, which can't be garbage.
942IEEEFloat::IEEEFloat(const fltSemantics &ourSemantics, uninitializedTag tag)
943 : IEEEFloat(ourSemantics) {}
944
945IEEEFloat::IEEEFloat(const IEEEFloat &rhs) {
946 initialize(rhs.semantics);
947 assign(rhs);
948}
949
950IEEEFloat::IEEEFloat(IEEEFloat &&rhs) : semantics(&semBogus) {
951 *this = std::move(rhs);
952}
953
954IEEEFloat::~IEEEFloat() { freeSignificand(); }
955
956unsigned int IEEEFloat::partCount() const {
957 return partCountForBits(semantics->precision + 1);
958}
959
960const IEEEFloat::integerPart *IEEEFloat::significandParts() const {
961 return const_cast<IEEEFloat *>(this)->significandParts();
962}
963
964IEEEFloat::integerPart *IEEEFloat::significandParts() {
965 if (partCount() > 1)
966 return significand.parts;
967 else
968 return &significand.part;
969}
970
971void IEEEFloat::zeroSignificand() {
972 APInt::tcSet(significandParts(), 0, partCount());
973}
974
975/* Increment an fcNormal floating point number's significand. */
976void IEEEFloat::incrementSignificand() {
977 integerPart carry;
978
979 carry = APInt::tcIncrement(significandParts(), partCount());
980
981 /* Our callers should never cause us to overflow. */
982 assert(carry == 0)((void)0);
983 (void)carry;
984}
985
986/* Add the significand of the RHS. Returns the carry flag. */
987IEEEFloat::integerPart IEEEFloat::addSignificand(const IEEEFloat &rhs) {
988 integerPart *parts;
989
990 parts = significandParts();
991
992 assert(semantics == rhs.semantics)((void)0);
993 assert(exponent == rhs.exponent)((void)0);
994
995 return APInt::tcAdd(parts, rhs.significandParts(), 0, partCount());
996}
997
998/* Subtract the significand of the RHS with a borrow flag. Returns
999 the borrow flag. */
1000IEEEFloat::integerPart IEEEFloat::subtractSignificand(const IEEEFloat &rhs,
1001 integerPart borrow) {
1002 integerPart *parts;
1003
1004 parts = significandParts();
1005
1006 assert(semantics == rhs.semantics)((void)0);
1007 assert(exponent == rhs.exponent)((void)0);
1008
1009 return APInt::tcSubtract(parts, rhs.significandParts(), borrow,
1010 partCount());
1011}
1012
1013/* Multiply the significand of the RHS. If ADDEND is non-NULL, add it
1014 on to the full-precision result of the multiplication. Returns the
1015 lost fraction. */
1016lostFraction IEEEFloat::multiplySignificand(const IEEEFloat &rhs,
1017 IEEEFloat addend) {
1018 unsigned int omsb; // One, not zero, based MSB.
1019 unsigned int partsCount, newPartsCount, precision;
1020 integerPart *lhsSignificand;
1021 integerPart scratch[4];
1022 integerPart *fullSignificand;
1023 lostFraction lost_fraction;
1024 bool ignored;
1025
1026 assert(semantics == rhs.semantics)((void)0);
1027
1028 precision = semantics->precision;
1029
1030 // Allocate space for twice as many bits as the original significand, plus one
1031 // extra bit for the addition to overflow into.
1032 newPartsCount = partCountForBits(precision * 2 + 1);
1033
1034 if (newPartsCount > 4)
1035 fullSignificand = new integerPart[newPartsCount];
1036 else
1037 fullSignificand = scratch;
1038
1039 lhsSignificand = significandParts();
1040 partsCount = partCount();
1041
1042 APInt::tcFullMultiply(fullSignificand, lhsSignificand,
1043 rhs.significandParts(), partsCount, partsCount);
1044
1045 lost_fraction = lfExactlyZero;
1046 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
1047 exponent += rhs.exponent;
1048
1049 // Assume the operands involved in the multiplication are single-precision
1050 // FP, and the two multiplicants are:
1051 // *this = a23 . a22 ... a0 * 2^e1
1052 // rhs = b23 . b22 ... b0 * 2^e2
1053 // the result of multiplication is:
1054 // *this = c48 c47 c46 . c45 ... c0 * 2^(e1+e2)
1055 // Note that there are three significant bits at the left-hand side of the
1056 // radix point: two for the multiplication, and an overflow bit for the
1057 // addition (that will always be zero at this point). Move the radix point
1058 // toward left by two bits, and adjust exponent accordingly.
1059 exponent += 2;
1060
1061 if (addend.isNonZero()) {
1062 // The intermediate result of the multiplication has "2 * precision"
1063 // signicant bit; adjust the addend to be consistent with mul result.
1064 //
1065 Significand savedSignificand = significand;
1066 const fltSemantics *savedSemantics = semantics;
1067 fltSemantics extendedSemantics;
1068 opStatus status;
1069 unsigned int extendedPrecision;
1070
1071 // Normalize our MSB to one below the top bit to allow for overflow.
1072 extendedPrecision = 2 * precision + 1;
1073 if (omsb != extendedPrecision - 1) {
1074 assert(extendedPrecision > omsb)((void)0);
1075 APInt::tcShiftLeft(fullSignificand, newPartsCount,
1076 (extendedPrecision - 1) - omsb);
1077 exponent -= (extendedPrecision - 1) - omsb;
1078 }
1079
1080 /* Create new semantics. */
1081 extendedSemantics = *semantics;
1082 extendedSemantics.precision = extendedPrecision;
1083
1084 if (newPartsCount == 1)
1085 significand.part = fullSignificand[0];
1086 else
1087 significand.parts = fullSignificand;
1088 semantics = &extendedSemantics;
1089
1090 // Make a copy so we can convert it to the extended semantics.
1091 // Note that we cannot convert the addend directly, as the extendedSemantics
1092 // is a local variable (which we take a reference to).
1093 IEEEFloat extendedAddend(addend);
1094 status = extendedAddend.convert(extendedSemantics, rmTowardZero, &ignored);
1095 assert(status == opOK)((void)0);
1096 (void)status;
1097
1098 // Shift the significand of the addend right by one bit. This guarantees
1099 // that the high bit of the significand is zero (same as fullSignificand),
1100 // so the addition will overflow (if it does overflow at all) into the top bit.
1101 lost_fraction = extendedAddend.shiftSignificandRight(1);
1102 assert(lost_fraction == lfExactlyZero &&((void)0)
1103 "Lost precision while shifting addend for fused-multiply-add.")((void)0);
1104
1105 lost_fraction = addOrSubtractSignificand(extendedAddend, false);
1106
1107 /* Restore our state. */
1108 if (newPartsCount == 1)
1109 fullSignificand[0] = significand.part;
1110 significand = savedSignificand;
1111 semantics = savedSemantics;
1112
1113 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
1114 }
1115
1116 // Convert the result having "2 * precision" significant-bits back to the one
1117 // having "precision" significant-bits. First, move the radix point from
1118 // poision "2*precision - 1" to "precision - 1". The exponent need to be
1119 // adjusted by "2*precision - 1" - "precision - 1" = "precision".
1120 exponent -= precision + 1;
1121
1122 // In case MSB resides at the left-hand side of radix point, shift the
1123 // mantissa right by some amount to make sure the MSB reside right before
1124 // the radix point (i.e. "MSB . rest-significant-bits").
1125 //
1126 // Note that the result is not normalized when "omsb < precision". So, the
1127 // caller needs to call IEEEFloat::normalize() if normalized value is
1128 // expected.
1129 if (omsb > precision) {
1130 unsigned int bits, significantParts;
1131 lostFraction lf;
1132
1133 bits = omsb - precision;
1134 significantParts = partCountForBits(omsb);
1135 lf = shiftRight(fullSignificand, significantParts, bits);
1136 lost_fraction = combineLostFractions(lf, lost_fraction);
1137 exponent += bits;
1138 }
1139
1140 APInt::tcAssign(lhsSignificand, fullSignificand, partsCount);
1141
1142 if (newPartsCount > 4)
1143 delete [] fullSignificand;
1144
1145 return lost_fraction;
1146}
1147
1148lostFraction IEEEFloat::multiplySignificand(const IEEEFloat &rhs) {
1149 return multiplySignificand(rhs, IEEEFloat(*semantics));
1150}
1151
1152/* Multiply the significands of LHS and RHS to DST. */
1153lostFraction IEEEFloat::divideSignificand(const IEEEFloat &rhs) {
1154 unsigned int bit, i, partsCount;
1155 const integerPart *rhsSignificand;
1156 integerPart *lhsSignificand, *dividend, *divisor;
1157 integerPart scratch[4];
1158 lostFraction lost_fraction;
1159
1160 assert(semantics == rhs.semantics)((void)0);
1161
1162 lhsSignificand = significandParts();
1163 rhsSignificand = rhs.significandParts();
1164 partsCount = partCount();
1165
1166 if (partsCount > 2)
1167 dividend = new integerPart[partsCount * 2];
1168 else
1169 dividend = scratch;
1170
1171 divisor = dividend + partsCount;
1172
1173 /* Copy the dividend and divisor as they will be modified in-place. */
1174 for (i = 0; i < partsCount; i++) {
1175 dividend[i] = lhsSignificand[i];
1176 divisor[i] = rhsSignificand[i];
1177 lhsSignificand[i] = 0;
1178 }
1179
1180 exponent -= rhs.exponent;
1181
1182 unsigned int precision = semantics->precision;
1183
1184 /* Normalize the divisor. */
1185 bit = precision - APInt::tcMSB(divisor, partsCount) - 1;
1186 if (bit) {
1187 exponent += bit;
1188 APInt::tcShiftLeft(divisor, partsCount, bit);
1189 }
1190
1191 /* Normalize the dividend. */
1192 bit = precision - APInt::tcMSB(dividend, partsCount) - 1;
1193 if (bit) {
1194 exponent -= bit;
1195 APInt::tcShiftLeft(dividend, partsCount, bit);
1196 }
1197
1198 /* Ensure the dividend >= divisor initially for the loop below.
1199 Incidentally, this means that the division loop below is
1200 guaranteed to set the integer bit to one. */
1201 if (APInt::tcCompare(dividend, divisor, partsCount) < 0) {
1202 exponent--;
1203 APInt::tcShiftLeft(dividend, partsCount, 1);
1204 assert(APInt::tcCompare(dividend, divisor, partsCount) >= 0)((void)0);
1205 }
1206
1207 /* Long division. */
1208 for (bit = precision; bit; bit -= 1) {
1209 if (APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
1210 APInt::tcSubtract(dividend, divisor, 0, partsCount);
1211 APInt::tcSetBit(lhsSignificand, bit - 1);
1212 }
1213
1214 APInt::tcShiftLeft(dividend, partsCount, 1);
1215 }
1216
1217 /* Figure out the lost fraction. */
1218 int cmp = APInt::tcCompare(dividend, divisor, partsCount);
1219
1220 if (cmp > 0)
1221 lost_fraction = lfMoreThanHalf;
1222 else if (cmp == 0)
1223 lost_fraction = lfExactlyHalf;
1224 else if (APInt::tcIsZero(dividend, partsCount))
1225 lost_fraction = lfExactlyZero;
1226 else
1227 lost_fraction = lfLessThanHalf;
1228
1229 if (partsCount > 2)
1230 delete [] dividend;
1231
1232 return lost_fraction;
1233}
1234
1235unsigned int IEEEFloat::significandMSB() const {
1236 return APInt::tcMSB(significandParts(), partCount());
1237}
1238
1239unsigned int IEEEFloat::significandLSB() const {
1240 return APInt::tcLSB(significandParts(), partCount());
1241}
1242
1243/* Note that a zero result is NOT normalized to fcZero. */
1244lostFraction IEEEFloat::shiftSignificandRight(unsigned int bits) {
1245 /* Our exponent should not overflow. */
1246 assert((ExponentType) (exponent + bits) >= exponent)((void)0);
1247
1248 exponent += bits;
1249
1250 return shiftRight(significandParts(), partCount(), bits);
1251}
1252
1253/* Shift the significand left BITS bits, subtract BITS from its exponent. */
1254void IEEEFloat::shiftSignificandLeft(unsigned int bits) {
1255 assert(bits < semantics->precision)((void)0);
1256
1257 if (bits) {
1258 unsigned int partsCount = partCount();
1259
1260 APInt::tcShiftLeft(significandParts(), partsCount, bits);
1261 exponent -= bits;
1262
1263 assert(!APInt::tcIsZero(significandParts(), partsCount))((void)0);
1264 }
1265}
1266
1267IEEEFloat::cmpResult
1268IEEEFloat::compareAbsoluteValue(const IEEEFloat &rhs) const {
1269 int compare;
1270
1271 assert(semantics == rhs.semantics)((void)0);
1272 assert(isFiniteNonZero())((void)0);
1273 assert(rhs.isFiniteNonZero())((void)0);
1274
1275 compare = exponent - rhs.exponent;
1276
1277 /* If exponents are equal, do an unsigned bignum comparison of the
1278 significands. */
1279 if (compare == 0)
1280 compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
1281 partCount());
1282
1283 if (compare > 0)
1284 return cmpGreaterThan;
1285 else if (compare < 0)
1286 return cmpLessThan;
1287 else
1288 return cmpEqual;
1289}
1290
1291/* Handle overflow. Sign is preserved. We either become infinity or
1292 the largest finite number. */
1293IEEEFloat::opStatus IEEEFloat::handleOverflow(roundingMode rounding_mode) {
1294 /* Infinity? */
1295 if (rounding_mode == rmNearestTiesToEven ||
1296 rounding_mode == rmNearestTiesToAway ||
1297 (rounding_mode == rmTowardPositive && !sign) ||
1298 (rounding_mode == rmTowardNegative && sign)) {
1299 category = fcInfinity;
1300 return (opStatus) (opOverflow | opInexact);
1301 }
1302
1303 /* Otherwise we become the largest finite number. */
1304 category = fcNormal;
1305 exponent = semantics->maxExponent;
1306 APInt::tcSetLeastSignificantBits(significandParts(), partCount(),
1307 semantics->precision);
1308
1309 return opInexact;
1310}
1311
1312/* Returns TRUE if, when truncating the current number, with BIT the
1313 new LSB, with the given lost fraction and rounding mode, the result
1314 would need to be rounded away from zero (i.e., by increasing the
1315 signficand). This routine must work for fcZero of both signs, and
1316 fcNormal numbers. */
1317bool IEEEFloat::roundAwayFromZero(roundingMode rounding_mode,
1318 lostFraction lost_fraction,
1319 unsigned int bit) const {
1320 /* NaNs and infinities should not have lost fractions. */
1321 assert(isFiniteNonZero() || category == fcZero)((void)0);
1322
1323 /* Current callers never pass this so we don't handle it. */
1324 assert(lost_fraction != lfExactlyZero)((void)0);
1325
1326 switch (rounding_mode) {
1327 case rmNearestTiesToAway:
1328 return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf;
1329
1330 case rmNearestTiesToEven:
1331 if (lost_fraction == lfMoreThanHalf)
1332 return true;
1333
1334 /* Our zeroes don't have a significand to test. */
1335 if (lost_fraction == lfExactlyHalf && category != fcZero)
1336 return APInt::tcExtractBit(significandParts(), bit);
1337
1338 return false;
1339
1340 case rmTowardZero:
1341 return false;
1342
1343 case rmTowardPositive:
1344 return !sign;
1345
1346 case rmTowardNegative:
1347 return sign;
1348
1349 default:
1350 break;
1351 }
1352 llvm_unreachable("Invalid rounding mode found")__builtin_unreachable();
1353}
1354
1355IEEEFloat::opStatus IEEEFloat::normalize(roundingMode rounding_mode,
1356 lostFraction lost_fraction) {
1357 unsigned int omsb; /* One, not zero, based MSB. */
1358 int exponentChange;
1359
1360 if (!isFiniteNonZero())
1361 return opOK;
1362
1363 /* Before rounding normalize the exponent of fcNormal numbers. */
1364 omsb = significandMSB() + 1;
1365
1366 if (omsb) {
1367 /* OMSB is numbered from 1. We want to place it in the integer
1368 bit numbered PRECISION if possible, with a compensating change in
1369 the exponent. */
1370 exponentChange = omsb - semantics->precision;
1371
1372 /* If the resulting exponent is too high, overflow according to
1373 the rounding mode. */
1374 if (exponent + exponentChange > semantics->maxExponent)
1375 return handleOverflow(rounding_mode);
1376
1377 /* Subnormal numbers have exponent minExponent, and their MSB
1378 is forced based on that. */
1379 if (exponent + exponentChange < semantics->minExponent)
1380 exponentChange = semantics->minExponent - exponent;
1381
1382 /* Shifting left is easy as we don't lose precision. */
1383 if (exponentChange < 0) {
1384 assert(lost_fraction == lfExactlyZero)((void)0);
1385
1386 shiftSignificandLeft(-exponentChange);
1387
1388 return opOK;
1389 }
1390
1391 if (exponentChange > 0) {
1392 lostFraction lf;
1393
1394 /* Shift right and capture any new lost fraction. */
1395 lf = shiftSignificandRight(exponentChange);
1396
1397 lost_fraction = combineLostFractions(lf, lost_fraction);
1398
1399 /* Keep OMSB up-to-date. */
1400 if (omsb > (unsigned) exponentChange)
1401 omsb -= exponentChange;
1402 else
1403 omsb = 0;
1404 }
1405 }
1406
1407 /* Now round the number according to rounding_mode given the lost
1408 fraction. */
1409
1410 /* As specified in IEEE 754, since we do not trap we do not report
1411 underflow for exact results. */
1412 if (lost_fraction == lfExactlyZero) {
1413 /* Canonicalize zeroes. */
1414 if (omsb == 0)
1415 category = fcZero;
1416
1417 return opOK;
1418 }
1419
1420 /* Increment the significand if we're rounding away from zero. */
1421 if (roundAwayFromZero(rounding_mode, lost_fraction, 0)) {
1422 if (omsb == 0)
1423 exponent = semantics->minExponent;
1424
1425 incrementSignificand();
1426 omsb = significandMSB() + 1;
1427
1428 /* Did the significand increment overflow? */
1429 if (omsb == (unsigned) semantics->precision + 1) {
1430 /* Renormalize by incrementing the exponent and shifting our
1431 significand right one. However if we already have the
1432 maximum exponent we overflow to infinity. */
1433 if (exponent == semantics->maxExponent) {
1434 category = fcInfinity;
1435
1436 return (opStatus) (opOverflow | opInexact);
1437 }
1438
1439 shiftSignificandRight(1);
1440
1441 return opInexact;
1442 }
1443 }
1444
1445 /* The normal case - we were and are not denormal, and any
1446 significand increment above didn't overflow. */
1447 if (omsb == semantics->precision)
1448 return opInexact;
1449
1450 /* We have a non-zero denormal. */
1451 assert(omsb < semantics->precision)((void)0);
1452
1453 /* Canonicalize zeroes. */
1454 if (omsb == 0)
1455 category = fcZero;
1456
1457 /* The fcZero case is a denormal that underflowed to zero. */
1458 return (opStatus) (opUnderflow | opInexact);
1459}
1460
1461IEEEFloat::opStatus IEEEFloat::addOrSubtractSpecials(const IEEEFloat &rhs,
1462 bool subtract) {
1463 switch (PackCategoriesIntoKey(category, rhs.category)((category) * 4 + (rhs.category))) {
1464 default:
1465 llvm_unreachable(nullptr)__builtin_unreachable();
1466
1467 case PackCategoriesIntoKey(fcZero, fcNaN)((fcZero) * 4 + (fcNaN)):
1468 case PackCategoriesIntoKey(fcNormal, fcNaN)((fcNormal) * 4 + (fcNaN)):
1469 case PackCategoriesIntoKey(fcInfinity, fcNaN)((fcInfinity) * 4 + (fcNaN)):
1470 assign(rhs);
1471 LLVM_FALLTHROUGH[[gnu::fallthrough]];
1472 case PackCategoriesIntoKey(fcNaN, fcZero)((fcNaN) * 4 + (fcZero)):
1473 case PackCategoriesIntoKey(fcNaN, fcNormal)((fcNaN) * 4 + (fcNormal)):
1474 case PackCategoriesIntoKey(fcNaN, fcInfinity)((fcNaN) * 4 + (fcInfinity)):
1475 case PackCategoriesIntoKey(fcNaN, fcNaN)((fcNaN) * 4 + (fcNaN)):
1476 if (isSignaling()) {
1477 makeQuiet();
1478 return opInvalidOp;
1479 }
1480 return rhs.isSignaling() ? opInvalidOp : opOK;
1481
1482 case PackCategoriesIntoKey(fcNormal, fcZero)((fcNormal) * 4 + (fcZero)):
1483 case PackCategoriesIntoKey(fcInfinity, fcNormal)((fcInfinity) * 4 + (fcNormal)):
1484 case PackCategoriesIntoKey(fcInfinity, fcZero)((fcInfinity) * 4 + (fcZero)):
1485 return opOK;
1486
1487 case PackCategoriesIntoKey(fcNormal, fcInfinity)((fcNormal) * 4 + (fcInfinity)):
1488 case PackCategoriesIntoKey(fcZero, fcInfinity)((fcZero) * 4 + (fcInfinity)):
1489 category = fcInfinity;
1490 sign = rhs.sign ^ subtract;
1491 return opOK;
1492
1493 case PackCategoriesIntoKey(fcZero, fcNormal)((fcZero) * 4 + (fcNormal)):
1494 assign(rhs);
1495 sign = rhs.sign ^ subtract;
1496 return opOK;
1497
1498 case PackCategoriesIntoKey(fcZero, fcZero)((fcZero) * 4 + (fcZero)):
1499 /* Sign depends on rounding mode; handled by caller. */
1500 return opOK;
1501
1502 case PackCategoriesIntoKey(fcInfinity, fcInfinity)((fcInfinity) * 4 + (fcInfinity)):
1503 /* Differently signed infinities can only be validly
1504 subtracted. */
1505 if (((sign ^ rhs.sign)!=0) != subtract) {
1506 makeNaN();
1507 return opInvalidOp;
1508 }
1509
1510 return opOK;
1511
1512 case PackCategoriesIntoKey(fcNormal, fcNormal)((fcNormal) * 4 + (fcNormal)):
1513 return opDivByZero;
1514 }
1515}
1516
1517/* Add or subtract two normal numbers. */
1518lostFraction IEEEFloat::addOrSubtractSignificand(const IEEEFloat &rhs,
1519 bool subtract) {
1520 integerPart carry;
1521 lostFraction lost_fraction;
1522 int bits;
1523
1524 /* Determine if the operation on the absolute values is effectively
1525 an addition or subtraction. */
1526 subtract ^= static_cast<bool>(sign ^ rhs.sign);
1527
1528 /* Are we bigger exponent-wise than the RHS? */
1529 bits = exponent - rhs.exponent;
1530
1531 /* Subtraction is more subtle than one might naively expect. */
1532 if (subtract) {
1533 IEEEFloat temp_rhs(rhs);
1534
1535 if (bits == 0)
1536 lost_fraction = lfExactlyZero;
1537 else if (bits > 0) {
1538 lost_fraction = temp_rhs.shiftSignificandRight(bits - 1);
1539 shiftSignificandLeft(1);
1540 } else {
1541 lost_fraction = shiftSignificandRight(-bits - 1);
1542 temp_rhs.shiftSignificandLeft(1);
1543 }
1544
1545 // Should we reverse the subtraction.
1546 if (compareAbsoluteValue(temp_rhs) == cmpLessThan) {
1547 carry = temp_rhs.subtractSignificand
1548 (*this, lost_fraction != lfExactlyZero);
1549 copySignificand(temp_rhs);
1550 sign = !sign;
1551 } else {
1552 carry = subtractSignificand
1553 (temp_rhs, lost_fraction != lfExactlyZero);
1554 }
1555
1556 /* Invert the lost fraction - it was on the RHS and
1557 subtracted. */
1558 if (lost_fraction == lfLessThanHalf)
1559 lost_fraction = lfMoreThanHalf;
1560 else if (lost_fraction == lfMoreThanHalf)
1561 lost_fraction = lfLessThanHalf;
1562
1563 /* The code above is intended to ensure that no borrow is
1564 necessary. */
1565 assert(!carry)((void)0);
1566 (void)carry;
1567 } else {
1568 if (bits > 0) {
1569 IEEEFloat temp_rhs(rhs);
1570
1571 lost_fraction = temp_rhs.shiftSignificandRight(bits);
1572 carry = addSignificand(temp_rhs);
1573 } else {
1574 lost_fraction = shiftSignificandRight(-bits);
1575 carry = addSignificand(rhs);
1576 }
1577
1578 /* We have a guard bit; generating a carry cannot happen. */
1579 assert(!carry)((void)0);
1580 (void)carry;
1581 }
1582
1583 return lost_fraction;
1584}
1585
1586IEEEFloat::opStatus IEEEFloat::multiplySpecials(const IEEEFloat &rhs) {
1587 switch (PackCategoriesIntoKey(category, rhs.category)((category) * 4 + (rhs.category))) {
1588 default:
1589 llvm_unreachable(nullptr)__builtin_unreachable();
1590
1591 case PackCategoriesIntoKey(fcZero, fcNaN)((fcZero) * 4 + (fcNaN)):
1592 case PackCategoriesIntoKey(fcNormal, fcNaN)((fcNormal) * 4 + (fcNaN)):
1593 case PackCategoriesIntoKey(fcInfinity, fcNaN)((fcInfinity) * 4 + (fcNaN)):
1594 assign(rhs);
1595 sign = false;
1596 LLVM_FALLTHROUGH[[gnu::fallthrough]];
1597 case PackCategoriesIntoKey(fcNaN, fcZero)((fcNaN) * 4 + (fcZero)):
1598 case PackCategoriesIntoKey(fcNaN, fcNormal)((fcNaN) * 4 + (fcNormal)):
1599 case PackCategoriesIntoKey(fcNaN, fcInfinity)((fcNaN) * 4 + (fcInfinity)):
1600 case PackCategoriesIntoKey(fcNaN, fcNaN)((fcNaN) * 4 + (fcNaN)):
1601 sign ^= rhs.sign; // restore the original sign
1602 if (isSignaling()) {
1603 makeQuiet();
1604 return opInvalidOp;
1605 }
1606 return rhs.isSignaling() ? opInvalidOp : opOK;
1607
1608 case PackCategoriesIntoKey(fcNormal, fcInfinity)((fcNormal) * 4 + (fcInfinity)):
1609 case PackCategoriesIntoKey(fcInfinity, fcNormal)((fcInfinity) * 4 + (fcNormal)):
1610 case PackCategoriesIntoKey(fcInfinity, fcInfinity)((fcInfinity) * 4 + (fcInfinity)):
1611 category = fcInfinity;
1612 return opOK;
1613
1614 case PackCategoriesIntoKey(fcZero, fcNormal)((fcZero) * 4 + (fcNormal)):
1615 case PackCategoriesIntoKey(fcNormal, fcZero)((fcNormal) * 4 + (fcZero)):
1616 case PackCategoriesIntoKey(fcZero, fcZero)((fcZero) * 4 + (fcZero)):
1617 category = fcZero;
1618 return opOK;
1619
1620 case PackCategoriesIntoKey(fcZero, fcInfinity)((fcZero) * 4 + (fcInfinity)):
1621 case PackCategoriesIntoKey(fcInfinity, fcZero)((fcInfinity) * 4 + (fcZero)):
1622 makeNaN();
1623 return opInvalidOp;
1624
1625 case PackCategoriesIntoKey(fcNormal, fcNormal)((fcNormal) * 4 + (fcNormal)):
1626 return opOK;
1627 }
1628}
1629
1630IEEEFloat::opStatus IEEEFloat::divideSpecials(const IEEEFloat &rhs) {
1631 switch (PackCategoriesIntoKey(category, rhs.category)((category) * 4 + (rhs.category))) {
1632 default:
1633 llvm_unreachable(nullptr)__builtin_unreachable();
1634
1635 case PackCategoriesIntoKey(fcZero, fcNaN)((fcZero) * 4 + (fcNaN)):
1636 case PackCategoriesIntoKey(fcNormal, fcNaN)((fcNormal) * 4 + (fcNaN)):
1637 case PackCategoriesIntoKey(fcInfinity, fcNaN)((fcInfinity) * 4 + (fcNaN)):
1638 assign(rhs);
1639 sign = false;
1640 LLVM_FALLTHROUGH[[gnu::fallthrough]];
1641 case PackCategoriesIntoKey(fcNaN, fcZero)((fcNaN) * 4 + (fcZero)):
1642 case PackCategoriesIntoKey(fcNaN, fcNormal)((fcNaN) * 4 + (fcNormal)):
1643 case PackCategoriesIntoKey(fcNaN, fcInfinity)((fcNaN) * 4 + (fcInfinity)):
1644 case PackCategoriesIntoKey(fcNaN, fcNaN)((fcNaN) * 4 + (fcNaN)):
1645 sign ^= rhs.sign; // restore the original sign
1646 if (isSignaling()) {
1647 makeQuiet();
1648 return opInvalidOp;
1649 }
1650 return rhs.isSignaling() ? opInvalidOp : opOK;
1651
1652 case PackCategoriesIntoKey(fcInfinity, fcZero)((fcInfinity) * 4 + (fcZero)):
1653 case PackCategoriesIntoKey(fcInfinity, fcNormal)((fcInfinity) * 4 + (fcNormal)):
1654 case PackCategoriesIntoKey(fcZero, fcInfinity)((fcZero) * 4 + (fcInfinity)):
1655 case PackCategoriesIntoKey(fcZero, fcNormal)((fcZero) * 4 + (fcNormal)):
1656 return opOK;
1657
1658 case PackCategoriesIntoKey(fcNormal, fcInfinity)((fcNormal) * 4 + (fcInfinity)):
1659 category = fcZero;
1660 return opOK;
1661
1662 case PackCategoriesIntoKey(fcNormal, fcZero)((fcNormal) * 4 + (fcZero)):
1663 category = fcInfinity;
1664 return opDivByZero;
1665
1666 case PackCategoriesIntoKey(fcInfinity, fcInfinity)((fcInfinity) * 4 + (fcInfinity)):
1667 case PackCategoriesIntoKey(fcZero, fcZero)((fcZero) * 4 + (fcZero)):
1668 makeNaN();
1669 return opInvalidOp;
1670
1671 case PackCategoriesIntoKey(fcNormal, fcNormal)((fcNormal) * 4 + (fcNormal)):
1672 return opOK;
1673 }
1674}
1675
1676IEEEFloat::opStatus IEEEFloat::modSpecials(const IEEEFloat &rhs) {
1677 switch (PackCategoriesIntoKey(category, rhs.category)((category) * 4 + (rhs.category))) {
1678 default:
1679 llvm_unreachable(nullptr)__builtin_unreachable();
1680
1681 case PackCategoriesIntoKey(fcZero, fcNaN)((fcZero) * 4 + (fcNaN)):
1682 case PackCategoriesIntoKey(fcNormal, fcNaN)((fcNormal) * 4 + (fcNaN)):
1683 case PackCategoriesIntoKey(fcInfinity, fcNaN)((fcInfinity) * 4 + (fcNaN)):
1684 assign(rhs);
1685 LLVM_FALLTHROUGH[[gnu::fallthrough]];
1686 case PackCategoriesIntoKey(fcNaN, fcZero)((fcNaN) * 4 + (fcZero)):
1687 case PackCategoriesIntoKey(fcNaN, fcNormal)((fcNaN) * 4 + (fcNormal)):
1688 case PackCategoriesIntoKey(fcNaN, fcInfinity)((fcNaN) * 4 + (fcInfinity)):
1689 case PackCategoriesIntoKey(fcNaN, fcNaN)((fcNaN) * 4 + (fcNaN)):
1690 if (isSignaling()) {
1691 makeQuiet();
1692 return opInvalidOp;
1693 }
1694 return rhs.isSignaling() ? opInvalidOp : opOK;
1695
1696 case PackCategoriesIntoKey(fcZero, fcInfinity)((fcZero) * 4 + (fcInfinity)):
1697 case PackCategoriesIntoKey(fcZero, fcNormal)((fcZero) * 4 + (fcNormal)):
1698 case PackCategoriesIntoKey(fcNormal, fcInfinity)((fcNormal) * 4 + (fcInfinity)):
1699 return opOK;
1700
1701 case PackCategoriesIntoKey(fcNormal, fcZero)((fcNormal) * 4 + (fcZero)):
1702 case PackCategoriesIntoKey(fcInfinity, fcZero)((fcInfinity) * 4 + (fcZero)):
1703 case PackCategoriesIntoKey(fcInfinity, fcNormal)((fcInfinity) * 4 + (fcNormal)):
1704 case PackCategoriesIntoKey(fcInfinity, fcInfinity)((fcInfinity) * 4 + (fcInfinity)):
1705 case PackCategoriesIntoKey(fcZero, fcZero)((fcZero) * 4 + (fcZero)):
1706 makeNaN();
1707 return opInvalidOp;
1708
1709 case PackCategoriesIntoKey(fcNormal, fcNormal)((fcNormal) * 4 + (fcNormal)):
1710 return opOK;
1711 }
1712}
1713
1714IEEEFloat::opStatus IEEEFloat::remainderSpecials(const IEEEFloat &rhs) {
1715 switch (PackCategoriesIntoKey(category, rhs.category)((category) * 4 + (rhs.category))) {
1716 default:
1717 llvm_unreachable(nullptr)__builtin_unreachable();
1718
1719 case PackCategoriesIntoKey(fcZero, fcNaN)((fcZero) * 4 + (fcNaN)):
1720 case PackCategoriesIntoKey(fcNormal, fcNaN)((fcNormal) * 4 + (fcNaN)):
1721 case PackCategoriesIntoKey(fcInfinity, fcNaN)((fcInfinity) * 4 + (fcNaN)):
1722 assign(rhs);
1723 LLVM_FALLTHROUGH[[gnu::fallthrough]];
1724 case PackCategoriesIntoKey(fcNaN, fcZero)((fcNaN) * 4 + (fcZero)):
1725 case PackCategoriesIntoKey(fcNaN, fcNormal)((fcNaN) * 4 + (fcNormal)):
1726 case PackCategoriesIntoKey(fcNaN, fcInfinity)((fcNaN) * 4 + (fcInfinity)):
1727 case PackCategoriesIntoKey(fcNaN, fcNaN)((fcNaN) * 4 + (fcNaN)):
1728 if (isSignaling()) {
1729 makeQuiet();
1730 return opInvalidOp;
1731 }
1732 return rhs.isSignaling() ? opInvalidOp : opOK;
1733
1734 case PackCategoriesIntoKey(fcZero, fcInfinity)((fcZero) * 4 + (fcInfinity)):
1735 case PackCategoriesIntoKey(fcZero, fcNormal)((fcZero) * 4 + (fcNormal)):
1736 case PackCategoriesIntoKey(fcNormal, fcInfinity)((fcNormal) * 4 + (fcInfinity)):
1737 return opOK;
1738
1739 case PackCategoriesIntoKey(fcNormal, fcZero)((fcNormal) * 4 + (fcZero)):
1740 case PackCategoriesIntoKey(fcInfinity, fcZero)((fcInfinity) * 4 + (fcZero)):
1741 case PackCategoriesIntoKey(fcInfinity, fcNormal)((fcInfinity) * 4 + (fcNormal)):
1742 case PackCategoriesIntoKey(fcInfinity, fcInfinity)((fcInfinity) * 4 + (fcInfinity)):
1743 case PackCategoriesIntoKey(fcZero, fcZero)((fcZero) * 4 + (fcZero)):
1744 makeNaN();
1745 return opInvalidOp;
1746
1747 case PackCategoriesIntoKey(fcNormal, fcNormal)((fcNormal) * 4 + (fcNormal)):
1748 return opDivByZero; // fake status, indicating this is not a special case
1749 }
1750}
1751
1752/* Change sign. */
1753void IEEEFloat::changeSign() {
1754 /* Look mummy, this one's easy. */
1755 sign = !sign;
1756}
1757
1758/* Normalized addition or subtraction. */
1759IEEEFloat::opStatus IEEEFloat::addOrSubtract(const IEEEFloat &rhs,
1760 roundingMode rounding_mode,
1761 bool subtract) {
1762 opStatus fs;
1763
1764 fs = addOrSubtractSpecials(rhs, subtract);
1765
1766 /* This return code means it was not a simple case. */
1767 if (fs == opDivByZero) {
1768 lostFraction lost_fraction;
1769
1770 lost_fraction = addOrSubtractSignificand(rhs, subtract);
1771 fs = normalize(rounding_mode, lost_fraction);
1772
1773 /* Can only be zero if we lost no fraction. */
1774 assert(category != fcZero || lost_fraction == lfExactlyZero)((void)0);
1775 }
1776
1777 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1778 positive zero unless rounding to minus infinity, except that
1779 adding two like-signed zeroes gives that zero. */
1780 if (category == fcZero) {
1781 if (rhs.category != fcZero || (sign == rhs.sign) == subtract)
1782 sign = (rounding_mode == rmTowardNegative);
1783 }
1784
1785 return fs;
1786}
1787
1788/* Normalized addition. */
1789IEEEFloat::opStatus IEEEFloat::add(const IEEEFloat &rhs,
1790 roundingMode rounding_mode) {
1791 return addOrSubtract(rhs, rounding_mode, false);
1792}
1793
1794/* Normalized subtraction. */
1795IEEEFloat::opStatus IEEEFloat::subtract(const IEEEFloat &rhs,
1796 roundingMode rounding_mode) {
1797 return addOrSubtract(rhs, rounding_mode, true);
1798}
1799
1800/* Normalized multiply. */
1801IEEEFloat::opStatus IEEEFloat::multiply(const IEEEFloat &rhs,
1802 roundingMode rounding_mode) {
1803 opStatus fs;
1804
1805 sign ^= rhs.sign;
1806 fs = multiplySpecials(rhs);
1807
1808 if (isFiniteNonZero()) {
1809 lostFraction lost_fraction = multiplySignificand(rhs);
1810 fs = normalize(rounding_mode, lost_fraction);
1811 if (lost_fraction != lfExactlyZero)
1812 fs = (opStatus) (fs | opInexact);
1813 }
1814
1815 return fs;
1816}
1817
1818/* Normalized divide. */
1819IEEEFloat::opStatus IEEEFloat::divide(const IEEEFloat &rhs,
1820 roundingMode rounding_mode) {
1821 opStatus fs;
1822
1823 sign ^= rhs.sign;
1824 fs = divideSpecials(rhs);
1825
1826 if (isFiniteNonZero()) {
1827 lostFraction lost_fraction = divideSignificand(rhs);
1828 fs = normalize(rounding_mode, lost_fraction);
1829 if (lost_fraction != lfExactlyZero)
1830 fs = (opStatus) (fs | opInexact);
1831 }
1832
1833 return fs;
1834}
1835
1836/* Normalized remainder. */
1837IEEEFloat::opStatus IEEEFloat::remainder(const IEEEFloat &rhs) {
1838 opStatus fs;
1839 unsigned int origSign = sign;
1840
1841 // First handle the special cases.
1842 fs = remainderSpecials(rhs);
1843 if (fs != opDivByZero)
1844 return fs;
1845
1846 fs = opOK;
1847
1848 // Make sure the current value is less than twice the denom. If the addition
1849 // did not succeed (an overflow has happened), which means that the finite
1850 // value we currently posses must be less than twice the denom (as we are
1851 // using the same semantics).
1852 IEEEFloat P2 = rhs;
1853 if (P2.add(rhs, rmNearestTiesToEven) == opOK) {
1854 fs = mod(P2);
1855 assert(fs == opOK)((void)0);
1856 }
1857
1858 // Lets work with absolute numbers.
1859 IEEEFloat P = rhs;
1860 P.sign = false;
1861 sign = false;
1862
1863 //
1864 // To calculate the remainder we use the following scheme.
1865 //
1866 // The remainder is defained as follows:
1867 //
1868 // remainder = numer - rquot * denom = x - r * p
1869 //
1870 // Where r is the result of: x/p, rounded toward the nearest integral value
1871 // (with halfway cases rounded toward the even number).
1872 //
1873 // Currently, (after x mod 2p):
1874 // r is the number of 2p's present inside x, which is inherently, an even
1875 // number of p's.
1876 //
1877 // We may split the remaining calculation into 4 options:
1878 // - if x < 0.5p then we round to the nearest number with is 0, and are done.
1879 // - if x == 0.5p then we round to the nearest even number which is 0, and we
1880 // are done as well.
1881 // - if 0.5p < x < p then we round to nearest number which is 1, and we have
1882 // to subtract 1p at least once.
1883 // - if x >= p then we must subtract p at least once, as x must be a
1884 // remainder.
1885 //
1886 // By now, we were done, or we added 1 to r, which in turn, now an odd number.
1887 //
1888 // We can now split the remaining calculation to the following 3 options:
1889 // - if x < 0.5p then we round to the nearest number with is 0, and are done.
1890 // - if x == 0.5p then we round to the nearest even number. As r is odd, we
1891 // must round up to the next even number. so we must subtract p once more.
1892 // - if x > 0.5p (and inherently x < p) then we must round r up to the next
1893 // integral, and subtract p once more.
1894 //
1895
1896 // Extend the semantics to prevent an overflow/underflow or inexact result.
1897 bool losesInfo;
1898 fltSemantics extendedSemantics = *semantics;
1899 extendedSemantics.maxExponent++;
1900 extendedSemantics.minExponent--;
1901 extendedSemantics.precision += 2;
1902
1903 IEEEFloat VEx = *this;
1904 fs = VEx.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
1905 assert(fs == opOK && !losesInfo)((void)0);
1906 IEEEFloat PEx = P;
1907 fs = PEx.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
1908 assert(fs == opOK && !losesInfo)((void)0);
1909
1910 // It is simpler to work with 2x instead of 0.5p, and we do not need to lose
1911 // any fraction.
1912 fs = VEx.add(VEx, rmNearestTiesToEven);
1913 assert(fs == opOK)((void)0);
1914
1915 if (VEx.compare(PEx) == cmpGreaterThan) {
1916 fs = subtract(P, rmNearestTiesToEven);
1917 assert(fs == opOK)((void)0);
1918
1919 // Make VEx = this.add(this), but because we have different semantics, we do
1920 // not want to `convert` again, so we just subtract PEx twice (which equals
1921 // to the desired value).
1922 fs = VEx.subtract(PEx, rmNearestTiesToEven);
1923 assert(fs == opOK)((void)0);
1924 fs = VEx.subtract(PEx, rmNearestTiesToEven);
1925 assert(fs == opOK)((void)0);
1926
1927 cmpResult result = VEx.compare(PEx);
1928 if (result == cmpGreaterThan || result == cmpEqual) {
1929 fs = subtract(P, rmNearestTiesToEven);
1930 assert(fs == opOK)((void)0);
1931 }
1932 }
1933
1934 if (isZero())
1935 sign = origSign; // IEEE754 requires this
1936 else
1937 sign ^= origSign;
1938 return fs;
1939}
1940
1941/* Normalized llvm frem (C fmod). */
1942IEEEFloat::opStatus IEEEFloat::mod(const IEEEFloat &rhs) {
1943 opStatus fs;
1944 fs = modSpecials(rhs);
1945 unsigned int origSign = sign;
1946
1947 while (isFiniteNonZero() && rhs.isFiniteNonZero() &&
1948 compareAbsoluteValue(rhs) != cmpLessThan) {
1949 IEEEFloat V = scalbn(rhs, ilogb(*this) - ilogb(rhs), rmNearestTiesToEven);
1950 if (compareAbsoluteValue(V) == cmpLessThan)
1951 V = scalbn(V, -1, rmNearestTiesToEven);
1952 V.sign = sign;
1953
1954 fs = subtract(V, rmNearestTiesToEven);
1955 assert(fs==opOK)((void)0);
1956 }
1957 if (isZero())
1958 sign = origSign; // fmod requires this
1959 return fs;
1960}
1961
1962/* Normalized fused-multiply-add. */
1963IEEEFloat::opStatus IEEEFloat::fusedMultiplyAdd(const IEEEFloat &multiplicand,
1964 const IEEEFloat &addend,
1965 roundingMode rounding_mode) {
1966 opStatus fs;
1967
1968 /* Post-multiplication sign, before addition. */
1969 sign ^= multiplicand.sign;
1970
1971 /* If and only if all arguments are normal do we need to do an
1972 extended-precision calculation. */
1973 if (isFiniteNonZero() &&
1974 multiplicand.isFiniteNonZero() &&
1975 addend.isFinite()) {
1976 lostFraction lost_fraction;
1977
1978 lost_fraction = multiplySignificand(multiplicand, addend);
1979 fs = normalize(rounding_mode, lost_fraction);
1980 if (lost_fraction != lfExactlyZero)
1981 fs = (opStatus) (fs | opInexact);
1982
1983 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1984 positive zero unless rounding to minus infinity, except that
1985 adding two like-signed zeroes gives that zero. */
1986 if (category == fcZero && !(fs & opUnderflow) && sign != addend.sign)
1987 sign = (rounding_mode == rmTowardNegative);
1988 } else {
1989 fs = multiplySpecials(multiplicand);
1990
1991 /* FS can only be opOK or opInvalidOp. There is no more work
1992 to do in the latter case. The IEEE-754R standard says it is
1993 implementation-defined in this case whether, if ADDEND is a
1994 quiet NaN, we raise invalid op; this implementation does so.
1995
1996 If we need to do the addition we can do so with normal
1997 precision. */
1998 if (fs == opOK)
1999 fs = addOrSubtract(addend, rounding_mode, false);
2000 }
2001
2002 return fs;
2003}
2004
2005/* Rounding-mode correct round to integral value. */
2006IEEEFloat::opStatus IEEEFloat::roundToIntegral(roundingMode rounding_mode) {
2007 opStatus fs;
2008
2009 if (isInfinity())
2010 // [IEEE Std 754-2008 6.1]:
2011 // The behavior of infinity in floating-point arithmetic is derived from the
2012 // limiting cases of real arithmetic with operands of arbitrarily
2013 // large magnitude, when such a limit exists.
2014 // ...
2015 // Operations on infinite operands are usually exact and therefore signal no
2016 // exceptions ...
2017 return opOK;
2018
2019 if (isNaN()) {
2020 if (isSignaling()) {
2021 // [IEEE Std 754-2008 6.2]:
2022 // Under default exception handling, any operation signaling an invalid
2023 // operation exception and for which a floating-point result is to be
2024 // delivered shall deliver a quiet NaN.
2025 makeQuiet();
2026 // [IEEE Std 754-2008 6.2]:
2027 // Signaling NaNs shall be reserved operands that, under default exception
2028 // handling, signal the invalid operation exception(see 7.2) for every
2029 // general-computational and signaling-computational operation except for
2030 // the conversions described in 5.12.
2031 return opInvalidOp;
2032 } else {
2033 // [IEEE Std 754-2008 6.2]:
2034 // For an operation with quiet NaN inputs, other than maximum and minimum
2035 // operations, if a floating-point result is to be delivered the result
2036 // shall be a quiet NaN which should be one of the input NaNs.
2037 // ...
2038 // Every general-computational and quiet-computational operation involving
2039 // one or more input NaNs, none of them signaling, shall signal no
2040 // exception, except fusedMultiplyAdd might signal the invalid operation
2041 // exception(see 7.2).
2042 return opOK;
2043 }
2044 }
2045
2046 if (isZero()) {
2047 // [IEEE Std 754-2008 6.3]:
2048 // ... the sign of the result of conversions, the quantize operation, the
2049 // roundToIntegral operations, and the roundToIntegralExact(see 5.3.1) is
2050 // the sign of the first or only operand.
2051 return opOK;
2052 }
2053
2054 // If the exponent is large enough, we know that this value is already
2055 // integral, and the arithmetic below would potentially cause it to saturate
2056 // to +/-Inf. Bail out early instead.
2057 if (exponent+1 >= (int)semanticsPrecision(*semantics))
2058 return opOK;
2059
2060 // The algorithm here is quite simple: we add 2^(p-1), where p is the
2061 // precision of our format, and then subtract it back off again. The choice
2062 // of rounding modes for the addition/subtraction determines the rounding mode
2063 // for our integral rounding as well.
2064 // NOTE: When the input value is negative, we do subtraction followed by
2065 // addition instead.
2066 APInt IntegerConstant(NextPowerOf2(semanticsPrecision(*semantics)), 1);
2067 IntegerConstant <<= semanticsPrecision(*semantics)-1;
2068 IEEEFloat MagicConstant(*semantics);
2069 fs = MagicConstant.convertFromAPInt(IntegerConstant, false,
2070 rmNearestTiesToEven);
2071 assert(fs == opOK)((void)0);
2072 MagicConstant.sign = sign;
2073
2074 // Preserve the input sign so that we can handle the case of zero result
2075 // correctly.
2076 bool inputSign = isNegative();
2077
2078 fs = add(MagicConstant, rounding_mode);
2079
2080 // Current value and 'MagicConstant' are both integers, so the result of the
2081 // subtraction is always exact according to Sterbenz' lemma.
2082 subtract(MagicConstant, rounding_mode);
2083
2084 // Restore the input sign.
2085 if (inputSign != isNegative())
2086 changeSign();
2087
2088 return fs;
2089}
2090
2091
2092/* Comparison requires normalized numbers. */
2093IEEEFloat::cmpResult IEEEFloat::compare(const IEEEFloat &rhs) const {
2094 cmpResult result;
2095
2096 assert(semantics == rhs.semantics)((void)0);
2097
2098 switch (PackCategoriesIntoKey(category, rhs.category)((category) * 4 + (rhs.category))) {
2099 default:
2100 llvm_unreachable(nullptr)__builtin_unreachable();
2101
2102 case PackCategoriesIntoKey(fcNaN, fcZero)((fcNaN) * 4 + (fcZero)):
2103 case PackCategoriesIntoKey(fcNaN, fcNormal)((fcNaN) * 4 + (fcNormal)):
2104 case PackCategoriesIntoKey(fcNaN, fcInfinity)((fcNaN) * 4 + (fcInfinity)):
2105 case PackCategoriesIntoKey(fcNaN, fcNaN)((fcNaN) * 4 + (fcNaN)):
2106 case PackCategoriesIntoKey(fcZero, fcNaN)((fcZero) * 4 + (fcNaN)):
2107 case PackCategoriesIntoKey(fcNormal, fcNaN)((fcNormal) * 4 + (fcNaN)):
2108 case PackCategoriesIntoKey(fcInfinity, fcNaN)((fcInfinity) * 4 + (fcNaN)):
2109 return cmpUnordered;
2110
2111 case PackCategoriesIntoKey(fcInfinity, fcNormal)((fcInfinity) * 4 + (fcNormal)):
2112 case PackCategoriesIntoKey(fcInfinity, fcZero)((fcInfinity) * 4 + (fcZero)):
2113 case PackCategoriesIntoKey(fcNormal, fcZero)((fcNormal) * 4 + (fcZero)):
2114 if (sign)
2115 return cmpLessThan;
2116 else
2117 return cmpGreaterThan;
2118
2119 case PackCategoriesIntoKey(fcNormal, fcInfinity)((fcNormal) * 4 + (fcInfinity)):
2120 case PackCategoriesIntoKey(fcZero, fcInfinity)((fcZero) * 4 + (fcInfinity)):
2121 case PackCategoriesIntoKey(fcZero, fcNormal)((fcZero) * 4 + (fcNormal)):
2122 if (rhs.sign)
2123 return cmpGreaterThan;
2124 else
2125 return cmpLessThan;
2126
2127 case PackCategoriesIntoKey(fcInfinity, fcInfinity)((fcInfinity) * 4 + (fcInfinity)):
2128 if (sign == rhs.sign)
2129 return cmpEqual;
2130 else if (sign)
2131 return cmpLessThan;
2132 else
2133 return cmpGreaterThan;
2134
2135 case PackCategoriesIntoKey(fcZero, fcZero)((fcZero) * 4 + (fcZero)):
2136 return cmpEqual;
2137
2138 case PackCategoriesIntoKey(fcNormal, fcNormal)((fcNormal) * 4 + (fcNormal)):
2139 break;
2140 }
2141
2142 /* Two normal numbers. Do they have the same sign? */
2143 if (sign != rhs.sign) {
2144 if (sign)
2145 result = cmpLessThan;
2146 else
2147 result = cmpGreaterThan;
2148 } else {
2149 /* Compare absolute values; invert result if negative. */
2150 result = compareAbsoluteValue(rhs);
2151
2152 if (sign) {
2153 if (result == cmpLessThan)
2154 result = cmpGreaterThan;
2155 else if (result == cmpGreaterThan)
2156 result = cmpLessThan;
2157 }
2158 }
2159
2160 return result;
2161}
2162
2163/// IEEEFloat::convert - convert a value of one floating point type to another.
2164/// The return value corresponds to the IEEE754 exceptions. *losesInfo
2165/// records whether the transformation lost information, i.e. whether
2166/// converting the result back to the original type will produce the
2167/// original value (this is almost the same as return value==fsOK, but there
2168/// are edge cases where this is not so).
2169
2170IEEEFloat::opStatus IEEEFloat::convert(const fltSemantics &toSemantics,
2171 roundingMode rounding_mode,
2172 bool *losesInfo) {
2173 lostFraction lostFraction;
2174 unsigned int newPartCount, oldPartCount;
2175 opStatus fs;
2176 int shift;
2177 const fltSemantics &fromSemantics = *semantics;
2178
2179 lostFraction = lfExactlyZero;
2180 newPartCount = partCountForBits(toSemantics.precision + 1);
2181 oldPartCount = partCount();
2182 shift = toSemantics.precision - fromSemantics.precision;
2183
2184 bool X86SpecialNan = false;
2185 if (&fromSemantics == &semX87DoubleExtended &&
19
←
Assuming the condition is false
→
2186 &toSemantics != &semX87DoubleExtended && category == fcNaN &&
2187 (!(*significandParts() & 0x8000000000000000ULL) ||
2188 !(*significandParts() & 0x4000000000000000ULL))) {
2189 // x86 has some unusual NaNs which cannot be represented in any other
2190 // format; note them here.
2191 X86SpecialNan = true;
2192 }
2193
2194 // If this is a truncation of a denormal number, and the target semantics
2195 // has larger exponent range than the source semantics (this can happen
2196 // when truncating from PowerPC double-double to double format), the
2197 // right shift could lose result mantissa bits. Adjust exponent instead
2198 // of performing excessive shift.
2199 if (shift
19.1
'shift' is >= 0
19.1
'shift' is >= 0
 < 0 && isFiniteNonZero()) {
2200 int exponentChange = significandMSB() + 1 - fromSemantics.precision;
2201 if (exponent + exponentChange < toSemantics.minExponent)
2202 exponentChange = toSemantics.minExponent - exponent;
2203 if (exponentChange < shift)
2204 exponentChange = shift;
2205 if (exponentChange < 0) {
2206 shift -= exponentChange;
2207 exponent += exponentChange;
2208 }
2209 }
2210
2211 // If this is a truncation, perform the shift before we narrow the storage.
2212 if (shift
19.2
'shift' is >= 0
19.2
'shift' is >= 0
 < 0 && (isFiniteNonZero() || category==fcNaN))
2213 lostFraction = shiftRight(significandParts(), oldPartCount, -shift);
2214
2215 // Fix the storage so it can hold to new value.
2216 if (newPartCount > oldPartCount) {
20
←
Assuming 'newPartCount' is <= 'oldPartCount'
→
21
←
Taking false branch
→
2217 // The new type requires more storage; make it available.
2218 integerPart *newParts;
2219 newParts = new integerPart[newPartCount];
2220 APInt::tcSet(newParts, 0, newPartCount);
2221 if (isFiniteNonZero() || category==fcNaN)
2222 APInt::tcAssign(newParts, significandParts(), oldPartCount);
2223 freeSignificand();
2224 significand.parts = newParts;
2225 } else if (newPartCount == 1 && oldPartCount != 1) {
22
←
Assuming 'newPartCount' is equal to 1
→
23
←
Assuming 'oldPartCount' is not equal to 1
→
24
←
Taking true branch
→
2226 // Switch to built-in storage for a single part.
2227 integerPart newPart = 0;
2228 if (isFiniteNonZero() || category==fcNaN)
25
←
Calling 'IEEEFloat::isFiniteNonZero'
→
28
←
Returning from 'IEEEFloat::isFiniteNonZero'
→
2229 newPart = significandParts()[0];
29
←
Assigned value is garbage or undefined
2230 freeSignificand();
2231 significand.part = newPart;
2232 }
2233
2234 // Now that we have the right storage, switch the semantics.
2235 semantics = &toSemantics;
2236
2237 // If this is an extension, perform the shift now that the storage is
2238 // available.
2239 if (shift > 0 && (isFiniteNonZero() || category==fcNaN))
2240 APInt::tcShiftLeft(significandParts(), newPartCount, shift);
2241
2242 if (isFiniteNonZero()) {
2243 fs = normalize(rounding_mode, lostFraction);
2244 *losesInfo = (fs != opOK);
2245 } else if (category == fcNaN) {
2246 *losesInfo = lostFraction != lfExactlyZero || X86SpecialNan;
2247
2248 // For x87 extended precision, we want to make a NaN, not a special NaN if
2249 // the input wasn't special either.
2250 if (!X86SpecialNan && semantics == &semX87DoubleExtended)
2251 APInt::tcSetBit(significandParts(), semantics->precision - 1);
2252
2253 // Convert of sNaN creates qNaN and raises an exception (invalid op).
2254 // This also guarantees that a sNaN does not become Inf on a truncation
2255 // that loses all payload bits.
2256 if (isSignaling()) {
2257 makeQuiet();
2258 fs = opInvalidOp;
2259 } else {
2260 fs = opOK;
2261 }
2262 } else {
2263 *losesInfo = false;
2264 fs = opOK;
2265 }
2266
2267 return fs;
2268}
2269
2270/* Convert a floating point number to an integer according to the
2271 rounding mode. If the rounded integer value is out of range this
2272 returns an invalid operation exception and the contents of the
2273 destination parts are unspecified. If the rounded value is in
2274 range but the floating point number is not the exact integer, the C
2275 standard doesn't require an inexact exception to be raised. IEEE
2276 854 does require it so we do that.
2277
2278 Note that for conversions to integer type the C standard requires
2279 round-to-zero to always be used. */
2280IEEEFloat::opStatus IEEEFloat::convertToSignExtendedInteger(
2281 MutableArrayRef<integerPart> parts, unsigned int width, bool isSigned,
2282 roundingMode rounding_mode, bool *isExact) const {
2283 lostFraction lost_fraction;
2284 const integerPart *src;
2285 unsigned int dstPartsCount, truncatedBits;
2286
2287 *isExact = false;
2288
2289 /* Handle the three special cases first. */
2290 if (category == fcInfinity || category == fcNaN)
2291 return opInvalidOp;
2292
2293 dstPartsCount = partCountForBits(width);
2294 assert(dstPartsCount <= parts.size() && "Integer too big")((void)0);
2295
2296 if (category == fcZero) {
2297 APInt::tcSet(parts.data(), 0, dstPartsCount);
2298 // Negative zero can't be represented as an int.
2299 *isExact = !sign;
2300 return opOK;
2301 }
2302
2303 src = significandParts();
2304
2305 /* Step 1: place our absolute value, with any fraction truncated, in
2306 the destination. */
2307 if (exponent < 0) {
2308 /* Our absolute value is less than one; truncate everything. */
2309 APInt::tcSet(parts.data(), 0, dstPartsCount);
2310 /* For exponent -1 the integer bit represents .5, look at that.
2311 For smaller exponents leftmost truncated bit is 0. */
2312 truncatedBits = semantics->precision -1U - exponent;
2313 } else {
2314 /* We want the most significant (exponent + 1) bits; the rest are
2315 truncated. */
2316 unsigned int bits = exponent + 1U;
2317
2318 /* Hopelessly large in magnitude? */
2319 if (bits > width)
2320 return opInvalidOp;
2321
2322 if (bits < semantics->precision) {
2323 /* We truncate (semantics->precision - bits) bits. */
2324 truncatedBits = semantics->precision - bits;
2325 APInt::tcExtract(parts.data(), dstPartsCount, src, bits, truncatedBits);
2326 } else {
2327 /* We want at least as many bits as are available. */
2328 APInt::tcExtract(parts.data(), dstPartsCount, src, semantics->precision,
2329 0);
2330 APInt::tcShiftLeft(parts.data(), dstPartsCount,
2331 bits - semantics->precision);
2332 truncatedBits = 0;
2333 }
2334 }
2335
2336 /* Step 2: work out any lost fraction, and increment the absolute
2337 value if we would round away from zero. */
2338 if (truncatedBits) {
2339 lost_fraction = lostFractionThroughTruncation(src, partCount(),
2340 truncatedBits);
2341 if (lost_fraction != lfExactlyZero &&
2342 roundAwayFromZero(rounding_mode, lost_fraction, truncatedBits)) {
2343 if (APInt::tcIncrement(parts.data(), dstPartsCount))
2344 return opInvalidOp; /* Overflow. */
2345 }
2346 } else {
2347 lost_fraction = lfExactlyZero;
2348 }
2349
2350 /* Step 3: check if we fit in the destination. */
2351 unsigned int omsb = APInt::tcMSB(parts.data(), dstPartsCount) + 1;
2352
2353 if (sign) {
2354 if (!isSigned) {
2355 /* Negative numbers cannot be represented as unsigned. */
2356 if (omsb != 0)
2357 return opInvalidOp;
2358 } else {
2359 /* It takes omsb bits to represent the unsigned integer value.
2360 We lose a bit for the sign, but care is needed as the
2361 maximally negative integer is a special case. */
2362 if (omsb == width &&
2363 APInt::tcLSB(parts.data(), dstPartsCount) + 1 != omsb)
2364 return opInvalidOp;
2365
2366 /* This case can happen because of rounding. */
2367 if (omsb > width)
2368 return opInvalidOp;
2369 }
2370
2371 APInt::tcNegate (parts.data(), dstPartsCount);
2372 } else {
2373 if (omsb >= width + !isSigned)
2374 return opInvalidOp;
2375 }
2376
2377 if (lost_fraction == lfExactlyZero) {
2378 *isExact = true;
2379 return opOK;
2380 } else
2381 return opInexact;
2382}
2383
2384/* Same as convertToSignExtendedInteger, except we provide
2385 deterministic values in case of an invalid operation exception,
2386 namely zero for NaNs and the minimal or maximal value respectively
2387 for underflow or overflow.
2388 The *isExact output tells whether the result is exact, in the sense
2389 that converting it back to the original floating point type produces
2390 the original value. This is almost equivalent to result==opOK,
2391 except for negative zeroes.
2392*/
2393IEEEFloat::opStatus
2394IEEEFloat::convertToInteger(MutableArrayRef<integerPart> parts,
2395 unsigned int width, bool isSigned,
2396 roundingMode rounding_mode, bool *isExact) const {
2397 opStatus fs;
2398
2399 fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode,
2400 isExact);
2401
2402 if (fs == opInvalidOp) {
2403 unsigned int bits, dstPartsCount;
2404
2405 dstPartsCount = partCountForBits(width);
2406 assert(dstPartsCount <= parts.size() && "Integer too big")((void)0);
2407
2408 if (category == fcNaN)
2409 bits = 0;
2410 else if (sign)
2411 bits = isSigned;
2412 else
2413 bits = width - isSigned;
2414
2415 APInt::tcSetLeastSignificantBits(parts.data(), dstPartsCount, bits);
2416 if (sign && isSigned)
2417 APInt::tcShiftLeft(parts.data(), dstPartsCount, width - 1);
2418 }
2419
2420 return fs;
2421}
2422
2423/* Convert an unsigned integer SRC to a floating point number,
2424 rounding according to ROUNDING_MODE. The sign of the floating
2425 point number is not modified. */
2426IEEEFloat::opStatus IEEEFloat::convertFromUnsignedParts(
2427 const integerPart *src, unsigned int srcCount, roundingMode rounding_mode) {
2428 unsigned int omsb, precision, dstCount;
2429 integerPart *dst;
2430 lostFraction lost_fraction;
2431
2432 category = fcNormal;
2433 omsb = APInt::tcMSB(src, srcCount) + 1;
2434 dst = significandParts();
2435 dstCount = partCount();
2436 precision = semantics->precision;
2437
2438 /* We want the most significant PRECISION bits of SRC. There may not
2439 be that many; extract what we can. */
2440 if (precision <= omsb) {
2441 exponent = omsb - 1;
2442 lost_fraction = lostFractionThroughTruncation(src, srcCount,
2443 omsb - precision);
2444 APInt::tcExtract(dst, dstCount, src, precision, omsb - precision);
2445 } else {
2446 exponent = precision - 1;
2447 lost_fraction = lfExactlyZero;
2448 APInt::tcExtract(dst, dstCount, src, omsb, 0);
2449 }
2450
2451 return normalize(rounding_mode, lost_fraction);
2452}
2453
2454IEEEFloat::opStatus IEEEFloat::convertFromAPInt(const APInt &Val, bool isSigned,
2455 roundingMode rounding_mode) {
2456 unsigned int partCount = Val.getNumWords();
2457 APInt api = Val;
2458
2459 sign = false;
2460 if (isSigned && api.isNegative()) {
2461 sign = true;
2462 api = -api;
2463 }
2464
2465 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
2466}
2467
2468/* Convert a two's complement integer SRC to a floating point number,
2469 rounding according to ROUNDING_MODE. ISSIGNED is true if the
2470 integer is signed, in which case it must be sign-extended. */
2471IEEEFloat::opStatus
2472IEEEFloat::convertFromSignExtendedInteger(const integerPart *src,
2473 unsigned int srcCount, bool isSigned,
2474 roundingMode rounding_mode) {
2475 opStatus status;
2476
2477 if (isSigned &&
2478 APInt::tcExtractBit(src, srcCount * integerPartWidth - 1)) {
2479 integerPart *copy;
2480
2481 /* If we're signed and negative negate a copy. */
2482 sign = true;
2483 copy = new integerPart[srcCount];
2484 APInt::tcAssign(copy, src, srcCount);
2485 APInt::tcNegate(copy, srcCount);
2486 status = convertFromUnsignedParts(copy, srcCount, rounding_mode);
2487 delete [] copy;
2488 } else {
2489 sign = false;
2490 status = convertFromUnsignedParts(src, srcCount, rounding_mode);
2491 }
2492
2493 return status;
2494}
2495
2496/* FIXME: should this just take a const APInt reference? */
2497IEEEFloat::opStatus
2498IEEEFloat::convertFromZeroExtendedInteger(const integerPart *parts,
2499 unsigned int width, bool isSigned,
2500 roundingMode rounding_mode) {
2501 unsigned int partCount = partCountForBits(width);
2502 APInt api = APInt(width, makeArrayRef(parts, partCount));
2503
2504 sign = false;
2505 if (isSigned && APInt::tcExtractBit(parts, width - 1)) {
2506 sign = true;
2507 api = -api;
2508 }
2509
2510 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
2511}
2512
2513Expected<IEEEFloat::opStatus>
2514IEEEFloat::convertFromHexadecimalString(StringRef s,
2515 roundingMode rounding_mode) {
2516 lostFraction lost_fraction = lfExactlyZero;
2517
2518 category = fcNormal;
2519 zeroSignificand();
2520 exponent = 0;
2521
2522 integerPart *significand = significandParts();
2523 unsigned partsCount = partCount();
2524 unsigned bitPos = partsCount * integerPartWidth;
2525 bool computedTrailingFraction = false;
2526
2527 // Skip leading zeroes and any (hexa)decimal point.
2528 StringRef::iterator begin = s.begin();
2529 StringRef::iterator end = s.end();
2530 StringRef::iterator dot;
2531 auto PtrOrErr = skipLeadingZeroesAndAnyDot(begin, end, &dot);
2532 if (!PtrOrErr)
2533 return PtrOrErr.takeError();
2534 StringRef::iterator p = *PtrOrErr;
2535 StringRef::iterator firstSignificantDigit = p;
2536
2537 while (p != end) {
2538 integerPart hex_value;
2539
2540 if (*p == '.') {
2541 if (dot != end)
2542 return createError("String contains multiple dots");
2543 dot = p++;
2544 continue;
2545 }
2546
2547 hex_value = hexDigitValue(*p);
2548 if (hex_value == -1U)
2549 break;
2550
2551 p++;
2552
2553 // Store the number while we have space.
2554 if (bitPos) {
2555 bitPos -= 4;
2556 hex_value <<= bitPos % integerPartWidth;
2557 significand[bitPos / integerPartWidth] |= hex_value;
2558 } else if (!computedTrailingFraction) {
2559 auto FractOrErr = trailingHexadecimalFraction(p, end, hex_value);
2560 if (!FractOrErr)
2561 return FractOrErr.takeError();
2562 lost_fraction = *FractOrErr;
2563 computedTrailingFraction = true;
2564 }
2565 }
2566
2567 /* Hex floats require an exponent but not a hexadecimal point. */
2568 if (p == end)
2569 return createError("Hex strings require an exponent");
2570 if (*p != 'p' && *p != 'P')
2571 return createError("Invalid character in significand");
2572 if (p == begin)
2573 return createError("Significand has no digits");
2574 if (dot != end && p - begin == 1)
2575 return createError("Significand has no digits");
2576
2577 /* Ignore the exponent if we are zero. */
2578 if (p != firstSignificantDigit) {
2579 int expAdjustment;
2580
2581 /* Implicit hexadecimal point? */
2582 if (dot == end)
2583 dot = p;
2584
2585 /* Calculate the exponent adjustment implicit in the number of
2586 significant digits. */
2587 expAdjustment = static_cast<int>(dot - firstSignificantDigit);
2588 if (expAdjustment < 0)
2589 expAdjustment++;
2590 expAdjustment = expAdjustment * 4 - 1;
2591
2592 /* Adjust for writing the significand starting at the most
2593 significant nibble. */
2594 expAdjustment += semantics->precision;
2595 expAdjustment -= partsCount * integerPartWidth;
2596
2597 /* Adjust for the given exponent. */
2598 auto ExpOrErr = totalExponent(p + 1, end, expAdjustment);
2599 if (!ExpOrErr)
2600 return ExpOrErr.takeError();
2601 exponent = *ExpOrErr;
2602 }
2603
2604 return normalize(rounding_mode, lost_fraction);
2605}
2606
2607IEEEFloat::opStatus
2608IEEEFloat::roundSignificandWithExponent(const integerPart *decSigParts,
2609 unsigned sigPartCount, int exp,
2610 roundingMode rounding_mode) {
2611 unsigned int parts, pow5PartCount;
2612 fltSemantics calcSemantics = { 32767, -32767, 0, 0 };
2613 integerPart pow5Parts[maxPowerOfFiveParts];
2614 bool isNearest;
2615
2616 isNearest = (rounding_mode == rmNearestTiesToEven ||
2617 rounding_mode == rmNearestTiesToAway);
2618
2619 parts = partCountForBits(semantics->precision + 11);
2620
2621 /* Calculate pow(5, abs(exp)). */
2622 pow5PartCount = powerOf5(pow5Parts, exp >= 0 ? exp: -exp);
2623
2624 for (;; parts *= 2) {
2625 opStatus sigStatus, powStatus;
2626 unsigned int excessPrecision, truncatedBits;
2627
2628 calcSemantics.precision = parts * integerPartWidth - 1;
2629 excessPrecision = calcSemantics.precision - semantics->precision;
2630 truncatedBits = excessPrecision;
2631
2632 IEEEFloat decSig(calcSemantics, uninitialized);
2633 decSig.makeZero(sign);
2634 IEEEFloat pow5(calcSemantics);
2635
2636 sigStatus = decSig.convertFromUnsignedParts(decSigParts, sigPartCount,
2637 rmNearestTiesToEven);
2638 powStatus = pow5.convertFromUnsignedParts(pow5Parts, pow5PartCount,
2639 rmNearestTiesToEven);
2640 /* Add exp, as 10^n = 5^n * 2^n. */
2641 decSig.exponent += exp;
2642
2643 lostFraction calcLostFraction;
2644 integerPart HUerr, HUdistance;
2645 unsigned int powHUerr;
2646
2647 if (exp >= 0) {
2648 /* multiplySignificand leaves the precision-th bit set to 1. */
2649 calcLostFraction = decSig.multiplySignificand(pow5);
2650 powHUerr = powStatus != opOK;
2651 } else {
2652 calcLostFraction = decSig.divideSignificand(pow5);
2653 /* Denormal numbers have less precision. */
2654 if (decSig.exponent < semantics->minExponent) {
2655 excessPrecision += (semantics->minExponent - decSig.exponent);
2656 truncatedBits = excessPrecision;
2657 if (excessPrecision > calcSemantics.precision)
2658 excessPrecision = calcSemantics.precision;
2659 }
2660 /* Extra half-ulp lost in reciprocal of exponent. */
2661 powHUerr = (powStatus == opOK && calcLostFraction == lfExactlyZero) ? 0:2;
2662 }
2663
2664 /* Both multiplySignificand and divideSignificand return the
2665 result with the integer bit set. */
2666 assert(APInt::tcExtractBit((void)0)
2667 (decSig.significandParts(), calcSemantics.precision - 1) == 1)((void)0);
2668
2669 HUerr = HUerrBound(calcLostFraction != lfExactlyZero, sigStatus != opOK,
2670 powHUerr);
2671 HUdistance = 2 * ulpsFromBoundary(decSig.significandParts(),
2672 excessPrecision, isNearest);
2673
2674 /* Are we guaranteed to round correctly if we truncate? */
2675 if (HUdistance >= HUerr) {
2676 APInt::tcExtract(significandParts(), partCount(), decSig.significandParts(),
2677 calcSemantics.precision - excessPrecision,
2678 excessPrecision);
2679 /* Take the exponent of decSig. If we tcExtract-ed less bits
2680 above we must adjust our exponent to compensate for the
2681 implicit right shift. */
2682 exponent = (decSig.exponent + semantics->precision
2683 - (calcSemantics.precision - excessPrecision));
2684 calcLostFraction = lostFractionThroughTruncation(decSig.significandParts(),
2685 decSig.partCount(),
2686 truncatedBits);
2687 return normalize(rounding_mode, calcLostFraction);
2688 }
2689 }
2690}
2691
2692Expected<IEEEFloat::opStatus>
2693IEEEFloat::convertFromDecimalString(StringRef str, roundingMode rounding_mode) {
2694 decimalInfo D;
2695 opStatus fs;
2696
2697 /* Scan the text. */
2698 StringRef::iterator p = str.begin();
2699 if (Error Err = interpretDecimal(p, str.end(), &D))
2700 return std::move(Err);
2701
2702 /* Handle the quick cases. First the case of no significant digits,
2703 i.e. zero, and then exponents that are obviously too large or too
2704 small. Writing L for log 10 / log 2, a number d.ddddd*10^exp
2705 definitely overflows if
2706
2707 (exp - 1) * L >= maxExponent
2708
2709 and definitely underflows to zero where
2710
2711 (exp + 1) * L <= minExponent - precision
2712
2713 With integer arithmetic the tightest bounds for L are
2714
2715 93/28 < L < 196/59 [ numerator <= 256 ]
2716 42039/12655 < L < 28738/8651 [ numerator <= 65536 ]
2717 */
2718
2719 // Test if we have a zero number allowing for strings with no null terminators
2720 // and zero decimals with non-zero exponents.
2721 //
2722 // We computed firstSigDigit by ignoring all zeros and dots. Thus if
2723 // D->firstSigDigit equals str.end(), every digit must be a zero and there can
2724 // be at most one dot. On the other hand, if we have a zero with a non-zero
2725 // exponent, then we know that D.firstSigDigit will be non-numeric.
2726 if (D.firstSigDigit == str.end() || decDigitValue(*D.firstSigDigit) >= 10U) {
2727 category = fcZero;
2728 fs = opOK;
2729
2730 /* Check whether the normalized exponent is high enough to overflow
2731 max during the log-rebasing in the max-exponent check below. */
2732 } else if (D.normalizedExponent - 1 > INT_MAX2147483647 / 42039) {
2733 fs = handleOverflow(rounding_mode);
2734
2735 /* If it wasn't, then it also wasn't high enough to overflow max
2736 during the log-rebasing in the min-exponent check. Check that it
2737 won't overflow min in either check, then perform the min-exponent
2738 check. */
2739 } else if (D.normalizedExponent - 1 < INT_MIN(-2147483647 -1) / 42039 ||
2740 (D.normalizedExponent + 1) * 28738 <=
2741 8651 * (semantics->minExponent - (int) semantics->precision)) {
2742 /* Underflow to zero and round. */
2743 category = fcNormal;
2744 zeroSignificand();
2745 fs = normalize(rounding_mode, lfLessThanHalf);
2746
2747 /* We can finally safely perform the max-exponent check. */
2748 } else if ((D.normalizedExponent - 1) * 42039
2749 >= 12655 * semantics->maxExponent) {
2750 /* Overflow and round. */
2751 fs = handleOverflow(rounding_mode);
2752 } else {
2753 integerPart *decSignificand;
2754 unsigned int partCount;
2755
2756 /* A tight upper bound on number of bits required to hold an
2757 N-digit decimal integer is N * 196 / 59. Allocate enough space
2758 to hold the full significand, and an extra part required by
2759 tcMultiplyPart. */
2760 partCount = static_cast<unsigned int>(D.lastSigDigit - D.firstSigDigit) + 1;
2761 partCount = partCountForBits(1 + 196 * partCount / 59);
2762 decSignificand = new integerPart[partCount + 1];
2763 partCount = 0;
2764
2765 /* Convert to binary efficiently - we do almost all multiplication
2766 in an integerPart. When this would overflow do we do a single
2767 bignum multiplication, and then revert again to multiplication
2768 in an integerPart. */
2769 do {
2770 integerPart decValue, val, multiplier;
2771
2772 val = 0;
2773 multiplier = 1;
2774
2775 do {
2776 if (*p == '.') {
2777 p++;
2778 if (p == str.end()) {
2779 break;
2780 }
2781 }
2782 decValue = decDigitValue(*p++);
2783 if (decValue >= 10U) {
2784 delete[] decSignificand;
2785 return createError("Invalid character in significand");
2786 }
2787 multiplier *= 10;
2788 val = val * 10 + decValue;
2789 /* The maximum number that can be multiplied by ten with any
2790 digit added without overflowing an integerPart. */
2791 } while (p <= D.lastSigDigit && multiplier <= (~ (integerPart) 0 - 9) / 10);
2792
2793 /* Multiply out the current part. */
2794 APInt::tcMultiplyPart(decSignificand, decSignificand, multiplier, val,
2795 partCount, partCount + 1, false);
2796
2797 /* If we used another part (likely but not guaranteed), increase
2798 the count. */
2799 if (decSignificand[partCount])
2800 partCount++;
2801 } while (p <= D.lastSigDigit);
2802
2803 category = fcNormal;
2804 fs = roundSignificandWithExponent(decSignificand, partCount,
2805 D.exponent, rounding_mode);
2806
2807 delete [] decSignificand;
2808 }
2809
2810 return fs;
2811}
2812
2813bool IEEEFloat::convertFromStringSpecials(StringRef str) {
2814 const size_t MIN_NAME_SIZE = 3;
2815
2816 if (str.size() < MIN_NAME_SIZE)
2817 return false;
2818
2819 if (str.equals("inf") || str.equals("INFINITY") || str.equals("+Inf")) {
2820 makeInf(false);
2821 return true;
2822 }
2823
2824 bool IsNegative = str.front() == '-';
2825 if (IsNegative) {
2826 str = str.drop_front();
2827 if (str.size() < MIN_NAME_SIZE)
2828 return false;
2829
2830 if (str.equals("inf") || str.equals("INFINITY") || str.equals("Inf")) {
2831 makeInf(true);
2832 return true;
2833 }
2834 }
2835
2836 // If we have a 's' (or 'S') prefix, then this is a Signaling NaN.
2837 bool IsSignaling = str.front() == 's' || str.front() == 'S';
2838 if (IsSignaling) {
2839 str = str.drop_front();
2840 if (str.size() < MIN_NAME_SIZE)
2841 return false;
2842 }
2843
2844 if (str.startswith("nan") || str.startswith("NaN")) {
2845 str = str.drop_front(3);
2846
2847 // A NaN without payload.
2848 if (str.empty()) {
2849 makeNaN(IsSignaling, IsNegative);
2850 return true;
2851 }
2852
2853 // Allow the payload to be inside parentheses.
2854 if (str.front() == '(') {
2855 // Parentheses should be balanced (and not empty).
2856 if (str.size() <= 2 || str.back() != ')')
2857 return false;
2858
2859 str = str.slice(1, str.size() - 1);
2860 }
2861
2862 // Determine the payload number's radix.
2863 unsigned Radix = 10;
2864 if (str[0] == '0') {
2865 if (str.size() > 1 && tolower(str[1]) == 'x') {
2866 str = str.drop_front(2);
2867 Radix = 16;
2868 } else
2869 Radix = 8;
2870 }
2871
2872 // Parse the payload and make the NaN.
2873 APInt Payload;
2874 if (!str.getAsInteger(Radix, Payload)) {
2875 makeNaN(IsSignaling, IsNegative, &Payload);
2876 return true;
2877 }
2878 }
2879
2880 return false;
2881}
2882
2883Expected<IEEEFloat::opStatus>
2884IEEEFloat::convertFromString(StringRef str, roundingMode rounding_mode) {
2885 if (str.empty())
2886 return createError("Invalid string length");
2887
2888 // Handle special cases.
2889 if (convertFromStringSpecials(str))
2890 return opOK;
2891
2892 /* Handle a leading minus sign. */
2893 StringRef::iterator p = str.begin();
2894 size_t slen = str.size();
2895 sign = *p == '-' ? 1 : 0;
2896 if (*p == '-' || *p == '+') {
2897 p++;
2898 slen--;
2899 if (!slen)
2900 return createError("String has no digits");
2901 }
2902
2903 if (slen >= 2 && p[0] == '0' && (p[1] == 'x' || p[1] == 'X')) {
2904 if (slen == 2)
2905 return createError("Invalid string");
2906 return convertFromHexadecimalString(StringRef(p + 2, slen - 2),
2907 rounding_mode);
2908 }
2909
2910 return convertFromDecimalString(StringRef(p, slen), rounding_mode);
2911}
2912
2913/* Write out a hexadecimal representation of the floating point value
2914 to DST, which must be of sufficient size, in the C99 form
2915 [-]0xh.hhhhp[+-]d. Return the number of characters written,
2916 excluding the terminating NUL.
2917
2918 If UPPERCASE, the output is in upper case, otherwise in lower case.
2919
2920 HEXDIGITS digits appear altogether, rounding the value if
2921 necessary. If HEXDIGITS is 0, the minimal precision to display the
2922 number precisely is used instead. If nothing would appear after
2923 the decimal point it is suppressed.
2924
2925 The decimal exponent is always printed and has at least one digit.
2926 Zero values display an exponent of zero. Infinities and NaNs
2927 appear as "infinity" or "nan" respectively.
2928
2929 The above rules are as specified by C99. There is ambiguity about
2930 what the leading hexadecimal digit should be. This implementation
2931 uses whatever is necessary so that the exponent is displayed as
2932 stored. This implies the exponent will fall within the IEEE format
2933 range, and the leading hexadecimal digit will be 0 (for denormals),
2934 1 (normal numbers) or 2 (normal numbers rounded-away-from-zero with
2935 any other digits zero).
2936*/
2937unsigned int IEEEFloat::convertToHexString(char *dst, unsigned int hexDigits,
2938 bool upperCase,
2939 roundingMode rounding_mode) const {
2940 char *p;
2941
2942 p = dst;
2943 if (sign)
2944 *dst++ = '-';
2945
2946 switch (category) {
2947 case fcInfinity:
2948 memcpy (dst, upperCase ? infinityU: infinityL, sizeof infinityU - 1);
2949 dst += sizeof infinityL - 1;
2950 break;
2951
2952 case fcNaN:
2953 memcpy (dst, upperCase ? NaNU: NaNL, sizeof NaNU - 1);
2954 dst += sizeof NaNU - 1;
2955 break;
2956
2957 case fcZero:
2958 *dst++ = '0';
2959 *dst++ = upperCase ? 'X': 'x';
2960 *dst++ = '0';
2961 if (hexDigits > 1) {
2962 *dst++ = '.';
2963 memset (dst, '0', hexDigits - 1);
2964 dst += hexDigits - 1;
2965 }
2966 *dst++ = upperCase ? 'P': 'p';
2967 *dst++ = '0';
2968 break;
2969
2970 case fcNormal:
2971 dst = convertNormalToHexString (dst, hexDigits, upperCase, rounding_mode);
2972 break;
2973 }
2974
2975 *dst = 0;
2976
2977 return static_cast<unsigned int>(dst - p);
2978}
2979
2980/* Does the hard work of outputting the correctly rounded hexadecimal
2981 form of a normal floating point number with the specified number of
2982 hexadecimal digits. If HEXDIGITS is zero the minimum number of
2983 digits necessary to print the value precisely is output. */
2984char *IEEEFloat::convertNormalToHexString(char *dst, unsigned int hexDigits,
2985 bool upperCase,
2986 roundingMode rounding_mode) const {
2987 unsigned int count, valueBits, shift, partsCount, outputDigits;
2988 const char *hexDigitChars;
2989 const integerPart *significand;
2990 char *p;
2991 bool roundUp;
2992
2993 *dst++ = '0';
2994 *dst++ = upperCase ? 'X': 'x';
2995
2996 roundUp = false;
2997 hexDigitChars = upperCase ? hexDigitsUpper: hexDigitsLower;
2998
2999 significand = significandParts();
3000 partsCount = partCount();
3001
3002 /* +3 because the first digit only uses the single integer bit, so
3003 we have 3 virtual zero most-significant-bits. */
3004 valueBits = semantics->precision + 3;
3005 shift = integerPartWidth - valueBits % integerPartWidth;
3006
3007 /* The natural number of digits required ignoring trailing
3008 insignificant zeroes. */
3009 outputDigits = (valueBits - significandLSB () + 3) / 4;
3010
3011 /* hexDigits of zero means use the required number for the
3012 precision. Otherwise, see if we are truncating. If we are,
3013 find out if we need to round away from zero. */
3014 if (hexDigits) {
3015 if (hexDigits < outputDigits) {
3016 /* We are dropping non-zero bits, so need to check how to round.
3017 "bits" is the number of dropped bits. */
3018 unsigned int bits;
3019 lostFraction fraction;
3020
3021 bits = valueBits - hexDigits * 4;
3022 fraction = lostFractionThroughTruncation (significand, partsCount, bits);
3023 roundUp = roundAwayFromZero(rounding_mode, fraction, bits);
3024 }
3025 outputDigits = hexDigits;
3026 }
3027
3028 /* Write the digits consecutively, and start writing in the location
3029 of the hexadecimal point. We move the most significant digit
3030 left and add the hexadecimal point later. */
3031 p = ++dst;
3032
3033 count = (valueBits + integerPartWidth - 1) / integerPartWidth;
3034
3035 while (outputDigits && count) {
3036 integerPart part;
3037
3038 /* Put the most significant integerPartWidth bits in "part". */
3039 if (--count == partsCount)
3040 part = 0; /* An imaginary higher zero part. */
3041 else
3042 part = significand[count] << shift;
3043
3044 if (count && shift)
3045 part |= significand[count - 1] >> (integerPartWidth - shift);
3046
3047 /* Convert as much of "part" to hexdigits as we can. */
3048 unsigned int curDigits = integerPartWidth / 4;
3049
3050 if (curDigits > outputDigits)
3051 curDigits = outputDigits;
3052 dst += partAsHex (dst, part, curDigits, hexDigitChars);
3053 outputDigits -= curDigits;
3054 }
3055
3056 if (roundUp) {
3057 char *q = dst;
3058
3059 /* Note that hexDigitChars has a trailing '0'. */
3060 do {
3061 q--;
3062 *q = hexDigitChars[hexDigitValue (*q) + 1];
3063 } while (*q == '0');
3064 assert(q >= p)((void)0);
3065 } else {
3066 /* Add trailing zeroes. */
3067 memset (dst, '0', outputDigits);
3068 dst += outputDigits;
3069 }
3070
3071 /* Move the most significant digit to before the point, and if there
3072 is something after the decimal point add it. This must come
3073 after rounding above. */
3074 p[-1] = p[0];
3075 if (dst -1 == p)
3076 dst--;
3077 else
3078 p[0] = '.';
3079
3080 /* Finally output the exponent. */
3081 *dst++ = upperCase ? 'P': 'p';
3082
3083 return writeSignedDecimal (dst, exponent);
3084}
3085
3086hash_code hash_value(const IEEEFloat &Arg) {
3087 if (!Arg.isFiniteNonZero())
3088 return hash_combine((uint8_t)Arg.category,
3089 // NaN has no sign, fix it at zero.
3090 Arg.isNaN() ? (uint8_t)0 : (uint8_t)Arg.sign,
3091 Arg.semantics->precision);
3092
3093 // Normal floats need their exponent and significand hashed.
3094 return hash_combine((uint8_t)Arg.category, (uint8_t)Arg.sign,
3095 Arg.semantics->precision, Arg.exponent,
3096 hash_combine_range(
3097 Arg.significandParts(),
3098 Arg.significandParts() + Arg.partCount()));
3099}
3100
3101// Conversion from APFloat to/from host float/double. It may eventually be
3102// possible to eliminate these and have everybody deal with APFloats, but that
3103// will take a while. This approach will not easily extend to long double.
3104// Current implementation requires integerPartWidth==64, which is correct at
3105// the moment but could be made more general.
3106
3107// Denormals have exponent minExponent in APFloat, but minExponent-1 in
3108// the actual IEEE respresentations. We compensate for that here.
3109
3110APInt IEEEFloat::convertF80LongDoubleAPFloatToAPInt() const {
3111 assert(semantics == (const llvm::fltSemantics*)&semX87DoubleExtended)((void)0);
3112 assert(partCount()==2)((void)0);
3113
3114 uint64_t myexponent, mysignificand;
3115
3116 if (isFiniteNonZero()) {
3117 myexponent = exponent+16383; //bias
3118 mysignificand = significandParts()[0];
3119 if (myexponent==1 && !(mysignificand & 0x8000000000000000ULL))
3120 myexponent = 0; // denormal
3121 } else if (category==fcZero) {
3122 myexponent = 0;
3123 mysignificand = 0;
3124 } else if (category==fcInfinity) {
3125 myexponent = 0x7fff;
3126 mysignificand = 0x8000000000000000ULL;
3127 } else {
3128 assert(category == fcNaN && "Unknown category")((void)0);
3129 myexponent = 0x7fff;
3130 mysignificand = significandParts()[0];
3131 }
3132
3133 uint64_t words[2];
3134 words[0] = mysignificand;
3135 words[1] = ((uint64_t)(sign & 1) << 15) |
3136 (myexponent & 0x7fffLL);
3137 return APInt(80, words);
3138}
3139
3140APInt IEEEFloat::convertPPCDoubleDoubleAPFloatToAPInt() const {
3141 assert(semantics == (const llvm::fltSemantics *)&semPPCDoubleDoubleLegacy)((void)0);
3142 assert(partCount()==2)((void)0);
3143
3144 uint64_t words[2];
3145 opStatus fs;
3146 bool losesInfo;
3147
3148 // Convert number to double. To avoid spurious underflows, we re-
3149 // normalize against the "double" minExponent first, and only *then*
3150 // truncate the mantissa. The result of that second conversion
3151 // may be inexact, but should never underflow.
3152 // Declare fltSemantics before APFloat that uses it (and
3153 // saves pointer to it) to ensure correct destruction order.
3154 fltSemantics extendedSemantics = *semantics;
3155 extendedSemantics.minExponent = semIEEEdouble.minExponent;
3156 IEEEFloat extended(*this);
3157 fs = extended.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
18
←
Calling 'IEEEFloat::convert'
→
3158 assert(fs == opOK && !losesInfo)((void)0);
3159 (void)fs;
3160
3161 IEEEFloat u(extended);
3162 fs = u.convert(semIEEEdouble, rmNearestTiesToEven, &losesInfo);
3163 assert(fs == opOK || fs == opInexact)((void)0);
3164 (void)fs;
3165 words[0] = *u.convertDoubleAPFloatToAPInt().getRawData();
3166
3167 // If conversion was exact or resulted in a special case, we're done;
3168 // just set the second double to zero. Otherwise, re-convert back to
3169 // the extended format and compute the difference. This now should
3170 // convert exactly to double.
3171 if (u.isFiniteNonZero() && losesInfo) {
3172 fs = u.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
3173 assert(fs == opOK && !losesInfo)((void)0);
3174 (void)fs;
3175
3176 IEEEFloat v(extended);
3177 v.subtract(u, rmNearestTiesToEven);
3178 fs = v.convert(semIEEEdouble, rmNearestTiesToEven, &losesInfo);
3179 assert(fs == opOK && !losesInfo)((void)0);
3180 (void)fs;
3181 words[1] = *v.convertDoubleAPFloatToAPInt().getRawData();
3182 } else {
3183 words[1] = 0;
3184 }
3185
3186 return APInt(128, words);
3187}
3188
3189APInt IEEEFloat::convertQuadrupleAPFloatToAPInt() const {
3190 assert(semantics == (const llvm::fltSemantics*)&semIEEEquad)((void)0);
3191 assert(partCount()==2)((void)0);
3192
3193 uint64_t myexponent, mysignificand, mysignificand2;
3194
3195 if (isFiniteNonZero()) {
3196 myexponent = exponent+16383; //bias
3197 mysignificand = significandParts()[0];
3198 mysignificand2 = significandParts()[1];
3199 if (myexponent==1 && !(mysignificand2 & 0x1000000000000LL))
3200 myexponent = 0; // denormal
3201 } else if (category==fcZero) {
3202 myexponent = 0;
3203 mysignificand = mysignificand2 = 0;
3204 } else if (category==fcInfinity) {
3205 myexponent = 0x7fff;
3206 mysignificand = mysignificand2 = 0;
3207 } else {
3208 assert(category == fcNaN && "Unknown category!")((void)0);
3209 myexponent = 0x7fff;
3210 mysignificand = significandParts()[0];
3211 mysignificand2 = significandParts()[1];
3212 }
3213
3214 uint64_t words[2];
3215 words[0] = mysignificand;
3216 words[1] = ((uint64_t)(sign & 1) << 63) |
3217 ((myexponent & 0x7fff) << 48) |
3218 (mysignificand2 & 0xffffffffffffLL);
3219
3220 return APInt(128, words);
3221}
3222
3223APInt IEEEFloat::convertDoubleAPFloatToAPInt() const {
3224 assert(semantics == (const llvm::fltSemantics*)&semIEEEdouble)((void)0);
3225 assert(partCount()==1)((void)0);
3226
3227 uint64_t myexponent, mysignificand;
3228
3229 if (isFiniteNonZero()) {
3230 myexponent = exponent+1023; //bias
3231 mysignificand = *significandParts();
3232 if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
3233 myexponent = 0; // denormal
3234 } else if (category==fcZero) {
3235 myexponent = 0;
3236 mysignificand = 0;
3237 } else if (category==fcInfinity) {
3238 myexponent = 0x7ff;
3239 mysignificand = 0;
3240 } else {
3241 assert(category == fcNaN && "Unknown category!")((void)0);
3242 myexponent = 0x7ff;
3243 mysignificand = *significandParts();
3244 }
3245
3246 return APInt(64, ((((uint64_t)(sign & 1) << 63) |
3247 ((myexponent & 0x7ff) << 52) |
3248 (mysignificand & 0xfffffffffffffLL))));
3249}
3250
3251APInt IEEEFloat::convertFloatAPFloatToAPInt() const {
3252 assert(semantics == (const llvm::fltSemantics*)&semIEEEsingle)((void)0);
3253 assert(partCount()==1)((void)0);
3254
3255 uint32_t myexponent, mysignificand;
3256
3257 if (isFiniteNonZero()) {
3258 myexponent = exponent+127; //bias
3259 mysignificand = (uint32_t)*significandParts();
3260 if (myexponent == 1 && !(mysignificand & 0x800000))
3261 myexponent = 0; // denormal
3262 } else if (category==fcZero) {
3263 myexponent = 0;
3264 mysignificand = 0;
3265 } else if (category==fcInfinity) {
3266 myexponent = 0xff;
3267 mysignificand = 0;
3268 } else {
3269 assert(category == fcNaN && "Unknown category!")((void)0);
3270 myexponent = 0xff;
3271 mysignificand = (uint32_t)*significandParts();
3272 }
3273
3274 return APInt(32, (((sign&1) << 31) | ((myexponent&0xff) << 23) |
3275 (mysignificand & 0x7fffff)));
3276}
3277
3278APInt IEEEFloat::convertBFloatAPFloatToAPInt() const {
3279 assert(semantics == (const llvm::fltSemantics *)&semBFloat)((void)0);
3280 assert(partCount() == 1)((void)0);
3281
3282 uint32_t myexponent, mysignificand;
3283
3284 if (isFiniteNonZero()) {
3285 myexponent = exponent + 127; // bias
3286 mysignificand = (uint32_t)*significandParts();
3287 if (myexponent == 1 && !(mysignificand & 0x80))
3288 myexponent = 0; // denormal
3289 } else if (category == fcZero) {
3290 myexponent = 0;
3291 mysignificand = 0;
3292 } else if (category == fcInfinity) {
3293 myexponent = 0xff;
3294 mysignificand = 0;
3295 } else {
3296 assert(category == fcNaN && "Unknown category!")((void)0);
3297 myexponent = 0xff;
3298 mysignificand = (uint32_t)*significandParts();
3299 }
3300
3301 return APInt(16, (((sign & 1) << 15) | ((myexponent & 0xff) << 7) |
3302 (mysignificand & 0x7f)));
3303}
3304
3305APInt IEEEFloat::convertHalfAPFloatToAPInt() const {
3306 assert(semantics == (const llvm::fltSemantics*)&semIEEEhalf)((void)0);
3307 assert(partCount()==1)((void)0);
3308
3309 uint32_t myexponent, mysignificand;
3310
3311 if (isFiniteNonZero()) {
3312 myexponent = exponent+15; //bias
3313 mysignificand = (uint32_t)*significandParts();
3314 if (myexponent == 1 && !(mysignificand & 0x400))
3315 myexponent = 0; // denormal
3316 } else if (category==fcZero) {
3317 myexponent = 0;
3318 mysignificand = 0;
3319 } else if (category==fcInfinity) {
3320 myexponent = 0x1f;
3321 mysignificand = 0;
3322 } else {
3323 assert(category == fcNaN && "Unknown category!")((void)0);
3324 myexponent = 0x1f;
3325 mysignificand = (uint32_t)*significandParts();
3326 }
3327
3328 return APInt(16, (((sign&1) << 15) | ((myexponent&0x1f) << 10) |
3329 (mysignificand & 0x3ff)));
3330}
3331
3332// This function creates an APInt that is just a bit map of the floating
3333// point constant as it would appear in memory. It is not a conversion,
3334// and treating the result as a normal integer is unlikely to be useful.
3335
3336APInt IEEEFloat::bitcastToAPInt() const {
3337 if (semantics == (const llvm::fltSemantics*)&semIEEEhalf)
5
←
Assuming the condition is false
→
6
←
Taking false branch
→
3338 return convertHalfAPFloatToAPInt();
3339
3340 if (semantics == (const llvm::fltSemantics *)&semBFloat)
7
←
Assuming the condition is false
→
8
←
Taking false branch
→
3341 return convertBFloatAPFloatToAPInt();
3342
3343 if (semantics == (const llvm::fltSemantics*)&semIEEEsingle)
9
←
Assuming the condition is false
→
10
←
Taking false branch
→
3344 return convertFloatAPFloatToAPInt();
3345
3346 if (semantics == (const llvm::fltSemantics*)&semIEEEdouble)
11
←
Assuming the condition is false
→
12
←
Taking false branch
→
3347 return convertDoubleAPFloatToAPInt();
3348
3349 if (semantics == (const llvm::fltSemantics*)&semIEEEquad)
13
←
Assuming the condition is false
→
14
←
Taking false branch
→
3350 return convertQuadrupleAPFloatToAPInt();
3351
3352 if (semantics == (const llvm::fltSemantics *)&semPPCDoubleDoubleLegacy)
15
←
Assuming the condition is true
→
16
←
Taking true branch
→
3353 return convertPPCDoubleDoubleAPFloatToAPInt();
17
←
Calling 'IEEEFloat::convertPPCDoubleDoubleAPFloatToAPInt'
→
3354
3355 assert(semantics == (const llvm::fltSemantics*)&semX87DoubleExtended &&((void)0)
3356 "unknown format!")((void)0);
3357 return convertF80LongDoubleAPFloatToAPInt();
3358}
3359
3360float IEEEFloat::convertToFloat() const {
3361 assert(semantics == (const llvm::fltSemantics*)&semIEEEsingle &&((void)0)
3362 "Float semantics are not IEEEsingle")((void)0);
3363 APInt api = bitcastToAPInt();
4
←
Calling 'IEEEFloat::bitcastToAPInt'
→
3364 return api.bitsToFloat();
3365}
3366
3367double IEEEFloat::convertToDouble() const {
3368 assert(semantics == (const llvm::fltSemantics*)&semIEEEdouble &&((void)0)
3369 "Float semantics are not IEEEdouble")((void)0);
3370 APInt api = bitcastToAPInt();
3371 return api.bitsToDouble();
3372}
3373
3374/// Integer bit is explicit in this format. Intel hardware (387 and later)
3375/// does not support these bit patterns:
3376/// exponent = all 1's, integer bit 0, significand 0 ("pseudoinfinity")
3377/// exponent = all 1's, integer bit 0, significand nonzero ("pseudoNaN")
3378/// exponent!=0 nor all 1's, integer bit 0 ("unnormal")
3379/// exponent = 0, integer bit 1 ("pseudodenormal")
3380/// At the moment, the first three are treated as NaNs, the last one as Normal.
3381void IEEEFloat::initFromF80LongDoubleAPInt(const APInt &api) {
3382 assert(api.getBitWidth()==80)((void)0);
3383 uint64_t i1 = api.getRawData()[0];
3384 uint64_t i2 = api.getRawData()[1];
3385 uint64_t myexponent = (i2 & 0x7fff);
3386 uint64_t mysignificand = i1;
3387 uint8_t myintegerbit = mysignificand >> 63;
3388
3389 initialize(&semX87DoubleExtended);
3390 assert(partCount()==2)((void)0);
3391
3392 sign = static_cast<unsigned int>(i2>>15);
3393 if (myexponent == 0 && mysignificand == 0) {
3394 makeZero(sign);
3395 } else if (myexponent==0x7fff && mysignificand==0x8000000000000000ULL) {
3396 makeInf(sign);
3397 } else if ((myexponent == 0x7fff && mysignificand != 0x8000000000000000ULL) ||
3398 (myexponent != 0x7fff && myexponent != 0 && myintegerbit == 0)) {
3399 category = fcNaN;
3400 exponent = exponentNaN();
3401 significandParts()[0] = mysignificand;
3402 significandParts()[1] = 0;
3403 } else {
3404 category = fcNormal;
3405 exponent = myexponent - 16383;
3406 significandParts()[0] = mysignificand;
3407 significandParts()[1] = 0;
3408 if (myexponent==0) // denormal
3409 exponent = -16382;
3410 }
3411}
3412
3413void IEEEFloat::initFromPPCDoubleDoubleAPInt(const APInt &api) {
3414 assert(api.getBitWidth()==128)((void)0);
3415 uint64_t i1 = api.getRawData()[0];
3416 uint64_t i2 = api.getRawData()[1];
3417 opStatus fs;
3418 bool losesInfo;
3419
3420 // Get the first double and convert to our format.
3421 initFromDoubleAPInt(APInt(64, i1));
3422 fs = convert(semPPCDoubleDoubleLegacy, rmNearestTiesToEven, &losesInfo);
3423 assert(fs == opOK && !losesInfo)((void)0);
3424 (void)fs;
3425
3426 // Unless we have a special case, add in second double.
3427 if (isFiniteNonZero()) {
3428 IEEEFloat v(semIEEEdouble, APInt(64, i2));
3429 fs = v.convert(semPPCDoubleDoubleLegacy, rmNearestTiesToEven, &losesInfo);
3430 assert(fs == opOK && !losesInfo)((void)0);
3431 (void)fs;
3432
3433 add(v, rmNearestTiesToEven);
3434 }
3435}
3436
3437void IEEEFloat::initFromQuadrupleAPInt(const APInt &api) {
3438 assert(api.getBitWidth()==128)((void)0);
3439 uint64_t i1 = api.getRawData()[0];
3440 uint64_t i2 = api.getRawData()[1];
3441 uint64_t myexponent = (i2 >> 48) & 0x7fff;
3442 uint64_t mysignificand = i1;
3443 uint64_t mysignificand2 = i2 & 0xffffffffffffLL;
3444
3445 initialize(&semIEEEquad);
3446 assert(partCount()==2)((void)0);
3447
3448 sign = static_cast<unsigned int>(i2>>63);
3449 if (myexponent==0 &&
3450 (mysignificand==0 && mysignificand2==0)) {
3451 makeZero(sign);
3452 } else if (myexponent==0x7fff &&
3453 (mysignificand==0 && mysignificand2==0)) {
3454 makeInf(sign);
3455 } else if (myexponent==0x7fff &&
3456 (mysignificand!=0 || mysignificand2 !=0)) {
3457 category = fcNaN;
3458 exponent = exponentNaN();
3459 significandParts()[0] = mysignificand;
3460 significandParts()[1] = mysignificand2;
3461 } else {
3462 category = fcNormal;
3463 exponent = myexponent - 16383;
3464 significandParts()[0] = mysignificand;
3465 significandParts()[1] = mysignificand2;
3466 if (myexponent==0) // denormal
3467 exponent = -16382;
3468 else
3469 significandParts()[1] |= 0x1000000000000LL; // integer bit
3470 }
3471}
3472
3473void IEEEFloat::initFromDoubleAPInt(const APInt &api) {
3474 assert(api.getBitWidth()==64)((void)0);
3475 uint64_t i = *api.getRawData();
3476 uint64_t myexponent = (i >> 52) & 0x7ff;
3477 uint64_t mysignificand = i & 0xfffffffffffffLL;
3478
3479 initialize(&semIEEEdouble);
3480 assert(partCount()==1)((void)0);
3481
3482 sign = static_cast<unsigned int>(i>>63);
3483 if (myexponent==0 && mysignificand==0) {
3484 makeZero(sign);
3485 } else if (myexponent==0x7ff && mysignificand==0) {
3486 makeInf(sign);
3487 } else if (myexponent==0x7ff && mysignificand!=0) {
3488 category = fcNaN;
3489 exponent = exponentNaN();
3490 *significandParts() = mysignificand;
3491 } else {
3492 category = fcNormal;
3493 exponent = myexponent - 1023;
3494 *significandParts() = mysignificand;
3495 if (myexponent==0) // denormal
3496 exponent = -1022;
3497 else
3498 *significandParts() |= 0x10000000000000LL; // integer bit
3499 }
3500}
3501
3502void IEEEFloat::initFromFloatAPInt(const APInt &api) {
3503 assert(api.getBitWidth()==32)((void)0);
3504 uint32_t i = (uint32_t)*api.getRawData();
3505 uint32_t myexponent = (i >> 23) & 0xff;
3506 uint32_t mysignificand = i & 0x7fffff;
3507
3508 initialize(&semIEEEsingle);
3509 assert(partCount()==1)((void)0);
3510
3511 sign = i >> 31;
3512 if (myexponent==0 && mysignificand==0) {
3513 makeZero(sign);
3514 } else if (myexponent==0xff && mysignificand==0) {
3515 makeInf(sign);
3516 } else if (myexponent==0xff && mysignificand!=0) {
3517 category = fcNaN;
3518 exponent = exponentNaN();
3519 *significandParts() = mysignificand;
3520 } else {
3521 category = fcNormal;
3522 exponent = myexponent - 127; //bias
3523 *significandParts() = mysignificand;
3524 if (myexponent==0) // denormal
3525 exponent = -126;
3526 else
3527 *significandParts() |= 0x800000; // integer bit
3528 }
3529}
3530
3531void IEEEFloat::initFromBFloatAPInt(const APInt &api) {
3532 assert(api.getBitWidth() == 16)((void)0);
3533 uint32_t i = (uint32_t)*api.getRawData();
3534 uint32_t myexponent = (i >> 7) & 0xff;
3535 uint32_t mysignificand = i & 0x7f;
3536
3537 initialize(&semBFloat);
3538 assert(partCount() == 1)((void)0);
3539
3540 sign = i >> 15;
3541 if (myexponent == 0 && mysignificand == 0) {
3542 makeZero(sign);
3543 } else if (myexponent == 0xff && mysignificand == 0) {
3544 makeInf(sign);
3545 } else if (myexponent == 0xff && mysignificand != 0) {
3546 category = fcNaN;
3547 exponent = exponentNaN();
3548 *significandParts() = mysignificand;
3549 } else {
3550 category = fcNormal;
3551 exponent = myexponent - 127; // bias
3552 *significandParts() = mysignificand;
3553 if (myexponent == 0) // denormal
3554 exponent = -126;
3555 else
3556 *significandParts() |= 0x80; // integer bit
3557 }
3558}
3559
3560void IEEEFloat::initFromHalfAPInt(const APInt &api) {
3561 assert(api.getBitWidth()==16)((void)0);
3562 uint32_t i = (uint32_t)*api.getRawData();
3563 uint32_t myexponent = (i >> 10) & 0x1f;
3564 uint32_t mysignificand = i & 0x3ff;
3565
3566 initialize(&semIEEEhalf);
3567 assert(partCount()==1)((void)0);
3568
3569 sign = i >> 15;
3570 if (myexponent==0 && mysignificand==0) {
3571 makeZero(sign);
3572 } else if (myexponent==0x1f && mysignificand==0) {
3573 makeInf(sign);
3574 } else if (myexponent==0x1f && mysignificand!=0) {
3575 category = fcNaN;
3576 exponent = exponentNaN();
3577 *significandParts() = mysignificand;
3578 } else {
3579 category = fcNormal;
3580 exponent = myexponent - 15; //bias
3581 *significandParts() = mysignificand;
3582 if (myexponent==0) // denormal
3583 exponent = -14;
3584 else
3585 *significandParts() |= 0x400; // integer bit
3586 }
3587}
3588
3589/// Treat api as containing the bits of a floating point number. Currently
3590/// we infer the floating point type from the size of the APInt. The
3591/// isIEEE argument distinguishes between PPC128 and IEEE128 (not meaningful
3592/// when the size is anything else).
3593void IEEEFloat::initFromAPInt(const fltSemantics *Sem, const APInt &api) {
3594 if (Sem == &semIEEEhalf)
3595 return initFromHalfAPInt(api);
3596 if (Sem == &semBFloat)
3597 return initFromBFloatAPInt(api);
3598 if (Sem == &semIEEEsingle)
3599 return initFromFloatAPInt(api);
3600 if (Sem == &semIEEEdouble)
3601 return initFromDoubleAPInt(api);
3602 if (Sem == &semX87DoubleExtended)
3603 return initFromF80LongDoubleAPInt(api);
3604 if (Sem == &semIEEEquad)
3605 return initFromQuadrupleAPInt(api);
3606 if (Sem == &semPPCDoubleDoubleLegacy)
3607 return initFromPPCDoubleDoubleAPInt(api);
3608
3609 llvm_unreachable(nullptr)__builtin_unreachable();
3610}
3611
3612/// Make this number the largest magnitude normal number in the given
3613/// semantics.
3614void IEEEFloat::makeLargest(bool Negative) {
3615 // We want (in interchange format):
3616 // sign = {Negative}
3617 // exponent = 1..10
3618 // significand = 1..1
3619 category = fcNormal;
3620 sign = Negative;
3621 exponent = semantics->maxExponent;
3622
3623 // Use memset to set all but the highest integerPart to all ones.
3624 integerPart *significand = significandParts();
3625 unsigned PartCount = partCount();
3626 memset(significand, 0xFF, sizeof(integerPart)*(PartCount - 1));
3627
3628 // Set the high integerPart especially setting all unused top bits for
3629 // internal consistency.
3630 const unsigned NumUnusedHighBits =
3631 PartCount*integerPartWidth - semantics->precision;
3632 significand[PartCount - 1] = (NumUnusedHighBits < integerPartWidth)
3633 ? (~integerPart(0) >> NumUnusedHighBits)
3634 : 0;
3635}
3636
3637/// Make this number the smallest magnitude denormal number in the given
3638/// semantics.
3639void IEEEFloat::makeSmallest(bool Negative) {
3640 // We want (in interchange format):
3641 // sign = {Negative}
3642 // exponent = 0..0
3643 // significand = 0..01
3644 category = fcNormal;
3645 sign = Negative;
3646 exponent = semantics->minExponent;
3647 APInt::tcSet(significandParts(), 1, partCount());
3648}
3649
3650void IEEEFloat::makeSmallestNormalized(bool Negative) {
3651 // We want (in interchange format):
3652 // sign = {Negative}
3653 // exponent = 0..0
3654 // significand = 10..0
3655
3656 category = fcNormal;
3657 zeroSignificand();
3658 sign = Negative;
3659 exponent = semantics->minExponent;
3660 significandParts()[partCountForBits(semantics->precision) - 1] |=
3661 (((integerPart)1) << ((semantics->precision - 1) % integerPartWidth));
3662}
3663
3664IEEEFloat::IEEEFloat(const fltSemantics &Sem, const APInt &API) {
3665 initFromAPInt(&Sem, API);
3666}
3667
3668IEEEFloat::IEEEFloat(float f) {
3669 initFromAPInt(&semIEEEsingle, APInt::floatToBits(f));
3670}
3671
3672IEEEFloat::IEEEFloat(double d) {
3673 initFromAPInt(&semIEEEdouble, APInt::doubleToBits(d));
3674}
3675
3676namespace {
3677 void append(SmallVectorImpl<char> &Buffer, StringRef Str) {
3678 Buffer.append(Str.begin(), Str.end());
3679 }
3680
3681 /// Removes data from the given significand until it is no more
3682 /// precise than is required for the desired precision.
3683 void AdjustToPrecision(APInt &significand,
3684 int &exp, unsigned FormatPrecision) {
3685 unsigned bits = significand.getActiveBits();
3686
3687 // 196/59 is a very slight overestimate of lg_2(10).
3688 unsigned bitsRequired = (FormatPrecision * 196 + 58) / 59;
3689
3690 if (bits <= bitsRequired) return;
3691
3692 unsigned tensRemovable = (bits - bitsRequired) * 59 / 196;
3693 if (!tensRemovable) return;
3694
3695 exp += tensRemovable;
3696
3697 APInt divisor(significand.getBitWidth(), 1);
3698 APInt powten(significand.getBitWidth(), 10);
3699 while (true) {
3700 if (tensRemovable & 1)
3701 divisor *= powten;
3702 tensRemovable >>= 1;
3703 if (!tensRemovable) break;
3704 powten *= powten;
3705 }
3706
3707 significand = significand.udiv(divisor);
3708
3709 // Truncate the significand down to its active bit count.
3710 significand = significand.trunc(significand.getActiveBits());
3711 }
3712
3713
3714 void AdjustToPrecision(SmallVectorImpl<char> &buffer,
3715 int &exp, unsigned FormatPrecision) {
3716 unsigned N = buffer.size();
3717 if (N <= FormatPrecision) return;
3718
3719 // The most significant figures are the last ones in the buffer.
3720 unsigned FirstSignificant = N - FormatPrecision;
3721
3722 // Round.
3723 // FIXME: this probably shouldn't use 'round half up'.
3724
3725 // Rounding down is just a truncation, except we also want to drop
3726 // trailing zeros from the new result.
3727 if (buffer[FirstSignificant - 1] < '5') {
3728 while (FirstSignificant < N && buffer[FirstSignificant] == '0')
3729 FirstSignificant++;
3730
3731 exp += FirstSignificant;
3732 buffer.erase(&buffer[0], &buffer[FirstSignificant]);
3733 return;
3734 }
3735
3736 // Rounding up requires a decimal add-with-carry. If we continue
3737 // the carry, the newly-introduced zeros will just be truncated.
3738 for (unsigned I = FirstSignificant; I != N; ++I) {
3739 if (buffer[I] == '9') {
3740 FirstSignificant++;
3741 } else {
3742 buffer[I]++;
3743 break;
3744 }
3745 }
3746
3747 // If we carried through, we have exactly one digit of precision.
3748 if (FirstSignificant == N) {
3749 exp += FirstSignificant;
3750 buffer.clear();
3751 buffer.push_back('1');
3752 return;
3753 }
3754
3755 exp += FirstSignificant;
3756 buffer.erase(&buffer[0], &buffer[FirstSignificant]);
3757 }
3758} // namespace
3759
3760void IEEEFloat::toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision,
3761 unsigned FormatMaxPadding, bool TruncateZero) const {
3762 switch (category) {
3763 case fcInfinity:
3764 if (isNegative())
3765 return append(Str, "-Inf");
3766 else
3767 return append(Str, "+Inf");
3768
3769 case fcNaN: return append(Str, "NaN");
3770
3771 case fcZero:
3772 if (isNegative())
3773 Str.push_back('-');
3774
3775 if (!FormatMaxPadding) {
3776 if (TruncateZero)
3777 append(Str, "0.0E+0");
3778 else {
3779 append(Str, "0.0");
3780 if (FormatPrecision > 1)
3781 Str.append(FormatPrecision - 1, '0');
3782 append(Str, "e+00");
3783 }
3784 } else
3785 Str.push_back('0');
3786 return;
3787
3788 case fcNormal:
3789 break;
3790 }
3791
3792 if (isNegative())
3793 Str.push_back('-');
3794
3795 // Decompose the number into an APInt and an exponent.
3796 int exp = exponent - ((int) semantics->precision - 1);
3797 APInt significand(semantics->precision,
3798 makeArrayRef(significandParts(),
3799 partCountForBits(semantics->precision)));
3800
3801 // Set FormatPrecision if zero. We want to do this before we
3802 // truncate trailing zeros, as those are part of the precision.
3803 if (!FormatPrecision) {
3804 // We use enough digits so the number can be round-tripped back to an
3805 // APFloat. The formula comes from "How to Print Floating-Point Numbers
3806 // Accurately" by Steele and White.
3807 // FIXME: Using a formula based purely on the precision is conservative;
3808 // we can print fewer digits depending on the actual value being printed.
3809
3810 // FormatPrecision = 2 + floor(significandBits / lg_2(10))
3811 FormatPrecision = 2 + semantics->precision * 59 / 196;
3812 }
3813
3814 // Ignore trailing binary zeros.
3815 int trailingZeros = significand.countTrailingZeros();
3816 exp += trailingZeros;
3817 significand.lshrInPlace(trailingZeros);
3818
3819 // Change the exponent from 2^e to 10^e.
3820 if (exp == 0) {
3821 // Nothing to do.
3822 } else if (exp > 0) {
3823 // Just shift left.
3824 significand = significand.zext(semantics->precision + exp);
3825 significand <<= exp;
3826 exp = 0;
3827 } else { /* exp < 0 */
3828 int texp = -exp;
3829
3830 // We transform this using the identity:
3831 // (N)(2^-e) == (N)(5^e)(10^-e)
3832 // This means we have to multiply N (the significand) by 5^e.
3833 // To avoid overflow, we have to operate on numbers large
3834 // enough to store N * 5^e:
3835 // log2(N * 5^e) == log2(N) + e * log2(5)
3836 // <= semantics->precision + e * 137 / 59
3837 // (log_2(5) ~ 2.321928 < 2.322034 ~ 137/59)
3838
3839 unsigned precision = semantics->precision + (137 * texp + 136) / 59;
3840
3841 // Multiply significand by 5^e.
3842 // N * 5^0101 == N * 5^(1*1) * 5^(0*2) * 5^(1*4) * 5^(0*8)
3843 significand = significand.zext(precision);
3844 APInt five_to_the_i(precision, 5);
3845 while (true) {
3846 if (texp & 1) significand *= five_to_the_i;
3847
3848 texp >>= 1;
3849 if (!texp) break;
3850 five_to_the_i *= five_to_the_i;
3851 }
3852 }
3853
3854 AdjustToPrecision(significand, exp, FormatPrecision);
3855
3856 SmallVector<char, 256> buffer;
3857
3858 // Fill the buffer.
3859 unsigned precision = significand.getBitWidth();
3860 APInt ten(precision, 10);
3861 APInt digit(precision, 0);
3862
3863 bool inTrail = true;
3864 while (significand != 0) {
3865 // digit <- significand % 10
3866 // significand <- significand / 10
3867 APInt::udivrem(significand, ten, significand, digit);
3868
3869 unsigned d = digit.getZExtValue();
3870
3871 // Drop trailing zeros.
3872 if (inTrail && !d) exp++;
3873 else {
3874 buffer.push_back((char) ('0' + d));
3875 inTrail = false;
3876 }
3877 }
3878
3879 assert(!buffer.empty() && "no characters in buffer!")((void)0);
3880
3881 // Drop down to FormatPrecision.
3882 // TODO: don't do more precise calculations above than are required.
3883 AdjustToPrecision(buffer, exp, FormatPrecision);
3884
3885 unsigned NDigits = buffer.size();
3886
3887 // Check whether we should use scientific notation.
3888 bool FormatScientific;
3889 if (!FormatMaxPadding)
3890 FormatScientific = true;
3891 else {
3892 if (exp >= 0) {
3893 // 765e3 --> 765000
3894 // ^^^
3895 // But we shouldn't make the number look more precise than it is.
3896 FormatScientific = ((unsigned) exp > FormatMaxPadding ||
3897 NDigits + (unsigned) exp > FormatPrecision);
3898 } else {
3899 // Power of the most significant digit.
3900 int MSD = exp + (int) (NDigits - 1);
3901 if (MSD >= 0) {
3902 // 765e-2 == 7.65
3903 FormatScientific = false;
3904 } else {
3905 // 765e-5 == 0.00765
3906 // ^ ^^
3907 FormatScientific = ((unsigned) -MSD) > FormatMaxPadding;
3908 }
3909 }
3910 }
3911
3912 // Scientific formatting is pretty straightforward.
3913 if (FormatScientific) {
3914 exp += (NDigits - 1);
3915
3916 Str.push_back(buffer[NDigits-1]);
3917 Str.push_back('.');
3918 if (NDigits == 1 && TruncateZero)
3919 Str.push_back('0');
3920 else
3921 for (unsigned I = 1; I != NDigits; ++I)
3922 Str.push_back(buffer[NDigits-1-I]);
3923 // Fill with zeros up to FormatPrecision.
3924 if (!TruncateZero && FormatPrecision > NDigits - 1)
3925 Str.append(FormatPrecision - NDigits + 1, '0');
3926 // For !TruncateZero we use lower 'e'.
3927 Str.push_back(TruncateZero ? 'E' : 'e');
3928
3929 Str.push_back(exp >= 0 ? '+' : '-');
3930 if (exp < 0) exp = -exp;
3931 SmallVector<char, 6> expbuf;
3932 do {
3933 expbuf.push_back((char) ('0' + (exp % 10)));
3934 exp /= 10;
3935 } while (exp);
3936 // Exponent always at least two digits if we do not truncate zeros.
3937 if (!TruncateZero && expbuf.size() < 2)
3938 expbuf.push_back('0');
3939 for (unsigned I = 0, E = expbuf.size(); I != E; ++I)
3940 Str.push_back(expbuf[E-1-I]);
3941 return;
3942 }
3943
3944 // Non-scientific, positive exponents.
3945 if (exp >= 0) {
3946 for (unsigned I = 0; I != NDigits; ++I)
3947 Str.push_back(buffer[NDigits-1-I]);
3948 for (unsigned I = 0; I != (unsigned) exp; ++I)
3949 Str.push_back('0');
3950 return;
3951 }
3952
3953 // Non-scientific, negative exponents.
3954
3955 // The number of digits to the left of the decimal point.
3956 int NWholeDigits = exp + (int) NDigits;
3957
3958 unsigned I = 0;
3959 if (NWholeDigits > 0) {
3960 for (; I != (unsigned) NWholeDigits; ++I)
3961 Str.push_back(buffer[NDigits-I-1]);
3962 Str.push_back('.');
3963 } else {
3964 unsigned NZeros = 1 + (unsigned) -NWholeDigits;
3965
3966 Str.push_back('0');
3967 Str.push_back('.');
3968 for (unsigned Z = 1; Z != NZeros; ++Z)
3969 Str.push_back('0');
3970 }
3971
3972 for (; I != NDigits; ++I)
3973 Str.push_back(buffer[NDigits-I-1]);
3974}
3975
3976bool IEEEFloat::getExactInverse(APFloat *inv) const {
3977 // Special floats and denormals have no exact inverse.
3978 if (!isFiniteNonZero())
3979 return false;
3980
3981 // Check that the number is a power of two by making sure that only the
3982 // integer bit is set in the significand.
3983 if (significandLSB() != semantics->precision - 1)
3984 return false;
3985
3986 // Get the inverse.
3987 IEEEFloat reciprocal(*semantics, 1ULL);
3988 if (reciprocal.divide(*this, rmNearestTiesToEven) != opOK)
3989 return false;
3990
3991 // Avoid multiplication with a denormal, it is not safe on all platforms and
3992 // may be slower than a normal division.
3993 if (reciprocal.isDenormal())
3994 return false;
3995
3996 assert(reciprocal.isFiniteNonZero() &&((void)0)
3997 reciprocal.significandLSB() == reciprocal.semantics->precision - 1)((void)0);
3998
3999 if (inv)
4000 *inv = APFloat(reciprocal, *semantics);
4001
4002 return true;
4003}
4004
4005bool IEEEFloat::isSignaling() const {
4006 if (!isNaN())
4007 return false;
4008
4009 // IEEE-754R 2008 6.2.1: A signaling NaN bit string should be encoded with the
4010 // first bit of the trailing significand being 0.
4011 return !APInt::tcExtractBit(significandParts(), semantics->precision - 2);
4012}
4013
4014/// IEEE-754R 2008 5.3.1: nextUp/nextDown.
4015///
4016/// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with
4017/// appropriate sign switching before/after the computation.
4018IEEEFloat::opStatus IEEEFloat::next(bool nextDown) {
4019 // If we are performing nextDown, swap sign so we have -x.
4020 if (nextDown)
4021 changeSign();
4022
4023 // Compute nextUp(x)
4024 opStatus result = opOK;
4025
4026 // Handle each float category separately.
4027 switch (category) {
4028 case fcInfinity:
4029 // nextUp(+inf) = +inf
4030 if (!isNegative())
4031 break;
4032 // nextUp(-inf) = -getLargest()
4033 makeLargest(true);
4034 break;
4035 case fcNaN:
4036 // IEEE-754R 2008 6.2 Par 2: nextUp(sNaN) = qNaN. Set Invalid flag.
4037 // IEEE-754R 2008 6.2: nextUp(qNaN) = qNaN. Must be identity so we do not
4038 // change the payload.
4039 if (isSignaling()) {
4040 result = opInvalidOp;
4041 // For consistency, propagate the sign of the sNaN to the qNaN.
4042 makeNaN(false, isNegative(), nullptr);
4043 }
4044 break;
4045 case fcZero:
4046 // nextUp(pm 0) = +getSmallest()
4047 makeSmallest(false);
4048 break;
4049 case fcNormal:
4050 // nextUp(-getSmallest()) = -0
4051 if (isSmallest() && isNegative()) {
4052 APInt::tcSet(significandParts(), 0, partCount());
4053 category = fcZero;
4054 exponent = 0;
4055 break;
4056 }
4057
4058 // nextUp(getLargest()) == INFINITY
4059 if (isLargest() && !isNegative()) {
4060 APInt::tcSet(significandParts(), 0, partCount());
4061 category = fcInfinity;
4062 exponent = semantics->maxExponent + 1;
4063 break;
4064 }
4065
4066 // nextUp(normal) == normal + inc.
4067 if (isNegative()) {
4068 // If we are negative, we need to decrement the significand.
4069
4070 // We only cross a binade boundary that requires adjusting the exponent
4071 // if:
4072 // 1. exponent != semantics->minExponent. This implies we are not in the
4073 // smallest binade or are dealing with denormals.
4074 // 2. Our significand excluding the integral bit is all zeros.
4075 bool WillCrossBinadeBoundary =
4076 exponent != semantics->minExponent && isSignificandAllZeros();
4077
4078 // Decrement the significand.
4079 //
4080 // We always do this since:
4081 // 1. If we are dealing with a non-binade decrement, by definition we
4082 // just decrement the significand.
4083 // 2. If we are dealing with a normal -> normal binade decrement, since
4084 // we have an explicit integral bit the fact that all bits but the
4085 // integral bit are zero implies that subtracting one will yield a
4086 // significand with 0 integral bit and 1 in all other spots. Thus we
4087 // must just adjust the exponent and set the integral bit to 1.
4088 // 3. If we are dealing with a normal -> denormal binade decrement,
4089 // since we set the integral bit to 0 when we represent denormals, we
4090 // just decrement the significand.
4091 integerPart *Parts = significandParts();
4092 APInt::tcDecrement(Parts, partCount());
4093
4094 if (WillCrossBinadeBoundary) {
4095 // Our result is a normal number. Do the following:
4096 // 1. Set the integral bit to 1.
4097 // 2. Decrement the exponent.
4098 APInt::tcSetBit(Parts, semantics->precision - 1);
4099 exponent--;
4100 }
4101 } else {
4102 // If we are positive, we need to increment the significand.
4103
4104 // We only cross a binade boundary that requires adjusting the exponent if
4105 // the input is not a denormal and all of said input's significand bits
4106 // are set. If all of said conditions are true: clear the significand, set
4107 // the integral bit to 1, and increment the exponent. If we have a
4108 // denormal always increment since moving denormals and the numbers in the
4109 // smallest normal binade have the same exponent in our representation.
4110 bool WillCrossBinadeBoundary = !isDenormal() && isSignificandAllOnes();
4111
4112 if (WillCrossBinadeBoundary) {
4113 integerPart *Parts = significandParts();
4114 APInt::tcSet(Parts, 0, partCount());
4115 APInt::tcSetBit(Parts, semantics->precision - 1);
4116 assert(exponent != semantics->maxExponent &&((void)0)
4117 "We can not increment an exponent beyond the maxExponent allowed"((void)0)
4118 " by the given floating point semantics.")((void)0);
4119 exponent++;
4120 } else {
4121 incrementSignificand();
4122 }
4123 }
4124 break;
4125 }
4126
4127 // If we are performing nextDown, swap sign so we have -nextUp(-x)
4128 if (nextDown)
4129 changeSign();
4130
4131 return result;
4132}
4133
4134APFloatBase::ExponentType IEEEFloat::exponentNaN() const {
4135 return semantics->maxExponent + 1;
4136}
4137
4138APFloatBase::ExponentType IEEEFloat::exponentInf() const {
4139 return semantics->maxExponent + 1;
4140}
4141
4142APFloatBase::ExponentType IEEEFloat::exponentZero() const {
4143 return semantics->minExponent - 1;
4144}
4145
4146void IEEEFloat::makeInf(bool Negative) {
4147 category = fcInfinity;
4148 sign = Negative;
4149 exponent = exponentInf();
4150 APInt::tcSet(significandParts(), 0, partCount());
4151}
4152
4153void IEEEFloat::makeZero(bool Negative) {
4154 category = fcZero;
4155 sign = Negative;
4156 exponent = exponentZero();
4157 APInt::tcSet(significandParts(), 0, partCount());
4158}
4159
4160void IEEEFloat::makeQuiet() {
4161 assert(isNaN())((void)0);
4162 APInt::tcSetBit(significandParts(), semantics->precision - 2);
4163}
4164
4165int ilogb(const IEEEFloat &Arg) {
4166 if (Arg.isNaN())
4167 return IEEEFloat::IEK_NaN;
4168 if (Arg.isZero())
4169 return IEEEFloat::IEK_Zero;
4170 if (Arg.isInfinity())
4171 return IEEEFloat::IEK_Inf;
4172 if (!Arg.isDenormal())
4173 return Arg.exponent;
4174
4175 IEEEFloat Normalized(Arg);
4176 int SignificandBits = Arg.getSemantics().precision - 1;
4177
4178 Normalized.exponent += SignificandBits;
4179 Normalized.normalize(IEEEFloat::rmNearestTiesToEven, lfExactlyZero);
4180 return Normalized.exponent - SignificandBits;
4181}
4182
4183IEEEFloat scalbn(IEEEFloat X, int Exp, IEEEFloat::roundingMode RoundingMode) {
4184 auto MaxExp = X.getSemantics().maxExponent;
4185 auto MinExp = X.getSemantics().minExponent;
4186
4187 // If Exp is wildly out-of-scale, simply adding it to X.exponent will
4188 // overflow; clamp it to a safe range before adding, but ensure that the range
4189 // is large enough that the clamp does not change the result. The range we
4190 // need to support is the difference between the largest possible exponent and
4191 // the normalized exponent of half the smallest denormal.
4192
4193 int SignificandBits = X.getSemantics().precision - 1;
4194 int MaxIncrement = MaxExp - (MinExp - SignificandBits) + 1;
4195
4196 // Clamp to one past the range ends to let normalize handle overlflow.
4197 X.exponent += std::min(std::max(Exp, -MaxIncrement - 1), MaxIncrement);
4198 X.normalize(RoundingMode, lfExactlyZero);
4199 if (X.isNaN())
4200 X.makeQuiet();
4201 return X;
4202}
4203
4204IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM) {
4205 Exp = ilogb(Val);
4206
4207 // Quiet signalling nans.
4208 if (Exp == IEEEFloat::IEK_NaN) {
4209 IEEEFloat Quiet(Val);
4210 Quiet.makeQuiet();
4211 return Quiet;
4212 }
4213
4214 if (Exp == IEEEFloat::IEK_Inf)
4215 return Val;
4216
4217 // 1 is added because frexp is defined to return a normalized fraction in
4218 // +/-[0.5, 1.0), rather than the usual +/-[1.0, 2.0).
4219 Exp = Exp == IEEEFloat::IEK_Zero ? 0 : Exp + 1;
4220 return scalbn(Val, -Exp, RM);
4221}
4222
4223DoubleAPFloat::DoubleAPFloat(const fltSemantics &S)
4224 : Semantics(&S),
4225 Floats(new APFloat[2]{APFloat(semIEEEdouble), APFloat(semIEEEdouble)}) {
4226 assert(Semantics == &semPPCDoubleDouble)((void)0);
4227}
4228
4229DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, uninitializedTag)
4230 : Semantics(&S),
4231 Floats(new APFloat[2]{APFloat(semIEEEdouble, uninitialized),
4232 APFloat(semIEEEdouble, uninitialized)}) {
4233 assert(Semantics == &semPPCDoubleDouble)((void)0);
4234}
4235
4236DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, integerPart I)
4237 : Semantics(&S), Floats(new APFloat[2]{APFloat(semIEEEdouble, I),
4238 APFloat(semIEEEdouble)}) {
4239 assert(Semantics == &semPPCDoubleDouble)((void)0);
4240}
4241
4242DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, const APInt &I)
4243 : Semantics(&S),
4244 Floats(new APFloat[2]{
4245 APFloat(semIEEEdouble, APInt(64, I.getRawData()[0])),
4246 APFloat(semIEEEdouble, APInt(64, I.getRawData()[1]))}) {
4247 assert(Semantics == &semPPCDoubleDouble)((void)0);
4248}
4249
4250DoubleAPFloat::DoubleAPFloat(const fltSemantics &S, APFloat &&First,
4251 APFloat &&Second)
4252 : Semantics(&S),
4253 Floats(new APFloat[2]{std::move(First), std::move(Second)}) {
4254 assert(Semantics == &semPPCDoubleDouble)((void)0);
4255 assert(&Floats[0].getSemantics() == &semIEEEdouble)((void)0);
4256 assert(&Floats[1].getSemantics() == &semIEEEdouble)((void)0);
4257}
4258
4259DoubleAPFloat::DoubleAPFloat(const DoubleAPFloat &RHS)
4260 : Semantics(RHS.Semantics),
4261 Floats(RHS.Floats ? new APFloat[2]{APFloat(RHS.Floats[0]),
4262 APFloat(RHS.Floats[1])}
4263 : nullptr) {
4264 assert(Semantics == &semPPCDoubleDouble)((void)0);
4265}
4266
4267DoubleAPFloat::DoubleAPFloat(DoubleAPFloat &&RHS)
4268 : Semantics(RHS.Semantics), Floats(std::move(RHS.Floats)) {
4269 RHS.Semantics = &semBogus;
4270 assert(Semantics == &semPPCDoubleDouble)((void)0);
4271}
4272
4273DoubleAPFloat &DoubleAPFloat::operator=(const DoubleAPFloat &RHS) {
4274 if (Semantics == RHS.Semantics && RHS.Floats) {
4275 Floats[0] = RHS.Floats[0];
4276 Floats[1] = RHS.Floats[1];
4277 } else if (this != &RHS) {
4278 this->~DoubleAPFloat();
4279 new (this) DoubleAPFloat(RHS);
4280 }
4281 return *this;
4282}
4283
4284// Implement addition, subtraction, multiplication and division based on:
4285// "Software for Doubled-Precision Floating-Point Computations",
4286// by Seppo Linnainmaa, ACM TOMS vol 7 no 3, September 1981, pages 272-283.
4287APFloat::opStatus DoubleAPFloat::addImpl(const APFloat &a, const APFloat &aa,
4288 const APFloat &c, const APFloat &cc,
4289 roundingMode RM) {
4290 int Status = opOK;
4291 APFloat z = a;
4292 Status |= z.add(c, RM);
4293 if (!z.isFinite()) {
4294 if (!z.isInfinity()) {
4295 Floats[0] = std::move(z);
4296 Floats[1].makeZero(/* Neg = */ false);
4297 return (opStatus)Status;
4298 }
4299 Status = opOK;
4300 auto AComparedToC = a.compareAbsoluteValue(c);
4301 z = cc;
4302 Status |= z.add(aa, RM);
4303 if (AComparedToC == APFloat::cmpGreaterThan) {
4304 // z = cc + aa + c + a;
4305 Status |= z.add(c, RM);
4306 Status |= z.add(a, RM);
4307 } else {
4308 // z = cc + aa + a + c;
4309 Status |= z.add(a, RM);
4310 Status |= z.add(c, RM);
4311 }
4312 if (!z.isFinite()) {
4313 Floats[0] = std::move(z);
4314 Floats[1].makeZero(/* Neg = */ false);
4315 return (opStatus)Status;
4316 }
4317 Floats[0] = z;
4318 APFloat zz = aa;
4319 Status |= zz.add(cc, RM);
4320 if (AComparedToC == APFloat::cmpGreaterThan) {
4321 // Floats[1] = a - z + c + zz;
4322 Floats[1] = a;
4323 Status |= Floats[1].subtract(z, RM);
4324 Status |= Floats[1].add(c, RM);
4325 Status |= Floats[1].add(zz, RM);
4326 } else {
4327 // Floats[1] = c - z + a + zz;
4328 Floats[1] = c;
4329 Status |= Floats[1].subtract(z, RM);
4330 Status |= Floats[1].add(a, RM);
4331 Status |= Floats[1].add(zz, RM);
4332 }
4333 } else {
4334 // q = a - z;
4335 APFloat q = a;
4336 Status |= q.subtract(z, RM);
4337
4338 // zz = q + c + (a - (q + z)) + aa + cc;
4339 // Compute a - (q + z) as -((q + z) - a) to avoid temporary copies.
4340 auto zz = q;
4341 Status |= zz.add(c, RM);
4342 Status |= q.add(z, RM);
4343 Status |= q.subtract(a, RM);
4344 q.changeSign();
4345 Status |= zz.add(q, RM);
4346 Status |= zz.add(aa, RM);
4347 Status |= zz.add(cc, RM);
4348 if (zz.isZero() && !zz.isNegative()) {
4349 Floats[0] = std::move(z);
4350 Floats[1].makeZero(/* Neg = */ false);
4351 return opOK;
4352 }
4353 Floats[0] = z;
4354 Status |= Floats[0].add(zz, RM);
4355 if (!Floats[0].isFinite()) {
4356 Floats[1].makeZero(/* Neg = */ false);
4357 return (opStatus)Status;
4358 }
4359 Floats[1] = std::move(z);
4360 Status |= Floats[1].subtract(Floats[0], RM);
4361 Status |= Floats[1].add(zz, RM);
4362 }
4363 return (opStatus)Status;
4364}
4365
4366APFloat::opStatus DoubleAPFloat::addWithSpecial(const DoubleAPFloat &LHS,
4367 const DoubleAPFloat &RHS,
4368 DoubleAPFloat &Out,
4369 roundingMode RM) {
4370 if (LHS.getCategory() == fcNaN) {
4371 Out = LHS;
4372 return opOK;
4373 }
4374 if (RHS.getCategory() == fcNaN) {
4375 Out = RHS;
4376 return opOK;
4377 }
4378 if (LHS.getCategory() == fcZero) {
4379 Out = RHS;
4380 return opOK;
4381 }
4382 if (RHS.getCategory() == fcZero) {
4383 Out = LHS;
4384 return opOK;
4385 }
4386 if (LHS.getCategory() == fcInfinity && RHS.getCategory() == fcInfinity &&
4387 LHS.isNegative() != RHS.isNegative()) {
4388 Out.makeNaN(false, Out.isNegative(), nullptr);
4389 return opInvalidOp;
4390 }
4391 if (LHS.getCategory() == fcInfinity) {
4392 Out = LHS;
4393 return opOK;
4394 }
4395 if (RHS.getCategory() == fcInfinity) {
4396 Out = RHS;
4397 return opOK;
4398 }
4399 assert(LHS.getCategory() == fcNormal && RHS.getCategory() == fcNormal)((void)0);
4400
4401 APFloat A(LHS.Floats[0]), AA(LHS.Floats[1]), C(RHS.Floats[0]),
4402 CC(RHS.Floats[1]);
4403 assert(&A.getSemantics() == &semIEEEdouble)((void)0);
4404 assert(&AA.getSemantics() == &semIEEEdouble)((void)0);
4405 assert(&C.getSemantics() == &semIEEEdouble)((void)0);
4406 assert(&CC.getSemantics() == &semIEEEdouble)((void)0);
4407 assert(&Out.Floats[0].getSemantics() == &semIEEEdouble)((void)0);
4408 assert(&Out.Floats[1].getSemantics() == &semIEEEdouble)((void)0);
4409 return Out.addImpl(A, AA, C, CC, RM);
4410}
4411
4412APFloat::opStatus DoubleAPFloat::add(const DoubleAPFloat &RHS,
4413 roundingMode RM) {
4414 return addWithSpecial(*this, RHS, *this, RM);
4415}
4416
4417APFloat::opStatus DoubleAPFloat::subtract(const DoubleAPFloat &RHS,
4418 roundingMode RM) {
4419 changeSign();
4420 auto Ret = add(RHS, RM);
4421 changeSign();
4422 return Ret;
4423}
4424
4425APFloat::opStatus DoubleAPFloat::multiply(const DoubleAPFloat &RHS,
4426 APFloat::roundingMode RM) {
4427 const auto &LHS = *this;
4428 auto &Out = *this;
4429 /* Interesting observation: For special categories, finding the lowest
4430 common ancestor of the following layered graph gives the correct
4431 return category:
4432
4433 NaN
4434 / \
4435 Zero Inf
4436 \ /
4437 Normal
4438
4439 e.g. NaN * NaN = NaN
4440 Zero * Inf = NaN
4441 Normal * Zero = Zero
4442 Normal * Inf = Inf
4443 */
4444 if (LHS.getCategory() == fcNaN) {
4445 Out = LHS;
4446 return opOK;
4447 }
4448 if (RHS.getCategory() == fcNaN) {
4449 Out = RHS;
4450 return opOK;
4451 }
4452 if ((LHS.getCategory() == fcZero && RHS.getCategory() == fcInfinity) ||
4453 (LHS.getCategory() == fcInfinity && RHS.getCategory() == fcZero)) {
4454 Out.makeNaN(false, false, nullptr);
4455 return opOK;
4456 }
4457 if (LHS.getCategory() == fcZero || LHS.getCategory() == fcInfinity) {
4458 Out = LHS;
4459 return opOK;
4460 }
4461 if (RHS.getCategory() == fcZero || RHS.getCategory() == fcInfinity) {
4462 Out = RHS;
4463 return opOK;
4464 }
4465 assert(LHS.getCategory() == fcNormal && RHS.getCategory() == fcNormal &&((void)0)
4466 "Special cases not handled exhaustively")((void)0);
4467
4468 int Status = opOK;
4469 APFloat A = Floats[0], B = Floats[1], C = RHS.Floats[0], D = RHS.Floats[1];
4470 // t = a * c
4471 APFloat T = A;
4472 Status |= T.multiply(C, RM);
4473 if (!T.isFiniteNonZero()) {
4474 Floats[0] = T;
4475 Floats[1].makeZero(/* Neg = */ false);
4476 return (opStatus)Status;
4477 }
4478
4479 // tau = fmsub(a, c, t), that is -fmadd(-a, c, t).
4480 APFloat Tau = A;
4481 T.changeSign();
4482 Status |= Tau.fusedMultiplyAdd(C, T, RM);
4483 T.changeSign();
4484 {
4485 // v = a * d
4486 APFloat V = A;
4487 Status |= V.multiply(D, RM);
4488 // w = b * c
4489 APFloat W = B;
4490 Status |= W.multiply(C, RM);
4491 Status |= V.add(W, RM);
4492 // tau += v + w
4493 Status |= Tau.add(V, RM);
4494 }
4495 // u = t + tau
4496 APFloat U = T;
4497 Status |= U.add(Tau, RM);
4498
4499 Floats[0] = U;
4500 if (!U.isFinite()) {
4501 Floats[1].makeZero(/* Neg = */ false);
4502 } else {
4503 // Floats[1] = (t - u) + tau
4504 Status |= T.subtract(U, RM);
4505 Status |= T.add(Tau, RM);
4506 Floats[1] = T;
4507 }
4508 return (opStatus)Status;
4509}
4510
4511APFloat::opStatus DoubleAPFloat::divide(const DoubleAPFloat &RHS,
4512 APFloat::roundingMode RM) {
4513 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4514 APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
4515 auto Ret =
4516 Tmp.divide(APFloat(semPPCDoubleDoubleLegacy, RHS.bitcastToAPInt()), RM);
4517 *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
4518 return Ret;
4519}
4520
4521APFloat::opStatus DoubleAPFloat::remainder(const DoubleAPFloat &RHS) {
4522 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4523 APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
4524 auto Ret =
4525 Tmp.remainder(APFloat(semPPCDoubleDoubleLegacy, RHS.bitcastToAPInt()));
4526 *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
4527 return Ret;
4528}
4529
4530APFloat::opStatus DoubleAPFloat::mod(const DoubleAPFloat &RHS) {
4531 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4532 APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
4533 auto Ret = Tmp.mod(APFloat(semPPCDoubleDoubleLegacy, RHS.bitcastToAPInt()));
4534 *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
4535 return Ret;
4536}
4537
4538APFloat::opStatus
4539DoubleAPFloat::fusedMultiplyAdd(const DoubleAPFloat &Multiplicand,
4540 const DoubleAPFloat &Addend,
4541 APFloat::roundingMode RM) {
4542 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4543 APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
4544 auto Ret = Tmp.fusedMultiplyAdd(
4545 APFloat(semPPCDoubleDoubleLegacy, Multiplicand.bitcastToAPInt()),
4546 APFloat(semPPCDoubleDoubleLegacy, Addend.bitcastToAPInt()), RM);
4547 *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
4548 return Ret;
4549}
4550
4551APFloat::opStatus DoubleAPFloat::roundToIntegral(APFloat::roundingMode RM) {
4552 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4553 APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
4554 auto Ret = Tmp.roundToIntegral(RM);
4555 *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
4556 return Ret;
4557}
4558
4559void DoubleAPFloat::changeSign() {
4560 Floats[0].changeSign();
4561 Floats[1].changeSign();
4562}
4563
4564APFloat::cmpResult
4565DoubleAPFloat::compareAbsoluteValue(const DoubleAPFloat &RHS) const {
4566 auto Result = Floats[0].compareAbsoluteValue(RHS.Floats[0]);
4567 if (Result != cmpEqual)
4568 return Result;
4569 Result = Floats[1].compareAbsoluteValue(RHS.Floats[1]);
4570 if (Result == cmpLessThan || Result == cmpGreaterThan) {
4571 auto Against = Floats[0].isNegative() ^ Floats[1].isNegative();
4572 auto RHSAgainst = RHS.Floats[0].isNegative() ^ RHS.Floats[1].isNegative();
4573 if (Against && !RHSAgainst)
4574 return cmpLessThan;
4575 if (!Against && RHSAgainst)
4576 return cmpGreaterThan;
4577 if (!Against && !RHSAgainst)
4578 return Result;
4579 if (Against && RHSAgainst)
4580 return (cmpResult)(cmpLessThan + cmpGreaterThan - Result);
4581 }
4582 return Result;
4583}
4584
4585APFloat::fltCategory DoubleAPFloat::getCategory() const {
4586 return Floats[0].getCategory();
4587}
4588
4589bool DoubleAPFloat::isNegative() const { return Floats[0].isNegative(); }
4590
4591void DoubleAPFloat::makeInf(bool Neg) {
4592 Floats[0].makeInf(Neg);
4593 Floats[1].makeZero(/* Neg = */ false);
4594}
4595
4596void DoubleAPFloat::makeZero(bool Neg) {
4597 Floats[0].makeZero(Neg);
4598 Floats[1].makeZero(/* Neg = */ false);
4599}
4600
4601void DoubleAPFloat::makeLargest(bool Neg) {
4602 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4603 Floats[0] = APFloat(semIEEEdouble, APInt(64, 0x7fefffffffffffffull));
4604 Floats[1] = APFloat(semIEEEdouble, APInt(64, 0x7c8ffffffffffffeull));
4605 if (Neg)
4606 changeSign();
4607}
4608
4609void DoubleAPFloat::makeSmallest(bool Neg) {
4610 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4611 Floats[0].makeSmallest(Neg);
4612 Floats[1].makeZero(/* Neg = */ false);
4613}
4614
4615void DoubleAPFloat::makeSmallestNormalized(bool Neg) {
4616 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4617 Floats[0] = APFloat(semIEEEdouble, APInt(64, 0x0360000000000000ull));
4618 if (Neg)
4619 Floats[0].changeSign();
4620 Floats[1].makeZero(/* Neg = */ false);
4621}
4622
4623void DoubleAPFloat::makeNaN(bool SNaN, bool Neg, const APInt *fill) {
4624 Floats[0].makeNaN(SNaN, Neg, fill);
4625 Floats[1].makeZero(/* Neg = */ false);
4626}
4627
4628APFloat::cmpResult DoubleAPFloat::compare(const DoubleAPFloat &RHS) const {
4629 auto Result = Floats[0].compare(RHS.Floats[0]);
4630 // |Float[0]| > |Float[1]|
4631 if (Result == APFloat::cmpEqual)
4632 return Floats[1].compare(RHS.Floats[1]);
4633 return Result;
4634}
4635
4636bool DoubleAPFloat::bitwiseIsEqual(const DoubleAPFloat &RHS) const {
4637 return Floats[0].bitwiseIsEqual(RHS.Floats[0]) &&
4638 Floats[1].bitwiseIsEqual(RHS.Floats[1]);
4639}
4640
4641hash_code hash_value(const DoubleAPFloat &Arg) {
4642 if (Arg.Floats)
4643 return hash_combine(hash_value(Arg.Floats[0]), hash_value(Arg.Floats[1]));
4644 return hash_combine(Arg.Semantics);
4645}
4646
4647APInt DoubleAPFloat::bitcastToAPInt() const {
4648 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4649 uint64_t Data[] = {
4650 Floats[0].bitcastToAPInt().getRawData()[0],
4651 Floats[1].bitcastToAPInt().getRawData()[0],
4652 };
4653 return APInt(128, 2, Data);
4654}
4655
4656Expected<APFloat::opStatus> DoubleAPFloat::convertFromString(StringRef S,
4657 roundingMode RM) {
4658 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4659 APFloat Tmp(semPPCDoubleDoubleLegacy);
4660 auto Ret = Tmp.convertFromString(S, RM);
4661 *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
4662 return Ret;
4663}
4664
4665APFloat::opStatus DoubleAPFloat::next(bool nextDown) {
4666 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4667 APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
4668 auto Ret = Tmp.next(nextDown);
4669 *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
4670 return Ret;
4671}
4672
4673APFloat::opStatus
4674DoubleAPFloat::convertToInteger(MutableArrayRef<integerPart> Input,
4675 unsigned int Width, bool IsSigned,
4676 roundingMode RM, bool *IsExact) const {
4677 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4678 return APFloat(semPPCDoubleDoubleLegacy, bitcastToAPInt())
4679 .convertToInteger(Input, Width, IsSigned, RM, IsExact);
4680}
4681
4682APFloat::opStatus DoubleAPFloat::convertFromAPInt(const APInt &Input,
4683 bool IsSigned,
4684 roundingMode RM) {
4685 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4686 APFloat Tmp(semPPCDoubleDoubleLegacy);
4687 auto Ret = Tmp.convertFromAPInt(Input, IsSigned, RM);
4688 *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
4689 return Ret;
4690}
4691
4692APFloat::opStatus
4693DoubleAPFloat::convertFromSignExtendedInteger(const integerPart *Input,
4694 unsigned int InputSize,
4695 bool IsSigned, roundingMode RM) {
4696 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4697 APFloat Tmp(semPPCDoubleDoubleLegacy);
4698 auto Ret = Tmp.convertFromSignExtendedInteger(Input, InputSize, IsSigned, RM);
4699 *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
4700 return Ret;
4701}
4702
4703APFloat::opStatus
4704DoubleAPFloat::convertFromZeroExtendedInteger(const integerPart *Input,
4705 unsigned int InputSize,
4706 bool IsSigned, roundingMode RM) {
4707 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4708 APFloat Tmp(semPPCDoubleDoubleLegacy);
4709 auto Ret = Tmp.convertFromZeroExtendedInteger(Input, InputSize, IsSigned, RM);
4710 *this = DoubleAPFloat(semPPCDoubleDouble, Tmp.bitcastToAPInt());
4711 return Ret;
4712}
4713
4714unsigned int DoubleAPFloat::convertToHexString(char *DST,
4715 unsigned int HexDigits,
4716 bool UpperCase,
4717 roundingMode RM) const {
4718 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4719 return APFloat(semPPCDoubleDoubleLegacy, bitcastToAPInt())
4720 .convertToHexString(DST, HexDigits, UpperCase, RM);
4721}
4722
4723bool DoubleAPFloat::isDenormal() const {
4724 return getCategory() == fcNormal &&
4725 (Floats[0].isDenormal() || Floats[1].isDenormal() ||
4726 // (double)(Hi + Lo) == Hi defines a normal number.
4727 Floats[0] != Floats[0] + Floats[1]);
4728}
4729
4730bool DoubleAPFloat::isSmallest() const {
4731 if (getCategory() != fcNormal)
4732 return false;
4733 DoubleAPFloat Tmp(*this);
4734 Tmp.makeSmallest(this->isNegative());
4735 return Tmp.compare(*this) == cmpEqual;
4736}
4737
4738bool DoubleAPFloat::isLargest() const {
4739 if (getCategory() != fcNormal)
4740 return false;
4741 DoubleAPFloat Tmp(*this);
4742 Tmp.makeLargest(this->isNegative());
4743 return Tmp.compare(*this) == cmpEqual;
4744}
4745
4746bool DoubleAPFloat::isInteger() const {
4747 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4748 return Floats[0].isInteger() && Floats[1].isInteger();
4749}
4750
4751void DoubleAPFloat::toString(SmallVectorImpl<char> &Str,
4752 unsigned FormatPrecision,
4753 unsigned FormatMaxPadding,
4754 bool TruncateZero) const {
4755 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4756 APFloat(semPPCDoubleDoubleLegacy, bitcastToAPInt())
4757 .toString(Str, FormatPrecision, FormatMaxPadding, TruncateZero);
4758}
4759
4760bool DoubleAPFloat::getExactInverse(APFloat *inv) const {
4761 assert(Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4762 APFloat Tmp(semPPCDoubleDoubleLegacy, bitcastToAPInt());
4763 if (!inv)
4764 return Tmp.getExactInverse(nullptr);
4765 APFloat Inv(semPPCDoubleDoubleLegacy);
4766 auto Ret = Tmp.getExactInverse(&Inv);
4767 *inv = APFloat(semPPCDoubleDouble, Inv.bitcastToAPInt());
4768 return Ret;
4769}
4770
4771DoubleAPFloat scalbn(const DoubleAPFloat &Arg, int Exp,
4772 APFloat::roundingMode RM) {
4773 assert(Arg.Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4774 return DoubleAPFloat(semPPCDoubleDouble, scalbn(Arg.Floats[0], Exp, RM),
4775 scalbn(Arg.Floats[1], Exp, RM));
4776}
4777
4778DoubleAPFloat frexp(const DoubleAPFloat &Arg, int &Exp,
4779 APFloat::roundingMode RM) {
4780 assert(Arg.Semantics == &semPPCDoubleDouble && "Unexpected Semantics")((void)0);
4781 APFloat First = frexp(Arg.Floats[0], Exp, RM);
4782 APFloat Second = Arg.Floats[1];
4783 if (Arg.getCategory() == APFloat::fcNormal)
4784 Second = scalbn(Second, -Exp, RM);
4785 return DoubleAPFloat(semPPCDoubleDouble, std::move(First), std::move(Second));
4786}
4787
4788} // namespace detail
4789
4790APFloat::Storage::Storage(IEEEFloat F, const fltSemantics &Semantics) {
4791 if (usesLayout<IEEEFloat>(Semantics)) {
4792 new (&IEEE) IEEEFloat(std::move(F));
4793 return;
4794 }
4795 if (usesLayout<DoubleAPFloat>(Semantics)) {
4796 const fltSemantics& S = F.getSemantics();
4797 new (&Double)
4798 DoubleAPFloat(Semantics, APFloat(std::move(F), S),
4799 APFloat(semIEEEdouble));
4800 return;
4801 }
4802 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
4803}
4804
4805Expected<APFloat::opStatus> APFloat::convertFromString(StringRef Str,
4806 roundingMode RM) {
4807 APFLOAT_DISPATCH_ON_SEMANTICS(convertFromString(Str, RM));
4808}
4809
4810hash_code hash_value(const APFloat &Arg) {
4811 if (APFloat::usesLayout<detail::IEEEFloat>(Arg.getSemantics()))
4812 return hash_value(Arg.U.IEEE);
4813 if (APFloat::usesLayout<detail::DoubleAPFloat>(Arg.getSemantics()))
4814 return hash_value(Arg.U.Double);
4815 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
4816}
4817
4818APFloat::APFloat(const fltSemantics &Semantics, StringRef S)
4819 : APFloat(Semantics) {
4820 auto StatusOrErr = convertFromString(S, rmNearestTiesToEven);
4821 assert(StatusOrErr && "Invalid floating point representation")((void)0);
4822 consumeError(StatusOrErr.takeError());
4823}
4824
4825APFloat::opStatus APFloat::convert(const fltSemantics &ToSemantics,
4826 roundingMode RM, bool *losesInfo) {
4827 if (&getSemantics() == &ToSemantics) {
4828 *losesInfo = false;
4829 return opOK;
4830 }
4831 if (usesLayout<IEEEFloat>(getSemantics()) &&
4832 usesLayout<IEEEFloat>(ToSemantics))
4833 return U.IEEE.convert(ToSemantics, RM, losesInfo);
4834 if (usesLayout<IEEEFloat>(getSemantics()) &&
4835 usesLayout<DoubleAPFloat>(ToSemantics)) {
4836 assert(&ToSemantics == &semPPCDoubleDouble)((void)0);
4837 auto Ret = U.IEEE.convert(semPPCDoubleDoubleLegacy, RM, losesInfo);
4838 *this = APFloat(ToSemantics, U.IEEE.bitcastToAPInt());
4839 return Ret;
4840 }
4841 if (usesLayout<DoubleAPFloat>(getSemantics()) &&
4842 usesLayout<IEEEFloat>(ToSemantics)) {
4843 auto Ret = getIEEE().convert(ToSemantics, RM, losesInfo);
4844 *this = APFloat(std::move(getIEEE()), ToSemantics);
4845 return Ret;
4846 }
4847 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
4848}
4849
4850APFloat APFloat::getAllOnesValue(const fltSemantics &Semantics,
4851 unsigned BitWidth) {
4852 return APFloat(Semantics, APInt::getAllOnesValue(BitWidth));
4853}
4854
4855void APFloat::print(raw_ostream &OS) const {
4856 SmallVector<char, 16> Buffer;
4857 toString(Buffer);
4858 OS << Buffer << "\n";
4859}
4860
4861#if !defined(NDEBUG1) || defined(LLVM_ENABLE_DUMP)
4862LLVM_DUMP_METHOD__attribute__((noinline)) void APFloat::dump() const { print(dbgs()); }
4863#endif
4864
4865void APFloat::Profile(FoldingSetNodeID &NID) const {
4866 NID.Add(bitcastToAPInt());
4867}
4868
4869/* Same as convertToInteger(integerPart*, ...), except the result is returned in
4870 an APSInt, whose initial bit-width and signed-ness are used to determine the
4871 precision of the conversion.
4872 */
4873APFloat::opStatus APFloat::convertToInteger(APSInt &result,
4874 roundingMode rounding_mode,
4875 bool *isExact) const {
4876 unsigned bitWidth = result.getBitWidth();
4877 SmallVector<uint64_t, 4> parts(result.getNumWords());
4878 opStatus status = convertToInteger(parts, bitWidth, result.isSigned(),
4879 rounding_mode, isExact);
4880 // Keeps the original signed-ness.
4881 result = APInt(bitWidth, parts);
4882 return status;
4883}
4884
4885double APFloat::convertToDouble() const {
4886 if (&getSemantics() == (const llvm::fltSemantics *)&semIEEEdouble)
4887 return getIEEE().convertToDouble();
4888 assert(getSemantics().isRepresentableBy(semIEEEdouble) &&((void)0)
4889 "Float semantics is not representable by IEEEdouble")((void)0);
4890 APFloat Temp = *this;
4891 bool LosesInfo;
4892 opStatus St = Temp.convert(semIEEEdouble, rmNearestTiesToEven, &LosesInfo);
4893 assert(!(St & opInexact) && !LosesInfo && "Unexpected imprecision")((void)0);
4894 (void)St;
4895 return Temp.getIEEE().convertToDouble();
4896}
4897
4898float APFloat::convertToFloat() const {
4899 if (&getSemantics() == (const llvm::fltSemantics *)&semIEEEsingle)
1
Assuming the condition is true
→
2
←
Taking true branch
→
4900 return getIEEE().convertToFloat();
3
←
Calling 'IEEEFloat::convertToFloat'
→
4901 assert(getSemantics().isRepresentableBy(semIEEEsingle) &&((void)0)
4902 "Float semantics is not representable by IEEEsingle")((void)0);
4903 APFloat Temp = *this;
4904 bool LosesInfo;
4905 opStatus St = Temp.convert(semIEEEsingle, rmNearestTiesToEven, &LosesInfo);
4906 assert(!(St & opInexact) && !LosesInfo && "Unexpected imprecision")((void)0);
4907 (void)St;
4908 return Temp.getIEEE().convertToFloat();
4909}
4910
4911} // namespace llvm
4912
4913#undef APFLOAT_DISPATCH_ON_SEMANTICS
←

/usr/src/gnu/usr.bin/clang/libLLVM/../../../llvm/llvm/include/llvm/ADT/APFloat.h

1//===- llvm/ADT/APFloat.h - Arbitrary Precision Floating Point ---*- C++ -*-==//
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/// \file
10/// \brief
11/// This file declares a class to represent arbitrary precision floating point
12/// values and provide a variety of arithmetic operations on them.
13///
14//===----------------------------------------------------------------------===//
15
16#ifndef LLVM_ADT_APFLOAT_H
17#define LLVM_ADT_APFLOAT_H
18
19#include "llvm/ADT/APInt.h"
20#include "llvm/ADT/ArrayRef.h"
21#include "llvm/ADT/FloatingPointMode.h"
22#include "llvm/Support/ErrorHandling.h"
23#include <memory>
24
25#define APFLOAT_DISPATCH_ON_SEMANTICS(METHOD_CALL) \
26 do { \
27 if (usesLayout<IEEEFloat>(getSemantics())) \
28 return U.IEEE.METHOD_CALL; \
29 if (usesLayout<DoubleAPFloat>(getSemantics())) \
30 return U.Double.METHOD_CALL; \
31 llvm_unreachable("Unexpected semantics")__builtin_unreachable(); \
32 } while (false)
33
34namespace llvm {
35
36struct fltSemantics;
37class APSInt;
38class StringRef;
39class APFloat;
40class raw_ostream;
41
42template <typename T> class Expected;
43template <typename T> class SmallVectorImpl;
44
45/// Enum that represents what fraction of the LSB truncated bits of an fp number
46/// represent.
47///
48/// This essentially combines the roles of guard and sticky bits.
49enum lostFraction { // Example of truncated bits:
50 lfExactlyZero, // 000000
51 lfLessThanHalf, // 0xxxxx x's not all zero
52 lfExactlyHalf, // 100000
53 lfMoreThanHalf // 1xxxxx x's not all zero
54};
55
56/// A self-contained host- and target-independent arbitrary-precision
57/// floating-point software implementation.
58///
59/// APFloat uses bignum integer arithmetic as provided by static functions in
60/// the APInt class. The library will work with bignum integers whose parts are
61/// any unsigned type at least 16 bits wide, but 64 bits is recommended.
62///
63/// Written for clarity rather than speed, in particular with a view to use in
64/// the front-end of a cross compiler so that target arithmetic can be correctly
65/// performed on the host. Performance should nonetheless be reasonable,
66/// particularly for its intended use. It may be useful as a base
67/// implementation for a run-time library during development of a faster
68/// target-specific one.
69///
70/// All 5 rounding modes in the IEEE-754R draft are handled correctly for all
71/// implemented operations. Currently implemented operations are add, subtract,
72/// multiply, divide, fused-multiply-add, conversion-to-float,
73/// conversion-to-integer and conversion-from-integer. New rounding modes
74/// (e.g. away from zero) can be added with three or four lines of code.
75///
76/// Four formats are built-in: IEEE single precision, double precision,
77/// quadruple precision, and x87 80-bit extended double (when operating with
78/// full extended precision). Adding a new format that obeys IEEE semantics
79/// only requires adding two lines of code: a declaration and definition of the
80/// format.
81///
82/// All operations return the status of that operation as an exception bit-mask,
83/// so multiple operations can be done consecutively with their results or-ed
84/// together. The returned status can be useful for compiler diagnostics; e.g.,
85/// inexact, underflow and overflow can be easily diagnosed on constant folding,
86/// and compiler optimizers can determine what exceptions would be raised by
87/// folding operations and optimize, or perhaps not optimize, accordingly.
88///
89/// At present, underflow tininess is detected after rounding; it should be
90/// straight forward to add support for the before-rounding case too.
91///
92/// The library reads hexadecimal floating point numbers as per C99, and
93/// correctly rounds if necessary according to the specified rounding mode.
94/// Syntax is required to have been validated by the caller. It also converts
95/// floating point numbers to hexadecimal text as per the C99 %a and %A
96/// conversions. The output precision (or alternatively the natural minimal
97/// precision) can be specified; if the requested precision is less than the
98/// natural precision the output is correctly rounded for the specified rounding
99/// mode.
100///
101/// It also reads decimal floating point numbers and correctly rounds according
102/// to the specified rounding mode.
103///
104/// Conversion to decimal text is not currently implemented.
105///
106/// Non-zero finite numbers are represented internally as a sign bit, a 16-bit
107/// signed exponent, and the significand as an array of integer parts. After
108/// normalization of a number of precision P the exponent is within the range of
109/// the format, and if the number is not denormal the P-th bit of the
110/// significand is set as an explicit integer bit. For denormals the most
111/// significant bit is shifted right so that the exponent is maintained at the
112/// format's minimum, so that the smallest denormal has just the least
113/// significant bit of the significand set. The sign of zeroes and infinities
114/// is significant; the exponent and significand of such numbers is not stored,
115/// but has a known implicit (deterministic) value: 0 for the significands, 0
116/// for zero exponent, all 1 bits for infinity exponent. For NaNs the sign and
117/// significand are deterministic, although not really meaningful, and preserved
118/// in non-conversion operations. The exponent is implicitly all 1 bits.
119///
120/// APFloat does not provide any exception handling beyond default exception
121/// handling. We represent Signaling NaNs via IEEE-754R 2008 6.2.1 should clause
122/// by encoding Signaling NaNs with the first bit of its trailing significand as
123/// 0.
124///
125/// TODO
126/// ====
127///
128/// Some features that may or may not be worth adding:
129///
130/// Binary to decimal conversion (hard).
131///
132/// Optional ability to detect underflow tininess before rounding.
133///
134/// New formats: x87 in single and double precision mode (IEEE apart from
135/// extended exponent range) (hard).
136///
137/// New operations: sqrt, IEEE remainder, C90 fmod, nexttoward.
138///
139
140// This is the common type definitions shared by APFloat and its internal
141// implementation classes. This struct should not define any non-static data
142// members.
143struct APFloatBase {
144 typedef APInt::WordType integerPart;
145 static constexpr unsigned integerPartWidth = APInt::APINT_BITS_PER_WORD;
146
147 /// A signed type to represent a floating point numbers unbiased exponent.
148 typedef int32_t ExponentType;
149
150 /// \name Floating Point Semantics.
151 /// @{
152 enum Semantics {
153 S_IEEEhalf,
154 S_BFloat,
155 S_IEEEsingle,
156 S_IEEEdouble,
157 S_x87DoubleExtended,
158 S_IEEEquad,
159 S_PPCDoubleDouble
160 };
161
162 static const llvm::fltSemantics &EnumToSemantics(Semantics S);
163 static Semantics SemanticsToEnum(const llvm::fltSemantics &Sem);
164
165 static const fltSemantics &IEEEhalf() LLVM_READNONE__attribute__((__const__));
166 static const fltSemantics &BFloat() LLVM_READNONE__attribute__((__const__));
167 static const fltSemantics &IEEEsingle() LLVM_READNONE__attribute__((__const__));
168 static const fltSemantics &IEEEdouble() LLVM_READNONE__attribute__((__const__));
169 static const fltSemantics &IEEEquad() LLVM_READNONE__attribute__((__const__));
170 static const fltSemantics &PPCDoubleDouble() LLVM_READNONE__attribute__((__const__));
171 static const fltSemantics &x87DoubleExtended() LLVM_READNONE__attribute__((__const__));
172
173 /// A Pseudo fltsemantic used to construct APFloats that cannot conflict with
174 /// anything real.
175 static const fltSemantics &Bogus() LLVM_READNONE__attribute__((__const__));
176
177 /// @}
178
179 /// IEEE-754R 5.11: Floating Point Comparison Relations.
180 enum cmpResult {
181 cmpLessThan,
182 cmpEqual,
183 cmpGreaterThan,
184 cmpUnordered
185 };
186
187 /// IEEE-754R 4.3: Rounding-direction attributes.
188 using roundingMode = llvm::RoundingMode;
189
190 static constexpr roundingMode rmNearestTiesToEven =
191 RoundingMode::NearestTiesToEven;
192 static constexpr roundingMode rmTowardPositive = RoundingMode::TowardPositive;
193 static constexpr roundingMode rmTowardNegative = RoundingMode::TowardNegative;
194 static constexpr roundingMode rmTowardZero = RoundingMode::TowardZero;
195 static constexpr roundingMode rmNearestTiesToAway =
196 RoundingMode::NearestTiesToAway;
197
198 /// IEEE-754R 7: Default exception handling.
199 ///
200 /// opUnderflow or opOverflow are always returned or-ed with opInexact.
201 ///
202 /// APFloat models this behavior specified by IEEE-754:
203 /// "For operations producing results in floating-point format, the default
204 /// result of an operation that signals the invalid operation exception
205 /// shall be a quiet NaN."
206 enum opStatus {
207 opOK = 0x00,
208 opInvalidOp = 0x01,
209 opDivByZero = 0x02,
210 opOverflow = 0x04,
211 opUnderflow = 0x08,
212 opInexact = 0x10
213 };
214
215 /// Category of internally-represented number.
216 enum fltCategory {
217 fcInfinity,
218 fcNaN,
219 fcNormal,
220 fcZero
221 };
222
223 /// Convenience enum used to construct an uninitialized APFloat.
224 enum uninitializedTag {
225 uninitialized
226 };
227
228 /// Enumeration of \c ilogb error results.
229 enum IlogbErrorKinds {
230 IEK_Zero = INT_MIN(-2147483647 -1) + 1,
231 IEK_NaN = INT_MIN(-2147483647 -1),
232 IEK_Inf = INT_MAX2147483647
233 };
234
235 static unsigned int semanticsPrecision(const fltSemantics &);
236 static ExponentType semanticsMinExponent(const fltSemantics &);
237 static ExponentType semanticsMaxExponent(const fltSemantics &);
238 static unsigned int semanticsSizeInBits(const fltSemantics &);
239
240 /// Returns the size of the floating point number (in bits) in the given
241 /// semantics.
242 static unsigned getSizeInBits(const fltSemantics &Sem);
243};
244
245namespace detail {
246
247class IEEEFloat final : public APFloatBase {
248public:
249 /// \name Constructors
250 /// @{
251
252 IEEEFloat(const fltSemantics &); // Default construct to +0.0
253 IEEEFloat(const fltSemantics &, integerPart);
254 IEEEFloat(const fltSemantics &, uninitializedTag);
255 IEEEFloat(const fltSemantics &, const APInt &);
256 explicit IEEEFloat(double d);
257 explicit IEEEFloat(float f);
258 IEEEFloat(const IEEEFloat &);
259 IEEEFloat(IEEEFloat &&);
260 ~IEEEFloat();
261
262 /// @}
263
264 /// Returns whether this instance allocated memory.
265 bool needsCleanup() const { return partCount() > 1; }
266
267 /// \name Convenience "constructors"
268 /// @{
269
270 /// @}
271
272 /// \name Arithmetic
273 /// @{
274
275 opStatus add(const IEEEFloat &, roundingMode);
276 opStatus subtract(const IEEEFloat &, roundingMode);
277 opStatus multiply(const IEEEFloat &, roundingMode);
278 opStatus divide(const IEEEFloat &, roundingMode);
279 /// IEEE remainder.
280 opStatus remainder(const IEEEFloat &);
281 /// C fmod, or llvm frem.
282 opStatus mod(const IEEEFloat &);
283 opStatus fusedMultiplyAdd(const IEEEFloat &, const IEEEFloat &, roundingMode);
284 opStatus roundToIntegral(roundingMode);
285 /// IEEE-754R 5.3.1: nextUp/nextDown.
286 opStatus next(bool nextDown);
287
288 /// @}
289
290 /// \name Sign operations.
291 /// @{
292
293 void changeSign();
294
295 /// @}
296
297 /// \name Conversions
298 /// @{
299
300 opStatus convert(const fltSemantics &, roundingMode, bool *);
301 opStatus convertToInteger(MutableArrayRef<integerPart>, unsigned int, bool,
302 roundingMode, bool *) const;
303 opStatus convertFromAPInt(const APInt &, bool, roundingMode);
304 opStatus convertFromSignExtendedInteger(const integerPart *, unsigned int,
305 bool, roundingMode);
306 opStatus convertFromZeroExtendedInteger(const integerPart *, unsigned int,
307 bool, roundingMode);
308 Expected<opStatus> convertFromString(StringRef, roundingMode);
309 APInt bitcastToAPInt() const;
310 double convertToDouble() const;
311 float convertToFloat() const;
312
313 /// @}
314
315 /// The definition of equality is not straightforward for floating point, so
316 /// we won't use operator==. Use one of the following, or write whatever it
317 /// is you really mean.
318 bool operator==(const IEEEFloat &) const = delete;
319
320 /// IEEE comparison with another floating point number (NaNs compare
321 /// unordered, 0==-0).
322 cmpResult compare(const IEEEFloat &) const;
323
324 /// Bitwise comparison for equality (QNaNs compare equal, 0!=-0).
325 bool bitwiseIsEqual(const IEEEFloat &) const;
326
327 /// Write out a hexadecimal representation of the floating point value to DST,
328 /// which must be of sufficient size, in the C99 form [-]0xh.hhhhp[+-]d.
329 /// Return the number of characters written, excluding the terminating NUL.
330 unsigned int convertToHexString(char *dst, unsigned int hexDigits,
331 bool upperCase, roundingMode) const;
332
333 /// \name IEEE-754R 5.7.2 General operations.
334 /// @{
335
336 /// IEEE-754R isSignMinus: Returns true if and only if the current value is
337 /// negative.
338 ///
339 /// This applies to zeros and NaNs as well.
340 bool isNegative() const { return sign; }
341
342 /// IEEE-754R isNormal: Returns true if and only if the current value is normal.
343 ///
344 /// This implies that the current value of the float is not zero, subnormal,
345 /// infinite, or NaN following the definition of normality from IEEE-754R.
346 bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }
347
348 /// Returns true if and only if the current value is zero, subnormal, or
349 /// normal.
350 ///
351 /// This means that the value is not infinite or NaN.
352 bool isFinite() const { return !isNaN() && !isInfinity(); }
353
354 /// Returns true if and only if the float is plus or minus zero.
355 bool isZero() const { return category == fcZero; }
356
357 /// IEEE-754R isSubnormal(): Returns true if and only if the float is a
358 /// denormal.
359 bool isDenormal() const;
360
361 /// IEEE-754R isInfinite(): Returns true if and only if the float is infinity.
362 bool isInfinity() const { return category == fcInfinity; }
363
364 /// Returns true if and only if the float is a quiet or signaling NaN.
365 bool isNaN() const { return category == fcNaN; }
366
367 /// Returns true if and only if the float is a signaling NaN.
368 bool isSignaling() const;
369
370 /// @}
371
372 /// \name Simple Queries
373 /// @{
374
375 fltCategory getCategory() const { return category; }
376 const fltSemantics &getSemantics() const { return *semantics; }
377 bool isNonZero() const { return category != fcZero; }
378 bool isFiniteNonZero() const { return isFinite() && !isZero(); }
26
←
Assuming the condition is true
→
27
←
Returning the value 1, which participates in a condition later
→
379 bool isPosZero() const { return isZero() && !isNegative(); }
380 bool isNegZero() const { return isZero() && isNegative(); }
381
382 /// Returns true if and only if the number has the smallest possible non-zero
383 /// magnitude in the current semantics.
384 bool isSmallest() const;
385
386 /// Returns true if and only if the number has the largest possible finite
387 /// magnitude in the current semantics.
388 bool isLargest() const;
389
390 /// Returns true if and only if the number is an exact integer.
391 bool isInteger() const;
392
393 /// @}
394
395 IEEEFloat &operator=(const IEEEFloat &);
396 IEEEFloat &operator=(IEEEFloat &&);
397
398 /// Overload to compute a hash code for an APFloat value.
399 ///
400 /// Note that the use of hash codes for floating point values is in general
401 /// frought with peril. Equality is hard to define for these values. For
402 /// example, should negative and positive zero hash to different codes? Are
403 /// they equal or not? This hash value implementation specifically
404 /// emphasizes producing different codes for different inputs in order to
405 /// be used in canonicalization and memoization. As such, equality is
406 /// bitwiseIsEqual, and 0 != -0.
407 friend hash_code hash_value(const IEEEFloat &Arg);
408
409 /// Converts this value into a decimal string.
410 ///
411 /// \param FormatPrecision The maximum number of digits of
412 /// precision to output. If there are fewer digits available,
413 /// zero padding will not be used unless the value is
414 /// integral and small enough to be expressed in
415 /// FormatPrecision digits. 0 means to use the natural
416 /// precision of the number.
417 /// \param FormatMaxPadding The maximum number of zeros to
418 /// consider inserting before falling back to scientific
419 /// notation. 0 means to always use scientific notation.
420 ///
421 /// \param TruncateZero Indicate whether to remove the trailing zero in
422 /// fraction part or not. Also setting this parameter to false forcing
423 /// producing of output more similar to default printf behavior.
424 /// Specifically the lower e is used as exponent delimiter and exponent
425 /// always contains no less than two digits.
426 ///
427 /// Number Precision MaxPadding Result
428 /// ------ --------- ---------- ------
429 /// 1.01E+4 5 2 10100
430 /// 1.01E+4 4 2 1.01E+4
431 /// 1.01E+4 5 1 1.01E+4
432 /// 1.01E-2 5 2 0.0101
433 /// 1.01E-2 4 2 0.0101
434 /// 1.01E-2 4 1 1.01E-2
435 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision = 0,
436 unsigned FormatMaxPadding = 3, bool TruncateZero = true) const;
437
438 /// If this value has an exact multiplicative inverse, store it in inv and
439 /// return true.
440 bool getExactInverse(APFloat *inv) const;
441
442 /// Returns the exponent of the internal representation of the APFloat.
443 ///
444 /// Because the radix of APFloat is 2, this is equivalent to floor(log2(x)).
445 /// For special APFloat values, this returns special error codes:
446 ///
447 /// NaN -> \c IEK_NaN
448 /// 0 -> \c IEK_Zero
449 /// Inf -> \c IEK_Inf
450 ///
451 friend int ilogb(const IEEEFloat &Arg);
452
453 /// Returns: X * 2^Exp for integral exponents.
454 friend IEEEFloat scalbn(IEEEFloat X, int Exp, roundingMode);
455
456 friend IEEEFloat frexp(const IEEEFloat &X, int &Exp, roundingMode);
457
458 /// \name Special value setters.
459 /// @{
460
461 void makeLargest(bool Neg = false);
462 void makeSmallest(bool Neg = false);
463 void makeNaN(bool SNaN = false, bool Neg = false,
464 const APInt *fill = nullptr);
465 void makeInf(bool Neg = false);
466 void makeZero(bool Neg = false);
467 void makeQuiet();
468
469 /// Returns the smallest (by magnitude) normalized finite number in the given
470 /// semantics.
471 ///
472 /// \param Negative - True iff the number should be negative
473 void makeSmallestNormalized(bool Negative = false);
474
475 /// @}
476
477 cmpResult compareAbsoluteValue(const IEEEFloat &) const;
478
479private:
480 /// \name Simple Queries
481 /// @{
482
483 integerPart *significandParts();
484 const integerPart *significandParts() const;
485 unsigned int partCount() const;
486
487 /// @}
488
489 /// \name Significand operations.
490 /// @{
491
492 integerPart addSignificand(const IEEEFloat &);
493 integerPart subtractSignificand(const IEEEFloat &, integerPart);
494 lostFraction addOrSubtractSignificand(const IEEEFloat &, bool subtract);
495 lostFraction multiplySignificand(const IEEEFloat &, IEEEFloat);
496 lostFraction multiplySignificand(const IEEEFloat&);
497 lostFraction divideSignificand(const IEEEFloat &);
498 void incrementSignificand();
499 void initialize(const fltSemantics *);
500 void shiftSignificandLeft(unsigned int);
501 lostFraction shiftSignificandRight(unsigned int);
502 unsigned int significandLSB() const;
503 unsigned int significandMSB() const;
504 void zeroSignificand();
505 /// Return true if the significand excluding the integral bit is all ones.
506 bool isSignificandAllOnes() const;
507 /// Return true if the significand excluding the integral bit is all zeros.
508 bool isSignificandAllZeros() const;
509
510 /// @}
511
512 /// \name Arithmetic on special values.
513 /// @{
514
515 opStatus addOrSubtractSpecials(const IEEEFloat &, bool subtract);
516 opStatus divideSpecials(const IEEEFloat &);
517 opStatus multiplySpecials(const IEEEFloat &);
518 opStatus modSpecials(const IEEEFloat &);
519 opStatus remainderSpecials(const IEEEFloat&);
520
521 /// @}
522
523 /// \name Miscellany
524 /// @{
525
526 bool convertFromStringSpecials(StringRef str);
527 opStatus normalize(roundingMode, lostFraction);
528 opStatus addOrSubtract(const IEEEFloat &, roundingMode, bool subtract);
529 opStatus handleOverflow(roundingMode);
530 bool roundAwayFromZero(roundingMode, lostFraction, unsigned int) const;
531 opStatus convertToSignExtendedInteger(MutableArrayRef<integerPart>,
532 unsigned int, bool, roundingMode,
533 bool *) const;
534 opStatus convertFromUnsignedParts(const integerPart *, unsigned int,
535 roundingMode);
536 Expected<opStatus> convertFromHexadecimalString(StringRef, roundingMode);
537 Expected<opStatus> convertFromDecimalString(StringRef, roundingMode);
538 char *convertNormalToHexString(char *, unsigned int, bool,
539 roundingMode) const;
540 opStatus roundSignificandWithExponent(const integerPart *, unsigned int, int,
541 roundingMode);
542 ExponentType exponentNaN() const;
543 ExponentType exponentInf() const;
544 ExponentType exponentZero() const;
545
546 /// @}
547
548 APInt convertHalfAPFloatToAPInt() const;
549 APInt convertBFloatAPFloatToAPInt() const;
550 APInt convertFloatAPFloatToAPInt() const;
551 APInt convertDoubleAPFloatToAPInt() const;
552 APInt convertQuadrupleAPFloatToAPInt() const;
553 APInt convertF80LongDoubleAPFloatToAPInt() const;
554 APInt convertPPCDoubleDoubleAPFloatToAPInt() const;
555 void initFromAPInt(const fltSemantics *Sem, const APInt &api);
556 void initFromHalfAPInt(const APInt &api);
557 void initFromBFloatAPInt(const APInt &api);
558 void initFromFloatAPInt(const APInt &api);
559 void initFromDoubleAPInt(const APInt &api);
560 void initFromQuadrupleAPInt(const APInt &api);
561 void initFromF80LongDoubleAPInt(const APInt &api);
562 void initFromPPCDoubleDoubleAPInt(const APInt &api);
563
564 void assign(const IEEEFloat &);
565 void copySignificand(const IEEEFloat &);
566 void freeSignificand();
567
568 /// Note: this must be the first data member.
569 /// The semantics that this value obeys.
570 const fltSemantics *semantics;
571
572 /// A binary fraction with an explicit integer bit.
573 ///
574 /// The significand must be at least one bit wider than the target precision.
575 union Significand {
576 integerPart part;
577 integerPart *parts;
578 } significand;
579
580 /// The signed unbiased exponent of the value.
581 ExponentType exponent;
582
583 /// What kind of floating point number this is.
584 ///
585 /// Only 2 bits are required, but VisualStudio incorrectly sign extends it.
586 /// Using the extra bit keeps it from failing under VisualStudio.
587 fltCategory category : 3;
588
589 /// Sign bit of the number.
590 unsigned int sign : 1;
591};
592
593hash_code hash_value(const IEEEFloat &Arg);
594int ilogb(const IEEEFloat &Arg);
595IEEEFloat scalbn(IEEEFloat X, int Exp, IEEEFloat::roundingMode);
596IEEEFloat frexp(const IEEEFloat &Val, int &Exp, IEEEFloat::roundingMode RM);
597
598// This mode implements more precise float in terms of two APFloats.
599// The interface and layout is designed for arbitrary underlying semantics,
600// though currently only PPCDoubleDouble semantics are supported, whose
601// corresponding underlying semantics are IEEEdouble.
602class DoubleAPFloat final : public APFloatBase {
603 // Note: this must be the first data member.
604 const fltSemantics *Semantics;
605 std::unique_ptr<APFloat[]> Floats;
606
607 opStatus addImpl(const APFloat &a, const APFloat &aa, const APFloat &c,
608 const APFloat &cc, roundingMode RM);
609
610 opStatus addWithSpecial(const DoubleAPFloat &LHS, const DoubleAPFloat &RHS,
611 DoubleAPFloat &Out, roundingMode RM);
612
613public:
614 DoubleAPFloat(const fltSemantics &S);
615 DoubleAPFloat(const fltSemantics &S, uninitializedTag);
616 DoubleAPFloat(const fltSemantics &S, integerPart);
617 DoubleAPFloat(const fltSemantics &S, const APInt &I);
618 DoubleAPFloat(const fltSemantics &S, APFloat &&First, APFloat &&Second);
619 DoubleAPFloat(const DoubleAPFloat &RHS);
620 DoubleAPFloat(DoubleAPFloat &&RHS);
621
622 DoubleAPFloat &operator=(const DoubleAPFloat &RHS);
623
624 DoubleAPFloat &operator=(DoubleAPFloat &&RHS) {
625 if (this != &RHS) {
626 this->~DoubleAPFloat();
627 new (this) DoubleAPFloat(std::move(RHS));
628 }
629 return *this;
630 }
631
632 bool needsCleanup() const { return Floats != nullptr; }
633
634 APFloat &getFirst() { return Floats[0]; }
635 const APFloat &getFirst() const { return Floats[0]; }
636 APFloat &getSecond() { return Floats[1]; }
637 const APFloat &getSecond() const { return Floats[1]; }
638
639 opStatus add(const DoubleAPFloat &RHS, roundingMode RM);
640 opStatus subtract(const DoubleAPFloat &RHS, roundingMode RM);
641 opStatus multiply(const DoubleAPFloat &RHS, roundingMode RM);
642 opStatus divide(const DoubleAPFloat &RHS, roundingMode RM);
643 opStatus remainder(const DoubleAPFloat &RHS);
644 opStatus mod(const DoubleAPFloat &RHS);
645 opStatus fusedMultiplyAdd(const DoubleAPFloat &Multiplicand,
646 const DoubleAPFloat &Addend, roundingMode RM);
647 opStatus roundToIntegral(roundingMode RM);
648 void changeSign();
649 cmpResult compareAbsoluteValue(const DoubleAPFloat &RHS) const;
650
651 fltCategory getCategory() const;
652 bool isNegative() const;
653
654 void makeInf(bool Neg);
655 void makeZero(bool Neg);
656 void makeLargest(bool Neg);
657 void makeSmallest(bool Neg);
658 void makeSmallestNormalized(bool Neg);
659 void makeNaN(bool SNaN, bool Neg, const APInt *fill);
660
661 cmpResult compare(const DoubleAPFloat &RHS) const;
662 bool bitwiseIsEqual(const DoubleAPFloat &RHS) const;
663 APInt bitcastToAPInt() const;
664 Expected<opStatus> convertFromString(StringRef, roundingMode);
665 opStatus next(bool nextDown);
666
667 opStatus convertToInteger(MutableArrayRef<integerPart> Input,
668 unsigned int Width, bool IsSigned, roundingMode RM,
669 bool *IsExact) const;
670 opStatus convertFromAPInt(const APInt &Input, bool IsSigned, roundingMode RM);
671 opStatus convertFromSignExtendedInteger(const integerPart *Input,
672 unsigned int InputSize, bool IsSigned,
673 roundingMode RM);
674 opStatus convertFromZeroExtendedInteger(const integerPart *Input,
675 unsigned int InputSize, bool IsSigned,
676 roundingMode RM);
677 unsigned int convertToHexString(char *DST, unsigned int HexDigits,
678 bool UpperCase, roundingMode RM) const;
679
680 bool isDenormal() const;
681 bool isSmallest() const;
682 bool isLargest() const;
683 bool isInteger() const;
684
685 void toString(SmallVectorImpl<char> &Str, unsigned FormatPrecision,
686 unsigned FormatMaxPadding, bool TruncateZero = true) const;
687
688 bool getExactInverse(APFloat *inv) const;
689
690 friend DoubleAPFloat scalbn(const DoubleAPFloat &X, int Exp, roundingMode);
691 friend DoubleAPFloat frexp(const DoubleAPFloat &X, int &Exp, roundingMode);
692 friend hash_code hash_value(const DoubleAPFloat &Arg);
693};
694
695hash_code hash_value(const DoubleAPFloat &Arg);
696
697} // End detail namespace
698
699// This is a interface class that is currently forwarding functionalities from
700// detail::IEEEFloat.
701class APFloat : public APFloatBase {
702 typedef detail::IEEEFloat IEEEFloat;
703 typedef detail::DoubleAPFloat DoubleAPFloat;
704
705 static_assert(std::is_standard_layout<IEEEFloat>::value, "");
706
707 union Storage {
708 const fltSemantics *semantics;
709 IEEEFloat IEEE;
710 DoubleAPFloat Double;
711
712 explicit Storage(IEEEFloat F, const fltSemantics &S);
713 explicit Storage(DoubleAPFloat F, const fltSemantics &S)
714 : Double(std::move(F)) {
715 assert(&S == &PPCDoubleDouble())((void)0);
716 }
717
718 template <typename... ArgTypes>
719 Storage(const fltSemantics &Semantics, ArgTypes &&... Args) {
720 if (usesLayout<IEEEFloat>(Semantics)) {
721 new (&IEEE) IEEEFloat(Semantics, std::forward<ArgTypes>(Args)...);
722 return;
723 }
724 if (usesLayout<DoubleAPFloat>(Semantics)) {
725 new (&Double) DoubleAPFloat(Semantics, std::forward<ArgTypes>(Args)...);
726 return;
727 }
728 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
729 }
730
731 ~Storage() {
732 if (usesLayout<IEEEFloat>(*semantics)) {
733 IEEE.~IEEEFloat();
734 return;
735 }
736 if (usesLayout<DoubleAPFloat>(*semantics)) {
737 Double.~DoubleAPFloat();
738 return;
739 }
740 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
741 }
742
743 Storage(const Storage &RHS) {
744 if (usesLayout<IEEEFloat>(*RHS.semantics)) {
745 new (this) IEEEFloat(RHS.IEEE);
746 return;
747 }
748 if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
749 new (this) DoubleAPFloat(RHS.Double);
750 return;
751 }
752 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
753 }
754
755 Storage(Storage &&RHS) {
756 if (usesLayout<IEEEFloat>(*RHS.semantics)) {
757 new (this) IEEEFloat(std::move(RHS.IEEE));
758 return;
759 }
760 if (usesLayout<DoubleAPFloat>(*RHS.semantics)) {
761 new (this) DoubleAPFloat(std::move(RHS.Double));
762 return;
763 }
764 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
765 }
766
767 Storage &operator=(const Storage &RHS) {
768 if (usesLayout<IEEEFloat>(*semantics) &&
769 usesLayout<IEEEFloat>(*RHS.semantics)) {
770 IEEE = RHS.IEEE;
771 } else if (usesLayout<DoubleAPFloat>(*semantics) &&
772 usesLayout<DoubleAPFloat>(*RHS.semantics)) {
773 Double = RHS.Double;
774 } else if (this != &RHS) {
775 this->~Storage();
776 new (this) Storage(RHS);
777 }
778 return *this;
779 }
780
781 Storage &operator=(Storage &&RHS) {
782 if (usesLayout<IEEEFloat>(*semantics) &&
783 usesLayout<IEEEFloat>(*RHS.semantics)) {
784 IEEE = std::move(RHS.IEEE);
785 } else if (usesLayout<DoubleAPFloat>(*semantics) &&
786 usesLayout<DoubleAPFloat>(*RHS.semantics)) {
787 Double = std::move(RHS.Double);
788 } else if (this != &RHS) {
789 this->~Storage();
790 new (this) Storage(std::move(RHS));
791 }
792 return *this;
793 }
794 } U;
795
796 template <typename T> static bool usesLayout(const fltSemantics &Semantics) {
797 static_assert(std::is_same<T, IEEEFloat>::value ||
798 std::is_same<T, DoubleAPFloat>::value, "");
799 if (std::is_same<T, DoubleAPFloat>::value) {
800 return &Semantics == &PPCDoubleDouble();
801 }
802 return &Semantics != &PPCDoubleDouble();
803 }
804
805 IEEEFloat &getIEEE() {
806 if (usesLayout<IEEEFloat>(*U.semantics))
807 return U.IEEE;
808 if (usesLayout<DoubleAPFloat>(*U.semantics))
809 return U.Double.getFirst().U.IEEE;
810 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
811 }
812
813 const IEEEFloat &getIEEE() const {
814 if (usesLayout<IEEEFloat>(*U.semantics))
815 return U.IEEE;
816 if (usesLayout<DoubleAPFloat>(*U.semantics))
817 return U.Double.getFirst().U.IEEE;
818 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
819 }
820
821 void makeZero(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeZero(Neg)); }
822
823 void makeInf(bool Neg) { APFLOAT_DISPATCH_ON_SEMANTICS(makeInf(Neg)); }
824
825 void makeNaN(bool SNaN, bool Neg, const APInt *fill) {
826 APFLOAT_DISPATCH_ON_SEMANTICS(makeNaN(SNaN, Neg, fill));
827 }
828
829 void makeLargest(bool Neg) {
830 APFLOAT_DISPATCH_ON_SEMANTICS(makeLargest(Neg));
831 }
832
833 void makeSmallest(bool Neg) {
834 APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallest(Neg));
835 }
836
837 void makeSmallestNormalized(bool Neg) {
838 APFLOAT_DISPATCH_ON_SEMANTICS(makeSmallestNormalized(Neg));
839 }
840
841 // FIXME: This is due to clang 3.3 (or older version) always checks for the
842 // default constructor in an array aggregate initialization, even if no
843 // elements in the array is default initialized.
844 APFloat() : U(IEEEdouble()) {
845 llvm_unreachable("This is a workaround for old clang.")__builtin_unreachable();
846 }
847
848 explicit APFloat(IEEEFloat F, const fltSemantics &S) : U(std::move(F), S) {}
849 explicit APFloat(DoubleAPFloat F, const fltSemantics &S)
850 : U(std::move(F), S) {}
851
852 cmpResult compareAbsoluteValue(const APFloat &RHS) const {
853 assert(&getSemantics() == &RHS.getSemantics() &&((void)0)
854 "Should only compare APFloats with the same semantics")((void)0);
855 if (usesLayout<IEEEFloat>(getSemantics()))
856 return U.IEEE.compareAbsoluteValue(RHS.U.IEEE);
857 if (usesLayout<DoubleAPFloat>(getSemantics()))
858 return U.Double.compareAbsoluteValue(RHS.U.Double);
859 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
860 }
861
862public:
863 APFloat(const fltSemantics &Semantics) : U(Semantics) {}
864 APFloat(const fltSemantics &Semantics, StringRef S);
865 APFloat(const fltSemantics &Semantics, integerPart I) : U(Semantics, I) {}
866 template <typename T,
867 typename = std::enable_if_t<std::is_floating_point<T>::value>>
868 APFloat(const fltSemantics &Semantics, T V) = delete;
869 // TODO: Remove this constructor. This isn't faster than the first one.
870 APFloat(const fltSemantics &Semantics, uninitializedTag)
871 : U(Semantics, uninitialized) {}
872 APFloat(const fltSemantics &Semantics, const APInt &I) : U(Semantics, I) {}
873 explicit APFloat(double d) : U(IEEEFloat(d), IEEEdouble()) {}
874 explicit APFloat(float f) : U(IEEEFloat(f), IEEEsingle()) {}
875 APFloat(const APFloat &RHS) = default;
876 APFloat(APFloat &&RHS) = default;
877
878 ~APFloat() = default;
879
880 bool needsCleanup() const { APFLOAT_DISPATCH_ON_SEMANTICS(needsCleanup()); }
881
882 /// Factory for Positive and Negative Zero.
883 ///
884 /// \param Negative True iff the number should be negative.
885 static APFloat getZero(const fltSemantics &Sem, bool Negative = false) {
886 APFloat Val(Sem, uninitialized);
887 Val.makeZero(Negative);
888 return Val;
889 }
890
891 /// Factory for Positive and Negative Infinity.
892 ///
893 /// \param Negative True iff the number should be negative.
894 static APFloat getInf(const fltSemantics &Sem, bool Negative = false) {
895 APFloat Val(Sem, uninitialized);
896 Val.makeInf(Negative);
897 return Val;
898 }
899
900 /// Factory for NaN values.
901 ///
902 /// \param Negative - True iff the NaN generated should be negative.
903 /// \param payload - The unspecified fill bits for creating the NaN, 0 by
904 /// default. The value is truncated as necessary.
905 static APFloat getNaN(const fltSemantics &Sem, bool Negative = false,
906 uint64_t payload = 0) {
907 if (payload) {
908 APInt intPayload(64, payload);
909 return getQNaN(Sem, Negative, &intPayload);
910 } else {
911 return getQNaN(Sem, Negative, nullptr);
912 }
913 }
914
915 /// Factory for QNaN values.
916 static APFloat getQNaN(const fltSemantics &Sem, bool Negative = false,
917 const APInt *payload = nullptr) {
918 APFloat Val(Sem, uninitialized);
919 Val.makeNaN(false, Negative, payload);
920 return Val;
921 }
922
923 /// Factory for SNaN values.
924 static APFloat getSNaN(const fltSemantics &Sem, bool Negative = false,
925 const APInt *payload = nullptr) {
926 APFloat Val(Sem, uninitialized);
927 Val.makeNaN(true, Negative, payload);
928 return Val;
929 }
930
931 /// Returns the largest finite number in the given semantics.
932 ///
933 /// \param Negative - True iff the number should be negative
934 static APFloat getLargest(const fltSemantics &Sem, bool Negative = false) {
935 APFloat Val(Sem, uninitialized);
936 Val.makeLargest(Negative);
937 return Val;
938 }
939
940 /// Returns the smallest (by magnitude) finite number in the given semantics.
941 /// Might be denormalized, which implies a relative loss of precision.
942 ///
943 /// \param Negative - True iff the number should be negative
944 static APFloat getSmallest(const fltSemantics &Sem, bool Negative = false) {
945 APFloat Val(Sem, uninitialized);
946 Val.makeSmallest(Negative);
947 return Val;
948 }
949
950 /// Returns the smallest (by magnitude) normalized finite number in the given
951 /// semantics.
952 ///
953 /// \param Negative - True iff the number should be negative
954 static APFloat getSmallestNormalized(const fltSemantics &Sem,
955 bool Negative = false) {
956 APFloat Val(Sem, uninitialized);
957 Val.makeSmallestNormalized(Negative);
958 return Val;
959 }
960
961 /// Returns a float which is bitcasted from an all one value int.
962 ///
963 /// \param Semantics - type float semantics
964 /// \param BitWidth - Select float type
965 static APFloat getAllOnesValue(const fltSemantics &Semantics,
966 unsigned BitWidth);
967
968 /// Used to insert APFloat objects, or objects that contain APFloat objects,
969 /// into FoldingSets.
970 void Profile(FoldingSetNodeID &NID) const;
971
972 opStatus add(const APFloat &RHS, roundingMode RM) {
973 assert(&getSemantics() == &RHS.getSemantics() &&((void)0)
974 "Should only call on two APFloats with the same semantics")((void)0);
975 if (usesLayout<IEEEFloat>(getSemantics()))
976 return U.IEEE.add(RHS.U.IEEE, RM);
977 if (usesLayout<DoubleAPFloat>(getSemantics()))
978 return U.Double.add(RHS.U.Double, RM);
979 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
980 }
981 opStatus subtract(const APFloat &RHS, roundingMode RM) {
982 assert(&getSemantics() == &RHS.getSemantics() &&((void)0)
983 "Should only call on two APFloats with the same semantics")((void)0);
984 if (usesLayout<IEEEFloat>(getSemantics()))
985 return U.IEEE.subtract(RHS.U.IEEE, RM);
986 if (usesLayout<DoubleAPFloat>(getSemantics()))
987 return U.Double.subtract(RHS.U.Double, RM);
988 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
989 }
990 opStatus multiply(const APFloat &RHS, roundingMode RM) {
991 assert(&getSemantics() == &RHS.getSemantics() &&((void)0)
992 "Should only call on two APFloats with the same semantics")((void)0);
993 if (usesLayout<IEEEFloat>(getSemantics()))
994 return U.IEEE.multiply(RHS.U.IEEE, RM);
995 if (usesLayout<DoubleAPFloat>(getSemantics()))
996 return U.Double.multiply(RHS.U.Double, RM);
997 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
998 }
999 opStatus divide(const APFloat &RHS, roundingMode RM) {
1000 assert(&getSemantics() == &RHS.getSemantics() &&((void)0)
1001 "Should only call on two APFloats with the same semantics")((void)0);
1002 if (usesLayout<IEEEFloat>(getSemantics()))
1003 return U.IEEE.divide(RHS.U.IEEE, RM);
1004 if (usesLayout<DoubleAPFloat>(getSemantics()))
1005 return U.Double.divide(RHS.U.Double, RM);
1006 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
1007 }
1008 opStatus remainder(const APFloat &RHS) {
1009 assert(&getSemantics() == &RHS.getSemantics() &&((void)0)
1010 "Should only call on two APFloats with the same semantics")((void)0);
1011 if (usesLayout<IEEEFloat>(getSemantics()))
1012 return U.IEEE.remainder(RHS.U.IEEE);
1013 if (usesLayout<DoubleAPFloat>(getSemantics()))
1014 return U.Double.remainder(RHS.U.Double);
1015 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
1016 }
1017 opStatus mod(const APFloat &RHS) {
1018 assert(&getSemantics() == &RHS.getSemantics() &&((void)0)
1019 "Should only call on two APFloats with the same semantics")((void)0);
1020 if (usesLayout<IEEEFloat>(getSemantics()))
1021 return U.IEEE.mod(RHS.U.IEEE);
1022 if (usesLayout<DoubleAPFloat>(getSemantics()))
1023 return U.Double.mod(RHS.U.Double);
1024 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
1025 }
1026 opStatus fusedMultiplyAdd(const APFloat &Multiplicand, const APFloat &Addend,
1027 roundingMode RM) {
1028 assert(&getSemantics() == &Multiplicand.getSemantics() &&((void)0)
1029 "Should only call on APFloats with the same semantics")((void)0);
1030 assert(&getSemantics() == &Addend.getSemantics() &&((void)0)
1031 "Should only call on APFloats with the same semantics")((void)0);
1032 if (usesLayout<IEEEFloat>(getSemantics()))
1033 return U.IEEE.fusedMultiplyAdd(Multiplicand.U.IEEE, Addend.U.IEEE, RM);
1034 if (usesLayout<DoubleAPFloat>(getSemantics()))
1035 return U.Double.fusedMultiplyAdd(Multiplicand.U.Double, Addend.U.Double,
1036 RM);
1037 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
1038 }
1039 opStatus roundToIntegral(roundingMode RM) {
1040 APFLOAT_DISPATCH_ON_SEMANTICS(roundToIntegral(RM));
1041 }
1042
1043 // TODO: bool parameters are not readable and a source of bugs.
1044 // Do something.
1045 opStatus next(bool nextDown) {
1046 APFLOAT_DISPATCH_ON_SEMANTICS(next(nextDown));
1047 }
1048
1049 /// Negate an APFloat.
1050 APFloat operator-() const {
1051 APFloat Result(*this);
1052 Result.changeSign();
1053 return Result;
1054 }
1055
1056 /// Add two APFloats, rounding ties to the nearest even.
1057 /// No error checking.
1058 APFloat operator+(const APFloat &RHS) const {
1059 APFloat Result(*this);
1060 (void)Result.add(RHS, rmNearestTiesToEven);
1061 return Result;
1062 }
1063
1064 /// Subtract two APFloats, rounding ties to the nearest even.
1065 /// No error checking.
1066 APFloat operator-(const APFloat &RHS) const {
1067 APFloat Result(*this);
1068 (void)Result.subtract(RHS, rmNearestTiesToEven);
1069 return Result;
1070 }
1071
1072 /// Multiply two APFloats, rounding ties to the nearest even.
1073 /// No error checking.
1074 APFloat operator*(const APFloat &RHS) const {
1075 APFloat Result(*this);
1076 (void)Result.multiply(RHS, rmNearestTiesToEven);
1077 return Result;
1078 }
1079
1080 /// Divide the first APFloat by the second, rounding ties to the nearest even.
1081 /// No error checking.
1082 APFloat operator/(const APFloat &RHS) const {
1083 APFloat Result(*this);
1084 (void)Result.divide(RHS, rmNearestTiesToEven);
1085 return Result;
1086 }
1087
1088 void changeSign() { APFLOAT_DISPATCH_ON_SEMANTICS(changeSign()); }
1089 void clearSign() {
1090 if (isNegative())
1091 changeSign();
1092 }
1093 void copySign(const APFloat &RHS) {
1094 if (isNegative() != RHS.isNegative())
1095 changeSign();
1096 }
1097
1098 /// A static helper to produce a copy of an APFloat value with its sign
1099 /// copied from some other APFloat.
1100 static APFloat copySign(APFloat Value, const APFloat &Sign) {
1101 Value.copySign(Sign);
1102 return Value;
1103 }
1104
1105 opStatus convert(const fltSemantics &ToSemantics, roundingMode RM,
1106 bool *losesInfo);
1107 opStatus convertToInteger(MutableArrayRef<integerPart> Input,
1108 unsigned int Width, bool IsSigned, roundingMode RM,
1109 bool *IsExact) const {
1110 APFLOAT_DISPATCH_ON_SEMANTICS(
1111 convertToInteger(Input, Width, IsSigned, RM, IsExact));
1112 }
1113 opStatus convertToInteger(APSInt &Result, roundingMode RM,
1114 bool *IsExact) const;
1115 opStatus convertFromAPInt(const APInt &Input, bool IsSigned,
1116 roundingMode RM) {
1117 APFLOAT_DISPATCH_ON_SEMANTICS(convertFromAPInt(Input, IsSigned, RM));
1118 }
1119 opStatus convertFromSignExtendedInteger(const integerPart *Input,
1120 unsigned int InputSize, bool IsSigned,
1121 roundingMode RM) {
1122 APFLOAT_DISPATCH_ON_SEMANTICS(
1123 convertFromSignExtendedInteger(Input, InputSize, IsSigned, RM));
1124 }
1125 opStatus convertFromZeroExtendedInteger(const integerPart *Input,
1126 unsigned int InputSize, bool IsSigned,
1127 roundingMode RM) {
1128 APFLOAT_DISPATCH_ON_SEMANTICS(
1129 convertFromZeroExtendedInteger(Input, InputSize, IsSigned, RM));
1130 }
1131 Expected<opStatus> convertFromString(StringRef, roundingMode);
1132 APInt bitcastToAPInt() const {
1133 APFLOAT_DISPATCH_ON_SEMANTICS(bitcastToAPInt());
1134 }
1135
1136 /// Converts this APFloat to host double value.
1137 ///
1138 /// \pre The APFloat must be built using semantics, that can be represented by
1139 /// the host double type without loss of precision. It can be IEEEdouble and
1140 /// shorter semantics, like IEEEsingle and others.
1141 double convertToDouble() const;
1142
1143 /// Converts this APFloat to host float value.
1144 ///
1145 /// \pre The APFloat must be built using semantics, that can be represented by
1146 /// the host float type without loss of precision. It can be IEEEsingle and
1147 /// shorter semantics, like IEEEhalf.
1148 float convertToFloat() const;
1149
1150 bool operator==(const APFloat &RHS) const { return compare(RHS) == cmpEqual; }
1151
1152 bool operator!=(const APFloat &RHS) const { return compare(RHS) != cmpEqual; }
1153
1154 bool operator<(const APFloat &RHS) const {
1155 return compare(RHS) == cmpLessThan;
1156 }
1157
1158 bool operator>(const APFloat &RHS) const {
1159 return compare(RHS) == cmpGreaterThan;
1160 }
1161
1162 bool operator<=(const APFloat &RHS) const {
1163 cmpResult Res = compare(RHS);
1164 return Res == cmpLessThan || Res == cmpEqual;
1165 }
1166
1167 bool operator>=(const APFloat &RHS) const {
1168 cmpResult Res = compare(RHS);
1169 return Res == cmpGreaterThan || Res == cmpEqual;
1170 }
1171
1172 cmpResult compare(const APFloat &RHS) const {
1173 assert(&getSemantics() == &RHS.getSemantics() &&((void)0)
1174 "Should only compare APFloats with the same semantics")((void)0);
1175 if (usesLayout<IEEEFloat>(getSemantics()))
1176 return U.IEEE.compare(RHS.U.IEEE);
1177 if (usesLayout<DoubleAPFloat>(getSemantics()))
1178 return U.Double.compare(RHS.U.Double);
1179 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
1180 }
1181
1182 bool bitwiseIsEqual(const APFloat &RHS) const {
1183 if (&getSemantics() != &RHS.getSemantics())
1184 return false;
1185 if (usesLayout<IEEEFloat>(getSemantics()))
1186 return U.IEEE.bitwiseIsEqual(RHS.U.IEEE);
1187 if (usesLayout<DoubleAPFloat>(getSemantics()))
1188 return U.Double.bitwiseIsEqual(RHS.U.Double);
1189 llvm_unreachable("Unexpected semantics")__builtin_unreachable();
1190 }
1191
1192 /// We don't rely on operator== working on double values, as
1193 /// it returns true for things that are clearly not equal, like -0.0 and 0.0.
1194 /// As such, this method can be used to do an exact bit-for-bit comparison of
1195 /// two floating point values.
1196 ///
1197 /// We leave the version with the double argument here because it's just so
1198 /// convenient to write "2.0" and the like. Without this function we'd
1199 /// have to duplicate its logic everywhere it's called.
1200 bool isExactlyValue(double V) const {
1201 bool ignored;
1202 APFloat Tmp(V);
1203 Tmp.convert(getSemantics(), APFloat::rmNearestTiesToEven, &ignored);
1204 return bitwiseIsEqual(Tmp);
1205 }
1206
1207 unsigned int convertToHexString(char *DST, unsigned int HexDigits,
1208 bool UpperCase, roundingMode RM) const {
1209 APFLOAT_DISPATCH_ON_SEMANTICS(
1210 convertToHexString(DST, HexDigits, UpperCase, RM));
1211 }
1212
1213 bool isZero() const { return getCategory() == fcZero; }
1214 bool isInfinity() const { return getCategory() == fcInfinity; }
1215 bool isNaN() const { return getCategory() == fcNaN; }
1216
1217 bool isNegative() const { return getIEEE().isNegative(); }
1218 bool isDenormal() const { APFLOAT_DISPATCH_ON_SEMANTICS(isDenormal()); }
1219 bool isSignaling() const { return getIEEE().isSignaling(); }
1220
1221 bool isNormal() const { return !isDenormal() && isFiniteNonZero(); }