/
real.h
410 lines (368 loc) · 13.8 KB
/
real.h
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
//===-- include/flang/Evaluate/real.h ---------------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#ifndef FORTRAN_EVALUATE_REAL_H_
#define FORTRAN_EVALUATE_REAL_H_
#include "formatting.h"
#include "integer.h"
#include "rounding-bits.h"
#include "flang/Common/real.h"
#include "flang/Evaluate/common.h"
#include <cinttypes>
#include <limits>
#include <string>
// Some environments, viz. clang on Darwin, allow the macro HUGE
// to leak out of <math.h> even when it is never directly included.
#undef HUGE
namespace llvm {
class raw_ostream;
}
namespace Fortran::evaluate::value {
// LOG10(2.)*1E12
static constexpr std::int64_t ScaledLogBaseTenOfTwo{301029995664};
// Models IEEE binary floating-point numbers (IEEE 754-2008,
// ISO/IEC/IEEE 60559.2011). The first argument to this
// class template must be (or look like) an instance of Integer<>;
// the second specifies the number of effective bits (binary precision)
// in the fraction.
template <typename WORD, int PREC>
class Real : public common::RealDetails<PREC> {
public:
using Word = WORD;
static constexpr int binaryPrecision{PREC};
using Details = common::RealDetails<PREC>;
using Details::exponentBias;
using Details::exponentBits;
using Details::isImplicitMSB;
using Details::maxExponent;
using Details::significandBits;
static constexpr int bits{Word::bits};
static_assert(bits >= Details::bits);
using Fraction = Integer<binaryPrecision>; // all bits made explicit
template <typename W, int P> friend class Real;
constexpr Real() {} // +0.0
constexpr Real(const Real &) = default;
constexpr Real(Real &&) = default;
constexpr Real(const Word &bits) : word_{bits} {}
constexpr Real &operator=(const Real &) = default;
constexpr Real &operator=(Real &&) = default;
constexpr bool operator==(const Real &that) const {
return word_ == that.word_;
}
constexpr bool IsSignBitSet() const { return word_.BTEST(bits - 1); }
constexpr bool IsNegative() const {
return !IsNotANumber() && IsSignBitSet();
}
constexpr bool IsNotANumber() const {
return Exponent() == maxExponent && !GetSignificand().IsZero();
}
constexpr bool IsQuietNaN() const {
return Exponent() == maxExponent &&
GetSignificand().BTEST(significandBits - 1);
}
constexpr bool IsSignalingNaN() const {
return IsNotANumber() && !GetSignificand().BTEST(significandBits - 1);
}
constexpr bool IsInfinite() const {
return Exponent() == maxExponent && GetSignificand().IsZero();
}
constexpr bool IsFinite() const { return Exponent() != maxExponent; }
constexpr bool IsZero() const {
return Exponent() == 0 && GetSignificand().IsZero();
}
constexpr bool IsSubnormal() const {
return Exponent() == 0 && !GetSignificand().IsZero();
}
constexpr Real ABS() const { // non-arithmetic, no flags returned
return {word_.IBCLR(bits - 1)};
}
constexpr Real SetSign(bool toNegative) const { // non-arithmetic
if (toNegative) {
return {word_.IBSET(bits - 1)};
} else {
return ABS();
}
}
constexpr Real SIGN(const Real &x) const { return SetSign(x.IsSignBitSet()); }
constexpr Real Negate() const { return {word_.IEOR(word_.MASKL(1))}; }
Relation Compare(const Real &) const;
ValueWithRealFlags<Real> Add(
const Real &, Rounding rounding = defaultRounding) const;
ValueWithRealFlags<Real> Subtract(
const Real &y, Rounding rounding = defaultRounding) const {
return Add(y.Negate(), rounding);
}
ValueWithRealFlags<Real> Multiply(
const Real &, Rounding rounding = defaultRounding) const;
ValueWithRealFlags<Real> Divide(
const Real &, Rounding rounding = defaultRounding) const;
ValueWithRealFlags<Real> SQRT(Rounding rounding = defaultRounding) const;
// HYPOT(x,y)=SQRT(x**2 + y**2) computed so as to avoid spurious
// intermediate overflows.
ValueWithRealFlags<Real> HYPOT(
const Real &, Rounding rounding = defaultRounding) const;
template <typename INT> constexpr INT EXPONENT() const {
if (Exponent() == maxExponent) {
return INT::HUGE();
} else if (IsZero()) {
return {0};
} else {
return {UnbiasedExponent() + 1};
}
}
static constexpr Real EPSILON() {
Real epsilon;
epsilon.Normalize(
false, exponentBias + 1 - binaryPrecision, Fraction::MASKL(1));
return epsilon;
}
static constexpr Real HUGE() {
Real huge;
huge.Normalize(false, maxExponent - 1, Fraction::MASKR(binaryPrecision));
return huge;
}
static constexpr Real TINY() {
Real tiny;
tiny.Normalize(false, 1, Fraction::MASKL(1)); // minimum *normal* number
return tiny;
}
static constexpr int DIGITS{binaryPrecision};
static constexpr int PRECISION{Details::decimalPrecision};
static constexpr int RANGE{Details::decimalRange};
static constexpr int MAXEXPONENT{maxExponent - exponentBias};
static constexpr int MINEXPONENT{2 - exponentBias};
// SCALE(); also known as IEEE_SCALB and (in IEEE-754 '08) ScaleB.
template <typename INT>
ValueWithRealFlags<Real> SCALE(
const INT &by, Rounding rounding = defaultRounding) const {
auto expo{exponentBias + by.ToInt64()};
if (IsZero()) {
expo = exponentBias; // ignore by, don't overflow
} else if (by > INT{maxExponent}) {
expo = maxExponent;
} else if (by < INT{-exponentBias}) {
expo = -1;
}
Real twoPow;
RealFlags flags{
twoPow.Normalize(false, static_cast<int>(expo), Fraction::MASKL(1))};
ValueWithRealFlags<Real> result{Multiply(twoPow, rounding)};
result.flags |= flags;
return result;
}
constexpr Real FlushSubnormalToZero() const {
if (IsSubnormal()) {
return Real{};
}
return *this;
}
// TODO: Configurable NotANumber representations
static constexpr Real NotANumber() {
return {Word{maxExponent}
.SHIFTL(significandBits)
.IBSET(significandBits - 1)
.IBSET(significandBits - 2)};
}
static constexpr Real Infinity(bool negative) {
Word infinity{maxExponent};
infinity = infinity.SHIFTL(significandBits);
if (negative) {
infinity = infinity.IBSET(infinity.bits - 1);
}
return {infinity};
}
template <typename INT>
static ValueWithRealFlags<Real> FromInteger(
const INT &n, Rounding rounding = defaultRounding) {
bool isNegative{n.IsNegative()};
INT absN{n};
if (isNegative) {
absN = n.Negate().value; // overflow is safe to ignore
}
int leadz{absN.LEADZ()};
if (leadz >= absN.bits) {
return {}; // all bits zero -> +0.0
}
ValueWithRealFlags<Real> result;
int exponent{exponentBias + absN.bits - leadz - 1};
int bitsNeeded{absN.bits - (leadz + isImplicitMSB)};
int bitsLost{bitsNeeded - significandBits};
if (bitsLost <= 0) {
Fraction fraction{Fraction::ConvertUnsigned(absN).value};
result.flags |= result.value.Normalize(
isNegative, exponent, fraction.SHIFTL(-bitsLost));
} else {
Fraction fraction{Fraction::ConvertUnsigned(absN.SHIFTR(bitsLost)).value};
result.flags |= result.value.Normalize(isNegative, exponent, fraction);
RoundingBits roundingBits{absN, bitsLost};
result.flags |= result.value.Round(rounding, roundingBits);
}
return result;
}
// Conversion to integer in the same real format (AINT(), ANINT())
ValueWithRealFlags<Real> ToWholeNumber(
common::RoundingMode = common::RoundingMode::ToZero) const;
// Conversion to an integer (INT(), NINT(), FLOOR(), CEILING())
template <typename INT>
constexpr ValueWithRealFlags<INT> ToInteger(
common::RoundingMode mode = common::RoundingMode::ToZero) const {
ValueWithRealFlags<INT> result;
if (IsNotANumber()) {
result.flags.set(RealFlag::InvalidArgument);
result.value = result.value.HUGE();
return result;
}
ValueWithRealFlags<Real> intPart{ToWholeNumber(mode)};
result.flags |= intPart.flags;
int exponent{intPart.value.Exponent()};
// shift positive -> left shift, negative -> right shift
int shift{exponent - exponentBias - binaryPrecision + 1};
// Apply any right shift before moving to the result type
auto rshifted{intPart.value.GetFraction().SHIFTR(-shift)};
auto converted{result.value.ConvertUnsigned(rshifted)};
if (converted.overflow) {
result.flags.set(RealFlag::Overflow);
}
result.value = converted.value.SHIFTL(shift);
if (converted.value.CompareUnsigned(result.value.SHIFTR(shift)) !=
Ordering::Equal) {
result.flags.set(RealFlag::Overflow);
}
if (IsSignBitSet()) {
result.value = result.value.Negate().value;
}
if (IsSignBitSet() != result.value.IsNegative()) {
result.flags.set(RealFlag::Overflow);
}
if (result.flags.test(RealFlag::Overflow)) {
result.value =
IsSignBitSet() ? result.value.MASKL(1) : result.value.HUGE();
}
return result;
}
template <typename A>
static ValueWithRealFlags<Real> Convert(
const A &x, Rounding rounding = defaultRounding) {
ValueWithRealFlags<Real> result;
if (x.IsNotANumber()) {
result.flags.set(RealFlag::InvalidArgument);
result.value = NotANumber();
return result;
}
bool isNegative{x.IsNegative()};
A absX{x};
if (isNegative) {
absX = x.Negate();
}
int exponent{exponentBias + x.UnbiasedExponent()};
int bitsLost{A::binaryPrecision - binaryPrecision};
if (exponent < 1) {
bitsLost += 1 - exponent;
exponent = 1;
}
typename A::Fraction xFraction{x.GetFraction()};
if (bitsLost <= 0) {
Fraction fraction{
Fraction::ConvertUnsigned(xFraction).value.SHIFTL(-bitsLost)};
result.flags |= result.value.Normalize(isNegative, exponent, fraction);
} else {
Fraction fraction{
Fraction::ConvertUnsigned(xFraction.SHIFTR(bitsLost)).value};
result.flags |= result.value.Normalize(isNegative, exponent, fraction);
RoundingBits roundingBits{xFraction, bitsLost};
result.flags |= result.value.Round(rounding, roundingBits);
}
return result;
}
constexpr Word RawBits() const { return word_; }
// Extracts "raw" biased exponent field.
constexpr int Exponent() const {
return word_.IBITS(significandBits, exponentBits).ToUInt64();
}
// Extracts the fraction; any implied bit is made explicit.
constexpr Fraction GetFraction() const {
Fraction result{Fraction::ConvertUnsigned(word_).value};
if constexpr (!isImplicitMSB) {
return result;
} else {
int exponent{Exponent()};
if (exponent > 0 && exponent < maxExponent) {
return result.IBSET(significandBits);
} else {
return result.IBCLR(significandBits);
}
}
}
// Extracts unbiased exponent value.
// Corrects the exponent value of a subnormal number.
// Note that the result is one less than the EXPONENT intrinsic;
// UnbiasedExponent(1.0) is 0, not 1.
constexpr int UnbiasedExponent() const {
int exponent{Exponent() - exponentBias};
if (IsSubnormal()) {
++exponent;
}
return exponent;
}
static ValueWithRealFlags<Real> Read(
const char *&, Rounding rounding = defaultRounding);
std::string DumpHexadecimal() const;
// Emits a character representation for an equivalent Fortran constant
// or parenthesized constant expression that produces this value.
llvm::raw_ostream &AsFortran(
llvm::raw_ostream &, int kind, bool minimal = false) const;
private:
using Significand = Integer<significandBits>; // no implicit bit
constexpr Significand GetSignificand() const {
return Significand::ConvertUnsigned(word_).value;
}
constexpr int CombineExponents(const Real &y, bool forDivide) const {
int exponent = Exponent(), yExponent = y.Exponent();
// A zero exponent field value has the same weight as 1.
exponent += !exponent;
yExponent += !yExponent;
if (forDivide) {
exponent += exponentBias - yExponent;
} else {
exponent += yExponent - exponentBias + 1;
}
return exponent;
}
static constexpr bool NextQuotientBit(
Fraction &top, bool &msb, const Fraction &divisor) {
bool greaterOrEqual{msb || top.CompareUnsigned(divisor) != Ordering::Less};
if (greaterOrEqual) {
top = top.SubtractSigned(divisor).value;
}
auto doubled{top.AddUnsigned(top)};
top = doubled.value;
msb = doubled.carry;
return greaterOrEqual;
}
// Normalizes and marshals the fields of a floating-point number in place.
// The value is a number, and a zero fraction means a zero value (i.e.,
// a maximal exponent and zero fraction doesn't signify infinity, although
// this member function will detect overflow and encode infinities).
RealFlags Normalize(bool negative, int exponent, const Fraction &fraction,
Rounding rounding = defaultRounding,
RoundingBits *roundingBits = nullptr);
// Rounds a result, if necessary, in place.
RealFlags Round(Rounding, const RoundingBits &, bool multiply = false);
static void NormalizeAndRound(ValueWithRealFlags<Real> &result,
bool isNegative, int exponent, const Fraction &, Rounding, RoundingBits,
bool multiply = false);
Word word_{}; // an Integer<>
};
extern template class Real<Integer<16>, 11>; // IEEE half format
extern template class Real<Integer<16>, 8>; // the "other" half format
extern template class Real<Integer<32>, 24>; // IEEE single
extern template class Real<Integer<64>, 53>; // IEEE double
extern template class Real<Integer<80>, 64>; // 80387 extended precision
extern template class Real<Integer<128>, 113>; // IEEE quad
// N.B. No "double-double" support.
} // namespace Fortran::evaluate::value
#endif // FORTRAN_EVALUATE_REAL_H_