xref: /llvm-project/flang/lib/Evaluate/real.cpp (revision 1f8790050b0e99e7b46cc69518aa84f46f50738e) 
1 //===-- lib/Evaluate/real.cpp ---------------------------------------------===//
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 #include "flang/Evaluate/real.h"
10 #include "int-power.h"
11 #include "flang/Common/idioms.h"
12 #include "flang/Decimal/decimal.h"
13 #include "flang/Parser/characters.h"
14 #include "llvm/Support/raw_ostream.h"
15 #include <limits>
16 
17 namespace Fortran::evaluate::value {
18 
19 template <typename W, int P> Relation Real<W, P>::Compare(const Real &y) const {
20   if (IsNotANumber() || y.IsNotANumber()) { // NaN vs x, x vs NaN
21     return Relation::Unordered;
22   } else if (IsInfinite()) {
23     if (y.IsInfinite()) {
24       if (IsNegative()) { // -Inf vs +/-Inf
25         return y.IsNegative() ? Relation::Equal : Relation::Less;
26       } else { // +Inf vs +/-Inf
27         return y.IsNegative() ? Relation::Greater : Relation::Equal;
28       }
29     } else { // +/-Inf vs finite
30       return IsNegative() ? Relation::Less : Relation::Greater;
31     }
32   } else if (y.IsInfinite()) { // finite vs +/-Inf
33     return y.IsNegative() ? Relation::Greater : Relation::Less;
34   } else { // two finite numbers
35     bool isNegative{IsNegative()};
36     if (isNegative != y.IsNegative()) {
37       if (word_.IOR(y.word_).IBCLR(bits - 1).IsZero()) {
38         return Relation::Equal; // +/-0.0 == -/+0.0
39       } else {
40         return isNegative ? Relation::Less : Relation::Greater;
41       }
42     } else {
43       // same sign
44       Ordering order{evaluate::Compare(Exponent(), y.Exponent())};
45       if (order == Ordering::Equal) {
46         order = GetSignificand().CompareUnsigned(y.GetSignificand());
47       }
48       if (isNegative) {
49         order = Reverse(order);
50       }
51       return RelationFromOrdering(order);
52     }
53   }
54 }
55 
56 template <typename W, int P>
57 ValueWithRealFlags<Real<W, P>> Real<W, P>::Add(
58     const Real &y, Rounding rounding) const {
59   ValueWithRealFlags<Real> result;
60   if (IsNotANumber() || y.IsNotANumber()) {
61     result.value = NotANumber(); // NaN + x -> NaN
62     if (IsSignalingNaN() || y.IsSignalingNaN()) {
63       result.flags.set(RealFlag::InvalidArgument);
64     }
65     return result;
66   }
67   bool isNegative{IsNegative()};
68   bool yIsNegative{y.IsNegative()};
69   if (IsInfinite()) {
70     if (y.IsInfinite()) {
71       if (isNegative == yIsNegative) {
72         result.value = *this; // +/-Inf + +/-Inf -> +/-Inf
73       } else {
74         result.value = NotANumber(); // +/-Inf + -/+Inf -> NaN
75         result.flags.set(RealFlag::InvalidArgument);
76       }
77     } else {
78       result.value = *this; // +/-Inf + x -> +/-Inf
79     }
80     return result;
81   }
82   if (y.IsInfinite()) {
83     result.value = y; // x + +/-Inf -> +/-Inf
84     return result;
85   }
86   int exponent{Exponent()};
87   int yExponent{y.Exponent()};
88   if (exponent < yExponent) {
89     // y is larger in magnitude; simplify by reversing operands
90     return y.Add(*this, rounding);
91   }
92   if (exponent == yExponent && isNegative != yIsNegative) {
93     Ordering order{GetSignificand().CompareUnsigned(y.GetSignificand())};
94     if (order == Ordering::Less) {
95       // Same exponent, opposite signs, and y is larger in magnitude
96       return y.Add(*this, rounding);
97     }
98     if (order == Ordering::Equal) {
99       // x + (-x) -> +0.0 unless rounding is directed downwards
100       if (rounding.mode == common::RoundingMode::Down) {
101         result.value.word_ = result.value.word_.IBSET(bits - 1); // -0.0
102       }
103       return result;
104     }
105   }
106   // Our exponent is greater than y's, or the exponents match and y is not
107   // of the opposite sign and greater magnitude.  So (x+y) will have the
108   // same sign as x.
109   Fraction fraction{GetFraction()};
110   Fraction yFraction{y.GetFraction()};
111   int rshift = exponent - yExponent;
112   if (exponent > 0 && yExponent == 0) {
113     --rshift; // correct overshift when only y is subnormal
114   }
115   RoundingBits roundingBits{yFraction, rshift};
116   yFraction = yFraction.SHIFTR(rshift);
117   bool carry{false};
118   if (isNegative != yIsNegative) {
119     // Opposite signs: subtract via addition of two's complement of y and
120     // the rounding bits.
121     yFraction = yFraction.NOT();
122     carry = roundingBits.Negate();
123   }
124   auto sum{fraction.AddUnsigned(yFraction, carry)};
125   fraction = sum.value;
126   if (isNegative == yIsNegative && sum.carry) {
127     roundingBits.ShiftRight(sum.value.BTEST(0));
128     fraction = fraction.SHIFTR(1).IBSET(fraction.bits - 1);
129     ++exponent;
130   }
131   NormalizeAndRound(
132       result, isNegative, exponent, fraction, rounding, roundingBits);
133   return result;
134 }
135 
136 template <typename W, int P>
137 ValueWithRealFlags<Real<W, P>> Real<W, P>::Multiply(
138     const Real &y, Rounding rounding) const {
139   ValueWithRealFlags<Real> result;
140   if (IsNotANumber() || y.IsNotANumber()) {
141     result.value = NotANumber(); // NaN * x -> NaN
142     if (IsSignalingNaN() || y.IsSignalingNaN()) {
143       result.flags.set(RealFlag::InvalidArgument);
144     }
145   } else {
146     bool isNegative{IsNegative() != y.IsNegative()};
147     if (IsInfinite() || y.IsInfinite()) {
148       if (IsZero() || y.IsZero()) {
149         result.value = NotANumber(); // 0 * Inf -> NaN
150         result.flags.set(RealFlag::InvalidArgument);
151       } else {
152         result.value = Infinity(isNegative);
153       }
154     } else {
155       auto product{GetFraction().MultiplyUnsigned(y.GetFraction())};
156       std::int64_t exponent{CombineExponents(y, false)};
157       if (exponent < 1) {
158         int rshift = 1 - exponent;
159         exponent = 1;
160         bool sticky{false};
161         if (rshift >= product.upper.bits + product.lower.bits) {
162           sticky = !product.lower.IsZero() || !product.upper.IsZero();
163         } else if (rshift >= product.lower.bits) {
164           sticky = !product.lower.IsZero() ||
165               !product.upper
166                    .IAND(product.upper.MASKR(rshift - product.lower.bits))
167                    .IsZero();
168         } else {
169           sticky = !product.lower.IAND(product.lower.MASKR(rshift)).IsZero();
170         }
171         product.lower = product.lower.SHIFTRWithFill(product.upper, rshift);
172         product.upper = product.upper.SHIFTR(rshift);
173         if (sticky) {
174           product.lower = product.lower.IBSET(0);
175         }
176       }
177       int leadz{product.upper.LEADZ()};
178       if (leadz >= product.upper.bits) {
179         leadz += product.lower.LEADZ();
180       }
181       int lshift{leadz};
182       if (lshift > exponent - 1) {
183         lshift = exponent - 1;
184       }
185       exponent -= lshift;
186       product.upper = product.upper.SHIFTLWithFill(product.lower, lshift);
187       product.lower = product.lower.SHIFTL(lshift);
188       RoundingBits roundingBits{product.lower, product.lower.bits};
189       NormalizeAndRound(result, isNegative, exponent, product.upper, rounding,
190           roundingBits, true /*multiply*/);
191     }
192   }
193   return result;
194 }
195 
196 template <typename W, int P>
197 ValueWithRealFlags<Real<W, P>> Real<W, P>::Divide(
198     const Real &y, Rounding rounding) const {
199   ValueWithRealFlags<Real> result;
200   if (IsNotANumber() || y.IsNotANumber()) {
201     result.value = NotANumber(); // NaN / x -> NaN, x / NaN -> NaN
202     if (IsSignalingNaN() || y.IsSignalingNaN()) {
203       result.flags.set(RealFlag::InvalidArgument);
204     }
205   } else {
206     bool isNegative{IsNegative() != y.IsNegative()};
207     if (IsInfinite()) {
208       if (y.IsInfinite()) {
209         result.value = NotANumber(); // Inf/Inf -> NaN
210         result.flags.set(RealFlag::InvalidArgument);
211       } else { // Inf/x -> Inf,  Inf/0 -> Inf
212         result.value = Infinity(isNegative);
213       }
214     } else if (y.IsZero()) {
215       if (IsZero()) { // 0/0 -> NaN
216         result.value = NotANumber();
217         result.flags.set(RealFlag::InvalidArgument);
218       } else { // x/0 -> Inf, Inf/0 -> Inf
219         result.value = Infinity(isNegative);
220         result.flags.set(RealFlag::DivideByZero);
221       }
222     } else if (IsZero() || y.IsInfinite()) { // 0/x, x/Inf -> 0
223       if (isNegative) {
224         result.value.word_ = result.value.word_.IBSET(bits - 1);
225       }
226     } else {
227       // dividend and divisor are both finite and nonzero numbers
228       Fraction top{GetFraction()}, divisor{y.GetFraction()};
229       std::int64_t exponent{CombineExponents(y, true)};
230       Fraction quotient;
231       bool msb{false};
232       if (!top.BTEST(top.bits - 1) || !divisor.BTEST(divisor.bits - 1)) {
233         // One or two subnormals
234         int topLshift{top.LEADZ()};
235         top = top.SHIFTL(topLshift);
236         int divisorLshift{divisor.LEADZ()};
237         divisor = divisor.SHIFTL(divisorLshift);
238         exponent += divisorLshift - topLshift;
239       }
240       for (int j{1}; j <= quotient.bits; ++j) {
241         if (NextQuotientBit(top, msb, divisor)) {
242           quotient = quotient.IBSET(quotient.bits - j);
243         }
244       }
245       bool guard{NextQuotientBit(top, msb, divisor)};
246       bool round{NextQuotientBit(top, msb, divisor)};
247       bool sticky{msb || !top.IsZero()};
248       RoundingBits roundingBits{guard, round, sticky};
249       if (exponent < 1) {
250         std::int64_t rshift{1 - exponent};
251         for (; rshift > 0; --rshift) {
252           roundingBits.ShiftRight(quotient.BTEST(0));
253           quotient = quotient.SHIFTR(1);
254         }
255         exponent = 1;
256       }
257       NormalizeAndRound(
258           result, isNegative, exponent, quotient, rounding, roundingBits);
259     }
260   }
261   return result;
262 }
263 
264 template <typename W, int P>
265 ValueWithRealFlags<Real<W, P>> Real<W, P>::ToWholeNumber(
266     common::RoundingMode mode) const {
267   ValueWithRealFlags<Real> result{*this};
268   if (IsNotANumber()) {
269     result.flags.set(RealFlag::InvalidArgument);
270     result.value = NotANumber();
271   } else if (IsInfinite()) {
272     result.flags.set(RealFlag::Overflow);
273   } else {
274     constexpr int noClipExponent{exponentBias + binaryPrecision - 1};
275     if (Exponent() < noClipExponent) {
276       Real adjust; // ABS(EPSILON(adjust)) == 0.5
277       adjust.Normalize(IsSignBitSet(), noClipExponent, Fraction::MASKL(1));
278       // Compute ival=(*this + adjust), losing any fractional bits; keep flags
279       result = Add(adjust, Rounding{mode});
280       result.flags.reset(RealFlag::Inexact); // result *is* exact
281       // Return (ival-adjust) with original sign in case we've generated a zero.
282       result.value =
283           result.value.Subtract(adjust, Rounding{common::RoundingMode::ToZero})
284               .value.SIGN(*this);
285     }
286   }
287   return result;
288 }
289 
290 template <typename W, int P>
291 RealFlags Real<W, P>::Normalize(bool negative, int exponent,
292     const Fraction &fraction, Rounding rounding, RoundingBits *roundingBits) {
293   int lshift{fraction.LEADZ()};
294   if (lshift == fraction.bits /* fraction is zero */ &&
295       (!roundingBits || roundingBits->empty())) {
296     // No fraction, no rounding bits -> +/-0.0
297     exponent = lshift = 0;
298   } else if (lshift < exponent) {
299     exponent -= lshift;
300   } else if (exponent > 0) {
301     lshift = exponent - 1;
302     exponent = 0;
303   } else if (lshift == 0) {
304     exponent = 1;
305   } else {
306     lshift = 0;
307   }
308   if (exponent >= maxExponent) {
309     // Infinity or overflow
310     if (rounding.mode == common::RoundingMode::TiesToEven ||
311         rounding.mode == common::RoundingMode::TiesAwayFromZero ||
312         (rounding.mode == common::RoundingMode::Up && !negative) ||
313         (rounding.mode == common::RoundingMode::Down && negative)) {
314       word_ = Word{maxExponent}.SHIFTL(significandBits); // Inf
315     } else {
316       // directed rounding: round to largest finite value rather than infinity
317       // (x86 does this, not sure whether it's standard behavior)
318       word_ = Word{word_.MASKR(word_.bits - 1)}.IBCLR(significandBits);
319     }
320     if (negative) {
321       word_ = word_.IBSET(bits - 1);
322     }
323     RealFlags flags{RealFlag::Overflow};
324     if (!fraction.IsZero()) {
325       flags.set(RealFlag::Inexact);
326     }
327     return flags;
328   }
329   word_ = Word::ConvertUnsigned(fraction).value;
330   if (lshift > 0) {
331     word_ = word_.SHIFTL(lshift);
332     if (roundingBits) {
333       for (; lshift > 0; --lshift) {
334         if (roundingBits->ShiftLeft()) {
335           word_ = word_.IBSET(lshift - 1);
336         }
337       }
338     }
339   }
340   if constexpr (isImplicitMSB) {
341     word_ = word_.IBCLR(significandBits);
342   }
343   word_ = word_.IOR(Word{exponent}.SHIFTL(significandBits));
344   if (negative) {
345     word_ = word_.IBSET(bits - 1);
346   }
347   return {};
348 }
349 
350 template <typename W, int P>
351 RealFlags Real<W, P>::Round(
352     Rounding rounding, const RoundingBits &bits, bool multiply) {
353   int origExponent{Exponent()};
354   RealFlags flags;
355   bool inexact{!bits.empty()};
356   if (inexact) {
357     flags.set(RealFlag::Inexact);
358   }
359   if (origExponent < maxExponent &&
360       bits.MustRound(rounding, IsNegative(), word_.BTEST(0) /* is odd */)) {
361     typename Fraction::ValueWithCarry sum{
362         GetFraction().AddUnsigned(Fraction{}, true)};
363     int newExponent{origExponent};
364     if (sum.carry) {
365       // The fraction was all ones before rounding; sum.value is now zero
366       sum.value = sum.value.IBSET(binaryPrecision - 1);
367       if (++newExponent >= maxExponent) {
368         flags.set(RealFlag::Overflow); // rounded away to an infinity
369       }
370     }
371     flags |= Normalize(IsNegative(), newExponent, sum.value);
372   }
373   if (inexact && origExponent == 0) {
374     // inexact subnormal input: signal Underflow unless in an x86-specific
375     // edge case
376     if (rounding.x86CompatibleBehavior && Exponent() != 0 && multiply &&
377         bits.sticky() &&
378         (bits.guard() ||
379             (rounding.mode != common::RoundingMode::Up &&
380                 rounding.mode != common::RoundingMode::Down))) {
381       // x86 edge case in which Underflow fails to signal when a subnormal
382       // inexact multiplication product rounds to a normal result when
383       // the guard bit is set or we're not using directed rounding
384     } else {
385       flags.set(RealFlag::Underflow);
386     }
387   }
388   return flags;
389 }
390 
391 template <typename W, int P>
392 void Real<W, P>::NormalizeAndRound(ValueWithRealFlags<Real> &result,
393     bool isNegative, int exponent, const Fraction &fraction, Rounding rounding,
394     RoundingBits roundingBits, bool multiply) {
395   result.flags |= result.value.Normalize(
396       isNegative, exponent, fraction, rounding, &roundingBits);
397   result.flags |= result.value.Round(rounding, roundingBits, multiply);
398 }
399 
400 inline enum decimal::FortranRounding MapRoundingMode(
401     common::RoundingMode rounding) {
402   switch (rounding) {
403   case common::RoundingMode::TiesToEven:
404     break;
405   case common::RoundingMode::ToZero:
406     return decimal::RoundToZero;
407   case common::RoundingMode::Down:
408     return decimal::RoundDown;
409   case common::RoundingMode::Up:
410     return decimal::RoundUp;
411   case common::RoundingMode::TiesAwayFromZero:
412     return decimal::RoundCompatible;
413   }
414   return decimal::RoundNearest; // dodge gcc warning about lack of result
415 }
416 
417 inline RealFlags MapFlags(decimal::ConversionResultFlags flags) {
418   RealFlags result;
419   if (flags & decimal::Overflow) {
420     result.set(RealFlag::Overflow);
421   }
422   if (flags & decimal::Inexact) {
423     result.set(RealFlag::Inexact);
424   }
425   if (flags & decimal::Invalid) {
426     result.set(RealFlag::InvalidArgument);
427   }
428   return result;
429 }
430 
431 template <typename W, int P>
432 ValueWithRealFlags<Real<W, P>> Real<W, P>::Read(
433     const char *&p, Rounding rounding) {
434   auto converted{
435       decimal::ConvertToBinary<P>(p, MapRoundingMode(rounding.mode))};
436   const auto *value{reinterpret_cast<Real<W, P> *>(&converted.binary)};
437   return {*value, MapFlags(converted.flags)};
438 }
439 
440 template <typename W, int P> std::string Real<W, P>::DumpHexadecimal() const {
441   if (IsNotANumber()) {
442     return "NaN 0x"s + word_.Hexadecimal();
443   } else if (IsNegative()) {
444     return "-"s + Negate().DumpHexadecimal();
445   } else if (IsInfinite()) {
446     return "Inf"s;
447   } else if (IsZero()) {
448     return "0.0"s;
449   } else {
450     Fraction frac{GetFraction()};
451     std::string result{"0x"};
452     char intPart = '0' + frac.BTEST(frac.bits - 1);
453     result += intPart;
454     result += '.';
455     int trailz{frac.TRAILZ()};
456     if (trailz >= frac.bits - 1) {
457       result += '0';
458     } else {
459       int remainingBits{frac.bits - 1 - trailz};
460       int wholeNybbles{remainingBits / 4};
461       int lostBits{remainingBits - 4 * wholeNybbles};
462       if (wholeNybbles > 0) {
463         std::string fracHex{frac.SHIFTR(trailz + lostBits)
464                                 .IAND(frac.MASKR(4 * wholeNybbles))
465                                 .Hexadecimal()};
466         std::size_t field = wholeNybbles;
467         if (fracHex.size() < field) {
468           result += std::string(field - fracHex.size(), '0');
469         }
470         result += fracHex;
471       }
472       if (lostBits > 0) {
473         result += frac.SHIFTR(trailz)
474                       .IAND(frac.MASKR(lostBits))
475                       .SHIFTL(4 - lostBits)
476                       .Hexadecimal();
477       }
478     }
479     result += 'p';
480     int exponent = Exponent() - exponentBias;
481     result += Integer<32>{exponent}.SignedDecimal();
482     return result;
483   }
484 }
485 
486 template <typename W, int P>
487 llvm::raw_ostream &Real<W, P>::AsFortran(
488     llvm::raw_ostream &o, int kind, bool minimal) const {
489   if (IsNotANumber()) {
490     o << "(0._" << kind << "/0.)";
491   } else if (IsInfinite()) {
492     if (IsNegative()) {
493       o << "(-1._" << kind << "/0.)";
494     } else {
495       o << "(1._" << kind << "/0.)";
496     }
497   } else {
498     using B = decimal::BinaryFloatingPointNumber<P>;
499     const auto *value{reinterpret_cast<const B *>(this)};
500     char buffer[24000]; // accommodate real*16
501     decimal::DecimalConversionFlags flags{}; // default: exact representation
502     if (minimal) {
503       flags = decimal::Minimize;
504     }
505     auto result{decimal::ConvertToDecimal<P>(buffer, sizeof buffer, flags,
506         static_cast<int>(sizeof buffer), decimal::RoundNearest, *value)};
507     const char *p{result.str};
508     if (DEREF(p) == '-' || *p == '+') {
509       o << *p++;
510     }
511     int expo{result.decimalExponent};
512     if (*p != '0') {
513       --expo;
514     }
515     o << *p << '.' << (p + 1);
516     if (expo != 0) {
517       o << 'e' << expo;
518     }
519     o << '_' << kind;
520   }
521   return o;
522 }
523 
524 template class Real<Integer<16>, 11>;
525 template class Real<Integer<16>, 8>;
526 template class Real<Integer<32>, 24>;
527 template class Real<Integer<64>, 53>;
528 template class Real<Integer<80>, 64>;
529 template class Real<Integer<128>, 113>;
530 } // namespace Fortran::evaluate::value
531