1 //===-- APFloat.cpp - Implement APFloat class -----------------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file implements a class to represent arbitrary precision floating
11 // point values and provide a variety of arithmetic operations on them.
13 //===----------------------------------------------------------------------===//
15 #include "llvm/ADT/APFloat.h"
16 #include "llvm/ADT/APSInt.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/Support/ErrorHandling.h"
22 #include "llvm/Support/MathExtras.h"
28 /// A macro used to combine two fcCategory enums into one key which can be used
29 /// in a switch statement to classify how the interaction of two APFloat's
30 /// categories affects an operation.
32 /// TODO: If clang source code is ever allowed to use constexpr in its own
33 /// codebase, change this into a static inline function.
34 #define PackCategoriesIntoKey(_lhs, _rhs) ((_lhs) * 4 + (_rhs))
36 /* Assumed in hexadecimal significand parsing, and conversion to
37 hexadecimal strings. */
38 #define COMPILE_TIME_ASSERT(cond) extern int CTAssert[(cond) ? 1 : -1]
39 COMPILE_TIME_ASSERT(integerPartWidth % 4 == 0);
43 /* Represents floating point arithmetic semantics. */
45 /* The largest E such that 2^E is representable; this matches the
46 definition of IEEE 754. */
47 APFloat::ExponentType maxExponent;
49 /* The smallest E such that 2^E is a normalized number; this
50 matches the definition of IEEE 754. */
51 APFloat::ExponentType minExponent;
53 /* Number of bits in the significand. This includes the integer
55 unsigned int precision;
58 const fltSemantics APFloat::IEEEhalf = { 15, -14, 11 };
59 const fltSemantics APFloat::IEEEsingle = { 127, -126, 24 };
60 const fltSemantics APFloat::IEEEdouble = { 1023, -1022, 53 };
61 const fltSemantics APFloat::IEEEquad = { 16383, -16382, 113 };
62 const fltSemantics APFloat::x87DoubleExtended = { 16383, -16382, 64 };
63 const fltSemantics APFloat::Bogus = { 0, 0, 0 };
65 /* The PowerPC format consists of two doubles. It does not map cleanly
66 onto the usual format above. It is approximated using twice the
67 mantissa bits. Note that for exponents near the double minimum,
68 we no longer can represent the full 106 mantissa bits, so those
69 will be treated as denormal numbers.
71 FIXME: While this approximation is equivalent to what GCC uses for
72 compile-time arithmetic on PPC double-double numbers, it is not able
73 to represent all possible values held by a PPC double-double number,
74 for example: (long double) 1.0 + (long double) 0x1p-106
75 Should this be replaced by a full emulation of PPC double-double? */
76 const fltSemantics APFloat::PPCDoubleDouble = { 1023, -1022 + 53, 53 + 53 };
78 /* A tight upper bound on number of parts required to hold the value
81 power * 815 / (351 * integerPartWidth) + 1
83 However, whilst the result may require only this many parts,
84 because we are multiplying two values to get it, the
85 multiplication may require an extra part with the excess part
86 being zero (consider the trivial case of 1 * 1, tcFullMultiply
87 requires two parts to hold the single-part result). So we add an
88 extra one to guarantee enough space whilst multiplying. */
89 const unsigned int maxExponent = 16383;
90 const unsigned int maxPrecision = 113;
91 const unsigned int maxPowerOfFiveExponent = maxExponent + maxPrecision - 1;
92 const unsigned int maxPowerOfFiveParts = 2 + ((maxPowerOfFiveExponent * 815)
93 / (351 * integerPartWidth));
96 /* A bunch of private, handy routines. */
98 static inline unsigned int
99 partCountForBits(unsigned int bits)
101 return ((bits) + integerPartWidth - 1) / integerPartWidth;
104 /* Returns 0U-9U. Return values >= 10U are not digits. */
105 static inline unsigned int
106 decDigitValue(unsigned int c)
111 /* Return the value of a decimal exponent of the form
114 If the exponent overflows, returns a large exponent with the
117 readExponent(StringRef::iterator begin, StringRef::iterator end)
120 unsigned int absExponent;
121 const unsigned int overlargeExponent = 24000; /* FIXME. */
122 StringRef::iterator p = begin;
124 assert(p != end && "Exponent has no digits");
126 isNegative = (*p == '-');
127 if (*p == '-' || *p == '+') {
129 assert(p != end && "Exponent has no digits");
132 absExponent = decDigitValue(*p++);
133 assert(absExponent < 10U && "Invalid character in exponent");
135 for (; p != end; ++p) {
138 value = decDigitValue(*p);
139 assert(value < 10U && "Invalid character in exponent");
141 value += absExponent * 10;
142 if (absExponent >= overlargeExponent) {
143 absExponent = overlargeExponent;
144 p = end; /* outwit assert below */
150 assert(p == end && "Invalid exponent in exponent");
153 return -(int) absExponent;
155 return (int) absExponent;
158 /* This is ugly and needs cleaning up, but I don't immediately see
159 how whilst remaining safe. */
161 totalExponent(StringRef::iterator p, StringRef::iterator end,
162 int exponentAdjustment)
164 int unsignedExponent;
165 bool negative, overflow;
168 assert(p != end && "Exponent has no digits");
170 negative = *p == '-';
171 if (*p == '-' || *p == '+') {
173 assert(p != end && "Exponent has no digits");
176 unsignedExponent = 0;
178 for (; p != end; ++p) {
181 value = decDigitValue(*p);
182 assert(value < 10U && "Invalid character in exponent");
184 unsignedExponent = unsignedExponent * 10 + value;
185 if (unsignedExponent > 32767) {
191 if (exponentAdjustment > 32767 || exponentAdjustment < -32768)
195 exponent = unsignedExponent;
197 exponent = -exponent;
198 exponent += exponentAdjustment;
199 if (exponent > 32767 || exponent < -32768)
204 exponent = negative ? -32768: 32767;
209 static StringRef::iterator
210 skipLeadingZeroesAndAnyDot(StringRef::iterator begin, StringRef::iterator end,
211 StringRef::iterator *dot)
213 StringRef::iterator p = begin;
215 while (*p == '0' && p != end)
221 assert(end - begin != 1 && "Significand has no digits");
223 while (*p == '0' && p != end)
230 /* Given a normal decimal floating point number of the form
234 where the decimal point and exponent are optional, fill out the
235 structure D. Exponent is appropriate if the significand is
236 treated as an integer, and normalizedExponent if the significand
237 is taken to have the decimal point after a single leading
240 If the value is zero, V->firstSigDigit points to a non-digit, and
241 the return exponent is zero.
244 const char *firstSigDigit;
245 const char *lastSigDigit;
247 int normalizedExponent;
251 interpretDecimal(StringRef::iterator begin, StringRef::iterator end,
254 StringRef::iterator dot = end;
255 StringRef::iterator p = skipLeadingZeroesAndAnyDot (begin, end, &dot);
257 D->firstSigDigit = p;
259 D->normalizedExponent = 0;
261 for (; p != end; ++p) {
263 assert(dot == end && "String contains multiple dots");
268 if (decDigitValue(*p) >= 10U)
273 assert((*p == 'e' || *p == 'E') && "Invalid character in significand");
274 assert(p != begin && "Significand has no digits");
275 assert((dot == end || p - begin != 1) && "Significand has no digits");
277 /* p points to the first non-digit in the string */
278 D->exponent = readExponent(p + 1, end);
280 /* Implied decimal point? */
285 /* If number is all zeroes accept any exponent. */
286 if (p != D->firstSigDigit) {
287 /* Drop insignificant trailing zeroes. */
292 while (p != begin && *p == '0');
293 while (p != begin && *p == '.');
296 /* Adjust the exponents for any decimal point. */
297 D->exponent += static_cast<APFloat::ExponentType>((dot - p) - (dot > p));
298 D->normalizedExponent = (D->exponent +
299 static_cast<APFloat::ExponentType>((p - D->firstSigDigit)
300 - (dot > D->firstSigDigit && dot < p)));
306 /* Return the trailing fraction of a hexadecimal number.
307 DIGITVALUE is the first hex digit of the fraction, P points to
310 trailingHexadecimalFraction(StringRef::iterator p, StringRef::iterator end,
311 unsigned int digitValue)
313 unsigned int hexDigit;
315 /* If the first trailing digit isn't 0 or 8 we can work out the
316 fraction immediately. */
318 return lfMoreThanHalf;
319 else if (digitValue < 8 && digitValue > 0)
320 return lfLessThanHalf;
322 // Otherwise we need to find the first non-zero digit.
323 while (p != end && (*p == '0' || *p == '.'))
326 assert(p != end && "Invalid trailing hexadecimal fraction!");
328 hexDigit = hexDigitValue(*p);
330 /* If we ran off the end it is exactly zero or one-half, otherwise
333 return digitValue == 0 ? lfExactlyZero: lfExactlyHalf;
335 return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf;
338 /* Return the fraction lost were a bignum truncated losing the least
339 significant BITS bits. */
341 lostFractionThroughTruncation(const integerPart *parts,
342 unsigned int partCount,
347 lsb = APInt::tcLSB(parts, partCount);
349 /* Note this is guaranteed true if bits == 0, or LSB == -1U. */
351 return lfExactlyZero;
353 return lfExactlyHalf;
354 if (bits <= partCount * integerPartWidth &&
355 APInt::tcExtractBit(parts, bits - 1))
356 return lfMoreThanHalf;
358 return lfLessThanHalf;
361 /* Shift DST right BITS bits noting lost fraction. */
363 shiftRight(integerPart *dst, unsigned int parts, unsigned int bits)
365 lostFraction lost_fraction;
367 lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
369 APInt::tcShiftRight(dst, parts, bits);
371 return lost_fraction;
374 /* Combine the effect of two lost fractions. */
376 combineLostFractions(lostFraction moreSignificant,
377 lostFraction lessSignificant)
379 if (lessSignificant != lfExactlyZero) {
380 if (moreSignificant == lfExactlyZero)
381 moreSignificant = lfLessThanHalf;
382 else if (moreSignificant == lfExactlyHalf)
383 moreSignificant = lfMoreThanHalf;
386 return moreSignificant;
389 /* The error from the true value, in half-ulps, on multiplying two
390 floating point numbers, which differ from the value they
391 approximate by at most HUE1 and HUE2 half-ulps, is strictly less
392 than the returned value.
394 See "How to Read Floating Point Numbers Accurately" by William D
397 HUerrBound(bool inexactMultiply, unsigned int HUerr1, unsigned int HUerr2)
399 assert(HUerr1 < 2 || HUerr2 < 2 || (HUerr1 + HUerr2 < 8));
401 if (HUerr1 + HUerr2 == 0)
402 return inexactMultiply * 2; /* <= inexactMultiply half-ulps. */
404 return inexactMultiply + 2 * (HUerr1 + HUerr2);
407 /* The number of ulps from the boundary (zero, or half if ISNEAREST)
408 when the least significant BITS are truncated. BITS cannot be
411 ulpsFromBoundary(const integerPart *parts, unsigned int bits, bool isNearest)
413 unsigned int count, partBits;
414 integerPart part, boundary;
419 count = bits / integerPartWidth;
420 partBits = bits % integerPartWidth + 1;
422 part = parts[count] & (~(integerPart) 0 >> (integerPartWidth - partBits));
425 boundary = (integerPart) 1 << (partBits - 1);
430 if (part - boundary <= boundary - part)
431 return part - boundary;
433 return boundary - part;
436 if (part == boundary) {
439 return ~(integerPart) 0; /* A lot. */
442 } else if (part == boundary - 1) {
445 return ~(integerPart) 0; /* A lot. */
450 return ~(integerPart) 0; /* A lot. */
453 /* Place pow(5, power) in DST, and return the number of parts used.
454 DST must be at least one part larger than size of the answer. */
456 powerOf5(integerPart *dst, unsigned int power)
458 static const integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125,
460 integerPart pow5s[maxPowerOfFiveParts * 2 + 5];
461 pow5s[0] = 78125 * 5;
463 unsigned int partsCount[16] = { 1 };
464 integerPart scratch[maxPowerOfFiveParts], *p1, *p2, *pow5;
466 assert(power <= maxExponent);
471 *p1 = firstEightPowers[power & 7];
477 for (unsigned int n = 0; power; power >>= 1, n++) {
482 /* Calculate pow(5,pow(2,n+3)) if we haven't yet. */
484 pc = partsCount[n - 1];
485 APInt::tcFullMultiply(pow5, pow5 - pc, pow5 - pc, pc, pc);
487 if (pow5[pc - 1] == 0)
495 APInt::tcFullMultiply(p2, p1, pow5, result, pc);
497 if (p2[result - 1] == 0)
500 /* Now result is in p1 with partsCount parts and p2 is scratch
502 tmp = p1, p1 = p2, p2 = tmp;
509 APInt::tcAssign(dst, p1, result);
514 /* Zero at the end to avoid modular arithmetic when adding one; used
515 when rounding up during hexadecimal output. */
516 static const char hexDigitsLower[] = "0123456789abcdef0";
517 static const char hexDigitsUpper[] = "0123456789ABCDEF0";
518 static const char infinityL[] = "infinity";
519 static const char infinityU[] = "INFINITY";
520 static const char NaNL[] = "nan";
521 static const char NaNU[] = "NAN";
523 /* Write out an integerPart in hexadecimal, starting with the most
524 significant nibble. Write out exactly COUNT hexdigits, return
527 partAsHex (char *dst, integerPart part, unsigned int count,
528 const char *hexDigitChars)
530 unsigned int result = count;
532 assert(count != 0 && count <= integerPartWidth / 4);
534 part >>= (integerPartWidth - 4 * count);
536 dst[count] = hexDigitChars[part & 0xf];
543 /* Write out an unsigned decimal integer. */
545 writeUnsignedDecimal (char *dst, unsigned int n)
561 /* Write out a signed decimal integer. */
563 writeSignedDecimal (char *dst, int value)
567 dst = writeUnsignedDecimal(dst, -(unsigned) value);
569 dst = writeUnsignedDecimal(dst, value);
576 APFloat::initialize(const fltSemantics *ourSemantics)
580 semantics = ourSemantics;
583 significand.parts = new integerPart[count];
587 APFloat::freeSignificand()
590 delete [] significand.parts;
594 APFloat::assign(const APFloat &rhs)
596 assert(semantics == rhs.semantics);
599 category = rhs.category;
600 exponent = rhs.exponent;
601 if (isFiniteNonZero() || category == fcNaN)
602 copySignificand(rhs);
606 APFloat::copySignificand(const APFloat &rhs)
608 assert(isFiniteNonZero() || category == fcNaN);
609 assert(rhs.partCount() >= partCount());
611 APInt::tcAssign(significandParts(), rhs.significandParts(),
615 /* Make this number a NaN, with an arbitrary but deterministic value
616 for the significand. If double or longer, this is a signalling NaN,
617 which may not be ideal. If float, this is QNaN(0). */
618 void APFloat::makeNaN(bool SNaN, bool Negative, const APInt *fill)
623 integerPart *significand = significandParts();
624 unsigned numParts = partCount();
626 // Set the significand bits to the fill.
627 if (!fill || fill->getNumWords() < numParts)
628 APInt::tcSet(significand, 0, numParts);
630 APInt::tcAssign(significand, fill->getRawData(),
631 std::min(fill->getNumWords(), numParts));
633 // Zero out the excess bits of the significand.
634 unsigned bitsToPreserve = semantics->precision - 1;
635 unsigned part = bitsToPreserve / 64;
636 bitsToPreserve %= 64;
637 significand[part] &= ((1ULL << bitsToPreserve) - 1);
638 for (part++; part != numParts; ++part)
639 significand[part] = 0;
642 unsigned QNaNBit = semantics->precision - 2;
645 // We always have to clear the QNaN bit to make it an SNaN.
646 APInt::tcClearBit(significand, QNaNBit);
648 // If there are no bits set in the payload, we have to set
649 // *something* to make it a NaN instead of an infinity;
650 // conventionally, this is the next bit down from the QNaN bit.
651 if (APInt::tcIsZero(significand, numParts))
652 APInt::tcSetBit(significand, QNaNBit - 1);
654 // We always have to set the QNaN bit to make it a QNaN.
655 APInt::tcSetBit(significand, QNaNBit);
658 // For x87 extended precision, we want to make a NaN, not a
659 // pseudo-NaN. Maybe we should expose the ability to make
661 if (semantics == &APFloat::x87DoubleExtended)
662 APInt::tcSetBit(significand, QNaNBit + 1);
665 APFloat APFloat::makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
667 APFloat value(Sem, uninitialized);
668 value.makeNaN(SNaN, Negative, fill);
673 APFloat::operator=(const APFloat &rhs)
676 if (semantics != rhs.semantics) {
678 initialize(rhs.semantics);
687 APFloat::operator=(APFloat &&rhs) {
690 semantics = rhs.semantics;
691 significand = rhs.significand;
692 exponent = rhs.exponent;
693 category = rhs.category;
696 rhs.semantics = &Bogus;
701 APFloat::isDenormal() const {
702 return isFiniteNonZero() && (exponent == semantics->minExponent) &&
703 (APInt::tcExtractBit(significandParts(),
704 semantics->precision - 1) == 0);
708 APFloat::isSmallest() const {
709 // The smallest number by magnitude in our format will be the smallest
710 // denormal, i.e. the floating point number with exponent being minimum
711 // exponent and significand bitwise equal to 1 (i.e. with MSB equal to 0).
712 return isFiniteNonZero() && exponent == semantics->minExponent &&
713 significandMSB() == 0;
716 bool APFloat::isSignificandAllOnes() const {
717 // Test if the significand excluding the integral bit is all ones. This allows
718 // us to test for binade boundaries.
719 const integerPart *Parts = significandParts();
720 const unsigned PartCount = partCount();
721 for (unsigned i = 0; i < PartCount - 1; i++)
725 // Set the unused high bits to all ones when we compare.
726 const unsigned NumHighBits =
727 PartCount*integerPartWidth - semantics->precision + 1;
728 assert(NumHighBits <= integerPartWidth && "Can not have more high bits to "
729 "fill than integerPartWidth");
730 const integerPart HighBitFill =
731 ~integerPart(0) << (integerPartWidth - NumHighBits);
732 if (~(Parts[PartCount - 1] | HighBitFill))
738 bool APFloat::isSignificandAllZeros() const {
739 // Test if the significand excluding the integral bit is all zeros. This
740 // allows us to test for binade boundaries.
741 const integerPart *Parts = significandParts();
742 const unsigned PartCount = partCount();
744 for (unsigned i = 0; i < PartCount - 1; i++)
748 const unsigned NumHighBits =
749 PartCount*integerPartWidth - semantics->precision + 1;
750 assert(NumHighBits <= integerPartWidth && "Can not have more high bits to "
751 "clear than integerPartWidth");
752 const integerPart HighBitMask = ~integerPart(0) >> NumHighBits;
754 if (Parts[PartCount - 1] & HighBitMask)
761 APFloat::isLargest() const {
762 // The largest number by magnitude in our format will be the floating point
763 // number with maximum exponent and with significand that is all ones.
764 return isFiniteNonZero() && exponent == semantics->maxExponent
765 && isSignificandAllOnes();
769 APFloat::bitwiseIsEqual(const APFloat &rhs) const {
772 if (semantics != rhs.semantics ||
773 category != rhs.category ||
776 if (category==fcZero || category==fcInfinity)
778 else if (isFiniteNonZero() && exponent!=rhs.exponent)
782 const integerPart* p=significandParts();
783 const integerPart* q=rhs.significandParts();
784 for (; i>0; i--, p++, q++) {
792 APFloat::APFloat(const fltSemantics &ourSemantics, integerPart value) {
793 initialize(&ourSemantics);
797 exponent = ourSemantics.precision - 1;
798 significandParts()[0] = value;
799 normalize(rmNearestTiesToEven, lfExactlyZero);
802 APFloat::APFloat(const fltSemantics &ourSemantics) {
803 initialize(&ourSemantics);
808 APFloat::APFloat(const fltSemantics &ourSemantics, uninitializedTag tag) {
809 // Allocates storage if necessary but does not initialize it.
810 initialize(&ourSemantics);
813 APFloat::APFloat(const fltSemantics &ourSemantics, StringRef text) {
814 initialize(&ourSemantics);
815 convertFromString(text, rmNearestTiesToEven);
818 APFloat::APFloat(const APFloat &rhs) {
819 initialize(rhs.semantics);
823 APFloat::APFloat(APFloat &&rhs) : semantics(&Bogus) {
824 *this = std::move(rhs);
832 // Profile - This method 'profiles' an APFloat for use with FoldingSet.
833 void APFloat::Profile(FoldingSetNodeID& ID) const {
834 ID.Add(bitcastToAPInt());
838 APFloat::partCount() const
840 return partCountForBits(semantics->precision + 1);
844 APFloat::semanticsPrecision(const fltSemantics &semantics)
846 return semantics.precision;
850 APFloat::significandParts() const
852 return const_cast<APFloat *>(this)->significandParts();
856 APFloat::significandParts()
859 return significand.parts;
861 return &significand.part;
865 APFloat::zeroSignificand()
867 APInt::tcSet(significandParts(), 0, partCount());
870 /* Increment an fcNormal floating point number's significand. */
872 APFloat::incrementSignificand()
876 carry = APInt::tcIncrement(significandParts(), partCount());
878 /* Our callers should never cause us to overflow. */
883 /* Add the significand of the RHS. Returns the carry flag. */
885 APFloat::addSignificand(const APFloat &rhs)
889 parts = significandParts();
891 assert(semantics == rhs.semantics);
892 assert(exponent == rhs.exponent);
894 return APInt::tcAdd(parts, rhs.significandParts(), 0, partCount());
897 /* Subtract the significand of the RHS with a borrow flag. Returns
900 APFloat::subtractSignificand(const APFloat &rhs, integerPart borrow)
904 parts = significandParts();
906 assert(semantics == rhs.semantics);
907 assert(exponent == rhs.exponent);
909 return APInt::tcSubtract(parts, rhs.significandParts(), borrow,
913 /* Multiply the significand of the RHS. If ADDEND is non-NULL, add it
914 on to the full-precision result of the multiplication. Returns the
917 APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
919 unsigned int omsb; // One, not zero, based MSB.
920 unsigned int partsCount, newPartsCount, precision;
921 integerPart *lhsSignificand;
922 integerPart scratch[4];
923 integerPart *fullSignificand;
924 lostFraction lost_fraction;
927 assert(semantics == rhs.semantics);
929 precision = semantics->precision;
930 newPartsCount = partCountForBits(precision * 2);
932 if (newPartsCount > 4)
933 fullSignificand = new integerPart[newPartsCount];
935 fullSignificand = scratch;
937 lhsSignificand = significandParts();
938 partsCount = partCount();
940 APInt::tcFullMultiply(fullSignificand, lhsSignificand,
941 rhs.significandParts(), partsCount, partsCount);
943 lost_fraction = lfExactlyZero;
944 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
945 exponent += rhs.exponent;
947 // Assume the operands involved in the multiplication are single-precision
948 // FP, and the two multiplicants are:
949 // *this = a23 . a22 ... a0 * 2^e1
950 // rhs = b23 . b22 ... b0 * 2^e2
951 // the result of multiplication is:
952 // *this = c47 c46 . c45 ... c0 * 2^(e1+e2)
953 // Note that there are two significant bits at the left-hand side of the
954 // radix point. Move the radix point toward left by one bit, and adjust
955 // exponent accordingly.
959 // The intermediate result of the multiplication has "2 * precision"
960 // signicant bit; adjust the addend to be consistent with mul result.
962 Significand savedSignificand = significand;
963 const fltSemantics *savedSemantics = semantics;
964 fltSemantics extendedSemantics;
966 unsigned int extendedPrecision;
968 /* Normalize our MSB. */
969 extendedPrecision = 2 * precision;
970 if (omsb != extendedPrecision) {
971 assert(extendedPrecision > omsb);
972 APInt::tcShiftLeft(fullSignificand, newPartsCount,
973 extendedPrecision - omsb);
974 exponent -= extendedPrecision - omsb;
977 /* Create new semantics. */
978 extendedSemantics = *semantics;
979 extendedSemantics.precision = extendedPrecision;
981 if (newPartsCount == 1)
982 significand.part = fullSignificand[0];
984 significand.parts = fullSignificand;
985 semantics = &extendedSemantics;
987 APFloat extendedAddend(*addend);
988 status = extendedAddend.convert(extendedSemantics, rmTowardZero, &ignored);
989 assert(status == opOK);
991 lost_fraction = addOrSubtractSignificand(extendedAddend, false);
993 /* Restore our state. */
994 if (newPartsCount == 1)
995 fullSignificand[0] = significand.part;
996 significand = savedSignificand;
997 semantics = savedSemantics;
999 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
1002 // Convert the result having "2 * precision" significant-bits back to the one
1003 // having "precision" significant-bits. First, move the radix point from
1004 // poision "2*precision - 1" to "precision - 1". The exponent need to be
1005 // adjusted by "2*precision - 1" - "precision - 1" = "precision".
1006 exponent -= precision;
1008 // In case MSB resides at the left-hand side of radix point, shift the
1009 // mantissa right by some amount to make sure the MSB reside right before
1010 // the radix point (i.e. "MSB . rest-significant-bits").
1012 // Note that the result is not normalized when "omsb < precision". So, the
1013 // caller needs to call APFloat::normalize() if normalized value is expected.
1014 if (omsb > precision) {
1015 unsigned int bits, significantParts;
1018 bits = omsb - precision;
1019 significantParts = partCountForBits(omsb);
1020 lf = shiftRight(fullSignificand, significantParts, bits);
1021 lost_fraction = combineLostFractions(lf, lost_fraction);
1025 APInt::tcAssign(lhsSignificand, fullSignificand, partsCount);
1027 if (newPartsCount > 4)
1028 delete [] fullSignificand;
1030 return lost_fraction;
1033 /* Multiply the significands of LHS and RHS to DST. */
1035 APFloat::divideSignificand(const APFloat &rhs)
1037 unsigned int bit, i, partsCount;
1038 const integerPart *rhsSignificand;
1039 integerPart *lhsSignificand, *dividend, *divisor;
1040 integerPart scratch[4];
1041 lostFraction lost_fraction;
1043 assert(semantics == rhs.semantics);
1045 lhsSignificand = significandParts();
1046 rhsSignificand = rhs.significandParts();
1047 partsCount = partCount();
1050 dividend = new integerPart[partsCount * 2];
1054 divisor = dividend + partsCount;
1056 /* Copy the dividend and divisor as they will be modified in-place. */
1057 for (i = 0; i < partsCount; i++) {
1058 dividend[i] = lhsSignificand[i];
1059 divisor[i] = rhsSignificand[i];
1060 lhsSignificand[i] = 0;
1063 exponent -= rhs.exponent;
1065 unsigned int precision = semantics->precision;
1067 /* Normalize the divisor. */
1068 bit = precision - APInt::tcMSB(divisor, partsCount) - 1;
1071 APInt::tcShiftLeft(divisor, partsCount, bit);
1074 /* Normalize the dividend. */
1075 bit = precision - APInt::tcMSB(dividend, partsCount) - 1;
1078 APInt::tcShiftLeft(dividend, partsCount, bit);
1081 /* Ensure the dividend >= divisor initially for the loop below.
1082 Incidentally, this means that the division loop below is
1083 guaranteed to set the integer bit to one. */
1084 if (APInt::tcCompare(dividend, divisor, partsCount) < 0) {
1086 APInt::tcShiftLeft(dividend, partsCount, 1);
1087 assert(APInt::tcCompare(dividend, divisor, partsCount) >= 0);
1090 /* Long division. */
1091 for (bit = precision; bit; bit -= 1) {
1092 if (APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
1093 APInt::tcSubtract(dividend, divisor, 0, partsCount);
1094 APInt::tcSetBit(lhsSignificand, bit - 1);
1097 APInt::tcShiftLeft(dividend, partsCount, 1);
1100 /* Figure out the lost fraction. */
1101 int cmp = APInt::tcCompare(dividend, divisor, partsCount);
1104 lost_fraction = lfMoreThanHalf;
1106 lost_fraction = lfExactlyHalf;
1107 else if (APInt::tcIsZero(dividend, partsCount))
1108 lost_fraction = lfExactlyZero;
1110 lost_fraction = lfLessThanHalf;
1115 return lost_fraction;
1119 APFloat::significandMSB() const
1121 return APInt::tcMSB(significandParts(), partCount());
1125 APFloat::significandLSB() const
1127 return APInt::tcLSB(significandParts(), partCount());
1130 /* Note that a zero result is NOT normalized to fcZero. */
1132 APFloat::shiftSignificandRight(unsigned int bits)
1134 /* Our exponent should not overflow. */
1135 assert((ExponentType) (exponent + bits) >= exponent);
1139 return shiftRight(significandParts(), partCount(), bits);
1142 /* Shift the significand left BITS bits, subtract BITS from its exponent. */
1144 APFloat::shiftSignificandLeft(unsigned int bits)
1146 assert(bits < semantics->precision);
1149 unsigned int partsCount = partCount();
1151 APInt::tcShiftLeft(significandParts(), partsCount, bits);
1154 assert(!APInt::tcIsZero(significandParts(), partsCount));
1159 APFloat::compareAbsoluteValue(const APFloat &rhs) const
1163 assert(semantics == rhs.semantics);
1164 assert(isFiniteNonZero());
1165 assert(rhs.isFiniteNonZero());
1167 compare = exponent - rhs.exponent;
1169 /* If exponents are equal, do an unsigned bignum comparison of the
1172 compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
1176 return cmpGreaterThan;
1177 else if (compare < 0)
1183 /* Handle overflow. Sign is preserved. We either become infinity or
1184 the largest finite number. */
1186 APFloat::handleOverflow(roundingMode rounding_mode)
1189 if (rounding_mode == rmNearestTiesToEven ||
1190 rounding_mode == rmNearestTiesToAway ||
1191 (rounding_mode == rmTowardPositive && !sign) ||
1192 (rounding_mode == rmTowardNegative && sign)) {
1193 category = fcInfinity;
1194 return (opStatus) (opOverflow | opInexact);
1197 /* Otherwise we become the largest finite number. */
1198 category = fcNormal;
1199 exponent = semantics->maxExponent;
1200 APInt::tcSetLeastSignificantBits(significandParts(), partCount(),
1201 semantics->precision);
1206 /* Returns TRUE if, when truncating the current number, with BIT the
1207 new LSB, with the given lost fraction and rounding mode, the result
1208 would need to be rounded away from zero (i.e., by increasing the
1209 signficand). This routine must work for fcZero of both signs, and
1210 fcNormal numbers. */
1212 APFloat::roundAwayFromZero(roundingMode rounding_mode,
1213 lostFraction lost_fraction,
1214 unsigned int bit) const
1216 /* NaNs and infinities should not have lost fractions. */
1217 assert(isFiniteNonZero() || category == fcZero);
1219 /* Current callers never pass this so we don't handle it. */
1220 assert(lost_fraction != lfExactlyZero);
1222 switch (rounding_mode) {
1223 case rmNearestTiesToAway:
1224 return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf;
1226 case rmNearestTiesToEven:
1227 if (lost_fraction == lfMoreThanHalf)
1230 /* Our zeroes don't have a significand to test. */
1231 if (lost_fraction == lfExactlyHalf && category != fcZero)
1232 return APInt::tcExtractBit(significandParts(), bit);
1239 case rmTowardPositive:
1240 return sign == false;
1242 case rmTowardNegative:
1243 return sign == true;
1245 llvm_unreachable("Invalid rounding mode found");
1249 APFloat::normalize(roundingMode rounding_mode,
1250 lostFraction lost_fraction)
1252 unsigned int omsb; /* One, not zero, based MSB. */
1255 if (!isFiniteNonZero())
1258 /* Before rounding normalize the exponent of fcNormal numbers. */
1259 omsb = significandMSB() + 1;
1262 /* OMSB is numbered from 1. We want to place it in the integer
1263 bit numbered PRECISION if possible, with a compensating change in
1265 exponentChange = omsb - semantics->precision;
1267 /* If the resulting exponent is too high, overflow according to
1268 the rounding mode. */
1269 if (exponent + exponentChange > semantics->maxExponent)
1270 return handleOverflow(rounding_mode);
1272 /* Subnormal numbers have exponent minExponent, and their MSB
1273 is forced based on that. */
1274 if (exponent + exponentChange < semantics->minExponent)
1275 exponentChange = semantics->minExponent - exponent;
1277 /* Shifting left is easy as we don't lose precision. */
1278 if (exponentChange < 0) {
1279 assert(lost_fraction == lfExactlyZero);
1281 shiftSignificandLeft(-exponentChange);
1286 if (exponentChange > 0) {
1289 /* Shift right and capture any new lost fraction. */
1290 lf = shiftSignificandRight(exponentChange);
1292 lost_fraction = combineLostFractions(lf, lost_fraction);
1294 /* Keep OMSB up-to-date. */
1295 if (omsb > (unsigned) exponentChange)
1296 omsb -= exponentChange;
1302 /* Now round the number according to rounding_mode given the lost
1305 /* As specified in IEEE 754, since we do not trap we do not report
1306 underflow for exact results. */
1307 if (lost_fraction == lfExactlyZero) {
1308 /* Canonicalize zeroes. */
1315 /* Increment the significand if we're rounding away from zero. */
1316 if (roundAwayFromZero(rounding_mode, lost_fraction, 0)) {
1318 exponent = semantics->minExponent;
1320 incrementSignificand();
1321 omsb = significandMSB() + 1;
1323 /* Did the significand increment overflow? */
1324 if (omsb == (unsigned) semantics->precision + 1) {
1325 /* Renormalize by incrementing the exponent and shifting our
1326 significand right one. However if we already have the
1327 maximum exponent we overflow to infinity. */
1328 if (exponent == semantics->maxExponent) {
1329 category = fcInfinity;
1331 return (opStatus) (opOverflow | opInexact);
1334 shiftSignificandRight(1);
1340 /* The normal case - we were and are not denormal, and any
1341 significand increment above didn't overflow. */
1342 if (omsb == semantics->precision)
1345 /* We have a non-zero denormal. */
1346 assert(omsb < semantics->precision);
1348 /* Canonicalize zeroes. */
1352 /* The fcZero case is a denormal that underflowed to zero. */
1353 return (opStatus) (opUnderflow | opInexact);
1357 APFloat::addOrSubtractSpecials(const APFloat &rhs, bool subtract)
1359 switch (PackCategoriesIntoKey(category, rhs.category)) {
1361 llvm_unreachable(nullptr);
1363 case PackCategoriesIntoKey(fcNaN, fcZero):
1364 case PackCategoriesIntoKey(fcNaN, fcNormal):
1365 case PackCategoriesIntoKey(fcNaN, fcInfinity):
1366 case PackCategoriesIntoKey(fcNaN, fcNaN):
1367 case PackCategoriesIntoKey(fcNormal, fcZero):
1368 case PackCategoriesIntoKey(fcInfinity, fcNormal):
1369 case PackCategoriesIntoKey(fcInfinity, fcZero):
1372 case PackCategoriesIntoKey(fcZero, fcNaN):
1373 case PackCategoriesIntoKey(fcNormal, fcNaN):
1374 case PackCategoriesIntoKey(fcInfinity, fcNaN):
1377 copySignificand(rhs);
1380 case PackCategoriesIntoKey(fcNormal, fcInfinity):
1381 case PackCategoriesIntoKey(fcZero, fcInfinity):
1382 category = fcInfinity;
1383 sign = rhs.sign ^ subtract;
1386 case PackCategoriesIntoKey(fcZero, fcNormal):
1388 sign = rhs.sign ^ subtract;
1391 case PackCategoriesIntoKey(fcZero, fcZero):
1392 /* Sign depends on rounding mode; handled by caller. */
1395 case PackCategoriesIntoKey(fcInfinity, fcInfinity):
1396 /* Differently signed infinities can only be validly
1398 if (((sign ^ rhs.sign)!=0) != subtract) {
1405 case PackCategoriesIntoKey(fcNormal, fcNormal):
1410 /* Add or subtract two normal numbers. */
1412 APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
1415 lostFraction lost_fraction;
1418 /* Determine if the operation on the absolute values is effectively
1419 an addition or subtraction. */
1420 subtract ^= (sign ^ rhs.sign) ? true : false;
1422 /* Are we bigger exponent-wise than the RHS? */
1423 bits = exponent - rhs.exponent;
1425 /* Subtraction is more subtle than one might naively expect. */
1427 APFloat temp_rhs(rhs);
1431 reverse = compareAbsoluteValue(temp_rhs) == cmpLessThan;
1432 lost_fraction = lfExactlyZero;
1433 } else if (bits > 0) {
1434 lost_fraction = temp_rhs.shiftSignificandRight(bits - 1);
1435 shiftSignificandLeft(1);
1438 lost_fraction = shiftSignificandRight(-bits - 1);
1439 temp_rhs.shiftSignificandLeft(1);
1444 carry = temp_rhs.subtractSignificand
1445 (*this, lost_fraction != lfExactlyZero);
1446 copySignificand(temp_rhs);
1449 carry = subtractSignificand
1450 (temp_rhs, lost_fraction != lfExactlyZero);
1453 /* Invert the lost fraction - it was on the RHS and
1455 if (lost_fraction == lfLessThanHalf)
1456 lost_fraction = lfMoreThanHalf;
1457 else if (lost_fraction == lfMoreThanHalf)
1458 lost_fraction = lfLessThanHalf;
1460 /* The code above is intended to ensure that no borrow is
1466 APFloat temp_rhs(rhs);
1468 lost_fraction = temp_rhs.shiftSignificandRight(bits);
1469 carry = addSignificand(temp_rhs);
1471 lost_fraction = shiftSignificandRight(-bits);
1472 carry = addSignificand(rhs);
1475 /* We have a guard bit; generating a carry cannot happen. */
1480 return lost_fraction;
1484 APFloat::multiplySpecials(const APFloat &rhs)
1486 switch (PackCategoriesIntoKey(category, rhs.category)) {
1488 llvm_unreachable(nullptr);
1490 case PackCategoriesIntoKey(fcNaN, fcZero):
1491 case PackCategoriesIntoKey(fcNaN, fcNormal):
1492 case PackCategoriesIntoKey(fcNaN, fcInfinity):
1493 case PackCategoriesIntoKey(fcNaN, fcNaN):
1497 case PackCategoriesIntoKey(fcZero, fcNaN):
1498 case PackCategoriesIntoKey(fcNormal, fcNaN):
1499 case PackCategoriesIntoKey(fcInfinity, fcNaN):
1502 copySignificand(rhs);
1505 case PackCategoriesIntoKey(fcNormal, fcInfinity):
1506 case PackCategoriesIntoKey(fcInfinity, fcNormal):
1507 case PackCategoriesIntoKey(fcInfinity, fcInfinity):
1508 category = fcInfinity;
1511 case PackCategoriesIntoKey(fcZero, fcNormal):
1512 case PackCategoriesIntoKey(fcNormal, fcZero):
1513 case PackCategoriesIntoKey(fcZero, fcZero):
1517 case PackCategoriesIntoKey(fcZero, fcInfinity):
1518 case PackCategoriesIntoKey(fcInfinity, fcZero):
1522 case PackCategoriesIntoKey(fcNormal, fcNormal):
1528 APFloat::divideSpecials(const APFloat &rhs)
1530 switch (PackCategoriesIntoKey(category, rhs.category)) {
1532 llvm_unreachable(nullptr);
1534 case PackCategoriesIntoKey(fcZero, fcNaN):
1535 case PackCategoriesIntoKey(fcNormal, fcNaN):
1536 case PackCategoriesIntoKey(fcInfinity, fcNaN):
1538 copySignificand(rhs);
1539 case PackCategoriesIntoKey(fcNaN, fcZero):
1540 case PackCategoriesIntoKey(fcNaN, fcNormal):
1541 case PackCategoriesIntoKey(fcNaN, fcInfinity):
1542 case PackCategoriesIntoKey(fcNaN, fcNaN):
1544 case PackCategoriesIntoKey(fcInfinity, fcZero):
1545 case PackCategoriesIntoKey(fcInfinity, fcNormal):
1546 case PackCategoriesIntoKey(fcZero, fcInfinity):
1547 case PackCategoriesIntoKey(fcZero, fcNormal):
1550 case PackCategoriesIntoKey(fcNormal, fcInfinity):
1554 case PackCategoriesIntoKey(fcNormal, fcZero):
1555 category = fcInfinity;
1558 case PackCategoriesIntoKey(fcInfinity, fcInfinity):
1559 case PackCategoriesIntoKey(fcZero, fcZero):
1563 case PackCategoriesIntoKey(fcNormal, fcNormal):
1569 APFloat::modSpecials(const APFloat &rhs)
1571 switch (PackCategoriesIntoKey(category, rhs.category)) {
1573 llvm_unreachable(nullptr);
1575 case PackCategoriesIntoKey(fcNaN, fcZero):
1576 case PackCategoriesIntoKey(fcNaN, fcNormal):
1577 case PackCategoriesIntoKey(fcNaN, fcInfinity):
1578 case PackCategoriesIntoKey(fcNaN, fcNaN):
1579 case PackCategoriesIntoKey(fcZero, fcInfinity):
1580 case PackCategoriesIntoKey(fcZero, fcNormal):
1581 case PackCategoriesIntoKey(fcNormal, fcInfinity):
1584 case PackCategoriesIntoKey(fcZero, fcNaN):
1585 case PackCategoriesIntoKey(fcNormal, fcNaN):
1586 case PackCategoriesIntoKey(fcInfinity, fcNaN):
1589 copySignificand(rhs);
1592 case PackCategoriesIntoKey(fcNormal, fcZero):
1593 case PackCategoriesIntoKey(fcInfinity, fcZero):
1594 case PackCategoriesIntoKey(fcInfinity, fcNormal):
1595 case PackCategoriesIntoKey(fcInfinity, fcInfinity):
1596 case PackCategoriesIntoKey(fcZero, fcZero):
1600 case PackCategoriesIntoKey(fcNormal, fcNormal):
1607 APFloat::changeSign()
1609 /* Look mummy, this one's easy. */
1614 APFloat::clearSign()
1616 /* So is this one. */
1621 APFloat::copySign(const APFloat &rhs)
1627 /* Normalized addition or subtraction. */
1629 APFloat::addOrSubtract(const APFloat &rhs, roundingMode rounding_mode,
1634 fs = addOrSubtractSpecials(rhs, subtract);
1636 /* This return code means it was not a simple case. */
1637 if (fs == opDivByZero) {
1638 lostFraction lost_fraction;
1640 lost_fraction = addOrSubtractSignificand(rhs, subtract);
1641 fs = normalize(rounding_mode, lost_fraction);
1643 /* Can only be zero if we lost no fraction. */
1644 assert(category != fcZero || lost_fraction == lfExactlyZero);
1647 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1648 positive zero unless rounding to minus infinity, except that
1649 adding two like-signed zeroes gives that zero. */
1650 if (category == fcZero) {
1651 if (rhs.category != fcZero || (sign == rhs.sign) == subtract)
1652 sign = (rounding_mode == rmTowardNegative);
1658 /* Normalized addition. */
1660 APFloat::add(const APFloat &rhs, roundingMode rounding_mode)
1662 return addOrSubtract(rhs, rounding_mode, false);
1665 /* Normalized subtraction. */
1667 APFloat::subtract(const APFloat &rhs, roundingMode rounding_mode)
1669 return addOrSubtract(rhs, rounding_mode, true);
1672 /* Normalized multiply. */
1674 APFloat::multiply(const APFloat &rhs, roundingMode rounding_mode)
1679 fs = multiplySpecials(rhs);
1681 if (isFiniteNonZero()) {
1682 lostFraction lost_fraction = multiplySignificand(rhs, nullptr);
1683 fs = normalize(rounding_mode, lost_fraction);
1684 if (lost_fraction != lfExactlyZero)
1685 fs = (opStatus) (fs | opInexact);
1691 /* Normalized divide. */
1693 APFloat::divide(const APFloat &rhs, roundingMode rounding_mode)
1698 fs = divideSpecials(rhs);
1700 if (isFiniteNonZero()) {
1701 lostFraction lost_fraction = divideSignificand(rhs);
1702 fs = normalize(rounding_mode, lost_fraction);
1703 if (lost_fraction != lfExactlyZero)
1704 fs = (opStatus) (fs | opInexact);
1710 /* Normalized remainder. This is not currently correct in all cases. */
1712 APFloat::remainder(const APFloat &rhs)
1716 unsigned int origSign = sign;
1718 fs = V.divide(rhs, rmNearestTiesToEven);
1719 if (fs == opDivByZero)
1722 int parts = partCount();
1723 integerPart *x = new integerPart[parts];
1725 fs = V.convertToInteger(x, parts * integerPartWidth, true,
1726 rmNearestTiesToEven, &ignored);
1727 if (fs==opInvalidOp)
1730 fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
1731 rmNearestTiesToEven);
1732 assert(fs==opOK); // should always work
1734 fs = V.multiply(rhs, rmNearestTiesToEven);
1735 assert(fs==opOK || fs==opInexact); // should not overflow or underflow
1737 fs = subtract(V, rmNearestTiesToEven);
1738 assert(fs==opOK || fs==opInexact); // likewise
1741 sign = origSign; // IEEE754 requires this
1746 /* Normalized llvm frem (C fmod).
1747 This is not currently correct in all cases. */
1749 APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
1752 fs = modSpecials(rhs);
1754 if (isFiniteNonZero() && rhs.isFiniteNonZero()) {
1756 unsigned int origSign = sign;
1758 fs = V.divide(rhs, rmNearestTiesToEven);
1759 if (fs == opDivByZero)
1762 int parts = partCount();
1763 integerPart *x = new integerPart[parts];
1765 fs = V.convertToInteger(x, parts * integerPartWidth, true,
1766 rmTowardZero, &ignored);
1767 if (fs==opInvalidOp)
1770 fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
1771 rmNearestTiesToEven);
1772 assert(fs==opOK); // should always work
1774 fs = V.multiply(rhs, rounding_mode);
1775 assert(fs==opOK || fs==opInexact); // should not overflow or underflow
1777 fs = subtract(V, rounding_mode);
1778 assert(fs==opOK || fs==opInexact); // likewise
1781 sign = origSign; // IEEE754 requires this
1787 /* Normalized fused-multiply-add. */
1789 APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
1790 const APFloat &addend,
1791 roundingMode rounding_mode)
1795 /* Post-multiplication sign, before addition. */
1796 sign ^= multiplicand.sign;
1798 /* If and only if all arguments are normal do we need to do an
1799 extended-precision calculation. */
1800 if (isFiniteNonZero() &&
1801 multiplicand.isFiniteNonZero() &&
1802 addend.isFiniteNonZero()) {
1803 lostFraction lost_fraction;
1805 lost_fraction = multiplySignificand(multiplicand, &addend);
1806 fs = normalize(rounding_mode, lost_fraction);
1807 if (lost_fraction != lfExactlyZero)
1808 fs = (opStatus) (fs | opInexact);
1810 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1811 positive zero unless rounding to minus infinity, except that
1812 adding two like-signed zeroes gives that zero. */
1813 if (category == fcZero && sign != addend.sign)
1814 sign = (rounding_mode == rmTowardNegative);
1816 fs = multiplySpecials(multiplicand);
1818 /* FS can only be opOK or opInvalidOp. There is no more work
1819 to do in the latter case. The IEEE-754R standard says it is
1820 implementation-defined in this case whether, if ADDEND is a
1821 quiet NaN, we raise invalid op; this implementation does so.
1823 If we need to do the addition we can do so with normal
1826 fs = addOrSubtract(addend, rounding_mode, false);
1832 /* Rounding-mode corrrect round to integral value. */
1833 APFloat::opStatus APFloat::roundToIntegral(roundingMode rounding_mode) {
1836 // If the exponent is large enough, we know that this value is already
1837 // integral, and the arithmetic below would potentially cause it to saturate
1838 // to +/-Inf. Bail out early instead.
1839 if (isFiniteNonZero() && exponent+1 >= (int)semanticsPrecision(*semantics))
1842 // The algorithm here is quite simple: we add 2^(p-1), where p is the
1843 // precision of our format, and then subtract it back off again. The choice
1844 // of rounding modes for the addition/subtraction determines the rounding mode
1845 // for our integral rounding as well.
1846 // NOTE: When the input value is negative, we do subtraction followed by
1847 // addition instead.
1848 APInt IntegerConstant(NextPowerOf2(semanticsPrecision(*semantics)), 1);
1849 IntegerConstant <<= semanticsPrecision(*semantics)-1;
1850 APFloat MagicConstant(*semantics);
1851 fs = MagicConstant.convertFromAPInt(IntegerConstant, false,
1852 rmNearestTiesToEven);
1853 MagicConstant.copySign(*this);
1858 // Preserve the input sign so that we can handle 0.0/-0.0 cases correctly.
1859 bool inputSign = isNegative();
1861 fs = add(MagicConstant, rounding_mode);
1862 if (fs != opOK && fs != opInexact)
1865 fs = subtract(MagicConstant, rounding_mode);
1867 // Restore the input sign.
1868 if (inputSign != isNegative())
1875 /* Comparison requires normalized numbers. */
1877 APFloat::compare(const APFloat &rhs) const
1881 assert(semantics == rhs.semantics);
1883 switch (PackCategoriesIntoKey(category, rhs.category)) {
1885 llvm_unreachable(nullptr);
1887 case PackCategoriesIntoKey(fcNaN, fcZero):
1888 case PackCategoriesIntoKey(fcNaN, fcNormal):
1889 case PackCategoriesIntoKey(fcNaN, fcInfinity):
1890 case PackCategoriesIntoKey(fcNaN, fcNaN):
1891 case PackCategoriesIntoKey(fcZero, fcNaN):
1892 case PackCategoriesIntoKey(fcNormal, fcNaN):
1893 case PackCategoriesIntoKey(fcInfinity, fcNaN):
1894 return cmpUnordered;
1896 case PackCategoriesIntoKey(fcInfinity, fcNormal):
1897 case PackCategoriesIntoKey(fcInfinity, fcZero):
1898 case PackCategoriesIntoKey(fcNormal, fcZero):
1902 return cmpGreaterThan;
1904 case PackCategoriesIntoKey(fcNormal, fcInfinity):
1905 case PackCategoriesIntoKey(fcZero, fcInfinity):
1906 case PackCategoriesIntoKey(fcZero, fcNormal):
1908 return cmpGreaterThan;
1912 case PackCategoriesIntoKey(fcInfinity, fcInfinity):
1913 if (sign == rhs.sign)
1918 return cmpGreaterThan;
1920 case PackCategoriesIntoKey(fcZero, fcZero):
1923 case PackCategoriesIntoKey(fcNormal, fcNormal):
1927 /* Two normal numbers. Do they have the same sign? */
1928 if (sign != rhs.sign) {
1930 result = cmpLessThan;
1932 result = cmpGreaterThan;
1934 /* Compare absolute values; invert result if negative. */
1935 result = compareAbsoluteValue(rhs);
1938 if (result == cmpLessThan)
1939 result = cmpGreaterThan;
1940 else if (result == cmpGreaterThan)
1941 result = cmpLessThan;
1948 /// APFloat::convert - convert a value of one floating point type to another.
1949 /// The return value corresponds to the IEEE754 exceptions. *losesInfo
1950 /// records whether the transformation lost information, i.e. whether
1951 /// converting the result back to the original type will produce the
1952 /// original value (this is almost the same as return value==fsOK, but there
1953 /// are edge cases where this is not so).
1956 APFloat::convert(const fltSemantics &toSemantics,
1957 roundingMode rounding_mode, bool *losesInfo)
1959 lostFraction lostFraction;
1960 unsigned int newPartCount, oldPartCount;
1963 const fltSemantics &fromSemantics = *semantics;
1965 lostFraction = lfExactlyZero;
1966 newPartCount = partCountForBits(toSemantics.precision + 1);
1967 oldPartCount = partCount();
1968 shift = toSemantics.precision - fromSemantics.precision;
1970 bool X86SpecialNan = false;
1971 if (&fromSemantics == &APFloat::x87DoubleExtended &&
1972 &toSemantics != &APFloat::x87DoubleExtended && category == fcNaN &&
1973 (!(*significandParts() & 0x8000000000000000ULL) ||
1974 !(*significandParts() & 0x4000000000000000ULL))) {
1975 // x86 has some unusual NaNs which cannot be represented in any other
1976 // format; note them here.
1977 X86SpecialNan = true;
1980 // If this is a truncation of a denormal number, and the target semantics
1981 // has larger exponent range than the source semantics (this can happen
1982 // when truncating from PowerPC double-double to double format), the
1983 // right shift could lose result mantissa bits. Adjust exponent instead
1984 // of performing excessive shift.
1985 if (shift < 0 && isFiniteNonZero()) {
1986 int exponentChange = significandMSB() + 1 - fromSemantics.precision;
1987 if (exponent + exponentChange < toSemantics.minExponent)
1988 exponentChange = toSemantics.minExponent - exponent;
1989 if (exponentChange < shift)
1990 exponentChange = shift;
1991 if (exponentChange < 0) {
1992 shift -= exponentChange;
1993 exponent += exponentChange;
1997 // If this is a truncation, perform the shift before we narrow the storage.
1998 if (shift < 0 && (isFiniteNonZero() || category==fcNaN))
1999 lostFraction = shiftRight(significandParts(), oldPartCount, -shift);
2001 // Fix the storage so it can hold to new value.
2002 if (newPartCount > oldPartCount) {
2003 // The new type requires more storage; make it available.
2004 integerPart *newParts;
2005 newParts = new integerPart[newPartCount];
2006 APInt::tcSet(newParts, 0, newPartCount);
2007 if (isFiniteNonZero() || category==fcNaN)
2008 APInt::tcAssign(newParts, significandParts(), oldPartCount);
2010 significand.parts = newParts;
2011 } else if (newPartCount == 1 && oldPartCount != 1) {
2012 // Switch to built-in storage for a single part.
2013 integerPart newPart = 0;
2014 if (isFiniteNonZero() || category==fcNaN)
2015 newPart = significandParts()[0];
2017 significand.part = newPart;
2020 // Now that we have the right storage, switch the semantics.
2021 semantics = &toSemantics;
2023 // If this is an extension, perform the shift now that the storage is
2025 if (shift > 0 && (isFiniteNonZero() || category==fcNaN))
2026 APInt::tcShiftLeft(significandParts(), newPartCount, shift);
2028 if (isFiniteNonZero()) {
2029 fs = normalize(rounding_mode, lostFraction);
2030 *losesInfo = (fs != opOK);
2031 } else if (category == fcNaN) {
2032 *losesInfo = lostFraction != lfExactlyZero || X86SpecialNan;
2034 // For x87 extended precision, we want to make a NaN, not a special NaN if
2035 // the input wasn't special either.
2036 if (!X86SpecialNan && semantics == &APFloat::x87DoubleExtended)
2037 APInt::tcSetBit(significandParts(), semantics->precision - 1);
2039 // gcc forces the Quiet bit on, which means (float)(double)(float_sNan)
2040 // does not give you back the same bits. This is dubious, and we
2041 // don't currently do it. You're really supposed to get
2042 // an invalid operation signal at runtime, but nobody does that.
2052 /* Convert a floating point number to an integer according to the
2053 rounding mode. If the rounded integer value is out of range this
2054 returns an invalid operation exception and the contents of the
2055 destination parts are unspecified. If the rounded value is in
2056 range but the floating point number is not the exact integer, the C
2057 standard doesn't require an inexact exception to be raised. IEEE
2058 854 does require it so we do that.
2060 Note that for conversions to integer type the C standard requires
2061 round-to-zero to always be used. */
2063 APFloat::convertToSignExtendedInteger(integerPart *parts, unsigned int width,
2065 roundingMode rounding_mode,
2066 bool *isExact) const
2068 lostFraction lost_fraction;
2069 const integerPart *src;
2070 unsigned int dstPartsCount, truncatedBits;
2074 /* Handle the three special cases first. */
2075 if (category == fcInfinity || category == fcNaN)
2078 dstPartsCount = partCountForBits(width);
2080 if (category == fcZero) {
2081 APInt::tcSet(parts, 0, dstPartsCount);
2082 // Negative zero can't be represented as an int.
2087 src = significandParts();
2089 /* Step 1: place our absolute value, with any fraction truncated, in
2092 /* Our absolute value is less than one; truncate everything. */
2093 APInt::tcSet(parts, 0, dstPartsCount);
2094 /* For exponent -1 the integer bit represents .5, look at that.
2095 For smaller exponents leftmost truncated bit is 0. */
2096 truncatedBits = semantics->precision -1U - exponent;
2098 /* We want the most significant (exponent + 1) bits; the rest are
2100 unsigned int bits = exponent + 1U;
2102 /* Hopelessly large in magnitude? */
2106 if (bits < semantics->precision) {
2107 /* We truncate (semantics->precision - bits) bits. */
2108 truncatedBits = semantics->precision - bits;
2109 APInt::tcExtract(parts, dstPartsCount, src, bits, truncatedBits);
2111 /* We want at least as many bits as are available. */
2112 APInt::tcExtract(parts, dstPartsCount, src, semantics->precision, 0);
2113 APInt::tcShiftLeft(parts, dstPartsCount, bits - semantics->precision);
2118 /* Step 2: work out any lost fraction, and increment the absolute
2119 value if we would round away from zero. */
2120 if (truncatedBits) {
2121 lost_fraction = lostFractionThroughTruncation(src, partCount(),
2123 if (lost_fraction != lfExactlyZero &&
2124 roundAwayFromZero(rounding_mode, lost_fraction, truncatedBits)) {
2125 if (APInt::tcIncrement(parts, dstPartsCount))
2126 return opInvalidOp; /* Overflow. */
2129 lost_fraction = lfExactlyZero;
2132 /* Step 3: check if we fit in the destination. */
2133 unsigned int omsb = APInt::tcMSB(parts, dstPartsCount) + 1;
2137 /* Negative numbers cannot be represented as unsigned. */
2141 /* It takes omsb bits to represent the unsigned integer value.
2142 We lose a bit for the sign, but care is needed as the
2143 maximally negative integer is a special case. */
2144 if (omsb == width && APInt::tcLSB(parts, dstPartsCount) + 1 != omsb)
2147 /* This case can happen because of rounding. */
2152 APInt::tcNegate (parts, dstPartsCount);
2154 if (omsb >= width + !isSigned)
2158 if (lost_fraction == lfExactlyZero) {
2165 /* Same as convertToSignExtendedInteger, except we provide
2166 deterministic values in case of an invalid operation exception,
2167 namely zero for NaNs and the minimal or maximal value respectively
2168 for underflow or overflow.
2169 The *isExact output tells whether the result is exact, in the sense
2170 that converting it back to the original floating point type produces
2171 the original value. This is almost equivalent to result==opOK,
2172 except for negative zeroes.
2175 APFloat::convertToInteger(integerPart *parts, unsigned int width,
2177 roundingMode rounding_mode, bool *isExact) const
2181 fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode,
2184 if (fs == opInvalidOp) {
2185 unsigned int bits, dstPartsCount;
2187 dstPartsCount = partCountForBits(width);
2189 if (category == fcNaN)
2194 bits = width - isSigned;
2196 APInt::tcSetLeastSignificantBits(parts, dstPartsCount, bits);
2197 if (sign && isSigned)
2198 APInt::tcShiftLeft(parts, dstPartsCount, width - 1);
2204 /* Same as convertToInteger(integerPart*, ...), except the result is returned in
2205 an APSInt, whose initial bit-width and signed-ness are used to determine the
2206 precision of the conversion.
2209 APFloat::convertToInteger(APSInt &result,
2210 roundingMode rounding_mode, bool *isExact) const
2212 unsigned bitWidth = result.getBitWidth();
2213 SmallVector<uint64_t, 4> parts(result.getNumWords());
2214 opStatus status = convertToInteger(
2215 parts.data(), bitWidth, result.isSigned(), rounding_mode, isExact);
2216 // Keeps the original signed-ness.
2217 result = APInt(bitWidth, parts);
2221 /* Convert an unsigned integer SRC to a floating point number,
2222 rounding according to ROUNDING_MODE. The sign of the floating
2223 point number is not modified. */
2225 APFloat::convertFromUnsignedParts(const integerPart *src,
2226 unsigned int srcCount,
2227 roundingMode rounding_mode)
2229 unsigned int omsb, precision, dstCount;
2231 lostFraction lost_fraction;
2233 category = fcNormal;
2234 omsb = APInt::tcMSB(src, srcCount) + 1;
2235 dst = significandParts();
2236 dstCount = partCount();
2237 precision = semantics->precision;
2239 /* We want the most significant PRECISION bits of SRC. There may not
2240 be that many; extract what we can. */
2241 if (precision <= omsb) {
2242 exponent = omsb - 1;
2243 lost_fraction = lostFractionThroughTruncation(src, srcCount,
2245 APInt::tcExtract(dst, dstCount, src, precision, omsb - precision);
2247 exponent = precision - 1;
2248 lost_fraction = lfExactlyZero;
2249 APInt::tcExtract(dst, dstCount, src, omsb, 0);
2252 return normalize(rounding_mode, lost_fraction);
2256 APFloat::convertFromAPInt(const APInt &Val,
2258 roundingMode rounding_mode)
2260 unsigned int partCount = Val.getNumWords();
2264 if (isSigned && api.isNegative()) {
2269 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
2272 /* Convert a two's complement integer SRC to a floating point number,
2273 rounding according to ROUNDING_MODE. ISSIGNED is true if the
2274 integer is signed, in which case it must be sign-extended. */
2276 APFloat::convertFromSignExtendedInteger(const integerPart *src,
2277 unsigned int srcCount,
2279 roundingMode rounding_mode)
2284 APInt::tcExtractBit(src, srcCount * integerPartWidth - 1)) {
2287 /* If we're signed and negative negate a copy. */
2289 copy = new integerPart[srcCount];
2290 APInt::tcAssign(copy, src, srcCount);
2291 APInt::tcNegate(copy, srcCount);
2292 status = convertFromUnsignedParts(copy, srcCount, rounding_mode);
2296 status = convertFromUnsignedParts(src, srcCount, rounding_mode);
2302 /* FIXME: should this just take a const APInt reference? */
2304 APFloat::convertFromZeroExtendedInteger(const integerPart *parts,
2305 unsigned int width, bool isSigned,
2306 roundingMode rounding_mode)
2308 unsigned int partCount = partCountForBits(width);
2309 APInt api = APInt(width, makeArrayRef(parts, partCount));
2312 if (isSigned && APInt::tcExtractBit(parts, width - 1)) {
2317 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
2321 APFloat::convertFromHexadecimalString(StringRef s, roundingMode rounding_mode)
2323 lostFraction lost_fraction = lfExactlyZero;
2325 category = fcNormal;
2329 integerPart *significand = significandParts();
2330 unsigned partsCount = partCount();
2331 unsigned bitPos = partsCount * integerPartWidth;
2332 bool computedTrailingFraction = false;
2334 // Skip leading zeroes and any (hexa)decimal point.
2335 StringRef::iterator begin = s.begin();
2336 StringRef::iterator end = s.end();
2337 StringRef::iterator dot;
2338 StringRef::iterator p = skipLeadingZeroesAndAnyDot(begin, end, &dot);
2339 StringRef::iterator firstSignificantDigit = p;
2342 integerPart hex_value;
2345 assert(dot == end && "String contains multiple dots");
2350 hex_value = hexDigitValue(*p);
2351 if (hex_value == -1U)
2356 // Store the number while we have space.
2359 hex_value <<= bitPos % integerPartWidth;
2360 significand[bitPos / integerPartWidth] |= hex_value;
2361 } else if (!computedTrailingFraction) {
2362 lost_fraction = trailingHexadecimalFraction(p, end, hex_value);
2363 computedTrailingFraction = true;
2367 /* Hex floats require an exponent but not a hexadecimal point. */
2368 assert(p != end && "Hex strings require an exponent");
2369 assert((*p == 'p' || *p == 'P') && "Invalid character in significand");
2370 assert(p != begin && "Significand has no digits");
2371 assert((dot == end || p - begin != 1) && "Significand has no digits");
2373 /* Ignore the exponent if we are zero. */
2374 if (p != firstSignificantDigit) {
2377 /* Implicit hexadecimal point? */
2381 /* Calculate the exponent adjustment implicit in the number of
2382 significant digits. */
2383 expAdjustment = static_cast<int>(dot - firstSignificantDigit);
2384 if (expAdjustment < 0)
2386 expAdjustment = expAdjustment * 4 - 1;
2388 /* Adjust for writing the significand starting at the most
2389 significant nibble. */
2390 expAdjustment += semantics->precision;
2391 expAdjustment -= partsCount * integerPartWidth;
2393 /* Adjust for the given exponent. */
2394 exponent = totalExponent(p + 1, end, expAdjustment);
2397 return normalize(rounding_mode, lost_fraction);
2401 APFloat::roundSignificandWithExponent(const integerPart *decSigParts,
2402 unsigned sigPartCount, int exp,
2403 roundingMode rounding_mode)
2405 unsigned int parts, pow5PartCount;
2406 fltSemantics calcSemantics = { 32767, -32767, 0 };
2407 integerPart pow5Parts[maxPowerOfFiveParts];
2410 isNearest = (rounding_mode == rmNearestTiesToEven ||
2411 rounding_mode == rmNearestTiesToAway);
2413 parts = partCountForBits(semantics->precision + 11);
2415 /* Calculate pow(5, abs(exp)). */
2416 pow5PartCount = powerOf5(pow5Parts, exp >= 0 ? exp: -exp);
2418 for (;; parts *= 2) {
2419 opStatus sigStatus, powStatus;
2420 unsigned int excessPrecision, truncatedBits;
2422 calcSemantics.precision = parts * integerPartWidth - 1;
2423 excessPrecision = calcSemantics.precision - semantics->precision;
2424 truncatedBits = excessPrecision;
2426 APFloat decSig = APFloat::getZero(calcSemantics, sign);
2427 APFloat pow5(calcSemantics);
2429 sigStatus = decSig.convertFromUnsignedParts(decSigParts, sigPartCount,
2430 rmNearestTiesToEven);
2431 powStatus = pow5.convertFromUnsignedParts(pow5Parts, pow5PartCount,
2432 rmNearestTiesToEven);
2433 /* Add exp, as 10^n = 5^n * 2^n. */
2434 decSig.exponent += exp;
2436 lostFraction calcLostFraction;
2437 integerPart HUerr, HUdistance;
2438 unsigned int powHUerr;
2441 /* multiplySignificand leaves the precision-th bit set to 1. */
2442 calcLostFraction = decSig.multiplySignificand(pow5, nullptr);
2443 powHUerr = powStatus != opOK;
2445 calcLostFraction = decSig.divideSignificand(pow5);
2446 /* Denormal numbers have less precision. */
2447 if (decSig.exponent < semantics->minExponent) {
2448 excessPrecision += (semantics->minExponent - decSig.exponent);
2449 truncatedBits = excessPrecision;
2450 if (excessPrecision > calcSemantics.precision)
2451 excessPrecision = calcSemantics.precision;
2453 /* Extra half-ulp lost in reciprocal of exponent. */
2454 powHUerr = (powStatus == opOK && calcLostFraction == lfExactlyZero) ? 0:2;
2457 /* Both multiplySignificand and divideSignificand return the
2458 result with the integer bit set. */
2459 assert(APInt::tcExtractBit
2460 (decSig.significandParts(), calcSemantics.precision - 1) == 1);
2462 HUerr = HUerrBound(calcLostFraction != lfExactlyZero, sigStatus != opOK,
2464 HUdistance = 2 * ulpsFromBoundary(decSig.significandParts(),
2465 excessPrecision, isNearest);
2467 /* Are we guaranteed to round correctly if we truncate? */
2468 if (HUdistance >= HUerr) {
2469 APInt::tcExtract(significandParts(), partCount(), decSig.significandParts(),
2470 calcSemantics.precision - excessPrecision,
2472 /* Take the exponent of decSig. If we tcExtract-ed less bits
2473 above we must adjust our exponent to compensate for the
2474 implicit right shift. */
2475 exponent = (decSig.exponent + semantics->precision
2476 - (calcSemantics.precision - excessPrecision));
2477 calcLostFraction = lostFractionThroughTruncation(decSig.significandParts(),
2480 return normalize(rounding_mode, calcLostFraction);
2486 APFloat::convertFromDecimalString(StringRef str, roundingMode rounding_mode)
2491 /* Scan the text. */
2492 StringRef::iterator p = str.begin();
2493 interpretDecimal(p, str.end(), &D);
2495 /* Handle the quick cases. First the case of no significant digits,
2496 i.e. zero, and then exponents that are obviously too large or too
2497 small. Writing L for log 10 / log 2, a number d.ddddd*10^exp
2498 definitely overflows if
2500 (exp - 1) * L >= maxExponent
2502 and definitely underflows to zero where
2504 (exp + 1) * L <= minExponent - precision
2506 With integer arithmetic the tightest bounds for L are
2508 93/28 < L < 196/59 [ numerator <= 256 ]
2509 42039/12655 < L < 28738/8651 [ numerator <= 65536 ]
2512 // Test if we have a zero number allowing for strings with no null terminators
2513 // and zero decimals with non-zero exponents.
2515 // We computed firstSigDigit by ignoring all zeros and dots. Thus if
2516 // D->firstSigDigit equals str.end(), every digit must be a zero and there can
2517 // be at most one dot. On the other hand, if we have a zero with a non-zero
2518 // exponent, then we know that D.firstSigDigit will be non-numeric.
2519 if (D.firstSigDigit == str.end() || decDigitValue(*D.firstSigDigit) >= 10U) {
2523 /* Check whether the normalized exponent is high enough to overflow
2524 max during the log-rebasing in the max-exponent check below. */
2525 } else if (D.normalizedExponent - 1 > INT_MAX / 42039) {
2526 fs = handleOverflow(rounding_mode);
2528 /* If it wasn't, then it also wasn't high enough to overflow max
2529 during the log-rebasing in the min-exponent check. Check that it
2530 won't overflow min in either check, then perform the min-exponent
2532 } else if (D.normalizedExponent - 1 < INT_MIN / 42039 ||
2533 (D.normalizedExponent + 1) * 28738 <=
2534 8651 * (semantics->minExponent - (int) semantics->precision)) {
2535 /* Underflow to zero and round. */
2536 category = fcNormal;
2538 fs = normalize(rounding_mode, lfLessThanHalf);
2540 /* We can finally safely perform the max-exponent check. */
2541 } else if ((D.normalizedExponent - 1) * 42039
2542 >= 12655 * semantics->maxExponent) {
2543 /* Overflow and round. */
2544 fs = handleOverflow(rounding_mode);
2546 integerPart *decSignificand;
2547 unsigned int partCount;
2549 /* A tight upper bound on number of bits required to hold an
2550 N-digit decimal integer is N * 196 / 59. Allocate enough space
2551 to hold the full significand, and an extra part required by
2553 partCount = static_cast<unsigned int>(D.lastSigDigit - D.firstSigDigit) + 1;
2554 partCount = partCountForBits(1 + 196 * partCount / 59);
2555 decSignificand = new integerPart[partCount + 1];
2558 /* Convert to binary efficiently - we do almost all multiplication
2559 in an integerPart. When this would overflow do we do a single
2560 bignum multiplication, and then revert again to multiplication
2561 in an integerPart. */
2563 integerPart decValue, val, multiplier;
2571 if (p == str.end()) {
2575 decValue = decDigitValue(*p++);
2576 assert(decValue < 10U && "Invalid character in significand");
2578 val = val * 10 + decValue;
2579 /* The maximum number that can be multiplied by ten with any
2580 digit added without overflowing an integerPart. */
2581 } while (p <= D.lastSigDigit && multiplier <= (~ (integerPart) 0 - 9) / 10);
2583 /* Multiply out the current part. */
2584 APInt::tcMultiplyPart(decSignificand, decSignificand, multiplier, val,
2585 partCount, partCount + 1, false);
2587 /* If we used another part (likely but not guaranteed), increase
2589 if (decSignificand[partCount])
2591 } while (p <= D.lastSigDigit);
2593 category = fcNormal;
2594 fs = roundSignificandWithExponent(decSignificand, partCount,
2595 D.exponent, rounding_mode);
2597 delete [] decSignificand;
2604 APFloat::convertFromStringSpecials(StringRef str) {
2605 if (str.equals("inf") || str.equals("INFINITY")) {
2610 if (str.equals("-inf") || str.equals("-INFINITY")) {
2615 if (str.equals("nan") || str.equals("NaN")) {
2616 makeNaN(false, false);
2620 if (str.equals("-nan") || str.equals("-NaN")) {
2621 makeNaN(false, true);
2629 APFloat::convertFromString(StringRef str, roundingMode rounding_mode)
2631 assert(!str.empty() && "Invalid string length");
2633 // Handle special cases.
2634 if (convertFromStringSpecials(str))
2637 /* Handle a leading minus sign. */
2638 StringRef::iterator p = str.begin();
2639 size_t slen = str.size();
2640 sign = *p == '-' ? 1 : 0;
2641 if (*p == '-' || *p == '+') {
2644 assert(slen && "String has no digits");
2647 if (slen >= 2 && p[0] == '0' && (p[1] == 'x' || p[1] == 'X')) {
2648 assert(slen - 2 && "Invalid string");
2649 return convertFromHexadecimalString(StringRef(p + 2, slen - 2),
2653 return convertFromDecimalString(StringRef(p, slen), rounding_mode);
2656 /* Write out a hexadecimal representation of the floating point value
2657 to DST, which must be of sufficient size, in the C99 form
2658 [-]0xh.hhhhp[+-]d. Return the number of characters written,
2659 excluding the terminating NUL.
2661 If UPPERCASE, the output is in upper case, otherwise in lower case.
2663 HEXDIGITS digits appear altogether, rounding the value if
2664 necessary. If HEXDIGITS is 0, the minimal precision to display the
2665 number precisely is used instead. If nothing would appear after
2666 the decimal point it is suppressed.
2668 The decimal exponent is always printed and has at least one digit.
2669 Zero values display an exponent of zero. Infinities and NaNs
2670 appear as "infinity" or "nan" respectively.
2672 The above rules are as specified by C99. There is ambiguity about
2673 what the leading hexadecimal digit should be. This implementation
2674 uses whatever is necessary so that the exponent is displayed as
2675 stored. This implies the exponent will fall within the IEEE format
2676 range, and the leading hexadecimal digit will be 0 (for denormals),
2677 1 (normal numbers) or 2 (normal numbers rounded-away-from-zero with
2678 any other digits zero).
2681 APFloat::convertToHexString(char *dst, unsigned int hexDigits,
2682 bool upperCase, roundingMode rounding_mode) const
2692 memcpy (dst, upperCase ? infinityU: infinityL, sizeof infinityU - 1);
2693 dst += sizeof infinityL - 1;
2697 memcpy (dst, upperCase ? NaNU: NaNL, sizeof NaNU - 1);
2698 dst += sizeof NaNU - 1;
2703 *dst++ = upperCase ? 'X': 'x';
2705 if (hexDigits > 1) {
2707 memset (dst, '0', hexDigits - 1);
2708 dst += hexDigits - 1;
2710 *dst++ = upperCase ? 'P': 'p';
2715 dst = convertNormalToHexString (dst, hexDigits, upperCase, rounding_mode);
2721 return static_cast<unsigned int>(dst - p);
2724 /* Does the hard work of outputting the correctly rounded hexadecimal
2725 form of a normal floating point number with the specified number of
2726 hexadecimal digits. If HEXDIGITS is zero the minimum number of
2727 digits necessary to print the value precisely is output. */
2729 APFloat::convertNormalToHexString(char *dst, unsigned int hexDigits,
2731 roundingMode rounding_mode) const
2733 unsigned int count, valueBits, shift, partsCount, outputDigits;
2734 const char *hexDigitChars;
2735 const integerPart *significand;
2740 *dst++ = upperCase ? 'X': 'x';
2743 hexDigitChars = upperCase ? hexDigitsUpper: hexDigitsLower;
2745 significand = significandParts();
2746 partsCount = partCount();
2748 /* +3 because the first digit only uses the single integer bit, so
2749 we have 3 virtual zero most-significant-bits. */
2750 valueBits = semantics->precision + 3;
2751 shift = integerPartWidth - valueBits % integerPartWidth;
2753 /* The natural number of digits required ignoring trailing
2754 insignificant zeroes. */
2755 outputDigits = (valueBits - significandLSB () + 3) / 4;
2757 /* hexDigits of zero means use the required number for the
2758 precision. Otherwise, see if we are truncating. If we are,
2759 find out if we need to round away from zero. */
2761 if (hexDigits < outputDigits) {
2762 /* We are dropping non-zero bits, so need to check how to round.
2763 "bits" is the number of dropped bits. */
2765 lostFraction fraction;
2767 bits = valueBits - hexDigits * 4;
2768 fraction = lostFractionThroughTruncation (significand, partsCount, bits);
2769 roundUp = roundAwayFromZero(rounding_mode, fraction, bits);
2771 outputDigits = hexDigits;
2774 /* Write the digits consecutively, and start writing in the location
2775 of the hexadecimal point. We move the most significant digit
2776 left and add the hexadecimal point later. */
2779 count = (valueBits + integerPartWidth - 1) / integerPartWidth;
2781 while (outputDigits && count) {
2784 /* Put the most significant integerPartWidth bits in "part". */
2785 if (--count == partsCount)
2786 part = 0; /* An imaginary higher zero part. */
2788 part = significand[count] << shift;
2791 part |= significand[count - 1] >> (integerPartWidth - shift);
2793 /* Convert as much of "part" to hexdigits as we can. */
2794 unsigned int curDigits = integerPartWidth / 4;
2796 if (curDigits > outputDigits)
2797 curDigits = outputDigits;
2798 dst += partAsHex (dst, part, curDigits, hexDigitChars);
2799 outputDigits -= curDigits;
2805 /* Note that hexDigitChars has a trailing '0'. */
2808 *q = hexDigitChars[hexDigitValue (*q) + 1];
2809 } while (*q == '0');
2812 /* Add trailing zeroes. */
2813 memset (dst, '0', outputDigits);
2814 dst += outputDigits;
2817 /* Move the most significant digit to before the point, and if there
2818 is something after the decimal point add it. This must come
2819 after rounding above. */
2826 /* Finally output the exponent. */
2827 *dst++ = upperCase ? 'P': 'p';
2829 return writeSignedDecimal (dst, exponent);
2832 hash_code llvm::hash_value(const APFloat &Arg) {
2833 if (!Arg.isFiniteNonZero())
2834 return hash_combine((uint8_t)Arg.category,
2835 // NaN has no sign, fix it at zero.
2836 Arg.isNaN() ? (uint8_t)0 : (uint8_t)Arg.sign,
2837 Arg.semantics->precision);
2839 // Normal floats need their exponent and significand hashed.
2840 return hash_combine((uint8_t)Arg.category, (uint8_t)Arg.sign,
2841 Arg.semantics->precision, Arg.exponent,
2843 Arg.significandParts(),
2844 Arg.significandParts() + Arg.partCount()));
2847 // Conversion from APFloat to/from host float/double. It may eventually be
2848 // possible to eliminate these and have everybody deal with APFloats, but that
2849 // will take a while. This approach will not easily extend to long double.
2850 // Current implementation requires integerPartWidth==64, which is correct at
2851 // the moment but could be made more general.
2853 // Denormals have exponent minExponent in APFloat, but minExponent-1 in
2854 // the actual IEEE respresentations. We compensate for that here.
2857 APFloat::convertF80LongDoubleAPFloatToAPInt() const
2859 assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended);
2860 assert(partCount()==2);
2862 uint64_t myexponent, mysignificand;
2864 if (isFiniteNonZero()) {
2865 myexponent = exponent+16383; //bias
2866 mysignificand = significandParts()[0];
2867 if (myexponent==1 && !(mysignificand & 0x8000000000000000ULL))
2868 myexponent = 0; // denormal
2869 } else if (category==fcZero) {
2872 } else if (category==fcInfinity) {
2873 myexponent = 0x7fff;
2874 mysignificand = 0x8000000000000000ULL;
2876 assert(category == fcNaN && "Unknown category");
2877 myexponent = 0x7fff;
2878 mysignificand = significandParts()[0];
2882 words[0] = mysignificand;
2883 words[1] = ((uint64_t)(sign & 1) << 15) |
2884 (myexponent & 0x7fffLL);
2885 return APInt(80, words);
2889 APFloat::convertPPCDoubleDoubleAPFloatToAPInt() const
2891 assert(semantics == (const llvm::fltSemantics*)&PPCDoubleDouble);
2892 assert(partCount()==2);
2898 // Convert number to double. To avoid spurious underflows, we re-
2899 // normalize against the "double" minExponent first, and only *then*
2900 // truncate the mantissa. The result of that second conversion
2901 // may be inexact, but should never underflow.
2902 // Declare fltSemantics before APFloat that uses it (and
2903 // saves pointer to it) to ensure correct destruction order.
2904 fltSemantics extendedSemantics = *semantics;
2905 extendedSemantics.minExponent = IEEEdouble.minExponent;
2906 APFloat extended(*this);
2907 fs = extended.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
2908 assert(fs == opOK && !losesInfo);
2911 APFloat u(extended);
2912 fs = u.convert(IEEEdouble, rmNearestTiesToEven, &losesInfo);
2913 assert(fs == opOK || fs == opInexact);
2915 words[0] = *u.convertDoubleAPFloatToAPInt().getRawData();
2917 // If conversion was exact or resulted in a special case, we're done;
2918 // just set the second double to zero. Otherwise, re-convert back to
2919 // the extended format and compute the difference. This now should
2920 // convert exactly to double.
2921 if (u.isFiniteNonZero() && losesInfo) {
2922 fs = u.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
2923 assert(fs == opOK && !losesInfo);
2926 APFloat v(extended);
2927 v.subtract(u, rmNearestTiesToEven);
2928 fs = v.convert(IEEEdouble, rmNearestTiesToEven, &losesInfo);
2929 assert(fs == opOK && !losesInfo);
2931 words[1] = *v.convertDoubleAPFloatToAPInt().getRawData();
2936 return APInt(128, words);
2940 APFloat::convertQuadrupleAPFloatToAPInt() const
2942 assert(semantics == (const llvm::fltSemantics*)&IEEEquad);
2943 assert(partCount()==2);
2945 uint64_t myexponent, mysignificand, mysignificand2;
2947 if (isFiniteNonZero()) {
2948 myexponent = exponent+16383; //bias
2949 mysignificand = significandParts()[0];
2950 mysignificand2 = significandParts()[1];
2951 if (myexponent==1 && !(mysignificand2 & 0x1000000000000LL))
2952 myexponent = 0; // denormal
2953 } else if (category==fcZero) {
2955 mysignificand = mysignificand2 = 0;
2956 } else if (category==fcInfinity) {
2957 myexponent = 0x7fff;
2958 mysignificand = mysignificand2 = 0;
2960 assert(category == fcNaN && "Unknown category!");
2961 myexponent = 0x7fff;
2962 mysignificand = significandParts()[0];
2963 mysignificand2 = significandParts()[1];
2967 words[0] = mysignificand;
2968 words[1] = ((uint64_t)(sign & 1) << 63) |
2969 ((myexponent & 0x7fff) << 48) |
2970 (mysignificand2 & 0xffffffffffffLL);
2972 return APInt(128, words);
2976 APFloat::convertDoubleAPFloatToAPInt() const
2978 assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
2979 assert(partCount()==1);
2981 uint64_t myexponent, mysignificand;
2983 if (isFiniteNonZero()) {
2984 myexponent = exponent+1023; //bias
2985 mysignificand = *significandParts();
2986 if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
2987 myexponent = 0; // denormal
2988 } else if (category==fcZero) {
2991 } else if (category==fcInfinity) {
2995 assert(category == fcNaN && "Unknown category!");
2997 mysignificand = *significandParts();
3000 return APInt(64, ((((uint64_t)(sign & 1) << 63) |
3001 ((myexponent & 0x7ff) << 52) |
3002 (mysignificand & 0xfffffffffffffLL))));
3006 APFloat::convertFloatAPFloatToAPInt() const
3008 assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
3009 assert(partCount()==1);
3011 uint32_t myexponent, mysignificand;
3013 if (isFiniteNonZero()) {
3014 myexponent = exponent+127; //bias
3015 mysignificand = (uint32_t)*significandParts();
3016 if (myexponent == 1 && !(mysignificand & 0x800000))
3017 myexponent = 0; // denormal
3018 } else if (category==fcZero) {
3021 } else if (category==fcInfinity) {
3025 assert(category == fcNaN && "Unknown category!");
3027 mysignificand = (uint32_t)*significandParts();
3030 return APInt(32, (((sign&1) << 31) | ((myexponent&0xff) << 23) |
3031 (mysignificand & 0x7fffff)));
3035 APFloat::convertHalfAPFloatToAPInt() const
3037 assert(semantics == (const llvm::fltSemantics*)&IEEEhalf);
3038 assert(partCount()==1);
3040 uint32_t myexponent, mysignificand;
3042 if (isFiniteNonZero()) {
3043 myexponent = exponent+15; //bias
3044 mysignificand = (uint32_t)*significandParts();
3045 if (myexponent == 1 && !(mysignificand & 0x400))
3046 myexponent = 0; // denormal
3047 } else if (category==fcZero) {
3050 } else if (category==fcInfinity) {
3054 assert(category == fcNaN && "Unknown category!");
3056 mysignificand = (uint32_t)*significandParts();
3059 return APInt(16, (((sign&1) << 15) | ((myexponent&0x1f) << 10) |
3060 (mysignificand & 0x3ff)));
3063 // This function creates an APInt that is just a bit map of the floating
3064 // point constant as it would appear in memory. It is not a conversion,
3065 // and treating the result as a normal integer is unlikely to be useful.
3068 APFloat::bitcastToAPInt() const
3070 if (semantics == (const llvm::fltSemantics*)&IEEEhalf)
3071 return convertHalfAPFloatToAPInt();
3073 if (semantics == (const llvm::fltSemantics*)&IEEEsingle)
3074 return convertFloatAPFloatToAPInt();
3076 if (semantics == (const llvm::fltSemantics*)&IEEEdouble)
3077 return convertDoubleAPFloatToAPInt();
3079 if (semantics == (const llvm::fltSemantics*)&IEEEquad)
3080 return convertQuadrupleAPFloatToAPInt();
3082 if (semantics == (const llvm::fltSemantics*)&PPCDoubleDouble)
3083 return convertPPCDoubleDoubleAPFloatToAPInt();
3085 assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended &&
3087 return convertF80LongDoubleAPFloatToAPInt();
3091 APFloat::convertToFloat() const
3093 assert(semantics == (const llvm::fltSemantics*)&IEEEsingle &&
3094 "Float semantics are not IEEEsingle");
3095 APInt api = bitcastToAPInt();
3096 return api.bitsToFloat();
3100 APFloat::convertToDouble() const
3102 assert(semantics == (const llvm::fltSemantics*)&IEEEdouble &&
3103 "Float semantics are not IEEEdouble");
3104 APInt api = bitcastToAPInt();
3105 return api.bitsToDouble();
3108 /// Integer bit is explicit in this format. Intel hardware (387 and later)
3109 /// does not support these bit patterns:
3110 /// exponent = all 1's, integer bit 0, significand 0 ("pseudoinfinity")
3111 /// exponent = all 1's, integer bit 0, significand nonzero ("pseudoNaN")
3112 /// exponent = 0, integer bit 1 ("pseudodenormal")
3113 /// exponent!=0 nor all 1's, integer bit 0 ("unnormal")
3114 /// At the moment, the first two are treated as NaNs, the second two as Normal.
3116 APFloat::initFromF80LongDoubleAPInt(const APInt &api)
3118 assert(api.getBitWidth()==80);
3119 uint64_t i1 = api.getRawData()[0];
3120 uint64_t i2 = api.getRawData()[1];
3121 uint64_t myexponent = (i2 & 0x7fff);
3122 uint64_t mysignificand = i1;
3124 initialize(&APFloat::x87DoubleExtended);
3125 assert(partCount()==2);
3127 sign = static_cast<unsigned int>(i2>>15);
3128 if (myexponent==0 && mysignificand==0) {
3129 // exponent, significand meaningless
3131 } else if (myexponent==0x7fff && mysignificand==0x8000000000000000ULL) {
3132 // exponent, significand meaningless
3133 category = fcInfinity;
3134 } else if (myexponent==0x7fff && mysignificand!=0x8000000000000000ULL) {
3135 // exponent meaningless
3137 significandParts()[0] = mysignificand;
3138 significandParts()[1] = 0;
3140 category = fcNormal;
3141 exponent = myexponent - 16383;
3142 significandParts()[0] = mysignificand;
3143 significandParts()[1] = 0;
3144 if (myexponent==0) // denormal
3150 APFloat::initFromPPCDoubleDoubleAPInt(const APInt &api)
3152 assert(api.getBitWidth()==128);
3153 uint64_t i1 = api.getRawData()[0];
3154 uint64_t i2 = api.getRawData()[1];
3158 // Get the first double and convert to our format.
3159 initFromDoubleAPInt(APInt(64, i1));
3160 fs = convert(PPCDoubleDouble, rmNearestTiesToEven, &losesInfo);
3161 assert(fs == opOK && !losesInfo);
3164 // Unless we have a special case, add in second double.
3165 if (isFiniteNonZero()) {
3166 APFloat v(IEEEdouble, APInt(64, i2));
3167 fs = v.convert(PPCDoubleDouble, rmNearestTiesToEven, &losesInfo);
3168 assert(fs == opOK && !losesInfo);
3171 add(v, rmNearestTiesToEven);
3176 APFloat::initFromQuadrupleAPInt(const APInt &api)
3178 assert(api.getBitWidth()==128);
3179 uint64_t i1 = api.getRawData()[0];
3180 uint64_t i2 = api.getRawData()[1];
3181 uint64_t myexponent = (i2 >> 48) & 0x7fff;
3182 uint64_t mysignificand = i1;
3183 uint64_t mysignificand2 = i2 & 0xffffffffffffLL;
3185 initialize(&APFloat::IEEEquad);
3186 assert(partCount()==2);
3188 sign = static_cast<unsigned int>(i2>>63);
3189 if (myexponent==0 &&
3190 (mysignificand==0 && mysignificand2==0)) {
3191 // exponent, significand meaningless
3193 } else if (myexponent==0x7fff &&
3194 (mysignificand==0 && mysignificand2==0)) {
3195 // exponent, significand meaningless
3196 category = fcInfinity;
3197 } else if (myexponent==0x7fff &&
3198 (mysignificand!=0 || mysignificand2 !=0)) {
3199 // exponent meaningless
3201 significandParts()[0] = mysignificand;
3202 significandParts()[1] = mysignificand2;
3204 category = fcNormal;
3205 exponent = myexponent - 16383;
3206 significandParts()[0] = mysignificand;
3207 significandParts()[1] = mysignificand2;
3208 if (myexponent==0) // denormal
3211 significandParts()[1] |= 0x1000000000000LL; // integer bit
3216 APFloat::initFromDoubleAPInt(const APInt &api)
3218 assert(api.getBitWidth()==64);
3219 uint64_t i = *api.getRawData();
3220 uint64_t myexponent = (i >> 52) & 0x7ff;
3221 uint64_t mysignificand = i & 0xfffffffffffffLL;
3223 initialize(&APFloat::IEEEdouble);
3224 assert(partCount()==1);
3226 sign = static_cast<unsigned int>(i>>63);
3227 if (myexponent==0 && mysignificand==0) {
3228 // exponent, significand meaningless
3230 } else if (myexponent==0x7ff && mysignificand==0) {
3231 // exponent, significand meaningless
3232 category = fcInfinity;
3233 } else if (myexponent==0x7ff && mysignificand!=0) {
3234 // exponent meaningless
3236 *significandParts() = mysignificand;
3238 category = fcNormal;
3239 exponent = myexponent - 1023;
3240 *significandParts() = mysignificand;
3241 if (myexponent==0) // denormal
3244 *significandParts() |= 0x10000000000000LL; // integer bit
3249 APFloat::initFromFloatAPInt(const APInt & api)
3251 assert(api.getBitWidth()==32);
3252 uint32_t i = (uint32_t)*api.getRawData();
3253 uint32_t myexponent = (i >> 23) & 0xff;
3254 uint32_t mysignificand = i & 0x7fffff;
3256 initialize(&APFloat::IEEEsingle);
3257 assert(partCount()==1);
3260 if (myexponent==0 && mysignificand==0) {
3261 // exponent, significand meaningless
3263 } else if (myexponent==0xff && mysignificand==0) {
3264 // exponent, significand meaningless
3265 category = fcInfinity;
3266 } else if (myexponent==0xff && mysignificand!=0) {
3267 // sign, exponent, significand meaningless
3269 *significandParts() = mysignificand;
3271 category = fcNormal;
3272 exponent = myexponent - 127; //bias
3273 *significandParts() = mysignificand;
3274 if (myexponent==0) // denormal
3277 *significandParts() |= 0x800000; // integer bit
3282 APFloat::initFromHalfAPInt(const APInt & api)
3284 assert(api.getBitWidth()==16);
3285 uint32_t i = (uint32_t)*api.getRawData();
3286 uint32_t myexponent = (i >> 10) & 0x1f;
3287 uint32_t mysignificand = i & 0x3ff;
3289 initialize(&APFloat::IEEEhalf);
3290 assert(partCount()==1);
3293 if (myexponent==0 && mysignificand==0) {
3294 // exponent, significand meaningless
3296 } else if (myexponent==0x1f && mysignificand==0) {
3297 // exponent, significand meaningless
3298 category = fcInfinity;
3299 } else if (myexponent==0x1f && mysignificand!=0) {
3300 // sign, exponent, significand meaningless
3302 *significandParts() = mysignificand;
3304 category = fcNormal;
3305 exponent = myexponent - 15; //bias
3306 *significandParts() = mysignificand;
3307 if (myexponent==0) // denormal
3310 *significandParts() |= 0x400; // integer bit
3314 /// Treat api as containing the bits of a floating point number. Currently
3315 /// we infer the floating point type from the size of the APInt. The
3316 /// isIEEE argument distinguishes between PPC128 and IEEE128 (not meaningful
3317 /// when the size is anything else).
3319 APFloat::initFromAPInt(const fltSemantics* Sem, const APInt& api)
3321 if (Sem == &IEEEhalf)
3322 return initFromHalfAPInt(api);
3323 if (Sem == &IEEEsingle)
3324 return initFromFloatAPInt(api);
3325 if (Sem == &IEEEdouble)
3326 return initFromDoubleAPInt(api);
3327 if (Sem == &x87DoubleExtended)
3328 return initFromF80LongDoubleAPInt(api);
3329 if (Sem == &IEEEquad)
3330 return initFromQuadrupleAPInt(api);
3331 if (Sem == &PPCDoubleDouble)
3332 return initFromPPCDoubleDoubleAPInt(api);
3334 llvm_unreachable(nullptr);
3338 APFloat::getAllOnesValue(unsigned BitWidth, bool isIEEE)
3342 return APFloat(IEEEhalf, APInt::getAllOnesValue(BitWidth));
3344 return APFloat(IEEEsingle, APInt::getAllOnesValue(BitWidth));
3346 return APFloat(IEEEdouble, APInt::getAllOnesValue(BitWidth));
3348 return APFloat(x87DoubleExtended, APInt::getAllOnesValue(BitWidth));
3351 return APFloat(IEEEquad, APInt::getAllOnesValue(BitWidth));
3352 return APFloat(PPCDoubleDouble, APInt::getAllOnesValue(BitWidth));
3354 llvm_unreachable("Unknown floating bit width");
3358 /// Make this number the largest magnitude normal number in the given
3360 void APFloat::makeLargest(bool Negative) {
3361 // We want (in interchange format):
3362 // sign = {Negative}
3364 // significand = 1..1
3365 category = fcNormal;
3367 exponent = semantics->maxExponent;
3369 // Use memset to set all but the highest integerPart to all ones.
3370 integerPart *significand = significandParts();
3371 unsigned PartCount = partCount();
3372 memset(significand, 0xFF, sizeof(integerPart)*(PartCount - 1));
3374 // Set the high integerPart especially setting all unused top bits for
3375 // internal consistency.
3376 const unsigned NumUnusedHighBits =
3377 PartCount*integerPartWidth - semantics->precision;
3378 significand[PartCount - 1] = ~integerPart(0) >> NumUnusedHighBits;
3381 /// Make this number the smallest magnitude denormal number in the given
3383 void APFloat::makeSmallest(bool Negative) {
3384 // We want (in interchange format):
3385 // sign = {Negative}
3387 // significand = 0..01
3388 category = fcNormal;
3390 exponent = semantics->minExponent;
3391 APInt::tcSet(significandParts(), 1, partCount());
3395 APFloat APFloat::getLargest(const fltSemantics &Sem, bool Negative) {
3396 // We want (in interchange format):
3397 // sign = {Negative}
3399 // significand = 1..1
3400 APFloat Val(Sem, uninitialized);
3401 Val.makeLargest(Negative);
3405 APFloat APFloat::getSmallest(const fltSemantics &Sem, bool Negative) {
3406 // We want (in interchange format):
3407 // sign = {Negative}
3409 // significand = 0..01
3410 APFloat Val(Sem, uninitialized);
3411 Val.makeSmallest(Negative);
3415 APFloat APFloat::getSmallestNormalized(const fltSemantics &Sem, bool Negative) {
3416 APFloat Val(Sem, uninitialized);
3418 // We want (in interchange format):
3419 // sign = {Negative}
3421 // significand = 10..0
3423 Val.category = fcNormal;
3424 Val.zeroSignificand();
3425 Val.sign = Negative;
3426 Val.exponent = Sem.minExponent;
3427 Val.significandParts()[partCountForBits(Sem.precision)-1] |=
3428 (((integerPart) 1) << ((Sem.precision - 1) % integerPartWidth));
3433 APFloat::APFloat(const fltSemantics &Sem, const APInt &API) {
3434 initFromAPInt(&Sem, API);
3437 APFloat::APFloat(float f) {
3438 initFromAPInt(&IEEEsingle, APInt::floatToBits(f));
3441 APFloat::APFloat(double d) {
3442 initFromAPInt(&IEEEdouble, APInt::doubleToBits(d));
3446 void append(SmallVectorImpl<char> &Buffer, StringRef Str) {
3447 Buffer.append(Str.begin(), Str.end());
3450 /// Removes data from the given significand until it is no more
3451 /// precise than is required for the desired precision.
3452 void AdjustToPrecision(APInt &significand,
3453 int &exp, unsigned FormatPrecision) {
3454 unsigned bits = significand.getActiveBits();
3456 // 196/59 is a very slight overestimate of lg_2(10).
3457 unsigned bitsRequired = (FormatPrecision * 196 + 58) / 59;
3459 if (bits <= bitsRequired) return;
3461 unsigned tensRemovable = (bits - bitsRequired) * 59 / 196;
3462 if (!tensRemovable) return;
3464 exp += tensRemovable;
3466 APInt divisor(significand.getBitWidth(), 1);
3467 APInt powten(significand.getBitWidth(), 10);
3469 if (tensRemovable & 1)
3471 tensRemovable >>= 1;
3472 if (!tensRemovable) break;
3476 significand = significand.udiv(divisor);
3478 // Truncate the significand down to its active bit count.
3479 significand = significand.trunc(significand.getActiveBits());
3483 void AdjustToPrecision(SmallVectorImpl<char> &buffer,
3484 int &exp, unsigned FormatPrecision) {
3485 unsigned N = buffer.size();
3486 if (N <= FormatPrecision) return;
3488 // The most significant figures are the last ones in the buffer.
3489 unsigned FirstSignificant = N - FormatPrecision;
3492 // FIXME: this probably shouldn't use 'round half up'.
3494 // Rounding down is just a truncation, except we also want to drop
3495 // trailing zeros from the new result.
3496 if (buffer[FirstSignificant - 1] < '5') {
3497 while (FirstSignificant < N && buffer[FirstSignificant] == '0')
3500 exp += FirstSignificant;
3501 buffer.erase(&buffer[0], &buffer[FirstSignificant]);
3505 // Rounding up requires a decimal add-with-carry. If we continue
3506 // the carry, the newly-introduced zeros will just be truncated.
3507 for (unsigned I = FirstSignificant; I != N; ++I) {
3508 if (buffer[I] == '9') {
3516 // If we carried through, we have exactly one digit of precision.
3517 if (FirstSignificant == N) {
3518 exp += FirstSignificant;
3520 buffer.push_back('1');
3524 exp += FirstSignificant;
3525 buffer.erase(&buffer[0], &buffer[FirstSignificant]);
3529 void APFloat::toString(SmallVectorImpl<char> &Str,
3530 unsigned FormatPrecision,
3531 unsigned FormatMaxPadding) const {
3535 return append(Str, "-Inf");
3537 return append(Str, "+Inf");
3539 case fcNaN: return append(Str, "NaN");
3545 if (!FormatMaxPadding)
3546 append(Str, "0.0E+0");
3558 // Decompose the number into an APInt and an exponent.
3559 int exp = exponent - ((int) semantics->precision - 1);
3560 APInt significand(semantics->precision,
3561 makeArrayRef(significandParts(),
3562 partCountForBits(semantics->precision)));
3564 // Set FormatPrecision if zero. We want to do this before we
3565 // truncate trailing zeros, as those are part of the precision.
3566 if (!FormatPrecision) {
3567 // We use enough digits so the number can be round-tripped back to an
3568 // APFloat. The formula comes from "How to Print Floating-Point Numbers
3569 // Accurately" by Steele and White.
3570 // FIXME: Using a formula based purely on the precision is conservative;
3571 // we can print fewer digits depending on the actual value being printed.
3573 // FormatPrecision = 2 + floor(significandBits / lg_2(10))
3574 FormatPrecision = 2 + semantics->precision * 59 / 196;
3577 // Ignore trailing binary zeros.
3578 int trailingZeros = significand.countTrailingZeros();
3579 exp += trailingZeros;
3580 significand = significand.lshr(trailingZeros);
3582 // Change the exponent from 2^e to 10^e.
3585 } else if (exp > 0) {
3587 significand = significand.zext(semantics->precision + exp);
3588 significand <<= exp;
3590 } else { /* exp < 0 */
3593 // We transform this using the identity:
3594 // (N)(2^-e) == (N)(5^e)(10^-e)
3595 // This means we have to multiply N (the significand) by 5^e.
3596 // To avoid overflow, we have to operate on numbers large
3597 // enough to store N * 5^e:
3598 // log2(N * 5^e) == log2(N) + e * log2(5)
3599 // <= semantics->precision + e * 137 / 59
3600 // (log_2(5) ~ 2.321928 < 2.322034 ~ 137/59)
3602 unsigned precision = semantics->precision + (137 * texp + 136) / 59;
3604 // Multiply significand by 5^e.
3605 // N * 5^0101 == N * 5^(1*1) * 5^(0*2) * 5^(1*4) * 5^(0*8)
3606 significand = significand.zext(precision);
3607 APInt five_to_the_i(precision, 5);
3609 if (texp & 1) significand *= five_to_the_i;
3613 five_to_the_i *= five_to_the_i;
3617 AdjustToPrecision(significand, exp, FormatPrecision);
3619 SmallVector<char, 256> buffer;
3622 unsigned precision = significand.getBitWidth();
3623 APInt ten(precision, 10);
3624 APInt digit(precision, 0);
3626 bool inTrail = true;
3627 while (significand != 0) {
3628 // digit <- significand % 10
3629 // significand <- significand / 10
3630 APInt::udivrem(significand, ten, significand, digit);
3632 unsigned d = digit.getZExtValue();
3634 // Drop trailing zeros.
3635 if (inTrail && !d) exp++;
3637 buffer.push_back((char) ('0' + d));
3642 assert(!buffer.empty() && "no characters in buffer!");
3644 // Drop down to FormatPrecision.
3645 // TODO: don't do more precise calculations above than are required.
3646 AdjustToPrecision(buffer, exp, FormatPrecision);
3648 unsigned NDigits = buffer.size();
3650 // Check whether we should use scientific notation.
3651 bool FormatScientific;
3652 if (!FormatMaxPadding)
3653 FormatScientific = true;
3658 // But we shouldn't make the number look more precise than it is.
3659 FormatScientific = ((unsigned) exp > FormatMaxPadding ||
3660 NDigits + (unsigned) exp > FormatPrecision);
3662 // Power of the most significant digit.
3663 int MSD = exp + (int) (NDigits - 1);
3666 FormatScientific = false;
3668 // 765e-5 == 0.00765
3670 FormatScientific = ((unsigned) -MSD) > FormatMaxPadding;
3675 // Scientific formatting is pretty straightforward.
3676 if (FormatScientific) {
3677 exp += (NDigits - 1);
3679 Str.push_back(buffer[NDigits-1]);
3684 for (unsigned I = 1; I != NDigits; ++I)
3685 Str.push_back(buffer[NDigits-1-I]);
3688 Str.push_back(exp >= 0 ? '+' : '-');
3689 if (exp < 0) exp = -exp;
3690 SmallVector<char, 6> expbuf;
3692 expbuf.push_back((char) ('0' + (exp % 10)));
3695 for (unsigned I = 0, E = expbuf.size(); I != E; ++I)
3696 Str.push_back(expbuf[E-1-I]);
3700 // Non-scientific, positive exponents.
3702 for (unsigned I = 0; I != NDigits; ++I)
3703 Str.push_back(buffer[NDigits-1-I]);
3704 for (unsigned I = 0; I != (unsigned) exp; ++I)
3709 // Non-scientific, negative exponents.
3711 // The number of digits to the left of the decimal point.
3712 int NWholeDigits = exp + (int) NDigits;
3715 if (NWholeDigits > 0) {
3716 for (; I != (unsigned) NWholeDigits; ++I)
3717 Str.push_back(buffer[NDigits-I-1]);
3720 unsigned NZeros = 1 + (unsigned) -NWholeDigits;
3724 for (unsigned Z = 1; Z != NZeros; ++Z)
3728 for (; I != NDigits; ++I)
3729 Str.push_back(buffer[NDigits-I-1]);
3732 bool APFloat::getExactInverse(APFloat *inv) const {
3733 // Special floats and denormals have no exact inverse.
3734 if (!isFiniteNonZero())
3737 // Check that the number is a power of two by making sure that only the
3738 // integer bit is set in the significand.
3739 if (significandLSB() != semantics->precision - 1)
3743 APFloat reciprocal(*semantics, 1ULL);
3744 if (reciprocal.divide(*this, rmNearestTiesToEven) != opOK)
3747 // Avoid multiplication with a denormal, it is not safe on all platforms and
3748 // may be slower than a normal division.
3749 if (reciprocal.isDenormal())
3752 assert(reciprocal.isFiniteNonZero() &&
3753 reciprocal.significandLSB() == reciprocal.semantics->precision - 1);
3761 bool APFloat::isSignaling() const {
3765 // IEEE-754R 2008 6.2.1: A signaling NaN bit string should be encoded with the
3766 // first bit of the trailing significand being 0.
3767 return !APInt::tcExtractBit(significandParts(), semantics->precision - 2);
3770 /// IEEE-754R 2008 5.3.1: nextUp/nextDown.
3772 /// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with
3773 /// appropriate sign switching before/after the computation.
3774 APFloat::opStatus APFloat::next(bool nextDown) {
3775 // If we are performing nextDown, swap sign so we have -x.
3779 // Compute nextUp(x)
3780 opStatus result = opOK;
3782 // Handle each float category separately.
3785 // nextUp(+inf) = +inf
3788 // nextUp(-inf) = -getLargest()
3792 // IEEE-754R 2008 6.2 Par 2: nextUp(sNaN) = qNaN. Set Invalid flag.
3793 // IEEE-754R 2008 6.2: nextUp(qNaN) = qNaN. Must be identity so we do not
3794 // change the payload.
3795 if (isSignaling()) {
3796 result = opInvalidOp;
3797 // For consistency, propagate the sign of the sNaN to the qNaN.
3798 makeNaN(false, isNegative(), nullptr);
3802 // nextUp(pm 0) = +getSmallest()
3803 makeSmallest(false);
3806 // nextUp(-getSmallest()) = -0
3807 if (isSmallest() && isNegative()) {
3808 APInt::tcSet(significandParts(), 0, partCount());
3814 // nextUp(getLargest()) == INFINITY
3815 if (isLargest() && !isNegative()) {
3816 APInt::tcSet(significandParts(), 0, partCount());
3817 category = fcInfinity;
3818 exponent = semantics->maxExponent + 1;
3822 // nextUp(normal) == normal + inc.
3824 // If we are negative, we need to decrement the significand.
3826 // We only cross a binade boundary that requires adjusting the exponent
3828 // 1. exponent != semantics->minExponent. This implies we are not in the
3829 // smallest binade or are dealing with denormals.
3830 // 2. Our significand excluding the integral bit is all zeros.
3831 bool WillCrossBinadeBoundary =
3832 exponent != semantics->minExponent && isSignificandAllZeros();
3834 // Decrement the significand.
3836 // We always do this since:
3837 // 1. If we are dealing with a non-binade decrement, by definition we
3838 // just decrement the significand.
3839 // 2. If we are dealing with a normal -> normal binade decrement, since
3840 // we have an explicit integral bit the fact that all bits but the
3841 // integral bit are zero implies that subtracting one will yield a
3842 // significand with 0 integral bit and 1 in all other spots. Thus we
3843 // must just adjust the exponent and set the integral bit to 1.
3844 // 3. If we are dealing with a normal -> denormal binade decrement,
3845 // since we set the integral bit to 0 when we represent denormals, we
3846 // just decrement the significand.
3847 integerPart *Parts = significandParts();
3848 APInt::tcDecrement(Parts, partCount());
3850 if (WillCrossBinadeBoundary) {
3851 // Our result is a normal number. Do the following:
3852 // 1. Set the integral bit to 1.
3853 // 2. Decrement the exponent.
3854 APInt::tcSetBit(Parts, semantics->precision - 1);
3858 // If we are positive, we need to increment the significand.
3860 // We only cross a binade boundary that requires adjusting the exponent if
3861 // the input is not a denormal and all of said input's significand bits
3862 // are set. If all of said conditions are true: clear the significand, set
3863 // the integral bit to 1, and increment the exponent. If we have a
3864 // denormal always increment since moving denormals and the numbers in the
3865 // smallest normal binade have the same exponent in our representation.
3866 bool WillCrossBinadeBoundary = !isDenormal() && isSignificandAllOnes();
3868 if (WillCrossBinadeBoundary) {
3869 integerPart *Parts = significandParts();
3870 APInt::tcSet(Parts, 0, partCount());
3871 APInt::tcSetBit(Parts, semantics->precision - 1);
3872 assert(exponent != semantics->maxExponent &&
3873 "We can not increment an exponent beyond the maxExponent allowed"
3874 " by the given floating point semantics.");
3877 incrementSignificand();
3883 // If we are performing nextDown, swap sign so we have -nextUp(-x)
3891 APFloat::makeInf(bool Negative) {
3892 category = fcInfinity;
3894 exponent = semantics->maxExponent + 1;
3895 APInt::tcSet(significandParts(), 0, partCount());
3899 APFloat::makeZero(bool Negative) {
3902 exponent = semantics->minExponent-1;
3903 APInt::tcSet(significandParts(), 0, partCount());