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. */
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::isDenormal() const {
688 return isFiniteNonZero() && (exponent == semantics->minExponent) &&
689 (APInt::tcExtractBit(significandParts(),
690 semantics->precision - 1) == 0);
694 APFloat::isSmallest() const {
695 // The smallest number by magnitude in our format will be the smallest
696 // denormal, i.e. the floating point number with exponent being minimum
697 // exponent and significand bitwise equal to 1 (i.e. with MSB equal to 0).
698 return isFiniteNonZero() && exponent == semantics->minExponent &&
699 significandMSB() == 0;
702 bool APFloat::isSignificandAllOnes() const {
703 // Test if the significand excluding the integral bit is all ones. This allows
704 // us to test for binade boundaries.
705 const integerPart *Parts = significandParts();
706 const unsigned PartCount = partCount();
707 for (unsigned i = 0; i < PartCount - 1; i++)
711 // Set the unused high bits to all ones when we compare.
712 const unsigned NumHighBits =
713 PartCount*integerPartWidth - semantics->precision + 1;
714 assert(NumHighBits <= integerPartWidth && "Can not have more high bits to "
715 "fill than integerPartWidth");
716 const integerPart HighBitFill =
717 ~integerPart(0) << (integerPartWidth - NumHighBits);
718 if (~(Parts[PartCount - 1] | HighBitFill))
724 bool APFloat::isSignificandAllZeros() const {
725 // Test if the significand excluding the integral bit is all zeros. This
726 // allows us to test for binade boundaries.
727 const integerPart *Parts = significandParts();
728 const unsigned PartCount = partCount();
730 for (unsigned i = 0; i < PartCount - 1; i++)
734 const unsigned NumHighBits =
735 PartCount*integerPartWidth - semantics->precision + 1;
736 assert(NumHighBits <= integerPartWidth && "Can not have more high bits to "
737 "clear than integerPartWidth");
738 const integerPart HighBitMask = ~integerPart(0) >> NumHighBits;
740 if (Parts[PartCount - 1] & HighBitMask)
747 APFloat::isLargest() const {
748 // The largest number by magnitude in our format will be the floating point
749 // number with maximum exponent and with significand that is all ones.
750 return isFiniteNonZero() && exponent == semantics->maxExponent
751 && isSignificandAllOnes();
755 APFloat::bitwiseIsEqual(const APFloat &rhs) const {
758 if (semantics != rhs.semantics ||
759 category != rhs.category ||
762 if (category==fcZero || category==fcInfinity)
764 else if (isFiniteNonZero() && exponent!=rhs.exponent)
768 const integerPart* p=significandParts();
769 const integerPart* q=rhs.significandParts();
770 for (; i>0; i--, p++, q++) {
778 APFloat::APFloat(const fltSemantics &ourSemantics, integerPart value) {
779 initialize(&ourSemantics);
782 exponent = ourSemantics.precision - 1;
783 significandParts()[0] = value;
784 normalize(rmNearestTiesToEven, lfExactlyZero);
787 APFloat::APFloat(const fltSemantics &ourSemantics) {
788 initialize(&ourSemantics);
793 APFloat::APFloat(const fltSemantics &ourSemantics, uninitializedTag tag) {
794 // Allocates storage if necessary but does not initialize it.
795 initialize(&ourSemantics);
798 APFloat::APFloat(const fltSemantics &ourSemantics, StringRef text) {
799 initialize(&ourSemantics);
800 convertFromString(text, rmNearestTiesToEven);
803 APFloat::APFloat(const APFloat &rhs) {
804 initialize(rhs.semantics);
813 // Profile - This method 'profiles' an APFloat for use with FoldingSet.
814 void APFloat::Profile(FoldingSetNodeID& ID) const {
815 ID.Add(bitcastToAPInt());
819 APFloat::partCount() const
821 return partCountForBits(semantics->precision + 1);
825 APFloat::semanticsPrecision(const fltSemantics &semantics)
827 return semantics.precision;
831 APFloat::significandParts() const
833 return const_cast<APFloat *>(this)->significandParts();
837 APFloat::significandParts()
840 return significand.parts;
842 return &significand.part;
846 APFloat::zeroSignificand()
849 APInt::tcSet(significandParts(), 0, partCount());
852 /* Increment an fcNormal floating point number's significand. */
854 APFloat::incrementSignificand()
858 carry = APInt::tcIncrement(significandParts(), partCount());
860 /* Our callers should never cause us to overflow. */
865 /* Add the significand of the RHS. Returns the carry flag. */
867 APFloat::addSignificand(const APFloat &rhs)
871 parts = significandParts();
873 assert(semantics == rhs.semantics);
874 assert(exponent == rhs.exponent);
876 return APInt::tcAdd(parts, rhs.significandParts(), 0, partCount());
879 /* Subtract the significand of the RHS with a borrow flag. Returns
882 APFloat::subtractSignificand(const APFloat &rhs, integerPart borrow)
886 parts = significandParts();
888 assert(semantics == rhs.semantics);
889 assert(exponent == rhs.exponent);
891 return APInt::tcSubtract(parts, rhs.significandParts(), borrow,
895 /* Multiply the significand of the RHS. If ADDEND is non-NULL, add it
896 on to the full-precision result of the multiplication. Returns the
899 APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
901 unsigned int omsb; // One, not zero, based MSB.
902 unsigned int partsCount, newPartsCount, precision;
903 integerPart *lhsSignificand;
904 integerPart scratch[4];
905 integerPart *fullSignificand;
906 lostFraction lost_fraction;
909 assert(semantics == rhs.semantics);
911 precision = semantics->precision;
912 newPartsCount = partCountForBits(precision * 2);
914 if (newPartsCount > 4)
915 fullSignificand = new integerPart[newPartsCount];
917 fullSignificand = scratch;
919 lhsSignificand = significandParts();
920 partsCount = partCount();
922 APInt::tcFullMultiply(fullSignificand, lhsSignificand,
923 rhs.significandParts(), partsCount, partsCount);
925 lost_fraction = lfExactlyZero;
926 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
927 exponent += rhs.exponent;
929 // Assume the operands involved in the multiplication are single-precision
930 // FP, and the two multiplicants are:
931 // *this = a23 . a22 ... a0 * 2^e1
932 // rhs = b23 . b22 ... b0 * 2^e2
933 // the result of multiplication is:
934 // *this = c47 c46 . c45 ... c0 * 2^(e1+e2)
935 // Note that there are two significant bits at the left-hand side of the
936 // radix point. Move the radix point toward left by one bit, and adjust
937 // exponent accordingly.
941 // The intermediate result of the multiplication has "2 * precision"
942 // signicant bit; adjust the addend to be consistent with mul result.
944 Significand savedSignificand = significand;
945 const fltSemantics *savedSemantics = semantics;
946 fltSemantics extendedSemantics;
948 unsigned int extendedPrecision;
950 /* Normalize our MSB. */
951 extendedPrecision = 2 * precision;
952 if (omsb != extendedPrecision) {
953 assert(extendedPrecision > omsb);
954 APInt::tcShiftLeft(fullSignificand, newPartsCount,
955 extendedPrecision - omsb);
956 exponent -= extendedPrecision - omsb;
959 /* Create new semantics. */
960 extendedSemantics = *semantics;
961 extendedSemantics.precision = extendedPrecision;
963 if (newPartsCount == 1)
964 significand.part = fullSignificand[0];
966 significand.parts = fullSignificand;
967 semantics = &extendedSemantics;
969 APFloat extendedAddend(*addend);
970 status = extendedAddend.convert(extendedSemantics, rmTowardZero, &ignored);
971 assert(status == opOK);
973 lost_fraction = addOrSubtractSignificand(extendedAddend, false);
975 /* Restore our state. */
976 if (newPartsCount == 1)
977 fullSignificand[0] = significand.part;
978 significand = savedSignificand;
979 semantics = savedSemantics;
981 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
984 // Convert the result having "2 * precision" significant-bits back to the one
985 // having "precision" significant-bits. First, move the radix point from
986 // poision "2*precision - 1" to "precision - 1". The exponent need to be
987 // adjusted by "2*precision - 1" - "precision - 1" = "precision".
988 exponent -= precision;
990 // In case MSB resides at the left-hand side of radix point, shift the
991 // mantissa right by some amount to make sure the MSB reside right before
992 // the radix point (i.e. "MSB . rest-significant-bits").
994 // Note that the result is not normalized when "omsb < precision". So, the
995 // caller needs to call APFloat::normalize() if normalized value is expected.
996 if (omsb > precision) {
997 unsigned int bits, significantParts;
1000 bits = omsb - precision;
1001 significantParts = partCountForBits(omsb);
1002 lf = shiftRight(fullSignificand, significantParts, bits);
1003 lost_fraction = combineLostFractions(lf, lost_fraction);
1007 APInt::tcAssign(lhsSignificand, fullSignificand, partsCount);
1009 if (newPartsCount > 4)
1010 delete [] fullSignificand;
1012 return lost_fraction;
1015 /* Multiply the significands of LHS and RHS to DST. */
1017 APFloat::divideSignificand(const APFloat &rhs)
1019 unsigned int bit, i, partsCount;
1020 const integerPart *rhsSignificand;
1021 integerPart *lhsSignificand, *dividend, *divisor;
1022 integerPart scratch[4];
1023 lostFraction lost_fraction;
1025 assert(semantics == rhs.semantics);
1027 lhsSignificand = significandParts();
1028 rhsSignificand = rhs.significandParts();
1029 partsCount = partCount();
1032 dividend = new integerPart[partsCount * 2];
1036 divisor = dividend + partsCount;
1038 /* Copy the dividend and divisor as they will be modified in-place. */
1039 for (i = 0; i < partsCount; i++) {
1040 dividend[i] = lhsSignificand[i];
1041 divisor[i] = rhsSignificand[i];
1042 lhsSignificand[i] = 0;
1045 exponent -= rhs.exponent;
1047 unsigned int precision = semantics->precision;
1049 /* Normalize the divisor. */
1050 bit = precision - APInt::tcMSB(divisor, partsCount) - 1;
1053 APInt::tcShiftLeft(divisor, partsCount, bit);
1056 /* Normalize the dividend. */
1057 bit = precision - APInt::tcMSB(dividend, partsCount) - 1;
1060 APInt::tcShiftLeft(dividend, partsCount, bit);
1063 /* Ensure the dividend >= divisor initially for the loop below.
1064 Incidentally, this means that the division loop below is
1065 guaranteed to set the integer bit to one. */
1066 if (APInt::tcCompare(dividend, divisor, partsCount) < 0) {
1068 APInt::tcShiftLeft(dividend, partsCount, 1);
1069 assert(APInt::tcCompare(dividend, divisor, partsCount) >= 0);
1072 /* Long division. */
1073 for (bit = precision; bit; bit -= 1) {
1074 if (APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
1075 APInt::tcSubtract(dividend, divisor, 0, partsCount);
1076 APInt::tcSetBit(lhsSignificand, bit - 1);
1079 APInt::tcShiftLeft(dividend, partsCount, 1);
1082 /* Figure out the lost fraction. */
1083 int cmp = APInt::tcCompare(dividend, divisor, partsCount);
1086 lost_fraction = lfMoreThanHalf;
1088 lost_fraction = lfExactlyHalf;
1089 else if (APInt::tcIsZero(dividend, partsCount))
1090 lost_fraction = lfExactlyZero;
1092 lost_fraction = lfLessThanHalf;
1097 return lost_fraction;
1101 APFloat::significandMSB() const
1103 return APInt::tcMSB(significandParts(), partCount());
1107 APFloat::significandLSB() const
1109 return APInt::tcLSB(significandParts(), partCount());
1112 /* Note that a zero result is NOT normalized to fcZero. */
1114 APFloat::shiftSignificandRight(unsigned int bits)
1116 /* Our exponent should not overflow. */
1117 assert((ExponentType) (exponent + bits) >= exponent);
1121 return shiftRight(significandParts(), partCount(), bits);
1124 /* Shift the significand left BITS bits, subtract BITS from its exponent. */
1126 APFloat::shiftSignificandLeft(unsigned int bits)
1128 assert(bits < semantics->precision);
1131 unsigned int partsCount = partCount();
1133 APInt::tcShiftLeft(significandParts(), partsCount, bits);
1136 assert(!APInt::tcIsZero(significandParts(), partsCount));
1141 APFloat::compareAbsoluteValue(const APFloat &rhs) const
1145 assert(semantics == rhs.semantics);
1146 assert(isFiniteNonZero());
1147 assert(rhs.isFiniteNonZero());
1149 compare = exponent - rhs.exponent;
1151 /* If exponents are equal, do an unsigned bignum comparison of the
1154 compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
1158 return cmpGreaterThan;
1159 else if (compare < 0)
1165 /* Handle overflow. Sign is preserved. We either become infinity or
1166 the largest finite number. */
1168 APFloat::handleOverflow(roundingMode rounding_mode)
1171 if (rounding_mode == rmNearestTiesToEven ||
1172 rounding_mode == rmNearestTiesToAway ||
1173 (rounding_mode == rmTowardPositive && !sign) ||
1174 (rounding_mode == rmTowardNegative && sign)) {
1175 category = fcInfinity;
1176 return (opStatus) (opOverflow | opInexact);
1179 /* Otherwise we become the largest finite number. */
1180 category = fcNormal;
1181 exponent = semantics->maxExponent;
1182 APInt::tcSetLeastSignificantBits(significandParts(), partCount(),
1183 semantics->precision);
1188 /* Returns TRUE if, when truncating the current number, with BIT the
1189 new LSB, with the given lost fraction and rounding mode, the result
1190 would need to be rounded away from zero (i.e., by increasing the
1191 signficand). This routine must work for fcZero of both signs, and
1192 fcNormal numbers. */
1194 APFloat::roundAwayFromZero(roundingMode rounding_mode,
1195 lostFraction lost_fraction,
1196 unsigned int bit) const
1198 /* NaNs and infinities should not have lost fractions. */
1199 assert(isFiniteNonZero() || category == fcZero);
1201 /* Current callers never pass this so we don't handle it. */
1202 assert(lost_fraction != lfExactlyZero);
1204 switch (rounding_mode) {
1205 case rmNearestTiesToAway:
1206 return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf;
1208 case rmNearestTiesToEven:
1209 if (lost_fraction == lfMoreThanHalf)
1212 /* Our zeroes don't have a significand to test. */
1213 if (lost_fraction == lfExactlyHalf && category != fcZero)
1214 return APInt::tcExtractBit(significandParts(), bit);
1221 case rmTowardPositive:
1222 return sign == false;
1224 case rmTowardNegative:
1225 return sign == true;
1227 llvm_unreachable("Invalid rounding mode found");
1231 APFloat::normalize(roundingMode rounding_mode,
1232 lostFraction lost_fraction)
1234 unsigned int omsb; /* One, not zero, based MSB. */
1237 if (!isFiniteNonZero())
1240 /* Before rounding normalize the exponent of fcNormal numbers. */
1241 omsb = significandMSB() + 1;
1244 /* OMSB is numbered from 1. We want to place it in the integer
1245 bit numbered PRECISION if possible, with a compensating change in
1247 exponentChange = omsb - semantics->precision;
1249 /* If the resulting exponent is too high, overflow according to
1250 the rounding mode. */
1251 if (exponent + exponentChange > semantics->maxExponent)
1252 return handleOverflow(rounding_mode);
1254 /* Subnormal numbers have exponent minExponent, and their MSB
1255 is forced based on that. */
1256 if (exponent + exponentChange < semantics->minExponent)
1257 exponentChange = semantics->minExponent - exponent;
1259 /* Shifting left is easy as we don't lose precision. */
1260 if (exponentChange < 0) {
1261 assert(lost_fraction == lfExactlyZero);
1263 shiftSignificandLeft(-exponentChange);
1268 if (exponentChange > 0) {
1271 /* Shift right and capture any new lost fraction. */
1272 lf = shiftSignificandRight(exponentChange);
1274 lost_fraction = combineLostFractions(lf, lost_fraction);
1276 /* Keep OMSB up-to-date. */
1277 if (omsb > (unsigned) exponentChange)
1278 omsb -= exponentChange;
1284 /* Now round the number according to rounding_mode given the lost
1287 /* As specified in IEEE 754, since we do not trap we do not report
1288 underflow for exact results. */
1289 if (lost_fraction == lfExactlyZero) {
1290 /* Canonicalize zeroes. */
1297 /* Increment the significand if we're rounding away from zero. */
1298 if (roundAwayFromZero(rounding_mode, lost_fraction, 0)) {
1300 exponent = semantics->minExponent;
1302 incrementSignificand();
1303 omsb = significandMSB() + 1;
1305 /* Did the significand increment overflow? */
1306 if (omsb == (unsigned) semantics->precision + 1) {
1307 /* Renormalize by incrementing the exponent and shifting our
1308 significand right one. However if we already have the
1309 maximum exponent we overflow to infinity. */
1310 if (exponent == semantics->maxExponent) {
1311 category = fcInfinity;
1313 return (opStatus) (opOverflow | opInexact);
1316 shiftSignificandRight(1);
1322 /* The normal case - we were and are not denormal, and any
1323 significand increment above didn't overflow. */
1324 if (omsb == semantics->precision)
1327 /* We have a non-zero denormal. */
1328 assert(omsb < semantics->precision);
1330 /* Canonicalize zeroes. */
1334 /* The fcZero case is a denormal that underflowed to zero. */
1335 return (opStatus) (opUnderflow | opInexact);
1339 APFloat::addOrSubtractSpecials(const APFloat &rhs, bool subtract)
1341 switch (PackCategoriesIntoKey(category, rhs.category)) {
1343 llvm_unreachable(0);
1345 case PackCategoriesIntoKey(fcNaN, fcZero):
1346 case PackCategoriesIntoKey(fcNaN, fcNormal):
1347 case PackCategoriesIntoKey(fcNaN, fcInfinity):
1348 case PackCategoriesIntoKey(fcNaN, fcNaN):
1349 case PackCategoriesIntoKey(fcNormal, fcZero):
1350 case PackCategoriesIntoKey(fcInfinity, fcNormal):
1351 case PackCategoriesIntoKey(fcInfinity, fcZero):
1354 case PackCategoriesIntoKey(fcZero, fcNaN):
1355 case PackCategoriesIntoKey(fcNormal, fcNaN):
1356 case PackCategoriesIntoKey(fcInfinity, fcNaN):
1358 copySignificand(rhs);
1361 case PackCategoriesIntoKey(fcNormal, fcInfinity):
1362 case PackCategoriesIntoKey(fcZero, fcInfinity):
1363 category = fcInfinity;
1364 sign = rhs.sign ^ subtract;
1367 case PackCategoriesIntoKey(fcZero, fcNormal):
1369 sign = rhs.sign ^ subtract;
1372 case PackCategoriesIntoKey(fcZero, fcZero):
1373 /* Sign depends on rounding mode; handled by caller. */
1376 case PackCategoriesIntoKey(fcInfinity, fcInfinity):
1377 /* Differently signed infinities can only be validly
1379 if (((sign ^ rhs.sign)!=0) != subtract) {
1386 case PackCategoriesIntoKey(fcNormal, fcNormal):
1391 /* Add or subtract two normal numbers. */
1393 APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
1396 lostFraction lost_fraction;
1399 /* Determine if the operation on the absolute values is effectively
1400 an addition or subtraction. */
1401 subtract ^= (sign ^ rhs.sign) ? true : false;
1403 /* Are we bigger exponent-wise than the RHS? */
1404 bits = exponent - rhs.exponent;
1406 /* Subtraction is more subtle than one might naively expect. */
1408 APFloat temp_rhs(rhs);
1412 reverse = compareAbsoluteValue(temp_rhs) == cmpLessThan;
1413 lost_fraction = lfExactlyZero;
1414 } else if (bits > 0) {
1415 lost_fraction = temp_rhs.shiftSignificandRight(bits - 1);
1416 shiftSignificandLeft(1);
1419 lost_fraction = shiftSignificandRight(-bits - 1);
1420 temp_rhs.shiftSignificandLeft(1);
1425 carry = temp_rhs.subtractSignificand
1426 (*this, lost_fraction != lfExactlyZero);
1427 copySignificand(temp_rhs);
1430 carry = subtractSignificand
1431 (temp_rhs, lost_fraction != lfExactlyZero);
1434 /* Invert the lost fraction - it was on the RHS and
1436 if (lost_fraction == lfLessThanHalf)
1437 lost_fraction = lfMoreThanHalf;
1438 else if (lost_fraction == lfMoreThanHalf)
1439 lost_fraction = lfLessThanHalf;
1441 /* The code above is intended to ensure that no borrow is
1447 APFloat temp_rhs(rhs);
1449 lost_fraction = temp_rhs.shiftSignificandRight(bits);
1450 carry = addSignificand(temp_rhs);
1452 lost_fraction = shiftSignificandRight(-bits);
1453 carry = addSignificand(rhs);
1456 /* We have a guard bit; generating a carry cannot happen. */
1461 return lost_fraction;
1465 APFloat::multiplySpecials(const APFloat &rhs)
1467 switch (PackCategoriesIntoKey(category, rhs.category)) {
1469 llvm_unreachable(0);
1471 case PackCategoriesIntoKey(fcNaN, fcZero):
1472 case PackCategoriesIntoKey(fcNaN, fcNormal):
1473 case PackCategoriesIntoKey(fcNaN, fcInfinity):
1474 case PackCategoriesIntoKey(fcNaN, fcNaN):
1477 case PackCategoriesIntoKey(fcZero, fcNaN):
1478 case PackCategoriesIntoKey(fcNormal, fcNaN):
1479 case PackCategoriesIntoKey(fcInfinity, fcNaN):
1481 copySignificand(rhs);
1484 case PackCategoriesIntoKey(fcNormal, fcInfinity):
1485 case PackCategoriesIntoKey(fcInfinity, fcNormal):
1486 case PackCategoriesIntoKey(fcInfinity, fcInfinity):
1487 category = fcInfinity;
1490 case PackCategoriesIntoKey(fcZero, fcNormal):
1491 case PackCategoriesIntoKey(fcNormal, fcZero):
1492 case PackCategoriesIntoKey(fcZero, fcZero):
1496 case PackCategoriesIntoKey(fcZero, fcInfinity):
1497 case PackCategoriesIntoKey(fcInfinity, fcZero):
1501 case PackCategoriesIntoKey(fcNormal, fcNormal):
1507 APFloat::divideSpecials(const APFloat &rhs)
1509 switch (PackCategoriesIntoKey(category, rhs.category)) {
1511 llvm_unreachable(0);
1513 case PackCategoriesIntoKey(fcNaN, fcZero):
1514 case PackCategoriesIntoKey(fcNaN, fcNormal):
1515 case PackCategoriesIntoKey(fcNaN, fcInfinity):
1516 case PackCategoriesIntoKey(fcNaN, fcNaN):
1517 case PackCategoriesIntoKey(fcInfinity, fcZero):
1518 case PackCategoriesIntoKey(fcInfinity, fcNormal):
1519 case PackCategoriesIntoKey(fcZero, fcInfinity):
1520 case PackCategoriesIntoKey(fcZero, fcNormal):
1523 case PackCategoriesIntoKey(fcZero, fcNaN):
1524 case PackCategoriesIntoKey(fcNormal, fcNaN):
1525 case PackCategoriesIntoKey(fcInfinity, fcNaN):
1527 copySignificand(rhs);
1530 case PackCategoriesIntoKey(fcNormal, fcInfinity):
1534 case PackCategoriesIntoKey(fcNormal, fcZero):
1535 category = fcInfinity;
1538 case PackCategoriesIntoKey(fcInfinity, fcInfinity):
1539 case PackCategoriesIntoKey(fcZero, fcZero):
1543 case PackCategoriesIntoKey(fcNormal, fcNormal):
1549 APFloat::modSpecials(const APFloat &rhs)
1551 switch (PackCategoriesIntoKey(category, rhs.category)) {
1553 llvm_unreachable(0);
1555 case PackCategoriesIntoKey(fcNaN, fcZero):
1556 case PackCategoriesIntoKey(fcNaN, fcNormal):
1557 case PackCategoriesIntoKey(fcNaN, fcInfinity):
1558 case PackCategoriesIntoKey(fcNaN, fcNaN):
1559 case PackCategoriesIntoKey(fcZero, fcInfinity):
1560 case PackCategoriesIntoKey(fcZero, fcNormal):
1561 case PackCategoriesIntoKey(fcNormal, fcInfinity):
1564 case PackCategoriesIntoKey(fcZero, fcNaN):
1565 case PackCategoriesIntoKey(fcNormal, fcNaN):
1566 case PackCategoriesIntoKey(fcInfinity, fcNaN):
1568 copySignificand(rhs);
1571 case PackCategoriesIntoKey(fcNormal, fcZero):
1572 case PackCategoriesIntoKey(fcInfinity, fcZero):
1573 case PackCategoriesIntoKey(fcInfinity, fcNormal):
1574 case PackCategoriesIntoKey(fcInfinity, fcInfinity):
1575 case PackCategoriesIntoKey(fcZero, fcZero):
1579 case PackCategoriesIntoKey(fcNormal, fcNormal):
1586 APFloat::changeSign()
1588 /* Look mummy, this one's easy. */
1593 APFloat::clearSign()
1595 /* So is this one. */
1600 APFloat::copySign(const APFloat &rhs)
1606 /* Normalized addition or subtraction. */
1608 APFloat::addOrSubtract(const APFloat &rhs, roundingMode rounding_mode,
1613 fs = addOrSubtractSpecials(rhs, subtract);
1615 /* This return code means it was not a simple case. */
1616 if (fs == opDivByZero) {
1617 lostFraction lost_fraction;
1619 lost_fraction = addOrSubtractSignificand(rhs, subtract);
1620 fs = normalize(rounding_mode, lost_fraction);
1622 /* Can only be zero if we lost no fraction. */
1623 assert(category != fcZero || lost_fraction == lfExactlyZero);
1626 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1627 positive zero unless rounding to minus infinity, except that
1628 adding two like-signed zeroes gives that zero. */
1629 if (category == fcZero) {
1630 if (rhs.category != fcZero || (sign == rhs.sign) == subtract)
1631 sign = (rounding_mode == rmTowardNegative);
1637 /* Normalized addition. */
1639 APFloat::add(const APFloat &rhs, roundingMode rounding_mode)
1641 return addOrSubtract(rhs, rounding_mode, false);
1644 /* Normalized subtraction. */
1646 APFloat::subtract(const APFloat &rhs, roundingMode rounding_mode)
1648 return addOrSubtract(rhs, rounding_mode, true);
1651 /* Normalized multiply. */
1653 APFloat::multiply(const APFloat &rhs, roundingMode rounding_mode)
1658 fs = multiplySpecials(rhs);
1660 if (isFiniteNonZero()) {
1661 lostFraction lost_fraction = multiplySignificand(rhs, 0);
1662 fs = normalize(rounding_mode, lost_fraction);
1663 if (lost_fraction != lfExactlyZero)
1664 fs = (opStatus) (fs | opInexact);
1670 /* Normalized divide. */
1672 APFloat::divide(const APFloat &rhs, roundingMode rounding_mode)
1677 fs = divideSpecials(rhs);
1679 if (isFiniteNonZero()) {
1680 lostFraction lost_fraction = divideSignificand(rhs);
1681 fs = normalize(rounding_mode, lost_fraction);
1682 if (lost_fraction != lfExactlyZero)
1683 fs = (opStatus) (fs | opInexact);
1689 /* Normalized remainder. This is not currently correct in all cases. */
1691 APFloat::remainder(const APFloat &rhs)
1695 unsigned int origSign = sign;
1697 fs = V.divide(rhs, rmNearestTiesToEven);
1698 if (fs == opDivByZero)
1701 int parts = partCount();
1702 integerPart *x = new integerPart[parts];
1704 fs = V.convertToInteger(x, parts * integerPartWidth, true,
1705 rmNearestTiesToEven, &ignored);
1706 if (fs==opInvalidOp)
1709 fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
1710 rmNearestTiesToEven);
1711 assert(fs==opOK); // should always work
1713 fs = V.multiply(rhs, rmNearestTiesToEven);
1714 assert(fs==opOK || fs==opInexact); // should not overflow or underflow
1716 fs = subtract(V, rmNearestTiesToEven);
1717 assert(fs==opOK || fs==opInexact); // likewise
1720 sign = origSign; // IEEE754 requires this
1725 /* Normalized llvm frem (C fmod).
1726 This is not currently correct in all cases. */
1728 APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
1731 fs = modSpecials(rhs);
1733 if (isFiniteNonZero() && rhs.isFiniteNonZero()) {
1735 unsigned int origSign = sign;
1737 fs = V.divide(rhs, rmNearestTiesToEven);
1738 if (fs == opDivByZero)
1741 int parts = partCount();
1742 integerPart *x = new integerPart[parts];
1744 fs = V.convertToInteger(x, parts * integerPartWidth, true,
1745 rmTowardZero, &ignored);
1746 if (fs==opInvalidOp)
1749 fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
1750 rmNearestTiesToEven);
1751 assert(fs==opOK); // should always work
1753 fs = V.multiply(rhs, rounding_mode);
1754 assert(fs==opOK || fs==opInexact); // should not overflow or underflow
1756 fs = subtract(V, rounding_mode);
1757 assert(fs==opOK || fs==opInexact); // likewise
1760 sign = origSign; // IEEE754 requires this
1766 /* Normalized fused-multiply-add. */
1768 APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
1769 const APFloat &addend,
1770 roundingMode rounding_mode)
1774 /* Post-multiplication sign, before addition. */
1775 sign ^= multiplicand.sign;
1777 /* If and only if all arguments are normal do we need to do an
1778 extended-precision calculation. */
1779 if (isFiniteNonZero() &&
1780 multiplicand.isFiniteNonZero() &&
1781 addend.isFiniteNonZero()) {
1782 lostFraction lost_fraction;
1784 lost_fraction = multiplySignificand(multiplicand, &addend);
1785 fs = normalize(rounding_mode, lost_fraction);
1786 if (lost_fraction != lfExactlyZero)
1787 fs = (opStatus) (fs | opInexact);
1789 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1790 positive zero unless rounding to minus infinity, except that
1791 adding two like-signed zeroes gives that zero. */
1792 if (category == fcZero && sign != addend.sign)
1793 sign = (rounding_mode == rmTowardNegative);
1795 fs = multiplySpecials(multiplicand);
1797 /* FS can only be opOK or opInvalidOp. There is no more work
1798 to do in the latter case. The IEEE-754R standard says it is
1799 implementation-defined in this case whether, if ADDEND is a
1800 quiet NaN, we raise invalid op; this implementation does so.
1802 If we need to do the addition we can do so with normal
1805 fs = addOrSubtract(addend, rounding_mode, false);
1811 /* Rounding-mode corrrect round to integral value. */
1812 APFloat::opStatus APFloat::roundToIntegral(roundingMode rounding_mode) {
1815 // If the exponent is large enough, we know that this value is already
1816 // integral, and the arithmetic below would potentially cause it to saturate
1817 // to +/-Inf. Bail out early instead.
1818 if (isFiniteNonZero() && exponent+1 >= (int)semanticsPrecision(*semantics))
1821 // The algorithm here is quite simple: we add 2^(p-1), where p is the
1822 // precision of our format, and then subtract it back off again. The choice
1823 // of rounding modes for the addition/subtraction determines the rounding mode
1824 // for our integral rounding as well.
1825 // NOTE: When the input value is negative, we do subtraction followed by
1826 // addition instead.
1827 APInt IntegerConstant(NextPowerOf2(semanticsPrecision(*semantics)), 1);
1828 IntegerConstant <<= semanticsPrecision(*semantics)-1;
1829 APFloat MagicConstant(*semantics);
1830 fs = MagicConstant.convertFromAPInt(IntegerConstant, false,
1831 rmNearestTiesToEven);
1832 MagicConstant.copySign(*this);
1837 // Preserve the input sign so that we can handle 0.0/-0.0 cases correctly.
1838 bool inputSign = isNegative();
1840 fs = add(MagicConstant, rounding_mode);
1841 if (fs != opOK && fs != opInexact)
1844 fs = subtract(MagicConstant, rounding_mode);
1846 // Restore the input sign.
1847 if (inputSign != isNegative())
1854 /* Comparison requires normalized numbers. */
1856 APFloat::compare(const APFloat &rhs) const
1860 assert(semantics == rhs.semantics);
1862 switch (PackCategoriesIntoKey(category, rhs.category)) {
1864 llvm_unreachable(0);
1866 case PackCategoriesIntoKey(fcNaN, fcZero):
1867 case PackCategoriesIntoKey(fcNaN, fcNormal):
1868 case PackCategoriesIntoKey(fcNaN, fcInfinity):
1869 case PackCategoriesIntoKey(fcNaN, fcNaN):
1870 case PackCategoriesIntoKey(fcZero, fcNaN):
1871 case PackCategoriesIntoKey(fcNormal, fcNaN):
1872 case PackCategoriesIntoKey(fcInfinity, fcNaN):
1873 return cmpUnordered;
1875 case PackCategoriesIntoKey(fcInfinity, fcNormal):
1876 case PackCategoriesIntoKey(fcInfinity, fcZero):
1877 case PackCategoriesIntoKey(fcNormal, fcZero):
1881 return cmpGreaterThan;
1883 case PackCategoriesIntoKey(fcNormal, fcInfinity):
1884 case PackCategoriesIntoKey(fcZero, fcInfinity):
1885 case PackCategoriesIntoKey(fcZero, fcNormal):
1887 return cmpGreaterThan;
1891 case PackCategoriesIntoKey(fcInfinity, fcInfinity):
1892 if (sign == rhs.sign)
1897 return cmpGreaterThan;
1899 case PackCategoriesIntoKey(fcZero, fcZero):
1902 case PackCategoriesIntoKey(fcNormal, fcNormal):
1906 /* Two normal numbers. Do they have the same sign? */
1907 if (sign != rhs.sign) {
1909 result = cmpLessThan;
1911 result = cmpGreaterThan;
1913 /* Compare absolute values; invert result if negative. */
1914 result = compareAbsoluteValue(rhs);
1917 if (result == cmpLessThan)
1918 result = cmpGreaterThan;
1919 else if (result == cmpGreaterThan)
1920 result = cmpLessThan;
1927 /// APFloat::convert - convert a value of one floating point type to another.
1928 /// The return value corresponds to the IEEE754 exceptions. *losesInfo
1929 /// records whether the transformation lost information, i.e. whether
1930 /// converting the result back to the original type will produce the
1931 /// original value (this is almost the same as return value==fsOK, but there
1932 /// are edge cases where this is not so).
1935 APFloat::convert(const fltSemantics &toSemantics,
1936 roundingMode rounding_mode, bool *losesInfo)
1938 lostFraction lostFraction;
1939 unsigned int newPartCount, oldPartCount;
1942 const fltSemantics &fromSemantics = *semantics;
1944 lostFraction = lfExactlyZero;
1945 newPartCount = partCountForBits(toSemantics.precision + 1);
1946 oldPartCount = partCount();
1947 shift = toSemantics.precision - fromSemantics.precision;
1949 bool X86SpecialNan = false;
1950 if (&fromSemantics == &APFloat::x87DoubleExtended &&
1951 &toSemantics != &APFloat::x87DoubleExtended && category == fcNaN &&
1952 (!(*significandParts() & 0x8000000000000000ULL) ||
1953 !(*significandParts() & 0x4000000000000000ULL))) {
1954 // x86 has some unusual NaNs which cannot be represented in any other
1955 // format; note them here.
1956 X86SpecialNan = true;
1959 // If this is a truncation, perform the shift before we narrow the storage.
1960 if (shift < 0 && (isFiniteNonZero() || category==fcNaN))
1961 lostFraction = shiftRight(significandParts(), oldPartCount, -shift);
1963 // Fix the storage so it can hold to new value.
1964 if (newPartCount > oldPartCount) {
1965 // The new type requires more storage; make it available.
1966 integerPart *newParts;
1967 newParts = new integerPart[newPartCount];
1968 APInt::tcSet(newParts, 0, newPartCount);
1969 if (isFiniteNonZero() || category==fcNaN)
1970 APInt::tcAssign(newParts, significandParts(), oldPartCount);
1972 significand.parts = newParts;
1973 } else if (newPartCount == 1 && oldPartCount != 1) {
1974 // Switch to built-in storage for a single part.
1975 integerPart newPart = 0;
1976 if (isFiniteNonZero() || category==fcNaN)
1977 newPart = significandParts()[0];
1979 significand.part = newPart;
1982 // Now that we have the right storage, switch the semantics.
1983 semantics = &toSemantics;
1985 // If this is an extension, perform the shift now that the storage is
1987 if (shift > 0 && (isFiniteNonZero() || category==fcNaN))
1988 APInt::tcShiftLeft(significandParts(), newPartCount, shift);
1990 if (isFiniteNonZero()) {
1991 fs = normalize(rounding_mode, lostFraction);
1992 *losesInfo = (fs != opOK);
1993 } else if (category == fcNaN) {
1994 *losesInfo = lostFraction != lfExactlyZero || X86SpecialNan;
1996 // For x87 extended precision, we want to make a NaN, not a special NaN if
1997 // the input wasn't special either.
1998 if (!X86SpecialNan && semantics == &APFloat::x87DoubleExtended)
1999 APInt::tcSetBit(significandParts(), semantics->precision - 1);
2001 // gcc forces the Quiet bit on, which means (float)(double)(float_sNan)
2002 // does not give you back the same bits. This is dubious, and we
2003 // don't currently do it. You're really supposed to get
2004 // an invalid operation signal at runtime, but nobody does that.
2014 /* Convert a floating point number to an integer according to the
2015 rounding mode. If the rounded integer value is out of range this
2016 returns an invalid operation exception and the contents of the
2017 destination parts are unspecified. If the rounded value is in
2018 range but the floating point number is not the exact integer, the C
2019 standard doesn't require an inexact exception to be raised. IEEE
2020 854 does require it so we do that.
2022 Note that for conversions to integer type the C standard requires
2023 round-to-zero to always be used. */
2025 APFloat::convertToSignExtendedInteger(integerPart *parts, unsigned int width,
2027 roundingMode rounding_mode,
2028 bool *isExact) const
2030 lostFraction lost_fraction;
2031 const integerPart *src;
2032 unsigned int dstPartsCount, truncatedBits;
2036 /* Handle the three special cases first. */
2037 if (category == fcInfinity || category == fcNaN)
2040 dstPartsCount = partCountForBits(width);
2042 if (category == fcZero) {
2043 APInt::tcSet(parts, 0, dstPartsCount);
2044 // Negative zero can't be represented as an int.
2049 src = significandParts();
2051 /* Step 1: place our absolute value, with any fraction truncated, in
2054 /* Our absolute value is less than one; truncate everything. */
2055 APInt::tcSet(parts, 0, dstPartsCount);
2056 /* For exponent -1 the integer bit represents .5, look at that.
2057 For smaller exponents leftmost truncated bit is 0. */
2058 truncatedBits = semantics->precision -1U - exponent;
2060 /* We want the most significant (exponent + 1) bits; the rest are
2062 unsigned int bits = exponent + 1U;
2064 /* Hopelessly large in magnitude? */
2068 if (bits < semantics->precision) {
2069 /* We truncate (semantics->precision - bits) bits. */
2070 truncatedBits = semantics->precision - bits;
2071 APInt::tcExtract(parts, dstPartsCount, src, bits, truncatedBits);
2073 /* We want at least as many bits as are available. */
2074 APInt::tcExtract(parts, dstPartsCount, src, semantics->precision, 0);
2075 APInt::tcShiftLeft(parts, dstPartsCount, bits - semantics->precision);
2080 /* Step 2: work out any lost fraction, and increment the absolute
2081 value if we would round away from zero. */
2082 if (truncatedBits) {
2083 lost_fraction = lostFractionThroughTruncation(src, partCount(),
2085 if (lost_fraction != lfExactlyZero &&
2086 roundAwayFromZero(rounding_mode, lost_fraction, truncatedBits)) {
2087 if (APInt::tcIncrement(parts, dstPartsCount))
2088 return opInvalidOp; /* Overflow. */
2091 lost_fraction = lfExactlyZero;
2094 /* Step 3: check if we fit in the destination. */
2095 unsigned int omsb = APInt::tcMSB(parts, dstPartsCount) + 1;
2099 /* Negative numbers cannot be represented as unsigned. */
2103 /* It takes omsb bits to represent the unsigned integer value.
2104 We lose a bit for the sign, but care is needed as the
2105 maximally negative integer is a special case. */
2106 if (omsb == width && APInt::tcLSB(parts, dstPartsCount) + 1 != omsb)
2109 /* This case can happen because of rounding. */
2114 APInt::tcNegate (parts, dstPartsCount);
2116 if (omsb >= width + !isSigned)
2120 if (lost_fraction == lfExactlyZero) {
2127 /* Same as convertToSignExtendedInteger, except we provide
2128 deterministic values in case of an invalid operation exception,
2129 namely zero for NaNs and the minimal or maximal value respectively
2130 for underflow or overflow.
2131 The *isExact output tells whether the result is exact, in the sense
2132 that converting it back to the original floating point type produces
2133 the original value. This is almost equivalent to result==opOK,
2134 except for negative zeroes.
2137 APFloat::convertToInteger(integerPart *parts, unsigned int width,
2139 roundingMode rounding_mode, bool *isExact) const
2143 fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode,
2146 if (fs == opInvalidOp) {
2147 unsigned int bits, dstPartsCount;
2149 dstPartsCount = partCountForBits(width);
2151 if (category == fcNaN)
2156 bits = width - isSigned;
2158 APInt::tcSetLeastSignificantBits(parts, dstPartsCount, bits);
2159 if (sign && isSigned)
2160 APInt::tcShiftLeft(parts, dstPartsCount, width - 1);
2166 /* Same as convertToInteger(integerPart*, ...), except the result is returned in
2167 an APSInt, whose initial bit-width and signed-ness are used to determine the
2168 precision of the conversion.
2171 APFloat::convertToInteger(APSInt &result,
2172 roundingMode rounding_mode, bool *isExact) const
2174 unsigned bitWidth = result.getBitWidth();
2175 SmallVector<uint64_t, 4> parts(result.getNumWords());
2176 opStatus status = convertToInteger(
2177 parts.data(), bitWidth, result.isSigned(), rounding_mode, isExact);
2178 // Keeps the original signed-ness.
2179 result = APInt(bitWidth, parts);
2183 /* Convert an unsigned integer SRC to a floating point number,
2184 rounding according to ROUNDING_MODE. The sign of the floating
2185 point number is not modified. */
2187 APFloat::convertFromUnsignedParts(const integerPart *src,
2188 unsigned int srcCount,
2189 roundingMode rounding_mode)
2191 unsigned int omsb, precision, dstCount;
2193 lostFraction lost_fraction;
2195 category = fcNormal;
2196 omsb = APInt::tcMSB(src, srcCount) + 1;
2197 dst = significandParts();
2198 dstCount = partCount();
2199 precision = semantics->precision;
2201 /* We want the most significant PRECISION bits of SRC. There may not
2202 be that many; extract what we can. */
2203 if (precision <= omsb) {
2204 exponent = omsb - 1;
2205 lost_fraction = lostFractionThroughTruncation(src, srcCount,
2207 APInt::tcExtract(dst, dstCount, src, precision, omsb - precision);
2209 exponent = precision - 1;
2210 lost_fraction = lfExactlyZero;
2211 APInt::tcExtract(dst, dstCount, src, omsb, 0);
2214 return normalize(rounding_mode, lost_fraction);
2218 APFloat::convertFromAPInt(const APInt &Val,
2220 roundingMode rounding_mode)
2222 unsigned int partCount = Val.getNumWords();
2226 if (isSigned && api.isNegative()) {
2231 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
2234 /* Convert a two's complement integer SRC to a floating point number,
2235 rounding according to ROUNDING_MODE. ISSIGNED is true if the
2236 integer is signed, in which case it must be sign-extended. */
2238 APFloat::convertFromSignExtendedInteger(const integerPart *src,
2239 unsigned int srcCount,
2241 roundingMode rounding_mode)
2246 APInt::tcExtractBit(src, srcCount * integerPartWidth - 1)) {
2249 /* If we're signed and negative negate a copy. */
2251 copy = new integerPart[srcCount];
2252 APInt::tcAssign(copy, src, srcCount);
2253 APInt::tcNegate(copy, srcCount);
2254 status = convertFromUnsignedParts(copy, srcCount, rounding_mode);
2258 status = convertFromUnsignedParts(src, srcCount, rounding_mode);
2264 /* FIXME: should this just take a const APInt reference? */
2266 APFloat::convertFromZeroExtendedInteger(const integerPart *parts,
2267 unsigned int width, bool isSigned,
2268 roundingMode rounding_mode)
2270 unsigned int partCount = partCountForBits(width);
2271 APInt api = APInt(width, makeArrayRef(parts, partCount));
2274 if (isSigned && APInt::tcExtractBit(parts, width - 1)) {
2279 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
2283 APFloat::convertFromHexadecimalString(StringRef s, roundingMode rounding_mode)
2285 lostFraction lost_fraction = lfExactlyZero;
2286 integerPart *significand;
2287 unsigned int bitPos, partsCount;
2288 StringRef::iterator dot, firstSignificantDigit;
2292 category = fcNormal;
2294 significand = significandParts();
2295 partsCount = partCount();
2296 bitPos = partsCount * integerPartWidth;
2298 /* Skip leading zeroes and any (hexa)decimal point. */
2299 StringRef::iterator begin = s.begin();
2300 StringRef::iterator end = s.end();
2301 StringRef::iterator p = skipLeadingZeroesAndAnyDot(begin, end, &dot);
2302 firstSignificantDigit = p;
2305 integerPart hex_value;
2308 assert(dot == end && "String contains multiple dots");
2315 hex_value = hexDigitValue(*p);
2316 if (hex_value == -1U) {
2325 /* Store the number whilst 4-bit nibbles remain. */
2328 hex_value <<= bitPos % integerPartWidth;
2329 significand[bitPos / integerPartWidth] |= hex_value;
2331 lost_fraction = trailingHexadecimalFraction(p, end, hex_value);
2332 while (p != end && hexDigitValue(*p) != -1U)
2339 /* Hex floats require an exponent but not a hexadecimal point. */
2340 assert(p != end && "Hex strings require an exponent");
2341 assert((*p == 'p' || *p == 'P') && "Invalid character in significand");
2342 assert(p != begin && "Significand has no digits");
2343 assert((dot == end || p - begin != 1) && "Significand has no digits");
2345 /* Ignore the exponent if we are zero. */
2346 if (p != firstSignificantDigit) {
2349 /* Implicit hexadecimal point? */
2353 /* Calculate the exponent adjustment implicit in the number of
2354 significant digits. */
2355 expAdjustment = static_cast<int>(dot - firstSignificantDigit);
2356 if (expAdjustment < 0)
2358 expAdjustment = expAdjustment * 4 - 1;
2360 /* Adjust for writing the significand starting at the most
2361 significant nibble. */
2362 expAdjustment += semantics->precision;
2363 expAdjustment -= partsCount * integerPartWidth;
2365 /* Adjust for the given exponent. */
2366 exponent = totalExponent(p + 1, end, expAdjustment);
2369 return normalize(rounding_mode, lost_fraction);
2373 APFloat::roundSignificandWithExponent(const integerPart *decSigParts,
2374 unsigned sigPartCount, int exp,
2375 roundingMode rounding_mode)
2377 unsigned int parts, pow5PartCount;
2378 fltSemantics calcSemantics = { 32767, -32767, 0 };
2379 integerPart pow5Parts[maxPowerOfFiveParts];
2382 isNearest = (rounding_mode == rmNearestTiesToEven ||
2383 rounding_mode == rmNearestTiesToAway);
2385 parts = partCountForBits(semantics->precision + 11);
2387 /* Calculate pow(5, abs(exp)). */
2388 pow5PartCount = powerOf5(pow5Parts, exp >= 0 ? exp: -exp);
2390 for (;; parts *= 2) {
2391 opStatus sigStatus, powStatus;
2392 unsigned int excessPrecision, truncatedBits;
2394 calcSemantics.precision = parts * integerPartWidth - 1;
2395 excessPrecision = calcSemantics.precision - semantics->precision;
2396 truncatedBits = excessPrecision;
2398 APFloat decSig = APFloat::getZero(calcSemantics, sign);
2399 APFloat pow5(calcSemantics);
2401 sigStatus = decSig.convertFromUnsignedParts(decSigParts, sigPartCount,
2402 rmNearestTiesToEven);
2403 powStatus = pow5.convertFromUnsignedParts(pow5Parts, pow5PartCount,
2404 rmNearestTiesToEven);
2405 /* Add exp, as 10^n = 5^n * 2^n. */
2406 decSig.exponent += exp;
2408 lostFraction calcLostFraction;
2409 integerPart HUerr, HUdistance;
2410 unsigned int powHUerr;
2413 /* multiplySignificand leaves the precision-th bit set to 1. */
2414 calcLostFraction = decSig.multiplySignificand(pow5, NULL);
2415 powHUerr = powStatus != opOK;
2417 calcLostFraction = decSig.divideSignificand(pow5);
2418 /* Denormal numbers have less precision. */
2419 if (decSig.exponent < semantics->minExponent) {
2420 excessPrecision += (semantics->minExponent - decSig.exponent);
2421 truncatedBits = excessPrecision;
2422 if (excessPrecision > calcSemantics.precision)
2423 excessPrecision = calcSemantics.precision;
2425 /* Extra half-ulp lost in reciprocal of exponent. */
2426 powHUerr = (powStatus == opOK && calcLostFraction == lfExactlyZero) ? 0:2;
2429 /* Both multiplySignificand and divideSignificand return the
2430 result with the integer bit set. */
2431 assert(APInt::tcExtractBit
2432 (decSig.significandParts(), calcSemantics.precision - 1) == 1);
2434 HUerr = HUerrBound(calcLostFraction != lfExactlyZero, sigStatus != opOK,
2436 HUdistance = 2 * ulpsFromBoundary(decSig.significandParts(),
2437 excessPrecision, isNearest);
2439 /* Are we guaranteed to round correctly if we truncate? */
2440 if (HUdistance >= HUerr) {
2441 APInt::tcExtract(significandParts(), partCount(), decSig.significandParts(),
2442 calcSemantics.precision - excessPrecision,
2444 /* Take the exponent of decSig. If we tcExtract-ed less bits
2445 above we must adjust our exponent to compensate for the
2446 implicit right shift. */
2447 exponent = (decSig.exponent + semantics->precision
2448 - (calcSemantics.precision - excessPrecision));
2449 calcLostFraction = lostFractionThroughTruncation(decSig.significandParts(),
2452 return normalize(rounding_mode, calcLostFraction);
2458 APFloat::convertFromDecimalString(StringRef str, roundingMode rounding_mode)
2463 /* Scan the text. */
2464 StringRef::iterator p = str.begin();
2465 interpretDecimal(p, str.end(), &D);
2467 /* Handle the quick cases. First the case of no significant digits,
2468 i.e. zero, and then exponents that are obviously too large or too
2469 small. Writing L for log 10 / log 2, a number d.ddddd*10^exp
2470 definitely overflows if
2472 (exp - 1) * L >= maxExponent
2474 and definitely underflows to zero where
2476 (exp + 1) * L <= minExponent - precision
2478 With integer arithmetic the tightest bounds for L are
2480 93/28 < L < 196/59 [ numerator <= 256 ]
2481 42039/12655 < L < 28738/8651 [ numerator <= 65536 ]
2484 // Test if we have a zero number allowing for strings with no null terminators
2485 // and zero decimals with non-zero exponents.
2487 // We computed firstSigDigit by ignoring all zeros and dots. Thus if
2488 // D->firstSigDigit equals str.end(), every digit must be a zero and there can
2489 // be at most one dot. On the other hand, if we have a zero with a non-zero
2490 // exponent, then we know that D.firstSigDigit will be non-numeric.
2491 if (D.firstSigDigit == str.end() || decDigitValue(*D.firstSigDigit) >= 10U) {
2495 /* Check whether the normalized exponent is high enough to overflow
2496 max during the log-rebasing in the max-exponent check below. */
2497 } else if (D.normalizedExponent - 1 > INT_MAX / 42039) {
2498 fs = handleOverflow(rounding_mode);
2500 /* If it wasn't, then it also wasn't high enough to overflow max
2501 during the log-rebasing in the min-exponent check. Check that it
2502 won't overflow min in either check, then perform the min-exponent
2504 } else if (D.normalizedExponent - 1 < INT_MIN / 42039 ||
2505 (D.normalizedExponent + 1) * 28738 <=
2506 8651 * (semantics->minExponent - (int) semantics->precision)) {
2507 /* Underflow to zero and round. */
2509 fs = normalize(rounding_mode, lfLessThanHalf);
2511 /* We can finally safely perform the max-exponent check. */
2512 } else if ((D.normalizedExponent - 1) * 42039
2513 >= 12655 * semantics->maxExponent) {
2514 /* Overflow and round. */
2515 fs = handleOverflow(rounding_mode);
2517 integerPart *decSignificand;
2518 unsigned int partCount;
2520 /* A tight upper bound on number of bits required to hold an
2521 N-digit decimal integer is N * 196 / 59. Allocate enough space
2522 to hold the full significand, and an extra part required by
2524 partCount = static_cast<unsigned int>(D.lastSigDigit - D.firstSigDigit) + 1;
2525 partCount = partCountForBits(1 + 196 * partCount / 59);
2526 decSignificand = new integerPart[partCount + 1];
2529 /* Convert to binary efficiently - we do almost all multiplication
2530 in an integerPart. When this would overflow do we do a single
2531 bignum multiplication, and then revert again to multiplication
2532 in an integerPart. */
2534 integerPart decValue, val, multiplier;
2542 if (p == str.end()) {
2546 decValue = decDigitValue(*p++);
2547 assert(decValue < 10U && "Invalid character in significand");
2549 val = val * 10 + decValue;
2550 /* The maximum number that can be multiplied by ten with any
2551 digit added without overflowing an integerPart. */
2552 } while (p <= D.lastSigDigit && multiplier <= (~ (integerPart) 0 - 9) / 10);
2554 /* Multiply out the current part. */
2555 APInt::tcMultiplyPart(decSignificand, decSignificand, multiplier, val,
2556 partCount, partCount + 1, false);
2558 /* If we used another part (likely but not guaranteed), increase
2560 if (decSignificand[partCount])
2562 } while (p <= D.lastSigDigit);
2564 category = fcNormal;
2565 fs = roundSignificandWithExponent(decSignificand, partCount,
2566 D.exponent, rounding_mode);
2568 delete [] decSignificand;
2575 APFloat::convertFromStringSpecials(StringRef str) {
2576 if (str.equals("inf") || str.equals("INFINITY")) {
2581 if (str.equals("-inf") || str.equals("-INFINITY")) {
2586 if (str.equals("nan") || str.equals("NaN")) {
2587 makeNaN(false, false);
2591 if (str.equals("-nan") || str.equals("-NaN")) {
2592 makeNaN(false, true);
2600 APFloat::convertFromString(StringRef str, roundingMode rounding_mode)
2602 assert(!str.empty() && "Invalid string length");
2604 // Handle special cases.
2605 if (convertFromStringSpecials(str))
2608 /* Handle a leading minus sign. */
2609 StringRef::iterator p = str.begin();
2610 size_t slen = str.size();
2611 sign = *p == '-' ? 1 : 0;
2612 if (*p == '-' || *p == '+') {
2615 assert(slen && "String has no digits");
2618 if (slen >= 2 && p[0] == '0' && (p[1] == 'x' || p[1] == 'X')) {
2619 assert(slen - 2 && "Invalid string");
2620 return convertFromHexadecimalString(StringRef(p + 2, slen - 2),
2624 return convertFromDecimalString(StringRef(p, slen), rounding_mode);
2627 /* Write out a hexadecimal representation of the floating point value
2628 to DST, which must be of sufficient size, in the C99 form
2629 [-]0xh.hhhhp[+-]d. Return the number of characters written,
2630 excluding the terminating NUL.
2632 If UPPERCASE, the output is in upper case, otherwise in lower case.
2634 HEXDIGITS digits appear altogether, rounding the value if
2635 necessary. If HEXDIGITS is 0, the minimal precision to display the
2636 number precisely is used instead. If nothing would appear after
2637 the decimal point it is suppressed.
2639 The decimal exponent is always printed and has at least one digit.
2640 Zero values display an exponent of zero. Infinities and NaNs
2641 appear as "infinity" or "nan" respectively.
2643 The above rules are as specified by C99. There is ambiguity about
2644 what the leading hexadecimal digit should be. This implementation
2645 uses whatever is necessary so that the exponent is displayed as
2646 stored. This implies the exponent will fall within the IEEE format
2647 range, and the leading hexadecimal digit will be 0 (for denormals),
2648 1 (normal numbers) or 2 (normal numbers rounded-away-from-zero with
2649 any other digits zero).
2652 APFloat::convertToHexString(char *dst, unsigned int hexDigits,
2653 bool upperCase, roundingMode rounding_mode) const
2663 memcpy (dst, upperCase ? infinityU: infinityL, sizeof infinityU - 1);
2664 dst += sizeof infinityL - 1;
2668 memcpy (dst, upperCase ? NaNU: NaNL, sizeof NaNU - 1);
2669 dst += sizeof NaNU - 1;
2674 *dst++ = upperCase ? 'X': 'x';
2676 if (hexDigits > 1) {
2678 memset (dst, '0', hexDigits - 1);
2679 dst += hexDigits - 1;
2681 *dst++ = upperCase ? 'P': 'p';
2686 dst = convertNormalToHexString (dst, hexDigits, upperCase, rounding_mode);
2692 return static_cast<unsigned int>(dst - p);
2695 /* Does the hard work of outputting the correctly rounded hexadecimal
2696 form of a normal floating point number with the specified number of
2697 hexadecimal digits. If HEXDIGITS is zero the minimum number of
2698 digits necessary to print the value precisely is output. */
2700 APFloat::convertNormalToHexString(char *dst, unsigned int hexDigits,
2702 roundingMode rounding_mode) const
2704 unsigned int count, valueBits, shift, partsCount, outputDigits;
2705 const char *hexDigitChars;
2706 const integerPart *significand;
2711 *dst++ = upperCase ? 'X': 'x';
2714 hexDigitChars = upperCase ? hexDigitsUpper: hexDigitsLower;
2716 significand = significandParts();
2717 partsCount = partCount();
2719 /* +3 because the first digit only uses the single integer bit, so
2720 we have 3 virtual zero most-significant-bits. */
2721 valueBits = semantics->precision + 3;
2722 shift = integerPartWidth - valueBits % integerPartWidth;
2724 /* The natural number of digits required ignoring trailing
2725 insignificant zeroes. */
2726 outputDigits = (valueBits - significandLSB () + 3) / 4;
2728 /* hexDigits of zero means use the required number for the
2729 precision. Otherwise, see if we are truncating. If we are,
2730 find out if we need to round away from zero. */
2732 if (hexDigits < outputDigits) {
2733 /* We are dropping non-zero bits, so need to check how to round.
2734 "bits" is the number of dropped bits. */
2736 lostFraction fraction;
2738 bits = valueBits - hexDigits * 4;
2739 fraction = lostFractionThroughTruncation (significand, partsCount, bits);
2740 roundUp = roundAwayFromZero(rounding_mode, fraction, bits);
2742 outputDigits = hexDigits;
2745 /* Write the digits consecutively, and start writing in the location
2746 of the hexadecimal point. We move the most significant digit
2747 left and add the hexadecimal point later. */
2750 count = (valueBits + integerPartWidth - 1) / integerPartWidth;
2752 while (outputDigits && count) {
2755 /* Put the most significant integerPartWidth bits in "part". */
2756 if (--count == partsCount)
2757 part = 0; /* An imaginary higher zero part. */
2759 part = significand[count] << shift;
2762 part |= significand[count - 1] >> (integerPartWidth - shift);
2764 /* Convert as much of "part" to hexdigits as we can. */
2765 unsigned int curDigits = integerPartWidth / 4;
2767 if (curDigits > outputDigits)
2768 curDigits = outputDigits;
2769 dst += partAsHex (dst, part, curDigits, hexDigitChars);
2770 outputDigits -= curDigits;
2776 /* Note that hexDigitChars has a trailing '0'. */
2779 *q = hexDigitChars[hexDigitValue (*q) + 1];
2780 } while (*q == '0');
2783 /* Add trailing zeroes. */
2784 memset (dst, '0', outputDigits);
2785 dst += outputDigits;
2788 /* Move the most significant digit to before the point, and if there
2789 is something after the decimal point add it. This must come
2790 after rounding above. */
2797 /* Finally output the exponent. */
2798 *dst++ = upperCase ? 'P': 'p';
2800 return writeSignedDecimal (dst, exponent);
2803 hash_code llvm::hash_value(const APFloat &Arg) {
2804 if (!Arg.isFiniteNonZero())
2805 return hash_combine((uint8_t)Arg.category,
2806 // NaN has no sign, fix it at zero.
2807 Arg.isNaN() ? (uint8_t)0 : (uint8_t)Arg.sign,
2808 Arg.semantics->precision);
2810 // Normal floats need their exponent and significand hashed.
2811 return hash_combine((uint8_t)Arg.category, (uint8_t)Arg.sign,
2812 Arg.semantics->precision, Arg.exponent,
2814 Arg.significandParts(),
2815 Arg.significandParts() + Arg.partCount()));
2818 // Conversion from APFloat to/from host float/double. It may eventually be
2819 // possible to eliminate these and have everybody deal with APFloats, but that
2820 // will take a while. This approach will not easily extend to long double.
2821 // Current implementation requires integerPartWidth==64, which is correct at
2822 // the moment but could be made more general.
2824 // Denormals have exponent minExponent in APFloat, but minExponent-1 in
2825 // the actual IEEE respresentations. We compensate for that here.
2828 APFloat::convertF80LongDoubleAPFloatToAPInt() const
2830 assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended);
2831 assert(partCount()==2);
2833 uint64_t myexponent, mysignificand;
2835 if (isFiniteNonZero()) {
2836 myexponent = exponent+16383; //bias
2837 mysignificand = significandParts()[0];
2838 if (myexponent==1 && !(mysignificand & 0x8000000000000000ULL))
2839 myexponent = 0; // denormal
2840 } else if (category==fcZero) {
2843 } else if (category==fcInfinity) {
2844 myexponent = 0x7fff;
2845 mysignificand = 0x8000000000000000ULL;
2847 assert(category == fcNaN && "Unknown category");
2848 myexponent = 0x7fff;
2849 mysignificand = significandParts()[0];
2853 words[0] = mysignificand;
2854 words[1] = ((uint64_t)(sign & 1) << 15) |
2855 (myexponent & 0x7fffLL);
2856 return APInt(80, words);
2860 APFloat::convertPPCDoubleDoubleAPFloatToAPInt() const
2862 assert(semantics == (const llvm::fltSemantics*)&PPCDoubleDouble);
2863 assert(partCount()==2);
2869 // Convert number to double. To avoid spurious underflows, we re-
2870 // normalize against the "double" minExponent first, and only *then*
2871 // truncate the mantissa. The result of that second conversion
2872 // may be inexact, but should never underflow.
2873 // Declare fltSemantics before APFloat that uses it (and
2874 // saves pointer to it) to ensure correct destruction order.
2875 fltSemantics extendedSemantics = *semantics;
2876 extendedSemantics.minExponent = IEEEdouble.minExponent;
2877 APFloat extended(*this);
2878 fs = extended.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
2879 assert(fs == opOK && !losesInfo);
2882 APFloat u(extended);
2883 fs = u.convert(IEEEdouble, rmNearestTiesToEven, &losesInfo);
2884 assert(fs == opOK || fs == opInexact);
2886 words[0] = *u.convertDoubleAPFloatToAPInt().getRawData();
2888 // If conversion was exact or resulted in a special case, we're done;
2889 // just set the second double to zero. Otherwise, re-convert back to
2890 // the extended format and compute the difference. This now should
2891 // convert exactly to double.
2892 if (u.isFiniteNonZero() && losesInfo) {
2893 fs = u.convert(extendedSemantics, rmNearestTiesToEven, &losesInfo);
2894 assert(fs == opOK && !losesInfo);
2897 APFloat v(extended);
2898 v.subtract(u, rmNearestTiesToEven);
2899 fs = v.convert(IEEEdouble, rmNearestTiesToEven, &losesInfo);
2900 assert(fs == opOK && !losesInfo);
2902 words[1] = *v.convertDoubleAPFloatToAPInt().getRawData();
2907 return APInt(128, words);
2911 APFloat::convertQuadrupleAPFloatToAPInt() const
2913 assert(semantics == (const llvm::fltSemantics*)&IEEEquad);
2914 assert(partCount()==2);
2916 uint64_t myexponent, mysignificand, mysignificand2;
2918 if (isFiniteNonZero()) {
2919 myexponent = exponent+16383; //bias
2920 mysignificand = significandParts()[0];
2921 mysignificand2 = significandParts()[1];
2922 if (myexponent==1 && !(mysignificand2 & 0x1000000000000LL))
2923 myexponent = 0; // denormal
2924 } else if (category==fcZero) {
2926 mysignificand = mysignificand2 = 0;
2927 } else if (category==fcInfinity) {
2928 myexponent = 0x7fff;
2929 mysignificand = mysignificand2 = 0;
2931 assert(category == fcNaN && "Unknown category!");
2932 myexponent = 0x7fff;
2933 mysignificand = significandParts()[0];
2934 mysignificand2 = significandParts()[1];
2938 words[0] = mysignificand;
2939 words[1] = ((uint64_t)(sign & 1) << 63) |
2940 ((myexponent & 0x7fff) << 48) |
2941 (mysignificand2 & 0xffffffffffffLL);
2943 return APInt(128, words);
2947 APFloat::convertDoubleAPFloatToAPInt() const
2949 assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
2950 assert(partCount()==1);
2952 uint64_t myexponent, mysignificand;
2954 if (isFiniteNonZero()) {
2955 myexponent = exponent+1023; //bias
2956 mysignificand = *significandParts();
2957 if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
2958 myexponent = 0; // denormal
2959 } else if (category==fcZero) {
2962 } else if (category==fcInfinity) {
2966 assert(category == fcNaN && "Unknown category!");
2968 mysignificand = *significandParts();
2971 return APInt(64, ((((uint64_t)(sign & 1) << 63) |
2972 ((myexponent & 0x7ff) << 52) |
2973 (mysignificand & 0xfffffffffffffLL))));
2977 APFloat::convertFloatAPFloatToAPInt() const
2979 assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
2980 assert(partCount()==1);
2982 uint32_t myexponent, mysignificand;
2984 if (isFiniteNonZero()) {
2985 myexponent = exponent+127; //bias
2986 mysignificand = (uint32_t)*significandParts();
2987 if (myexponent == 1 && !(mysignificand & 0x800000))
2988 myexponent = 0; // denormal
2989 } else if (category==fcZero) {
2992 } else if (category==fcInfinity) {
2996 assert(category == fcNaN && "Unknown category!");
2998 mysignificand = (uint32_t)*significandParts();
3001 return APInt(32, (((sign&1) << 31) | ((myexponent&0xff) << 23) |
3002 (mysignificand & 0x7fffff)));
3006 APFloat::convertHalfAPFloatToAPInt() const
3008 assert(semantics == (const llvm::fltSemantics*)&IEEEhalf);
3009 assert(partCount()==1);
3011 uint32_t myexponent, mysignificand;
3013 if (isFiniteNonZero()) {
3014 myexponent = exponent+15; //bias
3015 mysignificand = (uint32_t)*significandParts();
3016 if (myexponent == 1 && !(mysignificand & 0x400))
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(16, (((sign&1) << 15) | ((myexponent&0x1f) << 10) |
3031 (mysignificand & 0x3ff)));
3034 // This function creates an APInt that is just a bit map of the floating
3035 // point constant as it would appear in memory. It is not a conversion,
3036 // and treating the result as a normal integer is unlikely to be useful.
3039 APFloat::bitcastToAPInt() const
3041 if (semantics == (const llvm::fltSemantics*)&IEEEhalf)
3042 return convertHalfAPFloatToAPInt();
3044 if (semantics == (const llvm::fltSemantics*)&IEEEsingle)
3045 return convertFloatAPFloatToAPInt();
3047 if (semantics == (const llvm::fltSemantics*)&IEEEdouble)
3048 return convertDoubleAPFloatToAPInt();
3050 if (semantics == (const llvm::fltSemantics*)&IEEEquad)
3051 return convertQuadrupleAPFloatToAPInt();
3053 if (semantics == (const llvm::fltSemantics*)&PPCDoubleDouble)
3054 return convertPPCDoubleDoubleAPFloatToAPInt();
3056 assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended &&
3058 return convertF80LongDoubleAPFloatToAPInt();
3062 APFloat::convertToFloat() const
3064 assert(semantics == (const llvm::fltSemantics*)&IEEEsingle &&
3065 "Float semantics are not IEEEsingle");
3066 APInt api = bitcastToAPInt();
3067 return api.bitsToFloat();
3071 APFloat::convertToDouble() const
3073 assert(semantics == (const llvm::fltSemantics*)&IEEEdouble &&
3074 "Float semantics are not IEEEdouble");
3075 APInt api = bitcastToAPInt();
3076 return api.bitsToDouble();
3079 /// Integer bit is explicit in this format. Intel hardware (387 and later)
3080 /// does not support these bit patterns:
3081 /// exponent = all 1's, integer bit 0, significand 0 ("pseudoinfinity")
3082 /// exponent = all 1's, integer bit 0, significand nonzero ("pseudoNaN")
3083 /// exponent = 0, integer bit 1 ("pseudodenormal")
3084 /// exponent!=0 nor all 1's, integer bit 0 ("unnormal")
3085 /// At the moment, the first two are treated as NaNs, the second two as Normal.
3087 APFloat::initFromF80LongDoubleAPInt(const APInt &api)
3089 assert(api.getBitWidth()==80);
3090 uint64_t i1 = api.getRawData()[0];
3091 uint64_t i2 = api.getRawData()[1];
3092 uint64_t myexponent = (i2 & 0x7fff);
3093 uint64_t mysignificand = i1;
3095 initialize(&APFloat::x87DoubleExtended);
3096 assert(partCount()==2);
3098 sign = static_cast<unsigned int>(i2>>15);
3099 if (myexponent==0 && mysignificand==0) {
3100 // exponent, significand meaningless
3102 } else if (myexponent==0x7fff && mysignificand==0x8000000000000000ULL) {
3103 // exponent, significand meaningless
3104 category = fcInfinity;
3105 } else if (myexponent==0x7fff && mysignificand!=0x8000000000000000ULL) {
3106 // exponent meaningless
3108 significandParts()[0] = mysignificand;
3109 significandParts()[1] = 0;
3111 category = fcNormal;
3112 exponent = myexponent - 16383;
3113 significandParts()[0] = mysignificand;
3114 significandParts()[1] = 0;
3115 if (myexponent==0) // denormal
3121 APFloat::initFromPPCDoubleDoubleAPInt(const APInt &api)
3123 assert(api.getBitWidth()==128);
3124 uint64_t i1 = api.getRawData()[0];
3125 uint64_t i2 = api.getRawData()[1];
3129 // Get the first double and convert to our format.
3130 initFromDoubleAPInt(APInt(64, i1));
3131 fs = convert(PPCDoubleDouble, rmNearestTiesToEven, &losesInfo);
3132 assert(fs == opOK && !losesInfo);
3135 // Unless we have a special case, add in second double.
3136 if (isFiniteNonZero()) {
3137 APFloat v(IEEEdouble, APInt(64, i2));
3138 fs = v.convert(PPCDoubleDouble, rmNearestTiesToEven, &losesInfo);
3139 assert(fs == opOK && !losesInfo);
3142 add(v, rmNearestTiesToEven);
3147 APFloat::initFromQuadrupleAPInt(const APInt &api)
3149 assert(api.getBitWidth()==128);
3150 uint64_t i1 = api.getRawData()[0];
3151 uint64_t i2 = api.getRawData()[1];
3152 uint64_t myexponent = (i2 >> 48) & 0x7fff;
3153 uint64_t mysignificand = i1;
3154 uint64_t mysignificand2 = i2 & 0xffffffffffffLL;
3156 initialize(&APFloat::IEEEquad);
3157 assert(partCount()==2);
3159 sign = static_cast<unsigned int>(i2>>63);
3160 if (myexponent==0 &&
3161 (mysignificand==0 && mysignificand2==0)) {
3162 // exponent, significand meaningless
3164 } else if (myexponent==0x7fff &&
3165 (mysignificand==0 && mysignificand2==0)) {
3166 // exponent, significand meaningless
3167 category = fcInfinity;
3168 } else if (myexponent==0x7fff &&
3169 (mysignificand!=0 || mysignificand2 !=0)) {
3170 // exponent meaningless
3172 significandParts()[0] = mysignificand;
3173 significandParts()[1] = mysignificand2;
3175 category = fcNormal;
3176 exponent = myexponent - 16383;
3177 significandParts()[0] = mysignificand;
3178 significandParts()[1] = mysignificand2;
3179 if (myexponent==0) // denormal
3182 significandParts()[1] |= 0x1000000000000LL; // integer bit
3187 APFloat::initFromDoubleAPInt(const APInt &api)
3189 assert(api.getBitWidth()==64);
3190 uint64_t i = *api.getRawData();
3191 uint64_t myexponent = (i >> 52) & 0x7ff;
3192 uint64_t mysignificand = i & 0xfffffffffffffLL;
3194 initialize(&APFloat::IEEEdouble);
3195 assert(partCount()==1);
3197 sign = static_cast<unsigned int>(i>>63);
3198 if (myexponent==0 && mysignificand==0) {
3199 // exponent, significand meaningless
3201 } else if (myexponent==0x7ff && mysignificand==0) {
3202 // exponent, significand meaningless
3203 category = fcInfinity;
3204 } else if (myexponent==0x7ff && mysignificand!=0) {
3205 // exponent meaningless
3207 *significandParts() = mysignificand;
3209 category = fcNormal;
3210 exponent = myexponent - 1023;
3211 *significandParts() = mysignificand;
3212 if (myexponent==0) // denormal
3215 *significandParts() |= 0x10000000000000LL; // integer bit
3220 APFloat::initFromFloatAPInt(const APInt & api)
3222 assert(api.getBitWidth()==32);
3223 uint32_t i = (uint32_t)*api.getRawData();
3224 uint32_t myexponent = (i >> 23) & 0xff;
3225 uint32_t mysignificand = i & 0x7fffff;
3227 initialize(&APFloat::IEEEsingle);
3228 assert(partCount()==1);
3231 if (myexponent==0 && mysignificand==0) {
3232 // exponent, significand meaningless
3234 } else if (myexponent==0xff && mysignificand==0) {
3235 // exponent, significand meaningless
3236 category = fcInfinity;
3237 } else if (myexponent==0xff && mysignificand!=0) {
3238 // sign, exponent, significand meaningless
3240 *significandParts() = mysignificand;
3242 category = fcNormal;
3243 exponent = myexponent - 127; //bias
3244 *significandParts() = mysignificand;
3245 if (myexponent==0) // denormal
3248 *significandParts() |= 0x800000; // integer bit
3253 APFloat::initFromHalfAPInt(const APInt & api)
3255 assert(api.getBitWidth()==16);
3256 uint32_t i = (uint32_t)*api.getRawData();
3257 uint32_t myexponent = (i >> 10) & 0x1f;
3258 uint32_t mysignificand = i & 0x3ff;
3260 initialize(&APFloat::IEEEhalf);
3261 assert(partCount()==1);
3264 if (myexponent==0 && mysignificand==0) {
3265 // exponent, significand meaningless
3267 } else if (myexponent==0x1f && mysignificand==0) {
3268 // exponent, significand meaningless
3269 category = fcInfinity;
3270 } else if (myexponent==0x1f && mysignificand!=0) {
3271 // sign, exponent, significand meaningless
3273 *significandParts() = mysignificand;
3275 category = fcNormal;
3276 exponent = myexponent - 15; //bias
3277 *significandParts() = mysignificand;
3278 if (myexponent==0) // denormal
3281 *significandParts() |= 0x400; // integer bit
3285 /// Treat api as containing the bits of a floating point number. Currently
3286 /// we infer the floating point type from the size of the APInt. The
3287 /// isIEEE argument distinguishes between PPC128 and IEEE128 (not meaningful
3288 /// when the size is anything else).
3290 APFloat::initFromAPInt(const fltSemantics* Sem, const APInt& api)
3292 if (Sem == &IEEEhalf)
3293 return initFromHalfAPInt(api);
3294 if (Sem == &IEEEsingle)
3295 return initFromFloatAPInt(api);
3296 if (Sem == &IEEEdouble)
3297 return initFromDoubleAPInt(api);
3298 if (Sem == &x87DoubleExtended)
3299 return initFromF80LongDoubleAPInt(api);
3300 if (Sem == &IEEEquad)
3301 return initFromQuadrupleAPInt(api);
3302 if (Sem == &PPCDoubleDouble)
3303 return initFromPPCDoubleDoubleAPInt(api);
3305 llvm_unreachable(0);
3309 APFloat::getAllOnesValue(unsigned BitWidth, bool isIEEE)
3313 return APFloat(IEEEhalf, APInt::getAllOnesValue(BitWidth));
3315 return APFloat(IEEEsingle, APInt::getAllOnesValue(BitWidth));
3317 return APFloat(IEEEdouble, APInt::getAllOnesValue(BitWidth));
3319 return APFloat(x87DoubleExtended, APInt::getAllOnesValue(BitWidth));
3322 return APFloat(IEEEquad, APInt::getAllOnesValue(BitWidth));
3323 return APFloat(PPCDoubleDouble, APInt::getAllOnesValue(BitWidth));
3325 llvm_unreachable("Unknown floating bit width");
3329 /// Make this number the largest magnitude normal number in the given
3331 void APFloat::makeLargest(bool Negative) {
3332 // We want (in interchange format):
3333 // sign = {Negative}
3335 // significand = 1..1
3336 category = fcNormal;
3338 exponent = semantics->maxExponent;
3340 // Use memset to set all but the highest integerPart to all ones.
3341 integerPart *significand = significandParts();
3342 unsigned PartCount = partCount();
3343 memset(significand, 0xFF, sizeof(integerPart)*(PartCount - 1));
3345 // Set the high integerPart especially setting all unused top bits for
3346 // internal consistency.
3347 const unsigned NumUnusedHighBits =
3348 PartCount*integerPartWidth - semantics->precision;
3349 significand[PartCount - 1] = ~integerPart(0) >> NumUnusedHighBits;
3352 /// Make this number the smallest magnitude denormal number in the given
3354 void APFloat::makeSmallest(bool Negative) {
3355 // We want (in interchange format):
3356 // sign = {Negative}
3358 // significand = 0..01
3359 category = fcNormal;
3361 exponent = semantics->minExponent;
3362 APInt::tcSet(significandParts(), 1, partCount());
3366 APFloat APFloat::getLargest(const fltSemantics &Sem, bool Negative) {
3367 // We want (in interchange format):
3368 // sign = {Negative}
3370 // significand = 1..1
3371 APFloat Val(Sem, uninitialized);
3372 Val.makeLargest(Negative);
3376 APFloat APFloat::getSmallest(const fltSemantics &Sem, bool Negative) {
3377 // We want (in interchange format):
3378 // sign = {Negative}
3380 // significand = 0..01
3381 APFloat Val(Sem, uninitialized);
3382 Val.makeSmallest(Negative);
3386 APFloat APFloat::getSmallestNormalized(const fltSemantics &Sem, bool Negative) {
3387 APFloat Val(Sem, uninitialized);
3389 // We want (in interchange format):
3390 // sign = {Negative}
3392 // significand = 10..0
3394 Val.zeroSignificand();
3395 Val.sign = Negative;
3396 Val.exponent = Sem.minExponent;
3397 Val.significandParts()[partCountForBits(Sem.precision)-1] |=
3398 (((integerPart) 1) << ((Sem.precision - 1) % integerPartWidth));
3403 APFloat::APFloat(const fltSemantics &Sem, const APInt &API) {
3404 initFromAPInt(&Sem, API);
3407 APFloat::APFloat(float f) {
3408 initFromAPInt(&IEEEsingle, APInt::floatToBits(f));
3411 APFloat::APFloat(double d) {
3412 initFromAPInt(&IEEEdouble, APInt::doubleToBits(d));
3416 void append(SmallVectorImpl<char> &Buffer, StringRef Str) {
3417 Buffer.append(Str.begin(), Str.end());
3420 /// Removes data from the given significand until it is no more
3421 /// precise than is required for the desired precision.
3422 void AdjustToPrecision(APInt &significand,
3423 int &exp, unsigned FormatPrecision) {
3424 unsigned bits = significand.getActiveBits();
3426 // 196/59 is a very slight overestimate of lg_2(10).
3427 unsigned bitsRequired = (FormatPrecision * 196 + 58) / 59;
3429 if (bits <= bitsRequired) return;
3431 unsigned tensRemovable = (bits - bitsRequired) * 59 / 196;
3432 if (!tensRemovable) return;
3434 exp += tensRemovable;
3436 APInt divisor(significand.getBitWidth(), 1);
3437 APInt powten(significand.getBitWidth(), 10);
3439 if (tensRemovable & 1)
3441 tensRemovable >>= 1;
3442 if (!tensRemovable) break;
3446 significand = significand.udiv(divisor);
3448 // Truncate the significand down to its active bit count.
3449 significand = significand.trunc(significand.getActiveBits());
3453 void AdjustToPrecision(SmallVectorImpl<char> &buffer,
3454 int &exp, unsigned FormatPrecision) {
3455 unsigned N = buffer.size();
3456 if (N <= FormatPrecision) return;
3458 // The most significant figures are the last ones in the buffer.
3459 unsigned FirstSignificant = N - FormatPrecision;
3462 // FIXME: this probably shouldn't use 'round half up'.
3464 // Rounding down is just a truncation, except we also want to drop
3465 // trailing zeros from the new result.
3466 if (buffer[FirstSignificant - 1] < '5') {
3467 while (FirstSignificant < N && buffer[FirstSignificant] == '0')
3470 exp += FirstSignificant;
3471 buffer.erase(&buffer[0], &buffer[FirstSignificant]);
3475 // Rounding up requires a decimal add-with-carry. If we continue
3476 // the carry, the newly-introduced zeros will just be truncated.
3477 for (unsigned I = FirstSignificant; I != N; ++I) {
3478 if (buffer[I] == '9') {
3486 // If we carried through, we have exactly one digit of precision.
3487 if (FirstSignificant == N) {
3488 exp += FirstSignificant;
3490 buffer.push_back('1');
3494 exp += FirstSignificant;
3495 buffer.erase(&buffer[0], &buffer[FirstSignificant]);
3499 void APFloat::toString(SmallVectorImpl<char> &Str,
3500 unsigned FormatPrecision,
3501 unsigned FormatMaxPadding) const {
3505 return append(Str, "-Inf");
3507 return append(Str, "+Inf");
3509 case fcNaN: return append(Str, "NaN");
3515 if (!FormatMaxPadding)
3516 append(Str, "0.0E+0");
3528 // Decompose the number into an APInt and an exponent.
3529 int exp = exponent - ((int) semantics->precision - 1);
3530 APInt significand(semantics->precision,
3531 makeArrayRef(significandParts(),
3532 partCountForBits(semantics->precision)));
3534 // Set FormatPrecision if zero. We want to do this before we
3535 // truncate trailing zeros, as those are part of the precision.
3536 if (!FormatPrecision) {
3537 // It's an interesting question whether to use the nominal
3538 // precision or the active precision here for denormals.
3540 // FormatPrecision = ceil(significandBits / lg_2(10))
3541 FormatPrecision = (semantics->precision * 59 + 195) / 196;
3544 // Ignore trailing binary zeros.
3545 int trailingZeros = significand.countTrailingZeros();
3546 exp += trailingZeros;
3547 significand = significand.lshr(trailingZeros);
3549 // Change the exponent from 2^e to 10^e.
3552 } else if (exp > 0) {
3554 significand = significand.zext(semantics->precision + exp);
3555 significand <<= exp;
3557 } else { /* exp < 0 */
3560 // We transform this using the identity:
3561 // (N)(2^-e) == (N)(5^e)(10^-e)
3562 // This means we have to multiply N (the significand) by 5^e.
3563 // To avoid overflow, we have to operate on numbers large
3564 // enough to store N * 5^e:
3565 // log2(N * 5^e) == log2(N) + e * log2(5)
3566 // <= semantics->precision + e * 137 / 59
3567 // (log_2(5) ~ 2.321928 < 2.322034 ~ 137/59)
3569 unsigned precision = semantics->precision + (137 * texp + 136) / 59;
3571 // Multiply significand by 5^e.
3572 // N * 5^0101 == N * 5^(1*1) * 5^(0*2) * 5^(1*4) * 5^(0*8)
3573 significand = significand.zext(precision);
3574 APInt five_to_the_i(precision, 5);
3576 if (texp & 1) significand *= five_to_the_i;
3580 five_to_the_i *= five_to_the_i;
3584 AdjustToPrecision(significand, exp, FormatPrecision);
3586 SmallVector<char, 256> buffer;
3589 unsigned precision = significand.getBitWidth();
3590 APInt ten(precision, 10);
3591 APInt digit(precision, 0);
3593 bool inTrail = true;
3594 while (significand != 0) {
3595 // digit <- significand % 10
3596 // significand <- significand / 10
3597 APInt::udivrem(significand, ten, significand, digit);
3599 unsigned d = digit.getZExtValue();
3601 // Drop trailing zeros.
3602 if (inTrail && !d) exp++;
3604 buffer.push_back((char) ('0' + d));
3609 assert(!buffer.empty() && "no characters in buffer!");
3611 // Drop down to FormatPrecision.
3612 // TODO: don't do more precise calculations above than are required.
3613 AdjustToPrecision(buffer, exp, FormatPrecision);
3615 unsigned NDigits = buffer.size();
3617 // Check whether we should use scientific notation.
3618 bool FormatScientific;
3619 if (!FormatMaxPadding)
3620 FormatScientific = true;
3625 // But we shouldn't make the number look more precise than it is.
3626 FormatScientific = ((unsigned) exp > FormatMaxPadding ||
3627 NDigits + (unsigned) exp > FormatPrecision);
3629 // Power of the most significant digit.
3630 int MSD = exp + (int) (NDigits - 1);
3633 FormatScientific = false;
3635 // 765e-5 == 0.00765
3637 FormatScientific = ((unsigned) -MSD) > FormatMaxPadding;
3642 // Scientific formatting is pretty straightforward.
3643 if (FormatScientific) {
3644 exp += (NDigits - 1);
3646 Str.push_back(buffer[NDigits-1]);
3651 for (unsigned I = 1; I != NDigits; ++I)
3652 Str.push_back(buffer[NDigits-1-I]);
3655 Str.push_back(exp >= 0 ? '+' : '-');
3656 if (exp < 0) exp = -exp;
3657 SmallVector<char, 6> expbuf;
3659 expbuf.push_back((char) ('0' + (exp % 10)));
3662 for (unsigned I = 0, E = expbuf.size(); I != E; ++I)
3663 Str.push_back(expbuf[E-1-I]);
3667 // Non-scientific, positive exponents.
3669 for (unsigned I = 0; I != NDigits; ++I)
3670 Str.push_back(buffer[NDigits-1-I]);
3671 for (unsigned I = 0; I != (unsigned) exp; ++I)
3676 // Non-scientific, negative exponents.
3678 // The number of digits to the left of the decimal point.
3679 int NWholeDigits = exp + (int) NDigits;
3682 if (NWholeDigits > 0) {
3683 for (; I != (unsigned) NWholeDigits; ++I)
3684 Str.push_back(buffer[NDigits-I-1]);
3687 unsigned NZeros = 1 + (unsigned) -NWholeDigits;
3691 for (unsigned Z = 1; Z != NZeros; ++Z)
3695 for (; I != NDigits; ++I)
3696 Str.push_back(buffer[NDigits-I-1]);
3699 bool APFloat::getExactInverse(APFloat *inv) const {
3700 // Special floats and denormals have no exact inverse.
3701 if (!isFiniteNonZero())
3704 // Check that the number is a power of two by making sure that only the
3705 // integer bit is set in the significand.
3706 if (significandLSB() != semantics->precision - 1)
3710 APFloat reciprocal(*semantics, 1ULL);
3711 if (reciprocal.divide(*this, rmNearestTiesToEven) != opOK)
3714 // Avoid multiplication with a denormal, it is not safe on all platforms and
3715 // may be slower than a normal division.
3716 if (reciprocal.isDenormal())
3719 assert(reciprocal.isFiniteNonZero() &&
3720 reciprocal.significandLSB() == reciprocal.semantics->precision - 1);
3728 bool APFloat::isSignaling() const {
3732 // IEEE-754R 2008 6.2.1: A signaling NaN bit string should be encoded with the
3733 // first bit of the trailing significand being 0.
3734 return !APInt::tcExtractBit(significandParts(), semantics->precision - 2);
3737 /// IEEE-754R 2008 5.3.1: nextUp/nextDown.
3739 /// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with
3740 /// appropriate sign switching before/after the computation.
3741 APFloat::opStatus APFloat::next(bool nextDown) {
3742 // If we are performing nextDown, swap sign so we have -x.
3746 // Compute nextUp(x)
3747 opStatus result = opOK;
3749 // Handle each float category separately.
3752 // nextUp(+inf) = +inf
3755 // nextUp(-inf) = -getLargest()
3759 // IEEE-754R 2008 6.2 Par 2: nextUp(sNaN) = qNaN. Set Invalid flag.
3760 // IEEE-754R 2008 6.2: nextUp(qNaN) = qNaN. Must be identity so we do not
3761 // change the payload.
3762 if (isSignaling()) {
3763 result = opInvalidOp;
3764 // For consistency, propogate the sign of the sNaN to the qNaN.
3765 makeNaN(false, isNegative(), 0);
3769 // nextUp(pm 0) = +getSmallest()
3770 makeSmallest(false);
3773 // nextUp(-getSmallest()) = -0
3774 if (isSmallest() && isNegative()) {
3775 APInt::tcSet(significandParts(), 0, partCount());
3781 // nextUp(getLargest()) == INFINITY
3782 if (isLargest() && !isNegative()) {
3783 APInt::tcSet(significandParts(), 0, partCount());
3784 category = fcInfinity;
3785 exponent = semantics->maxExponent + 1;
3789 // nextUp(normal) == normal + inc.
3791 // If we are negative, we need to decrement the significand.
3793 // We only cross a binade boundary that requires adjusting the exponent
3795 // 1. exponent != semantics->minExponent. This implies we are not in the
3796 // smallest binade or are dealing with denormals.
3797 // 2. Our significand excluding the integral bit is all zeros.
3798 bool WillCrossBinadeBoundary =
3799 exponent != semantics->minExponent && isSignificandAllZeros();
3801 // Decrement the significand.
3803 // We always do this since:
3804 // 1. If we are dealing with a non binade decrement, by definition we
3805 // just decrement the significand.
3806 // 2. If we are dealing with a normal -> normal binade decrement, since
3807 // we have an explicit integral bit the fact that all bits but the
3808 // integral bit are zero implies that subtracting one will yield a
3809 // significand with 0 integral bit and 1 in all other spots. Thus we
3810 // must just adjust the exponent and set the integral bit to 1.
3811 // 3. If we are dealing with a normal -> denormal binade decrement,
3812 // since we set the integral bit to 0 when we represent denormals, we
3813 // just decrement the significand.
3814 integerPart *Parts = significandParts();
3815 APInt::tcDecrement(Parts, partCount());
3817 if (WillCrossBinadeBoundary) {
3818 // Our result is a normal number. Do the following:
3819 // 1. Set the integral bit to 1.
3820 // 2. Decrement the exponent.
3821 APInt::tcSetBit(Parts, semantics->precision - 1);
3825 // If we are positive, we need to increment the significand.
3827 // We only cross a binade boundary that requires adjusting the exponent if
3828 // the input is not a denormal and all of said input's significand bits
3829 // are set. If all of said conditions are true: clear the significand, set
3830 // the integral bit to 1, and increment the exponent. If we have a
3831 // denormal always increment since moving denormals and the numbers in the
3832 // smallest normal binade have the same exponent in our representation.
3833 bool WillCrossBinadeBoundary = !isDenormal() && isSignificandAllOnes();
3835 if (WillCrossBinadeBoundary) {
3836 integerPart *Parts = significandParts();
3837 APInt::tcSet(Parts, 0, partCount());
3838 APInt::tcSetBit(Parts, semantics->precision - 1);
3839 assert(exponent != semantics->maxExponent &&
3840 "We can not increment an exponent beyond the maxExponent allowed"
3841 " by the given floating point semantics.");
3844 incrementSignificand();
3850 // If we are performing nextDown, swap sign so we have -nextUp(-x)
3858 APFloat::makeInf(bool Negative) {
3859 category = fcInfinity;
3861 exponent = semantics->maxExponent + 1;
3862 APInt::tcSet(significandParts(), 0, partCount());
3866 APFloat::makeZero(bool Negative) {
3869 exponent = semantics->minExponent-1;
3870 APInt::tcSet(significandParts(), 0, partCount());