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/FoldingSet.h"
17 #include "llvm/Support/MathExtras.h"
22 #define convolve(lhs, rhs) ((lhs) * 4 + (rhs))
24 /* Assumed in hexadecimal significand parsing, and conversion to
25 hexadecimal strings. */
26 #define COMPILE_TIME_ASSERT(cond) extern int CTAssert[(cond) ? 1 : -1]
27 COMPILE_TIME_ASSERT(integerPartWidth % 4 == 0);
31 /* Represents floating point arithmetic semantics. */
33 /* The largest E such that 2^E is representable; this matches the
34 definition of IEEE 754. */
35 exponent_t maxExponent;
37 /* The smallest E such that 2^E is a normalized number; this
38 matches the definition of IEEE 754. */
39 exponent_t minExponent;
41 /* Number of bits in the significand. This includes the integer
43 unsigned int precision;
45 /* True if arithmetic is supported. */
46 unsigned int arithmeticOK;
49 const fltSemantics APFloat::IEEEsingle = { 127, -126, 24, true };
50 const fltSemantics APFloat::IEEEdouble = { 1023, -1022, 53, true };
51 const fltSemantics APFloat::IEEEquad = { 16383, -16382, 113, true };
52 const fltSemantics APFloat::x87DoubleExtended = { 16383, -16382, 64, true };
53 const fltSemantics APFloat::Bogus = { 0, 0, 0, true };
55 // The PowerPC format consists of two doubles. It does not map cleanly
56 // onto the usual format above. For now only storage of constants of
57 // this type is supported, no arithmetic.
58 const fltSemantics APFloat::PPCDoubleDouble = { 1023, -1022, 106, false };
60 /* A tight upper bound on number of parts required to hold the value
63 power * 815 / (351 * integerPartWidth) + 1
65 However, whilst the result may require only this many parts,
66 because we are multiplying two values to get it, the
67 multiplication may require an extra part with the excess part
68 being zero (consider the trivial case of 1 * 1, tcFullMultiply
69 requires two parts to hold the single-part result). So we add an
70 extra one to guarantee enough space whilst multiplying. */
71 const unsigned int maxExponent = 16383;
72 const unsigned int maxPrecision = 113;
73 const unsigned int maxPowerOfFiveExponent = maxExponent + maxPrecision - 1;
74 const unsigned int maxPowerOfFiveParts = 2 + ((maxPowerOfFiveExponent * 815)
75 / (351 * integerPartWidth));
78 /* Put a bunch of private, handy routines in an anonymous namespace. */
81 static inline unsigned int
82 partCountForBits(unsigned int bits)
84 return ((bits) + integerPartWidth - 1) / integerPartWidth;
87 /* Returns 0U-9U. Return values >= 10U are not digits. */
88 static inline unsigned int
89 decDigitValue(unsigned int c)
95 hexDigitValue(unsigned int c)
115 assertArithmeticOK(const llvm::fltSemantics &semantics) {
116 assert(semantics.arithmeticOK
117 && "Compile-time arithmetic does not support these semantics");
120 /* Return the value of a decimal exponent of the form
123 If the exponent overflows, returns a large exponent with the
126 readExponent(const char *p)
129 unsigned int absExponent;
130 const unsigned int overlargeExponent = 24000; /* FIXME. */
132 isNegative = (*p == '-');
133 if (*p == '-' || *p == '+')
136 absExponent = decDigitValue(*p++);
137 assert (absExponent < 10U);
142 value = decDigitValue(*p);
147 value += absExponent * 10;
148 if (absExponent >= overlargeExponent) {
149 absExponent = overlargeExponent;
156 return -(int) absExponent;
158 return (int) absExponent;
161 /* This is ugly and needs cleaning up, but I don't immediately see
162 how whilst remaining safe. */
164 totalExponent(const char *p, int exponentAdjustment)
166 int unsignedExponent;
167 bool negative, overflow;
170 /* Move past the exponent letter and sign to the digits. */
172 negative = *p == '-';
173 if(*p == '-' || *p == '+')
176 unsignedExponent = 0;
181 value = decDigitValue(*p);
186 unsignedExponent = unsignedExponent * 10 + value;
187 if(unsignedExponent > 65535)
191 if(exponentAdjustment > 65535 || exponentAdjustment < -65536)
195 exponent = unsignedExponent;
197 exponent = -exponent;
198 exponent += exponentAdjustment;
199 if(exponent > 65535 || exponent < -65536)
204 exponent = negative ? -65536: 65535;
210 skipLeadingZeroesAndAnyDot(const char *p, const char **dot)
225 /* Given a normal decimal floating point number of the form
229 where the decimal point and exponent are optional, fill out the
230 structure D. Exponent is appropriate if the significand is
231 treated as an integer, and normalizedExponent if the significand
232 is taken to have the decimal point after a single leading
235 If the value is zero, V->firstSigDigit points to a non-digit, and
236 the return exponent is zero.
239 const char *firstSigDigit;
240 const char *lastSigDigit;
242 int normalizedExponent;
246 interpretDecimal(const char *p, decimalInfo *D)
250 p = skipLeadingZeroesAndAnyDot (p, &dot);
252 D->firstSigDigit = p;
254 D->normalizedExponent = 0;
261 if (decDigitValue(*p) >= 10U)
266 /* If number is all zerooes accept any exponent. */
267 if (p != D->firstSigDigit) {
268 if (*p == 'e' || *p == 'E')
269 D->exponent = readExponent(p + 1);
271 /* Implied decimal point? */
275 /* Drop insignificant trailing zeroes. */
282 /* Adjust the exponents for any decimal point. */
283 D->exponent += static_cast<exponent_t>((dot - p) - (dot > p));
284 D->normalizedExponent = (D->exponent +
285 static_cast<exponent_t>((p - D->firstSigDigit)
286 - (dot > D->firstSigDigit && dot < p)));
292 /* Return the trailing fraction of a hexadecimal number.
293 DIGITVALUE is the first hex digit of the fraction, P points to
296 trailingHexadecimalFraction(const char *p, unsigned int digitValue)
298 unsigned int hexDigit;
300 /* If the first trailing digit isn't 0 or 8 we can work out the
301 fraction immediately. */
303 return lfMoreThanHalf;
304 else if(digitValue < 8 && digitValue > 0)
305 return lfLessThanHalf;
307 /* Otherwise we need to find the first non-zero digit. */
311 hexDigit = hexDigitValue(*p);
313 /* If we ran off the end it is exactly zero or one-half, otherwise
316 return digitValue == 0 ? lfExactlyZero: lfExactlyHalf;
318 return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf;
321 /* Return the fraction lost were a bignum truncated losing the least
322 significant BITS bits. */
324 lostFractionThroughTruncation(const integerPart *parts,
325 unsigned int partCount,
330 lsb = APInt::tcLSB(parts, partCount);
332 /* Note this is guaranteed true if bits == 0, or LSB == -1U. */
334 return lfExactlyZero;
336 return lfExactlyHalf;
337 if(bits <= partCount * integerPartWidth
338 && APInt::tcExtractBit(parts, bits - 1))
339 return lfMoreThanHalf;
341 return lfLessThanHalf;
344 /* Shift DST right BITS bits noting lost fraction. */
346 shiftRight(integerPart *dst, unsigned int parts, unsigned int bits)
348 lostFraction lost_fraction;
350 lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
352 APInt::tcShiftRight(dst, parts, bits);
354 return lost_fraction;
357 /* Combine the effect of two lost fractions. */
359 combineLostFractions(lostFraction moreSignificant,
360 lostFraction lessSignificant)
362 if(lessSignificant != lfExactlyZero) {
363 if(moreSignificant == lfExactlyZero)
364 moreSignificant = lfLessThanHalf;
365 else if(moreSignificant == lfExactlyHalf)
366 moreSignificant = lfMoreThanHalf;
369 return moreSignificant;
372 /* The error from the true value, in half-ulps, on multiplying two
373 floating point numbers, which differ from the value they
374 approximate by at most HUE1 and HUE2 half-ulps, is strictly less
375 than the returned value.
377 See "How to Read Floating Point Numbers Accurately" by William D
380 HUerrBound(bool inexactMultiply, unsigned int HUerr1, unsigned int HUerr2)
382 assert(HUerr1 < 2 || HUerr2 < 2 || (HUerr1 + HUerr2 < 8));
384 if (HUerr1 + HUerr2 == 0)
385 return inexactMultiply * 2; /* <= inexactMultiply half-ulps. */
387 return inexactMultiply + 2 * (HUerr1 + HUerr2);
390 /* The number of ulps from the boundary (zero, or half if ISNEAREST)
391 when the least significant BITS are truncated. BITS cannot be
394 ulpsFromBoundary(const integerPart *parts, unsigned int bits, bool isNearest)
396 unsigned int count, partBits;
397 integerPart part, boundary;
402 count = bits / integerPartWidth;
403 partBits = bits % integerPartWidth + 1;
405 part = parts[count] & (~(integerPart) 0 >> (integerPartWidth - partBits));
408 boundary = (integerPart) 1 << (partBits - 1);
413 if (part - boundary <= boundary - part)
414 return part - boundary;
416 return boundary - part;
419 if (part == boundary) {
422 return ~(integerPart) 0; /* A lot. */
425 } else if (part == boundary - 1) {
428 return ~(integerPart) 0; /* A lot. */
433 return ~(integerPart) 0; /* A lot. */
436 /* Place pow(5, power) in DST, and return the number of parts used.
437 DST must be at least one part larger than size of the answer. */
439 powerOf5(integerPart *dst, unsigned int power)
441 static const integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125,
443 static integerPart pow5s[maxPowerOfFiveParts * 2 + 5] = { 78125 * 5 };
444 static unsigned int partsCount[16] = { 1 };
446 integerPart scratch[maxPowerOfFiveParts], *p1, *p2, *pow5;
449 assert(power <= maxExponent);
454 *p1 = firstEightPowers[power & 7];
460 for (unsigned int n = 0; power; power >>= 1, n++) {
465 /* Calculate pow(5,pow(2,n+3)) if we haven't yet. */
467 pc = partsCount[n - 1];
468 APInt::tcFullMultiply(pow5, pow5 - pc, pow5 - pc, pc, pc);
470 if (pow5[pc - 1] == 0)
478 APInt::tcFullMultiply(p2, p1, pow5, result, pc);
480 if (p2[result - 1] == 0)
483 /* Now result is in p1 with partsCount parts and p2 is scratch
485 tmp = p1, p1 = p2, p2 = tmp;
492 APInt::tcAssign(dst, p1, result);
497 /* Zero at the end to avoid modular arithmetic when adding one; used
498 when rounding up during hexadecimal output. */
499 static const char hexDigitsLower[] = "0123456789abcdef0";
500 static const char hexDigitsUpper[] = "0123456789ABCDEF0";
501 static const char infinityL[] = "infinity";
502 static const char infinityU[] = "INFINITY";
503 static const char NaNL[] = "nan";
504 static const char NaNU[] = "NAN";
506 /* Write out an integerPart in hexadecimal, starting with the most
507 significant nibble. Write out exactly COUNT hexdigits, return
510 partAsHex (char *dst, integerPart part, unsigned int count,
511 const char *hexDigitChars)
513 unsigned int result = count;
515 assert (count != 0 && count <= integerPartWidth / 4);
517 part >>= (integerPartWidth - 4 * count);
519 dst[count] = hexDigitChars[part & 0xf];
526 /* Write out an unsigned decimal integer. */
528 writeUnsignedDecimal (char *dst, unsigned int n)
544 /* Write out a signed decimal integer. */
546 writeSignedDecimal (char *dst, int value)
550 dst = writeUnsignedDecimal(dst, -(unsigned) value);
552 dst = writeUnsignedDecimal(dst, value);
560 APFloat::initialize(const fltSemantics *ourSemantics)
564 semantics = ourSemantics;
567 significand.parts = new integerPart[count];
571 APFloat::freeSignificand()
574 delete [] significand.parts;
578 APFloat::assign(const APFloat &rhs)
580 assert(semantics == rhs.semantics);
583 category = rhs.category;
584 exponent = rhs.exponent;
586 exponent2 = rhs.exponent2;
587 if(category == fcNormal || category == fcNaN)
588 copySignificand(rhs);
592 APFloat::copySignificand(const APFloat &rhs)
594 assert(category == fcNormal || category == fcNaN);
595 assert(rhs.partCount() >= partCount());
597 APInt::tcAssign(significandParts(), rhs.significandParts(),
601 /* Make this number a NaN, with an arbitrary but deterministic value
602 for the significand. */
604 APFloat::makeNaN(void)
607 APInt::tcSet(significandParts(), ~0U, partCount());
611 APFloat::operator=(const APFloat &rhs)
614 if(semantics != rhs.semantics) {
616 initialize(rhs.semantics);
625 APFloat::bitwiseIsEqual(const APFloat &rhs) const {
628 if (semantics != rhs.semantics ||
629 category != rhs.category ||
632 if (semantics==(const llvm::fltSemantics*)&PPCDoubleDouble &&
635 if (category==fcZero || category==fcInfinity)
637 else if (category==fcNormal && exponent!=rhs.exponent)
639 else if (semantics==(const llvm::fltSemantics*)&PPCDoubleDouble &&
640 exponent2!=rhs.exponent2)
644 const integerPart* p=significandParts();
645 const integerPart* q=rhs.significandParts();
646 for (; i>0; i--, p++, q++) {
654 APFloat::APFloat(const fltSemantics &ourSemantics, integerPart value)
656 assertArithmeticOK(ourSemantics);
657 initialize(&ourSemantics);
660 exponent = ourSemantics.precision - 1;
661 significandParts()[0] = value;
662 normalize(rmNearestTiesToEven, lfExactlyZero);
665 APFloat::APFloat(const fltSemantics &ourSemantics,
666 fltCategory ourCategory, bool negative)
668 assertArithmeticOK(ourSemantics);
669 initialize(&ourSemantics);
670 category = ourCategory;
672 if(category == fcNormal)
674 else if (ourCategory == fcNaN)
678 APFloat::APFloat(const fltSemantics &ourSemantics, const char *text)
680 assertArithmeticOK(ourSemantics);
681 initialize(&ourSemantics);
682 convertFromString(text, rmNearestTiesToEven);
685 APFloat::APFloat(const APFloat &rhs)
687 initialize(rhs.semantics);
696 // Profile - This method 'profiles' an APFloat for use with FoldingSet.
697 void APFloat::Profile(FoldingSetNodeID& ID) const {
698 ID.Add(convertToAPInt());
702 APFloat::partCount() const
704 return partCountForBits(semantics->precision + 1);
708 APFloat::semanticsPrecision(const fltSemantics &semantics)
710 return semantics.precision;
714 APFloat::significandParts() const
716 return const_cast<APFloat *>(this)->significandParts();
720 APFloat::significandParts()
722 assert(category == fcNormal || category == fcNaN);
725 return significand.parts;
727 return &significand.part;
731 APFloat::zeroSignificand()
734 APInt::tcSet(significandParts(), 0, partCount());
737 /* Increment an fcNormal floating point number's significand. */
739 APFloat::incrementSignificand()
743 carry = APInt::tcIncrement(significandParts(), partCount());
745 /* Our callers should never cause us to overflow. */
749 /* Add the significand of the RHS. Returns the carry flag. */
751 APFloat::addSignificand(const APFloat &rhs)
755 parts = significandParts();
757 assert(semantics == rhs.semantics);
758 assert(exponent == rhs.exponent);
760 return APInt::tcAdd(parts, rhs.significandParts(), 0, partCount());
763 /* Subtract the significand of the RHS with a borrow flag. Returns
766 APFloat::subtractSignificand(const APFloat &rhs, integerPart borrow)
770 parts = significandParts();
772 assert(semantics == rhs.semantics);
773 assert(exponent == rhs.exponent);
775 return APInt::tcSubtract(parts, rhs.significandParts(), borrow,
779 /* Multiply the significand of the RHS. If ADDEND is non-NULL, add it
780 on to the full-precision result of the multiplication. Returns the
783 APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
785 unsigned int omsb; // One, not zero, based MSB.
786 unsigned int partsCount, newPartsCount, precision;
787 integerPart *lhsSignificand;
788 integerPart scratch[4];
789 integerPart *fullSignificand;
790 lostFraction lost_fraction;
792 assert(semantics == rhs.semantics);
794 precision = semantics->precision;
795 newPartsCount = partCountForBits(precision * 2);
797 if(newPartsCount > 4)
798 fullSignificand = new integerPart[newPartsCount];
800 fullSignificand = scratch;
802 lhsSignificand = significandParts();
803 partsCount = partCount();
805 APInt::tcFullMultiply(fullSignificand, lhsSignificand,
806 rhs.significandParts(), partsCount, partsCount);
808 lost_fraction = lfExactlyZero;
809 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
810 exponent += rhs.exponent;
813 Significand savedSignificand = significand;
814 const fltSemantics *savedSemantics = semantics;
815 fltSemantics extendedSemantics;
817 unsigned int extendedPrecision;
819 /* Normalize our MSB. */
820 extendedPrecision = precision + precision - 1;
821 if(omsb != extendedPrecision)
823 APInt::tcShiftLeft(fullSignificand, newPartsCount,
824 extendedPrecision - omsb);
825 exponent -= extendedPrecision - omsb;
828 /* Create new semantics. */
829 extendedSemantics = *semantics;
830 extendedSemantics.precision = extendedPrecision;
832 if(newPartsCount == 1)
833 significand.part = fullSignificand[0];
835 significand.parts = fullSignificand;
836 semantics = &extendedSemantics;
838 APFloat extendedAddend(*addend);
839 status = extendedAddend.convert(extendedSemantics, rmTowardZero);
840 assert(status == opOK);
841 lost_fraction = addOrSubtractSignificand(extendedAddend, false);
843 /* Restore our state. */
844 if(newPartsCount == 1)
845 fullSignificand[0] = significand.part;
846 significand = savedSignificand;
847 semantics = savedSemantics;
849 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
852 exponent -= (precision - 1);
854 if(omsb > precision) {
855 unsigned int bits, significantParts;
858 bits = omsb - precision;
859 significantParts = partCountForBits(omsb);
860 lf = shiftRight(fullSignificand, significantParts, bits);
861 lost_fraction = combineLostFractions(lf, lost_fraction);
865 APInt::tcAssign(lhsSignificand, fullSignificand, partsCount);
867 if(newPartsCount > 4)
868 delete [] fullSignificand;
870 return lost_fraction;
873 /* Multiply the significands of LHS and RHS to DST. */
875 APFloat::divideSignificand(const APFloat &rhs)
877 unsigned int bit, i, partsCount;
878 const integerPart *rhsSignificand;
879 integerPart *lhsSignificand, *dividend, *divisor;
880 integerPart scratch[4];
881 lostFraction lost_fraction;
883 assert(semantics == rhs.semantics);
885 lhsSignificand = significandParts();
886 rhsSignificand = rhs.significandParts();
887 partsCount = partCount();
890 dividend = new integerPart[partsCount * 2];
894 divisor = dividend + partsCount;
896 /* Copy the dividend and divisor as they will be modified in-place. */
897 for(i = 0; i < partsCount; i++) {
898 dividend[i] = lhsSignificand[i];
899 divisor[i] = rhsSignificand[i];
900 lhsSignificand[i] = 0;
903 exponent -= rhs.exponent;
905 unsigned int precision = semantics->precision;
907 /* Normalize the divisor. */
908 bit = precision - APInt::tcMSB(divisor, partsCount) - 1;
911 APInt::tcShiftLeft(divisor, partsCount, bit);
914 /* Normalize the dividend. */
915 bit = precision - APInt::tcMSB(dividend, partsCount) - 1;
918 APInt::tcShiftLeft(dividend, partsCount, bit);
921 /* Ensure the dividend >= divisor initially for the loop below.
922 Incidentally, this means that the division loop below is
923 guaranteed to set the integer bit to one. */
924 if(APInt::tcCompare(dividend, divisor, partsCount) < 0) {
926 APInt::tcShiftLeft(dividend, partsCount, 1);
927 assert(APInt::tcCompare(dividend, divisor, partsCount) >= 0);
931 for(bit = precision; bit; bit -= 1) {
932 if(APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
933 APInt::tcSubtract(dividend, divisor, 0, partsCount);
934 APInt::tcSetBit(lhsSignificand, bit - 1);
937 APInt::tcShiftLeft(dividend, partsCount, 1);
940 /* Figure out the lost fraction. */
941 int cmp = APInt::tcCompare(dividend, divisor, partsCount);
944 lost_fraction = lfMoreThanHalf;
946 lost_fraction = lfExactlyHalf;
947 else if(APInt::tcIsZero(dividend, partsCount))
948 lost_fraction = lfExactlyZero;
950 lost_fraction = lfLessThanHalf;
955 return lost_fraction;
959 APFloat::significandMSB() const
961 return APInt::tcMSB(significandParts(), partCount());
965 APFloat::significandLSB() const
967 return APInt::tcLSB(significandParts(), partCount());
970 /* Note that a zero result is NOT normalized to fcZero. */
972 APFloat::shiftSignificandRight(unsigned int bits)
974 /* Our exponent should not overflow. */
975 assert((exponent_t) (exponent + bits) >= exponent);
979 return shiftRight(significandParts(), partCount(), bits);
982 /* Shift the significand left BITS bits, subtract BITS from its exponent. */
984 APFloat::shiftSignificandLeft(unsigned int bits)
986 assert(bits < semantics->precision);
989 unsigned int partsCount = partCount();
991 APInt::tcShiftLeft(significandParts(), partsCount, bits);
994 assert(!APInt::tcIsZero(significandParts(), partsCount));
999 APFloat::compareAbsoluteValue(const APFloat &rhs) const
1003 assert(semantics == rhs.semantics);
1004 assert(category == fcNormal);
1005 assert(rhs.category == fcNormal);
1007 compare = exponent - rhs.exponent;
1009 /* If exponents are equal, do an unsigned bignum comparison of the
1012 compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
1016 return cmpGreaterThan;
1017 else if(compare < 0)
1023 /* Handle overflow. Sign is preserved. We either become infinity or
1024 the largest finite number. */
1026 APFloat::handleOverflow(roundingMode rounding_mode)
1029 if(rounding_mode == rmNearestTiesToEven
1030 || rounding_mode == rmNearestTiesToAway
1031 || (rounding_mode == rmTowardPositive && !sign)
1032 || (rounding_mode == rmTowardNegative && sign))
1034 category = fcInfinity;
1035 return (opStatus) (opOverflow | opInexact);
1038 /* Otherwise we become the largest finite number. */
1039 category = fcNormal;
1040 exponent = semantics->maxExponent;
1041 APInt::tcSetLeastSignificantBits(significandParts(), partCount(),
1042 semantics->precision);
1047 /* Returns TRUE if, when truncating the current number, with BIT the
1048 new LSB, with the given lost fraction and rounding mode, the result
1049 would need to be rounded away from zero (i.e., by increasing the
1050 signficand). This routine must work for fcZero of both signs, and
1051 fcNormal numbers. */
1053 APFloat::roundAwayFromZero(roundingMode rounding_mode,
1054 lostFraction lost_fraction,
1055 unsigned int bit) const
1057 /* NaNs and infinities should not have lost fractions. */
1058 assert(category == fcNormal || category == fcZero);
1060 /* Current callers never pass this so we don't handle it. */
1061 assert(lost_fraction != lfExactlyZero);
1063 switch(rounding_mode) {
1067 case rmNearestTiesToAway:
1068 return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf;
1070 case rmNearestTiesToEven:
1071 if(lost_fraction == lfMoreThanHalf)
1074 /* Our zeroes don't have a significand to test. */
1075 if(lost_fraction == lfExactlyHalf && category != fcZero)
1076 return APInt::tcExtractBit(significandParts(), bit);
1083 case rmTowardPositive:
1084 return sign == false;
1086 case rmTowardNegative:
1087 return sign == true;
1092 APFloat::normalize(roundingMode rounding_mode,
1093 lostFraction lost_fraction)
1095 unsigned int omsb; /* One, not zero, based MSB. */
1098 if(category != fcNormal)
1101 /* Before rounding normalize the exponent of fcNormal numbers. */
1102 omsb = significandMSB() + 1;
1105 /* OMSB is numbered from 1. We want to place it in the integer
1106 bit numbered PRECISON if possible, with a compensating change in
1108 exponentChange = omsb - semantics->precision;
1110 /* If the resulting exponent is too high, overflow according to
1111 the rounding mode. */
1112 if(exponent + exponentChange > semantics->maxExponent)
1113 return handleOverflow(rounding_mode);
1115 /* Subnormal numbers have exponent minExponent, and their MSB
1116 is forced based on that. */
1117 if(exponent + exponentChange < semantics->minExponent)
1118 exponentChange = semantics->minExponent - exponent;
1120 /* Shifting left is easy as we don't lose precision. */
1121 if(exponentChange < 0) {
1122 assert(lost_fraction == lfExactlyZero);
1124 shiftSignificandLeft(-exponentChange);
1129 if(exponentChange > 0) {
1132 /* Shift right and capture any new lost fraction. */
1133 lf = shiftSignificandRight(exponentChange);
1135 lost_fraction = combineLostFractions(lf, lost_fraction);
1137 /* Keep OMSB up-to-date. */
1138 if(omsb > (unsigned) exponentChange)
1139 omsb -= exponentChange;
1145 /* Now round the number according to rounding_mode given the lost
1148 /* As specified in IEEE 754, since we do not trap we do not report
1149 underflow for exact results. */
1150 if(lost_fraction == lfExactlyZero) {
1151 /* Canonicalize zeroes. */
1158 /* Increment the significand if we're rounding away from zero. */
1159 if(roundAwayFromZero(rounding_mode, lost_fraction, 0)) {
1161 exponent = semantics->minExponent;
1163 incrementSignificand();
1164 omsb = significandMSB() + 1;
1166 /* Did the significand increment overflow? */
1167 if(omsb == (unsigned) semantics->precision + 1) {
1168 /* Renormalize by incrementing the exponent and shifting our
1169 significand right one. However if we already have the
1170 maximum exponent we overflow to infinity. */
1171 if(exponent == semantics->maxExponent) {
1172 category = fcInfinity;
1174 return (opStatus) (opOverflow | opInexact);
1177 shiftSignificandRight(1);
1183 /* The normal case - we were and are not denormal, and any
1184 significand increment above didn't overflow. */
1185 if(omsb == semantics->precision)
1188 /* We have a non-zero denormal. */
1189 assert(omsb < semantics->precision);
1191 /* Canonicalize zeroes. */
1195 /* The fcZero case is a denormal that underflowed to zero. */
1196 return (opStatus) (opUnderflow | opInexact);
1200 APFloat::addOrSubtractSpecials(const APFloat &rhs, bool subtract)
1202 switch(convolve(category, rhs.category)) {
1206 case convolve(fcNaN, fcZero):
1207 case convolve(fcNaN, fcNormal):
1208 case convolve(fcNaN, fcInfinity):
1209 case convolve(fcNaN, fcNaN):
1210 case convolve(fcNormal, fcZero):
1211 case convolve(fcInfinity, fcNormal):
1212 case convolve(fcInfinity, fcZero):
1215 case convolve(fcZero, fcNaN):
1216 case convolve(fcNormal, fcNaN):
1217 case convolve(fcInfinity, fcNaN):
1219 copySignificand(rhs);
1222 case convolve(fcNormal, fcInfinity):
1223 case convolve(fcZero, fcInfinity):
1224 category = fcInfinity;
1225 sign = rhs.sign ^ subtract;
1228 case convolve(fcZero, fcNormal):
1230 sign = rhs.sign ^ subtract;
1233 case convolve(fcZero, fcZero):
1234 /* Sign depends on rounding mode; handled by caller. */
1237 case convolve(fcInfinity, fcInfinity):
1238 /* Differently signed infinities can only be validly
1240 if((sign ^ rhs.sign) != subtract) {
1247 case convolve(fcNormal, fcNormal):
1252 /* Add or subtract two normal numbers. */
1254 APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
1257 lostFraction lost_fraction;
1260 /* Determine if the operation on the absolute values is effectively
1261 an addition or subtraction. */
1262 subtract ^= (sign ^ rhs.sign) ? true : false;
1264 /* Are we bigger exponent-wise than the RHS? */
1265 bits = exponent - rhs.exponent;
1267 /* Subtraction is more subtle than one might naively expect. */
1269 APFloat temp_rhs(rhs);
1273 reverse = compareAbsoluteValue(temp_rhs) == cmpLessThan;
1274 lost_fraction = lfExactlyZero;
1275 } else if (bits > 0) {
1276 lost_fraction = temp_rhs.shiftSignificandRight(bits - 1);
1277 shiftSignificandLeft(1);
1280 lost_fraction = shiftSignificandRight(-bits - 1);
1281 temp_rhs.shiftSignificandLeft(1);
1286 carry = temp_rhs.subtractSignificand
1287 (*this, lost_fraction != lfExactlyZero);
1288 copySignificand(temp_rhs);
1291 carry = subtractSignificand
1292 (temp_rhs, lost_fraction != lfExactlyZero);
1295 /* Invert the lost fraction - it was on the RHS and
1297 if(lost_fraction == lfLessThanHalf)
1298 lost_fraction = lfMoreThanHalf;
1299 else if(lost_fraction == lfMoreThanHalf)
1300 lost_fraction = lfLessThanHalf;
1302 /* The code above is intended to ensure that no borrow is
1307 APFloat temp_rhs(rhs);
1309 lost_fraction = temp_rhs.shiftSignificandRight(bits);
1310 carry = addSignificand(temp_rhs);
1312 lost_fraction = shiftSignificandRight(-bits);
1313 carry = addSignificand(rhs);
1316 /* We have a guard bit; generating a carry cannot happen. */
1320 return lost_fraction;
1324 APFloat::multiplySpecials(const APFloat &rhs)
1326 switch(convolve(category, rhs.category)) {
1330 case convolve(fcNaN, fcZero):
1331 case convolve(fcNaN, fcNormal):
1332 case convolve(fcNaN, fcInfinity):
1333 case convolve(fcNaN, fcNaN):
1336 case convolve(fcZero, fcNaN):
1337 case convolve(fcNormal, fcNaN):
1338 case convolve(fcInfinity, fcNaN):
1340 copySignificand(rhs);
1343 case convolve(fcNormal, fcInfinity):
1344 case convolve(fcInfinity, fcNormal):
1345 case convolve(fcInfinity, fcInfinity):
1346 category = fcInfinity;
1349 case convolve(fcZero, fcNormal):
1350 case convolve(fcNormal, fcZero):
1351 case convolve(fcZero, fcZero):
1355 case convolve(fcZero, fcInfinity):
1356 case convolve(fcInfinity, fcZero):
1360 case convolve(fcNormal, fcNormal):
1366 APFloat::divideSpecials(const APFloat &rhs)
1368 switch(convolve(category, rhs.category)) {
1372 case convolve(fcNaN, fcZero):
1373 case convolve(fcNaN, fcNormal):
1374 case convolve(fcNaN, fcInfinity):
1375 case convolve(fcNaN, fcNaN):
1376 case convolve(fcInfinity, fcZero):
1377 case convolve(fcInfinity, fcNormal):
1378 case convolve(fcZero, fcInfinity):
1379 case convolve(fcZero, fcNormal):
1382 case convolve(fcZero, fcNaN):
1383 case convolve(fcNormal, fcNaN):
1384 case convolve(fcInfinity, fcNaN):
1386 copySignificand(rhs);
1389 case convolve(fcNormal, fcInfinity):
1393 case convolve(fcNormal, fcZero):
1394 category = fcInfinity;
1397 case convolve(fcInfinity, fcInfinity):
1398 case convolve(fcZero, fcZero):
1402 case convolve(fcNormal, fcNormal):
1409 APFloat::changeSign()
1411 /* Look mummy, this one's easy. */
1416 APFloat::clearSign()
1418 /* So is this one. */
1423 APFloat::copySign(const APFloat &rhs)
1429 /* Normalized addition or subtraction. */
1431 APFloat::addOrSubtract(const APFloat &rhs, roundingMode rounding_mode,
1436 assertArithmeticOK(*semantics);
1438 fs = addOrSubtractSpecials(rhs, subtract);
1440 /* This return code means it was not a simple case. */
1441 if(fs == opDivByZero) {
1442 lostFraction lost_fraction;
1444 lost_fraction = addOrSubtractSignificand(rhs, subtract);
1445 fs = normalize(rounding_mode, lost_fraction);
1447 /* Can only be zero if we lost no fraction. */
1448 assert(category != fcZero || lost_fraction == lfExactlyZero);
1451 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1452 positive zero unless rounding to minus infinity, except that
1453 adding two like-signed zeroes gives that zero. */
1454 if(category == fcZero) {
1455 if(rhs.category != fcZero || (sign == rhs.sign) == subtract)
1456 sign = (rounding_mode == rmTowardNegative);
1462 /* Normalized addition. */
1464 APFloat::add(const APFloat &rhs, roundingMode rounding_mode)
1466 return addOrSubtract(rhs, rounding_mode, false);
1469 /* Normalized subtraction. */
1471 APFloat::subtract(const APFloat &rhs, roundingMode rounding_mode)
1473 return addOrSubtract(rhs, rounding_mode, true);
1476 /* Normalized multiply. */
1478 APFloat::multiply(const APFloat &rhs, roundingMode rounding_mode)
1482 assertArithmeticOK(*semantics);
1484 fs = multiplySpecials(rhs);
1486 if(category == fcNormal) {
1487 lostFraction lost_fraction = multiplySignificand(rhs, 0);
1488 fs = normalize(rounding_mode, lost_fraction);
1489 if(lost_fraction != lfExactlyZero)
1490 fs = (opStatus) (fs | opInexact);
1496 /* Normalized divide. */
1498 APFloat::divide(const APFloat &rhs, roundingMode rounding_mode)
1502 assertArithmeticOK(*semantics);
1504 fs = divideSpecials(rhs);
1506 if(category == fcNormal) {
1507 lostFraction lost_fraction = divideSignificand(rhs);
1508 fs = normalize(rounding_mode, lost_fraction);
1509 if(lost_fraction != lfExactlyZero)
1510 fs = (opStatus) (fs | opInexact);
1516 /* Normalized remainder. This is not currently doing TRT. */
1518 APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
1522 unsigned int origSign = sign;
1524 assertArithmeticOK(*semantics);
1525 fs = V.divide(rhs, rmNearestTiesToEven);
1526 if (fs == opDivByZero)
1529 int parts = partCount();
1530 integerPart *x = new integerPart[parts];
1531 fs = V.convertToInteger(x, parts * integerPartWidth, true,
1532 rmNearestTiesToEven);
1533 if (fs==opInvalidOp)
1536 fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
1537 rmNearestTiesToEven);
1538 assert(fs==opOK); // should always work
1540 fs = V.multiply(rhs, rounding_mode);
1541 assert(fs==opOK || fs==opInexact); // should not overflow or underflow
1543 fs = subtract(V, rounding_mode);
1544 assert(fs==opOK || fs==opInexact); // likewise
1547 sign = origSign; // IEEE754 requires this
1552 /* Normalized fused-multiply-add. */
1554 APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
1555 const APFloat &addend,
1556 roundingMode rounding_mode)
1560 assertArithmeticOK(*semantics);
1562 /* Post-multiplication sign, before addition. */
1563 sign ^= multiplicand.sign;
1565 /* If and only if all arguments are normal do we need to do an
1566 extended-precision calculation. */
1567 if(category == fcNormal
1568 && multiplicand.category == fcNormal
1569 && addend.category == fcNormal) {
1570 lostFraction lost_fraction;
1572 lost_fraction = multiplySignificand(multiplicand, &addend);
1573 fs = normalize(rounding_mode, lost_fraction);
1574 if(lost_fraction != lfExactlyZero)
1575 fs = (opStatus) (fs | opInexact);
1577 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1578 positive zero unless rounding to minus infinity, except that
1579 adding two like-signed zeroes gives that zero. */
1580 if(category == fcZero && sign != addend.sign)
1581 sign = (rounding_mode == rmTowardNegative);
1583 fs = multiplySpecials(multiplicand);
1585 /* FS can only be opOK or opInvalidOp. There is no more work
1586 to do in the latter case. The IEEE-754R standard says it is
1587 implementation-defined in this case whether, if ADDEND is a
1588 quiet NaN, we raise invalid op; this implementation does so.
1590 If we need to do the addition we can do so with normal
1593 fs = addOrSubtract(addend, rounding_mode, false);
1599 /* Comparison requires normalized numbers. */
1601 APFloat::compare(const APFloat &rhs) const
1605 assertArithmeticOK(*semantics);
1606 assert(semantics == rhs.semantics);
1608 switch(convolve(category, rhs.category)) {
1612 case convolve(fcNaN, fcZero):
1613 case convolve(fcNaN, fcNormal):
1614 case convolve(fcNaN, fcInfinity):
1615 case convolve(fcNaN, fcNaN):
1616 case convolve(fcZero, fcNaN):
1617 case convolve(fcNormal, fcNaN):
1618 case convolve(fcInfinity, fcNaN):
1619 return cmpUnordered;
1621 case convolve(fcInfinity, fcNormal):
1622 case convolve(fcInfinity, fcZero):
1623 case convolve(fcNormal, fcZero):
1627 return cmpGreaterThan;
1629 case convolve(fcNormal, fcInfinity):
1630 case convolve(fcZero, fcInfinity):
1631 case convolve(fcZero, fcNormal):
1633 return cmpGreaterThan;
1637 case convolve(fcInfinity, fcInfinity):
1638 if(sign == rhs.sign)
1643 return cmpGreaterThan;
1645 case convolve(fcZero, fcZero):
1648 case convolve(fcNormal, fcNormal):
1652 /* Two normal numbers. Do they have the same sign? */
1653 if(sign != rhs.sign) {
1655 result = cmpLessThan;
1657 result = cmpGreaterThan;
1659 /* Compare absolute values; invert result if negative. */
1660 result = compareAbsoluteValue(rhs);
1663 if(result == cmpLessThan)
1664 result = cmpGreaterThan;
1665 else if(result == cmpGreaterThan)
1666 result = cmpLessThan;
1674 APFloat::convert(const fltSemantics &toSemantics,
1675 roundingMode rounding_mode)
1677 lostFraction lostFraction;
1678 unsigned int newPartCount, oldPartCount;
1681 assertArithmeticOK(*semantics);
1682 assertArithmeticOK(toSemantics);
1683 lostFraction = lfExactlyZero;
1684 newPartCount = partCountForBits(toSemantics.precision + 1);
1685 oldPartCount = partCount();
1687 /* Handle storage complications. If our new form is wider,
1688 re-allocate our bit pattern into wider storage. If it is
1689 narrower, we ignore the excess parts, but if narrowing to a
1690 single part we need to free the old storage.
1691 Be careful not to reference significandParts for zeroes
1692 and infinities, since it aborts. */
1693 if (newPartCount > oldPartCount) {
1694 integerPart *newParts;
1695 newParts = new integerPart[newPartCount];
1696 APInt::tcSet(newParts, 0, newPartCount);
1697 if (category==fcNormal || category==fcNaN)
1698 APInt::tcAssign(newParts, significandParts(), oldPartCount);
1700 significand.parts = newParts;
1701 } else if (newPartCount < oldPartCount) {
1702 /* Capture any lost fraction through truncation of parts so we get
1703 correct rounding whilst normalizing. */
1704 if (category==fcNormal)
1705 lostFraction = lostFractionThroughTruncation
1706 (significandParts(), oldPartCount, toSemantics.precision);
1707 if (newPartCount == 1) {
1708 integerPart newPart = 0;
1709 if (category==fcNormal || category==fcNaN)
1710 newPart = significandParts()[0];
1712 significand.part = newPart;
1716 if(category == fcNormal) {
1717 /* Re-interpret our bit-pattern. */
1718 exponent += toSemantics.precision - semantics->precision;
1719 semantics = &toSemantics;
1720 fs = normalize(rounding_mode, lostFraction);
1721 } else if (category == fcNaN) {
1722 int shift = toSemantics.precision - semantics->precision;
1723 // Do this now so significandParts gets the right answer
1724 const fltSemantics *oldSemantics = semantics;
1725 semantics = &toSemantics;
1727 // No normalization here, just truncate
1729 APInt::tcShiftLeft(significandParts(), newPartCount, shift);
1730 else if (shift < 0) {
1731 unsigned ushift = -shift;
1732 // We mark this as Inexact if we are losing information. This happens
1733 // if are shifting out something other than 0s, or if the x87 long
1734 // double input did not have its integer bit set (pseudo-NaN), or if the
1735 // x87 long double input did not have its QNan bit set (because the x87
1736 // hardware sets this bit when converting a lower-precision NaN to
1737 // x87 long double).
1738 if (APInt::tcLSB(significandParts(), newPartCount) < ushift)
1740 if (oldSemantics == &APFloat::x87DoubleExtended &&
1741 (!(*significandParts() & 0x8000000000000000ULL) ||
1742 !(*significandParts() & 0x4000000000000000ULL)))
1744 APInt::tcShiftRight(significandParts(), newPartCount, ushift);
1746 // gcc forces the Quiet bit on, which means (float)(double)(float_sNan)
1747 // does not give you back the same bits. This is dubious, and we
1748 // don't currently do it. You're really supposed to get
1749 // an invalid operation signal at runtime, but nobody does that.
1751 semantics = &toSemantics;
1758 /* Convert a floating point number to an integer according to the
1759 rounding mode. If the rounded integer value is out of range this
1760 returns an invalid operation exception and the contents of the
1761 destination parts are unspecified. If the rounded value is in
1762 range but the floating point number is not the exact integer, the C
1763 standard doesn't require an inexact exception to be raised. IEEE
1764 854 does require it so we do that.
1766 Note that for conversions to integer type the C standard requires
1767 round-to-zero to always be used. */
1769 APFloat::convertToSignExtendedInteger(integerPart *parts, unsigned int width,
1771 roundingMode rounding_mode) const
1773 lostFraction lost_fraction;
1774 const integerPart *src;
1775 unsigned int dstPartsCount, truncatedBits;
1777 assertArithmeticOK(*semantics);
1779 /* Handle the three special cases first. */
1780 if(category == fcInfinity || category == fcNaN)
1783 dstPartsCount = partCountForBits(width);
1785 if(category == fcZero) {
1786 APInt::tcSet(parts, 0, dstPartsCount);
1790 src = significandParts();
1792 /* Step 1: place our absolute value, with any fraction truncated, in
1795 /* Our absolute value is less than one; truncate everything. */
1796 APInt::tcSet(parts, 0, dstPartsCount);
1797 truncatedBits = semantics->precision;
1799 /* We want the most significant (exponent + 1) bits; the rest are
1801 unsigned int bits = exponent + 1U;
1803 /* Hopelessly large in magnitude? */
1807 if (bits < semantics->precision) {
1808 /* We truncate (semantics->precision - bits) bits. */
1809 truncatedBits = semantics->precision - bits;
1810 APInt::tcExtract(parts, dstPartsCount, src, bits, truncatedBits);
1812 /* We want at least as many bits as are available. */
1813 APInt::tcExtract(parts, dstPartsCount, src, semantics->precision, 0);
1814 APInt::tcShiftLeft(parts, dstPartsCount, bits - semantics->precision);
1819 /* Step 2: work out any lost fraction, and increment the absolute
1820 value if we would round away from zero. */
1821 if (truncatedBits) {
1822 lost_fraction = lostFractionThroughTruncation(src, partCount(),
1824 if (lost_fraction != lfExactlyZero
1825 && roundAwayFromZero(rounding_mode, lost_fraction, truncatedBits)) {
1826 if (APInt::tcIncrement(parts, dstPartsCount))
1827 return opInvalidOp; /* Overflow. */
1830 lost_fraction = lfExactlyZero;
1833 /* Step 3: check if we fit in the destination. */
1834 unsigned int omsb = APInt::tcMSB(parts, dstPartsCount) + 1;
1838 /* Negative numbers cannot be represented as unsigned. */
1842 /* It takes omsb bits to represent the unsigned integer value.
1843 We lose a bit for the sign, but care is needed as the
1844 maximally negative integer is a special case. */
1845 if (omsb == width && APInt::tcLSB(parts, dstPartsCount) + 1 != omsb)
1848 /* This case can happen because of rounding. */
1853 APInt::tcNegate (parts, dstPartsCount);
1855 if (omsb >= width + !isSigned)
1859 if (lost_fraction == lfExactlyZero)
1865 /* Same as convertToSignExtendedInteger, except we provide
1866 deterministic values in case of an invalid operation exception,
1867 namely zero for NaNs and the minimal or maximal value respectively
1868 for underflow or overflow. */
1870 APFloat::convertToInteger(integerPart *parts, unsigned int width,
1872 roundingMode rounding_mode) const
1876 fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode);
1878 if (fs == opInvalidOp) {
1879 unsigned int bits, dstPartsCount;
1881 dstPartsCount = partCountForBits(width);
1883 if (category == fcNaN)
1888 bits = width - isSigned;
1890 APInt::tcSetLeastSignificantBits(parts, dstPartsCount, bits);
1891 if (sign && isSigned)
1892 APInt::tcShiftLeft(parts, dstPartsCount, width - 1);
1898 /* Convert an unsigned integer SRC to a floating point number,
1899 rounding according to ROUNDING_MODE. The sign of the floating
1900 point number is not modified. */
1902 APFloat::convertFromUnsignedParts(const integerPart *src,
1903 unsigned int srcCount,
1904 roundingMode rounding_mode)
1906 unsigned int omsb, precision, dstCount;
1908 lostFraction lost_fraction;
1910 assertArithmeticOK(*semantics);
1911 category = fcNormal;
1912 omsb = APInt::tcMSB(src, srcCount) + 1;
1913 dst = significandParts();
1914 dstCount = partCount();
1915 precision = semantics->precision;
1917 /* We want the most significant PRECISON bits of SRC. There may not
1918 be that many; extract what we can. */
1919 if (precision <= omsb) {
1920 exponent = omsb - 1;
1921 lost_fraction = lostFractionThroughTruncation(src, srcCount,
1923 APInt::tcExtract(dst, dstCount, src, precision, omsb - precision);
1925 exponent = precision - 1;
1926 lost_fraction = lfExactlyZero;
1927 APInt::tcExtract(dst, dstCount, src, omsb, 0);
1930 return normalize(rounding_mode, lost_fraction);
1934 APFloat::convertFromAPInt(const APInt &Val,
1936 roundingMode rounding_mode)
1938 unsigned int partCount = Val.getNumWords();
1942 if (isSigned && api.isNegative()) {
1947 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
1950 /* Convert a two's complement integer SRC to a floating point number,
1951 rounding according to ROUNDING_MODE. ISSIGNED is true if the
1952 integer is signed, in which case it must be sign-extended. */
1954 APFloat::convertFromSignExtendedInteger(const integerPart *src,
1955 unsigned int srcCount,
1957 roundingMode rounding_mode)
1961 assertArithmeticOK(*semantics);
1963 && APInt::tcExtractBit(src, srcCount * integerPartWidth - 1)) {
1966 /* If we're signed and negative negate a copy. */
1968 copy = new integerPart[srcCount];
1969 APInt::tcAssign(copy, src, srcCount);
1970 APInt::tcNegate(copy, srcCount);
1971 status = convertFromUnsignedParts(copy, srcCount, rounding_mode);
1975 status = convertFromUnsignedParts(src, srcCount, rounding_mode);
1981 /* FIXME: should this just take a const APInt reference? */
1983 APFloat::convertFromZeroExtendedInteger(const integerPart *parts,
1984 unsigned int width, bool isSigned,
1985 roundingMode rounding_mode)
1987 unsigned int partCount = partCountForBits(width);
1988 APInt api = APInt(width, partCount, parts);
1991 if(isSigned && APInt::tcExtractBit(parts, width - 1)) {
1996 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
2000 APFloat::convertFromHexadecimalString(const char *p,
2001 roundingMode rounding_mode)
2003 lostFraction lost_fraction;
2004 integerPart *significand;
2005 unsigned int bitPos, partsCount;
2006 const char *dot, *firstSignificantDigit;
2010 category = fcNormal;
2012 significand = significandParts();
2013 partsCount = partCount();
2014 bitPos = partsCount * integerPartWidth;
2016 /* Skip leading zeroes and any (hexa)decimal point. */
2017 p = skipLeadingZeroesAndAnyDot(p, &dot);
2018 firstSignificantDigit = p;
2021 integerPart hex_value;
2028 hex_value = hexDigitValue(*p);
2029 if(hex_value == -1U) {
2030 lost_fraction = lfExactlyZero;
2036 /* Store the number whilst 4-bit nibbles remain. */
2039 hex_value <<= bitPos % integerPartWidth;
2040 significand[bitPos / integerPartWidth] |= hex_value;
2042 lost_fraction = trailingHexadecimalFraction(p, hex_value);
2043 while(hexDigitValue(*p) != -1U)
2049 /* Hex floats require an exponent but not a hexadecimal point. */
2050 assert(*p == 'p' || *p == 'P');
2052 /* Ignore the exponent if we are zero. */
2053 if(p != firstSignificantDigit) {
2056 /* Implicit hexadecimal point? */
2060 /* Calculate the exponent adjustment implicit in the number of
2061 significant digits. */
2062 expAdjustment = static_cast<int>(dot - firstSignificantDigit);
2063 if(expAdjustment < 0)
2065 expAdjustment = expAdjustment * 4 - 1;
2067 /* Adjust for writing the significand starting at the most
2068 significant nibble. */
2069 expAdjustment += semantics->precision;
2070 expAdjustment -= partsCount * integerPartWidth;
2072 /* Adjust for the given exponent. */
2073 exponent = totalExponent(p, expAdjustment);
2076 return normalize(rounding_mode, lost_fraction);
2080 APFloat::roundSignificandWithExponent(const integerPart *decSigParts,
2081 unsigned sigPartCount, int exp,
2082 roundingMode rounding_mode)
2084 unsigned int parts, pow5PartCount;
2085 fltSemantics calcSemantics = { 32767, -32767, 0, true };
2086 integerPart pow5Parts[maxPowerOfFiveParts];
2089 isNearest = (rounding_mode == rmNearestTiesToEven
2090 || rounding_mode == rmNearestTiesToAway);
2092 parts = partCountForBits(semantics->precision + 11);
2094 /* Calculate pow(5, abs(exp)). */
2095 pow5PartCount = powerOf5(pow5Parts, exp >= 0 ? exp: -exp);
2097 for (;; parts *= 2) {
2098 opStatus sigStatus, powStatus;
2099 unsigned int excessPrecision, truncatedBits;
2101 calcSemantics.precision = parts * integerPartWidth - 1;
2102 excessPrecision = calcSemantics.precision - semantics->precision;
2103 truncatedBits = excessPrecision;
2105 APFloat decSig(calcSemantics, fcZero, sign);
2106 APFloat pow5(calcSemantics, fcZero, false);
2108 sigStatus = decSig.convertFromUnsignedParts(decSigParts, sigPartCount,
2109 rmNearestTiesToEven);
2110 powStatus = pow5.convertFromUnsignedParts(pow5Parts, pow5PartCount,
2111 rmNearestTiesToEven);
2112 /* Add exp, as 10^n = 5^n * 2^n. */
2113 decSig.exponent += exp;
2115 lostFraction calcLostFraction;
2116 integerPart HUerr, HUdistance;
2117 unsigned int powHUerr;
2120 /* multiplySignificand leaves the precision-th bit set to 1. */
2121 calcLostFraction = decSig.multiplySignificand(pow5, NULL);
2122 powHUerr = powStatus != opOK;
2124 calcLostFraction = decSig.divideSignificand(pow5);
2125 /* Denormal numbers have less precision. */
2126 if (decSig.exponent < semantics->minExponent) {
2127 excessPrecision += (semantics->minExponent - decSig.exponent);
2128 truncatedBits = excessPrecision;
2129 if (excessPrecision > calcSemantics.precision)
2130 excessPrecision = calcSemantics.precision;
2132 /* Extra half-ulp lost in reciprocal of exponent. */
2133 powHUerr = (powStatus == opOK && calcLostFraction == lfExactlyZero) ? 0:2;
2136 /* Both multiplySignificand and divideSignificand return the
2137 result with the integer bit set. */
2138 assert (APInt::tcExtractBit
2139 (decSig.significandParts(), calcSemantics.precision - 1) == 1);
2141 HUerr = HUerrBound(calcLostFraction != lfExactlyZero, sigStatus != opOK,
2143 HUdistance = 2 * ulpsFromBoundary(decSig.significandParts(),
2144 excessPrecision, isNearest);
2146 /* Are we guaranteed to round correctly if we truncate? */
2147 if (HUdistance >= HUerr) {
2148 APInt::tcExtract(significandParts(), partCount(), decSig.significandParts(),
2149 calcSemantics.precision - excessPrecision,
2151 /* Take the exponent of decSig. If we tcExtract-ed less bits
2152 above we must adjust our exponent to compensate for the
2153 implicit right shift. */
2154 exponent = (decSig.exponent + semantics->precision
2155 - (calcSemantics.precision - excessPrecision));
2156 calcLostFraction = lostFractionThroughTruncation(decSig.significandParts(),
2159 return normalize(rounding_mode, calcLostFraction);
2165 APFloat::convertFromDecimalString(const char *p, roundingMode rounding_mode)
2170 /* Scan the text. */
2171 interpretDecimal(p, &D);
2173 /* Handle the quick cases. First the case of no significant digits,
2174 i.e. zero, and then exponents that are obviously too large or too
2175 small. Writing L for log 10 / log 2, a number d.ddddd*10^exp
2176 definitely overflows if
2178 (exp - 1) * L >= maxExponent
2180 and definitely underflows to zero where
2182 (exp + 1) * L <= minExponent - precision
2184 With integer arithmetic the tightest bounds for L are
2186 93/28 < L < 196/59 [ numerator <= 256 ]
2187 42039/12655 < L < 28738/8651 [ numerator <= 65536 ]
2190 if (decDigitValue(*D.firstSigDigit) >= 10U) {
2193 } else if ((D.normalizedExponent + 1) * 28738
2194 <= 8651 * (semantics->minExponent - (int) semantics->precision)) {
2195 /* Underflow to zero and round. */
2197 fs = normalize(rounding_mode, lfLessThanHalf);
2198 } else if ((D.normalizedExponent - 1) * 42039
2199 >= 12655 * semantics->maxExponent) {
2200 /* Overflow and round. */
2201 fs = handleOverflow(rounding_mode);
2203 integerPart *decSignificand;
2204 unsigned int partCount;
2206 /* A tight upper bound on number of bits required to hold an
2207 N-digit decimal integer is N * 196 / 59. Allocate enough space
2208 to hold the full significand, and an extra part required by
2210 partCount = static_cast<unsigned int>(D.lastSigDigit - D.firstSigDigit) + 1;
2211 partCount = partCountForBits(1 + 196 * partCount / 59);
2212 decSignificand = new integerPart[partCount + 1];
2215 /* Convert to binary efficiently - we do almost all multiplication
2216 in an integerPart. When this would overflow do we do a single
2217 bignum multiplication, and then revert again to multiplication
2218 in an integerPart. */
2220 integerPart decValue, val, multiplier;
2229 decValue = decDigitValue(*p++);
2231 val = val * 10 + decValue;
2232 /* The maximum number that can be multiplied by ten with any
2233 digit added without overflowing an integerPart. */
2234 } while (p <= D.lastSigDigit && multiplier <= (~ (integerPart) 0 - 9) / 10);
2236 /* Multiply out the current part. */
2237 APInt::tcMultiplyPart(decSignificand, decSignificand, multiplier, val,
2238 partCount, partCount + 1, false);
2240 /* If we used another part (likely but not guaranteed), increase
2242 if (decSignificand[partCount])
2244 } while (p <= D.lastSigDigit);
2246 category = fcNormal;
2247 fs = roundSignificandWithExponent(decSignificand, partCount,
2248 D.exponent, rounding_mode);
2250 delete [] decSignificand;
2257 APFloat::convertFromString(const char *p, roundingMode rounding_mode)
2259 assertArithmeticOK(*semantics);
2261 /* Handle a leading minus sign. */
2267 if(p[0] == '0' && (p[1] == 'x' || p[1] == 'X'))
2268 return convertFromHexadecimalString(p + 2, rounding_mode);
2270 return convertFromDecimalString(p, rounding_mode);
2273 /* Write out a hexadecimal representation of the floating point value
2274 to DST, which must be of sufficient size, in the C99 form
2275 [-]0xh.hhhhp[+-]d. Return the number of characters written,
2276 excluding the terminating NUL.
2278 If UPPERCASE, the output is in upper case, otherwise in lower case.
2280 HEXDIGITS digits appear altogether, rounding the value if
2281 necessary. If HEXDIGITS is 0, the minimal precision to display the
2282 number precisely is used instead. If nothing would appear after
2283 the decimal point it is suppressed.
2285 The decimal exponent is always printed and has at least one digit.
2286 Zero values display an exponent of zero. Infinities and NaNs
2287 appear as "infinity" or "nan" respectively.
2289 The above rules are as specified by C99. There is ambiguity about
2290 what the leading hexadecimal digit should be. This implementation
2291 uses whatever is necessary so that the exponent is displayed as
2292 stored. This implies the exponent will fall within the IEEE format
2293 range, and the leading hexadecimal digit will be 0 (for denormals),
2294 1 (normal numbers) or 2 (normal numbers rounded-away-from-zero with
2295 any other digits zero).
2298 APFloat::convertToHexString(char *dst, unsigned int hexDigits,
2299 bool upperCase, roundingMode rounding_mode) const
2303 assertArithmeticOK(*semantics);
2311 memcpy (dst, upperCase ? infinityU: infinityL, sizeof infinityU - 1);
2312 dst += sizeof infinityL - 1;
2316 memcpy (dst, upperCase ? NaNU: NaNL, sizeof NaNU - 1);
2317 dst += sizeof NaNU - 1;
2322 *dst++ = upperCase ? 'X': 'x';
2324 if (hexDigits > 1) {
2326 memset (dst, '0', hexDigits - 1);
2327 dst += hexDigits - 1;
2329 *dst++ = upperCase ? 'P': 'p';
2334 dst = convertNormalToHexString (dst, hexDigits, upperCase, rounding_mode);
2340 return static_cast<unsigned int>(dst - p);
2343 /* Does the hard work of outputting the correctly rounded hexadecimal
2344 form of a normal floating point number with the specified number of
2345 hexadecimal digits. If HEXDIGITS is zero the minimum number of
2346 digits necessary to print the value precisely is output. */
2348 APFloat::convertNormalToHexString(char *dst, unsigned int hexDigits,
2350 roundingMode rounding_mode) const
2352 unsigned int count, valueBits, shift, partsCount, outputDigits;
2353 const char *hexDigitChars;
2354 const integerPart *significand;
2359 *dst++ = upperCase ? 'X': 'x';
2362 hexDigitChars = upperCase ? hexDigitsUpper: hexDigitsLower;
2364 significand = significandParts();
2365 partsCount = partCount();
2367 /* +3 because the first digit only uses the single integer bit, so
2368 we have 3 virtual zero most-significant-bits. */
2369 valueBits = semantics->precision + 3;
2370 shift = integerPartWidth - valueBits % integerPartWidth;
2372 /* The natural number of digits required ignoring trailing
2373 insignificant zeroes. */
2374 outputDigits = (valueBits - significandLSB () + 3) / 4;
2376 /* hexDigits of zero means use the required number for the
2377 precision. Otherwise, see if we are truncating. If we are,
2378 find out if we need to round away from zero. */
2380 if (hexDigits < outputDigits) {
2381 /* We are dropping non-zero bits, so need to check how to round.
2382 "bits" is the number of dropped bits. */
2384 lostFraction fraction;
2386 bits = valueBits - hexDigits * 4;
2387 fraction = lostFractionThroughTruncation (significand, partsCount, bits);
2388 roundUp = roundAwayFromZero(rounding_mode, fraction, bits);
2390 outputDigits = hexDigits;
2393 /* Write the digits consecutively, and start writing in the location
2394 of the hexadecimal point. We move the most significant digit
2395 left and add the hexadecimal point later. */
2398 count = (valueBits + integerPartWidth - 1) / integerPartWidth;
2400 while (outputDigits && count) {
2403 /* Put the most significant integerPartWidth bits in "part". */
2404 if (--count == partsCount)
2405 part = 0; /* An imaginary higher zero part. */
2407 part = significand[count] << shift;
2410 part |= significand[count - 1] >> (integerPartWidth - shift);
2412 /* Convert as much of "part" to hexdigits as we can. */
2413 unsigned int curDigits = integerPartWidth / 4;
2415 if (curDigits > outputDigits)
2416 curDigits = outputDigits;
2417 dst += partAsHex (dst, part, curDigits, hexDigitChars);
2418 outputDigits -= curDigits;
2424 /* Note that hexDigitChars has a trailing '0'. */
2427 *q = hexDigitChars[hexDigitValue (*q) + 1];
2428 } while (*q == '0');
2431 /* Add trailing zeroes. */
2432 memset (dst, '0', outputDigits);
2433 dst += outputDigits;
2436 /* Move the most significant digit to before the point, and if there
2437 is something after the decimal point add it. This must come
2438 after rounding above. */
2445 /* Finally output the exponent. */
2446 *dst++ = upperCase ? 'P': 'p';
2448 return writeSignedDecimal (dst, exponent);
2451 // For good performance it is desirable for different APFloats
2452 // to produce different integers.
2454 APFloat::getHashValue() const
2456 if (category==fcZero) return sign<<8 | semantics->precision ;
2457 else if (category==fcInfinity) return sign<<9 | semantics->precision;
2458 else if (category==fcNaN) return 1<<10 | semantics->precision;
2460 uint32_t hash = sign<<11 | semantics->precision | exponent<<12;
2461 const integerPart* p = significandParts();
2462 for (int i=partCount(); i>0; i--, p++)
2463 hash ^= ((uint32_t)*p) ^ (uint32_t)((*p)>>32);
2468 // Conversion from APFloat to/from host float/double. It may eventually be
2469 // possible to eliminate these and have everybody deal with APFloats, but that
2470 // will take a while. This approach will not easily extend to long double.
2471 // Current implementation requires integerPartWidth==64, which is correct at
2472 // the moment but could be made more general.
2474 // Denormals have exponent minExponent in APFloat, but minExponent-1 in
2475 // the actual IEEE respresentations. We compensate for that here.
2478 APFloat::convertF80LongDoubleAPFloatToAPInt() const
2480 assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended);
2481 assert (partCount()==2);
2483 uint64_t myexponent, mysignificand;
2485 if (category==fcNormal) {
2486 myexponent = exponent+16383; //bias
2487 mysignificand = significandParts()[0];
2488 if (myexponent==1 && !(mysignificand & 0x8000000000000000ULL))
2489 myexponent = 0; // denormal
2490 } else if (category==fcZero) {
2493 } else if (category==fcInfinity) {
2494 myexponent = 0x7fff;
2495 mysignificand = 0x8000000000000000ULL;
2497 assert(category == fcNaN && "Unknown category");
2498 myexponent = 0x7fff;
2499 mysignificand = significandParts()[0];
2503 words[0] = ((uint64_t)(sign & 1) << 63) |
2504 ((myexponent & 0x7fffLL) << 48) |
2505 ((mysignificand >>16) & 0xffffffffffffLL);
2506 words[1] = mysignificand & 0xffff;
2507 return APInt(80, 2, words);
2511 APFloat::convertPPCDoubleDoubleAPFloatToAPInt() const
2513 assert(semantics == (const llvm::fltSemantics*)&PPCDoubleDouble);
2514 assert (partCount()==2);
2516 uint64_t myexponent, mysignificand, myexponent2, mysignificand2;
2518 if (category==fcNormal) {
2519 myexponent = exponent + 1023; //bias
2520 myexponent2 = exponent2 + 1023;
2521 mysignificand = significandParts()[0];
2522 mysignificand2 = significandParts()[1];
2523 if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
2524 myexponent = 0; // denormal
2525 if (myexponent2==1 && !(mysignificand2 & 0x10000000000000LL))
2526 myexponent2 = 0; // denormal
2527 } else if (category==fcZero) {
2532 } else if (category==fcInfinity) {
2538 assert(category == fcNaN && "Unknown category");
2540 mysignificand = significandParts()[0];
2541 myexponent2 = exponent2;
2542 mysignificand2 = significandParts()[1];
2546 words[0] = ((uint64_t)(sign & 1) << 63) |
2547 ((myexponent & 0x7ff) << 52) |
2548 (mysignificand & 0xfffffffffffffLL);
2549 words[1] = ((uint64_t)(sign2 & 1) << 63) |
2550 ((myexponent2 & 0x7ff) << 52) |
2551 (mysignificand2 & 0xfffffffffffffLL);
2552 return APInt(128, 2, words);
2556 APFloat::convertDoubleAPFloatToAPInt() const
2558 assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
2559 assert (partCount()==1);
2561 uint64_t myexponent, mysignificand;
2563 if (category==fcNormal) {
2564 myexponent = exponent+1023; //bias
2565 mysignificand = *significandParts();
2566 if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
2567 myexponent = 0; // denormal
2568 } else if (category==fcZero) {
2571 } else if (category==fcInfinity) {
2575 assert(category == fcNaN && "Unknown category!");
2577 mysignificand = *significandParts();
2580 return APInt(64, ((((uint64_t)(sign & 1) << 63) |
2581 ((myexponent & 0x7ff) << 52) |
2582 (mysignificand & 0xfffffffffffffLL))));
2586 APFloat::convertFloatAPFloatToAPInt() const
2588 assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
2589 assert (partCount()==1);
2591 uint32_t myexponent, mysignificand;
2593 if (category==fcNormal) {
2594 myexponent = exponent+127; //bias
2595 mysignificand = (uint32_t)*significandParts();
2596 if (myexponent == 1 && !(mysignificand & 0x800000))
2597 myexponent = 0; // denormal
2598 } else if (category==fcZero) {
2601 } else if (category==fcInfinity) {
2605 assert(category == fcNaN && "Unknown category!");
2607 mysignificand = (uint32_t)*significandParts();
2610 return APInt(32, (((sign&1) << 31) | ((myexponent&0xff) << 23) |
2611 (mysignificand & 0x7fffff)));
2614 // This function creates an APInt that is just a bit map of the floating
2615 // point constant as it would appear in memory. It is not a conversion,
2616 // and treating the result as a normal integer is unlikely to be useful.
2619 APFloat::convertToAPInt() const
2621 if (semantics == (const llvm::fltSemantics*)&IEEEsingle)
2622 return convertFloatAPFloatToAPInt();
2624 if (semantics == (const llvm::fltSemantics*)&IEEEdouble)
2625 return convertDoubleAPFloatToAPInt();
2627 if (semantics == (const llvm::fltSemantics*)&PPCDoubleDouble)
2628 return convertPPCDoubleDoubleAPFloatToAPInt();
2630 assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended &&
2632 return convertF80LongDoubleAPFloatToAPInt();
2636 APFloat::convertToFloat() const
2638 assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
2639 APInt api = convertToAPInt();
2640 return api.bitsToFloat();
2644 APFloat::convertToDouble() const
2646 assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
2647 APInt api = convertToAPInt();
2648 return api.bitsToDouble();
2651 /// Integer bit is explicit in this format. Intel hardware (387 and later)
2652 /// does not support these bit patterns:
2653 /// exponent = all 1's, integer bit 0, significand 0 ("pseudoinfinity")
2654 /// exponent = all 1's, integer bit 0, significand nonzero ("pseudoNaN")
2655 /// exponent = 0, integer bit 1 ("pseudodenormal")
2656 /// exponent!=0 nor all 1's, integer bit 0 ("unnormal")
2657 /// At the moment, the first two are treated as NaNs, the second two as Normal.
2659 APFloat::initFromF80LongDoubleAPInt(const APInt &api)
2661 assert(api.getBitWidth()==80);
2662 uint64_t i1 = api.getRawData()[0];
2663 uint64_t i2 = api.getRawData()[1];
2664 uint64_t myexponent = (i1 >> 48) & 0x7fff;
2665 uint64_t mysignificand = ((i1 << 16) & 0xffffffffffff0000ULL) |
2668 initialize(&APFloat::x87DoubleExtended);
2669 assert(partCount()==2);
2671 sign = static_cast<unsigned int>(i1>>63);
2672 if (myexponent==0 && mysignificand==0) {
2673 // exponent, significand meaningless
2675 } else if (myexponent==0x7fff && mysignificand==0x8000000000000000ULL) {
2676 // exponent, significand meaningless
2677 category = fcInfinity;
2678 } else if (myexponent==0x7fff && mysignificand!=0x8000000000000000ULL) {
2679 // exponent meaningless
2681 significandParts()[0] = mysignificand;
2682 significandParts()[1] = 0;
2684 category = fcNormal;
2685 exponent = myexponent - 16383;
2686 significandParts()[0] = mysignificand;
2687 significandParts()[1] = 0;
2688 if (myexponent==0) // denormal
2694 APFloat::initFromPPCDoubleDoubleAPInt(const APInt &api)
2696 assert(api.getBitWidth()==128);
2697 uint64_t i1 = api.getRawData()[0];
2698 uint64_t i2 = api.getRawData()[1];
2699 uint64_t myexponent = (i1 >> 52) & 0x7ff;
2700 uint64_t mysignificand = i1 & 0xfffffffffffffLL;
2701 uint64_t myexponent2 = (i2 >> 52) & 0x7ff;
2702 uint64_t mysignificand2 = i2 & 0xfffffffffffffLL;
2704 initialize(&APFloat::PPCDoubleDouble);
2705 assert(partCount()==2);
2707 sign = static_cast<unsigned int>(i1>>63);
2708 sign2 = static_cast<unsigned int>(i2>>63);
2709 if (myexponent==0 && mysignificand==0) {
2710 // exponent, significand meaningless
2711 // exponent2 and significand2 are required to be 0; we don't check
2713 } else if (myexponent==0x7ff && mysignificand==0) {
2714 // exponent, significand meaningless
2715 // exponent2 and significand2 are required to be 0; we don't check
2716 category = fcInfinity;
2717 } else if (myexponent==0x7ff && mysignificand!=0) {
2718 // exponent meaningless. So is the whole second word, but keep it
2721 exponent2 = myexponent2;
2722 significandParts()[0] = mysignificand;
2723 significandParts()[1] = mysignificand2;
2725 category = fcNormal;
2726 // Note there is no category2; the second word is treated as if it is
2727 // fcNormal, although it might be something else considered by itself.
2728 exponent = myexponent - 1023;
2729 exponent2 = myexponent2 - 1023;
2730 significandParts()[0] = mysignificand;
2731 significandParts()[1] = mysignificand2;
2732 if (myexponent==0) // denormal
2735 significandParts()[0] |= 0x10000000000000LL; // integer bit
2739 significandParts()[1] |= 0x10000000000000LL; // integer bit
2744 APFloat::initFromDoubleAPInt(const APInt &api)
2746 assert(api.getBitWidth()==64);
2747 uint64_t i = *api.getRawData();
2748 uint64_t myexponent = (i >> 52) & 0x7ff;
2749 uint64_t mysignificand = i & 0xfffffffffffffLL;
2751 initialize(&APFloat::IEEEdouble);
2752 assert(partCount()==1);
2754 sign = static_cast<unsigned int>(i>>63);
2755 if (myexponent==0 && mysignificand==0) {
2756 // exponent, significand meaningless
2758 } else if (myexponent==0x7ff && mysignificand==0) {
2759 // exponent, significand meaningless
2760 category = fcInfinity;
2761 } else if (myexponent==0x7ff && mysignificand!=0) {
2762 // exponent meaningless
2764 *significandParts() = mysignificand;
2766 category = fcNormal;
2767 exponent = myexponent - 1023;
2768 *significandParts() = mysignificand;
2769 if (myexponent==0) // denormal
2772 *significandParts() |= 0x10000000000000LL; // integer bit
2777 APFloat::initFromFloatAPInt(const APInt & api)
2779 assert(api.getBitWidth()==32);
2780 uint32_t i = (uint32_t)*api.getRawData();
2781 uint32_t myexponent = (i >> 23) & 0xff;
2782 uint32_t mysignificand = i & 0x7fffff;
2784 initialize(&APFloat::IEEEsingle);
2785 assert(partCount()==1);
2788 if (myexponent==0 && mysignificand==0) {
2789 // exponent, significand meaningless
2791 } else if (myexponent==0xff && mysignificand==0) {
2792 // exponent, significand meaningless
2793 category = fcInfinity;
2794 } else if (myexponent==0xff && mysignificand!=0) {
2795 // sign, exponent, significand meaningless
2797 *significandParts() = mysignificand;
2799 category = fcNormal;
2800 exponent = myexponent - 127; //bias
2801 *significandParts() = mysignificand;
2802 if (myexponent==0) // denormal
2805 *significandParts() |= 0x800000; // integer bit
2809 /// Treat api as containing the bits of a floating point number. Currently
2810 /// we infer the floating point type from the size of the APInt. The
2811 /// isIEEE argument distinguishes between PPC128 and IEEE128 (not meaningful
2812 /// when the size is anything else).
2814 APFloat::initFromAPInt(const APInt& api, bool isIEEE)
2816 if (api.getBitWidth() == 32)
2817 return initFromFloatAPInt(api);
2818 else if (api.getBitWidth()==64)
2819 return initFromDoubleAPInt(api);
2820 else if (api.getBitWidth()==80)
2821 return initFromF80LongDoubleAPInt(api);
2822 else if (api.getBitWidth()==128 && !isIEEE)
2823 return initFromPPCDoubleDoubleAPInt(api);
2828 APFloat::APFloat(const APInt& api, bool isIEEE)
2830 initFromAPInt(api, isIEEE);
2833 APFloat::APFloat(float f)
2835 APInt api = APInt(32, 0);
2836 initFromAPInt(api.floatToBits(f));
2839 APFloat::APFloat(double d)
2841 APInt api = APInt(64, 0);
2842 initFromAPInt(api.doubleToBits(d));