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(bitcastToAPInt());
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;
793 assert(semantics == rhs.semantics);
795 precision = semantics->precision;
796 newPartsCount = partCountForBits(precision * 2);
798 if(newPartsCount > 4)
799 fullSignificand = new integerPart[newPartsCount];
801 fullSignificand = scratch;
803 lhsSignificand = significandParts();
804 partsCount = partCount();
806 APInt::tcFullMultiply(fullSignificand, lhsSignificand,
807 rhs.significandParts(), partsCount, partsCount);
809 lost_fraction = lfExactlyZero;
810 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
811 exponent += rhs.exponent;
814 Significand savedSignificand = significand;
815 const fltSemantics *savedSemantics = semantics;
816 fltSemantics extendedSemantics;
818 unsigned int extendedPrecision;
820 /* Normalize our MSB. */
821 extendedPrecision = precision + precision - 1;
822 if(omsb != extendedPrecision)
824 APInt::tcShiftLeft(fullSignificand, newPartsCount,
825 extendedPrecision - omsb);
826 exponent -= extendedPrecision - omsb;
829 /* Create new semantics. */
830 extendedSemantics = *semantics;
831 extendedSemantics.precision = extendedPrecision;
833 if(newPartsCount == 1)
834 significand.part = fullSignificand[0];
836 significand.parts = fullSignificand;
837 semantics = &extendedSemantics;
839 APFloat extendedAddend(*addend);
840 status = extendedAddend.convert(extendedSemantics, rmTowardZero, &ignored);
841 assert(status == opOK);
842 lost_fraction = addOrSubtractSignificand(extendedAddend, false);
844 /* Restore our state. */
845 if(newPartsCount == 1)
846 fullSignificand[0] = significand.part;
847 significand = savedSignificand;
848 semantics = savedSemantics;
850 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
853 exponent -= (precision - 1);
855 if(omsb > precision) {
856 unsigned int bits, significantParts;
859 bits = omsb - precision;
860 significantParts = partCountForBits(omsb);
861 lf = shiftRight(fullSignificand, significantParts, bits);
862 lost_fraction = combineLostFractions(lf, lost_fraction);
866 APInt::tcAssign(lhsSignificand, fullSignificand, partsCount);
868 if(newPartsCount > 4)
869 delete [] fullSignificand;
871 return lost_fraction;
874 /* Multiply the significands of LHS and RHS to DST. */
876 APFloat::divideSignificand(const APFloat &rhs)
878 unsigned int bit, i, partsCount;
879 const integerPart *rhsSignificand;
880 integerPart *lhsSignificand, *dividend, *divisor;
881 integerPart scratch[4];
882 lostFraction lost_fraction;
884 assert(semantics == rhs.semantics);
886 lhsSignificand = significandParts();
887 rhsSignificand = rhs.significandParts();
888 partsCount = partCount();
891 dividend = new integerPart[partsCount * 2];
895 divisor = dividend + partsCount;
897 /* Copy the dividend and divisor as they will be modified in-place. */
898 for(i = 0; i < partsCount; i++) {
899 dividend[i] = lhsSignificand[i];
900 divisor[i] = rhsSignificand[i];
901 lhsSignificand[i] = 0;
904 exponent -= rhs.exponent;
906 unsigned int precision = semantics->precision;
908 /* Normalize the divisor. */
909 bit = precision - APInt::tcMSB(divisor, partsCount) - 1;
912 APInt::tcShiftLeft(divisor, partsCount, bit);
915 /* Normalize the dividend. */
916 bit = precision - APInt::tcMSB(dividend, partsCount) - 1;
919 APInt::tcShiftLeft(dividend, partsCount, bit);
922 /* Ensure the dividend >= divisor initially for the loop below.
923 Incidentally, this means that the division loop below is
924 guaranteed to set the integer bit to one. */
925 if(APInt::tcCompare(dividend, divisor, partsCount) < 0) {
927 APInt::tcShiftLeft(dividend, partsCount, 1);
928 assert(APInt::tcCompare(dividend, divisor, partsCount) >= 0);
932 for(bit = precision; bit; bit -= 1) {
933 if(APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
934 APInt::tcSubtract(dividend, divisor, 0, partsCount);
935 APInt::tcSetBit(lhsSignificand, bit - 1);
938 APInt::tcShiftLeft(dividend, partsCount, 1);
941 /* Figure out the lost fraction. */
942 int cmp = APInt::tcCompare(dividend, divisor, partsCount);
945 lost_fraction = lfMoreThanHalf;
947 lost_fraction = lfExactlyHalf;
948 else if(APInt::tcIsZero(dividend, partsCount))
949 lost_fraction = lfExactlyZero;
951 lost_fraction = lfLessThanHalf;
956 return lost_fraction;
960 APFloat::significandMSB() const
962 return APInt::tcMSB(significandParts(), partCount());
966 APFloat::significandLSB() const
968 return APInt::tcLSB(significandParts(), partCount());
971 /* Note that a zero result is NOT normalized to fcZero. */
973 APFloat::shiftSignificandRight(unsigned int bits)
975 /* Our exponent should not overflow. */
976 assert((exponent_t) (exponent + bits) >= exponent);
980 return shiftRight(significandParts(), partCount(), bits);
983 /* Shift the significand left BITS bits, subtract BITS from its exponent. */
985 APFloat::shiftSignificandLeft(unsigned int bits)
987 assert(bits < semantics->precision);
990 unsigned int partsCount = partCount();
992 APInt::tcShiftLeft(significandParts(), partsCount, bits);
995 assert(!APInt::tcIsZero(significandParts(), partsCount));
1000 APFloat::compareAbsoluteValue(const APFloat &rhs) const
1004 assert(semantics == rhs.semantics);
1005 assert(category == fcNormal);
1006 assert(rhs.category == fcNormal);
1008 compare = exponent - rhs.exponent;
1010 /* If exponents are equal, do an unsigned bignum comparison of the
1013 compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
1017 return cmpGreaterThan;
1018 else if(compare < 0)
1024 /* Handle overflow. Sign is preserved. We either become infinity or
1025 the largest finite number. */
1027 APFloat::handleOverflow(roundingMode rounding_mode)
1030 if(rounding_mode == rmNearestTiesToEven
1031 || rounding_mode == rmNearestTiesToAway
1032 || (rounding_mode == rmTowardPositive && !sign)
1033 || (rounding_mode == rmTowardNegative && sign))
1035 category = fcInfinity;
1036 return (opStatus) (opOverflow | opInexact);
1039 /* Otherwise we become the largest finite number. */
1040 category = fcNormal;
1041 exponent = semantics->maxExponent;
1042 APInt::tcSetLeastSignificantBits(significandParts(), partCount(),
1043 semantics->precision);
1048 /* Returns TRUE if, when truncating the current number, with BIT the
1049 new LSB, with the given lost fraction and rounding mode, the result
1050 would need to be rounded away from zero (i.e., by increasing the
1051 signficand). This routine must work for fcZero of both signs, and
1052 fcNormal numbers. */
1054 APFloat::roundAwayFromZero(roundingMode rounding_mode,
1055 lostFraction lost_fraction,
1056 unsigned int bit) const
1058 /* NaNs and infinities should not have lost fractions. */
1059 assert(category == fcNormal || category == fcZero);
1061 /* Current callers never pass this so we don't handle it. */
1062 assert(lost_fraction != lfExactlyZero);
1064 switch(rounding_mode) {
1068 case rmNearestTiesToAway:
1069 return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf;
1071 case rmNearestTiesToEven:
1072 if(lost_fraction == lfMoreThanHalf)
1075 /* Our zeroes don't have a significand to test. */
1076 if(lost_fraction == lfExactlyHalf && category != fcZero)
1077 return APInt::tcExtractBit(significandParts(), bit);
1084 case rmTowardPositive:
1085 return sign == false;
1087 case rmTowardNegative:
1088 return sign == true;
1093 APFloat::normalize(roundingMode rounding_mode,
1094 lostFraction lost_fraction)
1096 unsigned int omsb; /* One, not zero, based MSB. */
1099 if(category != fcNormal)
1102 /* Before rounding normalize the exponent of fcNormal numbers. */
1103 omsb = significandMSB() + 1;
1106 /* OMSB is numbered from 1. We want to place it in the integer
1107 bit numbered PRECISON if possible, with a compensating change in
1109 exponentChange = omsb - semantics->precision;
1111 /* If the resulting exponent is too high, overflow according to
1112 the rounding mode. */
1113 if(exponent + exponentChange > semantics->maxExponent)
1114 return handleOverflow(rounding_mode);
1116 /* Subnormal numbers have exponent minExponent, and their MSB
1117 is forced based on that. */
1118 if(exponent + exponentChange < semantics->minExponent)
1119 exponentChange = semantics->minExponent - exponent;
1121 /* Shifting left is easy as we don't lose precision. */
1122 if(exponentChange < 0) {
1123 assert(lost_fraction == lfExactlyZero);
1125 shiftSignificandLeft(-exponentChange);
1130 if(exponentChange > 0) {
1133 /* Shift right and capture any new lost fraction. */
1134 lf = shiftSignificandRight(exponentChange);
1136 lost_fraction = combineLostFractions(lf, lost_fraction);
1138 /* Keep OMSB up-to-date. */
1139 if(omsb > (unsigned) exponentChange)
1140 omsb -= exponentChange;
1146 /* Now round the number according to rounding_mode given the lost
1149 /* As specified in IEEE 754, since we do not trap we do not report
1150 underflow for exact results. */
1151 if(lost_fraction == lfExactlyZero) {
1152 /* Canonicalize zeroes. */
1159 /* Increment the significand if we're rounding away from zero. */
1160 if(roundAwayFromZero(rounding_mode, lost_fraction, 0)) {
1162 exponent = semantics->minExponent;
1164 incrementSignificand();
1165 omsb = significandMSB() + 1;
1167 /* Did the significand increment overflow? */
1168 if(omsb == (unsigned) semantics->precision + 1) {
1169 /* Renormalize by incrementing the exponent and shifting our
1170 significand right one. However if we already have the
1171 maximum exponent we overflow to infinity. */
1172 if(exponent == semantics->maxExponent) {
1173 category = fcInfinity;
1175 return (opStatus) (opOverflow | opInexact);
1178 shiftSignificandRight(1);
1184 /* The normal case - we were and are not denormal, and any
1185 significand increment above didn't overflow. */
1186 if(omsb == semantics->precision)
1189 /* We have a non-zero denormal. */
1190 assert(omsb < semantics->precision);
1192 /* Canonicalize zeroes. */
1196 /* The fcZero case is a denormal that underflowed to zero. */
1197 return (opStatus) (opUnderflow | opInexact);
1201 APFloat::addOrSubtractSpecials(const APFloat &rhs, bool subtract)
1203 switch(convolve(category, rhs.category)) {
1207 case convolve(fcNaN, fcZero):
1208 case convolve(fcNaN, fcNormal):
1209 case convolve(fcNaN, fcInfinity):
1210 case convolve(fcNaN, fcNaN):
1211 case convolve(fcNormal, fcZero):
1212 case convolve(fcInfinity, fcNormal):
1213 case convolve(fcInfinity, fcZero):
1216 case convolve(fcZero, fcNaN):
1217 case convolve(fcNormal, fcNaN):
1218 case convolve(fcInfinity, fcNaN):
1220 copySignificand(rhs);
1223 case convolve(fcNormal, fcInfinity):
1224 case convolve(fcZero, fcInfinity):
1225 category = fcInfinity;
1226 sign = rhs.sign ^ subtract;
1229 case convolve(fcZero, fcNormal):
1231 sign = rhs.sign ^ subtract;
1234 case convolve(fcZero, fcZero):
1235 /* Sign depends on rounding mode; handled by caller. */
1238 case convolve(fcInfinity, fcInfinity):
1239 /* Differently signed infinities can only be validly
1241 if((sign ^ rhs.sign) != subtract) {
1248 case convolve(fcNormal, fcNormal):
1253 /* Add or subtract two normal numbers. */
1255 APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
1258 lostFraction lost_fraction;
1261 /* Determine if the operation on the absolute values is effectively
1262 an addition or subtraction. */
1263 subtract ^= (sign ^ rhs.sign) ? true : false;
1265 /* Are we bigger exponent-wise than the RHS? */
1266 bits = exponent - rhs.exponent;
1268 /* Subtraction is more subtle than one might naively expect. */
1270 APFloat temp_rhs(rhs);
1274 reverse = compareAbsoluteValue(temp_rhs) == cmpLessThan;
1275 lost_fraction = lfExactlyZero;
1276 } else if (bits > 0) {
1277 lost_fraction = temp_rhs.shiftSignificandRight(bits - 1);
1278 shiftSignificandLeft(1);
1281 lost_fraction = shiftSignificandRight(-bits - 1);
1282 temp_rhs.shiftSignificandLeft(1);
1287 carry = temp_rhs.subtractSignificand
1288 (*this, lost_fraction != lfExactlyZero);
1289 copySignificand(temp_rhs);
1292 carry = subtractSignificand
1293 (temp_rhs, lost_fraction != lfExactlyZero);
1296 /* Invert the lost fraction - it was on the RHS and
1298 if(lost_fraction == lfLessThanHalf)
1299 lost_fraction = lfMoreThanHalf;
1300 else if(lost_fraction == lfMoreThanHalf)
1301 lost_fraction = lfLessThanHalf;
1303 /* The code above is intended to ensure that no borrow is
1308 APFloat temp_rhs(rhs);
1310 lost_fraction = temp_rhs.shiftSignificandRight(bits);
1311 carry = addSignificand(temp_rhs);
1313 lost_fraction = shiftSignificandRight(-bits);
1314 carry = addSignificand(rhs);
1317 /* We have a guard bit; generating a carry cannot happen. */
1321 return lost_fraction;
1325 APFloat::multiplySpecials(const APFloat &rhs)
1327 switch(convolve(category, rhs.category)) {
1331 case convolve(fcNaN, fcZero):
1332 case convolve(fcNaN, fcNormal):
1333 case convolve(fcNaN, fcInfinity):
1334 case convolve(fcNaN, fcNaN):
1337 case convolve(fcZero, fcNaN):
1338 case convolve(fcNormal, fcNaN):
1339 case convolve(fcInfinity, fcNaN):
1341 copySignificand(rhs);
1344 case convolve(fcNormal, fcInfinity):
1345 case convolve(fcInfinity, fcNormal):
1346 case convolve(fcInfinity, fcInfinity):
1347 category = fcInfinity;
1350 case convolve(fcZero, fcNormal):
1351 case convolve(fcNormal, fcZero):
1352 case convolve(fcZero, fcZero):
1356 case convolve(fcZero, fcInfinity):
1357 case convolve(fcInfinity, fcZero):
1361 case convolve(fcNormal, fcNormal):
1367 APFloat::divideSpecials(const APFloat &rhs)
1369 switch(convolve(category, rhs.category)) {
1373 case convolve(fcNaN, fcZero):
1374 case convolve(fcNaN, fcNormal):
1375 case convolve(fcNaN, fcInfinity):
1376 case convolve(fcNaN, fcNaN):
1377 case convolve(fcInfinity, fcZero):
1378 case convolve(fcInfinity, fcNormal):
1379 case convolve(fcZero, fcInfinity):
1380 case convolve(fcZero, fcNormal):
1383 case convolve(fcZero, fcNaN):
1384 case convolve(fcNormal, fcNaN):
1385 case convolve(fcInfinity, fcNaN):
1387 copySignificand(rhs);
1390 case convolve(fcNormal, fcInfinity):
1394 case convolve(fcNormal, fcZero):
1395 category = fcInfinity;
1398 case convolve(fcInfinity, fcInfinity):
1399 case convolve(fcZero, fcZero):
1403 case convolve(fcNormal, fcNormal):
1410 APFloat::changeSign()
1412 /* Look mummy, this one's easy. */
1417 APFloat::clearSign()
1419 /* So is this one. */
1424 APFloat::copySign(const APFloat &rhs)
1430 /* Normalized addition or subtraction. */
1432 APFloat::addOrSubtract(const APFloat &rhs, roundingMode rounding_mode,
1437 assertArithmeticOK(*semantics);
1439 fs = addOrSubtractSpecials(rhs, subtract);
1441 /* This return code means it was not a simple case. */
1442 if(fs == opDivByZero) {
1443 lostFraction lost_fraction;
1445 lost_fraction = addOrSubtractSignificand(rhs, subtract);
1446 fs = normalize(rounding_mode, lost_fraction);
1448 /* Can only be zero if we lost no fraction. */
1449 assert(category != fcZero || lost_fraction == lfExactlyZero);
1452 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1453 positive zero unless rounding to minus infinity, except that
1454 adding two like-signed zeroes gives that zero. */
1455 if(category == fcZero) {
1456 if(rhs.category != fcZero || (sign == rhs.sign) == subtract)
1457 sign = (rounding_mode == rmTowardNegative);
1463 /* Normalized addition. */
1465 APFloat::add(const APFloat &rhs, roundingMode rounding_mode)
1467 return addOrSubtract(rhs, rounding_mode, false);
1470 /* Normalized subtraction. */
1472 APFloat::subtract(const APFloat &rhs, roundingMode rounding_mode)
1474 return addOrSubtract(rhs, rounding_mode, true);
1477 /* Normalized multiply. */
1479 APFloat::multiply(const APFloat &rhs, roundingMode rounding_mode)
1483 assertArithmeticOK(*semantics);
1485 fs = multiplySpecials(rhs);
1487 if(category == fcNormal) {
1488 lostFraction lost_fraction = multiplySignificand(rhs, 0);
1489 fs = normalize(rounding_mode, lost_fraction);
1490 if(lost_fraction != lfExactlyZero)
1491 fs = (opStatus) (fs | opInexact);
1497 /* Normalized divide. */
1499 APFloat::divide(const APFloat &rhs, roundingMode rounding_mode)
1503 assertArithmeticOK(*semantics);
1505 fs = divideSpecials(rhs);
1507 if(category == fcNormal) {
1508 lostFraction lost_fraction = divideSignificand(rhs);
1509 fs = normalize(rounding_mode, lost_fraction);
1510 if(lost_fraction != lfExactlyZero)
1511 fs = (opStatus) (fs | opInexact);
1517 /* Normalized remainder. This is not currently correct in all cases. */
1519 APFloat::remainder(const APFloat &rhs)
1523 unsigned int origSign = sign;
1525 assertArithmeticOK(*semantics);
1526 fs = V.divide(rhs, rmNearestTiesToEven);
1527 if (fs == opDivByZero)
1530 int parts = partCount();
1531 integerPart *x = new integerPart[parts];
1533 fs = V.convertToInteger(x, parts * integerPartWidth, true,
1534 rmNearestTiesToEven, &ignored);
1535 if (fs==opInvalidOp)
1538 fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
1539 rmNearestTiesToEven);
1540 assert(fs==opOK); // should always work
1542 fs = V.multiply(rhs, rmNearestTiesToEven);
1543 assert(fs==opOK || fs==opInexact); // should not overflow or underflow
1545 fs = subtract(V, rmNearestTiesToEven);
1546 assert(fs==opOK || fs==opInexact); // likewise
1549 sign = origSign; // IEEE754 requires this
1554 /* Normalized llvm frem (C fmod).
1555 This is not currently correct in all cases. */
1557 APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
1561 unsigned int origSign = sign;
1563 assertArithmeticOK(*semantics);
1564 fs = V.divide(rhs, rmNearestTiesToEven);
1565 if (fs == opDivByZero)
1568 int parts = partCount();
1569 integerPart *x = new integerPart[parts];
1571 fs = V.convertToInteger(x, parts * integerPartWidth, true,
1572 rmTowardZero, &ignored);
1573 if (fs==opInvalidOp)
1576 fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
1577 rmNearestTiesToEven);
1578 assert(fs==opOK); // should always work
1580 fs = V.multiply(rhs, rounding_mode);
1581 assert(fs==opOK || fs==opInexact); // should not overflow or underflow
1583 fs = subtract(V, rounding_mode);
1584 assert(fs==opOK || fs==opInexact); // likewise
1587 sign = origSign; // IEEE754 requires this
1592 /* Normalized fused-multiply-add. */
1594 APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
1595 const APFloat &addend,
1596 roundingMode rounding_mode)
1600 assertArithmeticOK(*semantics);
1602 /* Post-multiplication sign, before addition. */
1603 sign ^= multiplicand.sign;
1605 /* If and only if all arguments are normal do we need to do an
1606 extended-precision calculation. */
1607 if(category == fcNormal
1608 && multiplicand.category == fcNormal
1609 && addend.category == fcNormal) {
1610 lostFraction lost_fraction;
1612 lost_fraction = multiplySignificand(multiplicand, &addend);
1613 fs = normalize(rounding_mode, lost_fraction);
1614 if(lost_fraction != lfExactlyZero)
1615 fs = (opStatus) (fs | opInexact);
1617 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1618 positive zero unless rounding to minus infinity, except that
1619 adding two like-signed zeroes gives that zero. */
1620 if(category == fcZero && sign != addend.sign)
1621 sign = (rounding_mode == rmTowardNegative);
1623 fs = multiplySpecials(multiplicand);
1625 /* FS can only be opOK or opInvalidOp. There is no more work
1626 to do in the latter case. The IEEE-754R standard says it is
1627 implementation-defined in this case whether, if ADDEND is a
1628 quiet NaN, we raise invalid op; this implementation does so.
1630 If we need to do the addition we can do so with normal
1633 fs = addOrSubtract(addend, rounding_mode, false);
1639 /* Comparison requires normalized numbers. */
1641 APFloat::compare(const APFloat &rhs) const
1645 assertArithmeticOK(*semantics);
1646 assert(semantics == rhs.semantics);
1648 switch(convolve(category, rhs.category)) {
1652 case convolve(fcNaN, fcZero):
1653 case convolve(fcNaN, fcNormal):
1654 case convolve(fcNaN, fcInfinity):
1655 case convolve(fcNaN, fcNaN):
1656 case convolve(fcZero, fcNaN):
1657 case convolve(fcNormal, fcNaN):
1658 case convolve(fcInfinity, fcNaN):
1659 return cmpUnordered;
1661 case convolve(fcInfinity, fcNormal):
1662 case convolve(fcInfinity, fcZero):
1663 case convolve(fcNormal, fcZero):
1667 return cmpGreaterThan;
1669 case convolve(fcNormal, fcInfinity):
1670 case convolve(fcZero, fcInfinity):
1671 case convolve(fcZero, fcNormal):
1673 return cmpGreaterThan;
1677 case convolve(fcInfinity, fcInfinity):
1678 if(sign == rhs.sign)
1683 return cmpGreaterThan;
1685 case convolve(fcZero, fcZero):
1688 case convolve(fcNormal, fcNormal):
1692 /* Two normal numbers. Do they have the same sign? */
1693 if(sign != rhs.sign) {
1695 result = cmpLessThan;
1697 result = cmpGreaterThan;
1699 /* Compare absolute values; invert result if negative. */
1700 result = compareAbsoluteValue(rhs);
1703 if(result == cmpLessThan)
1704 result = cmpGreaterThan;
1705 else if(result == cmpGreaterThan)
1706 result = cmpLessThan;
1713 /// APFloat::convert - convert a value of one floating point type to another.
1714 /// The return value corresponds to the IEEE754 exceptions. *losesInfo
1715 /// records whether the transformation lost information, i.e. whether
1716 /// converting the result back to the original type will produce the
1717 /// original value (this is almost the same as return value==fsOK, but there
1718 /// are edge cases where this is not so).
1721 APFloat::convert(const fltSemantics &toSemantics,
1722 roundingMode rounding_mode, bool *losesInfo)
1724 lostFraction lostFraction;
1725 unsigned int newPartCount, oldPartCount;
1728 assertArithmeticOK(*semantics);
1729 assertArithmeticOK(toSemantics);
1730 lostFraction = lfExactlyZero;
1731 newPartCount = partCountForBits(toSemantics.precision + 1);
1732 oldPartCount = partCount();
1734 /* Handle storage complications. If our new form is wider,
1735 re-allocate our bit pattern into wider storage. If it is
1736 narrower, we ignore the excess parts, but if narrowing to a
1737 single part we need to free the old storage.
1738 Be careful not to reference significandParts for zeroes
1739 and infinities, since it aborts. */
1740 if (newPartCount > oldPartCount) {
1741 integerPart *newParts;
1742 newParts = new integerPart[newPartCount];
1743 APInt::tcSet(newParts, 0, newPartCount);
1744 if (category==fcNormal || category==fcNaN)
1745 APInt::tcAssign(newParts, significandParts(), oldPartCount);
1747 significand.parts = newParts;
1748 } else if (newPartCount < oldPartCount) {
1749 /* Capture any lost fraction through truncation of parts so we get
1750 correct rounding whilst normalizing. */
1751 if (category==fcNormal)
1752 lostFraction = lostFractionThroughTruncation
1753 (significandParts(), oldPartCount, toSemantics.precision);
1754 if (newPartCount == 1) {
1755 integerPart newPart = 0;
1756 if (category==fcNormal || category==fcNaN)
1757 newPart = significandParts()[0];
1759 significand.part = newPart;
1763 if(category == fcNormal) {
1764 /* Re-interpret our bit-pattern. */
1765 exponent += toSemantics.precision - semantics->precision;
1766 semantics = &toSemantics;
1767 fs = normalize(rounding_mode, lostFraction);
1768 *losesInfo = (fs != opOK);
1769 } else if (category == fcNaN) {
1770 int shift = toSemantics.precision - semantics->precision;
1771 // Do this now so significandParts gets the right answer
1772 const fltSemantics *oldSemantics = semantics;
1773 semantics = &toSemantics;
1775 // No normalization here, just truncate
1777 APInt::tcShiftLeft(significandParts(), newPartCount, shift);
1778 else if (shift < 0) {
1779 unsigned ushift = -shift;
1780 // Figure out if we are losing information. This happens
1781 // if are shifting out something other than 0s, or if the x87 long
1782 // double input did not have its integer bit set (pseudo-NaN), or if the
1783 // x87 long double input did not have its QNan bit set (because the x87
1784 // hardware sets this bit when converting a lower-precision NaN to
1785 // x87 long double).
1786 if (APInt::tcLSB(significandParts(), newPartCount) < ushift)
1788 if (oldSemantics == &APFloat::x87DoubleExtended &&
1789 (!(*significandParts() & 0x8000000000000000ULL) ||
1790 !(*significandParts() & 0x4000000000000000ULL)))
1792 APInt::tcShiftRight(significandParts(), newPartCount, ushift);
1794 // gcc forces the Quiet bit on, which means (float)(double)(float_sNan)
1795 // does not give you back the same bits. This is dubious, and we
1796 // don't currently do it. You're really supposed to get
1797 // an invalid operation signal at runtime, but nobody does that.
1800 semantics = &toSemantics;
1808 /* Convert a floating point number to an integer according to the
1809 rounding mode. If the rounded integer value is out of range this
1810 returns an invalid operation exception and the contents of the
1811 destination parts are unspecified. If the rounded value is in
1812 range but the floating point number is not the exact integer, the C
1813 standard doesn't require an inexact exception to be raised. IEEE
1814 854 does require it so we do that.
1816 Note that for conversions to integer type the C standard requires
1817 round-to-zero to always be used. */
1819 APFloat::convertToSignExtendedInteger(integerPart *parts, unsigned int width,
1821 roundingMode rounding_mode,
1822 bool *isExact) const
1824 lostFraction lost_fraction;
1825 const integerPart *src;
1826 unsigned int dstPartsCount, truncatedBits;
1828 assertArithmeticOK(*semantics);
1832 /* Handle the three special cases first. */
1833 if(category == fcInfinity || category == fcNaN)
1836 dstPartsCount = partCountForBits(width);
1838 if(category == fcZero) {
1839 APInt::tcSet(parts, 0, dstPartsCount);
1840 // Negative zero can't be represented as an int.
1845 src = significandParts();
1847 /* Step 1: place our absolute value, with any fraction truncated, in
1850 /* Our absolute value is less than one; truncate everything. */
1851 APInt::tcSet(parts, 0, dstPartsCount);
1852 /* For exponent -1 the integer bit represents .5, look at that.
1853 For smaller exponents leftmost truncated bit is 0. */
1854 truncatedBits = semantics->precision -1U - exponent;
1856 /* We want the most significant (exponent + 1) bits; the rest are
1858 unsigned int bits = exponent + 1U;
1860 /* Hopelessly large in magnitude? */
1864 if (bits < semantics->precision) {
1865 /* We truncate (semantics->precision - bits) bits. */
1866 truncatedBits = semantics->precision - bits;
1867 APInt::tcExtract(parts, dstPartsCount, src, bits, truncatedBits);
1869 /* We want at least as many bits as are available. */
1870 APInt::tcExtract(parts, dstPartsCount, src, semantics->precision, 0);
1871 APInt::tcShiftLeft(parts, dstPartsCount, bits - semantics->precision);
1876 /* Step 2: work out any lost fraction, and increment the absolute
1877 value if we would round away from zero. */
1878 if (truncatedBits) {
1879 lost_fraction = lostFractionThroughTruncation(src, partCount(),
1881 if (lost_fraction != lfExactlyZero
1882 && roundAwayFromZero(rounding_mode, lost_fraction, truncatedBits)) {
1883 if (APInt::tcIncrement(parts, dstPartsCount))
1884 return opInvalidOp; /* Overflow. */
1887 lost_fraction = lfExactlyZero;
1890 /* Step 3: check if we fit in the destination. */
1891 unsigned int omsb = APInt::tcMSB(parts, dstPartsCount) + 1;
1895 /* Negative numbers cannot be represented as unsigned. */
1899 /* It takes omsb bits to represent the unsigned integer value.
1900 We lose a bit for the sign, but care is needed as the
1901 maximally negative integer is a special case. */
1902 if (omsb == width && APInt::tcLSB(parts, dstPartsCount) + 1 != omsb)
1905 /* This case can happen because of rounding. */
1910 APInt::tcNegate (parts, dstPartsCount);
1912 if (omsb >= width + !isSigned)
1916 if (lost_fraction == lfExactlyZero) {
1923 /* Same as convertToSignExtendedInteger, except we provide
1924 deterministic values in case of an invalid operation exception,
1925 namely zero for NaNs and the minimal or maximal value respectively
1926 for underflow or overflow.
1927 The *isExact output tells whether the result is exact, in the sense
1928 that converting it back to the original floating point type produces
1929 the original value. This is almost equivalent to result==opOK,
1930 except for negative zeroes.
1933 APFloat::convertToInteger(integerPart *parts, unsigned int width,
1935 roundingMode rounding_mode, bool *isExact) const
1939 fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode,
1942 if (fs == opInvalidOp) {
1943 unsigned int bits, dstPartsCount;
1945 dstPartsCount = partCountForBits(width);
1947 if (category == fcNaN)
1952 bits = width - isSigned;
1954 APInt::tcSetLeastSignificantBits(parts, dstPartsCount, bits);
1955 if (sign && isSigned)
1956 APInt::tcShiftLeft(parts, dstPartsCount, width - 1);
1962 /* Convert an unsigned integer SRC to a floating point number,
1963 rounding according to ROUNDING_MODE. The sign of the floating
1964 point number is not modified. */
1966 APFloat::convertFromUnsignedParts(const integerPart *src,
1967 unsigned int srcCount,
1968 roundingMode rounding_mode)
1970 unsigned int omsb, precision, dstCount;
1972 lostFraction lost_fraction;
1974 assertArithmeticOK(*semantics);
1975 category = fcNormal;
1976 omsb = APInt::tcMSB(src, srcCount) + 1;
1977 dst = significandParts();
1978 dstCount = partCount();
1979 precision = semantics->precision;
1981 /* We want the most significant PRECISON bits of SRC. There may not
1982 be that many; extract what we can. */
1983 if (precision <= omsb) {
1984 exponent = omsb - 1;
1985 lost_fraction = lostFractionThroughTruncation(src, srcCount,
1987 APInt::tcExtract(dst, dstCount, src, precision, omsb - precision);
1989 exponent = precision - 1;
1990 lost_fraction = lfExactlyZero;
1991 APInt::tcExtract(dst, dstCount, src, omsb, 0);
1994 return normalize(rounding_mode, lost_fraction);
1998 APFloat::convertFromAPInt(const APInt &Val,
2000 roundingMode rounding_mode)
2002 unsigned int partCount = Val.getNumWords();
2006 if (isSigned && api.isNegative()) {
2011 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
2014 /* Convert a two's complement integer SRC to a floating point number,
2015 rounding according to ROUNDING_MODE. ISSIGNED is true if the
2016 integer is signed, in which case it must be sign-extended. */
2018 APFloat::convertFromSignExtendedInteger(const integerPart *src,
2019 unsigned int srcCount,
2021 roundingMode rounding_mode)
2025 assertArithmeticOK(*semantics);
2027 && APInt::tcExtractBit(src, srcCount * integerPartWidth - 1)) {
2030 /* If we're signed and negative negate a copy. */
2032 copy = new integerPart[srcCount];
2033 APInt::tcAssign(copy, src, srcCount);
2034 APInt::tcNegate(copy, srcCount);
2035 status = convertFromUnsignedParts(copy, srcCount, rounding_mode);
2039 status = convertFromUnsignedParts(src, srcCount, rounding_mode);
2045 /* FIXME: should this just take a const APInt reference? */
2047 APFloat::convertFromZeroExtendedInteger(const integerPart *parts,
2048 unsigned int width, bool isSigned,
2049 roundingMode rounding_mode)
2051 unsigned int partCount = partCountForBits(width);
2052 APInt api = APInt(width, partCount, parts);
2055 if(isSigned && APInt::tcExtractBit(parts, width - 1)) {
2060 return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
2064 APFloat::convertFromHexadecimalString(const char *p,
2065 roundingMode rounding_mode)
2067 lostFraction lost_fraction;
2068 integerPart *significand;
2069 unsigned int bitPos, partsCount;
2070 const char *dot, *firstSignificantDigit;
2074 category = fcNormal;
2076 significand = significandParts();
2077 partsCount = partCount();
2078 bitPos = partsCount * integerPartWidth;
2080 /* Skip leading zeroes and any (hexa)decimal point. */
2081 p = skipLeadingZeroesAndAnyDot(p, &dot);
2082 firstSignificantDigit = p;
2085 integerPart hex_value;
2092 hex_value = hexDigitValue(*p);
2093 if(hex_value == -1U) {
2094 lost_fraction = lfExactlyZero;
2100 /* Store the number whilst 4-bit nibbles remain. */
2103 hex_value <<= bitPos % integerPartWidth;
2104 significand[bitPos / integerPartWidth] |= hex_value;
2106 lost_fraction = trailingHexadecimalFraction(p, hex_value);
2107 while(hexDigitValue(*p) != -1U)
2113 /* Hex floats require an exponent but not a hexadecimal point. */
2114 assert(*p == 'p' || *p == 'P');
2116 /* Ignore the exponent if we are zero. */
2117 if(p != firstSignificantDigit) {
2120 /* Implicit hexadecimal point? */
2124 /* Calculate the exponent adjustment implicit in the number of
2125 significant digits. */
2126 expAdjustment = static_cast<int>(dot - firstSignificantDigit);
2127 if(expAdjustment < 0)
2129 expAdjustment = expAdjustment * 4 - 1;
2131 /* Adjust for writing the significand starting at the most
2132 significant nibble. */
2133 expAdjustment += semantics->precision;
2134 expAdjustment -= partsCount * integerPartWidth;
2136 /* Adjust for the given exponent. */
2137 exponent = totalExponent(p, expAdjustment);
2140 return normalize(rounding_mode, lost_fraction);
2144 APFloat::roundSignificandWithExponent(const integerPart *decSigParts,
2145 unsigned sigPartCount, int exp,
2146 roundingMode rounding_mode)
2148 unsigned int parts, pow5PartCount;
2149 fltSemantics calcSemantics = { 32767, -32767, 0, true };
2150 integerPart pow5Parts[maxPowerOfFiveParts];
2153 isNearest = (rounding_mode == rmNearestTiesToEven
2154 || rounding_mode == rmNearestTiesToAway);
2156 parts = partCountForBits(semantics->precision + 11);
2158 /* Calculate pow(5, abs(exp)). */
2159 pow5PartCount = powerOf5(pow5Parts, exp >= 0 ? exp: -exp);
2161 for (;; parts *= 2) {
2162 opStatus sigStatus, powStatus;
2163 unsigned int excessPrecision, truncatedBits;
2165 calcSemantics.precision = parts * integerPartWidth - 1;
2166 excessPrecision = calcSemantics.precision - semantics->precision;
2167 truncatedBits = excessPrecision;
2169 APFloat decSig(calcSemantics, fcZero, sign);
2170 APFloat pow5(calcSemantics, fcZero, false);
2172 sigStatus = decSig.convertFromUnsignedParts(decSigParts, sigPartCount,
2173 rmNearestTiesToEven);
2174 powStatus = pow5.convertFromUnsignedParts(pow5Parts, pow5PartCount,
2175 rmNearestTiesToEven);
2176 /* Add exp, as 10^n = 5^n * 2^n. */
2177 decSig.exponent += exp;
2179 lostFraction calcLostFraction;
2180 integerPart HUerr, HUdistance;
2181 unsigned int powHUerr;
2184 /* multiplySignificand leaves the precision-th bit set to 1. */
2185 calcLostFraction = decSig.multiplySignificand(pow5, NULL);
2186 powHUerr = powStatus != opOK;
2188 calcLostFraction = decSig.divideSignificand(pow5);
2189 /* Denormal numbers have less precision. */
2190 if (decSig.exponent < semantics->minExponent) {
2191 excessPrecision += (semantics->minExponent - decSig.exponent);
2192 truncatedBits = excessPrecision;
2193 if (excessPrecision > calcSemantics.precision)
2194 excessPrecision = calcSemantics.precision;
2196 /* Extra half-ulp lost in reciprocal of exponent. */
2197 powHUerr = (powStatus == opOK && calcLostFraction == lfExactlyZero) ? 0:2;
2200 /* Both multiplySignificand and divideSignificand return the
2201 result with the integer bit set. */
2202 assert (APInt::tcExtractBit
2203 (decSig.significandParts(), calcSemantics.precision - 1) == 1);
2205 HUerr = HUerrBound(calcLostFraction != lfExactlyZero, sigStatus != opOK,
2207 HUdistance = 2 * ulpsFromBoundary(decSig.significandParts(),
2208 excessPrecision, isNearest);
2210 /* Are we guaranteed to round correctly if we truncate? */
2211 if (HUdistance >= HUerr) {
2212 APInt::tcExtract(significandParts(), partCount(), decSig.significandParts(),
2213 calcSemantics.precision - excessPrecision,
2215 /* Take the exponent of decSig. If we tcExtract-ed less bits
2216 above we must adjust our exponent to compensate for the
2217 implicit right shift. */
2218 exponent = (decSig.exponent + semantics->precision
2219 - (calcSemantics.precision - excessPrecision));
2220 calcLostFraction = lostFractionThroughTruncation(decSig.significandParts(),
2223 return normalize(rounding_mode, calcLostFraction);
2229 APFloat::convertFromDecimalString(const char *p, roundingMode rounding_mode)
2234 /* Scan the text. */
2235 interpretDecimal(p, &D);
2237 /* Handle the quick cases. First the case of no significant digits,
2238 i.e. zero, and then exponents that are obviously too large or too
2239 small. Writing L for log 10 / log 2, a number d.ddddd*10^exp
2240 definitely overflows if
2242 (exp - 1) * L >= maxExponent
2244 and definitely underflows to zero where
2246 (exp + 1) * L <= minExponent - precision
2248 With integer arithmetic the tightest bounds for L are
2250 93/28 < L < 196/59 [ numerator <= 256 ]
2251 42039/12655 < L < 28738/8651 [ numerator <= 65536 ]
2254 if (decDigitValue(*D.firstSigDigit) >= 10U) {
2257 } else if ((D.normalizedExponent + 1) * 28738
2258 <= 8651 * (semantics->minExponent - (int) semantics->precision)) {
2259 /* Underflow to zero and round. */
2261 fs = normalize(rounding_mode, lfLessThanHalf);
2262 } else if ((D.normalizedExponent - 1) * 42039
2263 >= 12655 * semantics->maxExponent) {
2264 /* Overflow and round. */
2265 fs = handleOverflow(rounding_mode);
2267 integerPart *decSignificand;
2268 unsigned int partCount;
2270 /* A tight upper bound on number of bits required to hold an
2271 N-digit decimal integer is N * 196 / 59. Allocate enough space
2272 to hold the full significand, and an extra part required by
2274 partCount = static_cast<unsigned int>(D.lastSigDigit - D.firstSigDigit) + 1;
2275 partCount = partCountForBits(1 + 196 * partCount / 59);
2276 decSignificand = new integerPart[partCount + 1];
2279 /* Convert to binary efficiently - we do almost all multiplication
2280 in an integerPart. When this would overflow do we do a single
2281 bignum multiplication, and then revert again to multiplication
2282 in an integerPart. */
2284 integerPart decValue, val, multiplier;
2293 decValue = decDigitValue(*p++);
2295 val = val * 10 + decValue;
2296 /* The maximum number that can be multiplied by ten with any
2297 digit added without overflowing an integerPart. */
2298 } while (p <= D.lastSigDigit && multiplier <= (~ (integerPart) 0 - 9) / 10);
2300 /* Multiply out the current part. */
2301 APInt::tcMultiplyPart(decSignificand, decSignificand, multiplier, val,
2302 partCount, partCount + 1, false);
2304 /* If we used another part (likely but not guaranteed), increase
2306 if (decSignificand[partCount])
2308 } while (p <= D.lastSigDigit);
2310 category = fcNormal;
2311 fs = roundSignificandWithExponent(decSignificand, partCount,
2312 D.exponent, rounding_mode);
2314 delete [] decSignificand;
2321 APFloat::convertFromString(const char *p, roundingMode rounding_mode)
2323 assertArithmeticOK(*semantics);
2325 /* Handle a leading minus sign. */
2331 if(p[0] == '0' && (p[1] == 'x' || p[1] == 'X'))
2332 return convertFromHexadecimalString(p + 2, rounding_mode);
2334 return convertFromDecimalString(p, rounding_mode);
2337 /* Write out a hexadecimal representation of the floating point value
2338 to DST, which must be of sufficient size, in the C99 form
2339 [-]0xh.hhhhp[+-]d. Return the number of characters written,
2340 excluding the terminating NUL.
2342 If UPPERCASE, the output is in upper case, otherwise in lower case.
2344 HEXDIGITS digits appear altogether, rounding the value if
2345 necessary. If HEXDIGITS is 0, the minimal precision to display the
2346 number precisely is used instead. If nothing would appear after
2347 the decimal point it is suppressed.
2349 The decimal exponent is always printed and has at least one digit.
2350 Zero values display an exponent of zero. Infinities and NaNs
2351 appear as "infinity" or "nan" respectively.
2353 The above rules are as specified by C99. There is ambiguity about
2354 what the leading hexadecimal digit should be. This implementation
2355 uses whatever is necessary so that the exponent is displayed as
2356 stored. This implies the exponent will fall within the IEEE format
2357 range, and the leading hexadecimal digit will be 0 (for denormals),
2358 1 (normal numbers) or 2 (normal numbers rounded-away-from-zero with
2359 any other digits zero).
2362 APFloat::convertToHexString(char *dst, unsigned int hexDigits,
2363 bool upperCase, roundingMode rounding_mode) const
2367 assertArithmeticOK(*semantics);
2375 memcpy (dst, upperCase ? infinityU: infinityL, sizeof infinityU - 1);
2376 dst += sizeof infinityL - 1;
2380 memcpy (dst, upperCase ? NaNU: NaNL, sizeof NaNU - 1);
2381 dst += sizeof NaNU - 1;
2386 *dst++ = upperCase ? 'X': 'x';
2388 if (hexDigits > 1) {
2390 memset (dst, '0', hexDigits - 1);
2391 dst += hexDigits - 1;
2393 *dst++ = upperCase ? 'P': 'p';
2398 dst = convertNormalToHexString (dst, hexDigits, upperCase, rounding_mode);
2404 return static_cast<unsigned int>(dst - p);
2407 /* Does the hard work of outputting the correctly rounded hexadecimal
2408 form of a normal floating point number with the specified number of
2409 hexadecimal digits. If HEXDIGITS is zero the minimum number of
2410 digits necessary to print the value precisely is output. */
2412 APFloat::convertNormalToHexString(char *dst, unsigned int hexDigits,
2414 roundingMode rounding_mode) const
2416 unsigned int count, valueBits, shift, partsCount, outputDigits;
2417 const char *hexDigitChars;
2418 const integerPart *significand;
2423 *dst++ = upperCase ? 'X': 'x';
2426 hexDigitChars = upperCase ? hexDigitsUpper: hexDigitsLower;
2428 significand = significandParts();
2429 partsCount = partCount();
2431 /* +3 because the first digit only uses the single integer bit, so
2432 we have 3 virtual zero most-significant-bits. */
2433 valueBits = semantics->precision + 3;
2434 shift = integerPartWidth - valueBits % integerPartWidth;
2436 /* The natural number of digits required ignoring trailing
2437 insignificant zeroes. */
2438 outputDigits = (valueBits - significandLSB () + 3) / 4;
2440 /* hexDigits of zero means use the required number for the
2441 precision. Otherwise, see if we are truncating. If we are,
2442 find out if we need to round away from zero. */
2444 if (hexDigits < outputDigits) {
2445 /* We are dropping non-zero bits, so need to check how to round.
2446 "bits" is the number of dropped bits. */
2448 lostFraction fraction;
2450 bits = valueBits - hexDigits * 4;
2451 fraction = lostFractionThroughTruncation (significand, partsCount, bits);
2452 roundUp = roundAwayFromZero(rounding_mode, fraction, bits);
2454 outputDigits = hexDigits;
2457 /* Write the digits consecutively, and start writing in the location
2458 of the hexadecimal point. We move the most significant digit
2459 left and add the hexadecimal point later. */
2462 count = (valueBits + integerPartWidth - 1) / integerPartWidth;
2464 while (outputDigits && count) {
2467 /* Put the most significant integerPartWidth bits in "part". */
2468 if (--count == partsCount)
2469 part = 0; /* An imaginary higher zero part. */
2471 part = significand[count] << shift;
2474 part |= significand[count - 1] >> (integerPartWidth - shift);
2476 /* Convert as much of "part" to hexdigits as we can. */
2477 unsigned int curDigits = integerPartWidth / 4;
2479 if (curDigits > outputDigits)
2480 curDigits = outputDigits;
2481 dst += partAsHex (dst, part, curDigits, hexDigitChars);
2482 outputDigits -= curDigits;
2488 /* Note that hexDigitChars has a trailing '0'. */
2491 *q = hexDigitChars[hexDigitValue (*q) + 1];
2492 } while (*q == '0');
2495 /* Add trailing zeroes. */
2496 memset (dst, '0', outputDigits);
2497 dst += outputDigits;
2500 /* Move the most significant digit to before the point, and if there
2501 is something after the decimal point add it. This must come
2502 after rounding above. */
2509 /* Finally output the exponent. */
2510 *dst++ = upperCase ? 'P': 'p';
2512 return writeSignedDecimal (dst, exponent);
2515 // For good performance it is desirable for different APFloats
2516 // to produce different integers.
2518 APFloat::getHashValue() const
2520 if (category==fcZero) return sign<<8 | semantics->precision ;
2521 else if (category==fcInfinity) return sign<<9 | semantics->precision;
2522 else if (category==fcNaN) return 1<<10 | semantics->precision;
2524 uint32_t hash = sign<<11 | semantics->precision | exponent<<12;
2525 const integerPart* p = significandParts();
2526 for (int i=partCount(); i>0; i--, p++)
2527 hash ^= ((uint32_t)*p) ^ (uint32_t)((*p)>>32);
2532 // Conversion from APFloat to/from host float/double. It may eventually be
2533 // possible to eliminate these and have everybody deal with APFloats, but that
2534 // will take a while. This approach will not easily extend to long double.
2535 // Current implementation requires integerPartWidth==64, which is correct at
2536 // the moment but could be made more general.
2538 // Denormals have exponent minExponent in APFloat, but minExponent-1 in
2539 // the actual IEEE respresentations. We compensate for that here.
2542 APFloat::convertF80LongDoubleAPFloatToAPInt() const
2544 assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended);
2545 assert (partCount()==2);
2547 uint64_t myexponent, mysignificand;
2549 if (category==fcNormal) {
2550 myexponent = exponent+16383; //bias
2551 mysignificand = significandParts()[0];
2552 if (myexponent==1 && !(mysignificand & 0x8000000000000000ULL))
2553 myexponent = 0; // denormal
2554 } else if (category==fcZero) {
2557 } else if (category==fcInfinity) {
2558 myexponent = 0x7fff;
2559 mysignificand = 0x8000000000000000ULL;
2561 assert(category == fcNaN && "Unknown category");
2562 myexponent = 0x7fff;
2563 mysignificand = significandParts()[0];
2567 words[0] = ((uint64_t)(sign & 1) << 63) |
2568 ((myexponent & 0x7fffLL) << 48) |
2569 ((mysignificand >>16) & 0xffffffffffffLL);
2570 words[1] = mysignificand & 0xffff;
2571 return APInt(80, 2, words);
2575 APFloat::convertPPCDoubleDoubleAPFloatToAPInt() const
2577 assert(semantics == (const llvm::fltSemantics*)&PPCDoubleDouble);
2578 assert (partCount()==2);
2580 uint64_t myexponent, mysignificand, myexponent2, mysignificand2;
2582 if (category==fcNormal) {
2583 myexponent = exponent + 1023; //bias
2584 myexponent2 = exponent2 + 1023;
2585 mysignificand = significandParts()[0];
2586 mysignificand2 = significandParts()[1];
2587 if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
2588 myexponent = 0; // denormal
2589 if (myexponent2==1 && !(mysignificand2 & 0x10000000000000LL))
2590 myexponent2 = 0; // denormal
2591 } else if (category==fcZero) {
2596 } else if (category==fcInfinity) {
2602 assert(category == fcNaN && "Unknown category");
2604 mysignificand = significandParts()[0];
2605 myexponent2 = exponent2;
2606 mysignificand2 = significandParts()[1];
2610 words[0] = ((uint64_t)(sign & 1) << 63) |
2611 ((myexponent & 0x7ff) << 52) |
2612 (mysignificand & 0xfffffffffffffLL);
2613 words[1] = ((uint64_t)(sign2 & 1) << 63) |
2614 ((myexponent2 & 0x7ff) << 52) |
2615 (mysignificand2 & 0xfffffffffffffLL);
2616 return APInt(128, 2, words);
2620 APFloat::convertDoubleAPFloatToAPInt() const
2622 assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
2623 assert (partCount()==1);
2625 uint64_t myexponent, mysignificand;
2627 if (category==fcNormal) {
2628 myexponent = exponent+1023; //bias
2629 mysignificand = *significandParts();
2630 if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
2631 myexponent = 0; // denormal
2632 } else if (category==fcZero) {
2635 } else if (category==fcInfinity) {
2639 assert(category == fcNaN && "Unknown category!");
2641 mysignificand = *significandParts();
2644 return APInt(64, ((((uint64_t)(sign & 1) << 63) |
2645 ((myexponent & 0x7ff) << 52) |
2646 (mysignificand & 0xfffffffffffffLL))));
2650 APFloat::convertFloatAPFloatToAPInt() const
2652 assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
2653 assert (partCount()==1);
2655 uint32_t myexponent, mysignificand;
2657 if (category==fcNormal) {
2658 myexponent = exponent+127; //bias
2659 mysignificand = (uint32_t)*significandParts();
2660 if (myexponent == 1 && !(mysignificand & 0x800000))
2661 myexponent = 0; // denormal
2662 } else if (category==fcZero) {
2665 } else if (category==fcInfinity) {
2669 assert(category == fcNaN && "Unknown category!");
2671 mysignificand = (uint32_t)*significandParts();
2674 return APInt(32, (((sign&1) << 31) | ((myexponent&0xff) << 23) |
2675 (mysignificand & 0x7fffff)));
2678 // This function creates an APInt that is just a bit map of the floating
2679 // point constant as it would appear in memory. It is not a conversion,
2680 // and treating the result as a normal integer is unlikely to be useful.
2683 APFloat::bitcastToAPInt() const
2685 if (semantics == (const llvm::fltSemantics*)&IEEEsingle)
2686 return convertFloatAPFloatToAPInt();
2688 if (semantics == (const llvm::fltSemantics*)&IEEEdouble)
2689 return convertDoubleAPFloatToAPInt();
2691 if (semantics == (const llvm::fltSemantics*)&PPCDoubleDouble)
2692 return convertPPCDoubleDoubleAPFloatToAPInt();
2694 assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended &&
2696 return convertF80LongDoubleAPFloatToAPInt();
2700 APFloat::convertToFloat() const
2702 assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
2703 APInt api = bitcastToAPInt();
2704 return api.bitsToFloat();
2708 APFloat::convertToDouble() const
2710 assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
2711 APInt api = bitcastToAPInt();
2712 return api.bitsToDouble();
2715 /// Integer bit is explicit in this format. Intel hardware (387 and later)
2716 /// does not support these bit patterns:
2717 /// exponent = all 1's, integer bit 0, significand 0 ("pseudoinfinity")
2718 /// exponent = all 1's, integer bit 0, significand nonzero ("pseudoNaN")
2719 /// exponent = 0, integer bit 1 ("pseudodenormal")
2720 /// exponent!=0 nor all 1's, integer bit 0 ("unnormal")
2721 /// At the moment, the first two are treated as NaNs, the second two as Normal.
2723 APFloat::initFromF80LongDoubleAPInt(const APInt &api)
2725 assert(api.getBitWidth()==80);
2726 uint64_t i1 = api.getRawData()[0];
2727 uint64_t i2 = api.getRawData()[1];
2728 uint64_t myexponent = (i1 >> 48) & 0x7fff;
2729 uint64_t mysignificand = ((i1 << 16) & 0xffffffffffff0000ULL) |
2732 initialize(&APFloat::x87DoubleExtended);
2733 assert(partCount()==2);
2735 sign = static_cast<unsigned int>(i1>>63);
2736 if (myexponent==0 && mysignificand==0) {
2737 // exponent, significand meaningless
2739 } else if (myexponent==0x7fff && mysignificand==0x8000000000000000ULL) {
2740 // exponent, significand meaningless
2741 category = fcInfinity;
2742 } else if (myexponent==0x7fff && mysignificand!=0x8000000000000000ULL) {
2743 // exponent meaningless
2745 significandParts()[0] = mysignificand;
2746 significandParts()[1] = 0;
2748 category = fcNormal;
2749 exponent = myexponent - 16383;
2750 significandParts()[0] = mysignificand;
2751 significandParts()[1] = 0;
2752 if (myexponent==0) // denormal
2758 APFloat::initFromPPCDoubleDoubleAPInt(const APInt &api)
2760 assert(api.getBitWidth()==128);
2761 uint64_t i1 = api.getRawData()[0];
2762 uint64_t i2 = api.getRawData()[1];
2763 uint64_t myexponent = (i1 >> 52) & 0x7ff;
2764 uint64_t mysignificand = i1 & 0xfffffffffffffLL;
2765 uint64_t myexponent2 = (i2 >> 52) & 0x7ff;
2766 uint64_t mysignificand2 = i2 & 0xfffffffffffffLL;
2768 initialize(&APFloat::PPCDoubleDouble);
2769 assert(partCount()==2);
2771 sign = static_cast<unsigned int>(i1>>63);
2772 sign2 = static_cast<unsigned int>(i2>>63);
2773 if (myexponent==0 && mysignificand==0) {
2774 // exponent, significand meaningless
2775 // exponent2 and significand2 are required to be 0; we don't check
2777 } else if (myexponent==0x7ff && mysignificand==0) {
2778 // exponent, significand meaningless
2779 // exponent2 and significand2 are required to be 0; we don't check
2780 category = fcInfinity;
2781 } else if (myexponent==0x7ff && mysignificand!=0) {
2782 // exponent meaningless. So is the whole second word, but keep it
2785 exponent2 = myexponent2;
2786 significandParts()[0] = mysignificand;
2787 significandParts()[1] = mysignificand2;
2789 category = fcNormal;
2790 // Note there is no category2; the second word is treated as if it is
2791 // fcNormal, although it might be something else considered by itself.
2792 exponent = myexponent - 1023;
2793 exponent2 = myexponent2 - 1023;
2794 significandParts()[0] = mysignificand;
2795 significandParts()[1] = mysignificand2;
2796 if (myexponent==0) // denormal
2799 significandParts()[0] |= 0x10000000000000LL; // integer bit
2803 significandParts()[1] |= 0x10000000000000LL; // integer bit
2808 APFloat::initFromDoubleAPInt(const APInt &api)
2810 assert(api.getBitWidth()==64);
2811 uint64_t i = *api.getRawData();
2812 uint64_t myexponent = (i >> 52) & 0x7ff;
2813 uint64_t mysignificand = i & 0xfffffffffffffLL;
2815 initialize(&APFloat::IEEEdouble);
2816 assert(partCount()==1);
2818 sign = static_cast<unsigned int>(i>>63);
2819 if (myexponent==0 && mysignificand==0) {
2820 // exponent, significand meaningless
2822 } else if (myexponent==0x7ff && mysignificand==0) {
2823 // exponent, significand meaningless
2824 category = fcInfinity;
2825 } else if (myexponent==0x7ff && mysignificand!=0) {
2826 // exponent meaningless
2828 *significandParts() = mysignificand;
2830 category = fcNormal;
2831 exponent = myexponent - 1023;
2832 *significandParts() = mysignificand;
2833 if (myexponent==0) // denormal
2836 *significandParts() |= 0x10000000000000LL; // integer bit
2841 APFloat::initFromFloatAPInt(const APInt & api)
2843 assert(api.getBitWidth()==32);
2844 uint32_t i = (uint32_t)*api.getRawData();
2845 uint32_t myexponent = (i >> 23) & 0xff;
2846 uint32_t mysignificand = i & 0x7fffff;
2848 initialize(&APFloat::IEEEsingle);
2849 assert(partCount()==1);
2852 if (myexponent==0 && mysignificand==0) {
2853 // exponent, significand meaningless
2855 } else if (myexponent==0xff && mysignificand==0) {
2856 // exponent, significand meaningless
2857 category = fcInfinity;
2858 } else if (myexponent==0xff && mysignificand!=0) {
2859 // sign, exponent, significand meaningless
2861 *significandParts() = mysignificand;
2863 category = fcNormal;
2864 exponent = myexponent - 127; //bias
2865 *significandParts() = mysignificand;
2866 if (myexponent==0) // denormal
2869 *significandParts() |= 0x800000; // integer bit
2873 /// Treat api as containing the bits of a floating point number. Currently
2874 /// we infer the floating point type from the size of the APInt. The
2875 /// isIEEE argument distinguishes between PPC128 and IEEE128 (not meaningful
2876 /// when the size is anything else).
2878 APFloat::initFromAPInt(const APInt& api, bool isIEEE)
2880 if (api.getBitWidth() == 32)
2881 return initFromFloatAPInt(api);
2882 else if (api.getBitWidth()==64)
2883 return initFromDoubleAPInt(api);
2884 else if (api.getBitWidth()==80)
2885 return initFromF80LongDoubleAPInt(api);
2886 else if (api.getBitWidth()==128 && !isIEEE)
2887 return initFromPPCDoubleDoubleAPInt(api);
2892 APFloat::APFloat(const APInt& api, bool isIEEE)
2894 initFromAPInt(api, isIEEE);
2897 APFloat::APFloat(float f)
2899 APInt api = APInt(32, 0);
2900 initFromAPInt(api.floatToBits(f));
2903 APFloat::APFloat(double d)
2905 APInt api = APInt(64, 0);
2906 initFromAPInt(api.doubleToBits(d));