1 //===-- APFloat.cpp - Implement APFloat class -----------------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by Neil Booth and is distributed under the
6 // University of Illinois Open Source 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 //===----------------------------------------------------------------------===//
16 #include "llvm/ADT/APFloat.h"
17 #include "llvm/Support/MathExtras.h"
21 #define convolve(lhs, rhs) ((lhs) * 4 + (rhs))
23 /* Assumed in hexadecimal significand parsing. */
24 COMPILE_TIME_ASSERT(integerPartWidth % 4 == 0);
28 /* Represents floating point arithmetic semantics. */
30 /* The largest E such that 2^E is representable; this matches the
31 definition of IEEE 754. */
32 exponent_t maxExponent;
34 /* The smallest E such that 2^E is a normalized number; this
35 matches the definition of IEEE 754. */
36 exponent_t minExponent;
38 /* Number of bits in the significand. This includes the integer
40 unsigned char precision;
42 /* If the target format has an implicit integer bit. */
43 bool implicitIntegerBit;
46 const fltSemantics APFloat::IEEEsingle = { 127, -126, 24, true };
47 const fltSemantics APFloat::IEEEdouble = { 1023, -1022, 53, true };
48 const fltSemantics APFloat::IEEEquad = { 16383, -16382, 113, true };
49 const fltSemantics APFloat::x87DoubleExtended = { 16383, -16382, 64, false };
50 const fltSemantics APFloat::Bogus = { 0, 0, 0, false };
53 /* Put a bunch of private, handy routines in an anonymous namespace. */
57 partCountForBits(unsigned int bits)
59 return ((bits) + integerPartWidth - 1) / integerPartWidth;
63 digitValue(unsigned int c)
75 hexDigitValue (unsigned int c)
94 /* This is ugly and needs cleaning up, but I don't immediately see
95 how whilst remaining safe. */
97 totalExponent(const char *p, int exponentAdjustment)
99 integerPart unsignedExponent;
100 bool negative, overflow;
103 /* Move past the exponent letter and sign to the digits. */
105 negative = *p == '-';
106 if(*p == '-' || *p == '+')
109 unsignedExponent = 0;
114 value = digitValue(*p);
119 unsignedExponent = unsignedExponent * 10 + value;
120 if(unsignedExponent > 65535)
124 if(exponentAdjustment > 65535 || exponentAdjustment < -65536)
128 exponent = unsignedExponent;
130 exponent = -exponent;
131 exponent += exponentAdjustment;
132 if(exponent > 65535 || exponent < -65536)
137 exponent = negative ? -65536: 65535;
143 skipLeadingZeroesAndAnyDot(const char *p, const char **dot)
158 /* Return the trailing fraction of a hexadecimal number.
159 DIGITVALUE is the first hex digit of the fraction, P points to
162 trailingHexadecimalFraction(const char *p, unsigned int digitValue)
164 unsigned int hexDigit;
166 /* If the first trailing digit isn't 0 or 8 we can work out the
167 fraction immediately. */
169 return lfMoreThanHalf;
170 else if(digitValue < 8 && digitValue > 0)
171 return lfLessThanHalf;
173 /* Otherwise we need to find the first non-zero digit. */
177 hexDigit = hexDigitValue(*p);
179 /* If we ran off the end it is exactly zero or one-half, otherwise
182 return digitValue == 0 ? lfExactlyZero: lfExactlyHalf;
184 return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf;
187 /* Return the fraction lost were a bignum truncated. */
189 lostFractionThroughTruncation(integerPart *parts,
190 unsigned int partCount,
195 lsb = APInt::tcLSB(parts, partCount);
197 /* Note this is guaranteed true if bits == 0, or LSB == -1U. */
199 return lfExactlyZero;
201 return lfExactlyHalf;
202 if(bits <= partCount * integerPartWidth
203 && APInt::tcExtractBit(parts, bits - 1))
204 return lfMoreThanHalf;
206 return lfLessThanHalf;
209 /* Shift DST right BITS bits noting lost fraction. */
211 shiftRight(integerPart *dst, unsigned int parts, unsigned int bits)
213 lostFraction lost_fraction;
215 lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
217 APInt::tcShiftRight(dst, parts, bits);
219 return lost_fraction;
225 APFloat::initialize(const fltSemantics *ourSemantics)
229 semantics = ourSemantics;
232 significand.parts = new integerPart[count];
236 APFloat::freeSignificand()
239 delete [] significand.parts;
243 APFloat::assign(const APFloat &rhs)
245 assert(semantics == rhs.semantics);
248 category = rhs.category;
249 exponent = rhs.exponent;
250 if(category == fcNormal || category == fcNaN)
251 copySignificand(rhs);
255 APFloat::copySignificand(const APFloat &rhs)
257 assert(category == fcNormal || category == fcNaN);
258 assert(rhs.partCount() >= partCount());
260 APInt::tcAssign(significandParts(), rhs.significandParts(),
265 APFloat::operator=(const APFloat &rhs)
268 if(semantics != rhs.semantics) {
270 initialize(rhs.semantics);
279 APFloat::bitwiseIsEqual(const APFloat &rhs) const {
282 if (semantics != rhs.semantics ||
283 category != rhs.category ||
286 if (category==fcZero || category==fcInfinity)
288 else if (category==fcNormal && exponent!=rhs.exponent)
292 const integerPart* p=significandParts();
293 const integerPart* q=rhs.significandParts();
294 for (; i>0; i--, p++, q++) {
302 APFloat::APFloat(const fltSemantics &ourSemantics, integerPart value)
304 initialize(&ourSemantics);
307 exponent = ourSemantics.precision - 1;
308 significandParts()[0] = value;
309 normalize(rmNearestTiesToEven, lfExactlyZero);
312 APFloat::APFloat(const fltSemantics &ourSemantics,
313 fltCategory ourCategory, bool negative)
315 initialize(&ourSemantics);
316 category = ourCategory;
318 if(category == fcNormal)
322 APFloat::APFloat(const fltSemantics &ourSemantics, const char *text)
324 initialize(&ourSemantics);
325 convertFromString(text, rmNearestTiesToEven);
328 APFloat::APFloat(const APFloat &rhs)
330 initialize(rhs.semantics);
340 APFloat::partCount() const
342 return partCountForBits(semantics->precision + 1);
346 APFloat::semanticsPrecision(const fltSemantics &semantics)
348 return semantics.precision;
352 APFloat::significandParts() const
354 return const_cast<APFloat *>(this)->significandParts();
358 APFloat::significandParts()
360 assert(category == fcNormal || category == fcNaN);
363 return significand.parts;
365 return &significand.part;
368 /* Combine the effect of two lost fractions. */
370 APFloat::combineLostFractions(lostFraction moreSignificant,
371 lostFraction lessSignificant)
373 if(lessSignificant != lfExactlyZero) {
374 if(moreSignificant == lfExactlyZero)
375 moreSignificant = lfLessThanHalf;
376 else if(moreSignificant == lfExactlyHalf)
377 moreSignificant = lfMoreThanHalf;
380 return moreSignificant;
384 APFloat::zeroSignificand()
387 APInt::tcSet(significandParts(), 0, partCount());
390 /* Increment an fcNormal floating point number's significand. */
392 APFloat::incrementSignificand()
396 carry = APInt::tcIncrement(significandParts(), partCount());
398 /* Our callers should never cause us to overflow. */
402 /* Add the significand of the RHS. Returns the carry flag. */
404 APFloat::addSignificand(const APFloat &rhs)
408 parts = significandParts();
410 assert(semantics == rhs.semantics);
411 assert(exponent == rhs.exponent);
413 return APInt::tcAdd(parts, rhs.significandParts(), 0, partCount());
416 /* Subtract the significand of the RHS with a borrow flag. Returns
419 APFloat::subtractSignificand(const APFloat &rhs, integerPart borrow)
423 parts = significandParts();
425 assert(semantics == rhs.semantics);
426 assert(exponent == rhs.exponent);
428 return APInt::tcSubtract(parts, rhs.significandParts(), borrow,
432 /* Multiply the significand of the RHS. If ADDEND is non-NULL, add it
433 on to the full-precision result of the multiplication. Returns the
436 APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
438 unsigned int omsb; // One, not zero, based MSB.
439 unsigned int partsCount, newPartsCount, precision;
440 integerPart *lhsSignificand;
441 integerPart scratch[4];
442 integerPart *fullSignificand;
443 lostFraction lost_fraction;
445 assert(semantics == rhs.semantics);
447 precision = semantics->precision;
448 newPartsCount = partCountForBits(precision * 2);
450 if(newPartsCount > 4)
451 fullSignificand = new integerPart[newPartsCount];
453 fullSignificand = scratch;
455 lhsSignificand = significandParts();
456 partsCount = partCount();
458 APInt::tcFullMultiply(fullSignificand, lhsSignificand,
459 rhs.significandParts(), partsCount);
461 lost_fraction = lfExactlyZero;
462 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
463 exponent += rhs.exponent;
466 Significand savedSignificand = significand;
467 const fltSemantics *savedSemantics = semantics;
468 fltSemantics extendedSemantics;
470 unsigned int extendedPrecision;
472 /* Normalize our MSB. */
473 extendedPrecision = precision + precision - 1;
474 if(omsb != extendedPrecision)
476 APInt::tcShiftLeft(fullSignificand, newPartsCount,
477 extendedPrecision - omsb);
478 exponent -= extendedPrecision - omsb;
481 /* Create new semantics. */
482 extendedSemantics = *semantics;
483 extendedSemantics.precision = extendedPrecision;
485 if(newPartsCount == 1)
486 significand.part = fullSignificand[0];
488 significand.parts = fullSignificand;
489 semantics = &extendedSemantics;
491 APFloat extendedAddend(*addend);
492 status = extendedAddend.convert(extendedSemantics, rmTowardZero);
493 assert(status == opOK);
494 lost_fraction = addOrSubtractSignificand(extendedAddend, false);
496 /* Restore our state. */
497 if(newPartsCount == 1)
498 fullSignificand[0] = significand.part;
499 significand = savedSignificand;
500 semantics = savedSemantics;
502 omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
505 exponent -= (precision - 1);
507 if(omsb > precision) {
508 unsigned int bits, significantParts;
511 bits = omsb - precision;
512 significantParts = partCountForBits(omsb);
513 lf = shiftRight(fullSignificand, significantParts, bits);
514 lost_fraction = combineLostFractions(lf, lost_fraction);
518 APInt::tcAssign(lhsSignificand, fullSignificand, partsCount);
520 if(newPartsCount > 4)
521 delete [] fullSignificand;
523 return lost_fraction;
526 /* Multiply the significands of LHS and RHS to DST. */
528 APFloat::divideSignificand(const APFloat &rhs)
530 unsigned int bit, i, partsCount;
531 const integerPart *rhsSignificand;
532 integerPart *lhsSignificand, *dividend, *divisor;
533 integerPart scratch[4];
534 lostFraction lost_fraction;
536 assert(semantics == rhs.semantics);
538 lhsSignificand = significandParts();
539 rhsSignificand = rhs.significandParts();
540 partsCount = partCount();
543 dividend = new integerPart[partsCount * 2];
547 divisor = dividend + partsCount;
549 /* Copy the dividend and divisor as they will be modified in-place. */
550 for(i = 0; i < partsCount; i++) {
551 dividend[i] = lhsSignificand[i];
552 divisor[i] = rhsSignificand[i];
553 lhsSignificand[i] = 0;
556 exponent -= rhs.exponent;
558 unsigned int precision = semantics->precision;
560 /* Normalize the divisor. */
561 bit = precision - APInt::tcMSB(divisor, partsCount) - 1;
564 APInt::tcShiftLeft(divisor, partsCount, bit);
567 /* Normalize the dividend. */
568 bit = precision - APInt::tcMSB(dividend, partsCount) - 1;
571 APInt::tcShiftLeft(dividend, partsCount, bit);
574 if(APInt::tcCompare(dividend, divisor, partsCount) < 0) {
576 APInt::tcShiftLeft(dividend, partsCount, 1);
577 assert(APInt::tcCompare(dividend, divisor, partsCount) >= 0);
581 for(bit = precision; bit; bit -= 1) {
582 if(APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
583 APInt::tcSubtract(dividend, divisor, 0, partsCount);
584 APInt::tcSetBit(lhsSignificand, bit - 1);
587 APInt::tcShiftLeft(dividend, partsCount, 1);
590 /* Figure out the lost fraction. */
591 int cmp = APInt::tcCompare(dividend, divisor, partsCount);
594 lost_fraction = lfMoreThanHalf;
596 lost_fraction = lfExactlyHalf;
597 else if(APInt::tcIsZero(dividend, partsCount))
598 lost_fraction = lfExactlyZero;
600 lost_fraction = lfLessThanHalf;
605 return lost_fraction;
609 APFloat::significandMSB() const
611 return APInt::tcMSB(significandParts(), partCount());
615 APFloat::significandLSB() const
617 return APInt::tcLSB(significandParts(), partCount());
620 /* Note that a zero result is NOT normalized to fcZero. */
622 APFloat::shiftSignificandRight(unsigned int bits)
624 /* Our exponent should not overflow. */
625 assert((exponent_t) (exponent + bits) >= exponent);
629 return shiftRight(significandParts(), partCount(), bits);
632 /* Shift the significand left BITS bits, subtract BITS from its exponent. */
634 APFloat::shiftSignificandLeft(unsigned int bits)
636 assert(bits < semantics->precision);
639 unsigned int partsCount = partCount();
641 APInt::tcShiftLeft(significandParts(), partsCount, bits);
644 assert(!APInt::tcIsZero(significandParts(), partsCount));
649 APFloat::compareAbsoluteValue(const APFloat &rhs) const
653 assert(semantics == rhs.semantics);
654 assert(category == fcNormal);
655 assert(rhs.category == fcNormal);
657 compare = exponent - rhs.exponent;
659 /* If exponents are equal, do an unsigned bignum comparison of the
662 compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
666 return cmpGreaterThan;
673 /* Handle overflow. Sign is preserved. We either become infinity or
674 the largest finite number. */
676 APFloat::handleOverflow(roundingMode rounding_mode)
679 if(rounding_mode == rmNearestTiesToEven
680 || rounding_mode == rmNearestTiesToAway
681 || (rounding_mode == rmTowardPositive && !sign)
682 || (rounding_mode == rmTowardNegative && sign))
684 category = fcInfinity;
685 return (opStatus) (opOverflow | opInexact);
688 /* Otherwise we become the largest finite number. */
690 exponent = semantics->maxExponent;
691 APInt::tcSetLeastSignificantBits(significandParts(), partCount(),
692 semantics->precision);
697 /* This routine must work for fcZero of both signs, and fcNormal
700 APFloat::roundAwayFromZero(roundingMode rounding_mode,
701 lostFraction lost_fraction)
703 /* NaNs and infinities should not have lost fractions. */
704 assert(category == fcNormal || category == fcZero);
706 /* Our caller has already handled this case. */
707 assert(lost_fraction != lfExactlyZero);
709 switch(rounding_mode) {
713 case rmNearestTiesToAway:
714 return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf;
716 case rmNearestTiesToEven:
717 if(lost_fraction == lfMoreThanHalf)
720 /* Our zeroes don't have a significand to test. */
721 if(lost_fraction == lfExactlyHalf && category != fcZero)
722 return significandParts()[0] & 1;
729 case rmTowardPositive:
730 return sign == false;
732 case rmTowardNegative:
738 APFloat::normalize(roundingMode rounding_mode,
739 lostFraction lost_fraction)
741 unsigned int omsb; /* One, not zero, based MSB. */
744 if(category != fcNormal)
747 /* Before rounding normalize the exponent of fcNormal numbers. */
748 omsb = significandMSB() + 1;
751 /* OMSB is numbered from 1. We want to place it in the integer
752 bit numbered PRECISON if possible, with a compensating change in
754 exponentChange = omsb - semantics->precision;
756 /* If the resulting exponent is too high, overflow according to
757 the rounding mode. */
758 if(exponent + exponentChange > semantics->maxExponent)
759 return handleOverflow(rounding_mode);
761 /* Subnormal numbers have exponent minExponent, and their MSB
762 is forced based on that. */
763 if(exponent + exponentChange < semantics->minExponent)
764 exponentChange = semantics->minExponent - exponent;
766 /* Shifting left is easy as we don't lose precision. */
767 if(exponentChange < 0) {
768 assert(lost_fraction == lfExactlyZero);
770 shiftSignificandLeft(-exponentChange);
775 if(exponentChange > 0) {
778 /* Shift right and capture any new lost fraction. */
779 lf = shiftSignificandRight(exponentChange);
781 lost_fraction = combineLostFractions(lf, lost_fraction);
783 /* Keep OMSB up-to-date. */
784 if(omsb > (unsigned) exponentChange)
785 omsb -= (unsigned) exponentChange;
791 /* Now round the number according to rounding_mode given the lost
794 /* As specified in IEEE 754, since we do not trap we do not report
795 underflow for exact results. */
796 if(lost_fraction == lfExactlyZero) {
797 /* Canonicalize zeroes. */
804 /* Increment the significand if we're rounding away from zero. */
805 if(roundAwayFromZero(rounding_mode, lost_fraction)) {
807 exponent = semantics->minExponent;
809 incrementSignificand();
810 omsb = significandMSB() + 1;
812 /* Did the significand increment overflow? */
813 if(omsb == (unsigned) semantics->precision + 1) {
814 /* Renormalize by incrementing the exponent and shifting our
815 significand right one. However if we already have the
816 maximum exponent we overflow to infinity. */
817 if(exponent == semantics->maxExponent) {
818 category = fcInfinity;
820 return (opStatus) (opOverflow | opInexact);
823 shiftSignificandRight(1);
829 /* The normal case - we were and are not denormal, and any
830 significand increment above didn't overflow. */
831 if(omsb == semantics->precision)
834 /* We have a non-zero denormal. */
835 assert(omsb < semantics->precision);
836 assert(exponent == semantics->minExponent);
838 /* Canonicalize zeroes. */
842 /* The fcZero case is a denormal that underflowed to zero. */
843 return (opStatus) (opUnderflow | opInexact);
847 APFloat::addOrSubtractSpecials(const APFloat &rhs, bool subtract)
849 switch(convolve(category, rhs.category)) {
853 case convolve(fcNaN, fcZero):
854 case convolve(fcNaN, fcNormal):
855 case convolve(fcNaN, fcInfinity):
856 case convolve(fcNaN, fcNaN):
857 case convolve(fcNormal, fcZero):
858 case convolve(fcInfinity, fcNormal):
859 case convolve(fcInfinity, fcZero):
862 case convolve(fcZero, fcNaN):
863 case convolve(fcNormal, fcNaN):
864 case convolve(fcInfinity, fcNaN):
866 copySignificand(rhs);
869 case convolve(fcNormal, fcInfinity):
870 case convolve(fcZero, fcInfinity):
871 category = fcInfinity;
872 sign = rhs.sign ^ subtract;
875 case convolve(fcZero, fcNormal):
877 sign = rhs.sign ^ subtract;
880 case convolve(fcZero, fcZero):
881 /* Sign depends on rounding mode; handled by caller. */
884 case convolve(fcInfinity, fcInfinity):
885 /* Differently signed infinities can only be validly
887 if(sign ^ rhs.sign != subtract) {
889 // Arbitrary but deterministic value for significand
890 APInt::tcSet(significandParts(), ~0U, partCount());
896 case convolve(fcNormal, fcNormal):
901 /* Add or subtract two normal numbers. */
903 APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
906 lostFraction lost_fraction;
909 /* Determine if the operation on the absolute values is effectively
910 an addition or subtraction. */
911 subtract ^= (sign ^ rhs.sign);
913 /* Are we bigger exponent-wise than the RHS? */
914 bits = exponent - rhs.exponent;
916 /* Subtraction is more subtle than one might naively expect. */
918 APFloat temp_rhs(rhs);
922 reverse = compareAbsoluteValue(temp_rhs) == cmpLessThan;
923 lost_fraction = lfExactlyZero;
924 } else if (bits > 0) {
925 lost_fraction = temp_rhs.shiftSignificandRight(bits - 1);
926 shiftSignificandLeft(1);
929 lost_fraction = shiftSignificandRight(-bits - 1);
930 temp_rhs.shiftSignificandLeft(1);
935 carry = temp_rhs.subtractSignificand
936 (*this, lost_fraction != lfExactlyZero);
937 copySignificand(temp_rhs);
940 carry = subtractSignificand
941 (temp_rhs, lost_fraction != lfExactlyZero);
944 /* Invert the lost fraction - it was on the RHS and
946 if(lost_fraction == lfLessThanHalf)
947 lost_fraction = lfMoreThanHalf;
948 else if(lost_fraction == lfMoreThanHalf)
949 lost_fraction = lfLessThanHalf;
951 /* The code above is intended to ensure that no borrow is
956 APFloat temp_rhs(rhs);
958 lost_fraction = temp_rhs.shiftSignificandRight(bits);
959 carry = addSignificand(temp_rhs);
961 lost_fraction = shiftSignificandRight(-bits);
962 carry = addSignificand(rhs);
965 /* We have a guard bit; generating a carry cannot happen. */
969 return lost_fraction;
973 APFloat::multiplySpecials(const APFloat &rhs)
975 switch(convolve(category, rhs.category)) {
979 case convolve(fcNaN, fcZero):
980 case convolve(fcNaN, fcNormal):
981 case convolve(fcNaN, fcInfinity):
982 case convolve(fcNaN, fcNaN):
985 case convolve(fcZero, fcNaN):
986 case convolve(fcNormal, fcNaN):
987 case convolve(fcInfinity, fcNaN):
989 copySignificand(rhs);
992 case convolve(fcNormal, fcInfinity):
993 case convolve(fcInfinity, fcNormal):
994 case convolve(fcInfinity, fcInfinity):
995 category = fcInfinity;
998 case convolve(fcZero, fcNormal):
999 case convolve(fcNormal, fcZero):
1000 case convolve(fcZero, fcZero):
1004 case convolve(fcZero, fcInfinity):
1005 case convolve(fcInfinity, fcZero):
1007 // Arbitrary but deterministic value for significand
1008 APInt::tcSet(significandParts(), ~0U, partCount());
1011 case convolve(fcNormal, fcNormal):
1017 APFloat::divideSpecials(const APFloat &rhs)
1019 switch(convolve(category, rhs.category)) {
1023 case convolve(fcNaN, fcZero):
1024 case convolve(fcNaN, fcNormal):
1025 case convolve(fcNaN, fcInfinity):
1026 case convolve(fcNaN, fcNaN):
1027 case convolve(fcInfinity, fcZero):
1028 case convolve(fcInfinity, fcNormal):
1029 case convolve(fcZero, fcInfinity):
1030 case convolve(fcZero, fcNormal):
1033 case convolve(fcZero, fcNaN):
1034 case convolve(fcNormal, fcNaN):
1035 case convolve(fcInfinity, fcNaN):
1037 copySignificand(rhs);
1040 case convolve(fcNormal, fcInfinity):
1044 case convolve(fcNormal, fcZero):
1045 category = fcInfinity;
1048 case convolve(fcInfinity, fcInfinity):
1049 case convolve(fcZero, fcZero):
1051 // Arbitrary but deterministic value for significand
1052 APInt::tcSet(significandParts(), ~0U, partCount());
1055 case convolve(fcNormal, fcNormal):
1062 APFloat::changeSign()
1064 /* Look mummy, this one's easy. */
1069 APFloat::clearSign()
1071 /* So is this one. */
1076 APFloat::copySign(const APFloat &rhs)
1082 /* Normalized addition or subtraction. */
1084 APFloat::addOrSubtract(const APFloat &rhs, roundingMode rounding_mode,
1089 fs = addOrSubtractSpecials(rhs, subtract);
1091 /* This return code means it was not a simple case. */
1092 if(fs == opDivByZero) {
1093 lostFraction lost_fraction;
1095 lost_fraction = addOrSubtractSignificand(rhs, subtract);
1096 fs = normalize(rounding_mode, lost_fraction);
1098 /* Can only be zero if we lost no fraction. */
1099 assert(category != fcZero || lost_fraction == lfExactlyZero);
1102 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1103 positive zero unless rounding to minus infinity, except that
1104 adding two like-signed zeroes gives that zero. */
1105 if(category == fcZero) {
1106 if(rhs.category != fcZero || (sign == rhs.sign) == subtract)
1107 sign = (rounding_mode == rmTowardNegative);
1113 /* Normalized addition. */
1115 APFloat::add(const APFloat &rhs, roundingMode rounding_mode)
1117 return addOrSubtract(rhs, rounding_mode, false);
1120 /* Normalized subtraction. */
1122 APFloat::subtract(const APFloat &rhs, roundingMode rounding_mode)
1124 return addOrSubtract(rhs, rounding_mode, true);
1127 /* Normalized multiply. */
1129 APFloat::multiply(const APFloat &rhs, roundingMode rounding_mode)
1134 fs = multiplySpecials(rhs);
1136 if(category == fcNormal) {
1137 lostFraction lost_fraction = multiplySignificand(rhs, 0);
1138 fs = normalize(rounding_mode, lost_fraction);
1139 if(lost_fraction != lfExactlyZero)
1140 fs = (opStatus) (fs | opInexact);
1146 /* Normalized divide. */
1148 APFloat::divide(const APFloat &rhs, roundingMode rounding_mode)
1153 fs = divideSpecials(rhs);
1155 if(category == fcNormal) {
1156 lostFraction lost_fraction = divideSignificand(rhs);
1157 fs = normalize(rounding_mode, lost_fraction);
1158 if(lost_fraction != lfExactlyZero)
1159 fs = (opStatus) (fs | opInexact);
1165 /* Normalized remainder. */
1167 APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
1171 fs = V.divide(rhs, rmNearestTiesToEven);
1172 if (fs == opDivByZero)
1176 fs = V.convertToInteger(&x, integerPartWidth, true, rmNearestTiesToEven);
1177 if (fs==opInvalidOp)
1180 fs = V.convertFromInteger(&x, integerPartWidth, true, rmNearestTiesToEven);
1181 assert(fs==opOK); // should always work
1182 fs = V.multiply(rhs, rounding_mode);
1183 assert(fs==opOK); // should not overflow or underflow
1184 fs = subtract(V, rounding_mode);
1189 /* Normalized fused-multiply-add. */
1191 APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
1192 const APFloat &addend,
1193 roundingMode rounding_mode)
1197 /* Post-multiplication sign, before addition. */
1198 sign ^= multiplicand.sign;
1200 /* If and only if all arguments are normal do we need to do an
1201 extended-precision calculation. */
1202 if(category == fcNormal
1203 && multiplicand.category == fcNormal
1204 && addend.category == fcNormal) {
1205 lostFraction lost_fraction;
1207 lost_fraction = multiplySignificand(multiplicand, &addend);
1208 fs = normalize(rounding_mode, lost_fraction);
1209 if(lost_fraction != lfExactlyZero)
1210 fs = (opStatus) (fs | opInexact);
1212 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1213 positive zero unless rounding to minus infinity, except that
1214 adding two like-signed zeroes gives that zero. */
1215 if(category == fcZero && sign != addend.sign)
1216 sign = (rounding_mode == rmTowardNegative);
1218 fs = multiplySpecials(multiplicand);
1220 /* FS can only be opOK or opInvalidOp. There is no more work
1221 to do in the latter case. The IEEE-754R standard says it is
1222 implementation-defined in this case whether, if ADDEND is a
1223 quiet NaN, we raise invalid op; this implementation does so.
1225 If we need to do the addition we can do so with normal
1228 fs = addOrSubtract(addend, rounding_mode, false);
1234 /* Comparison requires normalized numbers. */
1236 APFloat::compare(const APFloat &rhs) const
1240 assert(semantics == rhs.semantics);
1242 switch(convolve(category, rhs.category)) {
1246 case convolve(fcNaN, fcZero):
1247 case convolve(fcNaN, fcNormal):
1248 case convolve(fcNaN, fcInfinity):
1249 case convolve(fcNaN, fcNaN):
1250 case convolve(fcZero, fcNaN):
1251 case convolve(fcNormal, fcNaN):
1252 case convolve(fcInfinity, fcNaN):
1253 return cmpUnordered;
1255 case convolve(fcInfinity, fcNormal):
1256 case convolve(fcInfinity, fcZero):
1257 case convolve(fcNormal, fcZero):
1261 return cmpGreaterThan;
1263 case convolve(fcNormal, fcInfinity):
1264 case convolve(fcZero, fcInfinity):
1265 case convolve(fcZero, fcNormal):
1267 return cmpGreaterThan;
1271 case convolve(fcInfinity, fcInfinity):
1272 if(sign == rhs.sign)
1277 return cmpGreaterThan;
1279 case convolve(fcZero, fcZero):
1282 case convolve(fcNormal, fcNormal):
1286 /* Two normal numbers. Do they have the same sign? */
1287 if(sign != rhs.sign) {
1289 result = cmpLessThan;
1291 result = cmpGreaterThan;
1293 /* Compare absolute values; invert result if negative. */
1294 result = compareAbsoluteValue(rhs);
1297 if(result == cmpLessThan)
1298 result = cmpGreaterThan;
1299 else if(result == cmpGreaterThan)
1300 result = cmpLessThan;
1308 APFloat::convert(const fltSemantics &toSemantics,
1309 roundingMode rounding_mode)
1311 unsigned int newPartCount;
1314 newPartCount = partCountForBits(toSemantics.precision + 1);
1316 /* If our new form is wider, re-allocate our bit pattern into wider
1318 if(newPartCount > partCount()) {
1319 integerPart *newParts;
1321 newParts = new integerPart[newPartCount];
1322 APInt::tcSet(newParts, 0, newPartCount);
1323 APInt::tcAssign(newParts, significandParts(), partCount());
1325 significand.parts = newParts;
1328 if(category == fcNormal) {
1329 /* Re-interpret our bit-pattern. */
1330 exponent += toSemantics.precision - semantics->precision;
1331 semantics = &toSemantics;
1332 fs = normalize(rounding_mode, lfExactlyZero);
1334 semantics = &toSemantics;
1341 /* Convert a floating point number to an integer according to the
1342 rounding mode. If the rounded integer value is out of range this
1343 returns an invalid operation exception. If the rounded value is in
1344 range but the floating point number is not the exact integer, the C
1345 standard doesn't require an inexact exception to be raised. IEEE
1346 854 does require it so we do that.
1348 Note that for conversions to integer type the C standard requires
1349 round-to-zero to always be used. */
1351 APFloat::convertToInteger(integerPart *parts, unsigned int width,
1353 roundingMode rounding_mode) const
1355 lostFraction lost_fraction;
1356 unsigned int msb, partsCount;
1359 /* Handle the three special cases first. */
1360 if(category == fcInfinity || category == fcNaN)
1363 partsCount = partCountForBits(width);
1365 if(category == fcZero) {
1366 APInt::tcSet(parts, 0, partsCount);
1370 /* Shift the bit pattern so the fraction is lost. */
1373 bits = (int) semantics->precision - 1 - exponent;
1376 lost_fraction = tmp.shiftSignificandRight(bits);
1378 tmp.shiftSignificandLeft(-bits);
1379 lost_fraction = lfExactlyZero;
1382 if(lost_fraction != lfExactlyZero
1383 && tmp.roundAwayFromZero(rounding_mode, lost_fraction))
1384 tmp.incrementSignificand();
1386 msb = tmp.significandMSB();
1388 /* Negative numbers cannot be represented as unsigned. */
1389 if(!isSigned && tmp.sign && msb != -1U)
1392 /* It takes exponent + 1 bits to represent the truncated floating
1393 point number without its sign. We lose a bit for the sign, but
1394 the maximally negative integer is a special case. */
1395 if(msb + 1 > width) /* !! Not same as msb >= width !! */
1398 if(isSigned && msb + 1 == width
1399 && (!tmp.sign || tmp.significandLSB() != msb))
1402 APInt::tcAssign(parts, tmp.significandParts(), partsCount);
1405 APInt::tcNegate(parts, partsCount);
1407 if(lost_fraction == lfExactlyZero)
1414 APFloat::convertFromUnsignedInteger(integerPart *parts,
1415 unsigned int partCount,
1416 roundingMode rounding_mode)
1418 unsigned int msb, precision;
1419 lostFraction lost_fraction;
1421 msb = APInt::tcMSB(parts, partCount) + 1;
1422 precision = semantics->precision;
1424 category = fcNormal;
1425 exponent = precision - 1;
1427 if(msb > precision) {
1428 exponent += (msb - precision);
1429 lost_fraction = shiftRight(parts, partCount, msb - precision);
1432 lost_fraction = lfExactlyZero;
1434 /* Copy the bit image. */
1436 APInt::tcAssign(significandParts(), parts, partCountForBits(msb));
1438 return normalize(rounding_mode, lost_fraction);
1442 APFloat::convertFromInteger(const integerPart *parts,
1443 unsigned int partCount, bool isSigned,
1444 roundingMode rounding_mode)
1450 copy = new integerPart[partCount];
1451 APInt::tcAssign(copy, parts, partCount);
1453 width = partCount * integerPartWidth;
1456 if(isSigned && APInt::tcExtractBit(parts, width - 1)) {
1458 APInt::tcNegate(copy, partCount);
1461 status = convertFromUnsignedInteger(copy, partCount, rounding_mode);
1468 APFloat::convertFromHexadecimalString(const char *p,
1469 roundingMode rounding_mode)
1471 lostFraction lost_fraction;
1472 integerPart *significand;
1473 unsigned int bitPos, partsCount;
1474 const char *dot, *firstSignificantDigit;
1478 category = fcNormal;
1480 significand = significandParts();
1481 partsCount = partCount();
1482 bitPos = partsCount * integerPartWidth;
1484 /* Skip leading zeroes and any(hexa)decimal point. */
1485 p = skipLeadingZeroesAndAnyDot(p, &dot);
1486 firstSignificantDigit = p;
1489 integerPart hex_value;
1496 hex_value = hexDigitValue(*p);
1497 if(hex_value == -1U) {
1498 lost_fraction = lfExactlyZero;
1504 /* Store the number whilst 4-bit nibbles remain. */
1507 hex_value <<= bitPos % integerPartWidth;
1508 significand[bitPos / integerPartWidth] |= hex_value;
1510 lost_fraction = trailingHexadecimalFraction(p, hex_value);
1511 while(hexDigitValue(*p) != -1U)
1517 /* Hex floats require an exponent but not a hexadecimal point. */
1518 assert(*p == 'p' || *p == 'P');
1520 /* Ignore the exponent if we are zero. */
1521 if(p != firstSignificantDigit) {
1524 /* Implicit hexadecimal point? */
1528 /* Calculate the exponent adjustment implicit in the number of
1529 significant digits. */
1530 expAdjustment = dot - firstSignificantDigit;
1531 if(expAdjustment < 0)
1533 expAdjustment = expAdjustment * 4 - 1;
1535 /* Adjust for writing the significand starting at the most
1536 significant nibble. */
1537 expAdjustment += semantics->precision;
1538 expAdjustment -= partsCount * integerPartWidth;
1540 /* Adjust for the given exponent. */
1541 exponent = totalExponent(p, expAdjustment);
1544 return normalize(rounding_mode, lost_fraction);
1548 APFloat::convertFromString(const char *p, roundingMode rounding_mode) {
1549 /* Handle a leading minus sign. */
1555 if(p[0] == '0' && (p[1] == 'x' || p[1] == 'X'))
1556 return convertFromHexadecimalString(p + 2, rounding_mode);
1558 assert(0 && "Decimal to binary conversions not yet implemented");
1562 // For good performance it is desirable for different APFloats
1563 // to produce different integers.
1565 APFloat::getHashValue() const {
1566 if (category==fcZero) return sign<<8 | semantics->precision ;
1567 else if (category==fcInfinity) return sign<<9 | semantics->precision;
1568 else if (category==fcNaN) return 1<<10 | semantics->precision;
1570 uint32_t hash = sign<<11 | semantics->precision | exponent<<12;
1571 const integerPart* p = significandParts();
1572 for (int i=partCount(); i>0; i--, p++)
1573 hash ^= ((uint32_t)*p) ^ (*p)>>32;
1578 // Conversion from APFloat to/from host float/double. It may eventually be
1579 // possible to eliminate these and have everybody deal with APFloats, but that
1580 // will take a while. This approach will not easily extend to long double.
1581 // Current implementation requires partCount()==1, which is correct at the
1582 // moment but could be made more general.
1585 APFloat::convertToDouble() const {
1586 assert(semantics == (const llvm::fltSemantics* const)&IEEEdouble);
1587 assert (partCount()==1);
1589 uint64_t myexponent, mysignificand;
1591 if (category==fcNormal) {
1592 mysignificand = *significandParts();
1593 myexponent = exponent+1023; //bias
1594 } else if (category==fcZero) {
1597 } else if (category==fcInfinity) {
1600 } else if (category==fcNaN) {
1602 mysignificand = *significandParts();
1606 return BitsToDouble((((uint64_t)sign & 1) << 63) |
1607 ((myexponent & 0x7ff) << 52) |
1608 (mysignificand & 0xfffffffffffffLL));
1612 APFloat::convertToFloat() const {
1613 assert(semantics == (const llvm::fltSemantics* const)&IEEEsingle);
1614 assert (partCount()==1);
1616 uint32_t myexponent, mysignificand;
1618 if (category==fcNormal) {
1619 myexponent = exponent+127; //bias
1620 mysignificand = *significandParts();
1621 } else if (category==fcZero) {
1624 } else if (category==fcInfinity) {
1627 } else if (category==fcNaN) {
1629 mysignificand = *significandParts();
1633 return BitsToFloat(((sign&1) << 31) | ((myexponent&0xff) << 23) |
1634 (mysignificand & 0x7fffff));
1637 APFloat::APFloat(double d) {
1638 uint64_t i = DoubleToBits(d);
1639 uint64_t myexponent = (i >> 52) & 0x7ff;
1640 uint64_t mysignificand = i & 0xfffffffffffffLL;
1642 initialize(&APFloat::IEEEdouble);
1643 assert(partCount()==1);
1646 if (myexponent==0 && mysignificand==0) {
1647 // exponent, significand meaningless
1649 } else if (myexponent==0x7ff && mysignificand==0) {
1650 // exponent, significand meaningless
1651 category = fcInfinity;
1652 } else if (myexponent==0x7ff && mysignificand!=0) {
1653 // exponent meaningless
1655 *significandParts() = mysignificand;
1657 category = fcNormal;
1658 exponent = myexponent - 1023;
1659 *significandParts() = mysignificand | 0x10000000000000LL;
1663 APFloat::APFloat(float f) {
1664 uint32_t i = FloatToBits(f);
1665 uint32_t myexponent = (i >> 23) & 0xff;
1666 uint32_t mysignificand = i & 0x7fffff;
1668 initialize(&APFloat::IEEEsingle);
1669 assert(partCount()==1);
1672 if (myexponent==0 && mysignificand==0) {
1673 // exponent, significand meaningless
1675 } else if (myexponent==0xff && mysignificand==0) {
1676 // exponent, significand meaningless
1677 category = fcInfinity;
1678 } else if (myexponent==0xff && (mysignificand & 0x400000)) {
1679 // sign, exponent, significand meaningless
1681 *significandParts() = mysignificand;
1683 category = fcNormal;
1684 exponent = myexponent - 127; //bias
1685 *significandParts() = mysignificand | 0x800000; // integer bit