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 unsigned int origSign = sign;
1172 fs = V.divide(rhs, rmNearestTiesToEven);
1173 if (fs == opDivByZero)
1176 int parts = partCount();
1177 integerPart *x = new integerPart[parts];
1178 fs = V.convertToInteger(x, parts * integerPartWidth, true,
1179 rmNearestTiesToEven);
1180 if (fs==opInvalidOp)
1183 fs = V.convertFromInteger(x, parts, true, rmNearestTiesToEven);
1184 assert(fs==opOK); // should always work
1186 fs = V.multiply(rhs, rounding_mode);
1187 assert(fs==opOK || fs==opInexact); // should not overflow or underflow
1189 fs = subtract(V, rounding_mode);
1190 assert(fs==opOK || fs==opInexact); // likewise
1193 sign = origSign; // IEEE754 requires this
1198 /* Normalized fused-multiply-add. */
1200 APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
1201 const APFloat &addend,
1202 roundingMode rounding_mode)
1206 /* Post-multiplication sign, before addition. */
1207 sign ^= multiplicand.sign;
1209 /* If and only if all arguments are normal do we need to do an
1210 extended-precision calculation. */
1211 if(category == fcNormal
1212 && multiplicand.category == fcNormal
1213 && addend.category == fcNormal) {
1214 lostFraction lost_fraction;
1216 lost_fraction = multiplySignificand(multiplicand, &addend);
1217 fs = normalize(rounding_mode, lost_fraction);
1218 if(lost_fraction != lfExactlyZero)
1219 fs = (opStatus) (fs | opInexact);
1221 /* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
1222 positive zero unless rounding to minus infinity, except that
1223 adding two like-signed zeroes gives that zero. */
1224 if(category == fcZero && sign != addend.sign)
1225 sign = (rounding_mode == rmTowardNegative);
1227 fs = multiplySpecials(multiplicand);
1229 /* FS can only be opOK or opInvalidOp. There is no more work
1230 to do in the latter case. The IEEE-754R standard says it is
1231 implementation-defined in this case whether, if ADDEND is a
1232 quiet NaN, we raise invalid op; this implementation does so.
1234 If we need to do the addition we can do so with normal
1237 fs = addOrSubtract(addend, rounding_mode, false);
1243 /* Comparison requires normalized numbers. */
1245 APFloat::compare(const APFloat &rhs) const
1249 assert(semantics == rhs.semantics);
1251 switch(convolve(category, rhs.category)) {
1255 case convolve(fcNaN, fcZero):
1256 case convolve(fcNaN, fcNormal):
1257 case convolve(fcNaN, fcInfinity):
1258 case convolve(fcNaN, fcNaN):
1259 case convolve(fcZero, fcNaN):
1260 case convolve(fcNormal, fcNaN):
1261 case convolve(fcInfinity, fcNaN):
1262 return cmpUnordered;
1264 case convolve(fcInfinity, fcNormal):
1265 case convolve(fcInfinity, fcZero):
1266 case convolve(fcNormal, fcZero):
1270 return cmpGreaterThan;
1272 case convolve(fcNormal, fcInfinity):
1273 case convolve(fcZero, fcInfinity):
1274 case convolve(fcZero, fcNormal):
1276 return cmpGreaterThan;
1280 case convolve(fcInfinity, fcInfinity):
1281 if(sign == rhs.sign)
1286 return cmpGreaterThan;
1288 case convolve(fcZero, fcZero):
1291 case convolve(fcNormal, fcNormal):
1295 /* Two normal numbers. Do they have the same sign? */
1296 if(sign != rhs.sign) {
1298 result = cmpLessThan;
1300 result = cmpGreaterThan;
1302 /* Compare absolute values; invert result if negative. */
1303 result = compareAbsoluteValue(rhs);
1306 if(result == cmpLessThan)
1307 result = cmpGreaterThan;
1308 else if(result == cmpGreaterThan)
1309 result = cmpLessThan;
1317 APFloat::convert(const fltSemantics &toSemantics,
1318 roundingMode rounding_mode)
1320 unsigned int newPartCount;
1323 newPartCount = partCountForBits(toSemantics.precision + 1);
1325 /* If our new form is wider, re-allocate our bit pattern into wider
1327 If we're narrowing from multiple words to 1 words, copy to the single
1328 word. If we are losing information by doing this, we would have to
1329 worry about rounding; right now the only case is f80 -> shorter
1330 conversion, and we are keeping all 64 significant bits, so it's OK. */
1331 if(newPartCount > partCount()) {
1332 integerPart *newParts;
1334 newParts = new integerPart[newPartCount];
1335 APInt::tcSet(newParts, 0, newPartCount);
1336 APInt::tcAssign(newParts, significandParts(), partCount());
1338 significand.parts = newParts;
1339 } else if (newPartCount==1 && newPartCount < partCount()) {
1340 integerPart newPart;
1342 APInt::tcSet(&newPart, 0, newPartCount);
1343 APInt::tcAssign(&newPart, significandParts(), partCount());
1345 significand.part = newPart;
1348 if(category == fcNormal) {
1349 /* Re-interpret our bit-pattern. */
1350 exponent += toSemantics.precision - semantics->precision;
1351 semantics = &toSemantics;
1352 fs = normalize(rounding_mode, lfExactlyZero);
1354 semantics = &toSemantics;
1361 /* Convert a floating point number to an integer according to the
1362 rounding mode. If the rounded integer value is out of range this
1363 returns an invalid operation exception. If the rounded value is in
1364 range but the floating point number is not the exact integer, the C
1365 standard doesn't require an inexact exception to be raised. IEEE
1366 854 does require it so we do that.
1368 Note that for conversions to integer type the C standard requires
1369 round-to-zero to always be used. */
1371 APFloat::convertToInteger(integerPart *parts, unsigned int width,
1373 roundingMode rounding_mode) const
1375 lostFraction lost_fraction;
1376 unsigned int msb, partsCount;
1379 /* Handle the three special cases first. */
1380 if(category == fcInfinity || category == fcNaN)
1383 partsCount = partCountForBits(width);
1385 if(category == fcZero) {
1386 APInt::tcSet(parts, 0, partsCount);
1390 /* Shift the bit pattern so the fraction is lost. */
1393 bits = (int) semantics->precision - 1 - exponent;
1396 lost_fraction = tmp.shiftSignificandRight(bits);
1398 tmp.shiftSignificandLeft(-bits);
1399 lost_fraction = lfExactlyZero;
1402 if(lost_fraction != lfExactlyZero
1403 && tmp.roundAwayFromZero(rounding_mode, lost_fraction))
1404 tmp.incrementSignificand();
1406 msb = tmp.significandMSB();
1408 /* Negative numbers cannot be represented as unsigned. */
1409 if(!isSigned && tmp.sign && msb != -1U)
1412 /* It takes exponent + 1 bits to represent the truncated floating
1413 point number without its sign. We lose a bit for the sign, but
1414 the maximally negative integer is a special case. */
1415 if(msb + 1 > width) /* !! Not same as msb >= width !! */
1418 if(isSigned && msb + 1 == width
1419 && (!tmp.sign || tmp.significandLSB() != msb))
1422 APInt::tcAssign(parts, tmp.significandParts(), partsCount);
1425 APInt::tcNegate(parts, partsCount);
1427 if(lost_fraction == lfExactlyZero)
1434 APFloat::convertFromUnsignedInteger(integerPart *parts,
1435 unsigned int partCount,
1436 roundingMode rounding_mode)
1438 unsigned int msb, precision;
1439 lostFraction lost_fraction;
1441 msb = APInt::tcMSB(parts, partCount) + 1;
1442 precision = semantics->precision;
1444 category = fcNormal;
1445 exponent = precision - 1;
1447 if(msb > precision) {
1448 exponent += (msb - precision);
1449 lost_fraction = shiftRight(parts, partCount, msb - precision);
1452 lost_fraction = lfExactlyZero;
1454 /* Copy the bit image. */
1456 APInt::tcAssign(significandParts(), parts, partCountForBits(msb));
1458 return normalize(rounding_mode, lost_fraction);
1462 APFloat::convertFromInteger(const integerPart *parts,
1463 unsigned int partCount, bool isSigned,
1464 roundingMode rounding_mode)
1470 copy = new integerPart[partCount];
1471 APInt::tcAssign(copy, parts, partCount);
1473 width = partCount * integerPartWidth;
1476 if(isSigned && APInt::tcExtractBit(parts, width - 1)) {
1478 APInt::tcNegate(copy, partCount);
1481 status = convertFromUnsignedInteger(copy, partCount, rounding_mode);
1488 APFloat::convertFromHexadecimalString(const char *p,
1489 roundingMode rounding_mode)
1491 lostFraction lost_fraction;
1492 integerPart *significand;
1493 unsigned int bitPos, partsCount;
1494 const char *dot, *firstSignificantDigit;
1498 category = fcNormal;
1500 significand = significandParts();
1501 partsCount = partCount();
1502 bitPos = partsCount * integerPartWidth;
1504 /* Skip leading zeroes and any(hexa)decimal point. */
1505 p = skipLeadingZeroesAndAnyDot(p, &dot);
1506 firstSignificantDigit = p;
1509 integerPart hex_value;
1516 hex_value = hexDigitValue(*p);
1517 if(hex_value == -1U) {
1518 lost_fraction = lfExactlyZero;
1524 /* Store the number whilst 4-bit nibbles remain. */
1527 hex_value <<= bitPos % integerPartWidth;
1528 significand[bitPos / integerPartWidth] |= hex_value;
1530 lost_fraction = trailingHexadecimalFraction(p, hex_value);
1531 while(hexDigitValue(*p) != -1U)
1537 /* Hex floats require an exponent but not a hexadecimal point. */
1538 assert(*p == 'p' || *p == 'P');
1540 /* Ignore the exponent if we are zero. */
1541 if(p != firstSignificantDigit) {
1544 /* Implicit hexadecimal point? */
1548 /* Calculate the exponent adjustment implicit in the number of
1549 significant digits. */
1550 expAdjustment = dot - firstSignificantDigit;
1551 if(expAdjustment < 0)
1553 expAdjustment = expAdjustment * 4 - 1;
1555 /* Adjust for writing the significand starting at the most
1556 significant nibble. */
1557 expAdjustment += semantics->precision;
1558 expAdjustment -= partsCount * integerPartWidth;
1560 /* Adjust for the given exponent. */
1561 exponent = totalExponent(p, expAdjustment);
1564 return normalize(rounding_mode, lost_fraction);
1568 APFloat::convertFromString(const char *p, roundingMode rounding_mode) {
1569 /* Handle a leading minus sign. */
1575 if(p[0] == '0' && (p[1] == 'x' || p[1] == 'X'))
1576 return convertFromHexadecimalString(p + 2, rounding_mode);
1578 assert(0 && "Decimal to binary conversions not yet implemented");
1582 // For good performance it is desirable for different APFloats
1583 // to produce different integers.
1585 APFloat::getHashValue() const {
1586 if (category==fcZero) return sign<<8 | semantics->precision ;
1587 else if (category==fcInfinity) return sign<<9 | semantics->precision;
1588 else if (category==fcNaN) return 1<<10 | semantics->precision;
1590 uint32_t hash = sign<<11 | semantics->precision | exponent<<12;
1591 const integerPart* p = significandParts();
1592 for (int i=partCount(); i>0; i--, p++)
1593 hash ^= ((uint32_t)*p) ^ (*p)>>32;
1598 // Conversion from APFloat to/from host float/double. It may eventually be
1599 // possible to eliminate these and have everybody deal with APFloats, but that
1600 // will take a while. This approach will not easily extend to long double.
1601 // Current implementation requires integerPartWidth==64, which is correct at
1602 // the moment but could be made more general.
1604 // Denormals have exponent minExponent in APFloat, but minExponent-1 in
1605 // the actual IEEE respresentations. We compensate for that here.
1608 APFloat::convertF80LongDoubleAPFloatToAPInt() const {
1609 assert(semantics == (const llvm::fltSemantics* const)&x87DoubleExtended);
1610 assert (partCount()==2);
1612 uint64_t myexponent, mysignificand;
1614 if (category==fcNormal) {
1615 myexponent = exponent+16383; //bias
1616 mysignificand = significandParts()[0];
1617 if (myexponent==1 && !(mysignificand & 0x8000000000000000ULL))
1618 myexponent = 0; // denormal
1619 } else if (category==fcZero) {
1622 } else if (category==fcInfinity) {
1623 myexponent = 0x7fff;
1624 mysignificand = 0x8000000000000000ULL;
1625 } else if (category==fcNaN) {
1626 myexponent = 0x7fff;
1627 mysignificand = significandParts()[0];
1632 words[0] = (((uint64_t)sign & 1) << 63) |
1633 ((myexponent & 0x7fff) << 48) |
1634 ((mysignificand >>16) & 0xffffffffffffLL);
1635 words[1] = mysignificand & 0xffff;
1636 APInt api(80, 2, words);
1641 APFloat::convertDoubleAPFloatToAPInt() const {
1642 assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
1643 assert (partCount()==1);
1645 uint64_t myexponent, mysignificand;
1647 if (category==fcNormal) {
1648 myexponent = exponent+1023; //bias
1649 mysignificand = *significandParts();
1650 if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
1651 myexponent = 0; // denormal
1652 } else if (category==fcZero) {
1655 } else if (category==fcInfinity) {
1658 } else if (category==fcNaN) {
1660 mysignificand = *significandParts();
1664 APInt api(64, (((((uint64_t)sign & 1) << 63) |
1665 ((myexponent & 0x7ff) << 52) |
1666 (mysignificand & 0xfffffffffffffLL))));
1671 APFloat::convertFloatAPFloatToAPInt() const {
1672 assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
1673 assert (partCount()==1);
1675 uint32_t myexponent, mysignificand;
1677 if (category==fcNormal) {
1678 myexponent = exponent+127; //bias
1679 mysignificand = *significandParts();
1680 if (myexponent == 1 && !(mysignificand & 0x400000))
1681 myexponent = 0; // denormal
1682 } else if (category==fcZero) {
1685 } else if (category==fcInfinity) {
1688 } else if (category==fcNaN) {
1690 mysignificand = *significandParts();
1694 APInt api(32, (((sign&1) << 31) | ((myexponent&0xff) << 23) |
1695 (mysignificand & 0x7fffff)));
1700 APFloat::convertToAPInt() const {
1701 if (semantics == (const llvm::fltSemantics* const)&IEEEsingle)
1702 return convertFloatAPFloatToAPInt();
1703 else if (semantics == (const llvm::fltSemantics* const)&IEEEdouble)
1704 return convertDoubleAPFloatToAPInt();
1705 else if (semantics == (const llvm::fltSemantics* const)&x87DoubleExtended)
1706 return convertF80LongDoubleAPFloatToAPInt();
1712 APFloat::convertToFloat() const {
1713 assert(semantics == (const llvm::fltSemantics* const)&IEEEsingle);
1714 APInt api = convertToAPInt();
1715 return api.bitsToFloat();
1719 APFloat::convertToDouble() const {
1720 assert(semantics == (const llvm::fltSemantics* const)&IEEEdouble);
1721 APInt api = convertToAPInt();
1722 return api.bitsToDouble();
1725 /// Integer bit is explicit in this format. Current Intel book does not
1726 /// define meaning of:
1727 /// exponent = all 1's, integer bit not set.
1728 /// exponent = 0, integer bit set. (formerly "psuedodenormals")
1729 /// exponent!=0 nor all 1's, integer bit not set. (formerly "unnormals")
1731 APFloat::initFromF80LongDoubleAPInt(const APInt &api) {
1732 assert(api.getBitWidth()==80);
1733 uint64_t i1 = api.getRawData()[0];
1734 uint64_t i2 = api.getRawData()[1];
1735 uint64_t myexponent = (i1 >> 48) & 0x7fff;
1736 uint64_t mysignificand = ((i1 << 16) & 0xffffffffffff0000ULL) |
1739 initialize(&APFloat::x87DoubleExtended);
1740 assert(partCount()==2);
1743 if (myexponent==0 && mysignificand==0) {
1744 // exponent, significand meaningless
1746 } else if (myexponent==0x7fff && mysignificand==0x8000000000000000ULL) {
1747 // exponent, significand meaningless
1748 category = fcInfinity;
1749 } else if (myexponent==0x7fff && mysignificand!=0x8000000000000000ULL) {
1750 // exponent meaningless
1752 significandParts()[0] = mysignificand;
1753 significandParts()[1] = 0;
1755 category = fcNormal;
1756 exponent = myexponent - 16383;
1757 significandParts()[0] = mysignificand;
1758 significandParts()[1] = 0;
1759 if (myexponent==0) // denormal
1765 APFloat::initFromDoubleAPInt(const APInt &api) {
1766 assert(api.getBitWidth()==64);
1767 uint64_t i = *api.getRawData();
1768 uint64_t myexponent = (i >> 52) & 0x7ff;
1769 uint64_t mysignificand = i & 0xfffffffffffffLL;
1771 initialize(&APFloat::IEEEdouble);
1772 assert(partCount()==1);
1775 if (myexponent==0 && mysignificand==0) {
1776 // exponent, significand meaningless
1778 } else if (myexponent==0x7ff && mysignificand==0) {
1779 // exponent, significand meaningless
1780 category = fcInfinity;
1781 } else if (myexponent==0x7ff && mysignificand!=0) {
1782 // exponent meaningless
1784 *significandParts() = mysignificand;
1786 category = fcNormal;
1787 exponent = myexponent - 1023;
1788 *significandParts() = mysignificand;
1789 if (myexponent==0) // denormal
1792 *significandParts() |= 0x10000000000000LL; // integer bit
1797 APFloat::initFromFloatAPInt(const APInt & api) {
1798 assert(api.getBitWidth()==32);
1799 uint32_t i = (uint32_t)*api.getRawData();
1800 uint32_t myexponent = (i >> 23) & 0xff;
1801 uint32_t mysignificand = i & 0x7fffff;
1803 initialize(&APFloat::IEEEsingle);
1804 assert(partCount()==1);
1807 if (myexponent==0 && mysignificand==0) {
1808 // exponent, significand meaningless
1810 } else if (myexponent==0xff && mysignificand==0) {
1811 // exponent, significand meaningless
1812 category = fcInfinity;
1813 } else if (myexponent==0xff && (mysignificand & 0x400000)) {
1814 // sign, exponent, significand meaningless
1816 *significandParts() = mysignificand;
1818 category = fcNormal;
1819 exponent = myexponent - 127; //bias
1820 *significandParts() = mysignificand;
1821 if (myexponent==0) // denormal
1824 *significandParts() |= 0x800000; // integer bit
1828 /// Treat api as containing the bits of a floating point number. Currently
1829 /// we infer the floating point type from the size of the APInt. FIXME: This
1830 /// breaks when we get to PPC128 and IEEE128 (but both cannot exist in the
1831 /// same compile...)
1833 APFloat::initFromAPInt(const APInt& api) {
1834 if (api.getBitWidth() == 32)
1835 return initFromFloatAPInt(api);
1836 else if (api.getBitWidth()==64)
1837 return initFromDoubleAPInt(api);
1838 else if (api.getBitWidth()==80)
1839 return initFromF80LongDoubleAPInt(api);
1844 APFloat::APFloat(const APInt& api) {
1848 APFloat::APFloat(float f) {
1849 APInt api = APInt(32, 0);
1850 initFromAPInt(api.floatToBits(f));
1853 APFloat::APFloat(double d) {
1854 APInt api = APInt(64, 0);
1855 initFromAPInt(api.doubleToBits(d));