+APFloat APFloat::getSmallest(const fltSemantics &Sem, bool Negative) {
+ // We want (in interchange format):
+ // sign = {Negative}
+ // exponent = 0..0
+ // significand = 0..01
+ APFloat Val(Sem, uninitialized);
+ Val.makeSmallest(Negative);
+ return Val;
+}
+
+APFloat APFloat::getSmallestNormalized(const fltSemantics &Sem, bool Negative) {
+ APFloat Val(Sem, uninitialized);
+
+ // We want (in interchange format):
+ // sign = {Negative}
+ // exponent = 0..0
+ // significand = 10..0
+
+ Val.category = fcNormal;
+ Val.zeroSignificand();
+ Val.sign = Negative;
+ Val.exponent = Sem.minExponent;
+ Val.significandParts()[partCountForBits(Sem.precision)-1] |=
+ (((integerPart) 1) << ((Sem.precision - 1) % integerPartWidth));
+
+ return Val;
+}
+
+APFloat::APFloat(const fltSemantics &Sem, const APInt &API) {
+ initFromAPInt(&Sem, API);
+}
+
+APFloat::APFloat(float f) {
+ initFromAPInt(&IEEEsingle, APInt::floatToBits(f));
+}
+
+APFloat::APFloat(double d) {
+ initFromAPInt(&IEEEdouble, APInt::doubleToBits(d));
+}
+
+namespace {
+ void append(SmallVectorImpl<char> &Buffer, StringRef Str) {
+ Buffer.append(Str.begin(), Str.end());
+ }
+
+ /// Removes data from the given significand until it is no more
+ /// precise than is required for the desired precision.
+ void AdjustToPrecision(APInt &significand,
+ int &exp, unsigned FormatPrecision) {
+ unsigned bits = significand.getActiveBits();
+
+ // 196/59 is a very slight overestimate of lg_2(10).
+ unsigned bitsRequired = (FormatPrecision * 196 + 58) / 59;
+
+ if (bits <= bitsRequired) return;
+
+ unsigned tensRemovable = (bits - bitsRequired) * 59 / 196;
+ if (!tensRemovable) return;
+
+ exp += tensRemovable;
+
+ APInt divisor(significand.getBitWidth(), 1);
+ APInt powten(significand.getBitWidth(), 10);
+ while (true) {
+ if (tensRemovable & 1)
+ divisor *= powten;
+ tensRemovable >>= 1;
+ if (!tensRemovable) break;
+ powten *= powten;
+ }
+
+ significand = significand.udiv(divisor);
+
+ // Truncate the significand down to its active bit count.
+ significand = significand.trunc(significand.getActiveBits());
+ }
+
+
+ void AdjustToPrecision(SmallVectorImpl<char> &buffer,
+ int &exp, unsigned FormatPrecision) {
+ unsigned N = buffer.size();
+ if (N <= FormatPrecision) return;
+
+ // The most significant figures are the last ones in the buffer.
+ unsigned FirstSignificant = N - FormatPrecision;
+
+ // Round.
+ // FIXME: this probably shouldn't use 'round half up'.
+
+ // Rounding down is just a truncation, except we also want to drop
+ // trailing zeros from the new result.
+ if (buffer[FirstSignificant - 1] < '5') {
+ while (FirstSignificant < N && buffer[FirstSignificant] == '0')
+ FirstSignificant++;
+
+ exp += FirstSignificant;
+ buffer.erase(&buffer[0], &buffer[FirstSignificant]);
+ return;
+ }
+
+ // Rounding up requires a decimal add-with-carry. If we continue
+ // the carry, the newly-introduced zeros will just be truncated.
+ for (unsigned I = FirstSignificant; I != N; ++I) {
+ if (buffer[I] == '9') {
+ FirstSignificant++;
+ } else {
+ buffer[I]++;
+ break;
+ }
+ }
+
+ // If we carried through, we have exactly one digit of precision.
+ if (FirstSignificant == N) {
+ exp += FirstSignificant;
+ buffer.clear();
+ buffer.push_back('1');
+ return;
+ }
+
+ exp += FirstSignificant;
+ buffer.erase(&buffer[0], &buffer[FirstSignificant]);
+ }
+}
+
+void APFloat::toString(SmallVectorImpl<char> &Str,
+ unsigned FormatPrecision,
+ unsigned FormatMaxPadding) const {
+ switch (category) {
+ case fcInfinity:
+ if (isNegative())
+ return append(Str, "-Inf");
+ else
+ return append(Str, "+Inf");
+
+ case fcNaN: return append(Str, "NaN");
+
+ case fcZero:
+ if (isNegative())
+ Str.push_back('-');
+
+ if (!FormatMaxPadding)
+ append(Str, "0.0E+0");
+ else
+ Str.push_back('0');
+ return;
+
+ case fcNormal:
+ break;
+ }
+
+ if (isNegative())
+ Str.push_back('-');
+
+ // Decompose the number into an APInt and an exponent.
+ int exp = exponent - ((int) semantics->precision - 1);
+ APInt significand(semantics->precision,
+ makeArrayRef(significandParts(),
+ partCountForBits(semantics->precision)));
+
+ // Set FormatPrecision if zero. We want to do this before we
+ // truncate trailing zeros, as those are part of the precision.
+ if (!FormatPrecision) {
+ // We use enough digits so the number can be round-tripped back to an
+ // APFloat. The formula comes from "How to Print Floating-Point Numbers
+ // Accurately" by Steele and White.
+ // FIXME: Using a formula based purely on the precision is conservative;
+ // we can print fewer digits depending on the actual value being printed.
+
+ // FormatPrecision = 2 + floor(significandBits / lg_2(10))
+ FormatPrecision = 2 + semantics->precision * 59 / 196;
+ }
+
+ // Ignore trailing binary zeros.
+ int trailingZeros = significand.countTrailingZeros();
+ exp += trailingZeros;
+ significand = significand.lshr(trailingZeros);
+
+ // Change the exponent from 2^e to 10^e.
+ if (exp == 0) {
+ // Nothing to do.
+ } else if (exp > 0) {
+ // Just shift left.
+ significand = significand.zext(semantics->precision + exp);
+ significand <<= exp;
+ exp = 0;
+ } else { /* exp < 0 */
+ int texp = -exp;
+
+ // We transform this using the identity:
+ // (N)(2^-e) == (N)(5^e)(10^-e)
+ // This means we have to multiply N (the significand) by 5^e.
+ // To avoid overflow, we have to operate on numbers large
+ // enough to store N * 5^e:
+ // log2(N * 5^e) == log2(N) + e * log2(5)
+ // <= semantics->precision + e * 137 / 59
+ // (log_2(5) ~ 2.321928 < 2.322034 ~ 137/59)
+
+ unsigned precision = semantics->precision + (137 * texp + 136) / 59;
+
+ // Multiply significand by 5^e.
+ // N * 5^0101 == N * 5^(1*1) * 5^(0*2) * 5^(1*4) * 5^(0*8)
+ significand = significand.zext(precision);
+ APInt five_to_the_i(precision, 5);
+ while (true) {
+ if (texp & 1) significand *= five_to_the_i;
+
+ texp >>= 1;
+ if (!texp) break;
+ five_to_the_i *= five_to_the_i;
+ }
+ }
+
+ AdjustToPrecision(significand, exp, FormatPrecision);
+
+ SmallVector<char, 256> buffer;
+
+ // Fill the buffer.
+ unsigned precision = significand.getBitWidth();
+ APInt ten(precision, 10);
+ APInt digit(precision, 0);
+
+ bool inTrail = true;
+ while (significand != 0) {
+ // digit <- significand % 10
+ // significand <- significand / 10
+ APInt::udivrem(significand, ten, significand, digit);
+
+ unsigned d = digit.getZExtValue();
+
+ // Drop trailing zeros.
+ if (inTrail && !d) exp++;
+ else {
+ buffer.push_back((char) ('0' + d));
+ inTrail = false;
+ }
+ }
+
+ assert(!buffer.empty() && "no characters in buffer!");
+
+ // Drop down to FormatPrecision.
+ // TODO: don't do more precise calculations above than are required.
+ AdjustToPrecision(buffer, exp, FormatPrecision);
+
+ unsigned NDigits = buffer.size();
+
+ // Check whether we should use scientific notation.
+ bool FormatScientific;
+ if (!FormatMaxPadding)
+ FormatScientific = true;
+ else {
+ if (exp >= 0) {
+ // 765e3 --> 765000
+ // ^^^
+ // But we shouldn't make the number look more precise than it is.
+ FormatScientific = ((unsigned) exp > FormatMaxPadding ||
+ NDigits + (unsigned) exp > FormatPrecision);
+ } else {
+ // Power of the most significant digit.
+ int MSD = exp + (int) (NDigits - 1);
+ if (MSD >= 0) {
+ // 765e-2 == 7.65
+ FormatScientific = false;
+ } else {
+ // 765e-5 == 0.00765
+ // ^ ^^
+ FormatScientific = ((unsigned) -MSD) > FormatMaxPadding;
+ }
+ }
+ }
+
+ // Scientific formatting is pretty straightforward.
+ if (FormatScientific) {
+ exp += (NDigits - 1);
+
+ Str.push_back(buffer[NDigits-1]);
+ Str.push_back('.');
+ if (NDigits == 1)
+ Str.push_back('0');
+ else
+ for (unsigned I = 1; I != NDigits; ++I)
+ Str.push_back(buffer[NDigits-1-I]);
+ Str.push_back('E');
+
+ Str.push_back(exp >= 0 ? '+' : '-');
+ if (exp < 0) exp = -exp;
+ SmallVector<char, 6> expbuf;
+ do {
+ expbuf.push_back((char) ('0' + (exp % 10)));
+ exp /= 10;
+ } while (exp);
+ for (unsigned I = 0, E = expbuf.size(); I != E; ++I)
+ Str.push_back(expbuf[E-1-I]);
+ return;
+ }
+
+ // Non-scientific, positive exponents.
+ if (exp >= 0) {
+ for (unsigned I = 0; I != NDigits; ++I)
+ Str.push_back(buffer[NDigits-1-I]);
+ for (unsigned I = 0; I != (unsigned) exp; ++I)
+ Str.push_back('0');
+ return;
+ }
+
+ // Non-scientific, negative exponents.
+
+ // The number of digits to the left of the decimal point.
+ int NWholeDigits = exp + (int) NDigits;
+
+ unsigned I = 0;
+ if (NWholeDigits > 0) {
+ for (; I != (unsigned) NWholeDigits; ++I)
+ Str.push_back(buffer[NDigits-I-1]);
+ Str.push_back('.');
+ } else {
+ unsigned NZeros = 1 + (unsigned) -NWholeDigits;
+
+ Str.push_back('0');
+ Str.push_back('.');
+ for (unsigned Z = 1; Z != NZeros; ++Z)
+ Str.push_back('0');
+ }
+
+ for (; I != NDigits; ++I)
+ Str.push_back(buffer[NDigits-I-1]);
+}
+
+bool APFloat::getExactInverse(APFloat *inv) const {
+ // Special floats and denormals have no exact inverse.
+ if (!isFiniteNonZero())
+ return false;
+
+ // Check that the number is a power of two by making sure that only the
+ // integer bit is set in the significand.
+ if (significandLSB() != semantics->precision - 1)
+ return false;
+
+ // Get the inverse.
+ APFloat reciprocal(*semantics, 1ULL);
+ if (reciprocal.divide(*this, rmNearestTiesToEven) != opOK)
+ return false;
+
+ // Avoid multiplication with a denormal, it is not safe on all platforms and
+ // may be slower than a normal division.
+ if (reciprocal.isDenormal())
+ return false;
+
+ assert(reciprocal.isFiniteNonZero() &&
+ reciprocal.significandLSB() == reciprocal.semantics->precision - 1);
+
+ if (inv)
+ *inv = reciprocal;
+
+ return true;
+}
+
+bool APFloat::isSignaling() const {
+ if (!isNaN())
+ return false;
+
+ // IEEE-754R 2008 6.2.1: A signaling NaN bit string should be encoded with the
+ // first bit of the trailing significand being 0.
+ return !APInt::tcExtractBit(significandParts(), semantics->precision - 2);
+}
+
+/// IEEE-754R 2008 5.3.1: nextUp/nextDown.
+///
+/// *NOTE* since nextDown(x) = -nextUp(-x), we only implement nextUp with
+/// appropriate sign switching before/after the computation.
+APFloat::opStatus APFloat::next(bool nextDown) {
+ // If we are performing nextDown, swap sign so we have -x.
+ if (nextDown)
+ changeSign();
+
+ // Compute nextUp(x)
+ opStatus result = opOK;
+
+ // Handle each float category separately.
+ switch (category) {
+ case fcInfinity:
+ // nextUp(+inf) = +inf
+ if (!isNegative())
+ break;
+ // nextUp(-inf) = -getLargest()
+ makeLargest(true);
+ break;
+ case fcNaN:
+ // IEEE-754R 2008 6.2 Par 2: nextUp(sNaN) = qNaN. Set Invalid flag.
+ // IEEE-754R 2008 6.2: nextUp(qNaN) = qNaN. Must be identity so we do not
+ // change the payload.
+ if (isSignaling()) {
+ result = opInvalidOp;
+ // For consistency, propagate the sign of the sNaN to the qNaN.
+ makeNaN(false, isNegative(), 0);
+ }
+ break;
+ case fcZero:
+ // nextUp(pm 0) = +getSmallest()
+ makeSmallest(false);
+ break;
+ case fcNormal:
+ // nextUp(-getSmallest()) = -0
+ if (isSmallest() && isNegative()) {
+ APInt::tcSet(significandParts(), 0, partCount());
+ category = fcZero;
+ exponent = 0;
+ break;
+ }
+
+ // nextUp(getLargest()) == INFINITY
+ if (isLargest() && !isNegative()) {
+ APInt::tcSet(significandParts(), 0, partCount());
+ category = fcInfinity;
+ exponent = semantics->maxExponent + 1;
+ break;
+ }
+
+ // nextUp(normal) == normal + inc.
+ if (isNegative()) {
+ // If we are negative, we need to decrement the significand.
+
+ // We only cross a binade boundary that requires adjusting the exponent
+ // if:
+ // 1. exponent != semantics->minExponent. This implies we are not in the
+ // smallest binade or are dealing with denormals.
+ // 2. Our significand excluding the integral bit is all zeros.
+ bool WillCrossBinadeBoundary =
+ exponent != semantics->minExponent && isSignificandAllZeros();
+
+ // Decrement the significand.
+ //
+ // We always do this since:
+ // 1. If we are dealing with a non-binade decrement, by definition we
+ // just decrement the significand.
+ // 2. If we are dealing with a normal -> normal binade decrement, since
+ // we have an explicit integral bit the fact that all bits but the
+ // integral bit are zero implies that subtracting one will yield a
+ // significand with 0 integral bit and 1 in all other spots. Thus we
+ // must just adjust the exponent and set the integral bit to 1.
+ // 3. If we are dealing with a normal -> denormal binade decrement,
+ // since we set the integral bit to 0 when we represent denormals, we
+ // just decrement the significand.
+ integerPart *Parts = significandParts();
+ APInt::tcDecrement(Parts, partCount());
+
+ if (WillCrossBinadeBoundary) {
+ // Our result is a normal number. Do the following:
+ // 1. Set the integral bit to 1.
+ // 2. Decrement the exponent.
+ APInt::tcSetBit(Parts, semantics->precision - 1);
+ exponent--;
+ }
+ } else {
+ // If we are positive, we need to increment the significand.
+
+ // We only cross a binade boundary that requires adjusting the exponent if
+ // the input is not a denormal and all of said input's significand bits
+ // are set. If all of said conditions are true: clear the significand, set
+ // the integral bit to 1, and increment the exponent. If we have a
+ // denormal always increment since moving denormals and the numbers in the
+ // smallest normal binade have the same exponent in our representation.
+ bool WillCrossBinadeBoundary = !isDenormal() && isSignificandAllOnes();
+
+ if (WillCrossBinadeBoundary) {
+ integerPart *Parts = significandParts();
+ APInt::tcSet(Parts, 0, partCount());
+ APInt::tcSetBit(Parts, semantics->precision - 1);
+ assert(exponent != semantics->maxExponent &&
+ "We can not increment an exponent beyond the maxExponent allowed"
+ " by the given floating point semantics.");
+ exponent++;
+ } else {
+ incrementSignificand();
+ }
+ }
+ break;
+ }
+
+ // If we are performing nextDown, swap sign so we have -nextUp(-x)
+ if (nextDown)
+ changeSign();
+
+ return result;
+}
+
+void
+APFloat::makeInf(bool Negative) {
+ category = fcInfinity;
+ sign = Negative;
+ exponent = semantics->maxExponent + 1;
+ APInt::tcSet(significandParts(), 0, partCount());
+}
+
+void
+APFloat::makeZero(bool Negative) {
+ category = fcZero;
+ sign = Negative;
+ exponent = semantics->minExponent-1;
+ APInt::tcSet(significandParts(), 0, partCount());
projects / oota-llvm.git / blobdiff