//
// The LLVM Compiler Infrastructure
//
-// This file was developed by Neil Booth and is distributed under the
-// University of Illinois Open Source License. See LICENSE.TXT for details.
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
//
//===----------------------------------------------------------------------===//
-#include <cassert>
#include "llvm/ADT/APFloat.h"
+#include "llvm/ADT/FoldingSet.h"
+#include <cassert>
+#include <cstring>
#include "llvm/Support/MathExtras.h"
using namespace llvm;
#define convolve(lhs, rhs) ((lhs) * 4 + (rhs))
-/* Assumed in hexadecimal significand parsing. */
+/* Assumed in hexadecimal significand parsing, and conversion to
+ hexadecimal strings. */
COMPILE_TIME_ASSERT(integerPartWidth % 4 == 0);
namespace llvm {
/* Number of bits in the significand. This includes the integer
bit. */
- unsigned char precision;
+ unsigned int precision;
- /* If the target format has an implicit integer bit. */
- bool implicitIntegerBit;
+ /* True if arithmetic is supported. */
+ unsigned int arithmeticOK;
};
const fltSemantics APFloat::IEEEsingle = { 127, -126, 24, true };
const fltSemantics APFloat::IEEEdouble = { 1023, -1022, 53, true };
const fltSemantics APFloat::IEEEquad = { 16383, -16382, 113, true };
- const fltSemantics APFloat::x87DoubleExtended = { 16383, -16382, 64, false };
- const fltSemantics APFloat::Bogus = { 0, 0, 0, false };
+ const fltSemantics APFloat::x87DoubleExtended = { 16383, -16382, 64, true };
+ const fltSemantics APFloat::Bogus = { 0, 0, 0, true };
+
+ // The PowerPC format consists of two doubles. It does not map cleanly
+ // onto the usual format above. For now only storage of constants of
+ // this type is supported, no arithmetic.
+ const fltSemantics APFloat::PPCDoubleDouble = { 1023, -1022, 106, false };
+
+ /* A tight upper bound on number of parts required to hold the value
+ pow(5, power) is
+
+ power * 815 / (351 * integerPartWidth) + 1
+
+ However, whilst the result may require only this many parts,
+ because we are multiplying two values to get it, the
+ multiplication may require an extra part with the excess part
+ being zero (consider the trivial case of 1 * 1, tcFullMultiply
+ requires two parts to hold the single-part result). So we add an
+ extra one to guarantee enough space whilst multiplying. */
+ const unsigned int maxExponent = 16383;
+ const unsigned int maxPrecision = 113;
+ const unsigned int maxPowerOfFiveExponent = maxExponent + maxPrecision - 1;
+ const unsigned int maxPowerOfFiveParts = 2 + ((maxPowerOfFiveExponent * 815)
+ / (351 * integerPartWidth));
}
/* Put a bunch of private, handy routines in an anonymous namespace. */
return ((bits) + integerPartWidth - 1) / integerPartWidth;
}
- unsigned int
- digitValue(unsigned int c)
+ /* Returns 0U-9U. Return values >= 10U are not digits. */
+ inline unsigned int
+ decDigitValue(unsigned int c)
{
- unsigned int r;
-
- r = c - '0';
- if(r <= 9)
- return r;
-
- return -1U;
+ return c - '0';
}
unsigned int
- hexDigitValue (unsigned int c)
+ hexDigitValue(unsigned int c)
{
unsigned int r;
return -1U;
}
+ inline void
+ assertArithmeticOK(const llvm::fltSemantics &semantics) {
+ assert(semantics.arithmeticOK
+ && "Compile-time arithmetic does not support these semantics");
+ }
+
+ /* Return the value of a decimal exponent of the form
+ [+-]ddddddd.
+
+ If the exponent overflows, returns a large exponent with the
+ appropriate sign. */
+ int
+ readExponent(const char *p)
+ {
+ bool isNegative;
+ unsigned int absExponent;
+ const unsigned int overlargeExponent = 24000; /* FIXME. */
+
+ isNegative = (*p == '-');
+ if (*p == '-' || *p == '+')
+ p++;
+
+ absExponent = decDigitValue(*p++);
+ assert (absExponent < 10U);
+
+ for (;;) {
+ unsigned int value;
+
+ value = decDigitValue(*p);
+ if (value >= 10U)
+ break;
+
+ p++;
+ value += absExponent * 10;
+ if (absExponent >= overlargeExponent) {
+ absExponent = overlargeExponent;
+ break;
+ }
+ absExponent = value;
+ }
+
+ if (isNegative)
+ return -(int) absExponent;
+ else
+ return (int) absExponent;
+ }
+
/* This is ugly and needs cleaning up, but I don't immediately see
how whilst remaining safe. */
- static int
+ int
totalExponent(const char *p, int exponentAdjustment)
{
integerPart unsignedExponent;
for(;;) {
unsigned int value;
- value = digitValue(*p);
- if(value == -1U)
- break;
+ value = decDigitValue(*p);
+ if(value >= 10U)
+ break;
p++;
unsignedExponent = unsignedExponent * 10 + value;
if(unsignedExponent > 65535)
- overflow = true;
+ overflow = true;
}
if(exponentAdjustment > 65535 || exponentAdjustment < -65536)
if(!overflow) {
exponent = unsignedExponent;
if(negative)
- exponent = -exponent;
+ exponent = -exponent;
exponent += exponentAdjustment;
if(exponent > 65535 || exponent < -65536)
- overflow = true;
+ overflow = true;
}
if(overflow)
if(*p == '.') {
*dot = p++;
while(*p == '0')
- p++;
+ p++;
}
return p;
}
+ /* Given a normal decimal floating point number of the form
+
+ dddd.dddd[eE][+-]ddd
+
+ where the decimal point and exponent are optional, fill out the
+ structure D. Exponent is appropriate if the significand is
+ treated as an integer, and normalizedExponent if the significand
+ is taken to have the decimal point after a single leading
+ non-zero digit.
+
+ If the value is zero, V->firstSigDigit points to a non-digit, and
+ the return exponent is zero.
+ */
+ struct decimalInfo {
+ const char *firstSigDigit;
+ const char *lastSigDigit;
+ int exponent;
+ int normalizedExponent;
+ };
+
+ void
+ interpretDecimal(const char *p, decimalInfo *D)
+ {
+ const char *dot;
+
+ p = skipLeadingZeroesAndAnyDot (p, &dot);
+
+ D->firstSigDigit = p;
+ D->exponent = 0;
+ D->normalizedExponent = 0;
+
+ for (;;) {
+ if (*p == '.') {
+ assert(dot == 0);
+ dot = p++;
+ }
+ if (decDigitValue(*p) >= 10U)
+ break;
+ p++;
+ }
+
+ /* If number is all zerooes accept any exponent. */
+ if (p != D->firstSigDigit) {
+ if (*p == 'e' || *p == 'E')
+ D->exponent = readExponent(p + 1);
+
+ /* Implied decimal point? */
+ if (!dot)
+ dot = p;
+
+ /* Drop insignificant trailing zeroes. */
+ do
+ do
+ p--;
+ while (*p == '0');
+ while (*p == '.');
+
+ /* Adjust the exponents for any decimal point. */
+ D->exponent += (dot - p) - (dot > p);
+ D->normalizedExponent = (D->exponent + (p - D->firstSigDigit)
+ - (dot > D->firstSigDigit && dot < p));
+ }
+
+ D->lastSigDigit = p;
+ }
+
/* Return the trailing fraction of a hexadecimal number.
DIGITVALUE is the first hex digit of the fraction, P points to
the next digit. */
return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf;
}
- /* Return the fraction lost were a bignum truncated. */
+ /* Return the fraction lost were a bignum truncated losing the least
+ significant BITS bits. */
lostFraction
- lostFractionThroughTruncation(integerPart *parts,
- unsigned int partCount,
- unsigned int bits)
+ lostFractionThroughTruncation(const integerPart *parts,
+ unsigned int partCount,
+ unsigned int bits)
{
unsigned int lsb;
return lost_fraction;
}
+
+ /* Combine the effect of two lost fractions. */
+ lostFraction
+ combineLostFractions(lostFraction moreSignificant,
+ lostFraction lessSignificant)
+ {
+ if(lessSignificant != lfExactlyZero) {
+ if(moreSignificant == lfExactlyZero)
+ moreSignificant = lfLessThanHalf;
+ else if(moreSignificant == lfExactlyHalf)
+ moreSignificant = lfMoreThanHalf;
+ }
+
+ return moreSignificant;
+ }
+
+ /* The error from the true value, in half-ulps, on multiplying two
+ floating point numbers, which differ from the value they
+ approximate by at most HUE1 and HUE2 half-ulps, is strictly less
+ than the returned value.
+
+ See "How to Read Floating Point Numbers Accurately" by William D
+ Clinger. */
+ unsigned int
+ HUerrBound(bool inexactMultiply, unsigned int HUerr1, unsigned int HUerr2)
+ {
+ assert(HUerr1 < 2 || HUerr2 < 2 || (HUerr1 + HUerr2 < 8));
+
+ if (HUerr1 + HUerr2 == 0)
+ return inexactMultiply * 2; /* <= inexactMultiply half-ulps. */
+ else
+ return inexactMultiply + 2 * (HUerr1 + HUerr2);
+ }
+
+ /* The number of ulps from the boundary (zero, or half if ISNEAREST)
+ when the least significant BITS are truncated. BITS cannot be
+ zero. */
+ integerPart
+ ulpsFromBoundary(const integerPart *parts, unsigned int bits, bool isNearest)
+ {
+ unsigned int count, partBits;
+ integerPart part, boundary;
+
+ assert (bits != 0);
+
+ bits--;
+ count = bits / integerPartWidth;
+ partBits = bits % integerPartWidth + 1;
+
+ part = parts[count] & (~(integerPart) 0 >> (integerPartWidth - partBits));
+
+ if (isNearest)
+ boundary = (integerPart) 1 << (partBits - 1);
+ else
+ boundary = 0;
+
+ if (count == 0) {
+ if (part - boundary <= boundary - part)
+ return part - boundary;
+ else
+ return boundary - part;
+ }
+
+ if (part == boundary) {
+ while (--count)
+ if (parts[count])
+ return ~(integerPart) 0; /* A lot. */
+
+ return parts[0];
+ } else if (part == boundary - 1) {
+ while (--count)
+ if (~parts[count])
+ return ~(integerPart) 0; /* A lot. */
+
+ return -parts[0];
+ }
+
+ return ~(integerPart) 0; /* A lot. */
+ }
+
+ /* Place pow(5, power) in DST, and return the number of parts used.
+ DST must be at least one part larger than size of the answer. */
+ unsigned int
+ powerOf5(integerPart *dst, unsigned int power)
+ {
+ static integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125,
+ 15625, 78125 };
+ static integerPart pow5s[maxPowerOfFiveParts * 2 + 5] = { 78125 * 5 };
+ static unsigned int partsCount[16] = { 1 };
+
+ integerPart scratch[maxPowerOfFiveParts], *p1, *p2, *pow5;
+ unsigned int result;
+
+ assert(power <= maxExponent);
+
+ p1 = dst;
+ p2 = scratch;
+
+ *p1 = firstEightPowers[power & 7];
+ power >>= 3;
+
+ result = 1;
+ pow5 = pow5s;
+
+ for (unsigned int n = 0; power; power >>= 1, n++) {
+ unsigned int pc;
+
+ pc = partsCount[n];
+
+ /* Calculate pow(5,pow(2,n+3)) if we haven't yet. */
+ if (pc == 0) {
+ pc = partsCount[n - 1];
+ APInt::tcFullMultiply(pow5, pow5 - pc, pow5 - pc, pc, pc);
+ pc *= 2;
+ if (pow5[pc - 1] == 0)
+ pc--;
+ partsCount[n] = pc;
+ }
+
+ if (power & 1) {
+ integerPart *tmp;
+
+ APInt::tcFullMultiply(p2, p1, pow5, result, pc);
+ result += pc;
+ if (p2[result - 1] == 0)
+ result--;
+
+ /* Now result is in p1 with partsCount parts and p2 is scratch
+ space. */
+ tmp = p1, p1 = p2, p2 = tmp;
+ }
+
+ pow5 += pc;
+ }
+
+ if (p1 != dst)
+ APInt::tcAssign(dst, p1, result);
+
+ return result;
+ }
+
+ /* Zero at the end to avoid modular arithmetic when adding one; used
+ when rounding up during hexadecimal output. */
+ static const char hexDigitsLower[] = "0123456789abcdef0";
+ static const char hexDigitsUpper[] = "0123456789ABCDEF0";
+ static const char infinityL[] = "infinity";
+ static const char infinityU[] = "INFINITY";
+ static const char NaNL[] = "nan";
+ static const char NaNU[] = "NAN";
+
+ /* Write out an integerPart in hexadecimal, starting with the most
+ significant nibble. Write out exactly COUNT hexdigits, return
+ COUNT. */
+ unsigned int
+ partAsHex (char *dst, integerPart part, unsigned int count,
+ const char *hexDigitChars)
+ {
+ unsigned int result = count;
+
+ assert (count != 0 && count <= integerPartWidth / 4);
+
+ part >>= (integerPartWidth - 4 * count);
+ while (count--) {
+ dst[count] = hexDigitChars[part & 0xf];
+ part >>= 4;
+ }
+
+ return result;
+ }
+
+ /* Write out an unsigned decimal integer. */
+ char *
+ writeUnsignedDecimal (char *dst, unsigned int n)
+ {
+ char buff[40], *p;
+
+ p = buff;
+ do
+ *p++ = '0' + n % 10;
+ while (n /= 10);
+
+ do
+ *dst++ = *--p;
+ while (p != buff);
+
+ return dst;
+ }
+
+ /* Write out a signed decimal integer. */
+ char *
+ writeSignedDecimal (char *dst, int value)
+ {
+ if (value < 0) {
+ *dst++ = '-';
+ dst = writeUnsignedDecimal(dst, -(unsigned) value);
+ } else
+ dst = writeUnsignedDecimal(dst, value);
+
+ return dst;
+ }
}
/* Constructors. */
sign = rhs.sign;
category = rhs.category;
exponent = rhs.exponent;
+ sign2 = rhs.sign2;
+ exponent2 = rhs.exponent2;
if(category == fcNormal || category == fcNaN)
copySignificand(rhs);
}
assert(rhs.partCount() >= partCount());
APInt::tcAssign(significandParts(), rhs.significandParts(),
- partCount());
+ partCount());
+}
+
+/* Make this number a NaN, with an arbitrary but deterministic value
+ for the significand. */
+void
+APFloat::makeNaN(void)
+{
+ category = fcNaN;
+ APInt::tcSet(significandParts(), ~0U, partCount());
}
APFloat &
category != rhs.category ||
sign != rhs.sign)
return false;
+ if (semantics==(const llvm::fltSemantics*)&PPCDoubleDouble &&
+ sign2 != rhs.sign2)
+ return false;
if (category==fcZero || category==fcInfinity)
return true;
else if (category==fcNormal && exponent!=rhs.exponent)
return false;
+ else if (semantics==(const llvm::fltSemantics*)&PPCDoubleDouble &&
+ exponent2!=rhs.exponent2)
+ return false;
else {
int i= partCount();
const integerPart* p=significandParts();
APFloat::APFloat(const fltSemantics &ourSemantics, integerPart value)
{
+ assertArithmeticOK(ourSemantics);
initialize(&ourSemantics);
sign = 0;
zeroSignificand();
}
APFloat::APFloat(const fltSemantics &ourSemantics,
- fltCategory ourCategory, bool negative)
+ fltCategory ourCategory, bool negative)
{
+ assertArithmeticOK(ourSemantics);
initialize(&ourSemantics);
category = ourCategory;
sign = negative;
if(category == fcNormal)
category = fcZero;
+ else if (ourCategory == fcNaN)
+ makeNaN();
}
APFloat::APFloat(const fltSemantics &ourSemantics, const char *text)
{
+ assertArithmeticOK(ourSemantics);
initialize(&ourSemantics);
convertFromString(text, rmNearestTiesToEven);
}
freeSignificand();
}
+// Profile - This method 'profiles' an APFloat for use with FoldingSet.
+void APFloat::Profile(FoldingSetNodeID& ID) const {
+ ID.Add(convertToAPInt());
+}
+
unsigned int
APFloat::partCount() const
{
return &significand.part;
}
-/* Combine the effect of two lost fractions. */
-lostFraction
-APFloat::combineLostFractions(lostFraction moreSignificant,
- lostFraction lessSignificant)
-{
- if(lessSignificant != lfExactlyZero) {
- if(moreSignificant == lfExactlyZero)
- moreSignificant = lfLessThanHalf;
- else if(moreSignificant == lfExactlyHalf)
- moreSignificant = lfMoreThanHalf;
- }
-
- return moreSignificant;
-}
-
void
APFloat::zeroSignificand()
{
assert(exponent == rhs.exponent);
return APInt::tcSubtract(parts, rhs.significandParts(), borrow,
- partCount());
+ partCount());
}
/* Multiply the significand of the RHS. If ADDEND is non-NULL, add it
lostFraction
APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
{
- unsigned int omsb; // One, not zero, based MSB.
+ unsigned int omsb; // One, not zero, based MSB.
unsigned int partsCount, newPartsCount, precision;
integerPart *lhsSignificand;
integerPart scratch[4];
partsCount = partCount();
APInt::tcFullMultiply(fullSignificand, lhsSignificand,
- rhs.significandParts(), partsCount);
+ rhs.significandParts(), partsCount, partsCount);
lost_fraction = lfExactlyZero;
omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
extendedPrecision = precision + precision - 1;
if(omsb != extendedPrecision)
{
- APInt::tcShiftLeft(fullSignificand, newPartsCount,
- extendedPrecision - omsb);
- exponent -= extendedPrecision - omsb;
+ APInt::tcShiftLeft(fullSignificand, newPartsCount,
+ extendedPrecision - omsb);
+ exponent -= extendedPrecision - omsb;
}
/* Create new semantics. */
APInt::tcShiftLeft(dividend, partsCount, bit);
}
+ /* Ensure the dividend >= divisor initially for the loop below.
+ Incidentally, this means that the division loop below is
+ guaranteed to set the integer bit to one. */
if(APInt::tcCompare(dividend, divisor, partsCount) < 0) {
exponent--;
APInt::tcShiftLeft(dividend, partsCount, 1);
significands. */
if(compare == 0)
compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
- partCount());
+ partCount());
if(compare > 0)
return cmpGreaterThan;
category = fcNormal;
exponent = semantics->maxExponent;
APInt::tcSetLeastSignificantBits(significandParts(), partCount(),
- semantics->precision);
+ semantics->precision);
return opInexact;
}
-/* This routine must work for fcZero of both signs, and fcNormal
- numbers. */
+/* Returns TRUE if, when truncating the current number, with BIT the
+ new LSB, with the given lost fraction and rounding mode, the result
+ would need to be rounded away from zero (i.e., by increasing the
+ signficand). This routine must work for fcZero of both signs, and
+ fcNormal numbers. */
bool
APFloat::roundAwayFromZero(roundingMode rounding_mode,
- lostFraction lost_fraction)
+ lostFraction lost_fraction,
+ unsigned int bit) const
{
/* NaNs and infinities should not have lost fractions. */
assert(category == fcNormal || category == fcZero);
- /* Our caller has already handled this case. */
+ /* Current callers never pass this so we don't handle it. */
assert(lost_fraction != lfExactlyZero);
switch(rounding_mode) {
/* Our zeroes don't have a significand to test. */
if(lost_fraction == lfExactlyHalf && category != fcZero)
- return significandParts()[0] & 1;
+ return APInt::tcExtractBit(significandParts(), bit);
return false;
APFloat::opStatus
APFloat::normalize(roundingMode rounding_mode,
- lostFraction lost_fraction)
+ lostFraction lost_fraction)
{
- unsigned int omsb; /* One, not zero, based MSB. */
+ unsigned int omsb; /* One, not zero, based MSB. */
int exponentChange;
if(category != fcNormal)
/* Keep OMSB up-to-date. */
if(omsb > (unsigned) exponentChange)
- omsb -= (unsigned) exponentChange;
+ omsb -= exponentChange;
else
- omsb = 0;
+ omsb = 0;
}
}
}
/* Increment the significand if we're rounding away from zero. */
- if(roundAwayFromZero(rounding_mode, lost_fraction)) {
+ if(roundAwayFromZero(rounding_mode, lost_fraction, 0)) {
if(omsb == 0)
exponent = semantics->minExponent;
/* Did the significand increment overflow? */
if(omsb == (unsigned) semantics->precision + 1) {
/* Renormalize by incrementing the exponent and shifting our
- significand right one. However if we already have the
- maximum exponent we overflow to infinity. */
+ significand right one. However if we already have the
+ maximum exponent we overflow to infinity. */
if(exponent == semantics->maxExponent) {
- category = fcInfinity;
+ category = fcInfinity;
- return (opStatus) (opOverflow | opInexact);
+ return (opStatus) (opOverflow | opInexact);
}
shiftSignificandRight(1);
/* We have a non-zero denormal. */
assert(omsb < semantics->precision);
- assert(exponent == semantics->minExponent);
/* Canonicalize zeroes. */
if(omsb == 0)
case convolve(fcInfinity, fcInfinity):
/* Differently signed infinities can only be validly
subtracted. */
- if(sign ^ rhs.sign != subtract) {
- category = fcNaN;
- // Arbitrary but deterministic value for significand
- APInt::tcSet(significandParts(), ~0U, partCount());
+ if((sign ^ rhs.sign) != subtract) {
+ makeNaN();
return opInvalidOp;
}
/* Determine if the operation on the absolute values is effectively
an addition or subtraction. */
- subtract ^= (sign ^ rhs.sign);
+ subtract ^= (sign ^ rhs.sign) ? true : false;
/* Are we bigger exponent-wise than the RHS? */
bits = exponent - rhs.exponent;
if (reverse) {
carry = temp_rhs.subtractSignificand
- (*this, lost_fraction != lfExactlyZero);
+ (*this, lost_fraction != lfExactlyZero);
copySignificand(temp_rhs);
sign = !sign;
} else {
carry = subtractSignificand
- (temp_rhs, lost_fraction != lfExactlyZero);
+ (temp_rhs, lost_fraction != lfExactlyZero);
}
/* Invert the lost fraction - it was on the RHS and
case convolve(fcZero, fcInfinity):
case convolve(fcInfinity, fcZero):
- category = fcNaN;
- // Arbitrary but deterministic value for significand
- APInt::tcSet(significandParts(), ~0U, partCount());
+ makeNaN();
return opInvalidOp;
case convolve(fcNormal, fcNormal):
case convolve(fcInfinity, fcInfinity):
case convolve(fcZero, fcZero):
- category = fcNaN;
- // Arbitrary but deterministic value for significand
- APInt::tcSet(significandParts(), ~0U, partCount());
+ makeNaN();
return opInvalidOp;
case convolve(fcNormal, fcNormal):
/* Normalized addition or subtraction. */
APFloat::opStatus
APFloat::addOrSubtract(const APFloat &rhs, roundingMode rounding_mode,
- bool subtract)
+ bool subtract)
{
opStatus fs;
+ assertArithmeticOK(*semantics);
+
fs = addOrSubtractSpecials(rhs, subtract);
/* This return code means it was not a simple case. */
{
opStatus fs;
+ assertArithmeticOK(*semantics);
sign ^= rhs.sign;
fs = multiplySpecials(rhs);
{
opStatus fs;
+ assertArithmeticOK(*semantics);
sign ^= rhs.sign;
fs = divideSpecials(rhs);
return fs;
}
-/* Normalized remainder. */
+/* Normalized remainder. This is not currently doing TRT. */
APFloat::opStatus
APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
{
opStatus fs;
APFloat V = *this;
unsigned int origSign = sign;
+
+ assertArithmeticOK(*semantics);
fs = V.divide(rhs, rmNearestTiesToEven);
if (fs == opDivByZero)
return fs;
int parts = partCount();
integerPart *x = new integerPart[parts];
- fs = V.convertToInteger(x, parts * integerPartWidth, true,
+ fs = V.convertToInteger(x, parts * integerPartWidth, true,
rmNearestTiesToEven);
if (fs==opInvalidOp)
return fs;
- fs = V.convertFromInteger(x, parts * integerPartWidth, true,
- rmNearestTiesToEven);
+ fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
+ rmNearestTiesToEven);
assert(fs==opOK); // should always work
fs = V.multiply(rhs, rounding_mode);
/* Normalized fused-multiply-add. */
APFloat::opStatus
APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
- const APFloat &addend,
- roundingMode rounding_mode)
+ const APFloat &addend,
+ roundingMode rounding_mode)
{
opStatus fs;
+ assertArithmeticOK(*semantics);
+
/* Post-multiplication sign, before addition. */
sign ^= multiplicand.sign;
{
cmpResult result;
+ assertArithmeticOK(*semantics);
assert(semantics == rhs.semantics);
switch(convolve(category, rhs.category)) {
if(sign) {
if(result == cmpLessThan)
- result = cmpGreaterThan;
+ result = cmpGreaterThan;
else if(result == cmpGreaterThan)
- result = cmpLessThan;
+ result = cmpLessThan;
}
}
APFloat::opStatus
APFloat::convert(const fltSemantics &toSemantics,
- roundingMode rounding_mode)
+ roundingMode rounding_mode)
{
- unsigned int newPartCount;
+ lostFraction lostFraction;
+ unsigned int newPartCount, oldPartCount;
opStatus fs;
+ assertArithmeticOK(*semantics);
+ lostFraction = lfExactlyZero;
newPartCount = partCountForBits(toSemantics.precision + 1);
-
- /* If our new form is wider, re-allocate our bit pattern into wider
- storage.
- If we're narrowing from multiple words to 1 words, copy to the single
- word. If we are losing information by doing this, we would have to
- worry about rounding; right now the only case is f80 -> shorter
- conversion, and we are keeping all 64 significant bits, so it's OK. */
- if(newPartCount > partCount()) {
+ oldPartCount = partCount();
+
+ /* Handle storage complications. If our new form is wider,
+ re-allocate our bit pattern into wider storage. If it is
+ narrower, we ignore the excess parts, but if narrowing to a
+ single part we need to free the old storage.
+ Be careful not to reference significandParts for zeroes
+ and infinities, since it aborts. */
+ if (newPartCount > oldPartCount) {
integerPart *newParts;
-
newParts = new integerPart[newPartCount];
APInt::tcSet(newParts, 0, newPartCount);
- APInt::tcAssign(newParts, significandParts(), partCount());
+ if (category==fcNormal || category==fcNaN)
+ APInt::tcAssign(newParts, significandParts(), oldPartCount);
freeSignificand();
significand.parts = newParts;
- } else if (newPartCount==1 && newPartCount < partCount()) {
- integerPart newPart;
-
- APInt::tcSet(&newPart, 0, newPartCount);
- APInt::tcAssign(&newPart, significandParts(), partCount());
- freeSignificand();
- significand.part = newPart;
+ } else if (newPartCount < oldPartCount) {
+ /* Capture any lost fraction through truncation of parts so we get
+ correct rounding whilst normalizing. */
+ if (category==fcNormal)
+ lostFraction = lostFractionThroughTruncation
+ (significandParts(), oldPartCount, toSemantics.precision);
+ if (newPartCount == 1) {
+ integerPart newPart = 0;
+ if (category==fcNormal || category==fcNaN)
+ newPart = significandParts()[0];
+ freeSignificand();
+ significand.part = newPart;
+ }
}
if(category == fcNormal) {
/* Re-interpret our bit-pattern. */
exponent += toSemantics.precision - semantics->precision;
semantics = &toSemantics;
- fs = normalize(rounding_mode, lfExactlyZero);
+ fs = normalize(rounding_mode, lostFraction);
+ } else if (category == fcNaN) {
+ int shift = toSemantics.precision - semantics->precision;
+ // Do this now so significandParts gets the right answer
+ semantics = &toSemantics;
+ // No normalization here, just truncate
+ if (shift>0)
+ APInt::tcShiftLeft(significandParts(), newPartCount, shift);
+ else if (shift < 0)
+ APInt::tcShiftRight(significandParts(), newPartCount, -shift);
+ // gcc forces the Quiet bit on, which means (float)(double)(float_sNan)
+ // does not give you back the same bits. This is dubious, and we
+ // don't currently do it. You're really supposed to get
+ // an invalid operation signal at runtime, but nobody does that.
+ fs = opOK;
} else {
semantics = &toSemantics;
fs = opOK;
/* Convert a floating point number to an integer according to the
rounding mode. If the rounded integer value is out of range this
- returns an invalid operation exception. If the rounded value is in
+ returns an invalid operation exception and the contents of the
+ destination parts are unspecified. If the rounded value is in
range but the floating point number is not the exact integer, the C
standard doesn't require an inexact exception to be raised. IEEE
854 does require it so we do that.
Note that for conversions to integer type the C standard requires
round-to-zero to always be used. */
APFloat::opStatus
-APFloat::convertToInteger(integerPart *parts, unsigned int width,
- bool isSigned,
- roundingMode rounding_mode) const
+APFloat::convertToSignExtendedInteger(integerPart *parts, unsigned int width,
+ bool isSigned,
+ roundingMode rounding_mode) const
{
lostFraction lost_fraction;
- unsigned int msb, partsCount;
- int bits;
+ const integerPart *src;
+ unsigned int dstPartsCount, truncatedBits;
+
+ assertArithmeticOK(*semantics);
/* Handle the three special cases first. */
if(category == fcInfinity || category == fcNaN)
return opInvalidOp;
- partsCount = partCountForBits(width);
+ dstPartsCount = partCountForBits(width);
if(category == fcZero) {
- APInt::tcSet(parts, 0, partsCount);
+ APInt::tcSet(parts, 0, dstPartsCount);
return opOK;
}
- /* Shift the bit pattern so the fraction is lost. */
- APFloat tmp(*this);
+ src = significandParts();
+
+ /* Step 1: place our absolute value, with any fraction truncated, in
+ the destination. */
+ if (exponent < 0) {
+ /* Our absolute value is less than one; truncate everything. */
+ APInt::tcSet(parts, 0, dstPartsCount);
+ truncatedBits = semantics->precision;
+ } else {
+ /* We want the most significant (exponent + 1) bits; the rest are
+ truncated. */
+ unsigned int bits = exponent + 1U;
+
+ /* Hopelessly large in magnitude? */
+ if (bits > width)
+ return opInvalidOp;
- bits = (int) semantics->precision - 1 - exponent;
+ if (bits < semantics->precision) {
+ /* We truncate (semantics->precision - bits) bits. */
+ truncatedBits = semantics->precision - bits;
+ APInt::tcExtract(parts, dstPartsCount, src, bits, truncatedBits);
+ } else {
+ /* We want at least as many bits as are available. */
+ APInt::tcExtract(parts, dstPartsCount, src, semantics->precision, 0);
+ APInt::tcShiftLeft(parts, dstPartsCount, bits - semantics->precision);
+ truncatedBits = 0;
+ }
+ }
- if(bits > 0) {
- lost_fraction = tmp.shiftSignificandRight(bits);
+ /* Step 2: work out any lost fraction, and increment the absolute
+ value if we would round away from zero. */
+ if (truncatedBits) {
+ lost_fraction = lostFractionThroughTruncation(src, partCount(),
+ truncatedBits);
+ if (lost_fraction != lfExactlyZero
+ && roundAwayFromZero(rounding_mode, lost_fraction, truncatedBits)) {
+ if (APInt::tcIncrement(parts, dstPartsCount))
+ return opInvalidOp; /* Overflow. */
+ }
} else {
- tmp.shiftSignificandLeft(-bits);
lost_fraction = lfExactlyZero;
}
- if(lost_fraction != lfExactlyZero
- && tmp.roundAwayFromZero(rounding_mode, lost_fraction))
- tmp.incrementSignificand();
+ /* Step 3: check if we fit in the destination. */
+ unsigned int omsb = APInt::tcMSB(parts, dstPartsCount) + 1;
- msb = tmp.significandMSB();
+ if (sign) {
+ if (!isSigned) {
+ /* Negative numbers cannot be represented as unsigned. */
+ if (omsb != 0)
+ return opInvalidOp;
+ } else {
+ /* It takes omsb bits to represent the unsigned integer value.
+ We lose a bit for the sign, but care is needed as the
+ maximally negative integer is a special case. */
+ if (omsb == width && APInt::tcLSB(parts, dstPartsCount) + 1 != omsb)
+ return opInvalidOp;
+
+ /* This case can happen because of rounding. */
+ if (omsb > width)
+ return opInvalidOp;
+ }
- /* Negative numbers cannot be represented as unsigned. */
- if(!isSigned && tmp.sign && msb != -1U)
- return opInvalidOp;
+ APInt::tcNegate (parts, dstPartsCount);
+ } else {
+ if (omsb >= width + !isSigned)
+ return opInvalidOp;
+ }
- /* It takes exponent + 1 bits to represent the truncated floating
- point number without its sign. We lose a bit for the sign, but
- the maximally negative integer is a special case. */
- if(msb + 1 > width) /* !! Not same as msb >= width !! */
- return opInvalidOp;
+ if (lost_fraction == lfExactlyZero)
+ return opOK;
+ else
+ return opInexact;
+}
- if(isSigned && msb + 1 == width
- && (!tmp.sign || tmp.significandLSB() != msb))
- return opInvalidOp;
+/* Same as convertToSignExtendedInteger, except we provide
+ deterministic values in case of an invalid operation exception,
+ namely zero for NaNs and the minimal or maximal value respectively
+ for underflow or overflow. */
+APFloat::opStatus
+APFloat::convertToInteger(integerPart *parts, unsigned int width,
+ bool isSigned,
+ roundingMode rounding_mode) const
+{
+ opStatus fs;
- APInt::tcAssign(parts, tmp.significandParts(), partsCount);
+ fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode);
- if(tmp.sign)
- APInt::tcNegate(parts, partsCount);
+ if (fs == opInvalidOp) {
+ unsigned int bits, dstPartsCount;
- if(lost_fraction == lfExactlyZero)
- return opOK;
- else
- return opInexact;
+ dstPartsCount = partCountForBits(width);
+
+ if (category == fcNaN)
+ bits = 0;
+ else if (sign)
+ bits = isSigned;
+ else
+ bits = width - isSigned;
+
+ APInt::tcSetLeastSignificantBits(parts, dstPartsCount, bits);
+ if (sign && isSigned)
+ APInt::tcShiftLeft(parts, dstPartsCount, width - 1);
+ }
+
+ return fs;
}
+/* Convert an unsigned integer SRC to a floating point number,
+ rounding according to ROUNDING_MODE. The sign of the floating
+ point number is not modified. */
APFloat::opStatus
-APFloat::convertFromUnsignedInteger(integerPart *parts,
- unsigned int partCount,
- roundingMode rounding_mode)
+APFloat::convertFromUnsignedParts(const integerPart *src,
+ unsigned int srcCount,
+ roundingMode rounding_mode)
{
- unsigned int msb, precision;
+ unsigned int omsb, precision, dstCount;
+ integerPart *dst;
lostFraction lost_fraction;
- msb = APInt::tcMSB(parts, partCount) + 1;
- precision = semantics->precision;
-
+ assertArithmeticOK(*semantics);
category = fcNormal;
- exponent = precision - 1;
+ omsb = APInt::tcMSB(src, srcCount) + 1;
+ dst = significandParts();
+ dstCount = partCount();
+ precision = semantics->precision;
- if(msb > precision) {
- exponent += (msb - precision);
- lost_fraction = shiftRight(parts, partCount, msb - precision);
- msb = precision;
- } else
+ /* We want the most significant PRECISON bits of SRC. There may not
+ be that many; extract what we can. */
+ if (precision <= omsb) {
+ exponent = omsb - 1;
+ lost_fraction = lostFractionThroughTruncation(src, srcCount,
+ omsb - precision);
+ APInt::tcExtract(dst, dstCount, src, precision, omsb - precision);
+ } else {
+ exponent = precision - 1;
lost_fraction = lfExactlyZero;
-
- /* Copy the bit image. */
- zeroSignificand();
- APInt::tcAssign(significandParts(), parts, partCountForBits(msb));
+ APInt::tcExtract(dst, dstCount, src, omsb, 0);
+ }
return normalize(rounding_mode, lost_fraction);
}
APFloat::opStatus
-APFloat::convertFromInteger(const integerPart *parts, unsigned int width,
- bool isSigned, roundingMode rounding_mode)
+APFloat::convertFromAPInt(const APInt &Val,
+ bool isSigned,
+ roundingMode rounding_mode)
{
- unsigned int partCount = partCountForBits(width);
- opStatus status;
- APInt api = APInt(width, partCount, parts);
- integerPart *copy = new integerPart[partCount];
+ unsigned int partCount = Val.getNumWords();
+ APInt api = Val;
sign = false;
- if(isSigned) {
- if (APInt::tcExtractBit(parts, width - 1)) {
- sign = true;
- if (width < partCount * integerPartWidth)
- api = api.sext(partCount * integerPartWidth);
- }
- else if (width < partCount * integerPartWidth)
- api = api.zext(partCount * integerPartWidth);
+ if (isSigned && api.isNegative()) {
+ sign = true;
+ api = -api;
+ }
+
+ return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
+}
+
+/* Convert a two's complement integer SRC to a floating point number,
+ rounding according to ROUNDING_MODE. ISSIGNED is true if the
+ integer is signed, in which case it must be sign-extended. */
+APFloat::opStatus
+APFloat::convertFromSignExtendedInteger(const integerPart *src,
+ unsigned int srcCount,
+ bool isSigned,
+ roundingMode rounding_mode)
+{
+ opStatus status;
+
+ assertArithmeticOK(*semantics);
+ if (isSigned
+ && APInt::tcExtractBit(src, srcCount * integerPartWidth - 1)) {
+ integerPart *copy;
+
+ /* If we're signed and negative negate a copy. */
+ sign = true;
+ copy = new integerPart[srcCount];
+ APInt::tcAssign(copy, src, srcCount);
+ APInt::tcNegate(copy, srcCount);
+ status = convertFromUnsignedParts(copy, srcCount, rounding_mode);
+ delete [] copy;
} else {
- if (width < partCount * integerPartWidth)
- api = api.zext(partCount * integerPartWidth);
+ sign = false;
+ status = convertFromUnsignedParts(src, srcCount, rounding_mode);
}
- APInt::tcAssign(copy, api.getRawData(), partCount);
- status = convertFromUnsignedInteger(copy, partCount, rounding_mode);
return status;
}
+/* FIXME: should this just take a const APInt reference? */
+APFloat::opStatus
+APFloat::convertFromZeroExtendedInteger(const integerPart *parts,
+ unsigned int width, bool isSigned,
+ roundingMode rounding_mode)
+{
+ unsigned int partCount = partCountForBits(width);
+ APInt api = APInt(width, partCount, parts);
+
+ sign = false;
+ if(isSigned && APInt::tcExtractBit(parts, width - 1)) {
+ sign = true;
+ api = -api;
+ }
+
+ return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
+}
+
APFloat::opStatus
APFloat::convertFromHexadecimalString(const char *p,
- roundingMode rounding_mode)
+ roundingMode rounding_mode)
{
lostFraction lost_fraction;
integerPart *significand;
partsCount = partCount();
bitPos = partsCount * integerPartWidth;
- /* Skip leading zeroes and any(hexa)decimal point. */
+ /* Skip leading zeroes and any (hexa)decimal point. */
p = skipLeadingZeroesAndAnyDot(p, &dot);
firstSignificantDigit = p;
} else {
lost_fraction = trailingHexadecimalFraction(p, hex_value);
while(hexDigitValue(*p) != -1U)
- p++;
+ p++;
break;
}
}
}
APFloat::opStatus
-APFloat::convertFromString(const char *p, roundingMode rounding_mode) {
+APFloat::roundSignificandWithExponent(const integerPart *decSigParts,
+ unsigned sigPartCount, int exp,
+ roundingMode rounding_mode)
+{
+ unsigned int parts, pow5PartCount;
+ fltSemantics calcSemantics = { 32767, -32767, 0, true };
+ integerPart pow5Parts[maxPowerOfFiveParts];
+ bool isNearest;
+
+ isNearest = (rounding_mode == rmNearestTiesToEven
+ || rounding_mode == rmNearestTiesToAway);
+
+ parts = partCountForBits(semantics->precision + 11);
+
+ /* Calculate pow(5, abs(exp)). */
+ pow5PartCount = powerOf5(pow5Parts, exp >= 0 ? exp: -exp);
+
+ for (;; parts *= 2) {
+ opStatus sigStatus, powStatus;
+ unsigned int excessPrecision, truncatedBits;
+
+ calcSemantics.precision = parts * integerPartWidth - 1;
+ excessPrecision = calcSemantics.precision - semantics->precision;
+ truncatedBits = excessPrecision;
+
+ APFloat decSig(calcSemantics, fcZero, sign);
+ APFloat pow5(calcSemantics, fcZero, false);
+
+ sigStatus = decSig.convertFromUnsignedParts(decSigParts, sigPartCount,
+ rmNearestTiesToEven);
+ powStatus = pow5.convertFromUnsignedParts(pow5Parts, pow5PartCount,
+ rmNearestTiesToEven);
+ /* Add exp, as 10^n = 5^n * 2^n. */
+ decSig.exponent += exp;
+
+ lostFraction calcLostFraction;
+ integerPart HUerr, HUdistance, powHUerr;
+
+ if (exp >= 0) {
+ /* multiplySignificand leaves the precision-th bit set to 1. */
+ calcLostFraction = decSig.multiplySignificand(pow5, NULL);
+ powHUerr = powStatus != opOK;
+ } else {
+ calcLostFraction = decSig.divideSignificand(pow5);
+ /* Denormal numbers have less precision. */
+ if (decSig.exponent < semantics->minExponent) {
+ excessPrecision += (semantics->minExponent - decSig.exponent);
+ truncatedBits = excessPrecision;
+ if (excessPrecision > calcSemantics.precision)
+ excessPrecision = calcSemantics.precision;
+ }
+ /* Extra half-ulp lost in reciprocal of exponent. */
+ powHUerr = (powStatus == opOK && calcLostFraction == lfExactlyZero) ? 0: 2;
+ }
+
+ /* Both multiplySignificand and divideSignificand return the
+ result with the integer bit set. */
+ assert (APInt::tcExtractBit
+ (decSig.significandParts(), calcSemantics.precision - 1) == 1);
+
+ HUerr = HUerrBound(calcLostFraction != lfExactlyZero, sigStatus != opOK,
+ powHUerr);
+ HUdistance = 2 * ulpsFromBoundary(decSig.significandParts(),
+ excessPrecision, isNearest);
+
+ /* Are we guaranteed to round correctly if we truncate? */
+ if (HUdistance >= HUerr) {
+ APInt::tcExtract(significandParts(), partCount(), decSig.significandParts(),
+ calcSemantics.precision - excessPrecision,
+ excessPrecision);
+ /* Take the exponent of decSig. If we tcExtract-ed less bits
+ above we must adjust our exponent to compensate for the
+ implicit right shift. */
+ exponent = (decSig.exponent + semantics->precision
+ - (calcSemantics.precision - excessPrecision));
+ calcLostFraction = lostFractionThroughTruncation(decSig.significandParts(),
+ decSig.partCount(),
+ truncatedBits);
+ return normalize(rounding_mode, calcLostFraction);
+ }
+ }
+}
+
+APFloat::opStatus
+APFloat::convertFromDecimalString(const char *p, roundingMode rounding_mode)
+{
+ decimalInfo D;
+ opStatus fs;
+
+ /* Scan the text. */
+ interpretDecimal(p, &D);
+
+ /* Handle the quick cases. First the case of no significant digits,
+ i.e. zero, and then exponents that are obviously too large or too
+ small. Writing L for log 10 / log 2, a number d.ddddd*10^exp
+ definitely overflows if
+
+ (exp - 1) * L >= maxExponent
+
+ and definitely underflows to zero where
+
+ (exp + 1) * L <= minExponent - precision
+
+ With integer arithmetic the tightest bounds for L are
+
+ 93/28 < L < 196/59 [ numerator <= 256 ]
+ 42039/12655 < L < 28738/8651 [ numerator <= 65536 ]
+ */
+
+ if (decDigitValue(*D.firstSigDigit) >= 10U) {
+ category = fcZero;
+ fs = opOK;
+ } else if ((D.normalizedExponent + 1) * 28738
+ <= 8651 * (semantics->minExponent - (int) semantics->precision)) {
+ /* Underflow to zero and round. */
+ zeroSignificand();
+ fs = normalize(rounding_mode, lfLessThanHalf);
+ } else if ((D.normalizedExponent - 1) * 42039
+ >= 12655 * semantics->maxExponent) {
+ /* Overflow and round. */
+ fs = handleOverflow(rounding_mode);
+ } else {
+ integerPart *decSignificand;
+ unsigned int partCount;
+
+ /* A tight upper bound on number of bits required to hold an
+ N-digit decimal integer is N * 196 / 59. Allocate enough space
+ to hold the full significand, and an extra part required by
+ tcMultiplyPart. */
+ partCount = (D.lastSigDigit - D.firstSigDigit) + 1;
+ partCount = partCountForBits(1 + 196 * partCount / 59);
+ decSignificand = new integerPart[partCount + 1];
+ partCount = 0;
+
+ /* Convert to binary efficiently - we do almost all multiplication
+ in an integerPart. When this would overflow do we do a single
+ bignum multiplication, and then revert again to multiplication
+ in an integerPart. */
+ do {
+ integerPart decValue, val, multiplier;
+
+ val = 0;
+ multiplier = 1;
+
+ do {
+ if (*p == '.')
+ p++;
+
+ decValue = decDigitValue(*p++);
+ multiplier *= 10;
+ val = val * 10 + decValue;
+ /* The maximum number that can be multiplied by ten with any
+ digit added without overflowing an integerPart. */
+ } while (p <= D.lastSigDigit && multiplier <= (~ (integerPart) 0 - 9) / 10);
+
+ /* Multiply out the current part. */
+ APInt::tcMultiplyPart(decSignificand, decSignificand, multiplier, val,
+ partCount, partCount + 1, false);
+
+ /* If we used another part (likely but not guaranteed), increase
+ the count. */
+ if (decSignificand[partCount])
+ partCount++;
+ } while (p <= D.lastSigDigit);
+
+ category = fcNormal;
+ fs = roundSignificandWithExponent(decSignificand, partCount,
+ D.exponent, rounding_mode);
+
+ delete [] decSignificand;
+ }
+
+ return fs;
+}
+
+APFloat::opStatus
+APFloat::convertFromString(const char *p, roundingMode rounding_mode)
+{
+ assertArithmeticOK(*semantics);
+
/* Handle a leading minus sign. */
if(*p == '-')
sign = 1, p++;
if(p[0] == '0' && (p[1] == 'x' || p[1] == 'X'))
return convertFromHexadecimalString(p + 2, rounding_mode);
+ else
+ return convertFromDecimalString(p, rounding_mode);
+}
+
+/* Write out a hexadecimal representation of the floating point value
+ to DST, which must be of sufficient size, in the C99 form
+ [-]0xh.hhhhp[+-]d. Return the number of characters written,
+ excluding the terminating NUL.
+
+ If UPPERCASE, the output is in upper case, otherwise in lower case.
+
+ HEXDIGITS digits appear altogether, rounding the value if
+ necessary. If HEXDIGITS is 0, the minimal precision to display the
+ number precisely is used instead. If nothing would appear after
+ the decimal point it is suppressed.
+
+ The decimal exponent is always printed and has at least one digit.
+ Zero values display an exponent of zero. Infinities and NaNs
+ appear as "infinity" or "nan" respectively.
+
+ The above rules are as specified by C99. There is ambiguity about
+ what the leading hexadecimal digit should be. This implementation
+ uses whatever is necessary so that the exponent is displayed as
+ stored. This implies the exponent will fall within the IEEE format
+ range, and the leading hexadecimal digit will be 0 (for denormals),
+ 1 (normal numbers) or 2 (normal numbers rounded-away-from-zero with
+ any other digits zero).
+*/
+unsigned int
+APFloat::convertToHexString(char *dst, unsigned int hexDigits,
+ bool upperCase, roundingMode rounding_mode) const
+{
+ char *p;
+
+ assertArithmeticOK(*semantics);
+
+ p = dst;
+ if (sign)
+ *dst++ = '-';
+
+ switch (category) {
+ case fcInfinity:
+ memcpy (dst, upperCase ? infinityU: infinityL, sizeof infinityU - 1);
+ dst += sizeof infinityL - 1;
+ break;
+
+ case fcNaN:
+ memcpy (dst, upperCase ? NaNU: NaNL, sizeof NaNU - 1);
+ dst += sizeof NaNU - 1;
+ break;
+
+ case fcZero:
+ *dst++ = '0';
+ *dst++ = upperCase ? 'X': 'x';
+ *dst++ = '0';
+ if (hexDigits > 1) {
+ *dst++ = '.';
+ memset (dst, '0', hexDigits - 1);
+ dst += hexDigits - 1;
+ }
+ *dst++ = upperCase ? 'P': 'p';
+ *dst++ = '0';
+ break;
+
+ case fcNormal:
+ dst = convertNormalToHexString (dst, hexDigits, upperCase, rounding_mode);
+ break;
+ }
+
+ *dst = 0;
+
+ return dst - p;
+}
+
+/* Does the hard work of outputting the correctly rounded hexadecimal
+ form of a normal floating point number with the specified number of
+ hexadecimal digits. If HEXDIGITS is zero the minimum number of
+ digits necessary to print the value precisely is output. */
+char *
+APFloat::convertNormalToHexString(char *dst, unsigned int hexDigits,
+ bool upperCase,
+ roundingMode rounding_mode) const
+{
+ unsigned int count, valueBits, shift, partsCount, outputDigits;
+ const char *hexDigitChars;
+ const integerPart *significand;
+ char *p;
+ bool roundUp;
+
+ *dst++ = '0';
+ *dst++ = upperCase ? 'X': 'x';
+
+ roundUp = false;
+ hexDigitChars = upperCase ? hexDigitsUpper: hexDigitsLower;
+
+ significand = significandParts();
+ partsCount = partCount();
+
+ /* +3 because the first digit only uses the single integer bit, so
+ we have 3 virtual zero most-significant-bits. */
+ valueBits = semantics->precision + 3;
+ shift = integerPartWidth - valueBits % integerPartWidth;
+
+ /* The natural number of digits required ignoring trailing
+ insignificant zeroes. */
+ outputDigits = (valueBits - significandLSB () + 3) / 4;
+
+ /* hexDigits of zero means use the required number for the
+ precision. Otherwise, see if we are truncating. If we are,
+ find out if we need to round away from zero. */
+ if (hexDigits) {
+ if (hexDigits < outputDigits) {
+ /* We are dropping non-zero bits, so need to check how to round.
+ "bits" is the number of dropped bits. */
+ unsigned int bits;
+ lostFraction fraction;
+
+ bits = valueBits - hexDigits * 4;
+ fraction = lostFractionThroughTruncation (significand, partsCount, bits);
+ roundUp = roundAwayFromZero(rounding_mode, fraction, bits);
+ }
+ outputDigits = hexDigits;
+ }
+
+ /* Write the digits consecutively, and start writing in the location
+ of the hexadecimal point. We move the most significant digit
+ left and add the hexadecimal point later. */
+ p = ++dst;
+
+ count = (valueBits + integerPartWidth - 1) / integerPartWidth;
+
+ while (outputDigits && count) {
+ integerPart part;
+
+ /* Put the most significant integerPartWidth bits in "part". */
+ if (--count == partsCount)
+ part = 0; /* An imaginary higher zero part. */
+ else
+ part = significand[count] << shift;
+
+ if (count && shift)
+ part |= significand[count - 1] >> (integerPartWidth - shift);
- assert(0 && "Decimal to binary conversions not yet implemented");
- abort();
+ /* Convert as much of "part" to hexdigits as we can. */
+ unsigned int curDigits = integerPartWidth / 4;
+
+ if (curDigits > outputDigits)
+ curDigits = outputDigits;
+ dst += partAsHex (dst, part, curDigits, hexDigitChars);
+ outputDigits -= curDigits;
+ }
+
+ if (roundUp) {
+ char *q = dst;
+
+ /* Note that hexDigitChars has a trailing '0'. */
+ do {
+ q--;
+ *q = hexDigitChars[hexDigitValue (*q) + 1];
+ } while (*q == '0');
+ assert (q >= p);
+ } else {
+ /* Add trailing zeroes. */
+ memset (dst, '0', outputDigits);
+ dst += outputDigits;
+ }
+
+ /* Move the most significant digit to before the point, and if there
+ is something after the decimal point add it. This must come
+ after rounding above. */
+ p[-1] = p[0];
+ if (dst -1 == p)
+ dst--;
+ else
+ p[0] = '.';
+
+ /* Finally output the exponent. */
+ *dst++ = upperCase ? 'P': 'p';
+
+ return writeSignedDecimal (dst, exponent);
}
// For good performance it is desirable for different APFloats
// to produce different integers.
uint32_t
-APFloat::getHashValue() const {
+APFloat::getHashValue() const
+{
if (category==fcZero) return sign<<8 | semantics->precision ;
else if (category==fcInfinity) return sign<<9 | semantics->precision;
else if (category==fcNaN) return 1<<10 | semantics->precision;
// the actual IEEE respresentations. We compensate for that here.
APInt
-APFloat::convertF80LongDoubleAPFloatToAPInt() const {
- assert(semantics == (const llvm::fltSemantics* const)&x87DoubleExtended);
+APFloat::convertF80LongDoubleAPFloatToAPInt() const
+{
+ assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended);
assert (partCount()==2);
uint64_t myexponent, mysignificand;
} else if (category==fcInfinity) {
myexponent = 0x7fff;
mysignificand = 0x8000000000000000ULL;
- } else if (category==fcNaN) {
+ } else {
+ assert(category == fcNaN && "Unknown category");
myexponent = 0x7fff;
mysignificand = significandParts()[0];
- } else
- assert(0);
+ }
uint64_t words[2];
- words[0] = (((uint64_t)sign & 1) << 63) |
- ((myexponent & 0x7fff) << 48) |
+ words[0] = (((uint64_t)sign & 1) << 63) |
+ ((myexponent & 0x7fff) << 48) |
((mysignificand >>16) & 0xffffffffffffLL);
words[1] = mysignificand & 0xffff;
- APInt api(80, 2, words);
- return api;
+ return APInt(80, 2, words);
+}
+
+APInt
+APFloat::convertPPCDoubleDoubleAPFloatToAPInt() const
+{
+ assert(semantics == (const llvm::fltSemantics*)&PPCDoubleDouble);
+ assert (partCount()==2);
+
+ uint64_t myexponent, mysignificand, myexponent2, mysignificand2;
+
+ if (category==fcNormal) {
+ myexponent = exponent + 1023; //bias
+ myexponent2 = exponent2 + 1023;
+ mysignificand = significandParts()[0];
+ mysignificand2 = significandParts()[1];
+ if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
+ myexponent = 0; // denormal
+ if (myexponent2==1 && !(mysignificand2 & 0x10000000000000LL))
+ myexponent2 = 0; // denormal
+ } else if (category==fcZero) {
+ myexponent = 0;
+ mysignificand = 0;
+ myexponent2 = 0;
+ mysignificand2 = 0;
+ } else if (category==fcInfinity) {
+ myexponent = 0x7ff;
+ myexponent2 = 0;
+ mysignificand = 0;
+ mysignificand2 = 0;
+ } else {
+ assert(category == fcNaN && "Unknown category");
+ myexponent = 0x7ff;
+ mysignificand = significandParts()[0];
+ myexponent2 = exponent2;
+ mysignificand2 = significandParts()[1];
+ }
+
+ uint64_t words[2];
+ words[0] = (((uint64_t)sign & 1) << 63) |
+ ((myexponent & 0x7ff) << 52) |
+ (mysignificand & 0xfffffffffffffLL);
+ words[1] = (((uint64_t)sign2 & 1) << 63) |
+ ((myexponent2 & 0x7ff) << 52) |
+ (mysignificand2 & 0xfffffffffffffLL);
+ return APInt(128, 2, words);
}
APInt
-APFloat::convertDoubleAPFloatToAPInt() const {
+APFloat::convertDoubleAPFloatToAPInt() const
+{
assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
assert (partCount()==1);
} else if (category==fcInfinity) {
myexponent = 0x7ff;
mysignificand = 0;
- } else if (category==fcNaN) {
+ } else {
+ assert(category == fcNaN && "Unknown category!");
myexponent = 0x7ff;
mysignificand = *significandParts();
- } else
- assert(0);
+ }
- APInt api(64, (((((uint64_t)sign & 1) << 63) |
- ((myexponent & 0x7ff) << 52) |
- (mysignificand & 0xfffffffffffffLL))));
- return api;
+ return APInt(64, (((((uint64_t)sign & 1) << 63) |
+ ((myexponent & 0x7ff) << 52) |
+ (mysignificand & 0xfffffffffffffLL))));
}
APInt
-APFloat::convertFloatAPFloatToAPInt() const {
+APFloat::convertFloatAPFloatToAPInt() const
+{
assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
assert (partCount()==1);
-
+
uint32_t myexponent, mysignificand;
if (category==fcNormal) {
myexponent = exponent+127; //bias
mysignificand = *significandParts();
- if (myexponent == 1 && !(mysignificand & 0x400000))
+ if (myexponent == 1 && !(mysignificand & 0x800000))
myexponent = 0; // denormal
} else if (category==fcZero) {
myexponent = 0;
} else if (category==fcInfinity) {
myexponent = 0xff;
mysignificand = 0;
- } else if (category==fcNaN) {
+ } else {
+ assert(category == fcNaN && "Unknown category!");
myexponent = 0xff;
mysignificand = *significandParts();
- } else
- assert(0);
+ }
- APInt api(32, (((sign&1) << 31) | ((myexponent&0xff) << 23) |
- (mysignificand & 0x7fffff)));
- return api;
+ return APInt(32, (((sign&1) << 31) | ((myexponent&0xff) << 23) |
+ (mysignificand & 0x7fffff)));
}
+// This function creates an APInt that is just a bit map of the floating
+// point constant as it would appear in memory. It is not a conversion,
+// and treating the result as a normal integer is unlikely to be useful.
+
APInt
-APFloat::convertToAPInt() const {
- if (semantics == (const llvm::fltSemantics* const)&IEEEsingle)
+APFloat::convertToAPInt() const
+{
+ if (semantics == (const llvm::fltSemantics*)&IEEEsingle)
return convertFloatAPFloatToAPInt();
- else if (semantics == (const llvm::fltSemantics* const)&IEEEdouble)
+
+ if (semantics == (const llvm::fltSemantics*)&IEEEdouble)
return convertDoubleAPFloatToAPInt();
- else if (semantics == (const llvm::fltSemantics* const)&x87DoubleExtended)
- return convertF80LongDoubleAPFloatToAPInt();
- else
- assert(0);
+
+ if (semantics == (const llvm::fltSemantics*)&PPCDoubleDouble)
+ return convertPPCDoubleDoubleAPFloatToAPInt();
+
+ assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended &&
+ "unknown format!");
+ return convertF80LongDoubleAPFloatToAPInt();
}
-float
-APFloat::convertToFloat() const {
- assert(semantics == (const llvm::fltSemantics* const)&IEEEsingle);
+float
+APFloat::convertToFloat() const
+{
+ assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
APInt api = convertToAPInt();
return api.bitsToFloat();
}
-double
-APFloat::convertToDouble() const {
- assert(semantics == (const llvm::fltSemantics* const)&IEEEdouble);
+double
+APFloat::convertToDouble() const
+{
+ assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
APInt api = convertToAPInt();
return api.bitsToDouble();
}
/// exponent = 0, integer bit set. (formerly "psuedodenormals")
/// exponent!=0 nor all 1's, integer bit not set. (formerly "unnormals")
void
-APFloat::initFromF80LongDoubleAPInt(const APInt &api) {
+APFloat::initFromF80LongDoubleAPInt(const APInt &api)
+{
assert(api.getBitWidth()==80);
uint64_t i1 = api.getRawData()[0];
uint64_t i2 = api.getRawData()[1];
significandParts()[1] = 0;
if (myexponent==0) // denormal
exponent = -16382;
- }
+ }
+}
+
+void
+APFloat::initFromPPCDoubleDoubleAPInt(const APInt &api)
+{
+ assert(api.getBitWidth()==128);
+ uint64_t i1 = api.getRawData()[0];
+ uint64_t i2 = api.getRawData()[1];
+ uint64_t myexponent = (i1 >> 52) & 0x7ff;
+ uint64_t mysignificand = i1 & 0xfffffffffffffLL;
+ uint64_t myexponent2 = (i2 >> 52) & 0x7ff;
+ uint64_t mysignificand2 = i2 & 0xfffffffffffffLL;
+
+ initialize(&APFloat::PPCDoubleDouble);
+ assert(partCount()==2);
+
+ sign = i1>>63;
+ sign2 = i2>>63;
+ if (myexponent==0 && mysignificand==0) {
+ // exponent, significand meaningless
+ // exponent2 and significand2 are required to be 0; we don't check
+ category = fcZero;
+ } else if (myexponent==0x7ff && mysignificand==0) {
+ // exponent, significand meaningless
+ // exponent2 and significand2 are required to be 0; we don't check
+ category = fcInfinity;
+ } else if (myexponent==0x7ff && mysignificand!=0) {
+ // exponent meaningless. So is the whole second word, but keep it
+ // for determinism.
+ category = fcNaN;
+ exponent2 = myexponent2;
+ significandParts()[0] = mysignificand;
+ significandParts()[1] = mysignificand2;
+ } else {
+ category = fcNormal;
+ // Note there is no category2; the second word is treated as if it is
+ // fcNormal, although it might be something else considered by itself.
+ exponent = myexponent - 1023;
+ exponent2 = myexponent2 - 1023;
+ significandParts()[0] = mysignificand;
+ significandParts()[1] = mysignificand2;
+ if (myexponent==0) // denormal
+ exponent = -1022;
+ else
+ significandParts()[0] |= 0x10000000000000LL; // integer bit
+ if (myexponent2==0)
+ exponent2 = -1022;
+ else
+ significandParts()[1] |= 0x10000000000000LL; // integer bit
+ }
}
void
-APFloat::initFromDoubleAPInt(const APInt &api) {
+APFloat::initFromDoubleAPInt(const APInt &api)
+{
assert(api.getBitWidth()==64);
uint64_t i = *api.getRawData();
uint64_t myexponent = (i >> 52) & 0x7ff;
exponent = -1022;
else
*significandParts() |= 0x10000000000000LL; // integer bit
- }
+ }
}
void
-APFloat::initFromFloatAPInt(const APInt & api) {
+APFloat::initFromFloatAPInt(const APInt & api)
+{
assert(api.getBitWidth()==32);
uint32_t i = (uint32_t)*api.getRawData();
uint32_t myexponent = (i >> 23) & 0xff;
} else if (myexponent==0xff && mysignificand==0) {
// exponent, significand meaningless
category = fcInfinity;
- } else if (myexponent==0xff && (mysignificand & 0x400000)) {
+ } else if (myexponent==0xff && mysignificand!=0) {
// sign, exponent, significand meaningless
category = fcNaN;
*significandParts() = mysignificand;
}
/// Treat api as containing the bits of a floating point number. Currently
-/// we infer the floating point type from the size of the APInt. FIXME: This
-/// breaks when we get to PPC128 and IEEE128 (but both cannot exist in the
-/// same compile...)
+/// we infer the floating point type from the size of the APInt. The
+/// isIEEE argument distinguishes between PPC128 and IEEE128 (not meaningful
+/// when the size is anything else).
void
-APFloat::initFromAPInt(const APInt& api) {
+APFloat::initFromAPInt(const APInt& api, bool isIEEE)
+{
if (api.getBitWidth() == 32)
return initFromFloatAPInt(api);
else if (api.getBitWidth()==64)
return initFromDoubleAPInt(api);
else if (api.getBitWidth()==80)
return initFromF80LongDoubleAPInt(api);
+ else if (api.getBitWidth()==128 && !isIEEE)
+ return initFromPPCDoubleDoubleAPInt(api);
else
assert(0);
}
-APFloat::APFloat(const APInt& api) {
- initFromAPInt(api);
+APFloat::APFloat(const APInt& api, bool isIEEE)
+{
+ initFromAPInt(api, isIEEE);
}
-APFloat::APFloat(float f) {
+APFloat::APFloat(float f)
+{
APInt api = APInt(32, 0);
initFromAPInt(api.floatToBits(f));
}
-APFloat::APFloat(double d) {
+APFloat::APFloat(double d)
+{
APInt api = APInt(64, 0);
initFromAPInt(api.doubleToBits(d));
}
-
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