//
// 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 <cstring>
#include "llvm/ADT/APFloat.h"
+#include "llvm/ADT/StringRef.h"
+#include "llvm/ADT/FoldingSet.h"
+#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/MathExtras.h"
+#include <limits.h>
+#include <cstring>
using namespace llvm;
/* Assumed in hexadecimal significand parsing, and conversion to
hexadecimal strings. */
+#define COMPILE_TIME_ASSERT(cond) extern int CTAssert[(cond) ? 1 : -1]
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::IEEEhalf = { 15, -14, 11, true };
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. */
-namespace {
+/* A bunch of private, handy routines. */
+
+static inline unsigned int
+partCountForBits(unsigned int bits)
+{
+ return ((bits) + integerPartWidth - 1) / integerPartWidth;
+}
+
+/* Returns 0U-9U. Return values >= 10U are not digits. */
+static inline unsigned int
+decDigitValue(unsigned int c)
+{
+ return c - '0';
+}
+
+static unsigned int
+hexDigitValue(unsigned int c)
+{
+ unsigned int r;
+
+ r = c - '0';
+ if (r <= 9)
+ return r;
+
+ r = c - 'A';
+ if (r <= 5)
+ return r + 10;
+
+ r = c - 'a';
+ if (r <= 5)
+ return r + 10;
+
+ return -1U;
+}
+
+static 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. */
+static int
+readExponent(StringRef::iterator begin, StringRef::iterator end)
+{
+ bool isNegative;
+ unsigned int absExponent;
+ const unsigned int overlargeExponent = 24000; /* FIXME. */
+ StringRef::iterator p = begin;
+
+ assert(p != end && "Exponent has no digits");
+
+ isNegative = (*p == '-');
+ if (*p == '-' || *p == '+') {
+ p++;
+ assert(p != end && "Exponent has no digits");
+ }
+
+ absExponent = decDigitValue(*p++);
+ assert(absExponent < 10U && "Invalid character in exponent");
+
+ for (; p != end; ++p) {
+ unsigned int value;
+
+ value = decDigitValue(*p);
+ assert(value < 10U && "Invalid character in exponent");
- inline unsigned int
- partCountForBits(unsigned int bits)
- {
- return ((bits) + integerPartWidth - 1) / integerPartWidth;
+ value += absExponent * 10;
+ if (absExponent >= overlargeExponent) {
+ absExponent = overlargeExponent;
+ break;
+ }
+ absExponent = value;
}
- unsigned int
- digitValue(unsigned int c)
- {
- unsigned int r;
+ assert(p == end && "Invalid exponent in exponent");
+
+ 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
+totalExponent(StringRef::iterator p, StringRef::iterator end,
+ int exponentAdjustment)
+{
+ int unsignedExponent;
+ bool negative, overflow;
+ int exponent;
- r = c - '0';
- if(r <= 9)
- return r;
+ assert(p != end && "Exponent has no digits");
- return -1U;
+ negative = *p == '-';
+ if (*p == '-' || *p == '+') {
+ p++;
+ assert(p != end && "Exponent has no digits");
}
- unsigned int
- hexDigitValue (unsigned int c)
- {
- unsigned int r;
+ unsignedExponent = 0;
+ overflow = false;
+ for (; p != end; ++p) {
+ unsigned int value;
- r = c - '0';
- if(r <= 9)
- return r;
+ value = decDigitValue(*p);
+ assert(value < 10U && "Invalid character in exponent");
- r = c - 'A';
- if(r <= 5)
- return r + 10;
+ unsignedExponent = unsignedExponent * 10 + value;
+ if (unsignedExponent > 65535)
+ overflow = true;
+ }
- r = c - 'a';
- if(r <= 5)
- return r + 10;
+ if (exponentAdjustment > 65535 || exponentAdjustment < -65536)
+ overflow = true;
- return -1U;
+ if (!overflow) {
+ exponent = unsignedExponent;
+ if (negative)
+ exponent = -exponent;
+ exponent += exponentAdjustment;
+ if (exponent > 65535 || exponent < -65536)
+ overflow = true;
}
- /* This is ugly and needs cleaning up, but I don't immediately see
- how whilst remaining safe. */
- static int
- totalExponent(const char *p, int exponentAdjustment)
- {
- integerPart unsignedExponent;
- bool negative, overflow;
- long exponent;
+ if (overflow)
+ exponent = negative ? -65536: 65535;
+
+ return exponent;
+}
- /* Move past the exponent letter and sign to the digits. */
+static StringRef::iterator
+skipLeadingZeroesAndAnyDot(StringRef::iterator begin, StringRef::iterator end,
+ StringRef::iterator *dot)
+{
+ StringRef::iterator p = begin;
+ *dot = end;
+ while (*p == '0' && p != end)
p++;
- negative = *p == '-';
- if(*p == '-' || *p == '+')
- p++;
- unsignedExponent = 0;
- overflow = false;
- for(;;) {
- unsigned int value;
+ if (*p == '.') {
+ *dot = p++;
- value = digitValue(*p);
- if(value == -1U)
- break;
+ assert(end - begin != 1 && "Significand has no digits");
+ while (*p == '0' && p != end)
p++;
- unsignedExponent = unsignedExponent * 10 + value;
- if(unsignedExponent > 65535)
- overflow = true;
- }
+ }
- if(exponentAdjustment > 65535 || exponentAdjustment < -65536)
- overflow = true;
+ return p;
+}
- if(!overflow) {
- exponent = unsignedExponent;
- if(negative)
- exponent = -exponent;
- exponent += exponentAdjustment;
- if(exponent > 65535 || exponent < -65536)
- overflow = true;
- }
+/* Given a normal decimal floating point number of the form
+
+ dddd.dddd[eE][+-]ddd
- if(overflow)
- exponent = negative ? -65536: 65535;
+ 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.
- return exponent;
+ 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;
+};
+
+static void
+interpretDecimal(StringRef::iterator begin, StringRef::iterator end,
+ decimalInfo *D)
+{
+ StringRef::iterator dot = end;
+ StringRef::iterator p = skipLeadingZeroesAndAnyDot (begin, end, &dot);
+
+ D->firstSigDigit = p;
+ D->exponent = 0;
+ D->normalizedExponent = 0;
+
+ for (; p != end; ++p) {
+ if (*p == '.') {
+ assert(dot == end && "String contains multiple dots");
+ dot = p++;
+ if (p == end)
+ break;
+ }
+ if (decDigitValue(*p) >= 10U)
+ break;
}
- const char *
- skipLeadingZeroesAndAnyDot(const char *p, const char **dot)
- {
- *dot = 0;
- while(*p == '0')
- p++;
+ if (p != end) {
+ assert((*p == 'e' || *p == 'E') && "Invalid character in significand");
+ assert(p != begin && "Significand has no digits");
+ assert((dot == end || p - begin != 1) && "Significand has no digits");
+
+ /* p points to the first non-digit in the string */
+ D->exponent = readExponent(p + 1, end);
+
+ /* Implied decimal point? */
+ if (dot == end)
+ dot = p;
+ }
- if(*p == '.') {
- *dot = p++;
- while(*p == '0')
- p++;
+ /* If number is all zeroes accept any exponent. */
+ if (p != D->firstSigDigit) {
+ /* Drop insignificant trailing zeroes. */
+ if (p != begin) {
+ do
+ do
+ p--;
+ while (p != begin && *p == '0');
+ while (p != begin && *p == '.');
}
- return p;
+ /* Adjust the exponents for any decimal point. */
+ D->exponent += static_cast<exponent_t>((dot - p) - (dot > p));
+ D->normalizedExponent = (D->exponent +
+ static_cast<exponent_t>((p - D->firstSigDigit)
+ - (dot > D->firstSigDigit && dot < p)));
}
- /* Return the trailing fraction of a hexadecimal number.
- DIGITVALUE is the first hex digit of the fraction, P points to
- the next digit. */
- lostFraction
- trailingHexadecimalFraction(const char *p, unsigned int digitValue)
- {
- unsigned int hexDigit;
+ D->lastSigDigit = p;
+}
- /* If the first trailing digit isn't 0 or 8 we can work out the
- fraction immediately. */
- if(digitValue > 8)
- return lfMoreThanHalf;
- else if(digitValue < 8 && digitValue > 0)
- return lfLessThanHalf;
+/* Return the trailing fraction of a hexadecimal number.
+ DIGITVALUE is the first hex digit of the fraction, P points to
+ the next digit. */
+static lostFraction
+trailingHexadecimalFraction(StringRef::iterator p, StringRef::iterator end,
+ unsigned int digitValue)
+{
+ unsigned int hexDigit;
- /* Otherwise we need to find the first non-zero digit. */
- while(*p == '0')
- p++;
+ /* If the first trailing digit isn't 0 or 8 we can work out the
+ fraction immediately. */
+ if (digitValue > 8)
+ return lfMoreThanHalf;
+ else if (digitValue < 8 && digitValue > 0)
+ return lfLessThanHalf;
- hexDigit = hexDigitValue(*p);
+ /* Otherwise we need to find the first non-zero digit. */
+ while (*p == '0')
+ p++;
- /* If we ran off the end it is exactly zero or one-half, otherwise
- a little more. */
- if(hexDigit == -1U)
- return digitValue == 0 ? lfExactlyZero: lfExactlyHalf;
- else
- return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf;
- }
+ assert(p != end && "Invalid trailing hexadecimal fraction!");
+
+ hexDigit = hexDigitValue(*p);
- /* Return the fraction lost were a bignum truncated losing the least
- significant BITS bits. */
- lostFraction
- lostFractionThroughTruncation(const integerPart *parts,
- unsigned int partCount,
- unsigned int bits)
- {
- unsigned int lsb;
+ /* If we ran off the end it is exactly zero or one-half, otherwise
+ a little more. */
+ if (hexDigit == -1U)
+ return digitValue == 0 ? lfExactlyZero: lfExactlyHalf;
+ else
+ return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf;
+}
- lsb = APInt::tcLSB(parts, partCount);
+/* Return the fraction lost were a bignum truncated losing the least
+ significant BITS bits. */
+static lostFraction
+lostFractionThroughTruncation(const integerPart *parts,
+ unsigned int partCount,
+ unsigned int bits)
+{
+ unsigned int lsb;
- /* Note this is guaranteed true if bits == 0, or LSB == -1U. */
- if(bits <= lsb)
- return lfExactlyZero;
- if(bits == lsb + 1)
- return lfExactlyHalf;
- if(bits <= partCount * integerPartWidth
- && APInt::tcExtractBit(parts, bits - 1))
- return lfMoreThanHalf;
+ lsb = APInt::tcLSB(parts, partCount);
- return lfLessThanHalf;
+ /* Note this is guaranteed true if bits == 0, or LSB == -1U. */
+ if (bits <= lsb)
+ return lfExactlyZero;
+ if (bits == lsb + 1)
+ return lfExactlyHalf;
+ if (bits <= partCount * integerPartWidth &&
+ APInt::tcExtractBit(parts, bits - 1))
+ return lfMoreThanHalf;
+
+ return lfLessThanHalf;
+}
+
+/* Shift DST right BITS bits noting lost fraction. */
+static lostFraction
+shiftRight(integerPart *dst, unsigned int parts, unsigned int bits)
+{
+ lostFraction lost_fraction;
+
+ lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
+
+ APInt::tcShiftRight(dst, parts, bits);
+
+ return lost_fraction;
+}
+
+/* Combine the effect of two lost fractions. */
+static lostFraction
+combineLostFractions(lostFraction moreSignificant,
+ lostFraction lessSignificant)
+{
+ if (lessSignificant != lfExactlyZero) {
+ if (moreSignificant == lfExactlyZero)
+ moreSignificant = lfLessThanHalf;
+ else if (moreSignificant == lfExactlyHalf)
+ moreSignificant = lfMoreThanHalf;
}
- /* Shift DST right BITS bits noting lost fraction. */
- lostFraction
- shiftRight(integerPart *dst, unsigned int parts, unsigned int bits)
- {
- lostFraction lost_fraction;
+ 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. */
+static 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. */
+static 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;
- lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
+ part = parts[count] & (~(integerPart) 0 >> (integerPartWidth - partBits));
- APInt::tcShiftRight(dst, parts, bits);
+ 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;
+ }
- return lost_fraction;
+ 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. */
+static unsigned int
+powerOf5(integerPart *dst, unsigned int power)
+{
+ static const integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125,
+ 15625, 78125 };
+ integerPart pow5s[maxPowerOfFiveParts * 2 + 5];
+ pow5s[0] = 78125 * 5;
+
+ 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;
- /* 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";
+ 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;
+ }
- /* Write out an integerPart in hexadecimal, starting with the most
- significant nibble. Write out exactly COUNT hexdigits, return
- COUNT. */
- static unsigned int
- partAsHex (char *dst, integerPart part, unsigned int count,
- const char *hexDigitChars)
- {
- unsigned int result = count;
+ if (power & 1) {
+ integerPart *tmp;
- assert (count != 0 && count <= integerPartWidth / 4);
+ APInt::tcFullMultiply(p2, p1, pow5, result, pc);
+ result += pc;
+ if (p2[result - 1] == 0)
+ result--;
- part >>= (integerPartWidth - 4 * count);
- while (count--) {
- dst[count] = hexDigitChars[part & 0xf];
- part >>= 4;
+ /* Now result is in p1 with partsCount parts and p2 is scratch
+ space. */
+ tmp = p1, p1 = p2, p2 = tmp;
}
- return result;
+ pow5 += pc;
}
- /* Write out an unsigned decimal integer. */
- static char *
- writeUnsignedDecimal (char *dst, unsigned int n)
- {
- char buff[40], *p;
+ if (p1 != dst)
+ APInt::tcAssign(dst, p1, result);
- p = buff;
- do
- *p++ = '0' + n % 10;
- while (n /= 10);
+ return result;
+}
- do
- *dst++ = *--p;
- while (p != buff);
+/* 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";
- return dst;
- }
+/* Write out an integerPart in hexadecimal, starting with the most
+ significant nibble. Write out exactly COUNT hexdigits, return
+ COUNT. */
+static unsigned int
+partAsHex (char *dst, integerPart part, unsigned int count,
+ const char *hexDigitChars)
+{
+ unsigned int result = count;
- /* Write out a signed decimal integer. */
- static char *
- writeSignedDecimal (char *dst, int value)
- {
- if (value < 0) {
- *dst++ = '-';
- dst = writeUnsignedDecimal(dst, -(unsigned) value);
- } else
- dst = writeUnsignedDecimal(dst, value);
+ assert(count != 0 && count <= integerPartWidth / 4);
- return dst;
+ part >>= (integerPartWidth - 4 * count);
+ while (count--) {
+ dst[count] = hexDigitChars[part & 0xf];
+ part >>= 4;
}
+
+ return result;
+}
+
+/* Write out an unsigned decimal integer. */
+static 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. */
+static char *
+writeSignedDecimal (char *dst, int value)
+{
+ if (value < 0) {
+ *dst++ = '-';
+ dst = writeUnsignedDecimal(dst, -(unsigned) value);
+ } else
+ dst = writeUnsignedDecimal(dst, value);
+
+ return dst;
}
/* Constructors. */
semantics = ourSemantics;
count = partCount();
- if(count > 1)
+ if (count > 1)
significand.parts = new integerPart[count];
}
void
APFloat::freeSignificand()
{
- if(partCount() > 1)
+ if (partCount() > 1)
delete [] significand.parts;
}
sign = rhs.sign;
category = rhs.category;
exponent = rhs.exponent;
- if(category == fcNormal || category == fcNaN)
+ sign2 = rhs.sign2;
+ exponent2 = rhs.exponent2;
+ if (category == fcNormal || category == fcNaN)
copySignificand(rhs);
}
partCount());
}
+/* Make this number a NaN, with an arbitrary but deterministic value
+ for the significand. If double or longer, this is a signalling NaN,
+ which may not be ideal. If float, this is QNaN(0). */
+void APFloat::makeNaN(bool SNaN, bool Negative, const APInt *fill)
+{
+ category = fcNaN;
+ sign = Negative;
+
+ integerPart *significand = significandParts();
+ unsigned numParts = partCount();
+
+ // Set the significand bits to the fill.
+ if (!fill || fill->getNumWords() < numParts)
+ APInt::tcSet(significand, 0, numParts);
+ if (fill) {
+ APInt::tcAssign(significand, fill->getRawData(),
+ std::min(fill->getNumWords(), numParts));
+
+ // Zero out the excess bits of the significand.
+ unsigned bitsToPreserve = semantics->precision - 1;
+ unsigned part = bitsToPreserve / 64;
+ bitsToPreserve %= 64;
+ significand[part] &= ((1ULL << bitsToPreserve) - 1);
+ for (part++; part != numParts; ++part)
+ significand[part] = 0;
+ }
+
+ unsigned QNaNBit = semantics->precision - 2;
+
+ if (SNaN) {
+ // We always have to clear the QNaN bit to make it an SNaN.
+ APInt::tcClearBit(significand, QNaNBit);
+
+ // If there are no bits set in the payload, we have to set
+ // *something* to make it a NaN instead of an infinity;
+ // conventionally, this is the next bit down from the QNaN bit.
+ if (APInt::tcIsZero(significand, numParts))
+ APInt::tcSetBit(significand, QNaNBit - 1);
+ } else {
+ // We always have to set the QNaN bit to make it a QNaN.
+ APInt::tcSetBit(significand, QNaNBit);
+ }
+
+ // For x87 extended precision, we want to make a NaN, not a
+ // pseudo-NaN. Maybe we should expose the ability to make
+ // pseudo-NaNs?
+ if (semantics == &APFloat::x87DoubleExtended)
+ APInt::tcSetBit(significand, QNaNBit + 1);
+}
+
+APFloat APFloat::makeNaN(const fltSemantics &Sem, bool SNaN, bool Negative,
+ const APInt *fill) {
+ APFloat value(Sem, uninitialized);
+ value.makeNaN(SNaN, Negative, fill);
+ return value;
+}
+
APFloat &
APFloat::operator=(const APFloat &rhs)
{
- if(this != &rhs) {
- if(semantics != rhs.semantics) {
+ if (this != &rhs) {
+ if (semantics != rhs.semantics) {
freeSignificand();
initialize(rhs.semantics);
}
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();
normalize(rmNearestTiesToEven, lfExactlyZero);
}
+APFloat::APFloat(const fltSemantics &ourSemantics) {
+ assertArithmeticOK(ourSemantics);
+ initialize(&ourSemantics);
+ category = fcZero;
+ sign = false;
+}
+
+APFloat::APFloat(const fltSemantics &ourSemantics, uninitializedTag tag) {
+ assertArithmeticOK(ourSemantics);
+ // Allocates storage if necessary but does not initialize it.
+ initialize(&ourSemantics);
+}
+
APFloat::APFloat(const fltSemantics &ourSemantics,
fltCategory ourCategory, bool negative)
{
+ assertArithmeticOK(ourSemantics);
initialize(&ourSemantics);
category = ourCategory;
sign = negative;
- if(category == fcNormal)
+ if (category == fcNormal)
category = fcZero;
+ else if (ourCategory == fcNaN)
+ makeNaN();
}
-APFloat::APFloat(const fltSemantics &ourSemantics, const char *text)
+APFloat::APFloat(const fltSemantics &ourSemantics, const StringRef& 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(bitcastToAPInt());
+}
+
unsigned int
APFloat::partCount() const
{
{
assert(category == fcNormal || category == fcNaN);
- if(partCount() > 1)
+ if (partCount() > 1)
return significand.parts;
else
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()
{
integerPart scratch[4];
integerPart *fullSignificand;
lostFraction lost_fraction;
+ bool ignored;
assert(semantics == rhs.semantics);
precision = semantics->precision;
newPartsCount = partCountForBits(precision * 2);
- if(newPartsCount > 4)
+ if (newPartsCount > 4)
fullSignificand = new integerPart[newPartsCount];
else
fullSignificand = scratch;
omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
exponent += rhs.exponent;
- if(addend) {
+ if (addend) {
Significand savedSignificand = significand;
const fltSemantics *savedSemantics = semantics;
fltSemantics extendedSemantics;
/* Normalize our MSB. */
extendedPrecision = precision + precision - 1;
- if(omsb != extendedPrecision)
- {
- APInt::tcShiftLeft(fullSignificand, newPartsCount,
- extendedPrecision - omsb);
- exponent -= extendedPrecision - omsb;
- }
+ if (omsb != extendedPrecision) {
+ APInt::tcShiftLeft(fullSignificand, newPartsCount,
+ extendedPrecision - omsb);
+ exponent -= extendedPrecision - omsb;
+ }
/* Create new semantics. */
extendedSemantics = *semantics;
extendedSemantics.precision = extendedPrecision;
- if(newPartsCount == 1)
+ if (newPartsCount == 1)
significand.part = fullSignificand[0];
else
significand.parts = fullSignificand;
semantics = &extendedSemantics;
APFloat extendedAddend(*addend);
- status = extendedAddend.convert(extendedSemantics, rmTowardZero);
+ status = extendedAddend.convert(extendedSemantics, rmTowardZero, &ignored);
assert(status == opOK);
lost_fraction = addOrSubtractSignificand(extendedAddend, false);
/* Restore our state. */
- if(newPartsCount == 1)
+ if (newPartsCount == 1)
fullSignificand[0] = significand.part;
significand = savedSignificand;
semantics = savedSemantics;
exponent -= (precision - 1);
- if(omsb > precision) {
+ if (omsb > precision) {
unsigned int bits, significantParts;
lostFraction lf;
APInt::tcAssign(lhsSignificand, fullSignificand, partsCount);
- if(newPartsCount > 4)
+ if (newPartsCount > 4)
delete [] fullSignificand;
return lost_fraction;
rhsSignificand = rhs.significandParts();
partsCount = partCount();
- if(partsCount > 2)
+ if (partsCount > 2)
dividend = new integerPart[partsCount * 2];
else
dividend = scratch;
divisor = dividend + partsCount;
/* Copy the dividend and divisor as they will be modified in-place. */
- for(i = 0; i < partsCount; i++) {
+ for (i = 0; i < partsCount; i++) {
dividend[i] = lhsSignificand[i];
divisor[i] = rhsSignificand[i];
lhsSignificand[i] = 0;
/* Normalize the divisor. */
bit = precision - APInt::tcMSB(divisor, partsCount) - 1;
- if(bit) {
+ if (bit) {
exponent += bit;
APInt::tcShiftLeft(divisor, partsCount, bit);
}
/* Normalize the dividend. */
bit = precision - APInt::tcMSB(dividend, partsCount) - 1;
- if(bit) {
+ if (bit) {
exponent -= bit;
APInt::tcShiftLeft(dividend, partsCount, bit);
}
- if(APInt::tcCompare(dividend, divisor, partsCount) < 0) {
+ /* 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);
assert(APInt::tcCompare(dividend, divisor, partsCount) >= 0);
}
/* Long division. */
- for(bit = precision; bit; bit -= 1) {
- if(APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
+ for (bit = precision; bit; bit -= 1) {
+ if (APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
APInt::tcSubtract(dividend, divisor, 0, partsCount);
APInt::tcSetBit(lhsSignificand, bit - 1);
}
/* Figure out the lost fraction. */
int cmp = APInt::tcCompare(dividend, divisor, partsCount);
- if(cmp > 0)
+ if (cmp > 0)
lost_fraction = lfMoreThanHalf;
- else if(cmp == 0)
+ else if (cmp == 0)
lost_fraction = lfExactlyHalf;
- else if(APInt::tcIsZero(dividend, partsCount))
+ else if (APInt::tcIsZero(dividend, partsCount))
lost_fraction = lfExactlyZero;
else
lost_fraction = lfLessThanHalf;
- if(partsCount > 2)
+ if (partsCount > 2)
delete [] dividend;
return lost_fraction;
{
assert(bits < semantics->precision);
- if(bits) {
+ if (bits) {
unsigned int partsCount = partCount();
APInt::tcShiftLeft(significandParts(), partsCount, bits);
/* If exponents are equal, do an unsigned bignum comparison of the
significands. */
- if(compare == 0)
+ if (compare == 0)
compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
partCount());
- if(compare > 0)
+ if (compare > 0)
return cmpGreaterThan;
- else if(compare < 0)
+ else if (compare < 0)
return cmpLessThan;
else
return cmpEqual;
APFloat::handleOverflow(roundingMode rounding_mode)
{
/* Infinity? */
- if(rounding_mode == rmNearestTiesToEven
- || rounding_mode == rmNearestTiesToAway
- || (rounding_mode == rmTowardPositive && !sign)
- || (rounding_mode == rmTowardNegative && sign))
- {
- category = fcInfinity;
- return (opStatus) (opOverflow | opInexact);
- }
+ if (rounding_mode == rmNearestTiesToEven ||
+ rounding_mode == rmNearestTiesToAway ||
+ (rounding_mode == rmTowardPositive && !sign) ||
+ (rounding_mode == rmTowardNegative && sign)) {
+ category = fcInfinity;
+ return (opStatus) (opOverflow | opInexact);
+ }
/* Otherwise we become the largest finite number. */
category = fcNormal;
/* Current callers never pass this so we don't handle it. */
assert(lost_fraction != lfExactlyZero);
- switch(rounding_mode) {
+ switch (rounding_mode) {
default:
- assert(0);
+ llvm_unreachable(0);
case rmNearestTiesToAway:
return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf;
case rmNearestTiesToEven:
- if(lost_fraction == lfMoreThanHalf)
+ if (lost_fraction == lfMoreThanHalf)
return true;
/* Our zeroes don't have a significand to test. */
- if(lost_fraction == lfExactlyHalf && category != fcZero)
+ if (lost_fraction == lfExactlyHalf && category != fcZero)
return APInt::tcExtractBit(significandParts(), bit);
return false;
unsigned int omsb; /* One, not zero, based MSB. */
int exponentChange;
- if(category != fcNormal)
+ if (category != fcNormal)
return opOK;
/* Before rounding normalize the exponent of fcNormal numbers. */
omsb = significandMSB() + 1;
- if(omsb) {
+ if (omsb) {
/* OMSB is numbered from 1. We want to place it in the integer
bit numbered PRECISON if possible, with a compensating change in
the exponent. */
/* If the resulting exponent is too high, overflow according to
the rounding mode. */
- if(exponent + exponentChange > semantics->maxExponent)
+ if (exponent + exponentChange > semantics->maxExponent)
return handleOverflow(rounding_mode);
/* Subnormal numbers have exponent minExponent, and their MSB
is forced based on that. */
- if(exponent + exponentChange < semantics->minExponent)
+ if (exponent + exponentChange < semantics->minExponent)
exponentChange = semantics->minExponent - exponent;
/* Shifting left is easy as we don't lose precision. */
- if(exponentChange < 0) {
+ if (exponentChange < 0) {
assert(lost_fraction == lfExactlyZero);
shiftSignificandLeft(-exponentChange);
return opOK;
}
- if(exponentChange > 0) {
+ if (exponentChange > 0) {
lostFraction lf;
/* Shift right and capture any new lost fraction. */
lost_fraction = combineLostFractions(lf, lost_fraction);
/* Keep OMSB up-to-date. */
- if(omsb > (unsigned) exponentChange)
- omsb -= (unsigned) exponentChange;
+ if (omsb > (unsigned) exponentChange)
+ omsb -= exponentChange;
else
omsb = 0;
}
/* As specified in IEEE 754, since we do not trap we do not report
underflow for exact results. */
- if(lost_fraction == lfExactlyZero) {
+ if (lost_fraction == lfExactlyZero) {
/* Canonicalize zeroes. */
- if(omsb == 0)
+ if (omsb == 0)
category = fcZero;
return opOK;
}
/* Increment the significand if we're rounding away from zero. */
- if(roundAwayFromZero(rounding_mode, lost_fraction, 0)) {
- if(omsb == 0)
+ if (roundAwayFromZero(rounding_mode, lost_fraction, 0)) {
+ if (omsb == 0)
exponent = semantics->minExponent;
incrementSignificand();
omsb = significandMSB() + 1;
/* Did the significand increment overflow? */
- if(omsb == (unsigned) semantics->precision + 1) {
+ 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. */
- if(exponent == semantics->maxExponent) {
+ if (exponent == semantics->maxExponent) {
category = fcInfinity;
return (opStatus) (opOverflow | opInexact);
/* The normal case - we were and are not denormal, and any
significand increment above didn't overflow. */
- if(omsb == semantics->precision)
+ if (omsb == semantics->precision)
return opInexact;
/* We have a non-zero denormal. */
assert(omsb < semantics->precision);
- assert(exponent == semantics->minExponent);
/* Canonicalize zeroes. */
- if(omsb == 0)
+ if (omsb == 0)
category = fcZero;
/* The fcZero case is a denormal that underflowed to zero. */
APFloat::opStatus
APFloat::addOrSubtractSpecials(const APFloat &rhs, bool subtract)
{
- switch(convolve(category, rhs.category)) {
+ switch (convolve(category, rhs.category)) {
default:
- assert(0);
+ llvm_unreachable(0);
case convolve(fcNaN, fcZero):
case convolve(fcNaN, fcNormal):
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)!=0) != 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;
/* Subtraction is more subtle than one might naively expect. */
- if(subtract) {
+ if (subtract) {
APFloat temp_rhs(rhs);
bool reverse;
/* Invert the lost fraction - it was on the RHS and
subtracted. */
- if(lost_fraction == lfLessThanHalf)
+ if (lost_fraction == lfLessThanHalf)
lost_fraction = lfMoreThanHalf;
- else if(lost_fraction == lfMoreThanHalf)
+ else if (lost_fraction == lfMoreThanHalf)
lost_fraction = lfLessThanHalf;
/* The code above is intended to ensure that no borrow is
necessary. */
assert(!carry);
} else {
- if(bits > 0) {
+ if (bits > 0) {
APFloat temp_rhs(rhs);
lost_fraction = temp_rhs.shiftSignificandRight(bits);
APFloat::opStatus
APFloat::multiplySpecials(const APFloat &rhs)
{
- switch(convolve(category, rhs.category)) {
+ switch (convolve(category, rhs.category)) {
default:
- assert(0);
+ llvm_unreachable(0);
case convolve(fcNaN, fcZero):
case convolve(fcNaN, fcNormal):
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):
APFloat::opStatus
APFloat::divideSpecials(const APFloat &rhs)
{
- switch(convolve(category, rhs.category)) {
+ switch (convolve(category, rhs.category)) {
default:
- assert(0);
+ llvm_unreachable(0);
case convolve(fcNaN, fcZero):
case convolve(fcNaN, fcNormal):
case convolve(fcInfinity, fcInfinity):
case convolve(fcZero, fcZero):
+ makeNaN();
+ return opInvalidOp;
+
+ case convolve(fcNormal, fcNormal):
+ return opOK;
+ }
+}
+
+APFloat::opStatus
+APFloat::modSpecials(const APFloat &rhs)
+{
+ switch (convolve(category, rhs.category)) {
+ default:
+ llvm_unreachable(0);
+
+ case convolve(fcNaN, fcZero):
+ case convolve(fcNaN, fcNormal):
+ case convolve(fcNaN, fcInfinity):
+ case convolve(fcNaN, fcNaN):
+ case convolve(fcZero, fcInfinity):
+ case convolve(fcZero, fcNormal):
+ case convolve(fcNormal, fcInfinity):
+ return opOK;
+
+ case convolve(fcZero, fcNaN):
+ case convolve(fcNormal, fcNaN):
+ case convolve(fcInfinity, fcNaN):
category = fcNaN;
- // Arbitrary but deterministic value for significand
- APInt::tcSet(significandParts(), ~0U, partCount());
+ copySignificand(rhs);
+ return opOK;
+
+ case convolve(fcNormal, fcZero):
+ case convolve(fcInfinity, fcZero):
+ case convolve(fcInfinity, fcNormal):
+ case convolve(fcInfinity, fcInfinity):
+ case convolve(fcZero, fcZero):
+ makeNaN();
return opInvalidOp;
case convolve(fcNormal, fcNormal):
{
opStatus fs;
+ assertArithmeticOK(*semantics);
+
fs = addOrSubtractSpecials(rhs, subtract);
/* This return code means it was not a simple case. */
- if(fs == opDivByZero) {
+ if (fs == opDivByZero) {
lostFraction lost_fraction;
lost_fraction = addOrSubtractSignificand(rhs, subtract);
/* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
positive zero unless rounding to minus infinity, except that
adding two like-signed zeroes gives that zero. */
- if(category == fcZero) {
- if(rhs.category != fcZero || (sign == rhs.sign) == subtract)
+ if (category == fcZero) {
+ if (rhs.category != fcZero || (sign == rhs.sign) == subtract)
sign = (rounding_mode == rmTowardNegative);
}
{
opStatus fs;
+ assertArithmeticOK(*semantics);
sign ^= rhs.sign;
fs = multiplySpecials(rhs);
- if(category == fcNormal) {
+ if (category == fcNormal) {
lostFraction lost_fraction = multiplySignificand(rhs, 0);
fs = normalize(rounding_mode, lost_fraction);
- if(lost_fraction != lfExactlyZero)
+ if (lost_fraction != lfExactlyZero)
fs = (opStatus) (fs | opInexact);
}
{
opStatus fs;
+ assertArithmeticOK(*semantics);
sign ^= rhs.sign;
fs = divideSpecials(rhs);
- if(category == fcNormal) {
+ if (category == fcNormal) {
lostFraction lost_fraction = divideSignificand(rhs);
fs = normalize(rounding_mode, lost_fraction);
- if(lost_fraction != lfExactlyZero)
+ if (lost_fraction != lfExactlyZero)
fs = (opStatus) (fs | opInexact);
}
return fs;
}
-/* Normalized remainder. This is not currently doing TRT. */
+/* Normalized remainder. This is not currently correct in all cases. */
APFloat::opStatus
-APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
+APFloat::remainder(const APFloat &rhs)
{
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];
+ bool ignored;
fs = V.convertToInteger(x, parts * integerPartWidth, true,
- rmNearestTiesToEven);
+ rmNearestTiesToEven, &ignored);
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);
+ fs = V.multiply(rhs, rmNearestTiesToEven);
assert(fs==opOK || fs==opInexact); // should not overflow or underflow
- fs = subtract(V, rounding_mode);
+ fs = subtract(V, rmNearestTiesToEven);
assert(fs==opOK || fs==opInexact); // likewise
if (isZero())
return fs;
}
+/* Normalized llvm frem (C fmod).
+ This is not currently correct in all cases. */
+APFloat::opStatus
+APFloat::mod(const APFloat &rhs, roundingMode rounding_mode)
+{
+ opStatus fs;
+ assertArithmeticOK(*semantics);
+ fs = modSpecials(rhs);
+
+ if (category == fcNormal && rhs.category == fcNormal) {
+ APFloat V = *this;
+ unsigned int origSign = sign;
+
+ fs = V.divide(rhs, rmNearestTiesToEven);
+ if (fs == opDivByZero)
+ return fs;
+
+ int parts = partCount();
+ integerPart *x = new integerPart[parts];
+ bool ignored;
+ fs = V.convertToInteger(x, parts * integerPartWidth, true,
+ rmTowardZero, &ignored);
+ if (fs==opInvalidOp)
+ return fs;
+
+ fs = V.convertFromZeroExtendedInteger(x, parts * integerPartWidth, true,
+ rmNearestTiesToEven);
+ assert(fs==opOK); // should always work
+
+ fs = V.multiply(rhs, rounding_mode);
+ assert(fs==opOK || fs==opInexact); // should not overflow or underflow
+
+ fs = subtract(V, rounding_mode);
+ assert(fs==opOK || fs==opInexact); // likewise
+
+ if (isZero())
+ sign = origSign; // IEEE754 requires this
+ delete[] x;
+ }
+ return fs;
+}
+
/* Normalized fused-multiply-add. */
APFloat::opStatus
APFloat::fusedMultiplyAdd(const APFloat &multiplicand,
{
opStatus fs;
+ assertArithmeticOK(*semantics);
+
/* Post-multiplication sign, before addition. */
sign ^= multiplicand.sign;
/* If and only if all arguments are normal do we need to do an
extended-precision calculation. */
- if(category == fcNormal
- && multiplicand.category == fcNormal
- && addend.category == fcNormal) {
+ if (category == fcNormal &&
+ multiplicand.category == fcNormal &&
+ addend.category == fcNormal) {
lostFraction lost_fraction;
lost_fraction = multiplySignificand(multiplicand, &addend);
fs = normalize(rounding_mode, lost_fraction);
- if(lost_fraction != lfExactlyZero)
+ if (lost_fraction != lfExactlyZero)
fs = (opStatus) (fs | opInexact);
/* If two numbers add (exactly) to zero, IEEE 754 decrees it is a
positive zero unless rounding to minus infinity, except that
adding two like-signed zeroes gives that zero. */
- if(category == fcZero && sign != addend.sign)
+ if (category == fcZero && sign != addend.sign)
sign = (rounding_mode == rmTowardNegative);
} else {
fs = multiplySpecials(multiplicand);
If we need to do the addition we can do so with normal
precision. */
- if(fs == opOK)
+ if (fs == opOK)
fs = addOrSubtract(addend, rounding_mode, false);
}
{
cmpResult result;
+ assertArithmeticOK(*semantics);
assert(semantics == rhs.semantics);
- switch(convolve(category, rhs.category)) {
+ switch (convolve(category, rhs.category)) {
default:
- assert(0);
+ llvm_unreachable(0);
case convolve(fcNaN, fcZero):
case convolve(fcNaN, fcNormal):
case convolve(fcInfinity, fcNormal):
case convolve(fcInfinity, fcZero):
case convolve(fcNormal, fcZero):
- if(sign)
+ if (sign)
return cmpLessThan;
else
return cmpGreaterThan;
case convolve(fcNormal, fcInfinity):
case convolve(fcZero, fcInfinity):
case convolve(fcZero, fcNormal):
- if(rhs.sign)
+ if (rhs.sign)
return cmpGreaterThan;
else
return cmpLessThan;
case convolve(fcInfinity, fcInfinity):
- if(sign == rhs.sign)
+ if (sign == rhs.sign)
return cmpEqual;
- else if(sign)
+ else if (sign)
return cmpLessThan;
else
return cmpGreaterThan;
}
/* Two normal numbers. Do they have the same sign? */
- if(sign != rhs.sign) {
- if(sign)
+ if (sign != rhs.sign) {
+ if (sign)
result = cmpLessThan;
else
result = cmpGreaterThan;
/* Compare absolute values; invert result if negative. */
result = compareAbsoluteValue(rhs);
- if(sign) {
- if(result == cmpLessThan)
+ if (sign) {
+ if (result == cmpLessThan)
result = cmpGreaterThan;
- else if(result == cmpGreaterThan)
+ else if (result == cmpGreaterThan)
result = cmpLessThan;
}
}
return result;
}
+/// APFloat::convert - convert a value of one floating point type to another.
+/// The return value corresponds to the IEEE754 exceptions. *losesInfo
+/// records whether the transformation lost information, i.e. whether
+/// converting the result back to the original type will produce the
+/// original value (this is almost the same as return value==fsOK, but there
+/// are edge cases where this is not so).
+
APFloat::opStatus
APFloat::convert(const fltSemantics &toSemantics,
- roundingMode rounding_mode)
+ roundingMode rounding_mode, bool *losesInfo)
{
lostFraction lostFraction;
unsigned int newPartCount, oldPartCount;
opStatus fs;
+ assertArithmeticOK(*semantics);
+ assertArithmeticOK(toSemantics);
lostFraction = lfExactlyZero;
newPartCount = partCountForBits(toSemantics.precision + 1);
oldPartCount = partCount();
}
}
- if(category == fcNormal) {
+ if (category == fcNormal) {
/* Re-interpret our bit-pattern. */
exponent += toSemantics.precision - semantics->precision;
semantics = &toSemantics;
fs = normalize(rounding_mode, lostFraction);
+ *losesInfo = (fs != opOK);
} else if (category == fcNaN) {
int shift = toSemantics.precision - semantics->precision;
+ // Do this now so significandParts gets the right answer
+ const fltSemantics *oldSemantics = semantics;
+ semantics = &toSemantics;
+ *losesInfo = false;
// No normalization here, just truncate
if (shift>0)
APInt::tcShiftLeft(significandParts(), newPartCount, shift);
- else if (shift < 0)
- APInt::tcShiftRight(significandParts(), newPartCount, -shift);
+ else if (shift < 0) {
+ unsigned ushift = -shift;
+ // Figure out if we are losing information. This happens
+ // if are shifting out something other than 0s, or if the x87 long
+ // double input did not have its integer bit set (pseudo-NaN), or if the
+ // x87 long double input did not have its QNan bit set (because the x87
+ // hardware sets this bit when converting a lower-precision NaN to
+ // x87 long double).
+ if (APInt::tcLSB(significandParts(), newPartCount) < ushift)
+ *losesInfo = true;
+ if (oldSemantics == &APFloat::x87DoubleExtended &&
+ (!(*significandParts() & 0x8000000000000000ULL) ||
+ !(*significandParts() & 0x4000000000000000ULL)))
+ *losesInfo = true;
+ APInt::tcShiftRight(significandParts(), newPartCount, ushift);
+ }
// 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.
- semantics = &toSemantics;
fs = opOK;
} else {
semantics = &toSemantics;
fs = opOK;
+ *losesInfo = false;
}
return fs;
/* 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,
+ bool *isExact) const
{
lostFraction lost_fraction;
- unsigned int msb, partsCount;
- int bits;
+ const integerPart *src;
+ unsigned int dstPartsCount, truncatedBits;
- partsCount = partCountForBits(width);
+ assertArithmeticOK(*semantics);
- /* Handle the three special cases first. We produce
- a deterministic result even for the Invalid cases. */
- if (category == fcNaN) {
- // Neither sign nor isSigned affects this.
- APInt::tcSet(parts, 0, partsCount);
- return opInvalidOp;
- }
- if (category == fcInfinity) {
- if (!sign && isSigned)
- APInt::tcSetLeastSignificantBits(parts, partsCount, width-1);
- else if (!sign && !isSigned)
- APInt::tcSetLeastSignificantBits(parts, partsCount, width);
- else if (sign && isSigned) {
- APInt::tcSetLeastSignificantBits(parts, partsCount, 1);
- APInt::tcShiftLeft(parts, partsCount, width-1);
- } else // sign && !isSigned
- APInt::tcSet(parts, 0, partsCount);
+ *isExact = false;
+
+ /* Handle the three special cases first. */
+ if (category == fcInfinity || category == fcNaN)
return opInvalidOp;
- }
+
+ dstPartsCount = partCountForBits(width);
+
if (category == fcZero) {
- APInt::tcSet(parts, 0, partsCount);
+ APInt::tcSet(parts, 0, dstPartsCount);
+ // Negative zero can't be represented as an int.
+ *isExact = !sign;
return opOK;
}
- /* Shift the bit pattern so the fraction is lost. */
- APFloat tmp(*this);
-
- bits = (int) semantics->precision - 1 - exponent;
+ src = significandParts();
- if(bits > 0) {
- lost_fraction = tmp.shiftSignificandRight(bits);
+ /* 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);
+ /* For exponent -1 the integer bit represents .5, look at that.
+ For smaller exponents leftmost truncated bit is 0. */
+ truncatedBits = semantics->precision -1U - exponent;
} else {
- if (-bits >= semantics->precision) {
- // Unrepresentably large.
- if (!sign && isSigned)
- APInt::tcSetLeastSignificantBits(parts, partsCount, width-1);
- else if (!sign && !isSigned)
- APInt::tcSetLeastSignificantBits(parts, partsCount, width);
- else if (sign && isSigned) {
- APInt::tcSetLeastSignificantBits(parts, partsCount, 1);
- APInt::tcShiftLeft(parts, partsCount, width-1);
- } else // sign && !isSigned
- APInt::tcSet(parts, 0, partsCount);
- return (opStatus)(opOverflow | opInexact);
+ /* 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;
+
+ 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;
}
- tmp.shiftSignificandLeft(-bits);
- lost_fraction = lfExactlyZero;
}
- if(lost_fraction != lfExactlyZero
- && tmp.roundAwayFromZero(rounding_mode, lost_fraction, 0))
- tmp.incrementSignificand();
-
- msb = tmp.significandMSB();
+ /* 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 {
+ lost_fraction = lfExactlyZero;
+ }
- /* Negative numbers cannot be represented as unsigned. */
- if(!isSigned && tmp.sign && msb != -1U)
- return opInvalidOp;
+ /* Step 3: check if we fit in the destination. */
+ unsigned int omsb = APInt::tcMSB(parts, dstPartsCount) + 1;
- /* 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 (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;
+ }
- if(isSigned && msb + 1 == width
- && (!tmp.sign || tmp.significandLSB() != msb))
- return opInvalidOp;
+ APInt::tcNegate (parts, dstPartsCount);
+ } else {
+ if (omsb >= width + !isSigned)
+ return opInvalidOp;
+ }
- APInt::tcAssign(parts, tmp.significandParts(), partsCount);
-
- if(tmp.sign)
- APInt::tcNegate(parts, partsCount);
-
- if(lost_fraction == lfExactlyZero)
+ if (lost_fraction == lfExactlyZero) {
+ *isExact = true;
return opOK;
- else
+ } else
return opInexact;
}
+/* 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.
+ The *isExact output tells whether the result is exact, in the sense
+ that converting it back to the original floating point type produces
+ the original value. This is almost equivalent to result==opOK,
+ except for negative zeroes.
+*/
APFloat::opStatus
-APFloat::convertFromUnsignedInteger(integerPart *parts,
- unsigned int partCount,
- roundingMode rounding_mode)
+APFloat::convertToInteger(integerPart *parts, unsigned int width,
+ bool isSigned,
+ roundingMode rounding_mode, bool *isExact) const
{
- unsigned int msb, precision;
- lostFraction lost_fraction;
+ opStatus fs;
- msb = APInt::tcMSB(parts, partCount) + 1;
- precision = semantics->precision;
+ fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode,
+ isExact);
+
+ if (fs == opInvalidOp) {
+ unsigned int bits, dstPartsCount;
+
+ 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::convertFromUnsignedParts(const integerPart *src,
+ unsigned int srcCount,
+ roundingMode rounding_mode)
+{
+ unsigned int omsb, precision, dstCount;
+ integerPart *dst;
+ lostFraction lost_fraction;
+ 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 = Val.getNumWords();
+ APInt api = Val;
+
+ sign = false;
+ 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)
{
- unsigned int partCount = partCountForBits(width);
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 {
+ sign = false;
+ status = convertFromUnsignedParts(src, srcCount, 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);
- integerPart *copy = new integerPart[partCount];
sign = false;
- if(isSigned && APInt::tcExtractBit(parts, width - 1)) {
+ if (isSigned && APInt::tcExtractBit(parts, width - 1)) {
sign = true;
api = -api;
}
- APInt::tcAssign(copy, api.getRawData(), partCount);
- status = convertFromUnsignedInteger(copy, partCount, rounding_mode);
- return status;
+ return convertFromUnsignedParts(api.getRawData(), partCount, rounding_mode);
}
APFloat::opStatus
-APFloat::convertFromHexadecimalString(const char *p,
+APFloat::convertFromHexadecimalString(const StringRef &s,
roundingMode rounding_mode)
{
- lostFraction lost_fraction;
+ lostFraction lost_fraction = lfExactlyZero;
integerPart *significand;
unsigned int bitPos, partsCount;
- const char *dot, *firstSignificantDigit;
+ StringRef::iterator dot, firstSignificantDigit;
zeroSignificand();
exponent = 0;
partsCount = partCount();
bitPos = partsCount * integerPartWidth;
- /* Skip leading zeroes and any(hexa)decimal point. */
- p = skipLeadingZeroesAndAnyDot(p, &dot);
+ /* Skip leading zeroes and any (hexa)decimal point. */
+ StringRef::iterator begin = s.begin();
+ StringRef::iterator end = s.end();
+ StringRef::iterator p = skipLeadingZeroesAndAnyDot(begin, end, &dot);
firstSignificantDigit = p;
- for(;;) {
+ for (; p != end;) {
integerPart hex_value;
- if(*p == '.') {
- assert(dot == 0);
+ if (*p == '.') {
+ assert(dot == end && "String contains multiple dots");
dot = p++;
+ if (p == end) {
+ break;
+ }
}
hex_value = hexDigitValue(*p);
- if(hex_value == -1U) {
- lost_fraction = lfExactlyZero;
+ if (hex_value == -1U) {
break;
}
p++;
- /* Store the number whilst 4-bit nibbles remain. */
- if(bitPos) {
- bitPos -= 4;
- hex_value <<= bitPos % integerPartWidth;
- significand[bitPos / integerPartWidth] |= hex_value;
- } else {
- lost_fraction = trailingHexadecimalFraction(p, hex_value);
- while(hexDigitValue(*p) != -1U)
- p++;
+ if (p == end) {
break;
+ } else {
+ /* Store the number whilst 4-bit nibbles remain. */
+ if (bitPos) {
+ bitPos -= 4;
+ hex_value <<= bitPos % integerPartWidth;
+ significand[bitPos / integerPartWidth] |= hex_value;
+ } else {
+ lost_fraction = trailingHexadecimalFraction(p, end, hex_value);
+ while (p != end && hexDigitValue(*p) != -1U)
+ p++;
+ break;
+ }
}
}
/* Hex floats require an exponent but not a hexadecimal point. */
- assert(*p == 'p' || *p == 'P');
+ assert(p != end && "Hex strings require an exponent");
+ assert((*p == 'p' || *p == 'P') && "Invalid character in significand");
+ assert(p != begin && "Significand has no digits");
+ assert((dot == end || p - begin != 1) && "Significand has no digits");
/* Ignore the exponent if we are zero. */
- if(p != firstSignificantDigit) {
+ if (p != firstSignificantDigit) {
int expAdjustment;
/* Implicit hexadecimal point? */
- if(!dot)
+ if (dot == end)
dot = p;
/* Calculate the exponent adjustment implicit in the number of
significant digits. */
- expAdjustment = dot - firstSignificantDigit;
- if(expAdjustment < 0)
+ expAdjustment = static_cast<int>(dot - firstSignificantDigit);
+ if (expAdjustment < 0)
expAdjustment++;
expAdjustment = expAdjustment * 4 - 1;
expAdjustment -= partsCount * integerPartWidth;
/* Adjust for the given exponent. */
- exponent = totalExponent(p, expAdjustment);
+ exponent = totalExponent(p + 1, end, expAdjustment);
}
return normalize(rounding_mode, lost_fraction);
}
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;
+ unsigned int 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 StringRef &str, roundingMode rounding_mode)
+{
+ decimalInfo D;
+ opStatus fs;
+
+ /* Scan the text. */
+ StringRef::iterator p = str.begin();
+ interpretDecimal(p, str.end(), &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;
+
+ /* Check whether the normalized exponent is high enough to overflow
+ max during the log-rebasing in the max-exponent check below. */
+ } else if (D.normalizedExponent - 1 > INT_MAX / 42039) {
+ fs = handleOverflow(rounding_mode);
+
+ /* If it wasn't, then it also wasn't high enough to overflow max
+ during the log-rebasing in the min-exponent check. Check that it
+ won't overflow min in either check, then perform the min-exponent
+ check. */
+ } else if (D.normalizedExponent - 1 < INT_MIN / 42039 ||
+ (D.normalizedExponent + 1) * 28738 <=
+ 8651 * (semantics->minExponent - (int) semantics->precision)) {
+ /* Underflow to zero and round. */
+ zeroSignificand();
+ fs = normalize(rounding_mode, lfLessThanHalf);
+
+ /* We can finally safely perform the max-exponent check. */
+ } 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 = static_cast<unsigned int>(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++;
+ if (p == str.end()) {
+ break;
+ }
+ }
+ decValue = decDigitValue(*p++);
+ assert(decValue < 10U && "Invalid character in significand");
+ 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 StringRef &str, roundingMode rounding_mode)
{
+ assertArithmeticOK(*semantics);
+ assert(!str.empty() && "Invalid string length");
+
/* Handle a leading minus sign. */
- if(*p == '-')
- sign = 1, p++;
- else
- sign = 0;
+ StringRef::iterator p = str.begin();
+ size_t slen = str.size();
+ sign = *p == '-' ? 1 : 0;
+ if (*p == '-' || *p == '+') {
+ p++;
+ slen--;
+ assert(slen && "String has no digits");
+ }
- if(p[0] == '0' && (p[1] == 'x' || p[1] == 'X'))
- return convertFromHexadecimalString(p + 2, rounding_mode);
+ if (slen >= 2 && p[0] == '0' && (p[1] == 'x' || p[1] == 'X')) {
+ assert(slen - 2 && "Invalid string");
+ return convertFromHexadecimalString(StringRef(p + 2, slen - 2),
+ rounding_mode);
+ }
- assert(0 && "Decimal to binary conversions not yet implemented");
- abort();
+ return convertFromDecimalString(StringRef(p, slen), rounding_mode);
}
/* Write out a hexadecimal representation of the floating point value
{
char *p;
+ assertArithmeticOK(*semantics);
+
p = dst;
if (sign)
*dst++ = '-';
*dst = 0;
- return dst - p;
+ return static_cast<unsigned int>(dst - p);
}
/* Does the hard work of outputting the correctly rounded hexadecimal
q--;
*q = hexDigitChars[hexDigitValue (*q) + 1];
} while (*q == '0');
- assert (q >= p);
+ assert(q >= p);
} else {
/* Add trailing zeroes. */
memset (dst, '0', outputDigits);
uint32_t hash = sign<<11 | semantics->precision | exponent<<12;
const integerPart* p = significandParts();
for (int i=partCount(); i>0; i--, p++)
- hash ^= ((uint32_t)*p) ^ (*p)>>32;
+ hash ^= ((uint32_t)*p) ^ (uint32_t)((*p)>>32);
return hash;
}
}
APInt
APFloat::convertF80LongDoubleAPFloatToAPInt() const
{
- assert(semantics == (const llvm::fltSemantics* const)&x87DoubleExtended);
- assert (partCount()==2);
+ assert(semantics == (const llvm::fltSemantics*)&x87DoubleExtended);
+ assert(partCount()==2);
uint64_t myexponent, mysignificand;
}
uint64_t words[2];
- words[0] = (((uint64_t)sign & 1) << 63) |
- ((myexponent & 0x7fff) << 48) |
- ((mysignificand >>16) & 0xffffffffffffLL);
- words[1] = mysignificand & 0xffff;
+ words[0] = mysignificand;
+ words[1] = ((uint64_t)(sign & 1) << 15) |
+ (myexponent & 0x7fffLL);
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::convertQuadrupleAPFloatToAPInt() const
+{
+ assert(semantics == (const llvm::fltSemantics*)&IEEEquad);
+ assert(partCount()==2);
+
+ uint64_t myexponent, mysignificand, mysignificand2;
+
+ if (category==fcNormal) {
+ myexponent = exponent+16383; //bias
+ mysignificand = significandParts()[0];
+ mysignificand2 = significandParts()[1];
+ if (myexponent==1 && !(mysignificand2 & 0x1000000000000LL))
+ myexponent = 0; // denormal
+ } else if (category==fcZero) {
+ myexponent = 0;
+ mysignificand = mysignificand2 = 0;
+ } else if (category==fcInfinity) {
+ myexponent = 0x7fff;
+ mysignificand = mysignificand2 = 0;
+ } else {
+ assert(category == fcNaN && "Unknown category!");
+ myexponent = 0x7fff;
+ mysignificand = significandParts()[0];
+ mysignificand2 = significandParts()[1];
+ }
+
+ uint64_t words[2];
+ words[0] = mysignificand;
+ words[1] = ((uint64_t)(sign & 1) << 63) |
+ ((myexponent & 0x7fff) << 48) |
+ (mysignificand2 & 0xffffffffffffLL);
+
+ return APInt(128, 2, words);
+}
+
APInt
APFloat::convertDoubleAPFloatToAPInt() const
{
assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
- assert (partCount()==1);
+ assert(partCount()==1);
uint64_t myexponent, mysignificand;
mysignificand = *significandParts();
}
- return APInt(64, (((((uint64_t)sign & 1) << 63) |
+ return APInt(64, ((((uint64_t)(sign & 1) << 63) |
((myexponent & 0x7ff) << 52) |
(mysignificand & 0xfffffffffffffLL))));
}
APFloat::convertFloatAPFloatToAPInt() const
{
assert(semantics == (const llvm::fltSemantics*)&IEEEsingle);
- assert (partCount()==1);
+ assert(partCount()==1);
uint32_t myexponent, mysignificand;
if (category==fcNormal) {
myexponent = exponent+127; //bias
- mysignificand = *significandParts();
- if (myexponent == 1 && !(mysignificand & 0x400000))
+ mysignificand = (uint32_t)*significandParts();
+ if (myexponent == 1 && !(mysignificand & 0x800000))
myexponent = 0; // denormal
} else if (category==fcZero) {
myexponent = 0;
} else {
assert(category == fcNaN && "Unknown category!");
myexponent = 0xff;
- mysignificand = *significandParts();
+ mysignificand = (uint32_t)*significandParts();
}
return APInt(32, (((sign&1) << 31) | ((myexponent&0xff) << 23) |
}
APInt
-APFloat::convertToAPInt() const
+APFloat::convertHalfAPFloatToAPInt() const
{
- if (semantics == (const llvm::fltSemantics* const)&IEEEsingle)
+ assert(semantics == (const llvm::fltSemantics*)&IEEEhalf);
+ assert(partCount()==1);
+
+ uint32_t myexponent, mysignificand;
+
+ if (category==fcNormal) {
+ myexponent = exponent+15; //bias
+ mysignificand = (uint32_t)*significandParts();
+ if (myexponent == 1 && !(mysignificand & 0x400))
+ myexponent = 0; // denormal
+ } else if (category==fcZero) {
+ myexponent = 0;
+ mysignificand = 0;
+ } else if (category==fcInfinity) {
+ myexponent = 0x1f;
+ mysignificand = 0;
+ } else {
+ assert(category == fcNaN && "Unknown category!");
+ myexponent = 0x1f;
+ mysignificand = (uint32_t)*significandParts();
+ }
+
+ return APInt(16, (((sign&1) << 15) | ((myexponent&0x1f) << 10) |
+ (mysignificand & 0x3ff)));
+}
+
+// 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::bitcastToAPInt() const
+{
+ if (semantics == (const llvm::fltSemantics*)&IEEEhalf)
+ return convertHalfAPFloatToAPInt();
+
+ if (semantics == (const llvm::fltSemantics*)&IEEEsingle)
return convertFloatAPFloatToAPInt();
-
- if (semantics == (const llvm::fltSemantics* const)&IEEEdouble)
+
+ if (semantics == (const llvm::fltSemantics*)&IEEEdouble)
return convertDoubleAPFloatToAPInt();
- assert(semantics == (const llvm::fltSemantics* const)&x87DoubleExtended &&
+ if (semantics == (const llvm::fltSemantics*)&IEEEquad)
+ return convertQuadrupleAPFloatToAPInt();
+
+ 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);
- APInt api = convertToAPInt();
+ assert(semantics == (const llvm::fltSemantics*)&IEEEsingle &&
+ "Float semantics are not IEEEsingle");
+ APInt api = bitcastToAPInt();
return api.bitsToFloat();
}
double
APFloat::convertToDouble() const
{
- assert(semantics == (const llvm::fltSemantics* const)&IEEEdouble);
- APInt api = convertToAPInt();
+ assert(semantics == (const llvm::fltSemantics*)&IEEEdouble &&
+ "Float semantics are not IEEEdouble");
+ APInt api = bitcastToAPInt();
return api.bitsToDouble();
}
-/// Integer bit is explicit in this format. Current Intel book does not
-/// define meaning of:
-/// exponent = all 1's, integer bit not set.
-/// exponent = 0, integer bit set. (formerly "psuedodenormals")
-/// exponent!=0 nor all 1's, integer bit not set. (formerly "unnormals")
+/// Integer bit is explicit in this format. Intel hardware (387 and later)
+/// does not support these bit patterns:
+/// exponent = all 1's, integer bit 0, significand 0 ("pseudoinfinity")
+/// exponent = all 1's, integer bit 0, significand nonzero ("pseudoNaN")
+/// exponent = 0, integer bit 1 ("pseudodenormal")
+/// exponent!=0 nor all 1's, integer bit 0 ("unnormal")
+/// At the moment, the first two are treated as NaNs, the second two as Normal.
void
APFloat::initFromF80LongDoubleAPInt(const APInt &api)
{
assert(api.getBitWidth()==80);
uint64_t i1 = api.getRawData()[0];
uint64_t i2 = api.getRawData()[1];
- uint64_t myexponent = (i1 >> 48) & 0x7fff;
- uint64_t mysignificand = ((i1 << 16) & 0xffffffffffff0000ULL) |
- (i2 & 0xffff);
+ uint64_t myexponent = (i2 & 0x7fff);
+ uint64_t mysignificand = i1;
initialize(&APFloat::x87DoubleExtended);
assert(partCount()==2);
- sign = i1>>63;
+ sign = static_cast<unsigned int>(i2>>15);
if (myexponent==0 && mysignificand==0) {
// exponent, significand meaningless
category = fcZero;
}
}
+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 = static_cast<unsigned int>(i1>>63);
+ sign2 = static_cast<unsigned int>(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::initFromQuadrupleAPInt(const APInt &api)
+{
+ assert(api.getBitWidth()==128);
+ uint64_t i1 = api.getRawData()[0];
+ uint64_t i2 = api.getRawData()[1];
+ uint64_t myexponent = (i2 >> 48) & 0x7fff;
+ uint64_t mysignificand = i1;
+ uint64_t mysignificand2 = i2 & 0xffffffffffffLL;
+
+ initialize(&APFloat::IEEEquad);
+ assert(partCount()==2);
+
+ sign = static_cast<unsigned int>(i2>>63);
+ if (myexponent==0 &&
+ (mysignificand==0 && mysignificand2==0)) {
+ // exponent, significand meaningless
+ category = fcZero;
+ } else if (myexponent==0x7fff &&
+ (mysignificand==0 && mysignificand2==0)) {
+ // exponent, significand meaningless
+ category = fcInfinity;
+ } else if (myexponent==0x7fff &&
+ (mysignificand!=0 || mysignificand2 !=0)) {
+ // exponent meaningless
+ category = fcNaN;
+ significandParts()[0] = mysignificand;
+ significandParts()[1] = mysignificand2;
+ } else {
+ category = fcNormal;
+ exponent = myexponent - 16383;
+ significandParts()[0] = mysignificand;
+ significandParts()[1] = mysignificand2;
+ if (myexponent==0) // denormal
+ exponent = -16382;
+ else
+ significandParts()[1] |= 0x1000000000000LL; // integer bit
+ }
+}
+
void
APFloat::initFromDoubleAPInt(const APInt &api)
{
initialize(&APFloat::IEEEdouble);
assert(partCount()==1);
- sign = i>>63;
+ sign = static_cast<unsigned int>(i>>63);
if (myexponent==0 && mysignificand==0) {
// exponent, significand meaningless
category = fcZero;
}
}
+void
+APFloat::initFromHalfAPInt(const APInt & api)
+{
+ assert(api.getBitWidth()==16);
+ uint32_t i = (uint32_t)*api.getRawData();
+ uint32_t myexponent = (i >> 10) & 0x1f;
+ uint32_t mysignificand = i & 0x3ff;
+
+ initialize(&APFloat::IEEEhalf);
+ assert(partCount()==1);
+
+ sign = i >> 15;
+ if (myexponent==0 && mysignificand==0) {
+ // exponent, significand meaningless
+ category = fcZero;
+ } else if (myexponent==0x1f && mysignificand==0) {
+ // exponent, significand meaningless
+ category = fcInfinity;
+ } else if (myexponent==0x1f && mysignificand!=0) {
+ // sign, exponent, significand meaningless
+ category = fcNaN;
+ *significandParts() = mysignificand;
+ } else {
+ category = fcNormal;
+ exponent = myexponent - 15; //bias
+ *significandParts() = mysignificand;
+ if (myexponent==0) // denormal
+ exponent = -14;
+ else
+ *significandParts() |= 0x400; // integer bit
+ }
+}
+
/// 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)
+ if (api.getBitWidth() == 16)
+ return initFromHalfAPInt(api);
+ else 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)
+ return (isIEEE ?
+ initFromQuadrupleAPInt(api) : initFromPPCDoubleDoubleAPInt(api));
else
- assert(0);
+ llvm_unreachable(0);
+}
+
+APFloat APFloat::getLargest(const fltSemantics &Sem, bool Negative) {
+ APFloat Val(Sem, fcNormal, Negative);
+
+ // We want (in interchange format):
+ // sign = {Negative}
+ // exponent = 1..10
+ // significand = 1..1
+
+ Val.exponent = Sem.maxExponent; // unbiased
+
+ // 1-initialize all bits....
+ Val.zeroSignificand();
+ integerPart *significand = Val.significandParts();
+ unsigned N = partCountForBits(Sem.precision);
+ for (unsigned i = 0; i != N; ++i)
+ significand[i] = ~((integerPart) 0);
+
+ // ...and then clear the top bits for internal consistency.
+ significand[N-1] &=
+ (((integerPart) 1) << ((Sem.precision % integerPartWidth) - 1)) - 1;
+
+ return Val;
+}
+
+APFloat APFloat::getSmallest(const fltSemantics &Sem, bool Negative) {
+ APFloat Val(Sem, fcNormal, Negative);
+
+ // We want (in interchange format):
+ // sign = {Negative}
+ // exponent = 0..0
+ // significand = 0..01
+
+ Val.exponent = Sem.minExponent; // unbiased
+ Val.zeroSignificand();
+ Val.significandParts()[0] = 1;
+ return Val;
}
-APFloat::APFloat(const APInt& api)
+APFloat APFloat::getSmallestNormalized(const fltSemantics &Sem, bool Negative) {
+ APFloat Val(Sem, fcNormal, Negative);
+
+ // We want (in interchange format):
+ // sign = {Negative}
+ // exponent = 0..0
+ // significand = 10..0
+
+ Val.exponent = Sem.minExponent;
+ Val.zeroSignificand();
+ Val.significandParts()[partCountForBits(Sem.precision)-1] |=
+ (((integerPart) 1) << ((Sem.precision % integerPartWidth) - 1));
+
+ return Val;
+}
+
+APFloat::APFloat(const APInt& api, bool isIEEE)
{
- initFromAPInt(api);
+ initFromAPInt(api, isIEEE);
}
APFloat::APFloat(float f)
APInt api = APInt(64, 0);
initFromAPInt(api.doubleToBits(d));
}
+
+namespace {
+ static void append(SmallVectorImpl<char> &Buffer,
+ unsigned N, const char *Str) {
+ unsigned Start = Buffer.size();
+ Buffer.set_size(Start + N);
+ memcpy(&Buffer[Start], Str, N);
+ }
+
+ template <unsigned N>
+ void append(SmallVectorImpl<char> &Buffer, const char (&Str)[N]) {
+ append(Buffer, N, Str);
+ }
+
+ /// 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, but
+ // don't try to drop below 32.
+ unsigned newPrecision = std::max(32U, significand.getActiveBits());
+ significand.trunc(newPrecision);
+ }
+
+
+ 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 (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,
+ partCountForBits(semantics->precision),
+ significandParts());
+
+ // Set FormatPrecision if zero. We want to do this before we
+ // truncate trailing zeros, as those are part of the precision.
+ if (!FormatPrecision) {
+ // It's an interesting question whether to use the nominal
+ // precision or the active precision here for denormals.
+
+ // FormatPrecision = ceil(significandBits / lg_2(10))
+ FormatPrecision = (semantics->precision * 59 + 195) / 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.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 / 59;
+
+ // Multiply significand by 5^e.
+ // N * 5^0101 == N * 5^(1*1) * 5^(0*2) * 5^(1*4) * 5^(0*8)
+ 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);
+
+ llvm::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]);
+}
projects / oota-llvm.git / blobdiff