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d04447b7ae
memory rather than in a copy of the APFloat. This avoids problems when the destination is wider than our significand and is cleaner. Also provide deterministic values in all cases where conversion fails, namely zero for NaNs and the minimal or maximal value respectively for underflow or overflow. llvm-svn: 43626
2797 lines
78 KiB
C++
2797 lines
78 KiB
C++
//===-- APFloat.cpp - Implement APFloat class -----------------------------===//
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//
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// The LLVM Compiler Infrastructure
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//
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// This file was developed by Neil Booth and is distributed under the
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// University of Illinois Open Source License. See LICENSE.TXT for details.
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//
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//===----------------------------------------------------------------------===//
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//
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// This file implements a class to represent arbitrary precision floating
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// point values and provide a variety of arithmetic operations on them.
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//
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//===----------------------------------------------------------------------===//
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#include <cassert>
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#include <cstring>
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#include "llvm/ADT/APFloat.h"
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#include "llvm/Support/MathExtras.h"
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using namespace llvm;
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#define convolve(lhs, rhs) ((lhs) * 4 + (rhs))
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/* Assumed in hexadecimal significand parsing, and conversion to
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hexadecimal strings. */
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COMPILE_TIME_ASSERT(integerPartWidth % 4 == 0);
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namespace llvm {
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/* Represents floating point arithmetic semantics. */
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struct fltSemantics {
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/* The largest E such that 2^E is representable; this matches the
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definition of IEEE 754. */
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exponent_t maxExponent;
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/* The smallest E such that 2^E is a normalized number; this
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matches the definition of IEEE 754. */
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exponent_t minExponent;
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/* Number of bits in the significand. This includes the integer
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bit. */
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unsigned int precision;
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/* True if arithmetic is supported. */
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unsigned int arithmeticOK;
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};
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const fltSemantics APFloat::IEEEsingle = { 127, -126, 24, true };
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const fltSemantics APFloat::IEEEdouble = { 1023, -1022, 53, true };
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const fltSemantics APFloat::IEEEquad = { 16383, -16382, 113, true };
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const fltSemantics APFloat::x87DoubleExtended = { 16383, -16382, 64, true };
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const fltSemantics APFloat::Bogus = { 0, 0, 0, true };
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// The PowerPC format consists of two doubles. It does not map cleanly
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// onto the usual format above. For now only storage of constants of
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// this type is supported, no arithmetic.
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const fltSemantics APFloat::PPCDoubleDouble = { 1023, -1022, 106, false };
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/* A tight upper bound on number of parts required to hold the value
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pow(5, power) is
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power * 815 / (351 * integerPartWidth) + 1
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However, whilst the result may require only this many parts,
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because we are multiplying two values to get it, the
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multiplication may require an extra part with the excess part
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being zero (consider the trivial case of 1 * 1, tcFullMultiply
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requires two parts to hold the single-part result). So we add an
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extra one to guarantee enough space whilst multiplying. */
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const unsigned int maxExponent = 16383;
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const unsigned int maxPrecision = 113;
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const unsigned int maxPowerOfFiveExponent = maxExponent + maxPrecision - 1;
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const unsigned int maxPowerOfFiveParts = 2 + ((maxPowerOfFiveExponent * 815)
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/ (351 * integerPartWidth));
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}
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/* Put a bunch of private, handy routines in an anonymous namespace. */
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namespace {
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inline unsigned int
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partCountForBits(unsigned int bits)
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{
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return ((bits) + integerPartWidth - 1) / integerPartWidth;
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}
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/* Returns 0U-9U. Return values >= 10U are not digits. */
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inline unsigned int
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decDigitValue(unsigned int c)
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{
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return c - '0';
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}
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unsigned int
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hexDigitValue(unsigned int c)
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{
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unsigned int r;
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r = c - '0';
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if(r <= 9)
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return r;
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r = c - 'A';
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if(r <= 5)
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return r + 10;
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r = c - 'a';
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if(r <= 5)
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return r + 10;
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return -1U;
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}
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inline void
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assertArithmeticOK(const llvm::fltSemantics &semantics) {
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assert(semantics.arithmeticOK
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&& "Compile-time arithmetic does not support these semantics");
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}
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/* Return the value of a decimal exponent of the form
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[+-]ddddddd.
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If the exponent overflows, returns a large exponent with the
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appropriate sign. */
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static int
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readExponent(const char *p)
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{
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bool isNegative;
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unsigned int absExponent;
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const unsigned int overlargeExponent = 24000; /* FIXME. */
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isNegative = (*p == '-');
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if (*p == '-' || *p == '+')
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p++;
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absExponent = decDigitValue(*p++);
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assert (absExponent < 10U);
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for (;;) {
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unsigned int value;
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value = decDigitValue(*p);
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if (value >= 10U)
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break;
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p++;
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value += absExponent * 10;
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if (absExponent >= overlargeExponent) {
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absExponent = overlargeExponent;
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break;
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}
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absExponent = value;
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}
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if (isNegative)
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return -(int) absExponent;
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else
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return (int) absExponent;
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}
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/* This is ugly and needs cleaning up, but I don't immediately see
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how whilst remaining safe. */
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static int
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totalExponent(const char *p, int exponentAdjustment)
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{
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integerPart unsignedExponent;
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bool negative, overflow;
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long exponent;
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/* Move past the exponent letter and sign to the digits. */
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p++;
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negative = *p == '-';
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if(*p == '-' || *p == '+')
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p++;
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unsignedExponent = 0;
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overflow = false;
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for(;;) {
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unsigned int value;
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value = decDigitValue(*p);
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if(value >= 10U)
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break;
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p++;
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unsignedExponent = unsignedExponent * 10 + value;
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if(unsignedExponent > 65535)
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overflow = true;
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}
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if(exponentAdjustment > 65535 || exponentAdjustment < -65536)
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overflow = true;
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if(!overflow) {
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exponent = unsignedExponent;
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if(negative)
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exponent = -exponent;
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exponent += exponentAdjustment;
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if(exponent > 65535 || exponent < -65536)
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overflow = true;
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}
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if(overflow)
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exponent = negative ? -65536: 65535;
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return exponent;
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}
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const char *
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skipLeadingZeroesAndAnyDot(const char *p, const char **dot)
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{
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*dot = 0;
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while(*p == '0')
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p++;
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if(*p == '.') {
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*dot = p++;
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while(*p == '0')
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p++;
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}
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return p;
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}
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/* Given a normal decimal floating point number of the form
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dddd.dddd[eE][+-]ddd
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where the decimal point and exponent are optional, fill out the
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structure D. Exponent is appropriate if the significand is
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treated as an integer, and normalizedExponent if the significand
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is taken to have the decimal point after a single leading
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non-zero digit.
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If the value is zero, V->firstSigDigit points to a zero, and the
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return exponent is zero.
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*/
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struct decimalInfo {
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const char *firstSigDigit;
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const char *lastSigDigit;
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int exponent;
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int normalizedExponent;
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};
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void
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interpretDecimal(const char *p, decimalInfo *D)
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{
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const char *dot;
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p = skipLeadingZeroesAndAnyDot (p, &dot);
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D->firstSigDigit = p;
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D->exponent = 0;
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D->normalizedExponent = 0;
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for (;;) {
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if (*p == '.') {
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assert(dot == 0);
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dot = p++;
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}
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if (decDigitValue(*p) >= 10U)
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break;
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p++;
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}
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/* If number is all zerooes accept any exponent. */
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if (p != D->firstSigDigit) {
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if (*p == 'e' || *p == 'E')
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D->exponent = readExponent(p + 1);
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/* Implied decimal point? */
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if (!dot)
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dot = p;
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/* Drop insignificant trailing zeroes. */
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do
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do
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p--;
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while (*p == '0');
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while (*p == '.');
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/* Adjust the exponents for any decimal point. */
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D->exponent += (dot - p) - (dot > p);
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D->normalizedExponent = (D->exponent + (p - D->firstSigDigit)
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- (dot > D->firstSigDigit && dot < p));
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}
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D->lastSigDigit = p;
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}
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/* Return the trailing fraction of a hexadecimal number.
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DIGITVALUE is the first hex digit of the fraction, P points to
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the next digit. */
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lostFraction
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trailingHexadecimalFraction(const char *p, unsigned int digitValue)
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{
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unsigned int hexDigit;
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/* If the first trailing digit isn't 0 or 8 we can work out the
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fraction immediately. */
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if(digitValue > 8)
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return lfMoreThanHalf;
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else if(digitValue < 8 && digitValue > 0)
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return lfLessThanHalf;
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/* Otherwise we need to find the first non-zero digit. */
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while(*p == '0')
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p++;
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hexDigit = hexDigitValue(*p);
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/* If we ran off the end it is exactly zero or one-half, otherwise
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a little more. */
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if(hexDigit == -1U)
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return digitValue == 0 ? lfExactlyZero: lfExactlyHalf;
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else
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return digitValue == 0 ? lfLessThanHalf: lfMoreThanHalf;
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}
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/* Return the fraction lost were a bignum truncated losing the least
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significant BITS bits. */
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lostFraction
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lostFractionThroughTruncation(const integerPart *parts,
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unsigned int partCount,
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unsigned int bits)
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{
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unsigned int lsb;
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lsb = APInt::tcLSB(parts, partCount);
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/* Note this is guaranteed true if bits == 0, or LSB == -1U. */
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if(bits <= lsb)
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return lfExactlyZero;
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if(bits == lsb + 1)
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return lfExactlyHalf;
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if(bits <= partCount * integerPartWidth
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&& APInt::tcExtractBit(parts, bits - 1))
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return lfMoreThanHalf;
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return lfLessThanHalf;
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}
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/* Shift DST right BITS bits noting lost fraction. */
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lostFraction
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shiftRight(integerPart *dst, unsigned int parts, unsigned int bits)
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{
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lostFraction lost_fraction;
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lost_fraction = lostFractionThroughTruncation(dst, parts, bits);
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APInt::tcShiftRight(dst, parts, bits);
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return lost_fraction;
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}
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/* Combine the effect of two lost fractions. */
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lostFraction
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combineLostFractions(lostFraction moreSignificant,
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lostFraction lessSignificant)
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{
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if(lessSignificant != lfExactlyZero) {
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if(moreSignificant == lfExactlyZero)
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moreSignificant = lfLessThanHalf;
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else if(moreSignificant == lfExactlyHalf)
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moreSignificant = lfMoreThanHalf;
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}
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return moreSignificant;
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}
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/* The error from the true value, in half-ulps, on multiplying two
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floating point numbers, which differ from the value they
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approximate by at most HUE1 and HUE2 half-ulps, is strictly less
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than the returned value.
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See "How to Read Floating Point Numbers Accurately" by William D
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Clinger. */
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unsigned int
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HUerrBound(bool inexactMultiply, unsigned int HUerr1, unsigned int HUerr2)
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{
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assert(HUerr1 < 2 || HUerr2 < 2 || (HUerr1 + HUerr2 < 8));
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if (HUerr1 + HUerr2 == 0)
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return inexactMultiply * 2; /* <= inexactMultiply half-ulps. */
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else
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return inexactMultiply + 2 * (HUerr1 + HUerr2);
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}
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/* The number of ulps from the boundary (zero, or half if ISNEAREST)
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when the least significant BITS are truncated. BITS cannot be
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zero. */
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integerPart
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ulpsFromBoundary(const integerPart *parts, unsigned int bits, bool isNearest)
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{
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unsigned int count, partBits;
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integerPart part, boundary;
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assert (bits != 0);
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bits--;
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count = bits / integerPartWidth;
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partBits = bits % integerPartWidth + 1;
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part = parts[count] & (~(integerPart) 0 >> (integerPartWidth - partBits));
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if (isNearest)
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boundary = (integerPart) 1 << (partBits - 1);
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else
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boundary = 0;
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if (count == 0) {
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if (part - boundary <= boundary - part)
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return part - boundary;
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else
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return boundary - part;
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}
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if (part == boundary) {
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while (--count)
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if (parts[count])
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return ~(integerPart) 0; /* A lot. */
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return parts[0];
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} else if (part == boundary - 1) {
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while (--count)
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if (~parts[count])
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return ~(integerPart) 0; /* A lot. */
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return -parts[0];
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}
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return ~(integerPart) 0; /* A lot. */
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}
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/* Place pow(5, power) in DST, and return the number of parts used.
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DST must be at least one part larger than size of the answer. */
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static unsigned int
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powerOf5(integerPart *dst, unsigned int power)
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{
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static integerPart firstEightPowers[] = { 1, 5, 25, 125, 625, 3125,
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15625, 78125 };
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static integerPart pow5s[maxPowerOfFiveParts * 2 + 5] = { 78125 * 5 };
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static unsigned int partsCount[16] = { 1 };
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integerPart scratch[maxPowerOfFiveParts], *p1, *p2, *pow5;
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unsigned int result;
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assert(power <= maxExponent);
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p1 = dst;
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p2 = scratch;
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*p1 = firstEightPowers[power & 7];
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power >>= 3;
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result = 1;
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pow5 = pow5s;
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for (unsigned int n = 0; power; power >>= 1, n++) {
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unsigned int pc;
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pc = partsCount[n];
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/* Calculate pow(5,pow(2,n+3)) if we haven't yet. */
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if (pc == 0) {
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pc = partsCount[n - 1];
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APInt::tcFullMultiply(pow5, pow5 - pc, pow5 - pc, pc, pc);
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pc *= 2;
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if (pow5[pc - 1] == 0)
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pc--;
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partsCount[n] = pc;
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}
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if (power & 1) {
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integerPart *tmp;
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APInt::tcFullMultiply(p2, p1, pow5, result, pc);
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result += pc;
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if (p2[result - 1] == 0)
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result--;
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/* Now result is in p1 with partsCount parts and p2 is scratch
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space. */
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tmp = p1, p1 = p2, p2 = tmp;
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}
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pow5 += pc;
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}
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if (p1 != dst)
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APInt::tcAssign(dst, p1, result);
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return result;
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}
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/* Zero at the end to avoid modular arithmetic when adding one; used
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when rounding up during hexadecimal output. */
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static const char hexDigitsLower[] = "0123456789abcdef0";
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static const char hexDigitsUpper[] = "0123456789ABCDEF0";
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static const char infinityL[] = "infinity";
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static const char infinityU[] = "INFINITY";
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static const char NaNL[] = "nan";
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static const char NaNU[] = "NAN";
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/* Write out an integerPart in hexadecimal, starting with the most
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significant nibble. Write out exactly COUNT hexdigits, return
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COUNT. */
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static unsigned int
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partAsHex (char *dst, integerPart part, unsigned int count,
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const char *hexDigitChars)
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{
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unsigned int result = count;
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assert (count != 0 && count <= integerPartWidth / 4);
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part >>= (integerPartWidth - 4 * count);
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while (count--) {
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dst[count] = hexDigitChars[part & 0xf];
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part >>= 4;
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}
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return result;
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}
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/* Write out an unsigned decimal integer. */
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static char *
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writeUnsignedDecimal (char *dst, unsigned int n)
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{
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char buff[40], *p;
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p = buff;
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do
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*p++ = '0' + n % 10;
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while (n /= 10);
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do
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*dst++ = *--p;
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while (p != buff);
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return dst;
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}
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/* Write out a signed decimal integer. */
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static char *
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writeSignedDecimal (char *dst, int value)
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{
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if (value < 0) {
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*dst++ = '-';
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dst = writeUnsignedDecimal(dst, -(unsigned) value);
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} else
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dst = writeUnsignedDecimal(dst, value);
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return dst;
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}
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}
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|
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/* Constructors. */
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void
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APFloat::initialize(const fltSemantics *ourSemantics)
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{
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unsigned int count;
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semantics = ourSemantics;
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count = partCount();
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if(count > 1)
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significand.parts = new integerPart[count];
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}
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|
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void
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APFloat::freeSignificand()
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{
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if(partCount() > 1)
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delete [] significand.parts;
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}
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|
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void
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APFloat::assign(const APFloat &rhs)
|
|
{
|
|
assert(semantics == rhs.semantics);
|
|
|
|
sign = rhs.sign;
|
|
category = rhs.category;
|
|
exponent = rhs.exponent;
|
|
sign2 = rhs.sign2;
|
|
exponent2 = rhs.exponent2;
|
|
if(category == fcNormal || category == fcNaN)
|
|
copySignificand(rhs);
|
|
}
|
|
|
|
void
|
|
APFloat::copySignificand(const APFloat &rhs)
|
|
{
|
|
assert(category == fcNormal || category == fcNaN);
|
|
assert(rhs.partCount() >= partCount());
|
|
|
|
APInt::tcAssign(significandParts(), rhs.significandParts(),
|
|
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 &
|
|
APFloat::operator=(const APFloat &rhs)
|
|
{
|
|
if(this != &rhs) {
|
|
if(semantics != rhs.semantics) {
|
|
freeSignificand();
|
|
initialize(rhs.semantics);
|
|
}
|
|
assign(rhs);
|
|
}
|
|
|
|
return *this;
|
|
}
|
|
|
|
bool
|
|
APFloat::bitwiseIsEqual(const APFloat &rhs) const {
|
|
if (this == &rhs)
|
|
return true;
|
|
if (semantics != rhs.semantics ||
|
|
category != rhs.category ||
|
|
sign != rhs.sign)
|
|
return false;
|
|
if (semantics==(const llvm::fltSemantics* const)&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* const)&PPCDoubleDouble &&
|
|
exponent2!=rhs.exponent2)
|
|
return false;
|
|
else {
|
|
int i= partCount();
|
|
const integerPart* p=significandParts();
|
|
const integerPart* q=rhs.significandParts();
|
|
for (; i>0; i--, p++, q++) {
|
|
if (*p != *q)
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
}
|
|
|
|
APFloat::APFloat(const fltSemantics &ourSemantics, integerPart value)
|
|
{
|
|
assertArithmeticOK(ourSemantics);
|
|
initialize(&ourSemantics);
|
|
sign = 0;
|
|
zeroSignificand();
|
|
exponent = ourSemantics.precision - 1;
|
|
significandParts()[0] = value;
|
|
normalize(rmNearestTiesToEven, lfExactlyZero);
|
|
}
|
|
|
|
APFloat::APFloat(const fltSemantics &ourSemantics,
|
|
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);
|
|
}
|
|
|
|
APFloat::APFloat(const APFloat &rhs)
|
|
{
|
|
initialize(rhs.semantics);
|
|
assign(rhs);
|
|
}
|
|
|
|
APFloat::~APFloat()
|
|
{
|
|
freeSignificand();
|
|
}
|
|
|
|
unsigned int
|
|
APFloat::partCount() const
|
|
{
|
|
return partCountForBits(semantics->precision + 1);
|
|
}
|
|
|
|
unsigned int
|
|
APFloat::semanticsPrecision(const fltSemantics &semantics)
|
|
{
|
|
return semantics.precision;
|
|
}
|
|
|
|
const integerPart *
|
|
APFloat::significandParts() const
|
|
{
|
|
return const_cast<APFloat *>(this)->significandParts();
|
|
}
|
|
|
|
integerPart *
|
|
APFloat::significandParts()
|
|
{
|
|
assert(category == fcNormal || category == fcNaN);
|
|
|
|
if(partCount() > 1)
|
|
return significand.parts;
|
|
else
|
|
return &significand.part;
|
|
}
|
|
|
|
void
|
|
APFloat::zeroSignificand()
|
|
{
|
|
category = fcNormal;
|
|
APInt::tcSet(significandParts(), 0, partCount());
|
|
}
|
|
|
|
/* Increment an fcNormal floating point number's significand. */
|
|
void
|
|
APFloat::incrementSignificand()
|
|
{
|
|
integerPart carry;
|
|
|
|
carry = APInt::tcIncrement(significandParts(), partCount());
|
|
|
|
/* Our callers should never cause us to overflow. */
|
|
assert(carry == 0);
|
|
}
|
|
|
|
/* Add the significand of the RHS. Returns the carry flag. */
|
|
integerPart
|
|
APFloat::addSignificand(const APFloat &rhs)
|
|
{
|
|
integerPart *parts;
|
|
|
|
parts = significandParts();
|
|
|
|
assert(semantics == rhs.semantics);
|
|
assert(exponent == rhs.exponent);
|
|
|
|
return APInt::tcAdd(parts, rhs.significandParts(), 0, partCount());
|
|
}
|
|
|
|
/* Subtract the significand of the RHS with a borrow flag. Returns
|
|
the borrow flag. */
|
|
integerPart
|
|
APFloat::subtractSignificand(const APFloat &rhs, integerPart borrow)
|
|
{
|
|
integerPart *parts;
|
|
|
|
parts = significandParts();
|
|
|
|
assert(semantics == rhs.semantics);
|
|
assert(exponent == rhs.exponent);
|
|
|
|
return APInt::tcSubtract(parts, rhs.significandParts(), borrow,
|
|
partCount());
|
|
}
|
|
|
|
/* Multiply the significand of the RHS. If ADDEND is non-NULL, add it
|
|
on to the full-precision result of the multiplication. Returns the
|
|
lost fraction. */
|
|
lostFraction
|
|
APFloat::multiplySignificand(const APFloat &rhs, const APFloat *addend)
|
|
{
|
|
unsigned int omsb; // One, not zero, based MSB.
|
|
unsigned int partsCount, newPartsCount, precision;
|
|
integerPart *lhsSignificand;
|
|
integerPart scratch[4];
|
|
integerPart *fullSignificand;
|
|
lostFraction lost_fraction;
|
|
|
|
assert(semantics == rhs.semantics);
|
|
|
|
precision = semantics->precision;
|
|
newPartsCount = partCountForBits(precision * 2);
|
|
|
|
if(newPartsCount > 4)
|
|
fullSignificand = new integerPart[newPartsCount];
|
|
else
|
|
fullSignificand = scratch;
|
|
|
|
lhsSignificand = significandParts();
|
|
partsCount = partCount();
|
|
|
|
APInt::tcFullMultiply(fullSignificand, lhsSignificand,
|
|
rhs.significandParts(), partsCount, partsCount);
|
|
|
|
lost_fraction = lfExactlyZero;
|
|
omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
|
|
exponent += rhs.exponent;
|
|
|
|
if(addend) {
|
|
Significand savedSignificand = significand;
|
|
const fltSemantics *savedSemantics = semantics;
|
|
fltSemantics extendedSemantics;
|
|
opStatus status;
|
|
unsigned int extendedPrecision;
|
|
|
|
/* Normalize our MSB. */
|
|
extendedPrecision = precision + precision - 1;
|
|
if(omsb != extendedPrecision)
|
|
{
|
|
APInt::tcShiftLeft(fullSignificand, newPartsCount,
|
|
extendedPrecision - omsb);
|
|
exponent -= extendedPrecision - omsb;
|
|
}
|
|
|
|
/* Create new semantics. */
|
|
extendedSemantics = *semantics;
|
|
extendedSemantics.precision = extendedPrecision;
|
|
|
|
if(newPartsCount == 1)
|
|
significand.part = fullSignificand[0];
|
|
else
|
|
significand.parts = fullSignificand;
|
|
semantics = &extendedSemantics;
|
|
|
|
APFloat extendedAddend(*addend);
|
|
status = extendedAddend.convert(extendedSemantics, rmTowardZero);
|
|
assert(status == opOK);
|
|
lost_fraction = addOrSubtractSignificand(extendedAddend, false);
|
|
|
|
/* Restore our state. */
|
|
if(newPartsCount == 1)
|
|
fullSignificand[0] = significand.part;
|
|
significand = savedSignificand;
|
|
semantics = savedSemantics;
|
|
|
|
omsb = APInt::tcMSB(fullSignificand, newPartsCount) + 1;
|
|
}
|
|
|
|
exponent -= (precision - 1);
|
|
|
|
if(omsb > precision) {
|
|
unsigned int bits, significantParts;
|
|
lostFraction lf;
|
|
|
|
bits = omsb - precision;
|
|
significantParts = partCountForBits(omsb);
|
|
lf = shiftRight(fullSignificand, significantParts, bits);
|
|
lost_fraction = combineLostFractions(lf, lost_fraction);
|
|
exponent += bits;
|
|
}
|
|
|
|
APInt::tcAssign(lhsSignificand, fullSignificand, partsCount);
|
|
|
|
if(newPartsCount > 4)
|
|
delete [] fullSignificand;
|
|
|
|
return lost_fraction;
|
|
}
|
|
|
|
/* Multiply the significands of LHS and RHS to DST. */
|
|
lostFraction
|
|
APFloat::divideSignificand(const APFloat &rhs)
|
|
{
|
|
unsigned int bit, i, partsCount;
|
|
const integerPart *rhsSignificand;
|
|
integerPart *lhsSignificand, *dividend, *divisor;
|
|
integerPart scratch[4];
|
|
lostFraction lost_fraction;
|
|
|
|
assert(semantics == rhs.semantics);
|
|
|
|
lhsSignificand = significandParts();
|
|
rhsSignificand = rhs.significandParts();
|
|
partsCount = partCount();
|
|
|
|
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++) {
|
|
dividend[i] = lhsSignificand[i];
|
|
divisor[i] = rhsSignificand[i];
|
|
lhsSignificand[i] = 0;
|
|
}
|
|
|
|
exponent -= rhs.exponent;
|
|
|
|
unsigned int precision = semantics->precision;
|
|
|
|
/* Normalize the divisor. */
|
|
bit = precision - APInt::tcMSB(divisor, partsCount) - 1;
|
|
if(bit) {
|
|
exponent += bit;
|
|
APInt::tcShiftLeft(divisor, partsCount, bit);
|
|
}
|
|
|
|
/* Normalize the dividend. */
|
|
bit = precision - APInt::tcMSB(dividend, partsCount) - 1;
|
|
if(bit) {
|
|
exponent -= bit;
|
|
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);
|
|
assert(APInt::tcCompare(dividend, divisor, partsCount) >= 0);
|
|
}
|
|
|
|
/* Long division. */
|
|
for(bit = precision; bit; bit -= 1) {
|
|
if(APInt::tcCompare(dividend, divisor, partsCount) >= 0) {
|
|
APInt::tcSubtract(dividend, divisor, 0, partsCount);
|
|
APInt::tcSetBit(lhsSignificand, bit - 1);
|
|
}
|
|
|
|
APInt::tcShiftLeft(dividend, partsCount, 1);
|
|
}
|
|
|
|
/* Figure out the lost fraction. */
|
|
int cmp = APInt::tcCompare(dividend, divisor, partsCount);
|
|
|
|
if(cmp > 0)
|
|
lost_fraction = lfMoreThanHalf;
|
|
else if(cmp == 0)
|
|
lost_fraction = lfExactlyHalf;
|
|
else if(APInt::tcIsZero(dividend, partsCount))
|
|
lost_fraction = lfExactlyZero;
|
|
else
|
|
lost_fraction = lfLessThanHalf;
|
|
|
|
if(partsCount > 2)
|
|
delete [] dividend;
|
|
|
|
return lost_fraction;
|
|
}
|
|
|
|
unsigned int
|
|
APFloat::significandMSB() const
|
|
{
|
|
return APInt::tcMSB(significandParts(), partCount());
|
|
}
|
|
|
|
unsigned int
|
|
APFloat::significandLSB() const
|
|
{
|
|
return APInt::tcLSB(significandParts(), partCount());
|
|
}
|
|
|
|
/* Note that a zero result is NOT normalized to fcZero. */
|
|
lostFraction
|
|
APFloat::shiftSignificandRight(unsigned int bits)
|
|
{
|
|
/* Our exponent should not overflow. */
|
|
assert((exponent_t) (exponent + bits) >= exponent);
|
|
|
|
exponent += bits;
|
|
|
|
return shiftRight(significandParts(), partCount(), bits);
|
|
}
|
|
|
|
/* Shift the significand left BITS bits, subtract BITS from its exponent. */
|
|
void
|
|
APFloat::shiftSignificandLeft(unsigned int bits)
|
|
{
|
|
assert(bits < semantics->precision);
|
|
|
|
if(bits) {
|
|
unsigned int partsCount = partCount();
|
|
|
|
APInt::tcShiftLeft(significandParts(), partsCount, bits);
|
|
exponent -= bits;
|
|
|
|
assert(!APInt::tcIsZero(significandParts(), partsCount));
|
|
}
|
|
}
|
|
|
|
APFloat::cmpResult
|
|
APFloat::compareAbsoluteValue(const APFloat &rhs) const
|
|
{
|
|
int compare;
|
|
|
|
assert(semantics == rhs.semantics);
|
|
assert(category == fcNormal);
|
|
assert(rhs.category == fcNormal);
|
|
|
|
compare = exponent - rhs.exponent;
|
|
|
|
/* If exponents are equal, do an unsigned bignum comparison of the
|
|
significands. */
|
|
if(compare == 0)
|
|
compare = APInt::tcCompare(significandParts(), rhs.significandParts(),
|
|
partCount());
|
|
|
|
if(compare > 0)
|
|
return cmpGreaterThan;
|
|
else if(compare < 0)
|
|
return cmpLessThan;
|
|
else
|
|
return cmpEqual;
|
|
}
|
|
|
|
/* Handle overflow. Sign is preserved. We either become infinity or
|
|
the largest finite number. */
|
|
APFloat::opStatus
|
|
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);
|
|
}
|
|
|
|
/* Otherwise we become the largest finite number. */
|
|
category = fcNormal;
|
|
exponent = semantics->maxExponent;
|
|
APInt::tcSetLeastSignificantBits(significandParts(), partCount(),
|
|
semantics->precision);
|
|
|
|
return opInexact;
|
|
}
|
|
|
|
/* 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,
|
|
unsigned int bit) const
|
|
{
|
|
/* NaNs and infinities should not have lost fractions. */
|
|
assert(category == fcNormal || category == fcZero);
|
|
|
|
/* Current callers never pass this so we don't handle it. */
|
|
assert(lost_fraction != lfExactlyZero);
|
|
|
|
switch(rounding_mode) {
|
|
default:
|
|
assert(0);
|
|
|
|
case rmNearestTiesToAway:
|
|
return lost_fraction == lfExactlyHalf || lost_fraction == lfMoreThanHalf;
|
|
|
|
case rmNearestTiesToEven:
|
|
if(lost_fraction == lfMoreThanHalf)
|
|
return true;
|
|
|
|
/* Our zeroes don't have a significand to test. */
|
|
if(lost_fraction == lfExactlyHalf && category != fcZero)
|
|
return APInt::tcExtractBit(significandParts(), bit);
|
|
|
|
return false;
|
|
|
|
case rmTowardZero:
|
|
return false;
|
|
|
|
case rmTowardPositive:
|
|
return sign == false;
|
|
|
|
case rmTowardNegative:
|
|
return sign == true;
|
|
}
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::normalize(roundingMode rounding_mode,
|
|
lostFraction lost_fraction)
|
|
{
|
|
unsigned int omsb; /* One, not zero, based MSB. */
|
|
int exponentChange;
|
|
|
|
if(category != fcNormal)
|
|
return opOK;
|
|
|
|
/* Before rounding normalize the exponent of fcNormal numbers. */
|
|
omsb = significandMSB() + 1;
|
|
|
|
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. */
|
|
exponentChange = omsb - semantics->precision;
|
|
|
|
/* If the resulting exponent is too high, overflow according to
|
|
the rounding mode. */
|
|
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)
|
|
exponentChange = semantics->minExponent - exponent;
|
|
|
|
/* Shifting left is easy as we don't lose precision. */
|
|
if(exponentChange < 0) {
|
|
assert(lost_fraction == lfExactlyZero);
|
|
|
|
shiftSignificandLeft(-exponentChange);
|
|
|
|
return opOK;
|
|
}
|
|
|
|
if(exponentChange > 0) {
|
|
lostFraction lf;
|
|
|
|
/* Shift right and capture any new lost fraction. */
|
|
lf = shiftSignificandRight(exponentChange);
|
|
|
|
lost_fraction = combineLostFractions(lf, lost_fraction);
|
|
|
|
/* Keep OMSB up-to-date. */
|
|
if(omsb > (unsigned) exponentChange)
|
|
omsb -= exponentChange;
|
|
else
|
|
omsb = 0;
|
|
}
|
|
}
|
|
|
|
/* Now round the number according to rounding_mode given the lost
|
|
fraction. */
|
|
|
|
/* As specified in IEEE 754, since we do not trap we do not report
|
|
underflow for exact results. */
|
|
if(lost_fraction == lfExactlyZero) {
|
|
/* Canonicalize zeroes. */
|
|
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)
|
|
exponent = semantics->minExponent;
|
|
|
|
incrementSignificand();
|
|
omsb = significandMSB() + 1;
|
|
|
|
/* 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. */
|
|
if(exponent == semantics->maxExponent) {
|
|
category = fcInfinity;
|
|
|
|
return (opStatus) (opOverflow | opInexact);
|
|
}
|
|
|
|
shiftSignificandRight(1);
|
|
|
|
return opInexact;
|
|
}
|
|
}
|
|
|
|
/* The normal case - we were and are not denormal, and any
|
|
significand increment above didn't overflow. */
|
|
if(omsb == semantics->precision)
|
|
return opInexact;
|
|
|
|
/* We have a non-zero denormal. */
|
|
assert(omsb < semantics->precision);
|
|
|
|
/* Canonicalize zeroes. */
|
|
if(omsb == 0)
|
|
category = fcZero;
|
|
|
|
/* The fcZero case is a denormal that underflowed to zero. */
|
|
return (opStatus) (opUnderflow | opInexact);
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::addOrSubtractSpecials(const APFloat &rhs, bool subtract)
|
|
{
|
|
switch(convolve(category, rhs.category)) {
|
|
default:
|
|
assert(0);
|
|
|
|
case convolve(fcNaN, fcZero):
|
|
case convolve(fcNaN, fcNormal):
|
|
case convolve(fcNaN, fcInfinity):
|
|
case convolve(fcNaN, fcNaN):
|
|
case convolve(fcNormal, fcZero):
|
|
case convolve(fcInfinity, fcNormal):
|
|
case convolve(fcInfinity, fcZero):
|
|
return opOK;
|
|
|
|
case convolve(fcZero, fcNaN):
|
|
case convolve(fcNormal, fcNaN):
|
|
case convolve(fcInfinity, fcNaN):
|
|
category = fcNaN;
|
|
copySignificand(rhs);
|
|
return opOK;
|
|
|
|
case convolve(fcNormal, fcInfinity):
|
|
case convolve(fcZero, fcInfinity):
|
|
category = fcInfinity;
|
|
sign = rhs.sign ^ subtract;
|
|
return opOK;
|
|
|
|
case convolve(fcZero, fcNormal):
|
|
assign(rhs);
|
|
sign = rhs.sign ^ subtract;
|
|
return opOK;
|
|
|
|
case convolve(fcZero, fcZero):
|
|
/* Sign depends on rounding mode; handled by caller. */
|
|
return opOK;
|
|
|
|
case convolve(fcInfinity, fcInfinity):
|
|
/* Differently signed infinities can only be validly
|
|
subtracted. */
|
|
if((sign ^ rhs.sign) != subtract) {
|
|
makeNaN();
|
|
return opInvalidOp;
|
|
}
|
|
|
|
return opOK;
|
|
|
|
case convolve(fcNormal, fcNormal):
|
|
return opDivByZero;
|
|
}
|
|
}
|
|
|
|
/* Add or subtract two normal numbers. */
|
|
lostFraction
|
|
APFloat::addOrSubtractSignificand(const APFloat &rhs, bool subtract)
|
|
{
|
|
integerPart carry;
|
|
lostFraction lost_fraction;
|
|
int bits;
|
|
|
|
/* Determine if the operation on the absolute values is effectively
|
|
an addition or subtraction. */
|
|
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) {
|
|
APFloat temp_rhs(rhs);
|
|
bool reverse;
|
|
|
|
if (bits == 0) {
|
|
reverse = compareAbsoluteValue(temp_rhs) == cmpLessThan;
|
|
lost_fraction = lfExactlyZero;
|
|
} else if (bits > 0) {
|
|
lost_fraction = temp_rhs.shiftSignificandRight(bits - 1);
|
|
shiftSignificandLeft(1);
|
|
reverse = false;
|
|
} else {
|
|
lost_fraction = shiftSignificandRight(-bits - 1);
|
|
temp_rhs.shiftSignificandLeft(1);
|
|
reverse = true;
|
|
}
|
|
|
|
if (reverse) {
|
|
carry = temp_rhs.subtractSignificand
|
|
(*this, lost_fraction != lfExactlyZero);
|
|
copySignificand(temp_rhs);
|
|
sign = !sign;
|
|
} else {
|
|
carry = subtractSignificand
|
|
(temp_rhs, lost_fraction != lfExactlyZero);
|
|
}
|
|
|
|
/* Invert the lost fraction - it was on the RHS and
|
|
subtracted. */
|
|
if(lost_fraction == lfLessThanHalf)
|
|
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) {
|
|
APFloat temp_rhs(rhs);
|
|
|
|
lost_fraction = temp_rhs.shiftSignificandRight(bits);
|
|
carry = addSignificand(temp_rhs);
|
|
} else {
|
|
lost_fraction = shiftSignificandRight(-bits);
|
|
carry = addSignificand(rhs);
|
|
}
|
|
|
|
/* We have a guard bit; generating a carry cannot happen. */
|
|
assert(!carry);
|
|
}
|
|
|
|
return lost_fraction;
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::multiplySpecials(const APFloat &rhs)
|
|
{
|
|
switch(convolve(category, rhs.category)) {
|
|
default:
|
|
assert(0);
|
|
|
|
case convolve(fcNaN, fcZero):
|
|
case convolve(fcNaN, fcNormal):
|
|
case convolve(fcNaN, fcInfinity):
|
|
case convolve(fcNaN, fcNaN):
|
|
return opOK;
|
|
|
|
case convolve(fcZero, fcNaN):
|
|
case convolve(fcNormal, fcNaN):
|
|
case convolve(fcInfinity, fcNaN):
|
|
category = fcNaN;
|
|
copySignificand(rhs);
|
|
return opOK;
|
|
|
|
case convolve(fcNormal, fcInfinity):
|
|
case convolve(fcInfinity, fcNormal):
|
|
case convolve(fcInfinity, fcInfinity):
|
|
category = fcInfinity;
|
|
return opOK;
|
|
|
|
case convolve(fcZero, fcNormal):
|
|
case convolve(fcNormal, fcZero):
|
|
case convolve(fcZero, fcZero):
|
|
category = fcZero;
|
|
return opOK;
|
|
|
|
case convolve(fcZero, fcInfinity):
|
|
case convolve(fcInfinity, fcZero):
|
|
makeNaN();
|
|
return opInvalidOp;
|
|
|
|
case convolve(fcNormal, fcNormal):
|
|
return opOK;
|
|
}
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::divideSpecials(const APFloat &rhs)
|
|
{
|
|
switch(convolve(category, rhs.category)) {
|
|
default:
|
|
assert(0);
|
|
|
|
case convolve(fcNaN, fcZero):
|
|
case convolve(fcNaN, fcNormal):
|
|
case convolve(fcNaN, fcInfinity):
|
|
case convolve(fcNaN, fcNaN):
|
|
case convolve(fcInfinity, fcZero):
|
|
case convolve(fcInfinity, fcNormal):
|
|
case convolve(fcZero, fcInfinity):
|
|
case convolve(fcZero, fcNormal):
|
|
return opOK;
|
|
|
|
case convolve(fcZero, fcNaN):
|
|
case convolve(fcNormal, fcNaN):
|
|
case convolve(fcInfinity, fcNaN):
|
|
category = fcNaN;
|
|
copySignificand(rhs);
|
|
return opOK;
|
|
|
|
case convolve(fcNormal, fcInfinity):
|
|
category = fcZero;
|
|
return opOK;
|
|
|
|
case convolve(fcNormal, fcZero):
|
|
category = fcInfinity;
|
|
return opDivByZero;
|
|
|
|
case convolve(fcInfinity, fcInfinity):
|
|
case convolve(fcZero, fcZero):
|
|
makeNaN();
|
|
return opInvalidOp;
|
|
|
|
case convolve(fcNormal, fcNormal):
|
|
return opOK;
|
|
}
|
|
}
|
|
|
|
/* Change sign. */
|
|
void
|
|
APFloat::changeSign()
|
|
{
|
|
/* Look mummy, this one's easy. */
|
|
sign = !sign;
|
|
}
|
|
|
|
void
|
|
APFloat::clearSign()
|
|
{
|
|
/* So is this one. */
|
|
sign = 0;
|
|
}
|
|
|
|
void
|
|
APFloat::copySign(const APFloat &rhs)
|
|
{
|
|
/* And this one. */
|
|
sign = rhs.sign;
|
|
}
|
|
|
|
/* Normalized addition or subtraction. */
|
|
APFloat::opStatus
|
|
APFloat::addOrSubtract(const APFloat &rhs, roundingMode rounding_mode,
|
|
bool subtract)
|
|
{
|
|
opStatus fs;
|
|
|
|
assertArithmeticOK(*semantics);
|
|
|
|
fs = addOrSubtractSpecials(rhs, subtract);
|
|
|
|
/* This return code means it was not a simple case. */
|
|
if(fs == opDivByZero) {
|
|
lostFraction lost_fraction;
|
|
|
|
lost_fraction = addOrSubtractSignificand(rhs, subtract);
|
|
fs = normalize(rounding_mode, lost_fraction);
|
|
|
|
/* Can only be zero if we lost no fraction. */
|
|
assert(category != fcZero || lost_fraction == lfExactlyZero);
|
|
}
|
|
|
|
/* 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)
|
|
sign = (rounding_mode == rmTowardNegative);
|
|
}
|
|
|
|
return fs;
|
|
}
|
|
|
|
/* Normalized addition. */
|
|
APFloat::opStatus
|
|
APFloat::add(const APFloat &rhs, roundingMode rounding_mode)
|
|
{
|
|
return addOrSubtract(rhs, rounding_mode, false);
|
|
}
|
|
|
|
/* Normalized subtraction. */
|
|
APFloat::opStatus
|
|
APFloat::subtract(const APFloat &rhs, roundingMode rounding_mode)
|
|
{
|
|
return addOrSubtract(rhs, rounding_mode, true);
|
|
}
|
|
|
|
/* Normalized multiply. */
|
|
APFloat::opStatus
|
|
APFloat::multiply(const APFloat &rhs, roundingMode rounding_mode)
|
|
{
|
|
opStatus fs;
|
|
|
|
assertArithmeticOK(*semantics);
|
|
sign ^= rhs.sign;
|
|
fs = multiplySpecials(rhs);
|
|
|
|
if(category == fcNormal) {
|
|
lostFraction lost_fraction = multiplySignificand(rhs, 0);
|
|
fs = normalize(rounding_mode, lost_fraction);
|
|
if(lost_fraction != lfExactlyZero)
|
|
fs = (opStatus) (fs | opInexact);
|
|
}
|
|
|
|
return fs;
|
|
}
|
|
|
|
/* Normalized divide. */
|
|
APFloat::opStatus
|
|
APFloat::divide(const APFloat &rhs, roundingMode rounding_mode)
|
|
{
|
|
opStatus fs;
|
|
|
|
assertArithmeticOK(*semantics);
|
|
sign ^= rhs.sign;
|
|
fs = divideSpecials(rhs);
|
|
|
|
if(category == fcNormal) {
|
|
lostFraction lost_fraction = divideSignificand(rhs);
|
|
fs = normalize(rounding_mode, lost_fraction);
|
|
if(lost_fraction != lfExactlyZero)
|
|
fs = (opStatus) (fs | opInexact);
|
|
}
|
|
|
|
return fs;
|
|
}
|
|
|
|
/* 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,
|
|
rmNearestTiesToEven);
|
|
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,
|
|
const APFloat &addend,
|
|
roundingMode rounding_mode)
|
|
{
|
|
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) {
|
|
lostFraction lost_fraction;
|
|
|
|
lost_fraction = multiplySignificand(multiplicand, &addend);
|
|
fs = normalize(rounding_mode, lost_fraction);
|
|
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)
|
|
sign = (rounding_mode == rmTowardNegative);
|
|
} else {
|
|
fs = multiplySpecials(multiplicand);
|
|
|
|
/* FS can only be opOK or opInvalidOp. There is no more work
|
|
to do in the latter case. The IEEE-754R standard says it is
|
|
implementation-defined in this case whether, if ADDEND is a
|
|
quiet NaN, we raise invalid op; this implementation does so.
|
|
|
|
If we need to do the addition we can do so with normal
|
|
precision. */
|
|
if(fs == opOK)
|
|
fs = addOrSubtract(addend, rounding_mode, false);
|
|
}
|
|
|
|
return fs;
|
|
}
|
|
|
|
/* Comparison requires normalized numbers. */
|
|
APFloat::cmpResult
|
|
APFloat::compare(const APFloat &rhs) const
|
|
{
|
|
cmpResult result;
|
|
|
|
assertArithmeticOK(*semantics);
|
|
assert(semantics == rhs.semantics);
|
|
|
|
switch(convolve(category, rhs.category)) {
|
|
default:
|
|
assert(0);
|
|
|
|
case convolve(fcNaN, fcZero):
|
|
case convolve(fcNaN, fcNormal):
|
|
case convolve(fcNaN, fcInfinity):
|
|
case convolve(fcNaN, fcNaN):
|
|
case convolve(fcZero, fcNaN):
|
|
case convolve(fcNormal, fcNaN):
|
|
case convolve(fcInfinity, fcNaN):
|
|
return cmpUnordered;
|
|
|
|
case convolve(fcInfinity, fcNormal):
|
|
case convolve(fcInfinity, fcZero):
|
|
case convolve(fcNormal, fcZero):
|
|
if(sign)
|
|
return cmpLessThan;
|
|
else
|
|
return cmpGreaterThan;
|
|
|
|
case convolve(fcNormal, fcInfinity):
|
|
case convolve(fcZero, fcInfinity):
|
|
case convolve(fcZero, fcNormal):
|
|
if(rhs.sign)
|
|
return cmpGreaterThan;
|
|
else
|
|
return cmpLessThan;
|
|
|
|
case convolve(fcInfinity, fcInfinity):
|
|
if(sign == rhs.sign)
|
|
return cmpEqual;
|
|
else if(sign)
|
|
return cmpLessThan;
|
|
else
|
|
return cmpGreaterThan;
|
|
|
|
case convolve(fcZero, fcZero):
|
|
return cmpEqual;
|
|
|
|
case convolve(fcNormal, fcNormal):
|
|
break;
|
|
}
|
|
|
|
/* Two normal numbers. Do they have the same sign? */
|
|
if(sign != rhs.sign) {
|
|
if(sign)
|
|
result = cmpLessThan;
|
|
else
|
|
result = cmpGreaterThan;
|
|
} else {
|
|
/* Compare absolute values; invert result if negative. */
|
|
result = compareAbsoluteValue(rhs);
|
|
|
|
if(sign) {
|
|
if(result == cmpLessThan)
|
|
result = cmpGreaterThan;
|
|
else if(result == cmpGreaterThan)
|
|
result = cmpLessThan;
|
|
}
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
APFloat::opStatus
|
|
APFloat::convert(const fltSemantics &toSemantics,
|
|
roundingMode rounding_mode)
|
|
{
|
|
lostFraction lostFraction;
|
|
unsigned int newPartCount, oldPartCount;
|
|
opStatus fs;
|
|
|
|
assertArithmeticOK(*semantics);
|
|
lostFraction = lfExactlyZero;
|
|
newPartCount = partCountForBits(toSemantics.precision + 1);
|
|
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);
|
|
if (category==fcNormal || category==fcNaN)
|
|
APInt::tcAssign(newParts, significandParts(), oldPartCount);
|
|
freeSignificand();
|
|
significand.parts = newParts;
|
|
} 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, lostFraction);
|
|
} else if (category == fcNaN) {
|
|
int shift = toSemantics.precision - semantics->precision;
|
|
// 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.
|
|
semantics = &toSemantics;
|
|
fs = opOK;
|
|
} else {
|
|
semantics = &toSemantics;
|
|
fs = opOK;
|
|
}
|
|
|
|
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 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::convertToSignExtendedInteger(integerPart *parts, unsigned int width,
|
|
bool isSigned,
|
|
roundingMode rounding_mode) const
|
|
{
|
|
lostFraction lost_fraction;
|
|
const integerPart *src;
|
|
unsigned int dstPartsCount, truncatedBits;
|
|
|
|
/* Handle the three special cases first. */
|
|
if(category == fcInfinity || category == fcNaN)
|
|
return opInvalidOp;
|
|
|
|
dstPartsCount = partCountForBits(width);
|
|
|
|
if(category == fcZero) {
|
|
APInt::tcSet(parts, 0, dstPartsCount);
|
|
return opOK;
|
|
}
|
|
|
|
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;
|
|
|
|
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;
|
|
}
|
|
}
|
|
|
|
/* 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;
|
|
}
|
|
|
|
/* Step 3: check if we fit in the destination. */
|
|
unsigned int omsb = APInt::tcMSB(parts, dstPartsCount) + 1;
|
|
|
|
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;
|
|
}
|
|
|
|
APInt::tcNegate (parts, dstPartsCount);
|
|
} else {
|
|
if (omsb >= width + !isSigned)
|
|
return opInvalidOp;
|
|
}
|
|
|
|
if (lost_fraction == lfExactlyZero)
|
|
return opOK;
|
|
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. */
|
|
APFloat::opStatus
|
|
APFloat::convertToInteger(integerPart *parts, unsigned int width,
|
|
bool isSigned,
|
|
roundingMode rounding_mode) const
|
|
{
|
|
opStatus fs;
|
|
|
|
fs = convertToSignExtendedInteger(parts, width, isSigned, rounding_mode);
|
|
|
|
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;
|
|
omsb = APInt::tcMSB(src, srcCount) + 1;
|
|
dst = significandParts();
|
|
dstCount = partCount();
|
|
precision = semantics->precision;
|
|
|
|
/* 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;
|
|
APInt::tcExtract(dst, dstCount, src, omsb, 0);
|
|
}
|
|
|
|
return normalize(rounding_mode, lost_fraction);
|
|
}
|
|
|
|
/* 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 {
|
|
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);
|
|
|
|
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)
|
|
{
|
|
lostFraction lost_fraction;
|
|
integerPart *significand;
|
|
unsigned int bitPos, partsCount;
|
|
const char *dot, *firstSignificantDigit;
|
|
|
|
zeroSignificand();
|
|
exponent = 0;
|
|
category = fcNormal;
|
|
|
|
significand = significandParts();
|
|
partsCount = partCount();
|
|
bitPos = partsCount * integerPartWidth;
|
|
|
|
/* Skip leading zeroes and any (hexa)decimal point. */
|
|
p = skipLeadingZeroesAndAnyDot(p, &dot);
|
|
firstSignificantDigit = p;
|
|
|
|
for(;;) {
|
|
integerPart hex_value;
|
|
|
|
if(*p == '.') {
|
|
assert(dot == 0);
|
|
dot = p++;
|
|
}
|
|
|
|
hex_value = hexDigitValue(*p);
|
|
if(hex_value == -1U) {
|
|
lost_fraction = lfExactlyZero;
|
|
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++;
|
|
break;
|
|
}
|
|
}
|
|
|
|
/* Hex floats require an exponent but not a hexadecimal point. */
|
|
assert(*p == 'p' || *p == 'P');
|
|
|
|
/* Ignore the exponent if we are zero. */
|
|
if(p != firstSignificantDigit) {
|
|
int expAdjustment;
|
|
|
|
/* Implicit hexadecimal point? */
|
|
if(!dot)
|
|
dot = p;
|
|
|
|
/* Calculate the exponent adjustment implicit in the number of
|
|
significant digits. */
|
|
expAdjustment = dot - firstSignificantDigit;
|
|
if(expAdjustment < 0)
|
|
expAdjustment++;
|
|
expAdjustment = expAdjustment * 4 - 1;
|
|
|
|
/* Adjust for writing the significand starting at the most
|
|
significant nibble. */
|
|
expAdjustment += semantics->precision;
|
|
expAdjustment -= partsCount * integerPartWidth;
|
|
|
|
/* Adjust for the given exponent. */
|
|
exponent = totalExponent(p, expAdjustment);
|
|
}
|
|
|
|
return normalize(rounding_mode, lost_fraction);
|
|
}
|
|
|
|
APFloat::opStatus
|
|
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 (*D.firstSigDigit == '0') {
|
|
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);
|
|
|
|
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++;
|
|
else
|
|
sign = 0;
|
|
|
|
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);
|
|
|
|
/* 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
|
|
{
|
|
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;
|
|
else {
|
|
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;
|
|
return hash;
|
|
}
|
|
}
|
|
|
|
// Conversion from APFloat to/from host float/double. It may eventually be
|
|
// possible to eliminate these and have everybody deal with APFloats, but that
|
|
// will take a while. This approach will not easily extend to long double.
|
|
// Current implementation requires integerPartWidth==64, which is correct at
|
|
// the moment but could be made more general.
|
|
|
|
// Denormals have exponent minExponent in APFloat, but minExponent-1 in
|
|
// the actual IEEE respresentations. We compensate for that here.
|
|
|
|
APInt
|
|
APFloat::convertF80LongDoubleAPFloatToAPInt() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics* const)&x87DoubleExtended);
|
|
assert (partCount()==2);
|
|
|
|
uint64_t myexponent, mysignificand;
|
|
|
|
if (category==fcNormal) {
|
|
myexponent = exponent+16383; //bias
|
|
mysignificand = significandParts()[0];
|
|
if (myexponent==1 && !(mysignificand & 0x8000000000000000ULL))
|
|
myexponent = 0; // denormal
|
|
} else if (category==fcZero) {
|
|
myexponent = 0;
|
|
mysignificand = 0;
|
|
} else if (category==fcInfinity) {
|
|
myexponent = 0x7fff;
|
|
mysignificand = 0x8000000000000000ULL;
|
|
} else {
|
|
assert(category == fcNaN && "Unknown category");
|
|
myexponent = 0x7fff;
|
|
mysignificand = significandParts()[0];
|
|
}
|
|
|
|
uint64_t words[2];
|
|
words[0] = (((uint64_t)sign & 1) << 63) |
|
|
((myexponent & 0x7fff) << 48) |
|
|
((mysignificand >>16) & 0xffffffffffffLL);
|
|
words[1] = mysignificand & 0xffff;
|
|
return APInt(80, 2, words);
|
|
}
|
|
|
|
APInt
|
|
APFloat::convertPPCDoubleDoubleAPFloatToAPInt() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics* const)&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
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics*)&IEEEdouble);
|
|
assert (partCount()==1);
|
|
|
|
uint64_t myexponent, mysignificand;
|
|
|
|
if (category==fcNormal) {
|
|
myexponent = exponent+1023; //bias
|
|
mysignificand = *significandParts();
|
|
if (myexponent==1 && !(mysignificand & 0x10000000000000LL))
|
|
myexponent = 0; // denormal
|
|
} else if (category==fcZero) {
|
|
myexponent = 0;
|
|
mysignificand = 0;
|
|
} else if (category==fcInfinity) {
|
|
myexponent = 0x7ff;
|
|
mysignificand = 0;
|
|
} else {
|
|
assert(category == fcNaN && "Unknown category!");
|
|
myexponent = 0x7ff;
|
|
mysignificand = *significandParts();
|
|
}
|
|
|
|
return APInt(64, (((((uint64_t)sign & 1) << 63) |
|
|
((myexponent & 0x7ff) << 52) |
|
|
(mysignificand & 0xfffffffffffffLL))));
|
|
}
|
|
|
|
APInt
|
|
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))
|
|
myexponent = 0; // denormal
|
|
} else if (category==fcZero) {
|
|
myexponent = 0;
|
|
mysignificand = 0;
|
|
} else if (category==fcInfinity) {
|
|
myexponent = 0xff;
|
|
mysignificand = 0;
|
|
} else {
|
|
assert(category == fcNaN && "Unknown category!");
|
|
myexponent = 0xff;
|
|
mysignificand = *significandParts();
|
|
}
|
|
|
|
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)
|
|
return convertFloatAPFloatToAPInt();
|
|
|
|
if (semantics == (const llvm::fltSemantics* const)&IEEEdouble)
|
|
return convertDoubleAPFloatToAPInt();
|
|
|
|
if (semantics == (const llvm::fltSemantics* const)&PPCDoubleDouble)
|
|
return convertPPCDoubleDoubleAPFloatToAPInt();
|
|
|
|
assert(semantics == (const llvm::fltSemantics* const)&x87DoubleExtended &&
|
|
"unknown format!");
|
|
return convertF80LongDoubleAPFloatToAPInt();
|
|
}
|
|
|
|
float
|
|
APFloat::convertToFloat() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics* const)&IEEEsingle);
|
|
APInt api = convertToAPInt();
|
|
return api.bitsToFloat();
|
|
}
|
|
|
|
double
|
|
APFloat::convertToDouble() const
|
|
{
|
|
assert(semantics == (const llvm::fltSemantics* const)&IEEEdouble);
|
|
APInt api = convertToAPInt();
|
|
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")
|
|
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);
|
|
|
|
initialize(&APFloat::x87DoubleExtended);
|
|
assert(partCount()==2);
|
|
|
|
sign = i1>>63;
|
|
if (myexponent==0 && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcZero;
|
|
} else if (myexponent==0x7fff && mysignificand==0x8000000000000000ULL) {
|
|
// exponent, significand meaningless
|
|
category = fcInfinity;
|
|
} else if (myexponent==0x7fff && mysignificand!=0x8000000000000000ULL) {
|
|
// exponent meaningless
|
|
category = fcNaN;
|
|
significandParts()[0] = mysignificand;
|
|
significandParts()[1] = 0;
|
|
} else {
|
|
category = fcNormal;
|
|
exponent = myexponent - 16383;
|
|
significandParts()[0] = mysignificand;
|
|
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)
|
|
{
|
|
assert(api.getBitWidth()==64);
|
|
uint64_t i = *api.getRawData();
|
|
uint64_t myexponent = (i >> 52) & 0x7ff;
|
|
uint64_t mysignificand = i & 0xfffffffffffffLL;
|
|
|
|
initialize(&APFloat::IEEEdouble);
|
|
assert(partCount()==1);
|
|
|
|
sign = i>>63;
|
|
if (myexponent==0 && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcZero;
|
|
} else if (myexponent==0x7ff && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcInfinity;
|
|
} else if (myexponent==0x7ff && mysignificand!=0) {
|
|
// exponent meaningless
|
|
category = fcNaN;
|
|
*significandParts() = mysignificand;
|
|
} else {
|
|
category = fcNormal;
|
|
exponent = myexponent - 1023;
|
|
*significandParts() = mysignificand;
|
|
if (myexponent==0) // denormal
|
|
exponent = -1022;
|
|
else
|
|
*significandParts() |= 0x10000000000000LL; // integer bit
|
|
}
|
|
}
|
|
|
|
void
|
|
APFloat::initFromFloatAPInt(const APInt & api)
|
|
{
|
|
assert(api.getBitWidth()==32);
|
|
uint32_t i = (uint32_t)*api.getRawData();
|
|
uint32_t myexponent = (i >> 23) & 0xff;
|
|
uint32_t mysignificand = i & 0x7fffff;
|
|
|
|
initialize(&APFloat::IEEEsingle);
|
|
assert(partCount()==1);
|
|
|
|
sign = i >> 31;
|
|
if (myexponent==0 && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcZero;
|
|
} else if (myexponent==0xff && mysignificand==0) {
|
|
// exponent, significand meaningless
|
|
category = fcInfinity;
|
|
} else if (myexponent==0xff && mysignificand!=0) {
|
|
// sign, exponent, significand meaningless
|
|
category = fcNaN;
|
|
*significandParts() = mysignificand;
|
|
} else {
|
|
category = fcNormal;
|
|
exponent = myexponent - 127; //bias
|
|
*significandParts() = mysignificand;
|
|
if (myexponent==0) // denormal
|
|
exponent = -126;
|
|
else
|
|
*significandParts() |= 0x800000; // 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. The
|
|
/// isIEEE argument distinguishes between PPC128 and IEEE128 (not meaningful
|
|
/// when the size is anything else).
|
|
void
|
|
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, bool isIEEE)
|
|
{
|
|
initFromAPInt(api, isIEEE);
|
|
}
|
|
|
|
APFloat::APFloat(float f)
|
|
{
|
|
APInt api = APInt(32, 0);
|
|
initFromAPInt(api.floatToBits(f));
|
|
}
|
|
|
|
APFloat::APFloat(double d)
|
|
{
|
|
APInt api = APInt(64, 0);
|
|
initFromAPInt(api.doubleToBits(d));
|
|
}
|