forked from OSchip/llvm-project
367 lines
12 KiB
C++
367 lines
12 KiB
C++
//===-- lib/Decimal/big-radix-floating-point.h ------------------*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef FORTRAN_DECIMAL_BIG_RADIX_FLOATING_POINT_H_
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#define FORTRAN_DECIMAL_BIG_RADIX_FLOATING_POINT_H_
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// This is a helper class for use in floating-point conversions
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// between binary decimal representations. It holds a multiple-precision
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// integer value using digits of a radix that is a large even power of ten
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// (10,000,000,000,000,000 by default, 10**16). These digits are accompanied
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// by a signed exponent that denotes multiplication by a power of ten.
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// The effective radix point is to the right of the digits (i.e., they do
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// not represent a fraction).
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//
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// The operations supported by this class are limited to those required
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// for conversions between binary and decimal representations; it is not
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// a general-purpose facility.
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#include "flang/Common/bit-population-count.h"
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#include "flang/Common/leading-zero-bit-count.h"
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#include "flang/Common/uint128.h"
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#include "flang/Decimal/binary-floating-point.h"
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#include "flang/Decimal/decimal.h"
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#include <cinttypes>
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#include <limits>
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#include <type_traits>
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namespace Fortran::decimal {
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static constexpr std::uint64_t TenToThe(int power) {
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return power <= 0 ? 1 : 10 * TenToThe(power - 1);
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}
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// 10**(LOG10RADIX + 3) must be < 2**wordbits, and LOG10RADIX must be
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// even, so that pairs of decimal digits do not straddle Digits.
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// So LOG10RADIX must be 16 or 6.
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template <int PREC, int LOG10RADIX = 16> class BigRadixFloatingPointNumber {
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public:
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using Real = BinaryFloatingPointNumber<PREC>;
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static constexpr int log10Radix{LOG10RADIX};
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private:
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static constexpr std::uint64_t uint64Radix{TenToThe(log10Radix)};
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static constexpr int minDigitBits{
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64 - common::LeadingZeroBitCount(uint64Radix)};
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using Digit = common::HostUnsignedIntType<minDigitBits>;
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static constexpr Digit radix{uint64Radix};
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static_assert(radix < std::numeric_limits<Digit>::max() / 1000,
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"radix is somehow too big");
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static_assert(radix > std::numeric_limits<Digit>::max() / 10000,
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"radix is somehow too small");
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// The base-2 logarithm of the least significant bit that can arise
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// in a subnormal IEEE floating-point number.
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static constexpr int minLog2AnyBit{
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-Real::exponentBias - Real::binaryPrecision};
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// The number of Digits needed to represent the smallest subnormal.
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static constexpr int maxDigits{3 - minLog2AnyBit / log10Radix};
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public:
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explicit BigRadixFloatingPointNumber(
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enum FortranRounding rounding = RoundNearest)
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: rounding_{rounding} {}
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// Converts a binary floating point value.
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explicit BigRadixFloatingPointNumber(
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Real, enum FortranRounding = RoundNearest);
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BigRadixFloatingPointNumber &SetToZero() {
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isNegative_ = false;
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digits_ = 0;
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exponent_ = 0;
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return *this;
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}
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// Converts decimal floating-point to binary.
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ConversionToBinaryResult<PREC> ConvertToBinary();
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// Parses and converts to binary. Handles leading spaces,
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// "NaN", & optionally-signed "Inf". Does not skip internal
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// spaces.
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// The argument is a reference to a pointer that is left
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// pointing to the first character that wasn't parsed.
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ConversionToBinaryResult<PREC> ConvertToBinary(
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const char *&, const char *end = nullptr);
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// Formats a decimal floating-point number to a user buffer.
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// May emit "NaN" or "Inf", or an possibly-signed integer.
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// No decimal point is written, but if it were, it would be
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// after the last digit; the effective decimal exponent is
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// returned as part of the result structure so that it can be
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// formatted by the client.
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ConversionToDecimalResult ConvertToDecimal(
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char *, std::size_t, enum DecimalConversionFlags, int digits) const;
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// Discard decimal digits not needed to distinguish this value
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// from the decimal encodings of two others (viz., the nearest binary
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// floating-point numbers immediately below and above this one).
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// The last decimal digit may not be uniquely determined in all
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// cases, and will be the mean value when that is so (e.g., if
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// last decimal digit values 6-8 would all work, it'll be a 7).
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// This minimization necessarily assumes that the value will be
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// emitted and read back into the same (or less precise) format
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// with default rounding to the nearest value.
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void Minimize(
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BigRadixFloatingPointNumber &&less, BigRadixFloatingPointNumber &&more);
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template <typename STREAM> STREAM &Dump(STREAM &) const;
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private:
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BigRadixFloatingPointNumber(const BigRadixFloatingPointNumber &that)
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: digits_{that.digits_}, exponent_{that.exponent_},
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isNegative_{that.isNegative_}, rounding_{that.rounding_} {
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for (int j{0}; j < digits_; ++j) {
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digit_[j] = that.digit_[j];
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}
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}
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bool IsZero() const {
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// Don't assume normalization.
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for (int j{0}; j < digits_; ++j) {
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if (digit_[j] != 0) {
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return false;
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}
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}
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return true;
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}
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// Predicate: true when 10*value would cause a carry.
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// (When this happens during decimal-to-binary conversion,
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// there are more digits in the input string than can be
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// represented precisely.)
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bool IsFull() const {
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return digits_ == digitLimit_ && digit_[digits_ - 1] >= radix / 10;
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}
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// Sets *this to an unsigned integer value.
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// Returns any remainder.
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template <typename UINT> UINT SetTo(UINT n) {
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static_assert(
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std::is_same_v<UINT, common::uint128_t> || std::is_unsigned_v<UINT>);
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SetToZero();
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while (n != 0) {
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auto q{n / 10u};
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if (n != q * 10) {
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break;
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}
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++exponent_;
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n = q;
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}
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if constexpr (sizeof n < sizeof(Digit)) {
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if (n != 0) {
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digit_[digits_++] = n;
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}
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return 0;
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} else {
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while (n != 0 && digits_ < digitLimit_) {
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auto q{n / radix};
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digit_[digits_++] = static_cast<Digit>(n - q * radix);
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n = q;
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}
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return n;
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}
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}
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int RemoveLeastOrderZeroDigits() {
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int remove{0};
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if (digits_ > 0 && digit_[0] == 0) {
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while (remove < digits_ && digit_[remove] == 0) {
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++remove;
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}
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if (remove >= digits_) {
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digits_ = 0;
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} else if (remove > 0) {
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#if defined __GNUC__ && __GNUC__ < 8
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// (&& j + remove < maxDigits) was added to avoid GCC < 8 build failure
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// on -Werror=array-bounds. This can be removed if -Werror is disable.
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for (int j{0}; j + remove < digits_ && (j + remove < maxDigits); ++j) {
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#else
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for (int j{0}; j + remove < digits_; ++j) {
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#endif
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digit_[j] = digit_[j + remove];
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}
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digits_ -= remove;
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}
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}
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return remove;
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}
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void RemoveLeadingZeroDigits() {
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while (digits_ > 0 && digit_[digits_ - 1] == 0) {
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--digits_;
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}
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}
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void Normalize() {
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RemoveLeadingZeroDigits();
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exponent_ += RemoveLeastOrderZeroDigits() * log10Radix;
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}
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// This limited divisibility test only works for even divisors of the radix,
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// which is fine since it's only ever used with 2 and 5.
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template <int N> bool IsDivisibleBy() const {
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static_assert(N > 1 && radix % N == 0, "bad modulus");
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return digits_ == 0 || (digit_[0] % N) == 0;
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}
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template <unsigned DIVISOR> int DivideBy() {
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Digit remainder{0};
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for (int j{digits_ - 1}; j >= 0; --j) {
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Digit q{digit_[j] / DIVISOR};
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Digit nrem{digit_[j] - DIVISOR * q};
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digit_[j] = q + (radix / DIVISOR) * remainder;
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remainder = nrem;
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}
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return remainder;
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}
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void DivideByPowerOfTwo(int twoPow) { // twoPow <= log10Radix
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Digit remainder{0};
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auto mask{(Digit{1} << twoPow) - 1};
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auto coeff{radix >> twoPow};
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for (int j{digits_ - 1}; j >= 0; --j) {
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auto nrem{digit_[j] & mask};
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digit_[j] = (digit_[j] >> twoPow) + coeff * remainder;
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remainder = nrem;
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}
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}
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// Returns true on overflow
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bool DivideByPowerOfTwoInPlace(int twoPow) {
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if (digits_ > 0) {
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while (twoPow > 0) {
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int chunk{twoPow > log10Radix ? log10Radix : twoPow};
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if ((digit_[0] & ((Digit{1} << chunk) - 1)) == 0) {
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DivideByPowerOfTwo(chunk);
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twoPow -= chunk;
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continue;
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}
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twoPow -= chunk;
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if (digit_[digits_ - 1] >> chunk != 0) {
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if (digits_ == digitLimit_) {
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return true; // overflow
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}
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digit_[digits_++] = 0;
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}
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auto remainder{digit_[digits_ - 1]};
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exponent_ -= log10Radix;
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auto coeff{radix >> chunk}; // precise; radix is (5*2)**log10Radix
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auto mask{(Digit{1} << chunk) - 1};
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for (int j{digits_ - 1}; j >= 1; --j) {
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digit_[j] = (digit_[j - 1] >> chunk) + coeff * remainder;
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remainder = digit_[j - 1] & mask;
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}
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digit_[0] = coeff * remainder;
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}
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}
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return false; // no overflow
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}
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int AddCarry(int position = 0, int carry = 1) {
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for (; position < digits_; ++position) {
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Digit v{digit_[position] + carry};
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if (v < radix) {
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digit_[position] = v;
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return 0;
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}
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digit_[position] = v - radix;
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carry = 1;
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}
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if (digits_ < digitLimit_) {
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digit_[digits_++] = carry;
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return 0;
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}
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Normalize();
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if (digits_ < digitLimit_) {
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digit_[digits_++] = carry;
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return 0;
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}
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return carry;
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}
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void Decrement() {
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for (int j{0}; digit_[j]-- == 0; ++j) {
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digit_[j] = radix - 1;
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}
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}
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template <int N> int MultiplyByHelper(int carry = 0) {
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for (int j{0}; j < digits_; ++j) {
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auto v{N * digit_[j] + carry};
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carry = v / radix;
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digit_[j] = v - carry * radix; // i.e., v % radix
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}
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return carry;
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}
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template <int N> int MultiplyBy(int carry = 0) {
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if (int newCarry{MultiplyByHelper<N>(carry)}) {
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return AddCarry(digits_, newCarry);
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} else {
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return 0;
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}
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}
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template <int N> int MultiplyWithoutNormalization() {
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if (int carry{MultiplyByHelper<N>(0)}) {
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if (digits_ < digitLimit_) {
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digit_[digits_++] = carry;
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return 0;
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} else {
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return carry;
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}
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} else {
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return 0;
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}
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}
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void LoseLeastSignificantDigit(); // with rounding
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void PushCarry(int carry) {
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if (digits_ == maxDigits && RemoveLeastOrderZeroDigits() == 0) {
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LoseLeastSignificantDigit();
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digit_[digits_ - 1] += carry;
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} else {
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digit_[digits_++] = carry;
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}
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}
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// Adds another number and then divides by two.
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// Assumes same exponent and sign.
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// Returns true when the the result has effectively been rounded down.
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bool Mean(const BigRadixFloatingPointNumber &);
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// Parses a floating-point number; leaves the pointer reference
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// argument pointing at the next character after what was recognized.
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// The "end" argument can be left null if the caller is sure that the
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// string is properly terminated with an addressable character that
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// can't be in a valid floating-point character.
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bool ParseNumber(const char *&, bool &inexact, const char *end);
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using Raw = typename Real::RawType;
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constexpr Raw SignBit() const { return Raw{isNegative_} << (Real::bits - 1); }
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constexpr Raw Infinity() const {
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return (Raw{Real::maxExponent} << Real::significandBits) | SignBit();
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}
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static constexpr Raw NaN() {
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return (Raw{Real::maxExponent} << Real::significandBits) |
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(Raw{1} << (Real::significandBits - 2));
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}
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Digit digit_[maxDigits]; // in little-endian order: digit_[0] is LSD
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int digits_{0}; // # of elements in digit_[] array; zero when zero
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int digitLimit_{maxDigits}; // precision clamp
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int exponent_{0}; // signed power of ten
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bool isNegative_{false};
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enum FortranRounding rounding_ { RoundNearest };
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};
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} // namespace Fortran::decimal
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#endif
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