path: root/src/mongo/platform/decimal128.cpp

/*    Copyright 2014 MongoDB Inc.
 *
 *    This program is free software: you can redistribute it and/or  modify
 *    it under the terms of the GNU Affero General Public License, version 3,
 *    as published by the Free Software Foundation.
 *
 *    This program is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *    GNU Affero General Public License for more details.
 *
 *    You should have received a copy of the GNU Affero General Public License
 *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
 *
 *    As a special exception, the copyright holders give permission to link the
 *    code of portions of this program with the OpenSSL library under certain
 *    conditions as described in each individual source file and distribute
 *    linked combinations including the program with the OpenSSL library. You
 *    must comply with the GNU Affero General Public License in all respects
 *    for all of the code used other than as permitted herein. If you modify
 *    file(s) with this exception, you may extend this exception to your
 *    version of the file(s), but you are not obligated to do so. If you do not
 *    wish to do so, delete this exception statement from your version. If you
 *    delete this exception statement from all source files in the program,
 *    then also delete it in the license file.
 */

#include "mongo/platform/basic.h"
#include "mongo/platform/decimal128.h"

#include <cmath>
#include <cstdlib>
#include <iostream>
#include <memory>
#include <string>
#include <utility>
// The Intel C library typedefs wchar_t, but it is a distinct fundamental type
// in C++, so we #define _WCHAR_T here to prevent the library from trying to typedef.
#define _WCHAR_T
#include <third_party/IntelRDFPMathLib20U1/LIBRARY/src/bid_conf.h>
#include <third_party/IntelRDFPMathLib20U1/LIBRARY/src/bid_functions.h>
#undef _WCHAR_T

#include "mongo/config.h"
#include "mongo/util/assert_util.h"

namespace mongo {

namespace {
// Determine system's endian ordering in order to construct decimal 128 values directly
#if MONGO_CONFIG_BYTE_ORDER == 1234
const int kHigh64 = 1;
const int kLow64 = 0;
#else
const int kHigh64 = 0;
const int kLow64 = 1;
#endif

// The Intel library uses long long for BID_UINT128s parts, which on some
// systems is longer than a uint64_t.  We need to cast down, although there
// will not be data loss.
inline Decimal128::Value libraryTypeToValue(BID_UINT128 value) {
    return {static_cast<std::uint64_t>(value.w[kLow64]),
            static_cast<std::uint64_t>(value.w[kHigh64])};
}

/**
 * This helper function creates a library specific type for the
 * IntelRDFPMathLib20U1 library from Decimal128's _value
 */
BID_UINT128 decimal128ToLibraryType(Decimal128::Value value) {
    BID_UINT128 dec128;
    dec128.w[kLow64] = value.low64;
    dec128.w[kHigh64] = value.high64;
    return dec128;
}

/**
 * This helper function takes an intel decimal 128 library type and quantizes
 * it to 15 decimal digits.
 * BID_UINT128 value : the value to quantize
 * RoundingMode roundMode : the rounding mode to be used for quantizing operations
 * int base10Exp : the base 10 exponent of value to scale the quantizer by
 * uint32_t* signalingFlags : flags for signaling imprecise results
 */
BID_UINT128 quantizeTo15DecimalDigits(BID_UINT128 value,
                                      Decimal128::RoundingMode roundMode,
                                      int base10Exp,
                                      std::uint32_t* signalingFlags) {
    BID_UINT128 quantizerReference;

    // The quantizer starts at 1E-15
    quantizerReference.w[kHigh64] = 0x3022000000000000;
    quantizerReference.w[kLow64] = 0x0000000000000001;

    // Scale the quantizer by the base 10 exponent. This is necessary to keep
    // the scale of the quantizer reference correct. For example, the decimal value 101
    // needs a different quantizer (1E-12) than the decimal value 1001 (1E-11) to yield
    // a 15 digit decimal precision.
    quantizerReference = bid128_scalbn(quantizerReference, base10Exp, roundMode, signalingFlags);

    value = bid128_quantize(value, quantizerReference, roundMode, signalingFlags);
    return value;
}

}  // namespace

Decimal128::Decimal128(std::int32_t int32Value)
    : _value(libraryTypeToValue(bid128_from_int32(int32Value))) {}

Decimal128::Decimal128(std::int64_t int64Value)
    : _value(libraryTypeToValue(bid128_from_int64(int64Value))) {}

/**
 * Quantize a doubleValue argument to a Decimal128 with exactly 15 digits
 * of precision.
 *
 * To highlight the motivation for this function, consider doubleValue = 0.1.
 * The quantity 0.1 does not have an exact respresentation as a double.
 * The actual value stored in the 64-bit type is 0.1000000000000000055511...
 *
 * Although imprecise, the double type does guarantee a minimum of 15 digits
 * of decimal precision. When casting the double to a decimal type, we choose
 * to only appreciate the double's first 15 digits and round accordingly.
 *
 * To perform this operation, doubleValue is converted to a decimal and then quantized
 * with the appropriate quantum (Q) to yield exactly 15 digits of precision.
 * For example,
 *     doubleValue = 0.1
 *     dec128 = Decimal128(doubleValue)
 *     Q = 1E-16
 *     dec128.quantize(Q)
 *     ==> 0.100000000000000
 *
 * The value to quantize dec128 on (Q) is directly related to the base 10 exponent
 * of the passed in doubleValue,
 *     Q = 1 * 10 ^ (-15 + Base10Exp(doubleValue))
 *
 * doubleValue's exponent is stored in base 2 (binary floating point), so we need to
 * convert the base 2 exponent to base 10 to calculate Q.
 *
 * ===============================================================================
 *
 * Convert a double's base 2 exponent to base 10 using integer arithmetic.
 *
 * Given doubleValue with exponent Base2Exp, we would like to find Base10Exp such that:
 * (1) 10^Base10Exp >= |doubleValue|
 * (2) 10^(Base10Exp-1) < |doubleValue|
 *
 * We will use Base10Exp = E * 301 / 1000 as a starting guess.
 *
 * This formula is derived from the fact that 10^(E*log10(2)) == 2^E as
 * 301 / 1000 approximates log10(2).
 *
 * If there exists an M = Base10Exp-1 such that 10^M is also greater than doubleValue,
 * our guess was off and we will need to decrement Base10Exp and re-quantize our value.
 *
 * The total absolute error is caused by:
 *
 * - Rounding inaccuracy from using the fraction 0.301 instead of log10(2) = 0.301029...
 *   Max Absolute Error = Max(N) * RelError
 *                      = 308 * ((0.301 - log10(2)) / log10(2)) = -0.03069
 *
 * - Inaccuracy from the fact that our formula looks at comparing to 2^E instead of numbers
 *   up to but not including 2^(E+1)
 *   Max Absolute Error = -log10(2) = -0.30103
 *
 * - Integer arithmetic inaccuracy from one division (301/1000)
 *   Up until the integer division truncation, our total error is between -0.33072 and 0,
 *   which means after truncation our total error can be no more than -1. It is either 0 or -1.
 *
 * In the worst case, the total error is -1, so we never have to attempt to discover the
 * correct Base10Exp more than once extra.
 *
 * Since the above explanation does not take into account the sign of the double's binary
 * exponent, we do that now. We will use the Base2Exp E of +/- 5 to demonstrate.
 * For each doubleValue in the table, we would like to calculate a 'Shift' such that:
 *     doubleValue.quantize(10^Shift) has 15 digits of precision
 *
 *    +-------------+-------------------+----------------------+---------------------------+
 *    | doubleValue |      Base2Exp     |       Base10Exp      |   Shift (Q = 10^Shift)    |
 *    +-------------+-------------------+----------------------+---------------------------+
 *    | 100000      |                17 |                    5 | -15 + 6                   |
 *    | 500000      |                19 |                    5 | -15 + 6                   |
 *    | 999999      |                20 |                    6 | -15 + 6                   |
 *    | .00001      |               -16 |                   -4 | -15 - 4                   |
 *    | .00005      |               -14 |                   -4 | -15 - 4                   |
 *    | .00009      |               -13 |                   -3 | -15 - 4                   |
 *    +-------------+-------------------+----------------------+---------------------------+
 *    Note: This table was produced using C++'s integer truncation semantics, which
 *          rounds towards zero instead of flooring (ie -9/10 returns 0 not -1).
 *
 * For positive Base2Exp, we want a shift of 6.
 *  - Common case: Base10Exp = 5, so add 1 to get 6.
 *  - Uncommon case: Base10Exp = 6, but we added 1 to address the common case,
 *    so subtract 1 and requantize.
 *
 * For negative Base2Exp, we want a shift of -4
 *  - Common case: Base10Exp = -4, so leave as is.
 *  - Uncommon case: Base10Exp = -3, so subtract 1 and requantize.
 *
 * In the worst case, proven by the above error analysis, we only need to
 * requantize once to yield exactly 15 decimal digits of precision.
 */
Decimal128::Decimal128(double doubleValue,
                       RoundingPrecision roundPrecision,
                       RoundingMode roundMode) {
    BID_UINT128 convertedDoubleValue;
    std::uint32_t throwAwayFlag = 0;
    convertedDoubleValue = binary64_to_bid128(doubleValue, roundMode, &throwAwayFlag);

    // If the original number was zero, infinity, or NaN, there's no need to quantize
    if (doubleValue == 0.0 || std::isinf(doubleValue) || std::isnan(doubleValue) ||
        roundPrecision == kRoundTo34Digits) {
        _value = libraryTypeToValue(convertedDoubleValue);
        return;
    }

    // Get the base2 exponent from doubleValue
    int base2Exp;
    frexp(doubleValue, &base2Exp);

    // Estimate doubleValue's base10 exponent from its base2 exponent by
    // multiplying by an approximation of log10(2).
    // Since 10^(x*log10(2)) == 2^x, this initial guess gets us very close.
    int base10Exp = (base2Exp * 30103) / (100 * 1000);

    // Although both 1000 and .001 have a base 10 exponent of magnitude 3, they have
    // a different number of leading/trailing zeros. Adjust base10Exp to compensate.
    if (base2Exp >= 0)
        base10Exp++;

    _value = libraryTypeToValue(
        quantizeTo15DecimalDigits(convertedDoubleValue, roundMode, base10Exp, &throwAwayFlag));

    // Check if the quantization was done correctly: _value stores exactly 15
    // decimal digits of precision (15 digits can fit into the low 64 bits of the decimal)
    if (_value.low64 < 100000000000000ull || _value.low64 > 999999999999999ull) {
        // If we didn't precisely get 15 digits of precision, the original base 10 exponent
        // guess was 1 off, so quantize once more with base10Exp - 1
        base10Exp--;
        _value = libraryTypeToValue(
            quantizeTo15DecimalDigits(convertedDoubleValue, roundMode, base10Exp, &throwAwayFlag));
    }

    // The decimal must have exactly 15 digits of precision
    invariant(getCoefficientHigh() == 0);
    invariant(_value.low64 >= 100000000000000ull && _value.low64 <= 999999999999999ull);
}

Decimal128::Decimal128(std::string stringValue, RoundingMode roundMode) {
    std::uint32_t throwAwayFlag = 0;
    *this = Decimal128(stringValue, &throwAwayFlag, roundMode);
}

Decimal128::Decimal128(std::string stringValue,
                       std::uint32_t* signalingFlags,
                       RoundingMode roundMode) {
    std::unique_ptr<char[]> charInput(new char[stringValue.size() + 1]);
    std::copy(stringValue.begin(), stringValue.end(), charInput.get());
    charInput[stringValue.size()] = '\0';
    BID_UINT128 dec128;
    dec128 = bid128_from_string(charInput.get(), roundMode, signalingFlags);
    _value = libraryTypeToValue(dec128);
}

Decimal128::Value Decimal128::getValue() const {
    return _value;
}

Decimal128 Decimal128::toAbs() const {
    BID_UINT128 dec128 = decimal128ToLibraryType(_value);
    dec128 = bid128_abs(dec128);
    return Decimal128(libraryTypeToValue(dec128));
}

std::int32_t Decimal128::toInt(RoundingMode roundMode) const {
    std::uint32_t throwAwayFlag = 0;
    return toInt(&throwAwayFlag, roundMode);
}

std::int32_t Decimal128::toInt(std::uint32_t* signalingFlags, RoundingMode roundMode) const {
    BID_UINT128 dec128 = decimal128ToLibraryType(_value);
    switch (roundMode) {
        case kRoundTiesToEven:
            return bid128_to_int32_rnint(dec128, signalingFlags);
        case kRoundTowardNegative:
            return bid128_to_int32_floor(dec128, signalingFlags);
        case kRoundTowardPositive:
            return bid128_to_int32_ceil(dec128, signalingFlags);
        case kRoundTowardZero:
            return bid128_to_int32_int(dec128, signalingFlags);
        case kRoundTiesToAway:
            return bid128_to_int32_rninta(dec128, signalingFlags);
        default:
            return bid128_to_int32_rnint(dec128, signalingFlags);
    }
}

int64_t Decimal128::toLong(RoundingMode roundMode) const {
    std::uint32_t throwAwayFlag = 0;
    return toLong(&throwAwayFlag, roundMode);
}

int64_t Decimal128::toLong(std::uint32_t* signalingFlags, RoundingMode roundMode) const {
    BID_UINT128 dec128 = decimal128ToLibraryType(_value);
    switch (roundMode) {
        case kRoundTiesToEven:
            return bid128_to_int64_rnint(dec128, signalingFlags);
        case kRoundTowardNegative:
            return bid128_to_int64_floor(dec128, signalingFlags);
        case kRoundTowardPositive:
            return bid128_to_int64_ceil(dec128, signalingFlags);
        case kRoundTowardZero:
            return bid128_to_int64_int(dec128, signalingFlags);
        case kRoundTiesToAway:
            return bid128_to_int64_rninta(dec128, signalingFlags);
        default:
            return bid128_to_int64_rnint(dec128, signalingFlags);
    }
}

std::int32_t Decimal128::toIntExact(RoundingMode roundMode) const {
    std::uint32_t throwAwayFlag = 0;
    return toIntExact(&throwAwayFlag, roundMode);
}

std::int32_t Decimal128::toIntExact(std::uint32_t* signalingFlags, RoundingMode roundMode) const {
    BID_UINT128 dec128 = decimal128ToLibraryType(_value);
    switch (roundMode) {
        case kRoundTiesToEven:
            return bid128_to_int32_xrnint(dec128, signalingFlags);
        case kRoundTowardNegative:
            return bid128_to_int32_xfloor(dec128, signalingFlags);
        case kRoundTowardPositive:
            return bid128_to_int32_xceil(dec128, signalingFlags);
        case kRoundTowardZero:
            return bid128_to_int32_xint(dec128, signalingFlags);
        case kRoundTiesToAway:
            return bid128_to_int32_xrninta(dec128, signalingFlags);
        default:
            return bid128_to_int32_xrnint(dec128, signalingFlags);
    }
}

std::int64_t Decimal128::toLongExact(RoundingMode roundMode) const {
    std::uint32_t throwAwayFlag = 0;
    return toLongExact(&throwAwayFlag, roundMode);
}

std::int64_t Decimal128::toLongExact(std::uint32_t* signalingFlags, RoundingMode roundMode) const {
    BID_UINT128 dec128 = decimal128ToLibraryType(_value);
    switch (roundMode) {
        case kRoundTiesToEven:
            return bid128_to_int64_xrnint(dec128, signalingFlags);
        case kRoundTowardNegative:
            return bid128_to_int64_xfloor(dec128, signalingFlags);
        case kRoundTowardPositive:
            return bid128_to_int64_xceil(dec128, signalingFlags);
        case kRoundTowardZero:
            return bid128_to_int64_xint(dec128, signalingFlags);
        case kRoundTiesToAway:
            return bid128_to_int64_xrninta(dec128, signalingFlags);
        default:
            return bid128_to_int64_xrnint(dec128, signalingFlags);
    }
}

double Decimal128::toDouble(RoundingMode roundMode) const {
    std::uint32_t throwAwayFlag = 0;
    return toDouble(&throwAwayFlag, roundMode);
}

double Decimal128::toDouble(std::uint32_t* signalingFlags, RoundingMode roundMode) const {
    BID_UINT128 dec128 = decimal128ToLibraryType(_value);
    return bid128_to_binary64(dec128, roundMode, signalingFlags);
}

std::string Decimal128::toString() const {
    // If the decimal is a variant of NaN (i.e. sNaN, -NaN, +NaN, etc...) or a variant of
    // Inf (i.e. +Inf, Inf, -Inf), return either NaN, Infinity, or -Infinity
    if (!isFinite()) {
        if (this->isEqual(kPositiveInfinity)) {
            return "Infinity";
        } else if (this->isEqual(kNegativeInfinity)) {
            return "-Infinity";
        }
        invariant(isNaN());
        return "NaN";
    }
    BID_UINT128 dec128 = decimal128ToLibraryType(_value);
    char decimalCharRepresentation[1 /* mantissa sign */ + 34 /* mantissa */ +
                                   1 /* scientific E */ + 1 /* exponent sign */ + 4 /* exponent */ +
                                   1 /* null terminator */];
    std::uint32_t idec_signaling_flags = 0;
    /**
     * Use the library's defined to_string method, which returns a string composed of a
     * sign ('+' or '-')
     * 1 to 34 decimal digits (no leading zeros)
     * the character 'E'
     * sign ('+' or '-')
     * 1 to 4 decimal digits (no leading zeros)
     * For example: +10522E-3
     */
    bid128_to_string(decimalCharRepresentation, dec128, &idec_signaling_flags);

    std::string dec128String(decimalCharRepresentation);

    std::string::size_type ePos = dec128String.find("E");

    // Calculate the precision and exponent of the number and output it in a readable manner
    int precision = 0;
    int exponent = 0;
    int stringReadPosition = 0;

    std::string exponentString = dec128String.substr(ePos);

    // Get the value of the exponent, start at 2 to ignore the E and the sign
    for (std::string::size_type i = 2; i < exponentString.size(); ++i) {
        exponent = exponent * 10 + (exponentString[i] - '0');
    }
    if (exponentString[1] == '-') {
        exponent *= -1;
    }
    // Get the total precision of the number
    precision = dec128String.size() - exponentString.size() - 1 /* mantissa sign */;

    std::string result;
    // Initially result is set to equal just the sign of the dec128 string
    // For formatting, leave off the sign if it is positive
    if (dec128String[0] == '-')
        result = "-";
    stringReadPosition++;

    int scientificExponent = precision - 1 + exponent;

    // If the number is significantly large, small, or the user has specified an exponent
    // such that converting to string would need to append trailing zeros, display the
    // number in scientific notation
    if (scientificExponent >= 12 || scientificExponent <= -4 || exponent > 0) {
        // Output in scientific format
        result += dec128String.substr(stringReadPosition, 1);
        stringReadPosition++;
        precision--;
        if (precision)
            result += ".";
        result += dec128String.substr(stringReadPosition, precision);
        // Add the exponent
        result += "E";
        if (scientificExponent > 0)
            result += "+";
        result += std::to_string(scientificExponent);
    } else {
        // Regular format with no decimal place
        if (exponent >= 0) {
            result += dec128String.substr(stringReadPosition, precision);
            stringReadPosition += precision;
        } else {
            int radixPosition = precision + exponent;
            if (radixPosition > 0) {
                // Non-zero digits before radix point
                result += dec128String.substr(stringReadPosition, radixPosition);
                stringReadPosition += radixPosition;
            } else {
                // Leading zero before radix point
                result += "0";
            }

            result += ".";
            // Leading zeros after radix point
            while (radixPosition++ < 0)
                result += "0";

            result +=
                dec128String.substr(stringReadPosition, precision - std::max(radixPosition - 1, 0));
        }
    }

    return result;
}

bool Decimal128::isZero() const {
    return bid128_isZero(decimal128ToLibraryType(_value));
}

bool Decimal128::isNaN() const {
    return bid128_isNaN(decimal128ToLibraryType(_value));
}

bool Decimal128::isInfinite() const {
    return bid128_isInf(decimal128ToLibraryType(_value));
}

bool Decimal128::isFinite() const {
    return bid128_isFinite(decimal128ToLibraryType(_value));
}

bool Decimal128::isNegative() const {
    return bid128_isSigned(decimal128ToLibraryType(_value));
}

Decimal128 Decimal128::add(const Decimal128& other, RoundingMode roundMode) const {
    std::uint32_t throwAwayFlag = 0;
    return add(other, &throwAwayFlag, roundMode);
}

Decimal128 Decimal128::add(const Decimal128& other,
                           std::uint32_t* signalingFlags,
                           RoundingMode roundMode) const {
    BID_UINT128 current = decimal128ToLibraryType(_value);
    BID_UINT128 addend = decimal128ToLibraryType(other.getValue());
    current = bid128_add(current, addend, roundMode, signalingFlags);
    Decimal128::Value value = libraryTypeToValue(current);
    Decimal128 result(value);
    return result;
}

Decimal128 Decimal128::subtract(const Decimal128& other, RoundingMode roundMode) const {
    std::uint32_t throwAwayFlag = 0;
    return subtract(other, &throwAwayFlag, roundMode);
}

Decimal128 Decimal128::subtract(const Decimal128& other,
                                std::uint32_t* signalingFlags,
                                RoundingMode roundMode) const {
    BID_UINT128 current = decimal128ToLibraryType(_value);
    BID_UINT128 sub = decimal128ToLibraryType(other.getValue());
    current = bid128_sub(current, sub, roundMode, signalingFlags);
    Decimal128::Value value = libraryTypeToValue(current);
    Decimal128 result(value);
    return result;
}

Decimal128 Decimal128::multiply(const Decimal128& other, RoundingMode roundMode) const {
    std::uint32_t throwAwayFlag = 0;
    return multiply(other, &throwAwayFlag, roundMode);
}

Decimal128 Decimal128::multiply(const Decimal128& other,
                                std::uint32_t* signalingFlags,
                                RoundingMode roundMode) const {
    BID_UINT128 current = decimal128ToLibraryType(_value);
    BID_UINT128 factor = decimal128ToLibraryType(other.getValue());
    current = bid128_mul(current, factor, roundMode, signalingFlags);
    Decimal128::Value value = libraryTypeToValue(current);
    Decimal128 result(value);
    return result;
}

Decimal128 Decimal128::divide(const Decimal128& other, RoundingMode roundMode) const {
    std::uint32_t throwAwayFlag = 0;
    return divide(other, &throwAwayFlag, roundMode);
}

Decimal128 Decimal128::divide(const Decimal128& other,
                              std::uint32_t* signalingFlags,
                              RoundingMode roundMode) const {
    BID_UINT128 current = decimal128ToLibraryType(_value);
    BID_UINT128 divisor = decimal128ToLibraryType(other.getValue());
    current = bid128_div(current, divisor, roundMode, signalingFlags);
    Decimal128::Value value = libraryTypeToValue(current);
    Decimal128 result(value);
    return result;
}

Decimal128 Decimal128::quantize(const Decimal128& other, RoundingMode roundMode) const {
    std::uint32_t throwAwayFlag = 0;
    return quantize(other, &throwAwayFlag, roundMode);
}

Decimal128 Decimal128::quantize(const Decimal128& reference,
                                std::uint32_t* signalingFlags,
                                RoundingMode roundMode) const {
    BID_UINT128 current = decimal128ToLibraryType(_value);
    BID_UINT128 q = decimal128ToLibraryType(reference.getValue());
    BID_UINT128 quantizedResult = bid128_quantize(current, q, roundMode, signalingFlags);
    Decimal128::Value value = libraryTypeToValue(quantizedResult);
    Decimal128 result(value);
    return result;
}

bool Decimal128::isEqual(const Decimal128& other) const {
    std::uint32_t throwAwayFlag = 0;
    BID_UINT128 current = decimal128ToLibraryType(_value);
    BID_UINT128 compare = decimal128ToLibraryType(other.getValue());
    return bid128_quiet_equal(current, compare, &throwAwayFlag);
}

bool Decimal128::isNotEqual(const Decimal128& other) const {
    std::uint32_t throwAwayFlag = 0;
    BID_UINT128 current = decimal128ToLibraryType(_value);
    BID_UINT128 compare = decimal128ToLibraryType(other.getValue());
    return bid128_quiet_not_equal(current, compare, &throwAwayFlag);
}

bool Decimal128::isGreater(const Decimal128& other) const {
    std::uint32_t throwAwayFlag = 0;
    BID_UINT128 current = decimal128ToLibraryType(_value);
    BID_UINT128 compare = decimal128ToLibraryType(other.getValue());
    return bid128_quiet_greater(current, compare, &throwAwayFlag);
}

bool Decimal128::isGreaterEqual(const Decimal128& other) const {
    std::uint32_t throwAwayFlag = 0;
    BID_UINT128 current = decimal128ToLibraryType(_value);
    BID_UINT128 compare = decimal128ToLibraryType(other.getValue());
    return bid128_quiet_greater_equal(current, compare, &throwAwayFlag);
}

bool Decimal128::isLess(const Decimal128& other) const {
    std::uint32_t throwAwayFlag = 0;
    BID_UINT128 current = decimal128ToLibraryType(_value);
    BID_UINT128 compare = decimal128ToLibraryType(other.getValue());
    return bid128_quiet_less(current, compare, &throwAwayFlag);
}

bool Decimal128::isLessEqual(const Decimal128& other) const {
    std::uint32_t throwAwayFlag = 0;
    BID_UINT128 current = decimal128ToLibraryType(_value);
    BID_UINT128 compare = decimal128ToLibraryType(other.getValue());
    return bid128_quiet_less_equal(current, compare, &throwAwayFlag);
}

/**
 * The following static const variables are used to mathematically produce
 * frequently needed Decimal128 constants.
 */

namespace {
// Get the representation of 1 with 17 zeros (half of decimal128's 34 digit precision)
const std::uint64_t t17 = 100ull * 1000 * 1000 * 1000 * 1000 * 1000;
// Get the low 64 bits of 34 consecutive decimal 9's
// t17 * 17 gives 1 with 34 0's, so subtract 1 to get all 9's
const std::uint64_t t34lo64 = t17 * t17 - 1;
// Mod t17 by 2^32 to get the low 32 bits of t17's binary representation
const std::uint64_t t17lo32 = t17 % (1ull << 32);
// Divide t17 by 2^32 to get the high 32 bits of t17's binary representation
const std::uint64_t t17hi32 = t17 >> 32;
// Multiply t17 by t17 and keep the high 64 bits by distributing the operation to
// t17hi32*t17hi32 + 2*t17hi32*t17lo32 + t17lo32*t17lo32 where the 2nd term
// is shifted right by 32 and the 3rd term by 64 (which effectively drops the 3rd term)
const std::uint64_t t34hi64 = t17hi32 * t17hi32 + (((t17hi32 * t17lo32) >> 31));
static_assert(t34hi64 == 0x1ed09bead87c0, "");
static_assert(t34lo64 == 0x378d8e63ffffffff, "");
}  // namespace

// (t34hi64 << 64) + t34lo64 == 1e34 - 1
const Decimal128 Decimal128::kLargestPositive(0, Decimal128::kMaxBiasedExponent, t34hi64, t34lo64);
// The smallest positive decimal is 1 with the largest negative exponent of 0 (biased)
const Decimal128 Decimal128::kSmallestPositive(0, 0, 0, 1);

// Add a sign bit to the largest and smallest positive to get their corresponding negatives
const Decimal128 Decimal128::kLargestNegative(1, Decimal128::kMaxBiasedExponent, t34hi64, t34lo64);
const Decimal128 Decimal128::kSmallestNegative(1, 0, 0, 1);

// Get the representation of 0 (0E0).
const Decimal128 Decimal128::kNormalizedZero(Decimal128::Value(
    {0, static_cast<uint64_t>(Decimal128::kExponentBias) << Decimal128::kExponentFieldPos}));

// Get the representation of 0 with the most negative exponent
const Decimal128 Decimal128::kLargestNegativeExponentZero(Decimal128::Value({0ull, 0ull}));

// Shift the format of the combination bits to the right position to get Inf and NaN
// +Inf = 0111 1000 ... ... = 0x78 ... ..., -Inf = 1111 1000 ... ... = 0xf8 ... ...
// +NaN = 0111 1100 ... ... = 0x7c ... ..., -NaN = 1111 1100 ... ... = 0xfc ... ...
const Decimal128 Decimal128::kPositiveInfinity(Decimal128::Value({0ull, 0x78ull << 56}));
const Decimal128 Decimal128::kNegativeInfinity(Decimal128::Value({0ull, 0xf8ull << 56}));
const Decimal128 Decimal128::kPositiveNaN(Decimal128::Value({0ull, 0x7cull << 56}));
const Decimal128 Decimal128::kNegativeNaN(Decimal128::Value({0ull, 0xfcull << 56}));

std::ostream& operator<<(std::ostream& stream, const Decimal128& value) {
    return stream << value.toString();
}

}  // namespace mongo