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Diffstat (limited to 'sal/rtl/math.cxx')
| -rw-r--r-- | sal/rtl/math.cxx | 828 |
1 files changed, 828 insertions, 0 deletions
diff --git a/sal/rtl/math.cxx b/sal/rtl/math.cxx new file mode 100644 index 000000000..0d70e9718 --- /dev/null +++ b/sal/rtl/math.cxx @@ -0,0 +1,828 @@ +/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ +/* + * This file is part of the LibreOffice project. + * + * This Source Code Form is subject to the terms of the Mozilla Public + * License, v. 2.0. If a copy of the MPL was not distributed with this + * file, You can obtain one at http://mozilla.org/MPL/2.0/. + * + * This file incorporates work covered by the following license notice: + * + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed + * with this work for additional information regarding copyright + * ownership. The ASF licenses this file to you under the Apache + * License, Version 2.0 (the "License"); you may not use this file + * except in compliance with the License. You may obtain a copy of + * the License at http://www.apache.org/licenses/LICENSE-2.0 . + */ + +#include <rtl/math.h> + +#include <o3tl/safeint.hxx> +#include <osl/diagnose.h> +#include <rtl/character.hxx> +#include <rtl/math.hxx> + +#include <algorithm> +#include <cassert> +#include <cfenv> +#include <cmath> +#include <float.h> +#include <limits> +#include <limits.h> +#include <math.h> +#include <memory> +#include <stdlib.h> + +#include "strtmpl.hxx" + +#include <dtoa.h> + +constexpr int minExp = -323, maxExp = 308; +constexpr double n10s[] = { + 1e-323, 1e-322, 1e-321, 1e-320, 1e-319, 1e-318, 1e-317, 1e-316, 1e-315, 1e-314, 1e-313, 1e-312, + 1e-311, 1e-310, 1e-309, 1e-308, 1e-307, 1e-306, 1e-305, 1e-304, 1e-303, 1e-302, 1e-301, 1e-300, + 1e-299, 1e-298, 1e-297, 1e-296, 1e-295, 1e-294, 1e-293, 1e-292, 1e-291, 1e-290, 1e-289, 1e-288, + 1e-287, 1e-286, 1e-285, 1e-284, 1e-283, 1e-282, 1e-281, 1e-280, 1e-279, 1e-278, 1e-277, 1e-276, + 1e-275, 1e-274, 1e-273, 1e-272, 1e-271, 1e-270, 1e-269, 1e-268, 1e-267, 1e-266, 1e-265, 1e-264, + 1e-263, 1e-262, 1e-261, 1e-260, 1e-259, 1e-258, 1e-257, 1e-256, 1e-255, 1e-254, 1e-253, 1e-252, + 1e-251, 1e-250, 1e-249, 1e-248, 1e-247, 1e-246, 1e-245, 1e-244, 1e-243, 1e-242, 1e-241, 1e-240, + 1e-239, 1e-238, 1e-237, 1e-236, 1e-235, 1e-234, 1e-233, 1e-232, 1e-231, 1e-230, 1e-229, 1e-228, + 1e-227, 1e-226, 1e-225, 1e-224, 1e-223, 1e-222, 1e-221, 1e-220, 1e-219, 1e-218, 1e-217, 1e-216, + 1e-215, 1e-214, 1e-213, 1e-212, 1e-211, 1e-210, 1e-209, 1e-208, 1e-207, 1e-206, 1e-205, 1e-204, + 1e-203, 1e-202, 1e-201, 1e-200, 1e-199, 1e-198, 1e-197, 1e-196, 1e-195, 1e-194, 1e-193, 1e-192, + 1e-191, 1e-190, 1e-189, 1e-188, 1e-187, 1e-186, 1e-185, 1e-184, 1e-183, 1e-182, 1e-181, 1e-180, + 1e-179, 1e-178, 1e-177, 1e-176, 1e-175, 1e-174, 1e-173, 1e-172, 1e-171, 1e-170, 1e-169, 1e-168, + 1e-167, 1e-166, 1e-165, 1e-164, 1e-163, 1e-162, 1e-161, 1e-160, 1e-159, 1e-158, 1e-157, 1e-156, + 1e-155, 1e-154, 1e-153, 1e-152, 1e-151, 1e-150, 1e-149, 1e-148, 1e-147, 1e-146, 1e-145, 1e-144, + 1e-143, 1e-142, 1e-141, 1e-140, 1e-139, 1e-138, 1e-137, 1e-136, 1e-135, 1e-134, 1e-133, 1e-132, + 1e-131, 1e-130, 1e-129, 1e-128, 1e-127, 1e-126, 1e-125, 1e-124, 1e-123, 1e-122, 1e-121, 1e-120, + 1e-119, 1e-118, 1e-117, 1e-116, 1e-115, 1e-114, 1e-113, 1e-112, 1e-111, 1e-110, 1e-109, 1e-108, + 1e-107, 1e-106, 1e-105, 1e-104, 1e-103, 1e-102, 1e-101, 1e-100, 1e-99, 1e-98, 1e-97, 1e-96, + 1e-95, 1e-94, 1e-93, 1e-92, 1e-91, 1e-90, 1e-89, 1e-88, 1e-87, 1e-86, 1e-85, 1e-84, + 1e-83, 1e-82, 1e-81, 1e-80, 1e-79, 1e-78, 1e-77, 1e-76, 1e-75, 1e-74, 1e-73, 1e-72, + 1e-71, 1e-70, 1e-69, 1e-68, 1e-67, 1e-66, 1e-65, 1e-64, 1e-63, 1e-62, 1e-61, 1e-60, + 1e-59, 1e-58, 1e-57, 1e-56, 1e-55, 1e-54, 1e-53, 1e-52, 1e-51, 1e-50, 1e-49, 1e-48, + 1e-47, 1e-46, 1e-45, 1e-44, 1e-43, 1e-42, 1e-41, 1e-40, 1e-39, 1e-38, 1e-37, 1e-36, + 1e-35, 1e-34, 1e-33, 1e-32, 1e-31, 1e-30, 1e-29, 1e-28, 1e-27, 1e-26, 1e-25, 1e-24, + 1e-23, 1e-22, 1e-21, 1e-20, 1e-19, 1e-18, 1e-17, 1e-16, 1e-15, 1e-14, 1e-13, 1e-12, + 1e-11, 1e-10, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1e0, + 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, + 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22, 1e23, 1e24, + 1e25, 1e26, 1e27, 1e28, 1e29, 1e30, 1e31, 1e32, 1e33, 1e34, 1e35, 1e36, + 1e37, 1e38, 1e39, 1e40, 1e41, 1e42, 1e43, 1e44, 1e45, 1e46, 1e47, 1e48, + 1e49, 1e50, 1e51, 1e52, 1e53, 1e54, 1e55, 1e56, 1e57, 1e58, 1e59, 1e60, + 1e61, 1e62, 1e63, 1e64, 1e65, 1e66, 1e67, 1e68, 1e69, 1e70, 1e71, 1e72, + 1e73, 1e74, 1e75, 1e76, 1e77, 1e78, 1e79, 1e80, 1e81, 1e82, 1e83, 1e84, + 1e85, 1e86, 1e87, 1e88, 1e89, 1e90, 1e91, 1e92, 1e93, 1e94, 1e95, 1e96, + 1e97, 1e98, 1e99, 1e100, 1e101, 1e102, 1e103, 1e104, 1e105, 1e106, 1e107, 1e108, + 1e109, 1e110, 1e111, 1e112, 1e113, 1e114, 1e115, 1e116, 1e117, 1e118, 1e119, 1e120, + 1e121, 1e122, 1e123, 1e124, 1e125, 1e126, 1e127, 1e128, 1e129, 1e130, 1e131, 1e132, + 1e133, 1e134, 1e135, 1e136, 1e137, 1e138, 1e139, 1e140, 1e141, 1e142, 1e143, 1e144, + 1e145, 1e146, 1e147, 1e148, 1e149, 1e150, 1e151, 1e152, 1e153, 1e154, 1e155, 1e156, + 1e157, 1e158, 1e159, 1e160, 1e161, 1e162, 1e163, 1e164, 1e165, 1e166, 1e167, 1e168, + 1e169, 1e170, 1e171, 1e172, 1e173, 1e174, 1e175, 1e176, 1e177, 1e178, 1e179, 1e180, + 1e181, 1e182, 1e183, 1e184, 1e185, 1e186, 1e187, 1e188, 1e189, 1e190, 1e191, 1e192, + 1e193, 1e194, 1e195, 1e196, 1e197, 1e198, 1e199, 1e200, 1e201, 1e202, 1e203, 1e204, + 1e205, 1e206, 1e207, 1e208, 1e209, 1e210, 1e211, 1e212, 1e213, 1e214, 1e215, 1e216, + 1e217, 1e218, 1e219, 1e220, 1e221, 1e222, 1e223, 1e224, 1e225, 1e226, 1e227, 1e228, + 1e229, 1e230, 1e231, 1e232, 1e233, 1e234, 1e235, 1e236, 1e237, 1e238, 1e239, 1e240, + 1e241, 1e242, 1e243, 1e244, 1e245, 1e246, 1e247, 1e248, 1e249, 1e250, 1e251, 1e252, + 1e253, 1e254, 1e255, 1e256, 1e257, 1e258, 1e259, 1e260, 1e261, 1e262, 1e263, 1e264, + 1e265, 1e266, 1e267, 1e268, 1e269, 1e270, 1e271, 1e272, 1e273, 1e274, 1e275, 1e276, + 1e277, 1e278, 1e279, 1e280, 1e281, 1e282, 1e283, 1e284, 1e285, 1e286, 1e287, 1e288, + 1e289, 1e290, 1e291, 1e292, 1e293, 1e294, 1e295, 1e296, 1e297, 1e298, 1e299, 1e300, + 1e301, 1e302, 1e303, 1e304, 1e305, 1e306, 1e307, 1e308, +}; +static_assert(SAL_N_ELEMENTS(n10s) == maxExp - minExp + 1); + +// return pow(10.0,nExp) optimized for exponents in the interval [-323,308] (i.e., incl. denormals) +static double getN10Exp(int nExp) +{ + if (nExp < minExp || nExp > maxExp) + return pow(10.0, static_cast<double>(nExp)); // will return 0 or INF with IEEE 754 + return n10s[nExp - minExp]; +} + +namespace { + +/** If value (passed as absolute value) is an integer representable as double, + which we handle explicitly at some places. + */ +bool isRepresentableInteger(double fAbsValue) +{ + assert(fAbsValue >= 0.0); + const sal_Int64 kMaxInt = (static_cast< sal_Int64 >(1) << 53) - 1; + if (fAbsValue <= static_cast< double >(kMaxInt)) + { + sal_Int64 nInt = static_cast< sal_Int64 >(fAbsValue); + // Check the integer range again because double comparison may yield + // true within the precision range. + // XXX loplugin:fpcomparison complains about floating-point comparison + // for static_cast<double>(nInt) == fAbsValue, though we actually want + // this here. + if (nInt > kMaxInt) + return false; + double fInt = static_cast< double >(nInt); + return !(fInt < fAbsValue) && !(fInt > fAbsValue); + } + return false; +} + +// Returns 1-based index of least significant bit in a number, or zero if number is zero +int findFirstSetBit(unsigned n) +{ +#if defined _WIN32 + unsigned long pos; + unsigned char bNonZero = _BitScanForward(&pos, n); + return (bNonZero == 0) ? 0 : pos + 1; +#else + return __builtin_ffs(n); +#endif +} + +/** Returns number of binary bits for fractional part of the number + Expects a proper non-negative double value, not +-INF, not NAN + */ +int getBitsInFracPart(double fAbsValue) +{ + assert(std::isfinite(fAbsValue) && fAbsValue >= 0.0); + if (fAbsValue == 0.0) + return 0; + auto pValParts = reinterpret_cast< const sal_math_Double * >(&fAbsValue); + int nExponent = pValParts->inf_parts.exponent - 1023; + if (nExponent >= 52) + return 0; // All bits in fraction are in integer part of the number + int nLeastSignificant = findFirstSetBit(pValParts->inf_parts.fraction_lo); + if (nLeastSignificant == 0) + { + nLeastSignificant = findFirstSetBit(pValParts->inf_parts.fraction_hi); + if (nLeastSignificant == 0) + nLeastSignificant = 53; // the implied leading 1 is the least significant + else + nLeastSignificant += 32; + } + int nFracSignificant = 53 - nLeastSignificant; + int nBitsInFracPart = nFracSignificant - nExponent; + + return std::max(nBitsInFracPart, 0); +} + +} + +void SAL_CALL rtl_math_doubleToString(rtl_String ** pResult, + sal_Int32 * pResultCapacity, + sal_Int32 nResultOffset, double fValue, + rtl_math_StringFormat eFormat, + sal_Int32 nDecPlaces, + char cDecSeparator, + sal_Int32 const * pGroups, + char cGroupSeparator, + sal_Bool bEraseTrailingDecZeros) + SAL_THROW_EXTERN_C() +{ + rtl::str::doubleToString( + pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces, + cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros); +} + +void SAL_CALL rtl_math_doubleToUString(rtl_uString ** pResult, + sal_Int32 * pResultCapacity, + sal_Int32 nResultOffset, double fValue, + rtl_math_StringFormat eFormat, + sal_Int32 nDecPlaces, + sal_Unicode cDecSeparator, + sal_Int32 const * pGroups, + sal_Unicode cGroupSeparator, + sal_Bool bEraseTrailingDecZeros) + SAL_THROW_EXTERN_C() +{ + rtl::str::doubleToString( + pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces, + cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros); +} + +namespace { + +template< typename CharT > +double stringToDouble(CharT const * pBegin, CharT const * pEnd, + CharT cDecSeparator, CharT cGroupSeparator, + rtl_math_ConversionStatus * pStatus, + CharT const ** pParsedEnd) +{ + double fVal = 0.0; + rtl_math_ConversionStatus eStatus = rtl_math_ConversionStatus_Ok; + + CharT const * p0 = pBegin; + while (p0 != pEnd && (*p0 == CharT(' ') || *p0 == CharT('\t'))) + { + ++p0; + } + + bool bSign; + bool explicitSign = false; + if (p0 != pEnd && *p0 == CharT('-')) + { + bSign = true; + explicitSign = true; + ++p0; + } + else + { + bSign = false; + if (p0 != pEnd && *p0 == CharT('+')) + { + explicitSign = true; + ++p0; + } + } + + CharT const * p = p0; + bool bDone = false; + + // #i112652# XMLSchema-2 + if ((pEnd - p) >= 3) + { + if (!explicitSign && (CharT('N') == p[0]) && (CharT('a') == p[1]) + && (CharT('N') == p[2])) + { + p += 3; + fVal = std::numeric_limits<double>::quiet_NaN(); + bDone = true; + } + else if ((CharT('I') == p[0]) && (CharT('N') == p[1]) + && (CharT('F') == p[2])) + { + p += 3; + fVal = HUGE_VAL; + eStatus = rtl_math_ConversionStatus_OutOfRange; + bDone = true; + } + } + + if (!bDone) // do not recognize e.g. NaN1.23 + { + std::unique_ptr<char[]> bufInHeap; + std::unique_ptr<const CharT * []> bufInHeapMap; + constexpr int bufOnStackSize = 256; + char bufOnStack[bufOnStackSize]; + const CharT* bufOnStackMap[bufOnStackSize]; + char* buf = bufOnStack; + const CharT** bufmap = bufOnStackMap; + int bufpos = 0; + const size_t bufsize = pEnd - p + (bSign ? 2 : 1); + if (bufsize > bufOnStackSize) + { + bufInHeap = std::make_unique<char[]>(bufsize); + bufInHeapMap = std::make_unique<const CharT*[]>(bufsize); + buf = bufInHeap.get(); + bufmap = bufInHeapMap.get(); + } + + if (bSign) + { + buf[0] = '-'; + bufmap[0] = p; // yes, this may be the same pointer as for the next mapping + bufpos = 1; + } + // Put first zero to buffer for strings like "-0" + if (p != pEnd && *p == CharT('0')) + { + buf[bufpos] = '0'; + bufmap[bufpos] = p; + ++bufpos; + ++p; + } + // Leading zeros and group separators between digits may be safely + // ignored. p0 < p implies that there was a leading 0 already, + // consecutive group separators may not happen as *(p+1) is checked for + // digit. + while (p != pEnd && (*p == CharT('0') || (*p == cGroupSeparator + && p0 < p && p+1 < pEnd && rtl::isAsciiDigit(*(p+1))))) + { + ++p; + } + + // integer part of mantissa + for (; p != pEnd; ++p) + { + CharT c = *p; + if (rtl::isAsciiDigit(c)) + { + buf[bufpos] = static_cast<char>(c); + bufmap[bufpos] = p; + ++bufpos; + } + else if (c != cGroupSeparator) + { + break; + } + else if (p == p0 || (p+1 == pEnd) || !rtl::isAsciiDigit(*(p+1))) + { + // A leading or trailing (not followed by a digit) group + // separator character is not a group separator. + break; + } + } + + // fraction part of mantissa + if (p != pEnd && *p == cDecSeparator) + { + buf[bufpos] = '.'; + bufmap[bufpos] = p; + ++bufpos; + ++p; + + for (; p != pEnd; ++p) + { + CharT c = *p; + if (!rtl::isAsciiDigit(c)) + { + break; + } + buf[bufpos] = static_cast<char>(c); + bufmap[bufpos] = p; + ++bufpos; + } + } + + // Exponent + if (p != p0 && p != pEnd && (*p == CharT('E') || *p == CharT('e'))) + { + buf[bufpos] = 'E'; + bufmap[bufpos] = p; + ++bufpos; + ++p; + if (p != pEnd && *p == CharT('-')) + { + buf[bufpos] = '-'; + bufmap[bufpos] = p; + ++bufpos; + ++p; + } + else if (p != pEnd && *p == CharT('+')) + ++p; + + for (; p != pEnd; ++p) + { + CharT c = *p; + if (!rtl::isAsciiDigit(c)) + break; + + buf[bufpos] = static_cast<char>(c); + bufmap[bufpos] = p; + ++bufpos; + } + } + else if (p - p0 == 2 && p != pEnd && p[0] == CharT('#') + && p[-1] == cDecSeparator && p[-2] == CharT('1')) + { + if (pEnd - p >= 4 && p[1] == CharT('I') && p[2] == CharT('N') + && p[3] == CharT('F')) + { + // "1.#INF", "+1.#INF", "-1.#INF" + p += 4; + fVal = HUGE_VAL; + eStatus = rtl_math_ConversionStatus_OutOfRange; + // Eat any further digits: + while (p != pEnd && rtl::isAsciiDigit(*p)) + ++p; + bDone = true; + } + else if (pEnd - p >= 4 && p[1] == CharT('N') && p[2] == CharT('A') + && p[3] == CharT('N')) + { + // "1.#NAN", "+1.#NAN", "-1.#NAN" + p += 4; + fVal = std::copysign(std::numeric_limits<double>::quiet_NaN(), bSign ? -1.0 : 1.0); + bSign = false; // don't negate again + + // Eat any further digits: + while (p != pEnd && rtl::isAsciiDigit(*p)) + { + ++p; + } + bDone = true; + } + } + + if (!bDone) + { + buf[bufpos] = '\0'; + bufmap[bufpos] = p; + char* pCharParseEnd; + errno = 0; + fVal = strtod_nolocale(buf, &pCharParseEnd); + if (errno == ERANGE) + { + // Check for the dreaded rounded to 15 digits max value + // 1.79769313486232e+308 for 1.7976931348623157e+308 we wrote + // everywhere, accept with or without plus sign in exponent. + const char* b = buf; + if (b[0] == '-') + ++b; + if (((pCharParseEnd - b == 21) || (pCharParseEnd - b == 20)) + && !strncmp( b, "1.79769313486232", 16) + && (b[16] == 'e' || b[16] == 'E') + && (((pCharParseEnd - b == 21) && !strncmp( b+17, "+308", 4)) + || ((pCharParseEnd - b == 20) && !strncmp( b+17, "308", 3)))) + { + fVal = (buf < b) ? -DBL_MAX : DBL_MAX; + } + else + { + eStatus = rtl_math_ConversionStatus_OutOfRange; + } + } + p = bufmap[pCharParseEnd - buf]; + bSign = false; + } + } + + // overflow also if more than DBL_MAX_10_EXP digits without decimal + // separator, or 0. and more than DBL_MIN_10_EXP digits, ... + bool bHuge = fVal == HUGE_VAL; // g++ 3.0.1 requires it this way... + if (bHuge) + eStatus = rtl_math_ConversionStatus_OutOfRange; + + if (bSign) + fVal = -fVal; + + if (pStatus) + *pStatus = eStatus; + + if (pParsedEnd) + *pParsedEnd = p == p0 ? pBegin : p; + + return fVal; +} + +} + +double SAL_CALL rtl_math_stringToDouble(char const * pBegin, + char const * pEnd, + char cDecSeparator, + char cGroupSeparator, + rtl_math_ConversionStatus * pStatus, + char const ** pParsedEnd) + SAL_THROW_EXTERN_C() +{ + return stringToDouble( + reinterpret_cast<unsigned char const *>(pBegin), + reinterpret_cast<unsigned char const *>(pEnd), + static_cast<unsigned char>(cDecSeparator), + static_cast<unsigned char>(cGroupSeparator), pStatus, + reinterpret_cast<unsigned char const **>(pParsedEnd)); +} + +double SAL_CALL rtl_math_uStringToDouble(sal_Unicode const * pBegin, + sal_Unicode const * pEnd, + sal_Unicode cDecSeparator, + sal_Unicode cGroupSeparator, + rtl_math_ConversionStatus * pStatus, + sal_Unicode const ** pParsedEnd) + SAL_THROW_EXTERN_C() +{ + return stringToDouble(pBegin, pEnd, cDecSeparator, cGroupSeparator, pStatus, + pParsedEnd); +} + +double SAL_CALL rtl_math_round(double fValue, int nDecPlaces, + enum rtl_math_RoundingMode eMode) + SAL_THROW_EXTERN_C() +{ + if (!std::isfinite(fValue)) + return fValue; + + if (fValue == 0.0) + return fValue; + + if (nDecPlaces == 0) + { + switch (eMode) + { + case rtl_math_RoundingMode_Corrected: + return std::round(fValue); + case rtl_math_RoundingMode_HalfEven: + if (const int oldMode = std::fegetround(); std::fesetround(FE_TONEAREST) == 0) + { + fValue = std::nearbyint(fValue); + std::fesetround(oldMode); + return fValue; + } + break; + default: + break; + } + } + + const double fOrigValue = fValue; + + // sign adjustment + bool bSign = std::signbit( fValue ); + if (bSign) + fValue = -fValue; + + // Rounding to decimals between integer distance precision (gaps) does not + // make sense, do not even try to multiply/divide and introduce inaccuracy. + // For same reasons, do not attempt to round integers to decimals. + if (nDecPlaces >= 0 + && (fValue >= 0x1p52 + || isRepresentableInteger(fValue))) + return fOrigValue; + + double fFac = 0; + if (nDecPlaces != 0) + { + if (nDecPlaces > 0) + { + // Determine how many decimals are representable in the precision. + // Anything greater 2^52 and 0.0 was already ruled out above. + // Theoretically 0.5, 0.25, 0.125, 0.0625, 0.03125, ... + const sal_math_Double* pd = reinterpret_cast<const sal_math_Double*>(&fValue); + const sal_Int32 nDec = 52 - (pd->parts.exponent - 1023); + + if (nDec <= 0) + { + assert(!"Shouldn't this had been caught already as large number?"); + return fOrigValue; + } + + if (nDec < nDecPlaces) + nDecPlaces = nDec; + } + + // Avoid 1e-5 (1.0000000000000001e-05) and such inaccurate fractional + // factors that later when dividing back spoil things. For negative + // decimals divide first with the inverse, then multiply the rounded + // value back. + fFac = getN10Exp(abs(nDecPlaces)); + + if (fFac == 0.0 || (nDecPlaces < 0 && !std::isfinite(fFac))) + // Underflow, rounding to that many integer positions would be 0. + return 0.0; + + if (!std::isfinite(fFac)) + // Overflow with very small values and high number of decimals. + return fOrigValue; + + if (nDecPlaces < 0) + fValue /= fFac; + else + fValue *= fFac; + + if (!std::isfinite(fValue)) + return fOrigValue; + } + + // Round only if not already in distance precision gaps of integers, where + // for [2^52,2^53) adding 0.5 would even yield the next representable + // integer. + if (fValue < 0x1p52) + { + switch ( eMode ) + { + case rtl_math_RoundingMode_Corrected : + fValue = rtl::math::approxFloor(fValue + 0.5); + break; + case rtl_math_RoundingMode_Down: + fValue = rtl::math::approxFloor(fValue); + break; + case rtl_math_RoundingMode_Up: + fValue = rtl::math::approxCeil(fValue); + break; + case rtl_math_RoundingMode_Floor: + fValue = bSign ? rtl::math::approxCeil(fValue) + : rtl::math::approxFloor( fValue ); + break; + case rtl_math_RoundingMode_Ceiling: + fValue = bSign ? rtl::math::approxFloor(fValue) + : rtl::math::approxCeil(fValue); + break; + case rtl_math_RoundingMode_HalfDown : + { + double f = floor(fValue); + fValue = ((fValue - f) <= 0.5) ? f : ceil(fValue); + } + break; + case rtl_math_RoundingMode_HalfUp: + { + double f = floor(fValue); + fValue = ((fValue - f) < 0.5) ? f : ceil(fValue); + } + break; + case rtl_math_RoundingMode_HalfEven: +#if defined FLT_ROUNDS + /* + Use fast version. FLT_ROUNDS may be defined to a function by some compilers! + + DBL_EPSILON is the smallest fractional number which can be represented, + its reciprocal is therefore the smallest number that cannot have a + fractional part. Once you add this reciprocal to `x', its fractional part + is stripped off. Simply subtracting the reciprocal back out returns `x' + without its fractional component. + Simple, clever, and elegant - thanks to Ross Cottrell, the original author, + who placed it into public domain. + + volatile: prevent compiler from being too smart + */ + if (FLT_ROUNDS == 1) + { + volatile double x = fValue + 1.0 / DBL_EPSILON; + fValue = x - 1.0 / DBL_EPSILON; + } + else +#endif // FLT_ROUNDS + { + double f = floor(fValue); + if ((fValue - f) != 0.5) + { + fValue = floor( fValue + 0.5 ); + } + else + { + double g = f / 2.0; + fValue = (g == floor( g )) ? f : (f + 1.0); + } + } + break; + default: + OSL_ASSERT(false); + break; + } + } + + if (nDecPlaces != 0) + { + if (nDecPlaces < 0) + fValue *= fFac; + else + fValue /= fFac; + } + + if (!std::isfinite(fValue)) + return fOrigValue; + + return bSign ? -fValue : fValue; +} + +double SAL_CALL rtl_math_pow10Exp(double fValue, int nExp) SAL_THROW_EXTERN_C() +{ + return fValue * getN10Exp(nExp); +} + +double SAL_CALL rtl_math_approxValue( double fValue ) SAL_THROW_EXTERN_C() +{ + const double fBigInt = 0x1p41; // 2^41 -> only 11 bits left for fractional part, fine as decimal + if (fValue == 0.0 || fValue == HUGE_VAL || !std::isfinite( fValue) || fValue > fBigInt) + { + // We don't handle these conditions. Bail out. + return fValue; + } + + double fOrigValue = fValue; + + bool bSign = std::signbit(fValue); + if (bSign) + fValue = -fValue; + + // If the value is either integer representable as double, + // or only has small number of bits in fraction part, then we need not do any approximation + if (isRepresentableInteger(fValue) || getBitsInFracPart(fValue) <= 11) + return fOrigValue; + + int nExp = static_cast< int >(floor(log10(fValue))); + nExp = 14 - nExp; + double fExpValue = getN10Exp(abs(nExp)); + + if (nExp < 0) + fValue /= fExpValue; + else + fValue *= fExpValue; + + // If the original value was near DBL_MIN we got an overflow. Restore and + // bail out. + if (!std::isfinite(fValue)) + return fOrigValue; + + fValue = std::round(fValue); + + if (nExp < 0) + fValue *= fExpValue; + else + fValue /= fExpValue; + + // If the original value was near DBL_MAX we got an overflow. Restore and + // bail out. + if (!std::isfinite(fValue)) + return fOrigValue; + + return bSign ? -fValue : fValue; +} + +bool SAL_CALL rtl_math_approxEqual(double a, double b) SAL_THROW_EXTERN_C() +{ + static const double e48 = 0x1p-48; + static const double e44 = 0x1p-44; + + if (a == b) + return true; + + if (a == 0.0 || b == 0.0) + return false; + + const double d = fabs(a - b); + if (!std::isfinite(d)) + return false; // Nan or Inf involved + + a = fabs(a); + if (d > (a * e44)) + return false; + b = fabs(b); + if (d > (b * e44)) + return false; + + if (isRepresentableInteger(d) && isRepresentableInteger(a) && isRepresentableInteger(b)) + return false; // special case for representable integers. + + return (d < a * e48 && d < b * e48); +} + +double SAL_CALL rtl_math_expm1(double fValue) SAL_THROW_EXTERN_C() +{ + return expm1(fValue); +} + +double SAL_CALL rtl_math_log1p(double fValue) SAL_THROW_EXTERN_C() +{ +#ifdef __APPLE__ + if (fValue == -0.0) + return fValue; // macOS 10.8 libc returns 0.0 for -0.0 +#endif + + return log1p(fValue); +} + +double SAL_CALL rtl_math_atanh(double fValue) SAL_THROW_EXTERN_C() +{ + return ::atanh(fValue); +} + +/** Parent error function (erf) */ +double SAL_CALL rtl_math_erf(double x) SAL_THROW_EXTERN_C() +{ + return erf(x); +} + +/** Parent complementary error function (erfc) */ +double SAL_CALL rtl_math_erfc(double x) SAL_THROW_EXTERN_C() +{ + return erfc(x); +} + +/** improved accuracy of asinh for |x| large and for x near zero + @see #i97605# + */ +double SAL_CALL rtl_math_asinh(double fX) SAL_THROW_EXTERN_C() +{ + if ( fX == 0.0 ) + return 0.0; + + double fSign = 1.0; + if ( fX < 0.0 ) + { + fX = - fX; + fSign = -1.0; + } + + if ( fX < 0.125 ) + return fSign * rtl_math_log1p( fX + fX*fX / (1.0 + sqrt( 1.0 + fX*fX))); + + if ( fX < 1.25e7 ) + return fSign * log( fX + sqrt( 1.0 + fX*fX)); + + return fSign * log( 2.0*fX); +} + +/** improved accuracy of acosh for x large and for x near 1 + @see #i97605# + */ +double SAL_CALL rtl_math_acosh(double fX) SAL_THROW_EXTERN_C() +{ + volatile double fZ = fX - 1.0; + if (fX < 1.0) + return std::numeric_limits<double>::quiet_NaN(); + if ( fX == 1.0 ) + return 0.0; + + if ( fX < 1.1 ) + return rtl_math_log1p( fZ + sqrt( fZ*fZ + 2.0*fZ)); + + if ( fX < 1.25e7 ) + return log( fX + sqrt( fX*fX - 1.0)); + + return log( 2.0*fX); +} + +/* vim:set shiftwidth=4 softtabstop=4 expandtab: */ |