sal/rtl/math.cxx

   1 /* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
   2 /*
   3  * This file is part of the LibreOffice project.
   4  *
   5  * This Source Code Form is subject to the terms of the Mozilla Public
   6  * License, v. 2.0. If a copy of the MPL was not distributed with this
   7  * file, You can obtain one at http://mozilla.org/MPL/2.0/.
   8  *
   9  * This file incorporates work covered by the following license notice:
  10  *
  11  *   Licensed to the Apache Software Foundation (ASF) under one or more
  12  *   contributor license agreements. See the NOTICE file distributed
  13  *   with this work for additional information regarding copyright
  14  *   ownership. The ASF licenses this file to you under the Apache
  15  *   License, Version 2.0 (the "License"); you may not use this file
  16  *   except in compliance with the License. You may obtain a copy of
  17  *   the License at http://www.apache.org/licenses/LICENSE-2.0 .
  18  */
  19
  20 #include <rtl/math.h>
  21
  22 #include <o3tl/safeint.hxx>
  23 #include <osl/diagnose.h>
  24 #include <rtl/character.hxx>
  25 #include <rtl/math.hxx>
  26
  27 #include <algorithm>
  28 #include <cassert>
  29 #include <cfenv>
  30 #include <cmath>
  31 #include <float.h>
  32 #include <limits>
  33 #include <limits.h>
  34 #include <math.h>
  35 #include <memory>
  36 #include <stdlib.h>
  37
  38 #include "strtmpl.hxx"
  39
  40 #include <dtoa.h>
  41
  42 constexpr int minExp = -323, maxExp = 308;
  43 constexpr double n10s[] = {
  44     1e-323, 1e-322, 1e-321, 1e-320, 1e-319, 1e-318, 1e-317, 1e-316, 1e-315, 1e-314, 1e-313, 1e-312,
  45     1e-311, 1e-310, 1e-309, 1e-308, 1e-307, 1e-306, 1e-305, 1e-304, 1e-303, 1e-302, 1e-301, 1e-300,
  46     1e-299, 1e-298, 1e-297, 1e-296, 1e-295, 1e-294, 1e-293, 1e-292, 1e-291, 1e-290, 1e-289, 1e-288,
  47     1e-287, 1e-286, 1e-285, 1e-284, 1e-283, 1e-282, 1e-281, 1e-280, 1e-279, 1e-278, 1e-277, 1e-276,
  48     1e-275, 1e-274, 1e-273, 1e-272, 1e-271, 1e-270, 1e-269, 1e-268, 1e-267, 1e-266, 1e-265, 1e-264,
  49     1e-263, 1e-262, 1e-261, 1e-260, 1e-259, 1e-258, 1e-257, 1e-256, 1e-255, 1e-254, 1e-253, 1e-252,
  50     1e-251, 1e-250, 1e-249, 1e-248, 1e-247, 1e-246, 1e-245, 1e-244, 1e-243, 1e-242, 1e-241, 1e-240,
  51     1e-239, 1e-238, 1e-237, 1e-236, 1e-235, 1e-234, 1e-233, 1e-232, 1e-231, 1e-230, 1e-229, 1e-228,
  52     1e-227, 1e-226, 1e-225, 1e-224, 1e-223, 1e-222, 1e-221, 1e-220, 1e-219, 1e-218, 1e-217, 1e-216,
  53     1e-215, 1e-214, 1e-213, 1e-212, 1e-211, 1e-210, 1e-209, 1e-208, 1e-207, 1e-206, 1e-205, 1e-204,
  54     1e-203, 1e-202, 1e-201, 1e-200, 1e-199, 1e-198, 1e-197, 1e-196, 1e-195, 1e-194, 1e-193, 1e-192,
  55     1e-191, 1e-190, 1e-189, 1e-188, 1e-187, 1e-186, 1e-185, 1e-184, 1e-183, 1e-182, 1e-181, 1e-180,
  56     1e-179, 1e-178, 1e-177, 1e-176, 1e-175, 1e-174, 1e-173, 1e-172, 1e-171, 1e-170, 1e-169, 1e-168,
  57     1e-167, 1e-166, 1e-165, 1e-164, 1e-163, 1e-162, 1e-161, 1e-160, 1e-159, 1e-158, 1e-157, 1e-156,
  58     1e-155, 1e-154, 1e-153, 1e-152, 1e-151, 1e-150, 1e-149, 1e-148, 1e-147, 1e-146, 1e-145, 1e-144,
  59     1e-143, 1e-142, 1e-141, 1e-140, 1e-139, 1e-138, 1e-137, 1e-136, 1e-135, 1e-134, 1e-133, 1e-132,
  60     1e-131, 1e-130, 1e-129, 1e-128, 1e-127, 1e-126, 1e-125, 1e-124, 1e-123, 1e-122, 1e-121, 1e-120,
  61     1e-119, 1e-118, 1e-117, 1e-116, 1e-115, 1e-114, 1e-113, 1e-112, 1e-111, 1e-110, 1e-109, 1e-108,
  62     1e-107, 1e-106, 1e-105, 1e-104, 1e-103, 1e-102, 1e-101, 1e-100, 1e-99,  1e-98,  1e-97,  1e-96,
  63     1e-95,  1e-94,  1e-93,  1e-92,  1e-91,  1e-90,  1e-89,  1e-88,  1e-87,  1e-86,  1e-85,  1e-84,
  64     1e-83,  1e-82,  1e-81,  1e-80,  1e-79,  1e-78,  1e-77,  1e-76,  1e-75,  1e-74,  1e-73,  1e-72,
  65     1e-71,  1e-70,  1e-69,  1e-68,  1e-67,  1e-66,  1e-65,  1e-64,  1e-63,  1e-62,  1e-61,  1e-60,
  66     1e-59,  1e-58,  1e-57,  1e-56,  1e-55,  1e-54,  1e-53,  1e-52,  1e-51,  1e-50,  1e-49,  1e-48,
  67     1e-47,  1e-46,  1e-45,  1e-44,  1e-43,  1e-42,  1e-41,  1e-40,  1e-39,  1e-38,  1e-37,  1e-36,
  68     1e-35,  1e-34,  1e-33,  1e-32,  1e-31,  1e-30,  1e-29,  1e-28,  1e-27,  1e-26,  1e-25,  1e-24,
  69     1e-23,  1e-22,  1e-21,  1e-20,  1e-19,  1e-18,  1e-17,  1e-16,  1e-15,  1e-14,  1e-13,  1e-12,
  70     1e-11,  1e-10,  1e-9,   1e-8,   1e-7,   1e-6,   1e-5,   1e-4,   1e-3,   1e-2,   1e-1,   1e0,
  71     1e1,    1e2,    1e3,    1e4,    1e5,    1e6,    1e7,    1e8,    1e9,    1e10,   1e11,   1e12,
  72     1e13,   1e14,   1e15,   1e16,   1e17,   1e18,   1e19,   1e20,   1e21,   1e22,   1e23,   1e24,
  73     1e25,   1e26,   1e27,   1e28,   1e29,   1e30,   1e31,   1e32,   1e33,   1e34,   1e35,   1e36,
  74     1e37,   1e38,   1e39,   1e40,   1e41,   1e42,   1e43,   1e44,   1e45,   1e46,   1e47,   1e48,
  75     1e49,   1e50,   1e51,   1e52,   1e53,   1e54,   1e55,   1e56,   1e57,   1e58,   1e59,   1e60,
  76     1e61,   1e62,   1e63,   1e64,   1e65,   1e66,   1e67,   1e68,   1e69,   1e70,   1e71,   1e72,
  77     1e73,   1e74,   1e75,   1e76,   1e77,   1e78,   1e79,   1e80,   1e81,   1e82,   1e83,   1e84,
  78     1e85,   1e86,   1e87,   1e88,   1e89,   1e90,   1e91,   1e92,   1e93,   1e94,   1e95,   1e96,
  79     1e97,   1e98,   1e99,   1e100,  1e101,  1e102,  1e103,  1e104,  1e105,  1e106,  1e107,  1e108,
  80     1e109,  1e110,  1e111,  1e112,  1e113,  1e114,  1e115,  1e116,  1e117,  1e118,  1e119,  1e120,
  81     1e121,  1e122,  1e123,  1e124,  1e125,  1e126,  1e127,  1e128,  1e129,  1e130,  1e131,  1e132,
  82     1e133,  1e134,  1e135,  1e136,  1e137,  1e138,  1e139,  1e140,  1e141,  1e142,  1e143,  1e144,
  83     1e145,  1e146,  1e147,  1e148,  1e149,  1e150,  1e151,  1e152,  1e153,  1e154,  1e155,  1e156,
  84     1e157,  1e158,  1e159,  1e160,  1e161,  1e162,  1e163,  1e164,  1e165,  1e166,  1e167,  1e168,
  85     1e169,  1e170,  1e171,  1e172,  1e173,  1e174,  1e175,  1e176,  1e177,  1e178,  1e179,  1e180,
  86     1e181,  1e182,  1e183,  1e184,  1e185,  1e186,  1e187,  1e188,  1e189,  1e190,  1e191,  1e192,
  87     1e193,  1e194,  1e195,  1e196,  1e197,  1e198,  1e199,  1e200,  1e201,  1e202,  1e203,  1e204,
  88     1e205,  1e206,  1e207,  1e208,  1e209,  1e210,  1e211,  1e212,  1e213,  1e214,  1e215,  1e216,
  89     1e217,  1e218,  1e219,  1e220,  1e221,  1e222,  1e223,  1e224,  1e225,  1e226,  1e227,  1e228,
  90     1e229,  1e230,  1e231,  1e232,  1e233,  1e234,  1e235,  1e236,  1e237,  1e238,  1e239,  1e240,
  91     1e241,  1e242,  1e243,  1e244,  1e245,  1e246,  1e247,  1e248,  1e249,  1e250,  1e251,  1e252,
  92     1e253,  1e254,  1e255,  1e256,  1e257,  1e258,  1e259,  1e260,  1e261,  1e262,  1e263,  1e264,
  93     1e265,  1e266,  1e267,  1e268,  1e269,  1e270,  1e271,  1e272,  1e273,  1e274,  1e275,  1e276,
  94     1e277,  1e278,  1e279,  1e280,  1e281,  1e282,  1e283,  1e284,  1e285,  1e286,  1e287,  1e288,
  95     1e289,  1e290,  1e291,  1e292,  1e293,  1e294,  1e295,  1e296,  1e297,  1e298,  1e299,  1e300,
  96     1e301,  1e302,  1e303,  1e304,  1e305,  1e306,  1e307,  1e308,
  97 };
  98 static_assert(SAL_N_ELEMENTS(n10s) == maxExp - minExp + 1);
  99
 100 // return pow(10.0,nExp) optimized for exponents in the interval [-323,308] (i.e., incl. denormals)
 101 static double getN10Exp(int nExp)
 102 {
 103     if (nExp < minExp || nExp > maxExp)
 104         return pow(10.0, static_cast<double>(nExp)); // will return 0 or INF with IEEE 754
 105     return n10s[nExp - minExp];
 106 }
 107
 108 namespace {
 109
 110 /** If value (passed as absolute value) is an integer representable as double,
 111     which we handle explicitly at some places.
 112  */
 113 bool isRepresentableInteger(double fAbsValue)
 114 {
 115     assert(fAbsValue >= 0.0);
 116     const sal_Int64 kMaxInt = (static_cast< sal_Int64 >(1) << 53) - 1;
 117     if (fAbsValue <= static_cast< double >(kMaxInt))
 118     {
 119         sal_Int64 nInt = static_cast< sal_Int64 >(fAbsValue);
 120         // Check the integer range again because double comparison may yield
 121         // true within the precision range.
 122         // XXX loplugin:fpcomparison complains about floating-point comparison
 123         // for static_cast<double>(nInt) == fAbsValue, though we actually want
 124         // this here.
 125         if (nInt > kMaxInt)
 126             return false;
 127         double fInt = static_cast< double >(nInt);
 128         return !(fInt < fAbsValue) && !(fInt > fAbsValue);
 129     }
 130     return false;
 131 }
 132
 133 // Returns 1-based index of least significant bit in a number, or zero if number is zero
 134 int findFirstSetBit(unsigned n)
 135 {
 136 #if defined _WIN32
 137     unsigned long pos;
 138     unsigned char bNonZero = _BitScanForward(&pos, n);
 139     return (bNonZero == 0) ? 0 : pos + 1;
 140 #else
 141     return __builtin_ffs(n);
 142 #endif
 143 }
 144
 145 /** Returns number of binary bits for fractional part of the number
 146     Expects a proper non-negative double value, not +-INF, not NAN
 147  */
 148 int getBitsInFracPart(double fAbsValue)
 149 {
 150     assert(std::isfinite(fAbsValue) && fAbsValue >= 0.0);
 151     if (fAbsValue == 0.0)
 152         return 0;
 153     auto pValParts = reinterpret_cast< const sal_math_Double * >(&fAbsValue);
 154     int nExponent = pValParts->inf_parts.exponent - 1023;
 155     if (nExponent >= 52)
 156         return 0; // All bits in fraction are in integer part of the number
 157     int nLeastSignificant = findFirstSetBit(pValParts->inf_parts.fraction_lo);
 158     if (nLeastSignificant == 0)
 159     {
 160         nLeastSignificant = findFirstSetBit(pValParts->inf_parts.fraction_hi);
 161         if (nLeastSignificant == 0)
 162             nLeastSignificant = 53; // the implied leading 1 is the least significant
 163         else
 164             nLeastSignificant += 32;
 165     }
 166     int nFracSignificant = 53 - nLeastSignificant;
 167     int nBitsInFracPart = nFracSignificant - nExponent;
 168
 169     return std::max(nBitsInFracPart, 0);
 170 }
 171
 172 }
 173
 174 void SAL_CALL rtl_math_doubleToString(rtl_String ** pResult,
 175                                       sal_Int32 * pResultCapacity,
 176                                       sal_Int32 nResultOffset, double fValue,
 177                                       rtl_math_StringFormat eFormat,
 178                                       sal_Int32 nDecPlaces,
 179                                       char cDecSeparator,
 180                                       sal_Int32 const * pGroups,
 181                                       char cGroupSeparator,
 182                                       sal_Bool bEraseTrailingDecZeros)
 183     SAL_THROW_EXTERN_C()
 184 {
 185     rtl::str::doubleToString(
 186         pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces,
 187         cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros);
 188 }
 189
 190 void SAL_CALL rtl_math_doubleToUString(rtl_uString ** pResult,
 191                                        sal_Int32 * pResultCapacity,
 192                                        sal_Int32 nResultOffset, double fValue,
 193                                        rtl_math_StringFormat eFormat,
 194                                        sal_Int32 nDecPlaces,
 195                                        sal_Unicode cDecSeparator,
 196                                        sal_Int32 const * pGroups,
 197                                        sal_Unicode cGroupSeparator,
 198                                        sal_Bool bEraseTrailingDecZeros)
 199     SAL_THROW_EXTERN_C()
 200 {
 201     rtl::str::doubleToString(
 202         pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces,
 203         cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros);
 204 }
 205
 206 namespace {
 207
 208 template< typename CharT >
 209 double stringToDouble(CharT const * pBegin, CharT const * pEnd,
 210                              CharT cDecSeparator, CharT cGroupSeparator,
 211                              rtl_math_ConversionStatus * pStatus,
 212                              CharT const ** pParsedEnd)
 213 {
 214     double fVal = 0.0;
 215     rtl_math_ConversionStatus eStatus = rtl_math_ConversionStatus_Ok;
 216
 217     CharT const * p0 = pBegin;
 218     while (p0 != pEnd && (*p0 == CharT(' ') || *p0 == CharT('\t')))
 219     {
 220         ++p0;
 221     }
 222
 223     bool bSign;
 224     bool explicitSign = false;
 225     if (p0 != pEnd && *p0 == CharT('-'))
 226     {
 227         bSign = true;
 228         explicitSign = true;
 229         ++p0;
 230     }
 231     else
 232     {
 233         bSign = false;
 234         if (p0 != pEnd && *p0 == CharT('+'))
 235         {
 236             explicitSign = true;
 237             ++p0;
 238         }
 239     }
 240
 241     CharT const * p = p0;
 242     bool bDone = false;
 243
 244     // #i112652# XMLSchema-2
 245     if ((pEnd - p) >= 3)
 246     {
 247         if (!explicitSign && (CharT('N') == p[0]) && (CharT('a') == p[1])
 248             && (CharT('N') == p[2]))
 249         {
 250             p += 3;
 251             fVal = std::numeric_limits<double>::quiet_NaN();
 252             bDone = true;
 253         }
 254         else if ((CharT('I') == p[0]) && (CharT('N') == p[1])
 255                  && (CharT('F') == p[2]))
 256         {
 257             p += 3;
 258             fVal = HUGE_VAL;
 259             eStatus = rtl_math_ConversionStatus_OutOfRange;
 260             bDone = true;
 261         }
 262     }
 263
 264     if (!bDone) // do not recognize e.g. NaN1.23
 265     {
 266         std::unique_ptr<char[]> bufInHeap;
 267         std::unique_ptr<const CharT * []> bufInHeapMap;
 268         constexpr int bufOnStackSize = 256;
 269         char bufOnStack[bufOnStackSize];
 270         const CharT* bufOnStackMap[bufOnStackSize];
 271         char* buf = bufOnStack;
 272         const CharT** bufmap = bufOnStackMap;
 273         int bufpos = 0;
 274         const size_t bufsize = pEnd - p + (bSign ? 2 : 1);
 275         if (bufsize > bufOnStackSize)
 276         {
 277             bufInHeap = std::make_unique<char[]>(bufsize);
 278             bufInHeapMap = std::make_unique<const CharT*[]>(bufsize);
 279             buf = bufInHeap.get();
 280             bufmap = bufInHeapMap.get();
 281         }
 282
 283         if (bSign)
 284         {
 285             buf[0] = '-';
 286             bufmap[0] = p; // yes, this may be the same pointer as for the next mapping
 287             bufpos = 1;
 288         }
 289         // Put first zero to buffer for strings like "-0"
 290         if (p != pEnd && *p == CharT('0'))
 291         {
 292             buf[bufpos] = '0';
 293             bufmap[bufpos] = p;
 294             ++bufpos;
 295             ++p;
 296         }
 297         // Leading zeros and group separators between digits may be safely
 298         // ignored. p0 < p implies that there was a leading 0 already,
 299         // consecutive group separators may not happen as *(p+1) is checked for
 300         // digit.
 301         while (p != pEnd && (*p == CharT('0') || (*p == cGroupSeparator
 302                         && p0 < p && p+1 < pEnd && rtl::isAsciiDigit(*(p+1)))))
 303         {
 304             ++p;
 305         }
 306
 307         // integer part of mantissa
 308         for (; p != pEnd; ++p)
 309         {
 310             CharT c = *p;
 311             if (rtl::isAsciiDigit(c))
 312             {
 313                 buf[bufpos] = static_cast<char>(c);
 314                 bufmap[bufpos] = p;
 315                 ++bufpos;
 316             }
 317             else if (c != cGroupSeparator)
 318             {
 319                 break;
 320             }
 321             else if (p == p0 || (p+1 == pEnd) || !rtl::isAsciiDigit(*(p+1)))
 322             {
 323                 // A leading or trailing (not followed by a digit) group
 324                 // separator character is not a group separator.
 325                 break;
 326             }
 327         }
 328
 329         // fraction part of mantissa
 330         if (p != pEnd && *p == cDecSeparator)
 331         {
 332             buf[bufpos] = '.';
 333             bufmap[bufpos] = p;
 334             ++bufpos;
 335             ++p;
 336
 337             for (; p != pEnd; ++p)
 338             {
 339                 CharT c = *p;
 340                 if (!rtl::isAsciiDigit(c))
 341                 {
 342                     break;
 343                 }
 344                 buf[bufpos] = static_cast<char>(c);
 345                 bufmap[bufpos] = p;
 346                 ++bufpos;
 347             }
 348         }
 349
 350         // Exponent
 351         if (p != p0 && p != pEnd && (*p == CharT('E') || *p == CharT('e')))
 352         {
 353             buf[bufpos] = 'E';
 354             bufmap[bufpos] = p;
 355             ++bufpos;
 356             ++p;
 357             if (p != pEnd && *p == CharT('-'))
 358             {
 359                 buf[bufpos] = '-';
 360                 bufmap[bufpos] = p;
 361                 ++bufpos;
 362                 ++p;
 363             }
 364             else if (p != pEnd && *p == CharT('+'))
 365                 ++p;
 366
 367             for (; p != pEnd; ++p)
 368             {
 369                 CharT c = *p;
 370                 if (!rtl::isAsciiDigit(c))
 371                     break;
 372
 373                 buf[bufpos] = static_cast<char>(c);
 374                 bufmap[bufpos] = p;
 375                 ++bufpos;
 376             }
 377         }
 378         else if (p - p0 == 2 && p != pEnd && p[0] == CharT('#')
 379                  && p[-1] == cDecSeparator && p[-2] == CharT('1'))
 380         {
 381             if (pEnd - p >= 4 && p[1] == CharT('I') && p[2] == CharT('N')
 382                 && p[3] == CharT('F'))
 383             {
 384                 // "1.#INF", "+1.#INF", "-1.#INF"
 385                 p += 4;
 386                 fVal = HUGE_VAL;
 387                 eStatus = rtl_math_ConversionStatus_OutOfRange;
 388                 // Eat any further digits:
 389                 while (p != pEnd && rtl::isAsciiDigit(*p))
 390                     ++p;
 391                 bDone = true;
 392             }
 393             else if (pEnd - p >= 4 && p[1] == CharT('N') && p[2] == CharT('A')
 394                 && p[3] == CharT('N'))
 395             {
 396                 // "1.#NAN", "+1.#NAN", "-1.#NAN"
 397                 p += 4;
 398                 fVal = std::copysign(std::numeric_limits<double>::quiet_NaN(), bSign ? -1.0 : 1.0);
 399                 bSign = false; // don't negate again
 400
 401                 // Eat any further digits:
 402                 while (p != pEnd && rtl::isAsciiDigit(*p))
 403                 {
 404                     ++p;
 405                 }
 406                 bDone = true;
 407             }
 408         }
 409
 410         if (!bDone)
 411         {
 412             buf[bufpos] = '\0';
 413             bufmap[bufpos] = p;
 414             char* pCharParseEnd;
 415             errno = 0;
 416             fVal = strtod_nolocale(buf, &pCharParseEnd);
 417             if (errno == ERANGE)
 418             {
 419                 // Check for the dreaded rounded to 15 digits max value
 420                 // 1.79769313486232e+308 for 1.7976931348623157e+308 we wrote
 421                 // everywhere, accept with or without plus sign in exponent.
 422                 const char* b = buf;
 423                 if (b[0] == '-')
 424                     ++b;
 425                 if (((pCharParseEnd - b == 21) || (pCharParseEnd - b == 20))
 426                         && !strncmp( b, "1.79769313486232", 16)
 427                         && (b[16] == 'e' || b[16] == 'E')
 428                         && (((pCharParseEnd - b == 21) && !strncmp( b+17, "+308", 4))
 429                          || ((pCharParseEnd - b == 20) && !strncmp( b+17, "308", 3))))
 430                 {
 431                     fVal = (buf < b) ? -DBL_MAX : DBL_MAX;
 432                 }
 433                 else
 434                 {
 435                     eStatus = rtl_math_ConversionStatus_OutOfRange;
 436                 }
 437             }
 438             p = bufmap[pCharParseEnd - buf];
 439             bSign = false;
 440         }
 441     }
 442
 443     // overflow also if more than DBL_MAX_10_EXP digits without decimal
 444     // separator, or 0. and more than DBL_MIN_10_EXP digits, ...
 445     bool bHuge = fVal == HUGE_VAL; // g++ 3.0.1 requires it this way...
 446     if (bHuge)
 447         eStatus = rtl_math_ConversionStatus_OutOfRange;
 448
 449     if (bSign)
 450         fVal = -fVal;
 451
 452     if (pStatus)
 453         *pStatus = eStatus;
 454
 455     if (pParsedEnd)
 456         *pParsedEnd = p == p0 ? pBegin : p;
 457
 458     return fVal;
 459 }
 460
 461 }
 462
 463 double SAL_CALL rtl_math_stringToDouble(char const * pBegin,
 464                                         char const * pEnd,
 465                                         char cDecSeparator,
 466                                         char cGroupSeparator,
 467                                         rtl_math_ConversionStatus * pStatus,
 468                                         char const ** pParsedEnd)
 469     SAL_THROW_EXTERN_C()
 470 {
 471     return stringToDouble(
 472         reinterpret_cast<unsigned char const *>(pBegin),
 473         reinterpret_cast<unsigned char const *>(pEnd),
 474         static_cast<unsigned char>(cDecSeparator),
 475         static_cast<unsigned char>(cGroupSeparator), pStatus,
 476         reinterpret_cast<unsigned char const **>(pParsedEnd));
 477 }
 478
 479 double SAL_CALL rtl_math_uStringToDouble(sal_Unicode const * pBegin,
 480                                          sal_Unicode const * pEnd,
 481                                          sal_Unicode cDecSeparator,
 482                                          sal_Unicode cGroupSeparator,
 483                                          rtl_math_ConversionStatus * pStatus,
 484                                          sal_Unicode const ** pParsedEnd)
 485     SAL_THROW_EXTERN_C()
 486 {
 487     return stringToDouble(pBegin, pEnd, cDecSeparator, cGroupSeparator, pStatus,
 488                           pParsedEnd);
 489 }
 490
 491 double SAL_CALL rtl_math_round(double fValue, int nDecPlaces,
 492                                enum rtl_math_RoundingMode eMode)
 493     SAL_THROW_EXTERN_C()
 494 {
 495     if (!std::isfinite(fValue))
 496         return fValue;
 497
 498     if (fValue == 0.0)
 499         return fValue;
 500
 501     if (nDecPlaces == 0)
 502     {
 503         switch (eMode)
 504         {
 505             case rtl_math_RoundingMode_Corrected:
 506                 return std::round(fValue);
 507             case rtl_math_RoundingMode_HalfEven:
 508                 if (const int oldMode = std::fegetround(); std::fesetround(FE_TONEAREST) == 0)
 509                 {
 510                     fValue = std::nearbyint(fValue);
 511                     std::fesetround(oldMode);
 512                     return fValue;
 513                 }
 514                 break;
 515             default:
 516                 break;
 517         }
 518     }
 519
 520     const double fOrigValue = fValue;
 521
 522     // sign adjustment
 523     bool bSign = std::signbit( fValue );
 524     if (bSign)
 525         fValue = -fValue;
 526
 527     // Rounding to decimals between integer distance precision (gaps) does not
 528     // make sense, do not even try to multiply/divide and introduce inaccuracy.
 529     // For same reasons, do not attempt to round integers to decimals.
 530     if (nDecPlaces >= 0
 531             && (fValue >= 0x1p52
 532                 || isRepresentableInteger(fValue)))
 533         return fOrigValue;
 534
 535     double fFac = 0;
 536     if (nDecPlaces != 0)
 537     {
 538         if (nDecPlaces > 0)
 539         {
 540             // Determine how many decimals are representable in the precision.
 541             // Anything greater 2^52 and 0.0 was already ruled out above.
 542             // Theoretically 0.5, 0.25, 0.125, 0.0625, 0.03125, ...
 543             const sal_math_Double* pd = reinterpret_cast<const sal_math_Double*>(&fValue);
 544             const sal_Int32 nDec = 52 - (pd->parts.exponent - 1023);
 545
 546             if (nDec <= 0)
 547             {
 548                 assert(!"Shouldn't this had been caught already as large number?");
 549                 return fOrigValue;
 550             }
 551
 552             if (nDec < nDecPlaces)
 553                 nDecPlaces = nDec;
 554         }
 555
 556         // Avoid 1e-5 (1.0000000000000001e-05) and such inaccurate fractional
 557         // factors that later when dividing back spoil things. For negative
 558         // decimals divide first with the inverse, then multiply the rounded
 559         // value back.
 560         fFac = getN10Exp(abs(nDecPlaces));
 561
 562         if (fFac == 0.0 || (nDecPlaces < 0 && !std::isfinite(fFac)))
 563             // Underflow, rounding to that many integer positions would be 0.
 564             return 0.0;
 565
 566         if (!std::isfinite(fFac))
 567             // Overflow with very small values and high number of decimals.
 568             return fOrigValue;
 569
 570         if (nDecPlaces < 0)
 571             fValue /= fFac;
 572         else
 573             fValue *= fFac;
 574
 575         if (!std::isfinite(fValue))
 576             return fOrigValue;
 577     }
 578
 579     // Round only if not already in distance precision gaps of integers, where
 580     // for [2^52,2^53) adding 0.5 would even yield the next representable
 581     // integer.
 582     if (fValue < 0x1p52)
 583     {
 584         switch ( eMode )
 585         {
 586             case rtl_math_RoundingMode_Corrected :
 587                 fValue = rtl::math::approxFloor(fValue + 0.5);
 588             break;
 589             case rtl_math_RoundingMode_Down:
 590                 fValue = rtl::math::approxFloor(fValue);
 591             break;
 592             case rtl_math_RoundingMode_Up:
 593                 fValue = rtl::math::approxCeil(fValue);
 594             break;
 595             case rtl_math_RoundingMode_Floor:
 596                 fValue = bSign ? rtl::math::approxCeil(fValue)
 597                     : rtl::math::approxFloor( fValue );
 598             break;
 599             case rtl_math_RoundingMode_Ceiling:
 600                 fValue = bSign ? rtl::math::approxFloor(fValue)
 601                     : rtl::math::approxCeil(fValue);
 602             break;
 603             case rtl_math_RoundingMode_HalfDown :
 604                 {
 605                     double f = floor(fValue);
 606                     fValue = ((fValue - f) <= 0.5) ? f : ceil(fValue);
 607                 }
 608             break;
 609             case rtl_math_RoundingMode_HalfUp:
 610                 {
 611                     double f = floor(fValue);
 612                     fValue = ((fValue - f) < 0.5) ? f : ceil(fValue);
 613                 }
 614             break;
 615             case rtl_math_RoundingMode_HalfEven:
 616 #if defined FLT_ROUNDS
 617                 /*
 618                    Use fast version. FLT_ROUNDS may be defined to a function by some compilers!
 619
 620                    DBL_EPSILON is the smallest fractional number which can be represented,
 621                    its reciprocal is therefore the smallest number that cannot have a
 622                    fractional part. Once you add this reciprocal to `x', its fractional part
 623                    is stripped off. Simply subtracting the reciprocal back out returns `x'
 624                    without its fractional component.
 625                    Simple, clever, and elegant - thanks to Ross Cottrell, the original author,
 626                    who placed it into public domain.
 627
 628                    volatile: prevent compiler from being too smart
 629                 */
 630                 if (FLT_ROUNDS == 1)
 631                 {
 632                     volatile double x = fValue + 1.0 / DBL_EPSILON;
 633                     fValue = x - 1.0 / DBL_EPSILON;
 634                 }
 635                 else
 636 #endif // FLT_ROUNDS
 637                 {
 638                     double f = floor(fValue);
 639                     if ((fValue - f) != 0.5)
 640                     {
 641                         fValue = floor( fValue + 0.5 );
 642                     }
 643                     else
 644                     {
 645                         double g = f / 2.0;
 646                         fValue = (g == floor( g )) ? f : (f + 1.0);
 647                     }
 648                 }
 649             break;
 650             default:
 651                 OSL_ASSERT(false);
 652             break;
 653         }
 654     }
 655
 656     if (nDecPlaces != 0)
 657     {
 658         if (nDecPlaces < 0)
 659             fValue *= fFac;
 660         else
 661             fValue /= fFac;
 662     }
 663
 664     if (!std::isfinite(fValue))
 665         return fOrigValue;
 666
 667     return bSign ? -fValue : fValue;
 668 }
 669
 670 double SAL_CALL rtl_math_pow10Exp(double fValue, int nExp) SAL_THROW_EXTERN_C()
 671 {
 672     return fValue * getN10Exp(nExp);
 673 }
 674
 675 double SAL_CALL rtl_math_approxValue( double fValue ) SAL_THROW_EXTERN_C()
 676 {
 677     const double fBigInt = 0x1p41; // 2^41 -> only 11 bits left for fractional part, fine as decimal
 678     if (fValue == 0.0 || fValue == HUGE_VAL || !std::isfinite( fValue) || fValue > fBigInt)
 679     {
 680         // We don't handle these conditions.  Bail out.
 681         return fValue;
 682     }
 683
 684     double fOrigValue = fValue;
 685
 686     bool bSign = std::signbit(fValue);
 687     if (bSign)
 688         fValue = -fValue;
 689
 690     // If the value is either integer representable as double,
 691     // or only has small number of bits in fraction part, then we need not do any approximation
 692     if (isRepresentableInteger(fValue) || getBitsInFracPart(fValue) <= 11)
 693         return fOrigValue;
 694
 695     int nExp = static_cast< int >(floor(log10(fValue)));
 696     nExp = 14 - nExp;
 697     double fExpValue = getN10Exp(abs(nExp));
 698
 699     if (nExp < 0)
 700         fValue /= fExpValue;
 701     else
 702         fValue *= fExpValue;
 703
 704     // If the original value was near DBL_MIN we got an overflow. Restore and
 705     // bail out.
 706     if (!std::isfinite(fValue))
 707         return fOrigValue;
 708
 709     fValue = std::round(fValue);
 710
 711     if (nExp < 0)
 712         fValue *= fExpValue;
 713     else
 714         fValue /= fExpValue;
 715
 716     // If the original value was near DBL_MAX we got an overflow. Restore and
 717     // bail out.
 718     if (!std::isfinite(fValue))
 719         return fOrigValue;
 720
 721     return bSign ? -fValue : fValue;
 722 }
 723
 724 bool SAL_CALL rtl_math_approxEqual(double a, double b) SAL_THROW_EXTERN_C()
 725 {
 726     static const double e48 = 0x1p-48;
 727     static const double e44 = 0x1p-44;
 728
 729     if (a == b)
 730         return true;
 731
 732     if (a == 0.0 || b == 0.0)
 733         return false;
 734
 735     const double d = fabs(a - b);
 736     if (!std::isfinite(d))
 737         return false;   // Nan or Inf involved
 738
 739     a = fabs(a);
 740     if (d > (a * e44))
 741         return false;
 742     b = fabs(b);
 743     if (d > (b * e44))
 744         return false;
 745
 746     if (isRepresentableInteger(d) && isRepresentableInteger(a) && isRepresentableInteger(b))
 747         return false;   // special case for representable integers.
 748
 749     return (d < a * e48 && d < b * e48);
 750 }
 751
 752 double SAL_CALL rtl_math_expm1(double fValue) SAL_THROW_EXTERN_C()
 753 {
 754     return expm1(fValue);
 755 }
 756
 757 double SAL_CALL rtl_math_log1p(double fValue) SAL_THROW_EXTERN_C()
 758 {
 759 #ifdef __APPLE__
 760     if (fValue == -0.0)
 761         return fValue; // macOS 10.8 libc returns 0.0 for -0.0
 762 #endif
 763
 764     return log1p(fValue);
 765 }
 766
 767 double SAL_CALL rtl_math_atanh(double fValue) SAL_THROW_EXTERN_C()
 768 {
 769     return ::atanh(fValue);
 770 }
 771
 772 /** Parent error function (erf) */
 773 double SAL_CALL rtl_math_erf(double x) SAL_THROW_EXTERN_C()
 774 {
 775     return erf(x);
 776 }
 777
 778 /** Parent complementary error function (erfc) */
 779 double SAL_CALL rtl_math_erfc(double x) SAL_THROW_EXTERN_C()
 780 {
 781     return erfc(x);
 782 }
 783
 784 /** improved accuracy of asinh for |x| large and for x near zero
 785     @see #i97605#
 786  */
 787 double SAL_CALL rtl_math_asinh(double fX) SAL_THROW_EXTERN_C()
 788 {
 789     if ( fX == 0.0 )
 790         return 0.0;
 791
 792     double fSign = 1.0;
 793     if ( fX < 0.0 )
 794     {
 795         fX = - fX;
 796         fSign = -1.0;
 797     }
 798
 799     if ( fX < 0.125 )
 800         return fSign * rtl_math_log1p( fX + fX*fX / (1.0 + sqrt( 1.0 + fX*fX)));
 801
 802     if ( fX < 1.25e7 )
 803         return fSign * log( fX + sqrt( 1.0 + fX*fX));
 804
 805     return fSign * log( 2.0*fX);
 806 }
 807
 808 /** improved accuracy of acosh for x large and for x near 1
 809     @see #i97605#
 810  */
 811 double SAL_CALL rtl_math_acosh(double fX) SAL_THROW_EXTERN_C()
 812 {
 813     volatile double fZ = fX - 1.0;
 814     if (fX < 1.0)
 815         return std::numeric_limits<double>::quiet_NaN();
 816     if ( fX == 1.0 )
 817         return 0.0;
 818
 819     if ( fX < 1.1 )
 820         return rtl_math_log1p( fZ + sqrt( fZ*fZ + 2.0*fZ));
 821
 822     if ( fX < 1.25e7 )
 823         return log( fX + sqrt( fX*fX - 1.0));
 824
 825     return log( 2.0*fX);
 826 }
 827
 828 /* vim:set shiftwidth=4 softtabstop=4 expandtab: */