1 /************************************************************** 2 * 3 * Licensed to the Apache Software Foundation (ASF) under one 4 * or more contributor license agreements. See the NOTICE file 5 * distributed with this work for additional information 6 * regarding copyright ownership. The ASF licenses this file 7 * to you under the Apache License, Version 2.0 (the 8 * "License"); you may not use this file except in compliance 9 * with the License. You may obtain a copy of the License at 10 * 11 * http://www.apache.org/licenses/LICENSE-2.0 12 * 13 * Unless required by applicable law or agreed to in writing, 14 * software distributed under the License is distributed on an 15 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY 16 * KIND, either express or implied. See the License for the 17 * specific language governing permissions and limitations 18 * under the License. 19 * 20 *************************************************************/ 21 22 23 24 // MARKER(update_precomp.py): autogen include statement, do not remove 25 #include "precompiled_sal.hxx" 26 27 #include "rtl/math.h" 28 29 #include "osl/diagnose.h" 30 #include "rtl/alloc.h" 31 #include "rtl/math.hxx" 32 #include "rtl/strbuf.h" 33 #include "rtl/string.h" 34 #include "rtl/ustrbuf.h" 35 #include "rtl/ustring.h" 36 #include "sal/mathconf.h" 37 #include "sal/types.h" 38 39 #include <algorithm> 40 #include <float.h> 41 #include <limits.h> 42 #include <math.h> 43 #include <stdlib.h> 44 45 46 static int const n10Count = 16; 47 static double const n10s[2][n10Count] = { 48 { 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 49 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16 }, 50 { 1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7, 1e-8, 51 1e-9, 1e-10, 1e-11, 1e-12, 1e-13, 1e-14, 1e-15, 1e-16 } 52 }; 53 54 // return pow(10.0,nExp) optimized for exponents in the interval [-16,16] 55 static double getN10Exp( int nExp ) 56 { 57 if ( nExp < 0 ) 58 { 59 if ( -nExp <= n10Count ) 60 return n10s[1][-nExp-1]; 61 else 62 return pow( 10.0, static_cast<double>( nExp ) ); 63 } 64 else if ( nExp > 0 ) 65 { 66 if ( nExp <= n10Count ) 67 return n10s[0][nExp-1]; 68 else 69 return pow( 10.0, static_cast<double>( nExp ) ); 70 } 71 else // ( nExp == 0 ) 72 return 1.0; 73 } 74 75 /** Approximation algorithm for erf for 0 < x < 0.65. */ 76 void lcl_Erf0065( double x, double& fVal ) 77 { 78 static const double pn[] = { 79 1.12837916709551256, 80 1.35894887627277916E-1, 81 4.03259488531795274E-2, 82 1.20339380863079457E-3, 83 6.49254556481904354E-5 84 }; 85 static const double qn[] = { 86 1.00000000000000000, 87 4.53767041780002545E-1, 88 8.69936222615385890E-2, 89 8.49717371168693357E-3, 90 3.64915280629351082E-4 91 }; 92 double fPSum = 0.0; 93 double fQSum = 0.0; 94 double fXPow = 1.0; 95 for ( unsigned int i = 0; i <= 4; ++i ) 96 { 97 fPSum += pn[i]*fXPow; 98 fQSum += qn[i]*fXPow; 99 fXPow *= x*x; 100 } 101 fVal = x * fPSum / fQSum; 102 } 103 104 /** Approximation algorithm for erfc for 0.65 < x < 6.0. */ 105 void lcl_Erfc0600( double x, double& fVal ) 106 { 107 double fPSum = 0.0; 108 double fQSum = 0.0; 109 double fXPow = 1.0; 110 const double *pn; 111 const double *qn; 112 113 if ( x < 2.2 ) 114 { 115 static const double pn22[] = { 116 9.99999992049799098E-1, 117 1.33154163936765307, 118 8.78115804155881782E-1, 119 3.31899559578213215E-1, 120 7.14193832506776067E-2, 121 7.06940843763253131E-3 122 }; 123 static const double qn22[] = { 124 1.00000000000000000, 125 2.45992070144245533, 126 2.65383972869775752, 127 1.61876655543871376, 128 5.94651311286481502E-1, 129 1.26579413030177940E-1, 130 1.25304936549413393E-2 131 }; 132 pn = pn22; 133 qn = qn22; 134 } 135 else /* if ( x < 6.0 ) this is true, but the compiler does not know */ 136 { 137 static const double pn60[] = { 138 9.99921140009714409E-1, 139 1.62356584489366647, 140 1.26739901455873222, 141 5.81528574177741135E-1, 142 1.57289620742838702E-1, 143 2.25716982919217555E-2 144 }; 145 static const double qn60[] = { 146 1.00000000000000000, 147 2.75143870676376208, 148 3.37367334657284535, 149 2.38574194785344389, 150 1.05074004614827206, 151 2.78788439273628983E-1, 152 4.00072964526861362E-2 153 }; 154 pn = pn60; 155 qn = qn60; 156 } 157 158 for ( unsigned int i = 0; i < 6; ++i ) 159 { 160 fPSum += pn[i]*fXPow; 161 fQSum += qn[i]*fXPow; 162 fXPow *= x; 163 } 164 fQSum += qn[6]*fXPow; 165 fVal = exp( -1.0*x*x )* fPSum / fQSum; 166 } 167 168 /** Approximation algorithm for erfc for 6.0 < x < 26.54 (but used for all 169 x > 6.0). */ 170 void lcl_Erfc2654( double x, double& fVal ) 171 { 172 static const double pn[] = { 173 5.64189583547756078E-1, 174 8.80253746105525775, 175 3.84683103716117320E1, 176 4.77209965874436377E1, 177 8.08040729052301677 178 }; 179 static const double qn[] = { 180 1.00000000000000000, 181 1.61020914205869003E1, 182 7.54843505665954743E1, 183 1.12123870801026015E2, 184 3.73997570145040850E1 185 }; 186 187 double fPSum = 0.0; 188 double fQSum = 0.0; 189 double fXPow = 1.0; 190 191 for ( unsigned int i = 0; i <= 4; ++i ) 192 { 193 fPSum += pn[i]*fXPow; 194 fQSum += qn[i]*fXPow; 195 fXPow /= x*x; 196 } 197 fVal = exp(-1.0*x*x)*fPSum / (x*fQSum); 198 } 199 200 namespace { 201 202 double const nKorrVal[] = { 203 0, 9e-1, 9e-2, 9e-3, 9e-4, 9e-5, 9e-6, 9e-7, 9e-8, 204 9e-9, 9e-10, 9e-11, 9e-12, 9e-13, 9e-14, 9e-15 205 }; 206 207 struct StringTraits 208 { 209 typedef sal_Char Char; 210 211 typedef rtl_String String; 212 213 static inline void createString(rtl_String ** pString, 214 sal_Char const * pChars, sal_Int32 nLen) 215 { 216 rtl_string_newFromStr_WithLength(pString, pChars, nLen); 217 } 218 219 static inline void createBuffer(rtl_String ** pBuffer, 220 sal_Int32 * pCapacity) 221 { 222 rtl_string_new_WithLength(pBuffer, *pCapacity); 223 } 224 225 static inline void appendChar(rtl_String ** pBuffer, sal_Int32 * pCapacity, 226 sal_Int32 * pOffset, sal_Char cChar) 227 { 228 rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, &cChar, 1); 229 ++*pOffset; 230 } 231 232 static inline void appendChars(rtl_String ** pBuffer, sal_Int32 * pCapacity, 233 sal_Int32 * pOffset, sal_Char const * pChars, 234 sal_Int32 nLen) 235 { 236 rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, pChars, nLen); 237 *pOffset += nLen; 238 } 239 240 static inline void appendAscii(rtl_String ** pBuffer, sal_Int32 * pCapacity, 241 sal_Int32 * pOffset, sal_Char const * pStr, 242 sal_Int32 nLen) 243 { 244 rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, pStr, nLen); 245 *pOffset += nLen; 246 } 247 }; 248 249 struct UStringTraits 250 { 251 typedef sal_Unicode Char; 252 253 typedef rtl_uString String; 254 255 static inline void createString(rtl_uString ** pString, 256 sal_Unicode const * pChars, sal_Int32 nLen) 257 { 258 rtl_uString_newFromStr_WithLength(pString, pChars, nLen); 259 } 260 261 static inline void createBuffer(rtl_uString ** pBuffer, 262 sal_Int32 * pCapacity) 263 { 264 rtl_uString_new_WithLength(pBuffer, *pCapacity); 265 } 266 267 static inline void appendChar(rtl_uString ** pBuffer, sal_Int32 * pCapacity, 268 sal_Int32 * pOffset, sal_Unicode cChar) 269 { 270 rtl_uStringbuffer_insert(pBuffer, pCapacity, *pOffset, &cChar, 1); 271 ++*pOffset; 272 } 273 274 static inline void appendChars(rtl_uString ** pBuffer, 275 sal_Int32 * pCapacity, sal_Int32 * pOffset, 276 sal_Unicode const * pChars, sal_Int32 nLen) 277 { 278 rtl_uStringbuffer_insert(pBuffer, pCapacity, *pOffset, pChars, nLen); 279 *pOffset += nLen; 280 } 281 282 static inline void appendAscii(rtl_uString ** pBuffer, 283 sal_Int32 * pCapacity, sal_Int32 * pOffset, 284 sal_Char const * pStr, sal_Int32 nLen) 285 { 286 rtl_uStringbuffer_insert_ascii(pBuffer, pCapacity, *pOffset, pStr, 287 nLen); 288 *pOffset += nLen; 289 } 290 }; 291 292 293 // Solaris C++ 5.2 compiler has problems when "StringT ** pResult" is 294 // "typename T::String ** pResult" instead: 295 template< typename T, typename StringT > 296 inline void doubleToString(StringT ** pResult, 297 sal_Int32 * pResultCapacity, sal_Int32 nResultOffset, 298 double fValue, rtl_math_StringFormat eFormat, 299 sal_Int32 nDecPlaces, typename T::Char cDecSeparator, 300 sal_Int32 const * pGroups, 301 typename T::Char cGroupSeparator, 302 bool bEraseTrailingDecZeros) 303 { 304 static double const nRoundVal[] = { 305 5.0e+0, 0.5e+0, 0.5e-1, 0.5e-2, 0.5e-3, 0.5e-4, 0.5e-5, 0.5e-6, 306 0.5e-7, 0.5e-8, 0.5e-9, 0.5e-10,0.5e-11,0.5e-12,0.5e-13,0.5e-14 307 }; 308 309 // sign adjustment, instead of testing for fValue<0.0 this will also fetch 310 // -0.0 311 bool bSign = rtl::math::isSignBitSet( fValue ); 312 if( bSign ) 313 fValue = -fValue; 314 315 if ( rtl::math::isNan( fValue ) ) 316 { 317 // #i112652# XMLSchema-2 318 sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("NaN"); 319 if (pResultCapacity == 0) 320 { 321 pResultCapacity = &nCapacity; 322 T::createBuffer(pResult, pResultCapacity); 323 nResultOffset = 0; 324 } 325 T::appendAscii(pResult, pResultCapacity, &nResultOffset, 326 RTL_CONSTASCII_STRINGPARAM("NaN")); 327 328 return; 329 } 330 331 bool bHuge = fValue == HUGE_VAL; // g++ 3.0.1 requires it this way... 332 if ( bHuge || rtl::math::isInf( fValue ) ) 333 { 334 // #i112652# XMLSchema-2 335 sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("-INF"); 336 if (pResultCapacity == 0) 337 { 338 pResultCapacity = &nCapacity; 339 T::createBuffer(pResult, pResultCapacity); 340 nResultOffset = 0; 341 } 342 if ( bSign ) 343 T::appendAscii(pResult, pResultCapacity, &nResultOffset, 344 RTL_CONSTASCII_STRINGPARAM("-")); 345 T::appendAscii(pResult, pResultCapacity, &nResultOffset, 346 RTL_CONSTASCII_STRINGPARAM("INF")); 347 348 return; 349 } 350 351 // find the exponent 352 int nExp = 0; 353 if ( fValue > 0.0 ) 354 { 355 nExp = static_cast< int >( floor( log10( fValue ) ) ); 356 fValue /= getN10Exp( nExp ); 357 } 358 359 switch ( eFormat ) 360 { 361 case rtl_math_StringFormat_Automatic : 362 { // E or F depending on exponent magnitude 363 int nPrec; 364 if ( nExp <= -15 || nExp >= 15 ) // #58531# was <-16, >16 365 { 366 nPrec = 14; 367 eFormat = rtl_math_StringFormat_E; 368 } 369 else 370 { 371 if ( nExp < 14 ) 372 { 373 nPrec = 15 - nExp - 1; 374 eFormat = rtl_math_StringFormat_F; 375 } 376 else 377 { 378 nPrec = 15; 379 eFormat = rtl_math_StringFormat_F; 380 } 381 } 382 if ( nDecPlaces == rtl_math_DecimalPlaces_Max ) 383 nDecPlaces = nPrec; 384 } 385 break; 386 case rtl_math_StringFormat_G : 387 { // G-Point, similar to sprintf %G 388 if ( nDecPlaces == rtl_math_DecimalPlaces_DefaultSignificance ) 389 nDecPlaces = 6; 390 if ( nExp < -4 || nExp >= nDecPlaces ) 391 { 392 nDecPlaces = std::max< sal_Int32 >( 1, nDecPlaces - 1 ); 393 eFormat = rtl_math_StringFormat_E; 394 } 395 else 396 { 397 nDecPlaces = std::max< sal_Int32 >( 0, nDecPlaces - nExp - 1 ); 398 eFormat = rtl_math_StringFormat_F; 399 } 400 } 401 break; 402 default: 403 break; 404 } 405 406 sal_Int32 nDigits = nDecPlaces + 1; 407 408 if( eFormat == rtl_math_StringFormat_F ) 409 nDigits += nExp; 410 411 // Round the number 412 if( nDigits >= 0 ) 413 { 414 if( ( fValue += nRoundVal[ nDigits > 15 ? 15 : nDigits ] ) >= 10 ) 415 { 416 fValue = 1.0; 417 nExp++; 418 if( eFormat == rtl_math_StringFormat_F ) 419 nDigits++; 420 } 421 } 422 423 static sal_Int32 const nBufMax = 256; 424 typename T::Char aBuf[nBufMax]; 425 typename T::Char * pBuf; 426 sal_Int32 nBuf = static_cast< sal_Int32 > 427 ( nDigits <= 0 ? std::max< sal_Int32 >( nDecPlaces, abs(nExp) ) 428 : nDigits + nDecPlaces ) + 10 + (pGroups ? abs(nDigits) * 2 : 0); 429 if ( nBuf > nBufMax ) 430 { 431 pBuf = reinterpret_cast< typename T::Char * >( 432 rtl_allocateMemory(nBuf * sizeof (typename T::Char))); 433 OSL_ENSURE(pBuf != 0, "Out of memory"); 434 } 435 else 436 pBuf = aBuf; 437 typename T::Char * p = pBuf; 438 if ( bSign ) 439 *p++ = static_cast< typename T::Char >('-'); 440 441 bool bHasDec = false; 442 443 int nDecPos; 444 // Check for F format and number < 1 445 if( eFormat == rtl_math_StringFormat_F ) 446 { 447 if( nExp < 0 ) 448 { 449 *p++ = static_cast< typename T::Char >('0'); 450 if ( nDecPlaces > 0 ) 451 { 452 *p++ = cDecSeparator; 453 bHasDec = true; 454 } 455 sal_Int32 i = ( nDigits <= 0 ? nDecPlaces : -nExp - 1 ); 456 while( (i--) > 0 ) 457 *p++ = static_cast< typename T::Char >('0'); 458 nDecPos = 0; 459 } 460 else 461 nDecPos = nExp + 1; 462 } 463 else 464 nDecPos = 1; 465 466 int nGrouping = 0, nGroupSelector = 0, nGroupExceed = 0; 467 if ( nDecPos > 1 && pGroups && pGroups[0] && cGroupSeparator ) 468 { 469 while ( nGrouping + pGroups[nGroupSelector] < nDecPos ) 470 { 471 nGrouping += pGroups[ nGroupSelector ]; 472 if ( pGroups[nGroupSelector+1] ) 473 { 474 if ( nGrouping + pGroups[nGroupSelector+1] >= nDecPos ) 475 break; // while 476 ++nGroupSelector; 477 } 478 else if ( !nGroupExceed ) 479 nGroupExceed = nGrouping; 480 } 481 } 482 483 // print the number 484 if( nDigits > 0 ) 485 { 486 for ( int i = 0; ; i++ ) 487 { 488 if( i < 15 ) 489 { 490 int nDigit; 491 if (nDigits-1 == 0 && i > 0 && i < 14) 492 nDigit = static_cast< int >( floor( fValue 493 + nKorrVal[15-i] ) ); 494 else 495 nDigit = static_cast< int >( fValue + 1E-15 ); 496 if (nDigit >= 10) 497 { // after-treatment of up-rounding to the next decade 498 sal_Int32 sLen = static_cast< long >(p-pBuf)-1; 499 if (sLen == -1) 500 { 501 p = pBuf; 502 if ( eFormat == rtl_math_StringFormat_F ) 503 { 504 *p++ = static_cast< typename T::Char >('1'); 505 *p++ = static_cast< typename T::Char >('0'); 506 } 507 else 508 { 509 *p++ = static_cast< typename T::Char >('1'); 510 *p++ = cDecSeparator; 511 *p++ = static_cast< typename T::Char >('0'); 512 nExp++; 513 bHasDec = true; 514 } 515 } 516 else 517 { 518 for (sal_Int32 j = sLen; j >= 0; j--) 519 { 520 typename T::Char cS = pBuf[j]; 521 if (cS != cDecSeparator) 522 { 523 if ( cS != static_cast< typename T::Char >('9')) 524 { 525 pBuf[j] = ++cS; 526 j = -1; // break loop 527 } 528 else 529 { 530 pBuf[j] 531 = static_cast< typename T::Char >('0'); 532 if (j == 0) 533 { 534 if ( eFormat == rtl_math_StringFormat_F) 535 { // insert '1' 536 typename T::Char * px = p++; 537 while ( pBuf < px ) 538 { 539 *px = *(px-1); 540 px--; 541 } 542 pBuf[0] = static_cast< 543 typename T::Char >('1'); 544 } 545 else 546 { 547 pBuf[j] = static_cast< 548 typename T::Char >('1'); 549 nExp++; 550 } 551 } 552 } 553 } 554 } 555 *p++ = static_cast< typename T::Char >('0'); 556 } 557 fValue = 0.0; 558 } 559 else 560 { 561 *p++ = static_cast< typename T::Char >( 562 nDigit + static_cast< typename T::Char >('0') ); 563 fValue = ( fValue - nDigit ) * 10.0; 564 } 565 } 566 else 567 *p++ = static_cast< typename T::Char >('0'); 568 if( !--nDigits ) 569 break; // for 570 if( nDecPos ) 571 { 572 if( !--nDecPos ) 573 { 574 *p++ = cDecSeparator; 575 bHasDec = true; 576 } 577 else if ( nDecPos == nGrouping ) 578 { 579 *p++ = cGroupSeparator; 580 nGrouping -= pGroups[ nGroupSelector ]; 581 if ( nGroupSelector && nGrouping < nGroupExceed ) 582 --nGroupSelector; 583 } 584 } 585 } 586 } 587 588 if ( !bHasDec && eFormat == rtl_math_StringFormat_F ) 589 { // nDecPlaces < 0 did round the value 590 while ( --nDecPos > 0 ) 591 { // fill before decimal point 592 if ( nDecPos == nGrouping ) 593 { 594 *p++ = cGroupSeparator; 595 nGrouping -= pGroups[ nGroupSelector ]; 596 if ( nGroupSelector && nGrouping < nGroupExceed ) 597 --nGroupSelector; 598 } 599 *p++ = static_cast< typename T::Char >('0'); 600 } 601 } 602 603 if ( bEraseTrailingDecZeros && bHasDec && p > pBuf ) 604 { 605 while ( *(p-1) == static_cast< typename T::Char >('0') ) 606 p--; 607 if ( *(p-1) == cDecSeparator ) 608 p--; 609 } 610 611 // Print the exponent ('E', followed by '+' or '-', followed by exactly 612 // three digits). The code in rtl_[u]str_valueOf{Float|Double} relies on 613 // this format. 614 if( eFormat == rtl_math_StringFormat_E ) 615 { 616 if ( p == pBuf ) 617 *p++ = static_cast< typename T::Char >('1'); 618 // maybe no nDigits if nDecPlaces < 0 619 *p++ = static_cast< typename T::Char >('E'); 620 if( nExp < 0 ) 621 { 622 nExp = -nExp; 623 *p++ = static_cast< typename T::Char >('-'); 624 } 625 else 626 *p++ = static_cast< typename T::Char >('+'); 627 // if (nExp >= 100 ) 628 *p++ = static_cast< typename T::Char >( 629 nExp / 100 + static_cast< typename T::Char >('0') ); 630 nExp %= 100; 631 *p++ = static_cast< typename T::Char >( 632 nExp / 10 + static_cast< typename T::Char >('0') ); 633 *p++ = static_cast< typename T::Char >( 634 nExp % 10 + static_cast< typename T::Char >('0') ); 635 } 636 637 if (pResultCapacity == 0) 638 T::createString(pResult, pBuf, p - pBuf); 639 else 640 T::appendChars(pResult, pResultCapacity, &nResultOffset, pBuf, 641 p - pBuf); 642 643 if ( pBuf != &aBuf[0] ) 644 rtl_freeMemory(pBuf); 645 } 646 647 } 648 649 void SAL_CALL rtl_math_doubleToString(rtl_String ** pResult, 650 sal_Int32 * pResultCapacity, 651 sal_Int32 nResultOffset, double fValue, 652 rtl_math_StringFormat eFormat, 653 sal_Int32 nDecPlaces, 654 sal_Char cDecSeparator, 655 sal_Int32 const * pGroups, 656 sal_Char cGroupSeparator, 657 sal_Bool bEraseTrailingDecZeros) 658 SAL_THROW_EXTERN_C() 659 { 660 doubleToString< StringTraits, StringTraits::String >( 661 pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces, 662 cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros); 663 } 664 665 void SAL_CALL rtl_math_doubleToUString(rtl_uString ** pResult, 666 sal_Int32 * pResultCapacity, 667 sal_Int32 nResultOffset, double fValue, 668 rtl_math_StringFormat eFormat, 669 sal_Int32 nDecPlaces, 670 sal_Unicode cDecSeparator, 671 sal_Int32 const * pGroups, 672 sal_Unicode cGroupSeparator, 673 sal_Bool bEraseTrailingDecZeros) 674 SAL_THROW_EXTERN_C() 675 { 676 doubleToString< UStringTraits, UStringTraits::String >( 677 pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces, 678 cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros); 679 } 680 681 682 namespace { 683 684 // if nExp * 10 + nAdd would result in overflow 685 inline bool long10Overflow( long& nExp, int nAdd ) 686 { 687 if ( nExp > (LONG_MAX/10) 688 || (nExp == (LONG_MAX/10) && nAdd > (LONG_MAX%10)) ) 689 { 690 nExp = LONG_MAX; 691 return true; 692 } 693 return false; 694 } 695 696 // We are only concerned about ASCII arabic numerical digits here 697 template< typename CharT > 698 inline bool isDigit( CharT c ) 699 { 700 return 0x30 <= c && c <= 0x39; 701 } 702 703 template< typename CharT > 704 inline double stringToDouble(CharT const * pBegin, CharT const * pEnd, 705 CharT cDecSeparator, CharT cGroupSeparator, 706 rtl_math_ConversionStatus * pStatus, 707 CharT const ** pParsedEnd) 708 { 709 double fVal = 0.0; 710 rtl_math_ConversionStatus eStatus = rtl_math_ConversionStatus_Ok; 711 712 CharT const * p0 = pBegin; 713 while (p0 != pEnd && (*p0 == CharT(' ') || *p0 == CharT('\t'))) 714 ++p0; 715 bool bSign; 716 if (p0 != pEnd && *p0 == CharT('-')) 717 { 718 bSign = true; 719 ++p0; 720 } 721 else 722 { 723 bSign = false; 724 if (p0 != pEnd && *p0 == CharT('+')) 725 ++p0; 726 } 727 CharT const * p = p0; 728 bool bDone = false; 729 730 // #i112652# XMLSchema-2 731 if (3 >= (pEnd - p)) 732 { 733 if ((CharT('N') == p[0]) && (CharT('a') == p[1]) 734 && (CharT('N') == p[2])) 735 { 736 p += 3; 737 rtl::math::setNan( &fVal ); 738 bDone = true; 739 } 740 else if ((CharT('I') == p[0]) && (CharT('N') == p[1]) 741 && (CharT('F') == p[2])) 742 { 743 p += 3; 744 fVal = HUGE_VAL; 745 eStatus = rtl_math_ConversionStatus_OutOfRange; 746 bDone = true; 747 } 748 } 749 750 if (!bDone) // do not recognize e.g. NaN1.23 751 { 752 // leading zeros and group separators may be safely ignored 753 while (p != pEnd && (*p == CharT('0') || *p == cGroupSeparator)) 754 ++p; 755 756 long nValExp = 0; // carry along exponent of mantissa 757 758 // integer part of mantissa 759 for (; p != pEnd; ++p) 760 { 761 CharT c = *p; 762 if (isDigit(c)) 763 { 764 fVal = fVal * 10.0 + static_cast< double >( c - CharT('0') ); 765 ++nValExp; 766 } 767 else if (c != cGroupSeparator) 768 break; 769 } 770 771 // fraction part of mantissa 772 if (p != pEnd && *p == cDecSeparator) 773 { 774 ++p; 775 double fFrac = 0.0; 776 long nFracExp = 0; 777 while (p != pEnd && *p == CharT('0')) 778 { 779 --nFracExp; 780 ++p; 781 } 782 if ( nValExp == 0 ) 783 nValExp = nFracExp - 1; // no integer part => fraction exponent 784 // one decimal digit needs ld(10) ~= 3.32 bits 785 static const int nSigs = (DBL_MANT_DIG / 3) + 1; 786 int nDigs = 0; 787 for (; p != pEnd; ++p) 788 { 789 CharT c = *p; 790 if (!isDigit(c)) 791 break; 792 if ( nDigs < nSigs ) 793 { // further digits (more than nSigs) don't have any 794 // significance 795 fFrac = fFrac * 10.0 + static_cast<double>(c - CharT('0')); 796 --nFracExp; 797 ++nDigs; 798 } 799 } 800 if ( fFrac != 0.0 ) 801 fVal += rtl::math::pow10Exp( fFrac, nFracExp ); 802 else if ( nValExp < 0 ) 803 nValExp = 0; // no digit other than 0 after decimal point 804 } 805 806 if ( nValExp > 0 ) 807 --nValExp; // started with offset +1 at the first mantissa digit 808 809 // Exponent 810 if (p != p0 && p != pEnd && (*p == CharT('E') || *p == CharT('e'))) 811 { 812 ++p; 813 bool bExpSign; 814 if (p != pEnd && *p == CharT('-')) 815 { 816 bExpSign = true; 817 ++p; 818 } 819 else 820 { 821 bExpSign = false; 822 if (p != pEnd && *p == CharT('+')) 823 ++p; 824 } 825 if ( fVal == 0.0 ) 826 { // no matter what follows, zero stays zero, but carry on the 827 // offset 828 while (p != pEnd && isDigit(*p)) 829 ++p; 830 } 831 else 832 { 833 bool bOverFlow = false; 834 long nExp = 0; 835 for (; p != pEnd; ++p) 836 { 837 CharT c = *p; 838 if (!isDigit(c)) 839 break; 840 int i = c - CharT('0'); 841 if ( long10Overflow( nExp, i ) ) 842 bOverFlow = true; 843 else 844 nExp = nExp * 10 + i; 845 } 846 if ( nExp ) 847 { 848 if ( bExpSign ) 849 nExp = -nExp; 850 long nAllExp = ( bOverFlow ? 0 : nExp + nValExp ); 851 if ( nAllExp > DBL_MAX_10_EXP || (bOverFlow && !bExpSign) ) 852 { // overflow 853 fVal = HUGE_VAL; 854 eStatus = rtl_math_ConversionStatus_OutOfRange; 855 } 856 else if ((nAllExp < DBL_MIN_10_EXP) || 857 (bOverFlow && bExpSign) ) 858 { // underflow 859 fVal = 0.0; 860 eStatus = rtl_math_ConversionStatus_OutOfRange; 861 } 862 else if ( nExp > DBL_MAX_10_EXP || nExp < DBL_MIN_10_EXP ) 863 { // compensate exponents 864 fVal = rtl::math::pow10Exp( fVal, -nValExp ); 865 fVal = rtl::math::pow10Exp( fVal, nAllExp ); 866 } 867 else 868 fVal = rtl::math::pow10Exp( fVal, nExp ); // normal 869 } 870 } 871 } 872 else if (p - p0 == 2 && p != pEnd && p[0] == CharT('#') 873 && p[-1] == cDecSeparator && p[-2] == CharT('1')) 874 { 875 if (pEnd - p >= 4 && p[1] == CharT('I') && p[2] == CharT('N') 876 && p[3] == CharT('F')) 877 { 878 // "1.#INF", "+1.#INF", "-1.#INF" 879 p += 4; 880 fVal = HUGE_VAL; 881 eStatus = rtl_math_ConversionStatus_OutOfRange; 882 // Eat any further digits: 883 while (p != pEnd && isDigit(*p)) 884 ++p; 885 } 886 else if (pEnd - p >= 4 && p[1] == CharT('N') && p[2] == CharT('A') 887 && p[3] == CharT('N')) 888 { 889 // "1.#NAN", "+1.#NAN", "-1.#NAN" 890 p += 4; 891 rtl::math::setNan( &fVal ); 892 if (bSign) 893 { 894 union { 895 double sd; 896 sal_math_Double md; 897 } m; 898 m.sd = fVal; 899 m.md.w32_parts.msw |= 0x80000000; // create negative NaN 900 fVal = m.sd; 901 bSign = false; // don't negate again 902 } 903 // Eat any further digits: 904 while (p != pEnd && isDigit(*p)) 905 ++p; 906 } 907 } 908 } 909 910 // overflow also if more than DBL_MAX_10_EXP digits without decimal 911 // separator, or 0. and more than DBL_MIN_10_EXP digits, ... 912 bool bHuge = fVal == HUGE_VAL; // g++ 3.0.1 requires it this way... 913 if ( bHuge ) 914 eStatus = rtl_math_ConversionStatus_OutOfRange; 915 916 if ( bSign ) 917 fVal = -fVal; 918 919 if (pStatus != 0) 920 *pStatus = eStatus; 921 if (pParsedEnd != 0) 922 *pParsedEnd = p == p0 ? pBegin : p; 923 924 return fVal; 925 } 926 927 } 928 929 double SAL_CALL rtl_math_stringToDouble(sal_Char const * pBegin, 930 sal_Char const * pEnd, 931 sal_Char cDecSeparator, 932 sal_Char cGroupSeparator, 933 rtl_math_ConversionStatus * pStatus, 934 sal_Char const ** pParsedEnd) 935 SAL_THROW_EXTERN_C() 936 { 937 return stringToDouble(pBegin, pEnd, cDecSeparator, cGroupSeparator, pStatus, 938 pParsedEnd); 939 } 940 941 double SAL_CALL rtl_math_uStringToDouble(sal_Unicode const * pBegin, 942 sal_Unicode const * pEnd, 943 sal_Unicode cDecSeparator, 944 sal_Unicode cGroupSeparator, 945 rtl_math_ConversionStatus * pStatus, 946 sal_Unicode const ** pParsedEnd) 947 SAL_THROW_EXTERN_C() 948 { 949 return stringToDouble(pBegin, pEnd, cDecSeparator, cGroupSeparator, pStatus, 950 pParsedEnd); 951 } 952 953 double SAL_CALL rtl_math_round(double fValue, int nDecPlaces, 954 enum rtl_math_RoundingMode eMode) 955 SAL_THROW_EXTERN_C() 956 { 957 OSL_ASSERT(nDecPlaces >= -20 && nDecPlaces <= 20); 958 959 if ( fValue == 0.0 ) 960 return fValue; 961 962 // sign adjustment 963 bool bSign = rtl::math::isSignBitSet( fValue ); 964 if ( bSign ) 965 fValue = -fValue; 966 967 double fFac = 0; 968 if ( nDecPlaces != 0 ) 969 { 970 // max 20 decimals, we don't have unlimited precision 971 // #38810# and no overflow on fValue*=fFac 972 if ( nDecPlaces < -20 || 20 < nDecPlaces || fValue > (DBL_MAX / 1e20) ) 973 return bSign ? -fValue : fValue; 974 975 fFac = getN10Exp( nDecPlaces ); 976 fValue *= fFac; 977 } 978 //else //! uninitialized fFac, not needed 979 980 switch ( eMode ) 981 { 982 case rtl_math_RoundingMode_Corrected : 983 { 984 int nExp; // exponent for correction 985 if ( fValue > 0.0 ) 986 nExp = static_cast<int>( floor( log10( fValue ) ) ); 987 else 988 nExp = 0; 989 int nIndex = 15 - nExp; 990 if ( nIndex > 15 ) 991 nIndex = 15; 992 else if ( nIndex <= 1 ) 993 nIndex = 0; 994 fValue = floor( fValue + 0.5 + nKorrVal[nIndex] ); 995 } 996 break; 997 case rtl_math_RoundingMode_Down : 998 fValue = rtl::math::approxFloor( fValue ); 999 break; 1000 case rtl_math_RoundingMode_Up : 1001 fValue = rtl::math::approxCeil( fValue ); 1002 break; 1003 case rtl_math_RoundingMode_Floor : 1004 fValue = bSign ? rtl::math::approxCeil( fValue ) 1005 : rtl::math::approxFloor( fValue ); 1006 break; 1007 case rtl_math_RoundingMode_Ceiling : 1008 fValue = bSign ? rtl::math::approxFloor( fValue ) 1009 : rtl::math::approxCeil( fValue ); 1010 break; 1011 case rtl_math_RoundingMode_HalfDown : 1012 { 1013 double f = floor( fValue ); 1014 fValue = ((fValue - f) <= 0.5) ? f : ceil( fValue ); 1015 } 1016 break; 1017 case rtl_math_RoundingMode_HalfUp : 1018 { 1019 double f = floor( fValue ); 1020 fValue = ((fValue - f) < 0.5) ? f : ceil( fValue ); 1021 } 1022 break; 1023 case rtl_math_RoundingMode_HalfEven : 1024 #if defined FLT_ROUNDS 1025 /* 1026 Use fast version. FLT_ROUNDS may be defined to a function by some compilers! 1027 1028 DBL_EPSILON is the smallest fractional number which can be represented, 1029 its reciprocal is therefore the smallest number that cannot have a 1030 fractional part. Once you add this reciprocal to `x', its fractional part 1031 is stripped off. Simply subtracting the reciprocal back out returns `x' 1032 without its fractional component. 1033 Simple, clever, and elegant - thanks to Ross Cottrell, the original author, 1034 who placed it into public domain. 1035 1036 volatile: prevent compiler from being too smart 1037 */ 1038 if ( FLT_ROUNDS == 1 ) 1039 { 1040 volatile double x = fValue + 1.0 / DBL_EPSILON; 1041 fValue = x - 1.0 / DBL_EPSILON; 1042 } 1043 else 1044 #endif // FLT_ROUNDS 1045 { 1046 double f = floor( fValue ); 1047 if ( (fValue - f) != 0.5 ) 1048 fValue = floor( fValue + 0.5 ); 1049 else 1050 { 1051 double g = f / 2.0; 1052 fValue = (g == floor( g )) ? f : (f + 1.0); 1053 } 1054 } 1055 break; 1056 default: 1057 OSL_ASSERT(false); 1058 break; 1059 } 1060 1061 if ( nDecPlaces != 0 ) 1062 fValue /= fFac; 1063 1064 return bSign ? -fValue : fValue; 1065 } 1066 1067 1068 double SAL_CALL rtl_math_pow10Exp(double fValue, int nExp) SAL_THROW_EXTERN_C() 1069 { 1070 return fValue * getN10Exp( nExp ); 1071 } 1072 1073 1074 double SAL_CALL rtl_math_approxValue( double fValue ) SAL_THROW_EXTERN_C() 1075 { 1076 if (fValue == 0.0 || fValue == HUGE_VAL || !::rtl::math::isFinite( fValue)) 1077 // We don't handle these conditions. Bail out. 1078 return fValue; 1079 1080 double fOrigValue = fValue; 1081 1082 bool bSign = ::rtl::math::isSignBitSet( fValue); 1083 if (bSign) 1084 fValue = -fValue; 1085 1086 int nExp = static_cast<int>( floor( log10( fValue))); 1087 nExp = 14 - nExp; 1088 double fExpValue = getN10Exp( nExp); 1089 1090 fValue *= fExpValue; 1091 // If the original value was near DBL_MIN we got an overflow. Restore and 1092 // bail out. 1093 if (!rtl::math::isFinite( fValue)) 1094 return fOrigValue; 1095 fValue = rtl_math_round( fValue, 0, rtl_math_RoundingMode_Corrected); 1096 fValue /= fExpValue; 1097 // If the original value was near DBL_MAX we got an overflow. Restore and 1098 // bail out. 1099 if (!rtl::math::isFinite( fValue)) 1100 return fOrigValue; 1101 1102 return bSign ? -fValue : fValue; 1103 } 1104 1105 1106 double SAL_CALL rtl_math_expm1( double fValue ) SAL_THROW_EXTERN_C() 1107 { 1108 double fe = exp( fValue ); 1109 if (fe == 1.0) 1110 return fValue; 1111 if (fe-1.0 == -1.0) 1112 return -1.0; 1113 return (fe-1.0) * fValue / log(fe); 1114 } 1115 1116 double SAL_CALL rtl_math_powr( double fValue, double fExp ) SAL_THROW_EXTERN_C() 1117 { 1118 if ((fValue == 0.0 && fExp == 0.0) || 1119 (rtl::math::isInf( fExp ) && !rtl::math::isSignBitSet( fExp )) || 1120 (rtl::math::isInf( fValue ) && !rtl::math::isSignBitSet( fValue ))) 1121 { 1122 double fResult; 1123 ::rtl::math::setNan( &fResult ); 1124 return fResult; 1125 } 1126 return pow(fValue, fExp); 1127 } 1128 1129 1130 double SAL_CALL rtl_math_log1p( double fValue ) SAL_THROW_EXTERN_C() 1131 { 1132 // Use volatile because a compiler may be too smart "optimizing" the 1133 // condition such that in certain cases the else path was called even if 1134 // (fp==1.0) was true, where the term (fp-1.0) then resulted in 0.0 and 1135 // hence the entire expression resulted in NaN. 1136 // Happened with g++ 3.4.1 and an input value of 9.87E-18 1137 volatile double fp = 1.0 + fValue; 1138 if (fp == 1.0) 1139 return fValue; 1140 else 1141 return log(fp) * fValue / (fp-1.0); 1142 } 1143 1144 1145 double SAL_CALL rtl_math_atanh( double fValue ) SAL_THROW_EXTERN_C() 1146 { 1147 return 0.5 * rtl_math_log1p( 2.0 * fValue / (1.0-fValue) ); 1148 } 1149 1150 1151 /** Parent error function (erf) that calls different algorithms based on the 1152 value of x. It takes care of cases where x is negative as erf is an odd 1153 function i.e. erf(-x) = -erf(x). 1154 1155 Kramer, W., and Blomquist, F., 2000, Algorithms with Guaranteed Error Bounds 1156 for the Error Function and the Complementary Error Function 1157 1158 http://www.math.uni-wuppertal.de/wrswt/literatur_en.html 1159 1160 @author Kohei Yoshida <kohei@openoffice.org> 1161 1162 @see #i55735# 1163 */ 1164 double SAL_CALL rtl_math_erf( double x ) SAL_THROW_EXTERN_C() 1165 { 1166 if( x == 0.0 ) 1167 return 0.0; 1168 1169 bool bNegative = false; 1170 if ( x < 0.0 ) 1171 { 1172 x = fabs( x ); 1173 bNegative = true; 1174 } 1175 1176 double fErf = 1.0; 1177 if ( x < 1.0e-10 ) 1178 fErf = (double) (x*1.1283791670955125738961589031215452L); 1179 else if ( x < 0.65 ) 1180 lcl_Erf0065( x, fErf ); 1181 else 1182 fErf = 1.0 - rtl_math_erfc( x ); 1183 1184 if ( bNegative ) 1185 fErf *= -1.0; 1186 1187 return fErf; 1188 } 1189 1190 1191 /** Parent complementary error function (erfc) that calls different algorithms 1192 based on the value of x. It takes care of cases where x is negative as erfc 1193 satisfies relationship erfc(-x) = 2 - erfc(x). See the comment for Erf(x) 1194 for the source publication. 1195 1196 @author Kohei Yoshida <kohei@openoffice.org> 1197 1198 @see #i55735#, moved from module scaddins (#i97091#) 1199 1200 */ 1201 double SAL_CALL rtl_math_erfc( double x ) SAL_THROW_EXTERN_C() 1202 { 1203 if ( x == 0.0 ) 1204 return 1.0; 1205 1206 bool bNegative = false; 1207 if ( x < 0.0 ) 1208 { 1209 x = fabs( x ); 1210 bNegative = true; 1211 } 1212 1213 double fErfc = 0.0; 1214 if ( x >= 0.65 ) 1215 { 1216 if ( x < 6.0 ) 1217 lcl_Erfc0600( x, fErfc ); 1218 else 1219 lcl_Erfc2654( x, fErfc ); 1220 } 1221 else 1222 fErfc = 1.0 - rtl_math_erf( x ); 1223 1224 if ( bNegative ) 1225 fErfc = 2.0 - fErfc; 1226 1227 return fErfc; 1228 } 1229 1230 /** improved accuracy of asinh for |x| large and for x near zero 1231 @see #i97605# 1232 */ 1233 double SAL_CALL rtl_math_asinh( double fX ) SAL_THROW_EXTERN_C() 1234 { 1235 double fSign = 1.0; 1236 if ( fX == 0.0 ) 1237 return 0.0; 1238 else 1239 { 1240 if ( fX < 0.0 ) 1241 { 1242 fX = - fX; 1243 fSign = -1.0; 1244 } 1245 if ( fX < 0.125 ) 1246 return fSign * rtl_math_log1p( fX + fX*fX / (1.0 + sqrt( 1.0 + fX*fX))); 1247 else if ( fX < 1.25e7 ) 1248 return fSign * log( fX + sqrt( 1.0 + fX*fX)); 1249 else 1250 return fSign * log( 2.0*fX); 1251 } 1252 } 1253 1254 /** improved accuracy of acosh for x large and for x near 1 1255 @see #i97605# 1256 */ 1257 double SAL_CALL rtl_math_acosh( double fX ) SAL_THROW_EXTERN_C() 1258 { 1259 volatile double fZ = fX - 1.0; 1260 if ( fX < 1.0 ) 1261 { 1262 double fResult; 1263 ::rtl::math::setNan( &fResult ); 1264 return fResult; 1265 } 1266 else if ( fX == 1.0 ) 1267 return 0.0; 1268 else if ( fX < 1.1 ) 1269 return rtl_math_log1p( fZ + sqrt( fZ*fZ + 2.0*fZ)); 1270 else if ( fX < 1.25e7 ) 1271 return log( fX + sqrt( fX*fX - 1.0)); 1272 else 1273 return log( 2.0*fX); 1274 } 1275