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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 :
21 : #include "rtl/math.h"
22 :
23 : #include "osl/diagnose.h"
24 : #include "rtl/alloc.h"
25 : #include "rtl/math.hxx"
26 : #include "rtl/strbuf.h"
27 : #include "rtl/string.h"
28 : #include "rtl/ustrbuf.h"
29 : #include "rtl/ustring.h"
30 : #include "sal/mathconf.h"
31 : #include "sal/types.h"
32 :
33 : #include <algorithm>
34 : #include <float.h>
35 : #include <limits.h>
36 : #include <math.h>
37 : #include <stdlib.h>
38 :
39 :
40 : static int const n10Count = 16;
41 : static double const n10s[2][n10Count] = {
42 : { 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8,
43 : 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16 },
44 : { 1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7, 1e-8,
45 : 1e-9, 1e-10, 1e-11, 1e-12, 1e-13, 1e-14, 1e-15, 1e-16 }
46 : };
47 :
48 : // return pow(10.0,nExp) optimized for exponents in the interval [-16,16]
49 17342 : static double getN10Exp( int nExp )
50 : {
51 17342 : if ( nExp < 0 )
52 : {
53 : // && -nExp > 0 necessary for std::numeric_limits<int>::min()
54 : // because -nExp = nExp
55 4950 : if ( -nExp <= n10Count && -nExp > 0 )
56 4944 : return n10s[1][-nExp-1];
57 : else
58 6 : return pow( 10.0, static_cast<double>( nExp ) );
59 : }
60 12392 : else if ( nExp > 0 )
61 : {
62 10719 : if ( nExp <= n10Count )
63 10719 : return n10s[0][nExp-1];
64 : else
65 0 : return pow( 10.0, static_cast<double>( nExp ) );
66 : }
67 : else // ( nExp == 0 )
68 1673 : return 1.0;
69 : }
70 :
71 : /** Approximation algorithm for erf for 0 < x < 0.65. */
72 0 : static void lcl_Erf0065( double x, double& fVal )
73 : {
74 : static const double pn[] = {
75 : 1.12837916709551256,
76 : 1.35894887627277916E-1,
77 : 4.03259488531795274E-2,
78 : 1.20339380863079457E-3,
79 : 6.49254556481904354E-5
80 : };
81 : static const double qn[] = {
82 : 1.00000000000000000,
83 : 4.53767041780002545E-1,
84 : 8.69936222615385890E-2,
85 : 8.49717371168693357E-3,
86 : 3.64915280629351082E-4
87 : };
88 0 : double fPSum = 0.0;
89 0 : double fQSum = 0.0;
90 0 : double fXPow = 1.0;
91 0 : for ( unsigned int i = 0; i <= 4; ++i )
92 : {
93 0 : fPSum += pn[i]*fXPow;
94 0 : fQSum += qn[i]*fXPow;
95 0 : fXPow *= x*x;
96 : }
97 0 : fVal = x * fPSum / fQSum;
98 0 : }
99 :
100 : /** Approximation algorithm for erfc for 0.65 < x < 6.0. */
101 0 : static void lcl_Erfc0600( double x, double& fVal )
102 : {
103 0 : double fPSum = 0.0;
104 0 : double fQSum = 0.0;
105 0 : double fXPow = 1.0;
106 : const double *pn;
107 : const double *qn;
108 :
109 0 : if ( x < 2.2 )
110 : {
111 : static const double pn22[] = {
112 : 9.99999992049799098E-1,
113 : 1.33154163936765307,
114 : 8.78115804155881782E-1,
115 : 3.31899559578213215E-1,
116 : 7.14193832506776067E-2,
117 : 7.06940843763253131E-3
118 : };
119 : static const double qn22[] = {
120 : 1.00000000000000000,
121 : 2.45992070144245533,
122 : 2.65383972869775752,
123 : 1.61876655543871376,
124 : 5.94651311286481502E-1,
125 : 1.26579413030177940E-1,
126 : 1.25304936549413393E-2
127 : };
128 0 : pn = pn22;
129 0 : qn = qn22;
130 : }
131 : else /* if ( x < 6.0 ) this is true, but the compiler does not know */
132 : {
133 : static const double pn60[] = {
134 : 9.99921140009714409E-1,
135 : 1.62356584489366647,
136 : 1.26739901455873222,
137 : 5.81528574177741135E-1,
138 : 1.57289620742838702E-1,
139 : 2.25716982919217555E-2
140 : };
141 : static const double qn60[] = {
142 : 1.00000000000000000,
143 : 2.75143870676376208,
144 : 3.37367334657284535,
145 : 2.38574194785344389,
146 : 1.05074004614827206,
147 : 2.78788439273628983E-1,
148 : 4.00072964526861362E-2
149 : };
150 0 : pn = pn60;
151 0 : qn = qn60;
152 : }
153 :
154 0 : for ( unsigned int i = 0; i < 6; ++i )
155 : {
156 0 : fPSum += pn[i]*fXPow;
157 0 : fQSum += qn[i]*fXPow;
158 0 : fXPow *= x;
159 : }
160 0 : fQSum += qn[6]*fXPow;
161 0 : fVal = exp( -1.0*x*x )* fPSum / fQSum;
162 0 : }
163 :
164 : /** Approximation algorithm for erfc for 6.0 < x < 26.54 (but used for all
165 : x > 6.0). */
166 0 : static void lcl_Erfc2654( double x, double& fVal )
167 : {
168 : static const double pn[] = {
169 : 5.64189583547756078E-1,
170 : 8.80253746105525775,
171 : 3.84683103716117320E1,
172 : 4.77209965874436377E1,
173 : 8.08040729052301677
174 : };
175 : static const double qn[] = {
176 : 1.00000000000000000,
177 : 1.61020914205869003E1,
178 : 7.54843505665954743E1,
179 : 1.12123870801026015E2,
180 : 3.73997570145040850E1
181 : };
182 :
183 0 : double fPSum = 0.0;
184 0 : double fQSum = 0.0;
185 0 : double fXPow = 1.0;
186 :
187 0 : for ( unsigned int i = 0; i <= 4; ++i )
188 : {
189 0 : fPSum += pn[i]*fXPow;
190 0 : fQSum += qn[i]*fXPow;
191 0 : fXPow /= x*x;
192 : }
193 0 : fVal = exp(-1.0*x*x)*fPSum / (x*fQSum);
194 0 : }
195 :
196 : namespace {
197 :
198 : double const nKorrVal[] = {
199 : 0, 9e-1, 9e-2, 9e-3, 9e-4, 9e-5, 9e-6, 9e-7, 9e-8,
200 : 9e-9, 9e-10, 9e-11, 9e-12, 9e-13, 9e-14, 9e-15
201 : };
202 :
203 : struct StringTraits
204 : {
205 : typedef sal_Char Char;
206 :
207 : typedef rtl_String String;
208 :
209 615 : static inline void createString(rtl_String ** pString,
210 : sal_Char const * pChars, sal_Int32 nLen)
211 : {
212 615 : rtl_string_newFromStr_WithLength(pString, pChars, nLen);
213 615 : }
214 :
215 0 : static inline void createBuffer(rtl_String ** pBuffer,
216 : sal_Int32 * pCapacity)
217 : {
218 0 : rtl_string_new_WithLength(pBuffer, *pCapacity);
219 0 : }
220 :
221 : static inline void appendChar(rtl_String ** pBuffer, sal_Int32 * pCapacity,
222 : sal_Int32 * pOffset, sal_Char cChar)
223 : {
224 : rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, &cChar, 1);
225 : ++*pOffset;
226 : }
227 :
228 0 : static inline void appendChars(rtl_String ** pBuffer, sal_Int32 * pCapacity,
229 : sal_Int32 * pOffset, sal_Char const * pChars,
230 : sal_Int32 nLen)
231 : {
232 0 : rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, pChars, nLen);
233 0 : *pOffset += nLen;
234 0 : }
235 :
236 0 : static inline void appendAscii(rtl_String ** pBuffer, sal_Int32 * pCapacity,
237 : sal_Int32 * pOffset, sal_Char const * pStr,
238 : sal_Int32 nLen)
239 : {
240 0 : rtl_stringbuffer_insert(pBuffer, pCapacity, *pOffset, pStr, nLen);
241 0 : *pOffset += nLen;
242 0 : }
243 : };
244 :
245 : struct UStringTraits
246 : {
247 : typedef sal_Unicode Char;
248 :
249 : typedef rtl_uString String;
250 :
251 9119 : static inline void createString(rtl_uString ** pString,
252 : sal_Unicode const * pChars, sal_Int32 nLen)
253 : {
254 9119 : rtl_uString_newFromStr_WithLength(pString, pChars, nLen);
255 9119 : }
256 :
257 0 : static inline void createBuffer(rtl_uString ** pBuffer,
258 : sal_Int32 * pCapacity)
259 : {
260 0 : rtl_uString_new_WithLength(pBuffer, *pCapacity);
261 0 : }
262 :
263 : static inline void appendChar(rtl_uString ** pBuffer, sal_Int32 * pCapacity,
264 : sal_Int32 * pOffset, sal_Unicode cChar)
265 : {
266 : rtl_uStringbuffer_insert(pBuffer, pCapacity, *pOffset, &cChar, 1);
267 : ++*pOffset;
268 : }
269 :
270 121 : static inline void appendChars(rtl_uString ** pBuffer,
271 : sal_Int32 * pCapacity, sal_Int32 * pOffset,
272 : sal_Unicode const * pChars, sal_Int32 nLen)
273 : {
274 121 : rtl_uStringbuffer_insert(pBuffer, pCapacity, *pOffset, pChars, nLen);
275 121 : *pOffset += nLen;
276 121 : }
277 :
278 0 : static inline void appendAscii(rtl_uString ** pBuffer,
279 : sal_Int32 * pCapacity, sal_Int32 * pOffset,
280 : sal_Char const * pStr, sal_Int32 nLen)
281 : {
282 : rtl_uStringbuffer_insert_ascii(pBuffer, pCapacity, *pOffset, pStr,
283 0 : nLen);
284 0 : *pOffset += nLen;
285 0 : }
286 : };
287 :
288 :
289 : // Solaris C++ 5.2 compiler has problems when "StringT ** pResult" is
290 : // "typename T::String ** pResult" instead:
291 : template< typename T, typename StringT >
292 9855 : inline void doubleToString(StringT ** pResult,
293 : sal_Int32 * pResultCapacity, sal_Int32 nResultOffset,
294 : double fValue, rtl_math_StringFormat eFormat,
295 : sal_Int32 nDecPlaces, typename T::Char cDecSeparator,
296 : sal_Int32 const * pGroups,
297 : typename T::Char cGroupSeparator,
298 : bool bEraseTrailingDecZeros)
299 : {
300 : static double const nRoundVal[] = {
301 : 5.0e+0, 0.5e+0, 0.5e-1, 0.5e-2, 0.5e-3, 0.5e-4, 0.5e-5, 0.5e-6,
302 : 0.5e-7, 0.5e-8, 0.5e-9, 0.5e-10,0.5e-11,0.5e-12,0.5e-13,0.5e-14
303 : };
304 :
305 : // sign adjustment, instead of testing for fValue<0.0 this will also fetch
306 : // -0.0
307 9855 : bool bSign = rtl::math::isSignBitSet( fValue );
308 9855 : if( bSign )
309 1303 : fValue = -fValue;
310 :
311 9855 : if ( rtl::math::isNan( fValue ) )
312 : {
313 : // #i112652# XMLSchema-2
314 0 : sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("NaN");
315 0 : if (pResultCapacity == 0)
316 : {
317 0 : pResultCapacity = &nCapacity;
318 0 : T::createBuffer(pResult, pResultCapacity);
319 0 : nResultOffset = 0;
320 : }
321 0 : T::appendAscii(pResult, pResultCapacity, &nResultOffset,
322 : RTL_CONSTASCII_STRINGPARAM("NaN"));
323 :
324 : return;
325 : }
326 :
327 9855 : bool bHuge = fValue == HUGE_VAL; // g++ 3.0.1 requires it this way...
328 9855 : if ( bHuge || rtl::math::isInf( fValue ) )
329 : {
330 : // #i112652# XMLSchema-2
331 0 : sal_Int32 nCapacity = RTL_CONSTASCII_LENGTH("-INF");
332 0 : if (pResultCapacity == 0)
333 : {
334 0 : pResultCapacity = &nCapacity;
335 0 : T::createBuffer(pResult, pResultCapacity);
336 0 : nResultOffset = 0;
337 : }
338 0 : if ( bSign )
339 0 : T::appendAscii(pResult, pResultCapacity, &nResultOffset,
340 : RTL_CONSTASCII_STRINGPARAM("-"));
341 0 : T::appendAscii(pResult, pResultCapacity, &nResultOffset,
342 : RTL_CONSTASCII_STRINGPARAM("INF"));
343 :
344 : return;
345 : }
346 :
347 : // find the exponent
348 9855 : int nExp = 0;
349 9855 : if ( fValue > 0.0 )
350 : {
351 7912 : nExp = static_cast< int >( floor( log10( fValue ) ) );
352 7912 : fValue /= getN10Exp( nExp );
353 : }
354 :
355 9855 : switch ( eFormat )
356 : {
357 : case rtl_math_StringFormat_Automatic :
358 : { // E or F depending on exponent magnitude
359 : int nPrec;
360 148 : if ( nExp <= -15 || nExp >= 15 ) // #58531# was <-16, >16
361 : {
362 0 : nPrec = 14;
363 0 : eFormat = rtl_math_StringFormat_E;
364 : }
365 : else
366 : {
367 148 : if ( nExp < 14 )
368 : {
369 148 : nPrec = 15 - nExp - 1;
370 148 : eFormat = rtl_math_StringFormat_F;
371 : }
372 : else
373 : {
374 0 : nPrec = 15;
375 0 : eFormat = rtl_math_StringFormat_F;
376 : }
377 : }
378 148 : if ( nDecPlaces == rtl_math_DecimalPlaces_Max )
379 148 : nDecPlaces = nPrec;
380 : }
381 148 : break;
382 : case rtl_math_StringFormat_G :
383 : { // G-Point, similar to sprintf %G
384 4785 : if ( nDecPlaces == rtl_math_DecimalPlaces_DefaultSignificance )
385 0 : nDecPlaces = 6;
386 4785 : if ( nExp < -4 || nExp >= nDecPlaces )
387 : {
388 0 : nDecPlaces = std::max< sal_Int32 >( 1, nDecPlaces - 1 );
389 0 : eFormat = rtl_math_StringFormat_E;
390 : }
391 : else
392 : {
393 4785 : nDecPlaces = std::max< sal_Int32 >( 0, nDecPlaces - nExp - 1 );
394 4785 : eFormat = rtl_math_StringFormat_F;
395 : }
396 : }
397 4785 : break;
398 : default:
399 4922 : break;
400 : }
401 :
402 9855 : sal_Int32 nDigits = nDecPlaces + 1;
403 :
404 9855 : if( eFormat == rtl_math_StringFormat_F )
405 9845 : nDigits += nExp;
406 :
407 : // Round the number
408 9855 : if( nDigits >= 0 )
409 : {
410 9853 : if( ( fValue += nRoundVal[ nDigits > 15 ? 15 : nDigits ] ) >= 10 )
411 : {
412 0 : fValue = 1.0;
413 0 : nExp++;
414 0 : if( eFormat == rtl_math_StringFormat_F )
415 0 : nDigits++;
416 : }
417 : }
418 :
419 : static sal_Int32 const nBufMax = 256;
420 : typename T::Char aBuf[nBufMax];
421 : typename T::Char * pBuf;
422 : sal_Int32 nBuf = static_cast< sal_Int32 >
423 : ( nDigits <= 0 ? std::max< sal_Int32 >( nDecPlaces, abs(nExp) )
424 9855 : : nDigits + nDecPlaces ) + 10 + (pGroups ? abs(nDigits) * 2 : 0);
425 9855 : if ( nBuf > nBufMax )
426 : {
427 0 : pBuf = reinterpret_cast< typename T::Char * >(
428 : rtl_allocateMemory(nBuf * sizeof (typename T::Char)));
429 : OSL_ENSURE(pBuf != 0, "Out of memory");
430 : }
431 : else
432 9855 : pBuf = aBuf;
433 9855 : typename T::Char * p = pBuf;
434 9855 : if ( bSign )
435 1303 : *p++ = static_cast< typename T::Char >('-');
436 :
437 9855 : bool bHasDec = false;
438 :
439 : int nDecPos;
440 : // Check for F format and number < 1
441 9855 : if( eFormat == rtl_math_StringFormat_F )
442 : {
443 9845 : if( nExp < 0 )
444 : {
445 583 : *p++ = static_cast< typename T::Char >('0');
446 583 : if ( nDecPlaces > 0 )
447 : {
448 583 : *p++ = cDecSeparator;
449 583 : bHasDec = true;
450 : }
451 583 : sal_Int32 i = ( nDigits <= 0 ? nDecPlaces : -nExp - 1 );
452 1346 : while( (i--) > 0 )
453 180 : *p++ = static_cast< typename T::Char >('0');
454 583 : nDecPos = 0;
455 : }
456 : else
457 9262 : nDecPos = nExp + 1;
458 : }
459 : else
460 10 : nDecPos = 1;
461 :
462 9855 : int nGrouping = 0, nGroupSelector = 0, nGroupExceed = 0;
463 9855 : if ( nDecPos > 1 && pGroups && pGroups[0] && cGroupSeparator )
464 : {
465 0 : while ( nGrouping + pGroups[nGroupSelector] < nDecPos )
466 : {
467 0 : nGrouping += pGroups[ nGroupSelector ];
468 0 : if ( pGroups[nGroupSelector+1] )
469 : {
470 0 : if ( nGrouping + pGroups[nGroupSelector+1] >= nDecPos )
471 0 : break; // while
472 0 : ++nGroupSelector;
473 : }
474 0 : else if ( !nGroupExceed )
475 0 : nGroupExceed = nGrouping;
476 : }
477 : }
478 :
479 : // print the number
480 9855 : if( nDigits > 0 )
481 : {
482 137492 : for ( int i = 0; ; i++ )
483 : {
484 137492 : if( i < 15 )
485 : {
486 : int nDigit;
487 126776 : if (nDigits-1 == 0 && i > 0 && i < 14)
488 4014 : nDigit = static_cast< int >( floor( fValue
489 : + nKorrVal[15-i] ) );
490 : else
491 122762 : nDigit = static_cast< int >( fValue + 1E-15 );
492 126776 : if (nDigit >= 10)
493 : { // after-treatment of up-rounding to the next decade
494 0 : sal_Int32 sLen = static_cast< long >(p-pBuf)-1;
495 0 : if (sLen == -1)
496 : {
497 0 : p = pBuf;
498 0 : if ( eFormat == rtl_math_StringFormat_F )
499 : {
500 0 : *p++ = static_cast< typename T::Char >('1');
501 0 : *p++ = static_cast< typename T::Char >('0');
502 : }
503 : else
504 : {
505 0 : *p++ = static_cast< typename T::Char >('1');
506 0 : *p++ = cDecSeparator;
507 0 : *p++ = static_cast< typename T::Char >('0');
508 0 : nExp++;
509 0 : bHasDec = true;
510 : }
511 : }
512 : else
513 : {
514 0 : for (sal_Int32 j = sLen; j >= 0; j--)
515 : {
516 0 : typename T::Char cS = pBuf[j];
517 0 : if (cS != cDecSeparator)
518 : {
519 0 : if ( cS != static_cast< typename T::Char >('9'))
520 : {
521 0 : pBuf[j] = ++cS;
522 0 : j = -1; // break loop
523 : }
524 : else
525 : {
526 0 : pBuf[j]
527 : = static_cast< typename T::Char >('0');
528 0 : if (j == 0)
529 : {
530 0 : if ( eFormat == rtl_math_StringFormat_F)
531 : { // insert '1'
532 0 : typename T::Char * px = p++;
533 0 : while ( pBuf < px )
534 : {
535 0 : *px = *(px-1);
536 0 : px--;
537 : }
538 0 : pBuf[0] = static_cast<
539 : typename T::Char >('1');
540 : }
541 : else
542 : {
543 0 : pBuf[j] = static_cast<
544 : typename T::Char >('1');
545 0 : nExp++;
546 : }
547 : }
548 : }
549 : }
550 : }
551 0 : *p++ = static_cast< typename T::Char >('0');
552 : }
553 0 : fValue = 0.0;
554 : }
555 : else
556 : {
557 126776 : *p++ = static_cast< typename T::Char >(
558 : nDigit + static_cast< typename T::Char >('0') );
559 126776 : fValue = ( fValue - nDigit ) * 10.0;
560 : }
561 : }
562 : else
563 10716 : *p++ = static_cast< typename T::Char >('0');
564 137492 : if( !--nDigits )
565 9853 : break; // for
566 127639 : if( nDecPos )
567 : {
568 22192 : if( !--nDecPos )
569 : {
570 9100 : *p++ = cDecSeparator;
571 9100 : bHasDec = true;
572 : }
573 13092 : else if ( nDecPos == nGrouping )
574 : {
575 0 : *p++ = cGroupSeparator;
576 0 : nGrouping -= pGroups[ nGroupSelector ];
577 0 : if ( nGroupSelector && nGrouping < nGroupExceed )
578 0 : --nGroupSelector;
579 : }
580 : }
581 : }
582 : }
583 :
584 9855 : if ( !bHasDec && eFormat == rtl_math_StringFormat_F )
585 : { // nDecPlaces < 0 did round the value
586 344 : while ( --nDecPos > 0 )
587 : { // fill before decimal point
588 0 : if ( nDecPos == nGrouping )
589 : {
590 0 : *p++ = cGroupSeparator;
591 0 : nGrouping -= pGroups[ nGroupSelector ];
592 0 : if ( nGroupSelector && nGrouping < nGroupExceed )
593 0 : --nGroupSelector;
594 : }
595 0 : *p++ = static_cast< typename T::Char >('0');
596 : }
597 : }
598 :
599 9855 : if ( bEraseTrailingDecZeros && bHasDec && p > pBuf )
600 : {
601 124583 : while ( *(p-1) == static_cast< typename T::Char >('0') )
602 105607 : p--;
603 9488 : if ( *(p-1) == cDecSeparator )
604 8434 : p--;
605 : }
606 :
607 : // Print the exponent ('E', followed by '+' or '-', followed by exactly
608 : // three digits). The code in rtl_[u]str_valueOf{Float|Double} relies on
609 : // this format.
610 9855 : if( eFormat == rtl_math_StringFormat_E )
611 : {
612 10 : if ( p == pBuf )
613 0 : *p++ = static_cast< typename T::Char >('1');
614 : // maybe no nDigits if nDecPlaces < 0
615 10 : *p++ = static_cast< typename T::Char >('E');
616 10 : if( nExp < 0 )
617 : {
618 0 : nExp = -nExp;
619 0 : *p++ = static_cast< typename T::Char >('-');
620 : }
621 : else
622 10 : *p++ = static_cast< typename T::Char >('+');
623 : // if (nExp >= 100 )
624 10 : *p++ = static_cast< typename T::Char >(
625 : nExp / 100 + static_cast< typename T::Char >('0') );
626 10 : nExp %= 100;
627 10 : *p++ = static_cast< typename T::Char >(
628 : nExp / 10 + static_cast< typename T::Char >('0') );
629 10 : *p++ = static_cast< typename T::Char >(
630 : nExp % 10 + static_cast< typename T::Char >('0') );
631 : }
632 :
633 9855 : if (pResultCapacity == 0)
634 9734 : T::createString(pResult, pBuf, p - pBuf);
635 : else
636 121 : T::appendChars(pResult, pResultCapacity, &nResultOffset, pBuf,
637 : p - pBuf);
638 :
639 9855 : if ( pBuf != &aBuf[0] )
640 0 : rtl_freeMemory(pBuf);
641 : }
642 :
643 : }
644 :
645 615 : void SAL_CALL rtl_math_doubleToString(rtl_String ** pResult,
646 : sal_Int32 * pResultCapacity,
647 : sal_Int32 nResultOffset, double fValue,
648 : rtl_math_StringFormat eFormat,
649 : sal_Int32 nDecPlaces,
650 : sal_Char cDecSeparator,
651 : sal_Int32 const * pGroups,
652 : sal_Char cGroupSeparator,
653 : sal_Bool bEraseTrailingDecZeros)
654 : SAL_THROW_EXTERN_C()
655 : {
656 : doubleToString< StringTraits, StringTraits::String >(
657 : pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces,
658 615 : cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros);
659 615 : }
660 :
661 9240 : void SAL_CALL rtl_math_doubleToUString(rtl_uString ** pResult,
662 : sal_Int32 * pResultCapacity,
663 : sal_Int32 nResultOffset, double fValue,
664 : rtl_math_StringFormat eFormat,
665 : sal_Int32 nDecPlaces,
666 : sal_Unicode cDecSeparator,
667 : sal_Int32 const * pGroups,
668 : sal_Unicode cGroupSeparator,
669 : sal_Bool bEraseTrailingDecZeros)
670 : SAL_THROW_EXTERN_C()
671 : {
672 : doubleToString< UStringTraits, UStringTraits::String >(
673 : pResult, pResultCapacity, nResultOffset, fValue, eFormat, nDecPlaces,
674 9240 : cDecSeparator, pGroups, cGroupSeparator, bEraseTrailingDecZeros);
675 9240 : }
676 :
677 :
678 : namespace {
679 :
680 : // if nExp * 10 + nAdd would result in overflow
681 13 : inline bool long10Overflow( long& nExp, int nAdd )
682 : {
683 13 : if ( nExp > (LONG_MAX/10)
684 : || (nExp == (LONG_MAX/10) && nAdd > (LONG_MAX%10)) )
685 : {
686 0 : nExp = LONG_MAX;
687 0 : return true;
688 : }
689 13 : return false;
690 : }
691 :
692 : // We are only concerned about ASCII arabic numerical digits here
693 : template< typename CharT >
694 52533 : inline bool isDigit( CharT c )
695 : {
696 52533 : return 0x30 <= c && c <= 0x39;
697 : }
698 :
699 : template< typename CharT >
700 16538 : inline double stringToDouble(CharT const * pBegin, CharT const * pEnd,
701 : CharT cDecSeparator, CharT cGroupSeparator,
702 : rtl_math_ConversionStatus * pStatus,
703 : CharT const ** pParsedEnd)
704 : {
705 16538 : double fVal = 0.0;
706 16538 : rtl_math_ConversionStatus eStatus = rtl_math_ConversionStatus_Ok;
707 :
708 16538 : CharT const * p0 = pBegin;
709 33080 : while (p0 != pEnd && (*p0 == CharT(' ') || *p0 == CharT('\t')))
710 4 : ++p0;
711 : bool bSign;
712 16538 : if (p0 != pEnd && *p0 == CharT('-'))
713 : {
714 2207 : bSign = true;
715 2207 : ++p0;
716 : }
717 : else
718 : {
719 14331 : bSign = false;
720 14331 : if (p0 != pEnd && *p0 == CharT('+'))
721 2 : ++p0;
722 : }
723 16538 : CharT const * p = p0;
724 16538 : bool bDone = false;
725 :
726 : // #i112652# XMLSchema-2
727 16538 : if (3 >= (pEnd - p))
728 : {
729 8366 : if ((CharT('N') == p[0]) && (CharT('a') == p[1])
730 : && (CharT('N') == p[2]))
731 : {
732 0 : p += 3;
733 0 : rtl::math::setNan( &fVal );
734 0 : bDone = true;
735 : }
736 8366 : else if ((CharT('I') == p[0]) && (CharT('N') == p[1])
737 : && (CharT('F') == p[2]))
738 : {
739 0 : p += 3;
740 0 : fVal = HUGE_VAL;
741 0 : eStatus = rtl_math_ConversionStatus_OutOfRange;
742 0 : bDone = true;
743 : }
744 : }
745 :
746 16538 : if (!bDone) // do not recognize e.g. NaN1.23
747 : {
748 : // leading zeros and group separators may be safely ignored
749 36849 : while (p != pEnd && (*p == CharT('0') || *p == cGroupSeparator))
750 3773 : ++p;
751 :
752 16538 : long nValExp = 0; // carry along exponent of mantissa
753 :
754 : // integer part of mantissa
755 46547 : for (; p != pEnd; ++p)
756 : {
757 37259 : CharT c = *p;
758 37259 : if (isDigit(c))
759 : {
760 30007 : fVal = fVal * 10.0 + static_cast< double >( c - CharT('0') );
761 30007 : ++nValExp;
762 : }
763 7252 : else if (c != cGroupSeparator)
764 7250 : break;
765 : }
766 :
767 : // fraction part of mantissa
768 16538 : if (p != pEnd && *p == cDecSeparator)
769 : {
770 5895 : ++p;
771 5895 : double fFrac = 0.0;
772 5895 : long nFracExp = 0;
773 22167 : while (p != pEnd && *p == CharT('0'))
774 : {
775 10377 : --nFracExp;
776 10377 : ++p;
777 : }
778 5895 : if ( nValExp == 0 )
779 1917 : nValExp = nFracExp - 1; // no integer part => fraction exponent
780 : // one decimal digit needs ld(10) ~= 3.32 bits
781 : static const int nSigs = (DBL_MANT_DIG / 3) + 1;
782 5895 : int nDigs = 0;
783 21016 : for (; p != pEnd; ++p)
784 : {
785 15260 : CharT c = *p;
786 15260 : if (!isDigit(c))
787 139 : break;
788 15121 : if ( nDigs < nSigs )
789 : { // further digits (more than nSigs) don't have any
790 : // significance
791 15121 : fFrac = fFrac * 10.0 + static_cast<double>(c - CharT('0'));
792 15121 : --nFracExp;
793 15121 : ++nDigs;
794 : }
795 : }
796 5895 : if ( fFrac != 0.0 )
797 4202 : fVal += rtl::math::pow10Exp( fFrac, nFracExp );
798 1693 : else if ( nValExp < 0 )
799 840 : nValExp = 0; // no digit other than 0 after decimal point
800 : }
801 :
802 16538 : if ( nValExp > 0 )
803 12672 : --nValExp; // started with offset +1 at the first mantissa digit
804 :
805 : // Exponent
806 16538 : if (p != p0 && p != pEnd && (*p == CharT('E') || *p == CharT('e')))
807 : {
808 9 : ++p;
809 : bool bExpSign;
810 9 : if (p != pEnd && *p == CharT('-'))
811 : {
812 4 : bExpSign = true;
813 4 : ++p;
814 : }
815 : else
816 : {
817 5 : bExpSign = false;
818 5 : if (p != pEnd && *p == CharT('+'))
819 0 : ++p;
820 : }
821 9 : if ( fVal == 0.0 )
822 : { // no matter what follows, zero stays zero, but carry on the
823 : // offset
824 0 : while (p != pEnd && isDigit(*p))
825 0 : ++p;
826 : }
827 : else
828 : {
829 9 : bool bOverFlow = false;
830 9 : long nExp = 0;
831 22 : for (; p != pEnd; ++p)
832 : {
833 14 : CharT c = *p;
834 14 : if (!isDigit(c))
835 1 : break;
836 13 : int i = c - CharT('0');
837 13 : if ( long10Overflow( nExp, i ) )
838 0 : bOverFlow = true;
839 : else
840 13 : nExp = nExp * 10 + i;
841 : }
842 9 : if ( nExp )
843 : {
844 8 : if ( bExpSign )
845 4 : nExp = -nExp;
846 8 : long nAllExp = ( bOverFlow ? 0 : nExp + nValExp );
847 8 : if ( nAllExp > DBL_MAX_10_EXP || (bOverFlow && !bExpSign) )
848 : { // overflow
849 0 : fVal = HUGE_VAL;
850 0 : eStatus = rtl_math_ConversionStatus_OutOfRange;
851 : }
852 8 : else if ((nAllExp < DBL_MIN_10_EXP) ||
853 : (bOverFlow && bExpSign) )
854 : { // underflow
855 0 : fVal = 0.0;
856 0 : eStatus = rtl_math_ConversionStatus_OutOfRange;
857 : }
858 8 : else if ( nExp > DBL_MAX_10_EXP || nExp < DBL_MIN_10_EXP )
859 : { // compensate exponents
860 0 : fVal = rtl::math::pow10Exp( fVal, -nValExp );
861 0 : fVal = rtl::math::pow10Exp( fVal, nAllExp );
862 : }
863 : else
864 8 : fVal = rtl::math::pow10Exp( fVal, nExp ); // normal
865 : }
866 : }
867 : }
868 16529 : else if (p - p0 == 2 && p != pEnd && p[0] == CharT('#')
869 : && p[-1] == cDecSeparator && p[-2] == CharT('1'))
870 : {
871 0 : if (pEnd - p >= 4 && p[1] == CharT('I') && p[2] == CharT('N')
872 : && p[3] == CharT('F'))
873 : {
874 : // "1.#INF", "+1.#INF", "-1.#INF"
875 0 : p += 4;
876 0 : fVal = HUGE_VAL;
877 0 : eStatus = rtl_math_ConversionStatus_OutOfRange;
878 : // Eat any further digits:
879 0 : while (p != pEnd && isDigit(*p))
880 0 : ++p;
881 : }
882 0 : else if (pEnd - p >= 4 && p[1] == CharT('N') && p[2] == CharT('A')
883 : && p[3] == CharT('N'))
884 : {
885 : // "1.#NAN", "+1.#NAN", "-1.#NAN"
886 0 : p += 4;
887 0 : rtl::math::setNan( &fVal );
888 0 : if (bSign)
889 : {
890 : union {
891 : double sd;
892 : sal_math_Double md;
893 : } m;
894 0 : m.sd = fVal;
895 0 : m.md.w32_parts.msw |= 0x80000000; // create negative NaN
896 0 : fVal = m.sd;
897 0 : bSign = false; // don't negate again
898 : }
899 : // Eat any further digits:
900 0 : while (p != pEnd && isDigit(*p))
901 0 : ++p;
902 : }
903 : }
904 : }
905 :
906 : // overflow also if more than DBL_MAX_10_EXP digits without decimal
907 : // separator, or 0. and more than DBL_MIN_10_EXP digits, ...
908 16538 : bool bHuge = fVal == HUGE_VAL; // g++ 3.0.1 requires it this way...
909 16538 : if ( bHuge )
910 0 : eStatus = rtl_math_ConversionStatus_OutOfRange;
911 :
912 16538 : if ( bSign )
913 2207 : fVal = -fVal;
914 :
915 16538 : if (pStatus != 0)
916 7614 : *pStatus = eStatus;
917 16538 : if (pParsedEnd != 0)
918 7706 : *pParsedEnd = p == p0 ? pBegin : p;
919 :
920 16538 : return fVal;
921 : }
922 :
923 : }
924 :
925 5451 : double SAL_CALL rtl_math_stringToDouble(sal_Char const * pBegin,
926 : sal_Char const * pEnd,
927 : sal_Char cDecSeparator,
928 : sal_Char cGroupSeparator,
929 : rtl_math_ConversionStatus * pStatus,
930 : sal_Char const ** pParsedEnd)
931 : SAL_THROW_EXTERN_C()
932 : {
933 : return stringToDouble(pBegin, pEnd, cDecSeparator, cGroupSeparator, pStatus,
934 5451 : pParsedEnd);
935 : }
936 :
937 11087 : double SAL_CALL rtl_math_uStringToDouble(sal_Unicode const * pBegin,
938 : sal_Unicode const * pEnd,
939 : sal_Unicode cDecSeparator,
940 : sal_Unicode cGroupSeparator,
941 : rtl_math_ConversionStatus * pStatus,
942 : sal_Unicode const ** pParsedEnd)
943 : SAL_THROW_EXTERN_C()
944 : {
945 : return stringToDouble(pBegin, pEnd, cDecSeparator, cGroupSeparator, pStatus,
946 11087 : pParsedEnd);
947 : }
948 :
949 42715 : double SAL_CALL rtl_math_round(double fValue, int nDecPlaces,
950 : enum rtl_math_RoundingMode eMode)
951 : SAL_THROW_EXTERN_C()
952 : {
953 : OSL_ASSERT(nDecPlaces >= -20 && nDecPlaces <= 20);
954 :
955 42715 : if ( fValue == 0.0 )
956 37372 : return fValue;
957 :
958 : // sign adjustment
959 5343 : bool bSign = rtl::math::isSignBitSet( fValue );
960 5343 : if ( bSign )
961 82 : fValue = -fValue;
962 :
963 5343 : double fFac = 0;
964 5343 : if ( nDecPlaces != 0 )
965 : {
966 : // max 20 decimals, we don't have unlimited precision
967 : // #38810# and no overflow on fValue*=fFac
968 3439 : if ( nDecPlaces < -20 || 20 < nDecPlaces || fValue > (DBL_MAX / 1e20) )
969 0 : return bSign ? -fValue : fValue;
970 :
971 3439 : fFac = getN10Exp( nDecPlaces );
972 3439 : fValue *= fFac;
973 : }
974 : //else //! uninitialized fFac, not needed
975 :
976 5343 : switch ( eMode )
977 : {
978 : case rtl_math_RoundingMode_Corrected :
979 : {
980 : int nExp; // exponent for correction
981 5045 : if ( fValue > 0.0 )
982 5045 : nExp = static_cast<int>( floor( log10( fValue ) ) );
983 : else
984 0 : nExp = 0;
985 5045 : int nIndex = 15 - nExp;
986 5045 : if ( nIndex > 15 )
987 1 : nIndex = 15;
988 5044 : else if ( nIndex <= 1 )
989 1581 : nIndex = 0;
990 5045 : fValue = floor( fValue + 0.5 + nKorrVal[nIndex] );
991 : }
992 5045 : break;
993 : case rtl_math_RoundingMode_Down :
994 0 : fValue = rtl::math::approxFloor( fValue );
995 0 : break;
996 : case rtl_math_RoundingMode_Up :
997 0 : fValue = rtl::math::approxCeil( fValue );
998 0 : break;
999 : case rtl_math_RoundingMode_Floor :
1000 : fValue = bSign ? rtl::math::approxCeil( fValue )
1001 298 : : rtl::math::approxFloor( fValue );
1002 298 : break;
1003 : case rtl_math_RoundingMode_Ceiling :
1004 : fValue = bSign ? rtl::math::approxFloor( fValue )
1005 0 : : rtl::math::approxCeil( fValue );
1006 0 : break;
1007 : case rtl_math_RoundingMode_HalfDown :
1008 : {
1009 0 : double f = floor( fValue );
1010 0 : fValue = ((fValue - f) <= 0.5) ? f : ceil( fValue );
1011 : }
1012 0 : break;
1013 : case rtl_math_RoundingMode_HalfUp :
1014 : {
1015 0 : double f = floor( fValue );
1016 0 : fValue = ((fValue - f) < 0.5) ? f : ceil( fValue );
1017 : }
1018 0 : break;
1019 : case rtl_math_RoundingMode_HalfEven :
1020 : #if defined FLT_ROUNDS
1021 : /*
1022 : Use fast version. FLT_ROUNDS may be defined to a function by some compilers!
1023 :
1024 : DBL_EPSILON is the smallest fractional number which can be represented,
1025 : its reciprocal is therefore the smallest number that cannot have a
1026 : fractional part. Once you add this reciprocal to `x', its fractional part
1027 : is stripped off. Simply subtracting the reciprocal back out returns `x'
1028 : without its fractional component.
1029 : Simple, clever, and elegant - thanks to Ross Cottrell, the original author,
1030 : who placed it into public domain.
1031 :
1032 : volatile: prevent compiler from being too smart
1033 : */
1034 : if ( FLT_ROUNDS == 1 )
1035 : {
1036 0 : volatile double x = fValue + 1.0 / DBL_EPSILON;
1037 0 : fValue = x - 1.0 / DBL_EPSILON;
1038 : }
1039 : else
1040 : #endif // FLT_ROUNDS
1041 : {
1042 : double f = floor( fValue );
1043 : if ( (fValue - f) != 0.5 )
1044 : fValue = floor( fValue + 0.5 );
1045 : else
1046 : {
1047 : double g = f / 2.0;
1048 : fValue = (g == floor( g )) ? f : (f + 1.0);
1049 : }
1050 : }
1051 0 : break;
1052 : default:
1053 : OSL_ASSERT(false);
1054 0 : break;
1055 : }
1056 :
1057 5343 : if ( nDecPlaces != 0 )
1058 3439 : fValue /= fFac;
1059 :
1060 5343 : return bSign ? -fValue : fValue;
1061 : }
1062 :
1063 :
1064 4410 : double SAL_CALL rtl_math_pow10Exp(double fValue, int nExp) SAL_THROW_EXTERN_C()
1065 : {
1066 4410 : return fValue * getN10Exp( nExp );
1067 : }
1068 :
1069 :
1070 1660 : double SAL_CALL rtl_math_approxValue( double fValue ) SAL_THROW_EXTERN_C()
1071 : {
1072 1660 : if (fValue == 0.0 || fValue == HUGE_VAL || !::rtl::math::isFinite( fValue))
1073 : // We don't handle these conditions. Bail out.
1074 79 : return fValue;
1075 :
1076 1581 : double fOrigValue = fValue;
1077 :
1078 1581 : bool bSign = ::rtl::math::isSignBitSet( fValue);
1079 1581 : if (bSign)
1080 130 : fValue = -fValue;
1081 :
1082 1581 : int nExp = static_cast<int>( floor( log10( fValue)));
1083 1581 : nExp = 14 - nExp;
1084 1581 : double fExpValue = getN10Exp( nExp);
1085 :
1086 1581 : fValue *= fExpValue;
1087 : // If the original value was near DBL_MIN we got an overflow. Restore and
1088 : // bail out.
1089 1581 : if (!rtl::math::isFinite( fValue))
1090 0 : return fOrigValue;
1091 1581 : fValue = rtl_math_round( fValue, 0, rtl_math_RoundingMode_Corrected);
1092 1581 : fValue /= fExpValue;
1093 : // If the original value was near DBL_MAX we got an overflow. Restore and
1094 : // bail out.
1095 1581 : if (!rtl::math::isFinite( fValue))
1096 0 : return fOrigValue;
1097 :
1098 1581 : return bSign ? -fValue : fValue;
1099 : }
1100 :
1101 :
1102 0 : double SAL_CALL rtl_math_expm1( double fValue ) SAL_THROW_EXTERN_C()
1103 : {
1104 0 : double fe = exp( fValue );
1105 0 : if (fe == 1.0)
1106 0 : return fValue;
1107 0 : if (fe-1.0 == -1.0)
1108 0 : return -1.0;
1109 0 : return (fe-1.0) * fValue / log(fe);
1110 : }
1111 :
1112 :
1113 0 : double SAL_CALL rtl_math_log1p( double fValue ) SAL_THROW_EXTERN_C()
1114 : {
1115 : // Use volatile because a compiler may be too smart "optimizing" the
1116 : // condition such that in certain cases the else path was called even if
1117 : // (fp==1.0) was true, where the term (fp-1.0) then resulted in 0.0 and
1118 : // hence the entire expression resulted in NaN.
1119 : // Happened with g++ 3.4.1 and an input value of 9.87E-18
1120 0 : volatile double fp = 1.0 + fValue;
1121 0 : if (fp == 1.0)
1122 0 : return fValue;
1123 : else
1124 0 : return log(fp) * fValue / (fp-1.0);
1125 : }
1126 :
1127 :
1128 0 : double SAL_CALL rtl_math_atanh( double fValue ) SAL_THROW_EXTERN_C()
1129 : {
1130 0 : return 0.5 * rtl_math_log1p( 2.0 * fValue / (1.0-fValue) );
1131 : }
1132 :
1133 :
1134 : /** Parent error function (erf) that calls different algorithms based on the
1135 : value of x. It takes care of cases where x is negative as erf is an odd
1136 : function i.e. erf(-x) = -erf(x).
1137 :
1138 : Kramer, W., and Blomquist, F., 2000, Algorithms with Guaranteed Error Bounds
1139 : for the Error Function and the Complementary Error Function
1140 :
1141 : http://www.math.uni-wuppertal.de/wrswt/literatur_en.html
1142 :
1143 : @author Kohei Yoshida <kohei@openoffice.org>
1144 :
1145 : @see #i55735#
1146 : */
1147 0 : double SAL_CALL rtl_math_erf( double x ) SAL_THROW_EXTERN_C()
1148 : {
1149 0 : if( x == 0.0 )
1150 0 : return 0.0;
1151 :
1152 0 : bool bNegative = false;
1153 0 : if ( x < 0.0 )
1154 : {
1155 0 : x = fabs( x );
1156 0 : bNegative = true;
1157 : }
1158 :
1159 0 : double fErf = 1.0;
1160 0 : if ( x < 1.0e-10 )
1161 0 : fErf = (double) (x*1.1283791670955125738961589031215452L);
1162 0 : else if ( x < 0.65 )
1163 0 : lcl_Erf0065( x, fErf );
1164 : else
1165 0 : fErf = 1.0 - rtl_math_erfc( x );
1166 :
1167 0 : if ( bNegative )
1168 0 : fErf *= -1.0;
1169 :
1170 0 : return fErf;
1171 : }
1172 :
1173 :
1174 : /** Parent complementary error function (erfc) that calls different algorithms
1175 : based on the value of x. It takes care of cases where x is negative as erfc
1176 : satisfies relationship erfc(-x) = 2 - erfc(x). See the comment for Erf(x)
1177 : for the source publication.
1178 :
1179 : @author Kohei Yoshida <kohei@openoffice.org>
1180 :
1181 : @see #i55735#, moved from module scaddins (#i97091#)
1182 :
1183 : */
1184 0 : double SAL_CALL rtl_math_erfc( double x ) SAL_THROW_EXTERN_C()
1185 : {
1186 0 : if ( x == 0.0 )
1187 0 : return 1.0;
1188 :
1189 0 : bool bNegative = false;
1190 0 : if ( x < 0.0 )
1191 : {
1192 0 : x = fabs( x );
1193 0 : bNegative = true;
1194 : }
1195 :
1196 0 : double fErfc = 0.0;
1197 0 : if ( x >= 0.65 )
1198 : {
1199 0 : if ( x < 6.0 )
1200 0 : lcl_Erfc0600( x, fErfc );
1201 : else
1202 0 : lcl_Erfc2654( x, fErfc );
1203 : }
1204 : else
1205 0 : fErfc = 1.0 - rtl_math_erf( x );
1206 :
1207 0 : if ( bNegative )
1208 0 : fErfc = 2.0 - fErfc;
1209 :
1210 0 : return fErfc;
1211 : }
1212 :
1213 : /** improved accuracy of asinh for |x| large and for x near zero
1214 : @see #i97605#
1215 : */
1216 0 : double SAL_CALL rtl_math_asinh( double fX ) SAL_THROW_EXTERN_C()
1217 : {
1218 0 : if ( fX == 0.0 )
1219 0 : return 0.0;
1220 : else
1221 : {
1222 0 : double fSign = 1.0;
1223 0 : if ( fX < 0.0 )
1224 : {
1225 0 : fX = - fX;
1226 0 : fSign = -1.0;
1227 : }
1228 0 : if ( fX < 0.125 )
1229 0 : return fSign * rtl_math_log1p( fX + fX*fX / (1.0 + sqrt( 1.0 + fX*fX)));
1230 0 : else if ( fX < 1.25e7 )
1231 0 : return fSign * log( fX + sqrt( 1.0 + fX*fX));
1232 : else
1233 0 : return fSign * log( 2.0*fX);
1234 : }
1235 : }
1236 :
1237 : /** improved accuracy of acosh for x large and for x near 1
1238 : @see #i97605#
1239 : */
1240 1 : double SAL_CALL rtl_math_acosh( double fX ) SAL_THROW_EXTERN_C()
1241 : {
1242 1 : volatile double fZ = fX - 1.0;
1243 1 : if ( fX < 1.0 )
1244 : {
1245 : double fResult;
1246 0 : ::rtl::math::setNan( &fResult );
1247 0 : return fResult;
1248 : }
1249 1 : else if ( fX == 1.0 )
1250 1 : return 0.0;
1251 0 : else if ( fX < 1.1 )
1252 0 : return rtl_math_log1p( fZ + sqrt( fZ*fZ + 2.0*fZ));
1253 0 : else if ( fX < 1.25e7 )
1254 0 : return log( fX + sqrt( fX*fX - 1.0));
1255 : else
1256 0 : return log( 2.0*fX);
1257 : }
1258 :
1259 : /* vim:set shiftwidth=4 softtabstop=4 expandtab: */
|
