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1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // Copyright Christopher Kormanyos 2002 - 2013. | |
3 | // Copyright 2011 -2013 John Maddock. Distributed under the Boost | |
4 | // Software License, Version 1.0. (See accompanying file | |
5 | // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) | |
6 | // | |
7 | // This work is based on an earlier work: | |
8 | // "Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function Calculations", | |
9 | // in ACM TOMS, {VOL 37, ISSUE 4, (February 2011)} (C) ACM, 2011. http://doi.acm.org/10.1145/1916461.1916469 | |
10 | // | |
11 | // Note that there are no "noexcept" specifications on the functions in this file: there are too many | |
12 | // calls to lexical_cast (and similar) to easily analyse the code for correctness. So until compilers | |
13 | // can detect noexcept misuse at compile time, the only realistic option is to simply not use it here. | |
14 | // | |
15 | ||
16 | #ifndef BOOST_MP_CPP_DEC_FLOAT_BACKEND_HPP | |
17 | #define BOOST_MP_CPP_DEC_FLOAT_BACKEND_HPP | |
18 | ||
19 | #include <boost/config.hpp> | |
20 | #include <boost/cstdint.hpp> | |
21 | #include <limits> | |
22 | #ifndef BOOST_NO_CXX11_HDR_ARRAY | |
23 | #include <array> | |
24 | #else | |
25 | #include <boost/array.hpp> | |
26 | #endif | |
27 | #include <boost/cstdint.hpp> | |
28 | #include <boost/functional/hash_fwd.hpp> | |
29 | #include <boost/multiprecision/number.hpp> | |
30 | #include <boost/multiprecision/detail/big_lanczos.hpp> | |
31 | #include <boost/multiprecision/detail/dynamic_array.hpp> | |
32 | ||
33 | // | |
34 | // Headers required for Boost.Math integration: | |
35 | // | |
36 | #include <boost/math/policies/policy.hpp> | |
37 | // | |
38 | // Some includes we need from Boost.Math, since we rely on that library to provide these functions: | |
39 | // | |
40 | #include <boost/math/special_functions/asinh.hpp> | |
41 | #include <boost/math/special_functions/acosh.hpp> | |
42 | #include <boost/math/special_functions/atanh.hpp> | |
43 | #include <boost/math/special_functions/cbrt.hpp> | |
44 | #include <boost/math/special_functions/expm1.hpp> | |
45 | #include <boost/math/special_functions/gamma.hpp> | |
46 | ||
47 | #ifdef BOOST_MSVC | |
48 | #pragma warning(push) | |
49 | #pragma warning(disable:6326) // comparison of two constants | |
50 | #endif | |
51 | ||
52 | namespace boost{ | |
53 | namespace multiprecision{ | |
54 | namespace backends{ | |
55 | ||
56 | template <unsigned Digits10, class ExponentType = boost::int32_t, class Allocator = void> | |
57 | class cpp_dec_float; | |
58 | ||
59 | } // namespace | |
60 | ||
61 | template <unsigned Digits10, class ExponentType, class Allocator> | |
62 | struct number_category<backends::cpp_dec_float<Digits10, ExponentType, Allocator> > : public mpl::int_<number_kind_floating_point>{}; | |
63 | ||
64 | namespace backends{ | |
65 | ||
66 | template <unsigned Digits10, class ExponentType, class Allocator> | |
67 | class cpp_dec_float | |
68 | { | |
69 | private: | |
70 | static const boost::int32_t cpp_dec_float_digits10_setting = Digits10; | |
71 | ||
72 | // We need at least 16-bits in the exponent type to do anything sensible: | |
73 | BOOST_STATIC_ASSERT_MSG(boost::is_signed<ExponentType>::value, "ExponentType must be a signed built in integer type."); | |
74 | BOOST_STATIC_ASSERT_MSG(sizeof(ExponentType) > 1, "ExponentType is too small."); | |
75 | ||
76 | public: | |
77 | typedef mpl::list<boost::long_long_type> signed_types; | |
78 | typedef mpl::list<boost::ulong_long_type> unsigned_types; | |
79 | typedef mpl::list<long double> float_types; | |
80 | typedef ExponentType exponent_type; | |
81 | ||
82 | static const boost::int32_t cpp_dec_float_radix = 10L; | |
83 | static const boost::int32_t cpp_dec_float_digits10_limit_lo = 9L; | |
84 | static const boost::int32_t cpp_dec_float_digits10_limit_hi = boost::integer_traits<boost::int32_t>::const_max - 100; | |
85 | static const boost::int32_t cpp_dec_float_digits10 = ((cpp_dec_float_digits10_setting < cpp_dec_float_digits10_limit_lo) ? cpp_dec_float_digits10_limit_lo : ((cpp_dec_float_digits10_setting > cpp_dec_float_digits10_limit_hi) ? cpp_dec_float_digits10_limit_hi : cpp_dec_float_digits10_setting)); | |
86 | static const ExponentType cpp_dec_float_max_exp10 = (static_cast<ExponentType>(1) << (std::numeric_limits<ExponentType>::digits - 5)); | |
87 | static const ExponentType cpp_dec_float_min_exp10 = -cpp_dec_float_max_exp10; | |
88 | static const ExponentType cpp_dec_float_max_exp = cpp_dec_float_max_exp10; | |
89 | static const ExponentType cpp_dec_float_min_exp = cpp_dec_float_min_exp10; | |
90 | ||
91 | BOOST_STATIC_ASSERT((cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10 == -cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10)); | |
92 | ||
93 | private: | |
94 | static const boost::int32_t cpp_dec_float_elem_digits10 = 8L; | |
95 | static const boost::int32_t cpp_dec_float_elem_mask = 100000000L; | |
96 | ||
97 | BOOST_STATIC_ASSERT(0 == cpp_dec_float_max_exp10 % cpp_dec_float_elem_digits10); | |
98 | ||
99 | // There are three guard limbs. | |
100 | // 1) The first limb has 'play' from 1...8 decimal digits. | |
101 | // 2) The last limb also has 'play' from 1...8 decimal digits. | |
102 | // 3) One limb can get lost when justifying after multiply, | |
103 | // as only half of the triangle is multiplied and a carry | |
104 | // from below is missing. | |
105 | static const boost::int32_t cpp_dec_float_elem_number_request = static_cast<boost::int32_t>((cpp_dec_float_digits10 / cpp_dec_float_elem_digits10) + (((cpp_dec_float_digits10 % cpp_dec_float_elem_digits10) != 0) ? 1 : 0)); | |
106 | ||
107 | // The number of elements needed (with a minimum of two) plus three added guard limbs. | |
108 | static const boost::int32_t cpp_dec_float_elem_number = static_cast<boost::int32_t>(((cpp_dec_float_elem_number_request < 2L) ? 2L : cpp_dec_float_elem_number_request) + 3L); | |
109 | ||
110 | public: | |
111 | static const boost::int32_t cpp_dec_float_total_digits10 = static_cast<boost::int32_t>(cpp_dec_float_elem_number * cpp_dec_float_elem_digits10); | |
112 | ||
113 | private: | |
114 | ||
115 | typedef enum enum_fpclass_type | |
116 | { | |
117 | cpp_dec_float_finite, | |
118 | cpp_dec_float_inf, | |
119 | cpp_dec_float_NaN | |
120 | } | |
121 | fpclass_type; | |
122 | ||
123 | #ifndef BOOST_NO_CXX11_HDR_ARRAY | |
124 | typedef typename mpl::if_<is_void<Allocator>, | |
125 | std::array<boost::uint32_t, cpp_dec_float_elem_number>, | |
126 | detail::dynamic_array<boost::uint32_t, cpp_dec_float_elem_number, Allocator> | |
127 | >::type array_type; | |
128 | #else | |
129 | typedef typename mpl::if_<is_void<Allocator>, | |
130 | boost::array<boost::uint32_t, cpp_dec_float_elem_number>, | |
131 | detail::dynamic_array<boost::uint32_t, cpp_dec_float_elem_number, Allocator> | |
132 | >::type array_type; | |
133 | #endif | |
134 | ||
135 | array_type data; | |
136 | ExponentType exp; | |
137 | bool neg; | |
138 | fpclass_type fpclass; | |
139 | boost::int32_t prec_elem; | |
140 | ||
141 | // | |
142 | // Special values constructor: | |
143 | // | |
144 | cpp_dec_float(fpclass_type c) : | |
145 | data(), | |
146 | exp (static_cast<ExponentType>(0)), | |
147 | neg (false), | |
148 | fpclass (c), | |
149 | prec_elem(cpp_dec_float_elem_number) { } | |
150 | ||
151 | // | |
152 | // Static data initializer: | |
153 | // | |
154 | struct initializer | |
155 | { | |
156 | initializer() | |
157 | { | |
158 | cpp_dec_float<Digits10, ExponentType, Allocator>::nan(); | |
159 | cpp_dec_float<Digits10, ExponentType, Allocator>::inf(); | |
160 | (cpp_dec_float<Digits10, ExponentType, Allocator>::min)(); | |
161 | (cpp_dec_float<Digits10, ExponentType, Allocator>::max)(); | |
162 | cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); | |
163 | cpp_dec_float<Digits10, ExponentType, Allocator>::one(); | |
164 | cpp_dec_float<Digits10, ExponentType, Allocator>::two(); | |
165 | cpp_dec_float<Digits10, ExponentType, Allocator>::half(); | |
166 | cpp_dec_float<Digits10, ExponentType, Allocator>::double_min(); | |
167 | cpp_dec_float<Digits10, ExponentType, Allocator>::double_max(); | |
168 | cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_max(); | |
169 | cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_min(); | |
170 | cpp_dec_float<Digits10, ExponentType, Allocator>::long_long_max(); | |
171 | cpp_dec_float<Digits10, ExponentType, Allocator>::long_long_min(); | |
172 | cpp_dec_float<Digits10, ExponentType, Allocator>::ulong_long_max(); | |
173 | cpp_dec_float<Digits10, ExponentType, Allocator>::eps(); | |
174 | cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(0); | |
175 | } | |
176 | void do_nothing(){} | |
177 | }; | |
178 | ||
179 | static initializer init; | |
180 | ||
181 | public: | |
182 | // Constructors | |
183 | cpp_dec_float() BOOST_MP_NOEXCEPT_IF(noexcept(array_type())) : | |
184 | data(), | |
185 | exp (static_cast<ExponentType>(0)), | |
186 | neg (false), | |
187 | fpclass (cpp_dec_float_finite), | |
188 | prec_elem(cpp_dec_float_elem_number) { } | |
189 | ||
190 | cpp_dec_float(const char* s) : | |
191 | data(), | |
192 | exp (static_cast<ExponentType>(0)), | |
193 | neg (false), | |
194 | fpclass (cpp_dec_float_finite), | |
195 | prec_elem(cpp_dec_float_elem_number) | |
196 | { | |
197 | *this = s; | |
198 | } | |
199 | ||
200 | template<class I> | |
201 | cpp_dec_float(I i, typename enable_if<is_unsigned<I> >::type* = 0) : | |
202 | data(), | |
203 | exp (static_cast<ExponentType>(0)), | |
204 | neg (false), | |
205 | fpclass (cpp_dec_float_finite), | |
206 | prec_elem(cpp_dec_float_elem_number) | |
207 | { | |
208 | from_unsigned_long_long(i); | |
209 | } | |
210 | ||
211 | template <class I> | |
212 | cpp_dec_float(I i, typename enable_if<is_signed<I> >::type* = 0) : | |
213 | data(), | |
214 | exp (static_cast<ExponentType>(0)), | |
215 | neg (false), | |
216 | fpclass (cpp_dec_float_finite), | |
217 | prec_elem(cpp_dec_float_elem_number) | |
218 | { | |
219 | if(i < 0) | |
220 | { | |
221 | from_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(i)); | |
222 | negate(); | |
223 | } | |
224 | else | |
225 | from_unsigned_long_long(i); | |
226 | } | |
227 | ||
228 | cpp_dec_float(const cpp_dec_float& f) BOOST_MP_NOEXCEPT_IF(noexcept(array_type(std::declval<const array_type&>()))) : | |
229 | data (f.data), | |
230 | exp (f.exp), | |
231 | neg (f.neg), | |
232 | fpclass (f.fpclass), | |
233 | prec_elem(f.prec_elem) { } | |
234 | ||
235 | template <unsigned D, class ET, class A> | |
236 | cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename enable_if_c<D <= Digits10>::type* = 0) : | |
237 | data(), | |
238 | exp (f.exp), | |
239 | neg (f.neg), | |
240 | fpclass (static_cast<fpclass_type>(static_cast<int>(f.fpclass))), | |
241 | prec_elem(cpp_dec_float_elem_number) | |
242 | { | |
243 | std::copy(f.data.begin(), f.data.begin() + f.prec_elem, data.begin()); | |
244 | } | |
245 | template <unsigned D, class ET, class A> | |
246 | explicit cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename disable_if_c<D <= Digits10>::type* = 0) : | |
247 | data(), | |
248 | exp (f.exp), | |
249 | neg (f.neg), | |
250 | fpclass (static_cast<fpclass_type>(static_cast<int>(f.fpclass))), | |
251 | prec_elem(cpp_dec_float_elem_number) | |
252 | { | |
253 | // TODO: this doesn't round! | |
254 | std::copy(f.data.begin(), f.data.begin() + prec_elem, data.begin()); | |
255 | } | |
256 | ||
257 | template <class F> | |
258 | cpp_dec_float(const F val, typename enable_if<is_floating_point<F> >::type* = 0) : | |
259 | data(), | |
260 | exp (static_cast<ExponentType>(0)), | |
261 | neg (false), | |
262 | fpclass (cpp_dec_float_finite), | |
263 | prec_elem(cpp_dec_float_elem_number) | |
264 | { | |
265 | *this = val; | |
266 | } | |
267 | ||
268 | cpp_dec_float(const double mantissa, const ExponentType exponent); | |
269 | ||
270 | std::size_t hash()const | |
271 | { | |
272 | std::size_t result = 0; | |
273 | for(int i = 0; i < prec_elem; ++i) | |
274 | boost::hash_combine(result, data[i]); | |
275 | boost::hash_combine(result, exp); | |
276 | boost::hash_combine(result, neg); | |
277 | boost::hash_combine(result, fpclass); | |
278 | return result; | |
279 | } | |
280 | ||
281 | // Specific special values. | |
282 | static const cpp_dec_float& nan() | |
283 | { | |
284 | static const cpp_dec_float val(cpp_dec_float_NaN); | |
285 | init.do_nothing(); | |
286 | return val; | |
287 | } | |
288 | ||
289 | static const cpp_dec_float& inf() | |
290 | { | |
291 | static const cpp_dec_float val(cpp_dec_float_inf); | |
292 | init.do_nothing(); | |
293 | return val; | |
294 | } | |
295 | ||
296 | static const cpp_dec_float& (max)() | |
297 | { | |
298 | init.do_nothing(); | |
299 | static cpp_dec_float val_max = std::string("1.0e" + boost::lexical_cast<std::string>(cpp_dec_float_max_exp10)).c_str(); | |
300 | return val_max; | |
301 | } | |
302 | ||
303 | static const cpp_dec_float& (min)() | |
304 | { | |
305 | init.do_nothing(); | |
306 | static cpp_dec_float val_min = std::string("1.0e" + boost::lexical_cast<std::string>(cpp_dec_float_min_exp10)).c_str(); | |
307 | return val_min; | |
308 | } | |
309 | ||
310 | static const cpp_dec_float& zero() | |
311 | { | |
312 | init.do_nothing(); | |
313 | static cpp_dec_float val(static_cast<boost::ulong_long_type>(0u)); | |
314 | return val; | |
315 | } | |
316 | ||
317 | static const cpp_dec_float& one() | |
318 | { | |
319 | init.do_nothing(); | |
320 | static cpp_dec_float val(static_cast<boost::ulong_long_type>(1u)); | |
321 | return val; | |
322 | } | |
323 | ||
324 | static const cpp_dec_float& two() | |
325 | { | |
326 | init.do_nothing(); | |
327 | static cpp_dec_float val(static_cast<boost::ulong_long_type>(2u)); | |
328 | return val; | |
329 | } | |
330 | ||
331 | static const cpp_dec_float& half() | |
332 | { | |
333 | init.do_nothing(); | |
334 | static cpp_dec_float val(0.5L); | |
335 | return val; | |
336 | } | |
337 | ||
338 | static const cpp_dec_float& double_min() | |
339 | { | |
340 | init.do_nothing(); | |
341 | static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::min)())); | |
342 | return val; | |
343 | } | |
344 | ||
345 | static const cpp_dec_float& double_max() | |
346 | { | |
347 | init.do_nothing(); | |
348 | static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::max)())); | |
349 | return val; | |
350 | } | |
351 | ||
352 | static const cpp_dec_float& long_double_min() | |
353 | { | |
354 | init.do_nothing(); | |
355 | #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS | |
356 | static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::min)())); | |
357 | #else | |
358 | static cpp_dec_float val((std::numeric_limits<long double>::min)()); | |
359 | #endif | |
360 | return val; | |
361 | } | |
362 | ||
363 | static const cpp_dec_float& long_double_max() | |
364 | { | |
365 | init.do_nothing(); | |
366 | #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS | |
367 | static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::max)())); | |
368 | #else | |
369 | static cpp_dec_float val((std::numeric_limits<long double>::max)()); | |
370 | #endif | |
371 | return val; | |
372 | } | |
373 | ||
374 | static const cpp_dec_float& long_long_max() | |
375 | { | |
376 | init.do_nothing(); | |
377 | static cpp_dec_float val((std::numeric_limits<boost::long_long_type>::max)()); | |
378 | return val; | |
379 | } | |
380 | ||
381 | static const cpp_dec_float& long_long_min() | |
382 | { | |
383 | init.do_nothing(); | |
384 | static cpp_dec_float val((std::numeric_limits<boost::long_long_type>::min)()); | |
385 | return val; | |
386 | } | |
387 | ||
388 | static const cpp_dec_float& ulong_long_max() | |
389 | { | |
390 | init.do_nothing(); | |
391 | static cpp_dec_float val((std::numeric_limits<boost::ulong_long_type>::max)()); | |
392 | return val; | |
393 | } | |
394 | ||
395 | static const cpp_dec_float& eps() | |
396 | { | |
397 | init.do_nothing(); | |
398 | static cpp_dec_float val(1.0, 1 - static_cast<int>(cpp_dec_float_digits10)); | |
399 | return val; | |
400 | } | |
401 | ||
402 | // Basic operations. | |
403 | cpp_dec_float& operator=(const cpp_dec_float& v) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<array_type&>() = std::declval<const array_type&>())) | |
404 | { | |
405 | data = v.data; | |
406 | exp = v.exp; | |
407 | neg = v.neg; | |
408 | fpclass = v.fpclass; | |
409 | prec_elem = v.prec_elem; | |
410 | return *this; | |
411 | } | |
412 | ||
413 | template <unsigned D> | |
414 | cpp_dec_float& operator=(const cpp_dec_float<D>& f) | |
415 | { | |
416 | exp = f.exp; | |
417 | neg = f.neg; | |
418 | fpclass = static_cast<enum_fpclass_type>(static_cast<int>(f.fpclass)); | |
419 | unsigned elems = (std::min)(f.prec_elem, cpp_dec_float_elem_number); | |
420 | std::copy(f.data.begin(), f.data.begin() + elems, data.begin()); | |
421 | std::fill(data.begin() + elems, data.end(), 0); | |
422 | prec_elem = cpp_dec_float_elem_number; | |
423 | return *this; | |
424 | } | |
425 | ||
426 | cpp_dec_float& operator=(boost::long_long_type v) | |
427 | { | |
428 | if(v < 0) | |
429 | { | |
430 | from_unsigned_long_long(-v); | |
431 | negate(); | |
432 | } | |
433 | else | |
434 | from_unsigned_long_long(v); | |
435 | return *this; | |
436 | } | |
437 | ||
438 | cpp_dec_float& operator=(boost::ulong_long_type v) | |
439 | { | |
440 | from_unsigned_long_long(v); | |
441 | return *this; | |
442 | } | |
443 | ||
444 | cpp_dec_float& operator=(long double v); | |
445 | ||
446 | cpp_dec_float& operator=(const char* v) | |
447 | { | |
448 | rd_string(v); | |
449 | return *this; | |
450 | } | |
451 | ||
452 | cpp_dec_float& operator+=(const cpp_dec_float& v); | |
453 | cpp_dec_float& operator-=(const cpp_dec_float& v); | |
454 | cpp_dec_float& operator*=(const cpp_dec_float& v); | |
455 | cpp_dec_float& operator/=(const cpp_dec_float& v); | |
456 | ||
457 | cpp_dec_float& add_unsigned_long_long(const boost::ulong_long_type n) | |
458 | { | |
459 | cpp_dec_float t; | |
460 | t.from_unsigned_long_long(n); | |
461 | return *this += t; | |
462 | } | |
463 | ||
464 | cpp_dec_float& sub_unsigned_long_long(const boost::ulong_long_type n) | |
465 | { | |
466 | cpp_dec_float t; | |
467 | t.from_unsigned_long_long(n); | |
468 | return *this -= t; | |
469 | } | |
470 | ||
471 | cpp_dec_float& mul_unsigned_long_long(const boost::ulong_long_type n); | |
472 | cpp_dec_float& div_unsigned_long_long(const boost::ulong_long_type n); | |
473 | ||
474 | // Elementary primitives. | |
475 | cpp_dec_float& calculate_inv (); | |
476 | cpp_dec_float& calculate_sqrt(); | |
477 | ||
478 | void negate() | |
479 | { | |
480 | if(!iszero()) | |
481 | neg = !neg; | |
482 | } | |
483 | ||
484 | // Comparison functions | |
485 | bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_NaN); } | |
486 | bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_inf); } | |
487 | bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_finite); } | |
488 | ||
489 | bool iszero () const | |
490 | { | |
491 | return ((fpclass == cpp_dec_float_finite) && (data[0u] == 0u)); | |
492 | } | |
493 | ||
494 | bool isone () const; | |
495 | bool isint () const; | |
496 | bool isneg () const { return neg; } | |
497 | ||
498 | // Operators pre-increment and pre-decrement | |
499 | cpp_dec_float& operator++() | |
500 | { | |
501 | return *this += one(); | |
502 | } | |
503 | ||
504 | cpp_dec_float& operator--() | |
505 | { | |
506 | return *this -= one(); | |
507 | } | |
508 | ||
509 | std::string str(boost::intmax_t digits, std::ios_base::fmtflags f)const; | |
510 | ||
511 | int compare(const cpp_dec_float& v)const; | |
512 | ||
513 | template <class V> | |
514 | int compare(const V& v)const | |
515 | { | |
516 | cpp_dec_float<Digits10, ExponentType, Allocator> t; | |
517 | t = v; | |
518 | return compare(t); | |
519 | } | |
520 | ||
521 | void swap(cpp_dec_float& v) | |
522 | { | |
523 | data.swap(v.data); | |
524 | std::swap(exp, v.exp); | |
525 | std::swap(neg, v.neg); | |
526 | std::swap(fpclass, v.fpclass); | |
527 | std::swap(prec_elem, v.prec_elem); | |
528 | } | |
529 | ||
530 | double extract_double() const; | |
531 | long double extract_long_double() const; | |
532 | boost::long_long_type extract_signed_long_long() const; | |
533 | boost::ulong_long_type extract_unsigned_long_long() const; | |
534 | void extract_parts(double& mantissa, ExponentType& exponent) const; | |
535 | cpp_dec_float extract_integer_part() const; | |
536 | ||
537 | void precision(const boost::int32_t prec_digits) | |
538 | { | |
539 | if(prec_digits >= cpp_dec_float_total_digits10) | |
540 | { | |
541 | prec_elem = cpp_dec_float_elem_number; | |
542 | } | |
543 | else | |
544 | { | |
545 | const boost::int32_t elems = static_cast<boost::int32_t>( static_cast<boost::int32_t>( (prec_digits + (cpp_dec_float_elem_digits10 / 2)) / cpp_dec_float_elem_digits10) | |
546 | + static_cast<boost::int32_t>(((prec_digits % cpp_dec_float_elem_digits10) != 0) ? 1 : 0)); | |
547 | ||
548 | prec_elem = (std::min)(cpp_dec_float_elem_number, (std::max)(elems, static_cast<boost::int32_t>(2))); | |
549 | } | |
550 | } | |
551 | static cpp_dec_float pow2(boost::long_long_type i); | |
552 | ExponentType order()const | |
553 | { | |
554 | const bool bo_order_is_zero = ((!(isfinite)()) || (data[0] == static_cast<boost::uint32_t>(0u))); | |
555 | // | |
556 | // Binary search to find the order of the leading term: | |
557 | // | |
558 | ExponentType prefix = 0; | |
559 | ||
560 | if(data[0] >= 100000UL) | |
561 | { | |
562 | if(data[0] >= 10000000UL) | |
563 | { | |
564 | if(data[0] >= 100000000UL) | |
565 | { | |
566 | if(data[0] >= 1000000000UL) | |
567 | prefix = 9; | |
568 | else | |
569 | prefix = 8; | |
570 | } | |
571 | else | |
572 | prefix = 7; | |
573 | } | |
574 | else | |
575 | { | |
576 | if(data[0] >= 1000000UL) | |
577 | prefix = 6; | |
578 | else | |
579 | prefix = 5; | |
580 | } | |
581 | } | |
582 | else | |
583 | { | |
584 | if(data[0] >= 1000UL) | |
585 | { | |
586 | if(data[0] >= 10000UL) | |
587 | prefix = 4; | |
588 | else | |
589 | prefix = 3; | |
590 | } | |
591 | else | |
592 | { | |
593 | if(data[0] >= 100) | |
594 | prefix = 2; | |
595 | else if(data[0] >= 10) | |
596 | prefix = 1; | |
597 | } | |
598 | } | |
599 | ||
600 | return (bo_order_is_zero ? static_cast<ExponentType>(0) : static_cast<ExponentType>(exp + prefix)); | |
601 | } | |
602 | ||
603 | template<class Archive> | |
604 | void serialize(Archive & ar, const unsigned int /*version*/) | |
605 | { | |
606 | for(unsigned i = 0; i < data.size(); ++i) | |
607 | ar & data[i]; | |
608 | ar & exp; | |
609 | ar & neg; | |
610 | ar & fpclass; | |
611 | ar & prec_elem; | |
612 | } | |
613 | ||
614 | private: | |
615 | static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast<boost::uint32_t>(0u)); } | |
616 | static bool data_elem_is_non_nine_predicate(const boost::uint32_t& d) { return (d != static_cast<boost::uint32_t>(cpp_dec_float::cpp_dec_float_elem_mask - 1)); } | |
617 | static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast<char>('0')); } | |
618 | ||
619 | void from_unsigned_long_long(const boost::ulong_long_type u); | |
620 | ||
621 | int cmp_data(const array_type& vd) const; | |
622 | ||
623 | ||
624 | static boost::uint32_t mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p); | |
625 | static boost::uint32_t mul_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); | |
626 | static boost::uint32_t div_loop_n (boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p); | |
627 | ||
628 | bool rd_string(const char* const s); | |
629 | ||
630 | template <unsigned D, class ET, class A> | |
631 | friend class cpp_dec_float; | |
632 | }; | |
633 | ||
634 | template <unsigned Digits10, class ExponentType, class Allocator> | |
635 | typename cpp_dec_float<Digits10, ExponentType, Allocator>::initializer cpp_dec_float<Digits10, ExponentType, Allocator>::init; | |
636 | ||
637 | template <unsigned Digits10, class ExponentType, class Allocator> | |
638 | const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix; | |
639 | template <unsigned Digits10, class ExponentType, class Allocator> | |
640 | const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_setting; | |
641 | template <unsigned Digits10, class ExponentType, class Allocator> | |
642 | const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_lo; | |
643 | template <unsigned Digits10, class ExponentType, class Allocator> | |
644 | const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_hi; | |
645 | template <unsigned Digits10, class ExponentType, class Allocator> | |
646 | const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; | |
647 | template <unsigned Digits10, class ExponentType, class Allocator> | |
648 | const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp; | |
649 | template <unsigned Digits10, class ExponentType, class Allocator> | |
650 | const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp; | |
651 | template <unsigned Digits10, class ExponentType, class Allocator> | |
652 | const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10; | |
653 | template <unsigned Digits10, class ExponentType, class Allocator> | |
654 | const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10; | |
655 | template <unsigned Digits10, class ExponentType, class Allocator> | |
656 | const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_digits10; | |
657 | template <unsigned Digits10, class ExponentType, class Allocator> | |
658 | const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number_request; | |
659 | template <unsigned Digits10, class ExponentType, class Allocator> | |
660 | const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number; | |
661 | template <unsigned Digits10, class ExponentType, class Allocator> | |
662 | const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_mask; | |
663 | ||
664 | template <unsigned Digits10, class ExponentType, class Allocator> | |
665 | cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator+=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) | |
666 | { | |
667 | if((isnan)()) | |
668 | { | |
669 | return *this; | |
670 | } | |
671 | ||
672 | if((isinf)()) | |
673 | { | |
674 | if((v.isinf)() && (isneg() != v.isneg())) | |
675 | { | |
676 | *this = nan(); | |
677 | } | |
678 | return *this; | |
679 | } | |
680 | ||
681 | if(iszero()) | |
682 | { | |
683 | return operator=(v); | |
684 | } | |
685 | ||
686 | if((v.isnan)() || (v.isinf)()) | |
687 | { | |
688 | *this = v; | |
689 | return *this; | |
690 | } | |
691 | ||
692 | // Get the offset for the add/sub operation. | |
693 | static const ExponentType max_delta_exp = static_cast<ExponentType>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10); | |
694 | ||
695 | const ExponentType ofs_exp = static_cast<ExponentType>(exp - v.exp); | |
696 | ||
697 | // Check if the operation is out of range, requiring special handling. | |
698 | if(v.iszero() || (ofs_exp > max_delta_exp)) | |
699 | { | |
700 | // Result is *this unchanged since v is negligible compared to *this. | |
701 | return *this; | |
702 | } | |
703 | else if(ofs_exp < -max_delta_exp) | |
704 | { | |
705 | // Result is *this = v since *this is negligible compared to v. | |
706 | return operator=(v); | |
707 | } | |
708 | ||
709 | // Do the add/sub operation. | |
710 | ||
711 | typename array_type::iterator p_u = data.begin(); | |
712 | typename array_type::const_iterator p_v = v.data.begin(); | |
713 | bool b_copy = false; | |
714 | const boost::int32_t ofs = static_cast<boost::int32_t>(static_cast<boost::int32_t>(ofs_exp) / cpp_dec_float_elem_digits10); | |
715 | array_type n_data; | |
716 | ||
717 | if(neg == v.neg) | |
718 | { | |
719 | // Add v to *this, where the data array of either *this or v | |
720 | // might have to be treated with a positive, negative or zero offset. | |
721 | // The result is stored in *this. The data are added one element | |
722 | // at a time, each element with carry. | |
723 | if(ofs >= static_cast<boost::int32_t>(0)) | |
724 | { | |
725 | std::copy(v.data.begin(), v.data.end() - static_cast<size_t>(ofs), n_data.begin() + static_cast<size_t>(ofs)); | |
726 | std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(ofs), static_cast<boost::uint32_t>(0u)); | |
727 | p_v = n_data.begin(); | |
728 | } | |
729 | else | |
730 | { | |
731 | std::copy(data.begin(), data.end() - static_cast<size_t>(-ofs), n_data.begin() + static_cast<size_t>(-ofs)); | |
732 | std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(-ofs), static_cast<boost::uint32_t>(0u)); | |
733 | p_u = n_data.begin(); | |
734 | b_copy = true; | |
735 | } | |
736 | ||
737 | // Addition algorithm | |
738 | boost::uint32_t carry = static_cast<boost::uint32_t>(0u); | |
739 | ||
740 | for(boost::int32_t j = static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1)); j >= static_cast<boost::int32_t>(0); j--) | |
741 | { | |
742 | boost::uint32_t t = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(p_u[j] + p_v[j]) + carry); | |
743 | carry = t / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask); | |
744 | p_u[j] = static_cast<boost::uint32_t>(t - static_cast<boost::uint32_t>(carry * static_cast<boost::uint32_t>(cpp_dec_float_elem_mask))); | |
745 | } | |
746 | ||
747 | if(b_copy) | |
748 | { | |
749 | data = n_data; | |
750 | exp = v.exp; | |
751 | } | |
752 | ||
753 | // There needs to be a carry into the element -1 of the array data | |
754 | if(carry != static_cast<boost::uint32_t>(0u)) | |
755 | { | |
756 | std::copy_backward(data.begin(), data.end() - static_cast<std::size_t>(1u), data.end()); | |
757 | data[0] = carry; | |
758 | exp += static_cast<ExponentType>(cpp_dec_float_elem_digits10); | |
759 | } | |
760 | } | |
761 | else | |
762 | { | |
763 | // Subtract v from *this, where the data array of either *this or v | |
764 | // might have to be treated with a positive, negative or zero offset. | |
765 | if((ofs > static_cast<boost::int32_t>(0)) | |
766 | || ( (ofs == static_cast<boost::int32_t>(0)) | |
767 | && (cmp_data(v.data) > static_cast<boost::int32_t>(0))) | |
768 | ) | |
769 | { | |
770 | // In this case, |u| > |v| and ofs is positive. | |
771 | // Copy the data of v, shifted down to a lower value | |
772 | // into the data array m_n. Set the operand pointer p_v | |
773 | // to point to the copied, shifted data m_n. | |
774 | std::copy(v.data.begin(), v.data.end() - static_cast<size_t>(ofs), n_data.begin() + static_cast<size_t>(ofs)); | |
775 | std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(ofs), static_cast<boost::uint32_t>(0u)); | |
776 | p_v = n_data.begin(); | |
777 | } | |
778 | else | |
779 | { | |
780 | if(ofs != static_cast<boost::int32_t>(0)) | |
781 | { | |
782 | // In this case, |u| < |v| and ofs is negative. | |
783 | // Shift the data of u down to a lower value. | |
784 | std::copy_backward(data.begin(), data.end() - static_cast<size_t>(-ofs), data.end()); | |
785 | std::fill(data.begin(), data.begin() + static_cast<size_t>(-ofs), static_cast<boost::uint32_t>(0u)); | |
786 | } | |
787 | ||
788 | // Copy the data of v into the data array n_data. | |
789 | // Set the u-pointer p_u to point to m_n and the | |
790 | // operand pointer p_v to point to the shifted | |
791 | // data m_data. | |
792 | n_data = v.data; | |
793 | p_u = n_data.begin(); | |
794 | p_v = data.begin(); | |
795 | b_copy = true; | |
796 | } | |
797 | ||
798 | boost::int32_t j; | |
799 | ||
800 | // Subtraction algorithm | |
801 | boost::int32_t borrow = static_cast<boost::int32_t>(0); | |
802 | ||
803 | for(j = static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1)); j >= static_cast<boost::int32_t>(0); j--) | |
804 | { | |
805 | boost::int32_t t = static_cast<boost::int32_t>(static_cast<boost::int32_t>( static_cast<boost::int32_t>(p_u[j]) | |
806 | - static_cast<boost::int32_t>(p_v[j])) - borrow); | |
807 | ||
808 | // Underflow? Borrow? | |
809 | if(t < static_cast<boost::int32_t>(0)) | |
810 | { | |
811 | // Yes, underflow and borrow | |
812 | t += static_cast<boost::int32_t>(cpp_dec_float_elem_mask); | |
813 | borrow = static_cast<boost::int32_t>(1); | |
814 | } | |
815 | else | |
816 | { | |
817 | borrow = static_cast<boost::int32_t>(0); | |
818 | } | |
819 | ||
820 | p_u[j] = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(t) % static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); | |
821 | } | |
822 | ||
823 | if(b_copy) | |
824 | { | |
825 | data = n_data; | |
826 | exp = v.exp; | |
827 | neg = v.neg; | |
828 | } | |
829 | ||
830 | // Is it necessary to justify the data? | |
831 | const typename array_type::const_iterator first_nonzero_elem = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); | |
832 | ||
833 | if(first_nonzero_elem != data.begin()) | |
834 | { | |
835 | if(first_nonzero_elem == data.end()) | |
836 | { | |
837 | // This result of the subtraction is exactly zero. | |
838 | // Reset the sign and the exponent. | |
839 | neg = false; | |
840 | exp = static_cast<ExponentType>(0); | |
841 | } | |
842 | else | |
843 | { | |
844 | // Justify the data | |
845 | const std::size_t sj = static_cast<std::size_t>(std::distance<typename array_type::const_iterator>(data.begin(), first_nonzero_elem)); | |
846 | ||
847 | std::copy(data.begin() + static_cast<std::size_t>(sj), data.end(), data.begin()); | |
848 | std::fill(data.end() - sj, data.end(), static_cast<boost::uint32_t>(0u)); | |
849 | ||
850 | exp -= static_cast<ExponentType>(sj * static_cast<std::size_t>(cpp_dec_float_elem_digits10)); | |
851 | } | |
852 | } | |
853 | } | |
854 | ||
855 | // Handle underflow. | |
856 | if(iszero()) | |
857 | return (*this = zero()); | |
858 | ||
859 | // Check for potential overflow. | |
860 | const bool b_result_might_overflow = (exp >= static_cast<ExponentType>(cpp_dec_float_max_exp10)); | |
861 | ||
862 | // Handle overflow. | |
863 | if(b_result_might_overflow) | |
864 | { | |
865 | const bool b_result_is_neg = neg; | |
866 | neg = false; | |
867 | ||
868 | if(compare((cpp_dec_float::max)()) > 0) | |
869 | *this = inf(); | |
870 | ||
871 | neg = b_result_is_neg; | |
872 | } | |
873 | ||
874 | return *this; | |
875 | } | |
876 | ||
877 | template <unsigned Digits10, class ExponentType, class Allocator> | |
878 | cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator-=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) | |
879 | { | |
880 | // Use *this - v = -(-*this + v). | |
881 | negate(); | |
882 | *this += v; | |
883 | negate(); | |
884 | return *this; | |
885 | } | |
886 | ||
887 | template <unsigned Digits10, class ExponentType, class Allocator> | |
888 | cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator*=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) | |
889 | { | |
890 | // Evaluate the sign of the result. | |
891 | const bool b_result_is_neg = (neg != v.neg); | |
892 | ||
893 | // Artificially set the sign of the result to be positive. | |
894 | neg = false; | |
895 | ||
896 | // Handle special cases like zero, inf and NaN. | |
897 | const bool b_u_is_inf = (isinf)(); | |
898 | const bool b_v_is_inf = (v.isinf)(); | |
899 | const bool b_u_is_zero = iszero(); | |
900 | const bool b_v_is_zero = v.iszero(); | |
901 | ||
902 | if( ((isnan)() || (v.isnan)()) | |
903 | || (b_u_is_inf && b_v_is_zero) | |
904 | || (b_v_is_inf && b_u_is_zero) | |
905 | ) | |
906 | { | |
907 | *this = nan(); | |
908 | return *this; | |
909 | } | |
910 | ||
911 | if(b_u_is_inf || b_v_is_inf) | |
912 | { | |
913 | *this = inf(); | |
914 | if(b_result_is_neg) | |
915 | negate(); | |
916 | return *this; | |
917 | } | |
918 | ||
919 | if(b_u_is_zero || b_v_is_zero) | |
920 | { | |
921 | return *this = zero(); | |
922 | } | |
923 | ||
924 | // Check for potential overflow or underflow. | |
925 | const bool b_result_might_overflow = ((exp + v.exp) >= static_cast<ExponentType>(cpp_dec_float_max_exp10)); | |
926 | const bool b_result_might_underflow = ((exp + v.exp) <= static_cast<ExponentType>(cpp_dec_float_min_exp10)); | |
927 | ||
928 | // Set the exponent of the result. | |
929 | exp += v.exp; | |
930 | ||
931 | const boost::int32_t prec_mul = (std::min)(prec_elem, v.prec_elem); | |
932 | ||
933 | const boost::uint32_t carry = mul_loop_uv(data.data(), v.data.data(), prec_mul); | |
934 | ||
935 | // Handle a potential carry. | |
936 | if(carry != static_cast<boost::uint32_t>(0u)) | |
937 | { | |
938 | exp += cpp_dec_float_elem_digits10; | |
939 | ||
940 | // Shift the result of the multiplication one element to the right... | |
941 | std::copy_backward(data.begin(), | |
942 | data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)), | |
943 | data.begin() + static_cast<std::size_t>(prec_elem)); | |
944 | ||
945 | // ... And insert the carry. | |
946 | data.front() = carry; | |
947 | } | |
948 | ||
949 | // Handle overflow. | |
950 | if(b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0)) | |
951 | { | |
952 | *this = inf(); | |
953 | } | |
954 | ||
955 | // Handle underflow. | |
956 | if(b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0)) | |
957 | { | |
958 | *this = zero(); | |
959 | ||
960 | return *this; | |
961 | } | |
962 | ||
963 | // Set the sign of the result. | |
964 | neg = b_result_is_neg; | |
965 | ||
966 | return *this; | |
967 | } | |
968 | ||
969 | template <unsigned Digits10, class ExponentType, class Allocator> | |
970 | cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator/=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v) | |
971 | { | |
972 | if(iszero()) | |
973 | { | |
974 | if((v.isnan)()) | |
975 | { | |
976 | return *this = v; | |
977 | } | |
978 | else if(v.iszero()) | |
979 | { | |
980 | return *this = nan(); | |
981 | } | |
982 | } | |
983 | ||
984 | const bool u_and_v_are_finite_and_identical = ( (isfinite)() | |
985 | && (fpclass == v.fpclass) | |
986 | && (exp == v.exp) | |
987 | && (cmp_data(v.data) == static_cast<boost::int32_t>(0))); | |
988 | ||
989 | if(u_and_v_are_finite_and_identical) | |
990 | { | |
991 | if(neg != v.neg) | |
992 | { | |
993 | *this = one(); | |
994 | negate(); | |
995 | } | |
996 | else | |
997 | *this = one(); | |
998 | return *this; | |
999 | } | |
1000 | else | |
1001 | { | |
1002 | cpp_dec_float t(v); | |
1003 | t.calculate_inv(); | |
1004 | return operator*=(t); | |
1005 | } | |
1006 | } | |
1007 | ||
1008 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1009 | cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::mul_unsigned_long_long(const boost::ulong_long_type n) | |
1010 | { | |
1011 | // Multiply *this with a constant boost::ulong_long_type. | |
1012 | ||
1013 | // Evaluate the sign of the result. | |
1014 | const bool b_neg = neg; | |
1015 | ||
1016 | // Artificially set the sign of the result to be positive. | |
1017 | neg = false; | |
1018 | ||
1019 | // Handle special cases like zero, inf and NaN. | |
1020 | const bool b_u_is_inf = (isinf)(); | |
1021 | const bool b_n_is_zero = (n == static_cast<boost::int32_t>(0)); | |
1022 | ||
1023 | if((isnan)() || (b_u_is_inf && b_n_is_zero)) | |
1024 | { | |
1025 | return (*this = nan()); | |
1026 | } | |
1027 | ||
1028 | if(b_u_is_inf) | |
1029 | { | |
1030 | *this = inf(); | |
1031 | if(b_neg) | |
1032 | negate(); | |
1033 | return *this; | |
1034 | } | |
1035 | ||
1036 | if(iszero() || b_n_is_zero) | |
1037 | { | |
1038 | // Multiplication by zero. | |
1039 | return *this = zero(); | |
1040 | } | |
1041 | ||
1042 | if(n >= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask)) | |
1043 | { | |
1044 | neg = b_neg; | |
1045 | cpp_dec_float t; | |
1046 | t = n; | |
1047 | return operator*=(t); | |
1048 | } | |
1049 | ||
1050 | if(n == static_cast<boost::ulong_long_type>(1u)) | |
1051 | { | |
1052 | neg = b_neg; | |
1053 | return *this; | |
1054 | } | |
1055 | ||
1056 | // Set up the multiplication loop. | |
1057 | const boost::uint32_t nn = static_cast<boost::uint32_t>(n); | |
1058 | const boost::uint32_t carry = mul_loop_n(data.data(), nn, prec_elem); | |
1059 | ||
1060 | // Handle the carry and adjust the exponent. | |
1061 | if(carry != static_cast<boost::uint32_t>(0u)) | |
1062 | { | |
1063 | exp += static_cast<ExponentType>(cpp_dec_float_elem_digits10); | |
1064 | ||
1065 | // Shift the result of the multiplication one element to the right. | |
1066 | std::copy_backward(data.begin(), | |
1067 | data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)), | |
1068 | data.begin() + static_cast<std::size_t>(prec_elem)); | |
1069 | ||
1070 | data.front() = static_cast<boost::uint32_t>(carry); | |
1071 | } | |
1072 | ||
1073 | // Check for potential overflow. | |
1074 | const bool b_result_might_overflow = (exp >= cpp_dec_float_max_exp10); | |
1075 | ||
1076 | // Handle overflow. | |
1077 | if(b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0)) | |
1078 | { | |
1079 | *this = inf(); | |
1080 | } | |
1081 | ||
1082 | // Set the sign. | |
1083 | neg = b_neg; | |
1084 | ||
1085 | return *this; | |
1086 | } | |
1087 | ||
1088 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1089 | cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::div_unsigned_long_long(const boost::ulong_long_type n) | |
1090 | { | |
1091 | // Divide *this by a constant boost::ulong_long_type. | |
1092 | ||
1093 | // Evaluate the sign of the result. | |
1094 | const bool b_neg = neg; | |
1095 | ||
1096 | // Artificially set the sign of the result to be positive. | |
1097 | neg = false; | |
1098 | ||
1099 | // Handle special cases like zero, inf and NaN. | |
1100 | if((isnan)()) | |
1101 | { | |
1102 | return *this; | |
1103 | } | |
1104 | ||
1105 | if((isinf)()) | |
1106 | { | |
1107 | *this = inf(); | |
1108 | if(b_neg) | |
1109 | negate(); | |
1110 | return *this; | |
1111 | } | |
1112 | ||
1113 | if(n == static_cast<boost::ulong_long_type>(0u)) | |
1114 | { | |
1115 | // Divide by 0. | |
1116 | if(iszero()) | |
1117 | { | |
1118 | *this = nan(); | |
1119 | return *this; | |
1120 | } | |
1121 | else | |
1122 | { | |
1123 | *this = inf(); | |
1124 | if(isneg()) | |
1125 | negate(); | |
1126 | return *this; | |
1127 | } | |
1128 | } | |
1129 | ||
1130 | if(iszero()) | |
1131 | { | |
1132 | return *this; | |
1133 | } | |
1134 | ||
1135 | if(n >= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask)) | |
1136 | { | |
1137 | neg = b_neg; | |
1138 | cpp_dec_float t; | |
1139 | t = n; | |
1140 | return operator/=(t); | |
1141 | } | |
1142 | ||
1143 | const boost::uint32_t nn = static_cast<boost::uint32_t>(n); | |
1144 | ||
1145 | if(nn > static_cast<boost::uint32_t>(1u)) | |
1146 | { | |
1147 | // Do the division loop. | |
1148 | const boost::uint32_t prev = div_loop_n(data.data(), nn, prec_elem); | |
1149 | ||
1150 | // Determine if one leading zero is in the result data. | |
1151 | if(data[0] == static_cast<boost::uint32_t>(0u)) | |
1152 | { | |
1153 | // Adjust the exponent | |
1154 | exp -= static_cast<ExponentType>(cpp_dec_float_elem_digits10); | |
1155 | ||
1156 | // Shift result of the division one element to the left. | |
1157 | std::copy(data.begin() + static_cast<std::size_t>(1u), | |
1158 | data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)), | |
1159 | data.begin()); | |
1160 | ||
1161 | data[prec_elem - static_cast<boost::int32_t>(1)] = static_cast<boost::uint32_t>(static_cast<boost::uint64_t>(prev * static_cast<boost::uint64_t>(cpp_dec_float_elem_mask)) / nn); | |
1162 | } | |
1163 | } | |
1164 | ||
1165 | // Check for potential underflow. | |
1166 | const bool b_result_might_underflow = (exp <= cpp_dec_float_min_exp10); | |
1167 | ||
1168 | // Handle underflow. | |
1169 | if(b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0)) | |
1170 | return (*this = zero()); | |
1171 | ||
1172 | // Set the sign of the result. | |
1173 | neg = b_neg; | |
1174 | ||
1175 | return *this; | |
1176 | } | |
1177 | ||
1178 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1179 | cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_inv() | |
1180 | { | |
1181 | // Compute the inverse of *this. | |
1182 | const bool b_neg = neg; | |
1183 | ||
1184 | neg = false; | |
1185 | ||
1186 | // Handle special cases like zero, inf and NaN. | |
1187 | if(iszero()) | |
1188 | { | |
1189 | *this = inf(); | |
1190 | if(b_neg) | |
1191 | negate(); | |
1192 | return *this; | |
1193 | } | |
1194 | ||
1195 | if((isnan)()) | |
1196 | { | |
1197 | return *this; | |
1198 | } | |
1199 | ||
1200 | if((isinf)()) | |
1201 | { | |
1202 | return *this = zero(); | |
1203 | } | |
1204 | ||
1205 | if(isone()) | |
1206 | { | |
1207 | if(b_neg) | |
1208 | negate(); | |
1209 | return *this; | |
1210 | } | |
1211 | ||
1212 | // Save the original *this. | |
1213 | cpp_dec_float<Digits10, ExponentType, Allocator> x(*this); | |
1214 | ||
1215 | // Generate the initial estimate using division. | |
1216 | // Extract the mantissa and exponent for a "manual" | |
1217 | // computation of the estimate. | |
1218 | double dd; | |
1219 | ExponentType ne; | |
1220 | x.extract_parts(dd, ne); | |
1221 | ||
1222 | // Do the inverse estimate using double precision estimates of mantissa and exponent. | |
1223 | operator=(cpp_dec_float<Digits10, ExponentType, Allocator>(1.0 / dd, -ne)); | |
1224 | ||
1225 | // Compute the inverse of *this. Quadratically convergent Newton-Raphson iteration | |
1226 | // is used. During the iterative steps, the precision of the calculation is limited | |
1227 | // to the minimum required in order to minimize the run-time. | |
1228 | ||
1229 | static const boost::int32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3; | |
1230 | ||
1231 | for(boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= static_cast<boost::int32_t>(2)) | |
1232 | { | |
1233 | // Adjust precision of the terms. | |
1234 | precision(static_cast<boost::int32_t>((digits + 10) * static_cast<boost::int32_t>(2))); | |
1235 | x.precision(static_cast<boost::int32_t>((digits + 10) * static_cast<boost::int32_t>(2))); | |
1236 | ||
1237 | // Next iteration. | |
1238 | cpp_dec_float t(*this); | |
1239 | t *= x; | |
1240 | t -= two(); | |
1241 | t.negate(); | |
1242 | *this *= t; | |
1243 | } | |
1244 | ||
1245 | neg = b_neg; | |
1246 | ||
1247 | prec_elem = cpp_dec_float_elem_number; | |
1248 | ||
1249 | return *this; | |
1250 | } | |
1251 | ||
1252 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1253 | cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_sqrt() | |
1254 | { | |
1255 | // Compute the square root of *this. | |
1256 | ||
1257 | if(isneg() || (!(isfinite)())) | |
1258 | { | |
1259 | *this = nan(); | |
1260 | return *this; | |
1261 | } | |
1262 | ||
1263 | if(iszero() || isone()) | |
1264 | { | |
1265 | return *this; | |
1266 | } | |
1267 | ||
1268 | // Save the original *this. | |
1269 | cpp_dec_float<Digits10, ExponentType, Allocator> x(*this); | |
1270 | ||
1271 | // Generate the initial estimate using division. | |
1272 | // Extract the mantissa and exponent for a "manual" | |
1273 | // computation of the estimate. | |
1274 | double dd; | |
1275 | ExponentType ne; | |
1276 | extract_parts(dd, ne); | |
1277 | ||
1278 | // Force the exponent to be an even multiple of two. | |
1279 | if((ne % static_cast<ExponentType>(2)) != static_cast<ExponentType>(0)) | |
1280 | { | |
1281 | ++ne; | |
1282 | dd /= 10.0; | |
1283 | } | |
1284 | ||
1285 | // Setup the iteration. | |
1286 | // Estimate the square root using simple manipulations. | |
1287 | const double sqd = std::sqrt(dd); | |
1288 | ||
1289 | *this = cpp_dec_float<Digits10, ExponentType, Allocator>(sqd, static_cast<ExponentType>(ne / static_cast<ExponentType>(2))); | |
1290 | ||
1291 | // Estimate 1.0 / (2.0 * x0) using simple manipulations. | |
1292 | cpp_dec_float<Digits10, ExponentType, Allocator> vi(0.5 / sqd, static_cast<ExponentType>(-ne / static_cast<ExponentType>(2))); | |
1293 | ||
1294 | // Compute the square root of x. Coupled Newton iteration | |
1295 | // as described in "Pi Unleashed" is used. During the | |
1296 | // iterative steps, the precision of the calculation is | |
1297 | // limited to the minimum required in order to minimize | |
1298 | // the run-time. | |
1299 | // | |
1300 | // Book references: | |
1301 | // http://www.jjj.de/pibook/pibook.html | |
1302 | // http://www.amazon.com/exec/obidos/tg/detail/-/3540665722/qid=1035535482/sr=8-7/ref=sr_8_7/104-3357872-6059916?v=glance&n=507846 | |
1303 | ||
1304 | static const boost::uint32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3; | |
1305 | ||
1306 | for(boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= 2u) | |
1307 | { | |
1308 | // Adjust precision of the terms. | |
1309 | precision((digits + 10) * 2); | |
1310 | vi.precision((digits + 10) * 2); | |
1311 | ||
1312 | // Next iteration of vi | |
1313 | cpp_dec_float t(*this); | |
1314 | t *= vi; | |
1315 | t.negate(); | |
1316 | t.mul_unsigned_long_long(2u); | |
1317 | t += one(); | |
1318 | t *= vi; | |
1319 | vi += t; | |
1320 | ||
1321 | // Next iteration of *this | |
1322 | t = *this; | |
1323 | t *= *this; | |
1324 | t.negate(); | |
1325 | t += x; | |
1326 | t *= vi; | |
1327 | *this += t; | |
1328 | } | |
1329 | ||
1330 | prec_elem = cpp_dec_float_elem_number; | |
1331 | ||
1332 | return *this; | |
1333 | } | |
1334 | ||
1335 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1336 | int cpp_dec_float<Digits10, ExponentType, Allocator>::cmp_data(const array_type& vd) const | |
1337 | { | |
1338 | // Compare the data of *this with those of v. | |
1339 | // Return +1 for *this > v | |
1340 | // 0 for *this = v | |
1341 | // -1 for *this < v | |
1342 | ||
1343 | const std::pair<typename array_type::const_iterator, typename array_type::const_iterator> mismatch_pair = std::mismatch(data.begin(), data.end(), vd.begin()); | |
1344 | ||
1345 | const bool is_equal = ((mismatch_pair.first == data.end()) && (mismatch_pair.second == vd.end())); | |
1346 | ||
1347 | if(is_equal) | |
1348 | { | |
1349 | return 0; | |
1350 | } | |
1351 | else | |
1352 | { | |
1353 | return ((*mismatch_pair.first > *mismatch_pair.second) ? 1 : -1); | |
1354 | } | |
1355 | } | |
1356 | ||
1357 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1358 | int cpp_dec_float<Digits10, ExponentType, Allocator>::compare(const cpp_dec_float& v) const | |
1359 | { | |
1360 | // Compare v with *this. | |
1361 | // Return +1 for *this > v | |
1362 | // 0 for *this = v | |
1363 | // -1 for *this < v | |
1364 | ||
1365 | // Handle all non-finite cases. | |
1366 | if((!(isfinite)()) || (!(v.isfinite)())) | |
1367 | { | |
1368 | // NaN can never equal NaN. Return an implementation-dependent | |
1369 | // signed result. Also note that comparison of NaN with NaN | |
1370 | // using operators greater-than or less-than is undefined. | |
1371 | if((isnan)() || (v.isnan)()) { return ((isnan)() ? 1 : -1); } | |
1372 | ||
1373 | if((isinf)() && (v.isinf)()) | |
1374 | { | |
1375 | // Both *this and v are infinite. They are equal if they have the same sign. | |
1376 | // Otherwise, *this is less than v if and only if *this is negative. | |
1377 | return ((neg == v.neg) ? 0 : (neg ? -1 : 1)); | |
1378 | } | |
1379 | ||
1380 | if((isinf)()) | |
1381 | { | |
1382 | // *this is infinite, but v is finite. | |
1383 | // So negative infinite *this is less than any finite v. | |
1384 | // Whereas positive infinite *this is greater than any finite v. | |
1385 | return (isneg() ? -1 : 1); | |
1386 | } | |
1387 | else | |
1388 | { | |
1389 | // *this is finite, and v is infinite. | |
1390 | // So any finite *this is greater than negative infinite v. | |
1391 | // Whereas any finite *this is less than positive infinite v. | |
1392 | return (v.neg ? 1 : -1); | |
1393 | } | |
1394 | } | |
1395 | ||
1396 | // And now handle all *finite* cases. | |
1397 | if(iszero()) | |
1398 | { | |
1399 | // The value of *this is zero and v is either zero or non-zero. | |
1400 | return (v.iszero() ? 0 | |
1401 | : (v.neg ? 1 : -1)); | |
1402 | } | |
1403 | else if(v.iszero()) | |
1404 | { | |
1405 | // The value of v is zero and *this is non-zero. | |
1406 | return (neg ? -1 : 1); | |
1407 | } | |
1408 | else | |
1409 | { | |
1410 | // Both *this and v are non-zero. | |
1411 | ||
1412 | if(neg != v.neg) | |
1413 | { | |
1414 | // The signs are different. | |
1415 | return (neg ? -1 : 1); | |
1416 | } | |
1417 | else if(exp != v.exp) | |
1418 | { | |
1419 | // The signs are the same and the exponents are different. | |
1420 | const int val_cexpression = ((exp < v.exp) ? 1 : -1); | |
1421 | ||
1422 | return (neg ? val_cexpression : -val_cexpression); | |
1423 | } | |
1424 | else | |
1425 | { | |
1426 | // The signs are the same and the exponents are the same. | |
1427 | // Compare the data. | |
1428 | const int val_cmp_data = cmp_data(v.data); | |
1429 | ||
1430 | return ((!neg) ? val_cmp_data : -val_cmp_data); | |
1431 | } | |
1432 | } | |
1433 | } | |
1434 | ||
1435 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1436 | bool cpp_dec_float<Digits10, ExponentType, Allocator>::isone() const | |
1437 | { | |
1438 | // Check if the value of *this is identically 1 or very close to 1. | |
1439 | ||
1440 | const bool not_negative_and_is_finite = ((!neg) && (isfinite)()); | |
1441 | ||
1442 | if(not_negative_and_is_finite) | |
1443 | { | |
1444 | if((data[0u] == static_cast<boost::uint32_t>(1u)) && (exp == static_cast<ExponentType>(0))) | |
1445 | { | |
1446 | const typename array_type::const_iterator it_non_zero = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate); | |
1447 | return (it_non_zero == data.end()); | |
1448 | } | |
1449 | else if((data[0u] == static_cast<boost::uint32_t>(cpp_dec_float_elem_mask - 1)) && (exp == static_cast<ExponentType>(-cpp_dec_float_elem_digits10))) | |
1450 | { | |
1451 | const typename array_type::const_iterator it_non_nine = std::find_if(data.begin(), data.end(), data_elem_is_non_nine_predicate); | |
1452 | return (it_non_nine == data.end()); | |
1453 | } | |
1454 | } | |
1455 | ||
1456 | return false; | |
1457 | } | |
1458 | ||
1459 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1460 | bool cpp_dec_float<Digits10, ExponentType, Allocator>::isint() const | |
1461 | { | |
1462 | if(fpclass != cpp_dec_float_finite) { return false; } | |
1463 | ||
1464 | if(iszero()) { return true; } | |
1465 | ||
1466 | if(exp < static_cast<ExponentType>(0)) { return false; } // |*this| < 1. | |
1467 | ||
1468 | const typename array_type::size_type offset_decimal_part = static_cast<typename array_type::size_type>(exp / cpp_dec_float_elem_digits10) + 1u; | |
1469 | ||
1470 | if(offset_decimal_part >= static_cast<typename array_type::size_type>(cpp_dec_float_elem_number)) | |
1471 | { | |
1472 | // The number is too large to resolve the integer part. | |
1473 | // It considered to be a pure integer. | |
1474 | return true; | |
1475 | } | |
1476 | ||
1477 | typename array_type::const_iterator it_non_zero = std::find_if(data.begin() + offset_decimal_part, data.end(), data_elem_is_non_zero_predicate); | |
1478 | ||
1479 | return (it_non_zero == data.end()); | |
1480 | } | |
1481 | ||
1482 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1483 | void cpp_dec_float<Digits10, ExponentType, Allocator>::extract_parts(double& mantissa, ExponentType& exponent) const | |
1484 | { | |
1485 | // Extract the approximate parts mantissa and base-10 exponent from the input cpp_dec_float<Digits10, ExponentType, Allocator> value x. | |
1486 | ||
1487 | // Extracts the mantissa and exponent. | |
1488 | exponent = exp; | |
1489 | ||
1490 | boost::uint32_t p10 = static_cast<boost::uint32_t>(1u); | |
1491 | boost::uint32_t test = data[0u]; | |
1492 | ||
1493 | for(;;) | |
1494 | { | |
1495 | test /= static_cast<boost::uint32_t>(10u); | |
1496 | ||
1497 | if(test == static_cast<boost::uint32_t>(0u)) | |
1498 | { | |
1499 | break; | |
1500 | } | |
1501 | ||
1502 | p10 *= static_cast<boost::uint32_t>(10u); | |
1503 | ++exponent; | |
1504 | } | |
1505 | ||
1506 | // Establish the upper bound of limbs for extracting the double. | |
1507 | const int max_elem_in_double_count = static_cast<int>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) / cpp_dec_float_elem_digits10) | |
1508 | + (static_cast<int>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) % cpp_dec_float_elem_digits10) != 0 ? 1 : 0) | |
1509 | + 1; | |
1510 | ||
1511 | // And make sure this upper bound stays within bounds of the elems. | |
1512 | const std::size_t max_elem_extract_count = static_cast<std::size_t>((std::min)(static_cast<boost::int32_t>(max_elem_in_double_count), cpp_dec_float_elem_number)); | |
1513 | ||
1514 | // Extract into the mantissa the first limb, extracted as a double. | |
1515 | mantissa = static_cast<double>(data[0]); | |
1516 | double scale = 1.0; | |
1517 | ||
1518 | // Extract the rest of the mantissa piecewise from the limbs. | |
1519 | for(std::size_t i = 1u; i < max_elem_extract_count; i++) | |
1520 | { | |
1521 | scale /= static_cast<double>(cpp_dec_float_elem_mask); | |
1522 | mantissa += (static_cast<double>(data[i]) * scale); | |
1523 | } | |
1524 | ||
1525 | mantissa /= static_cast<double>(p10); | |
1526 | ||
1527 | if(neg) { mantissa = -mantissa; } | |
1528 | } | |
1529 | ||
1530 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1531 | double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_double() const | |
1532 | { | |
1533 | // Returns the double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>. | |
1534 | ||
1535 | // Check for non-normal cpp_dec_float<Digits10, ExponentType, Allocator>. | |
1536 | if(!(isfinite)()) | |
1537 | { | |
1538 | if((isnan)()) | |
1539 | { | |
1540 | return std::numeric_limits<double>::quiet_NaN(); | |
1541 | } | |
1542 | else | |
1543 | { | |
1544 | return ((!neg) ? std::numeric_limits<double>::infinity() | |
1545 | : -std::numeric_limits<double>::infinity()); | |
1546 | } | |
1547 | } | |
1548 | ||
1549 | cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this); | |
1550 | if(xx.isneg()) | |
1551 | xx.negate(); | |
1552 | ||
1553 | // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero. | |
1554 | if(iszero() || (xx.compare(double_min()) < 0)) | |
1555 | { | |
1556 | return 0.0; | |
1557 | } | |
1558 | ||
1559 | // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double. | |
1560 | if(xx.compare(double_max()) > 0) | |
1561 | { | |
1562 | return ((!neg) ? std::numeric_limits<double>::infinity() | |
1563 | : -std::numeric_limits<double>::infinity()); | |
1564 | } | |
1565 | ||
1566 | std::stringstream ss; | |
1567 | ||
1568 | ss << str(std::numeric_limits<double>::digits10 + (2 + 1), std::ios_base::scientific); | |
1569 | ||
1570 | double d; | |
1571 | ss >> d; | |
1572 | ||
1573 | return d; | |
1574 | } | |
1575 | ||
1576 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1577 | long double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_long_double() const | |
1578 | { | |
1579 | // Returns the long double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>. | |
1580 | ||
1581 | // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is subnormal. | |
1582 | if(!(isfinite)()) | |
1583 | { | |
1584 | if((isnan)()) | |
1585 | { | |
1586 | return std::numeric_limits<long double>::quiet_NaN(); | |
1587 | } | |
1588 | else | |
1589 | { | |
1590 | return ((!neg) ? std::numeric_limits<long double>::infinity() | |
1591 | : -std::numeric_limits<long double>::infinity()); | |
1592 | } | |
1593 | } | |
1594 | ||
1595 | cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this); | |
1596 | if(xx.isneg()) | |
1597 | xx.negate(); | |
1598 | ||
1599 | // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero. | |
1600 | if(iszero() || (xx.compare(long_double_min()) < 0)) | |
1601 | { | |
1602 | return static_cast<long double>(0.0); | |
1603 | } | |
1604 | ||
1605 | // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double. | |
1606 | if(xx.compare(long_double_max()) > 0) | |
1607 | { | |
1608 | return ((!neg) ? std::numeric_limits<long double>::infinity() | |
1609 | : -std::numeric_limits<long double>::infinity()); | |
1610 | } | |
1611 | ||
1612 | std::stringstream ss; | |
1613 | ||
1614 | ss << str(std::numeric_limits<long double>::digits10 + (2 + 1), std::ios_base::scientific); | |
1615 | ||
1616 | long double ld; | |
1617 | ss >> ld; | |
1618 | ||
1619 | return ld; | |
1620 | } | |
1621 | ||
1622 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1623 | boost::long_long_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_signed_long_long() const | |
1624 | { | |
1625 | // Extracts a signed long long from *this. | |
1626 | // If (x > maximum of long long) or (x < minimum of long long), | |
1627 | // then the maximum or minimum of long long is returned accordingly. | |
1628 | ||
1629 | if(exp < static_cast<ExponentType>(0)) | |
1630 | { | |
1631 | return static_cast<boost::long_long_type>(0); | |
1632 | } | |
1633 | ||
1634 | const bool b_neg = isneg(); | |
1635 | ||
1636 | boost::ulong_long_type val; | |
1637 | ||
1638 | if((!b_neg) && (compare(long_long_max()) > 0)) | |
1639 | { | |
1640 | return (std::numeric_limits<boost::long_long_type>::max)(); | |
1641 | } | |
1642 | else if(b_neg && (compare(long_long_min()) < 0)) | |
1643 | { | |
1644 | return (std::numeric_limits<boost::long_long_type>::min)(); | |
1645 | } | |
1646 | else | |
1647 | { | |
1648 | // Extract the data into an boost::ulong_long_type value. | |
1649 | cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part()); | |
1650 | if(xn.isneg()) | |
1651 | xn.negate(); | |
1652 | ||
1653 | val = static_cast<boost::ulong_long_type>(xn.data[0]); | |
1654 | ||
1655 | const boost::int32_t imax = (std::min)(static_cast<boost::int32_t>(static_cast<boost::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1))); | |
1656 | ||
1657 | for(boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++) | |
1658 | { | |
1659 | val *= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask); | |
1660 | val += static_cast<boost::ulong_long_type>(xn.data[i]); | |
1661 | } | |
1662 | } | |
1663 | ||
1664 | if (!b_neg) | |
1665 | { | |
1666 | return static_cast<boost::long_long_type>(val); | |
1667 | } | |
1668 | else | |
1669 | { | |
1670 | // This strange expression avoids a hardware trap in the corner case | |
1671 | // that val is the most negative value permitted in boost::long_long_type. | |
1672 | // See https://svn.boost.org/trac/boost/ticket/9740. | |
1673 | // | |
1674 | boost::long_long_type sval = static_cast<boost::long_long_type>(val - 1); | |
1675 | sval = -sval; | |
1676 | --sval; | |
1677 | return sval; | |
1678 | } | |
1679 | } | |
1680 | ||
1681 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1682 | boost::ulong_long_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_unsigned_long_long() const | |
1683 | { | |
1684 | // Extracts an boost::ulong_long_type from *this. | |
1685 | // If x exceeds the maximum of boost::ulong_long_type, | |
1686 | // then the maximum of boost::ulong_long_type is returned. | |
1687 | // If x is negative, then the boost::ulong_long_type cast of | |
1688 | // the long long extracted value is returned. | |
1689 | ||
1690 | if(isneg()) | |
1691 | { | |
1692 | return static_cast<boost::ulong_long_type>(extract_signed_long_long()); | |
1693 | } | |
1694 | ||
1695 | if(exp < static_cast<ExponentType>(0)) | |
1696 | { | |
1697 | return static_cast<boost::ulong_long_type>(0u); | |
1698 | } | |
1699 | ||
1700 | const cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part()); | |
1701 | ||
1702 | boost::ulong_long_type val; | |
1703 | ||
1704 | if(xn.compare(ulong_long_max()) > 0) | |
1705 | { | |
1706 | return (std::numeric_limits<boost::ulong_long_type>::max)(); | |
1707 | } | |
1708 | else | |
1709 | { | |
1710 | // Extract the data into an boost::ulong_long_type value. | |
1711 | val = static_cast<boost::ulong_long_type>(xn.data[0]); | |
1712 | ||
1713 | const boost::int32_t imax = (std::min)(static_cast<boost::int32_t>(static_cast<boost::int32_t>(xn.exp) / cpp_dec_float_elem_digits10), static_cast<boost::int32_t>(cpp_dec_float_elem_number - static_cast<boost::int32_t>(1))); | |
1714 | ||
1715 | for(boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++) | |
1716 | { | |
1717 | val *= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask); | |
1718 | val += static_cast<boost::ulong_long_type>(xn.data[i]); | |
1719 | } | |
1720 | } | |
1721 | ||
1722 | return val; | |
1723 | } | |
1724 | ||
1725 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1726 | cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::extract_integer_part() const | |
1727 | { | |
1728 | // Compute the signed integer part of x. | |
1729 | ||
1730 | if(!(isfinite)()) | |
1731 | { | |
1732 | return *this; | |
1733 | } | |
1734 | ||
1735 | if(exp < static_cast<ExponentType>(0)) | |
1736 | { | |
1737 | // The absolute value of the number is smaller than 1. | |
1738 | // Thus the integer part is zero. | |
1739 | return zero(); | |
1740 | } | |
1741 | ||
1742 | // Truncate the digits from the decimal part, including guard digits | |
1743 | // that do not belong to the integer part. | |
1744 | ||
1745 | // Make a local copy. | |
1746 | cpp_dec_float<Digits10, ExponentType, Allocator> x = *this; | |
1747 | ||
1748 | // Clear out the decimal portion | |
1749 | const size_t first_clear = (static_cast<size_t>(x.exp) / static_cast<size_t>(cpp_dec_float_elem_digits10)) + 1u; | |
1750 | const size_t last_clear = static_cast<size_t>(cpp_dec_float_elem_number); | |
1751 | ||
1752 | if(first_clear < last_clear) | |
1753 | std::fill(x.data.begin() + first_clear, x.data.begin() + last_clear, static_cast<boost::uint32_t>(0u)); | |
1754 | ||
1755 | return x; | |
1756 | } | |
1757 | ||
1758 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1759 | std::string cpp_dec_float<Digits10, ExponentType, Allocator>::str(boost::intmax_t number_of_digits, std::ios_base::fmtflags f) const | |
1760 | { | |
1761 | if((this->isinf)()) | |
1762 | { | |
1763 | if(this->isneg()) | |
1764 | return "-inf"; | |
1765 | else if(f & std::ios_base::showpos) | |
1766 | return "+inf"; | |
1767 | else | |
1768 | return "inf"; | |
1769 | } | |
1770 | else if((this->isnan)()) | |
1771 | { | |
1772 | return "nan"; | |
1773 | } | |
1774 | ||
1775 | std::string str; | |
1776 | boost::intmax_t org_digits(number_of_digits); | |
1777 | ExponentType my_exp = order(); | |
1778 | ||
1779 | if(number_of_digits == 0) | |
1780 | number_of_digits = cpp_dec_float_total_digits10; | |
1781 | ||
1782 | if(f & std::ios_base::fixed) | |
1783 | { | |
1784 | number_of_digits += my_exp + 1; | |
1785 | } | |
1786 | else if(f & std::ios_base::scientific) | |
1787 | ++number_of_digits; | |
1788 | // Determine the number of elements needed to provide the requested digits from cpp_dec_float<Digits10, ExponentType, Allocator>. | |
1789 | const std::size_t number_of_elements = (std::min)(static_cast<std::size_t>((number_of_digits / static_cast<std::size_t>(cpp_dec_float_elem_digits10)) + 2u), | |
1790 | static_cast<std::size_t>(cpp_dec_float_elem_number)); | |
1791 | ||
1792 | // Extract the remaining digits from cpp_dec_float<Digits10, ExponentType, Allocator> after the decimal point. | |
1793 | str = boost::lexical_cast<std::string>(data[0]); | |
1794 | ||
1795 | // Extract all of the digits from cpp_dec_float<Digits10, ExponentType, Allocator>, beginning with the first data element. | |
1796 | for(std::size_t i = static_cast<std::size_t>(1u); i < number_of_elements; i++) | |
1797 | { | |
1798 | std::stringstream ss; | |
1799 | ||
1800 | ss << std::setw(static_cast<std::streamsize>(cpp_dec_float_elem_digits10)) | |
1801 | << std::setfill(static_cast<char>('0')) | |
1802 | << data[i]; | |
1803 | ||
1804 | str += ss.str(); | |
1805 | } | |
1806 | ||
1807 | bool have_leading_zeros = false; | |
1808 | ||
1809 | if(number_of_digits == 0) | |
1810 | { | |
1811 | // We only get here if the output format is "fixed" and we just need to | |
1812 | // round the first non-zero digit. | |
1813 | number_of_digits -= my_exp + 1; // reset to original value | |
1814 | str.insert(static_cast<std::string::size_type>(0), std::string::size_type(number_of_digits), '0'); | |
1815 | have_leading_zeros = true; | |
1816 | } | |
1817 | ||
1818 | if(number_of_digits < 0) | |
1819 | { | |
1820 | str = "0"; | |
1821 | if(isneg()) | |
1822 | str.insert(static_cast<std::string::size_type>(0), 1, '-'); | |
1823 | boost::multiprecision::detail::format_float_string(str, 0, number_of_digits - my_exp - 1, f, this->iszero()); | |
1824 | return str; | |
1825 | } | |
1826 | else | |
1827 | { | |
1828 | // Cut the output to the size of the precision. | |
1829 | if(str.length() > static_cast<std::string::size_type>(number_of_digits)) | |
1830 | { | |
1831 | // Get the digit after the last needed digit for rounding | |
1832 | const boost::uint32_t round = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits)]) - static_cast<boost::uint32_t>('0')); | |
1833 | ||
1834 | bool need_round_up = round >= 5u; | |
1835 | ||
1836 | if(round == 5u) | |
1837 | { | |
1838 | const boost::uint32_t ix = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(str[static_cast<std::string::size_type>(number_of_digits - 1)]) - static_cast<boost::uint32_t>('0')); | |
1839 | if((ix & 1u) == 0) | |
1840 | { | |
1841 | // We have an even digit followed by a 5, so we might not actually need to round up | |
1842 | // if all the remaining digits are zero: | |
1843 | if(str.find_first_not_of('0', static_cast<std::string::size_type>(number_of_digits + 1)) == std::string::npos) | |
1844 | { | |
1845 | bool all_zeros = true; | |
1846 | // No none-zero trailing digits in the string, now check whatever parts we didn't convert to the string: | |
1847 | for(std::size_t i = number_of_elements; i < data.size(); i++) | |
1848 | { | |
1849 | if(data[i]) | |
1850 | { | |
1851 | all_zeros = false; | |
1852 | break; | |
1853 | } | |
1854 | } | |
1855 | if(all_zeros) | |
1856 | need_round_up = false; // tie break - round to even. | |
1857 | } | |
1858 | } | |
1859 | } | |
1860 | ||
1861 | // Truncate the string | |
1862 | str.erase(static_cast<std::string::size_type>(number_of_digits)); | |
1863 | ||
1864 | if(need_round_up) | |
1865 | { | |
1866 | std::size_t ix = static_cast<std::size_t>(str.length() - 1u); | |
1867 | ||
1868 | // Every trailing 9 must be rounded up | |
1869 | while(ix && (static_cast<boost::int32_t>(str.at(ix)) - static_cast<boost::int32_t>('0') == static_cast<boost::int32_t>(9))) | |
1870 | { | |
1871 | str.at(ix) = static_cast<char>('0'); | |
1872 | --ix; | |
1873 | } | |
1874 | ||
1875 | if(!ix) | |
1876 | { | |
1877 | // There were nothing but trailing nines. | |
1878 | if(static_cast<boost::int32_t>(static_cast<boost::int32_t>(str.at(ix)) - static_cast<boost::int32_t>(0x30)) == static_cast<boost::int32_t>(9)) | |
1879 | { | |
1880 | // Increment up to the next order and adjust exponent. | |
1881 | str.at(ix) = static_cast<char>('1'); | |
1882 | ++my_exp; | |
1883 | } | |
1884 | else | |
1885 | { | |
1886 | // Round up this digit. | |
1887 | ++str.at(ix); | |
1888 | } | |
1889 | } | |
1890 | else | |
1891 | { | |
1892 | // Round up the last digit. | |
1893 | ++str[ix]; | |
1894 | } | |
1895 | } | |
1896 | } | |
1897 | } | |
1898 | ||
1899 | if(have_leading_zeros) | |
1900 | { | |
1901 | // We need to take the zeros back out again, and correct the exponent | |
1902 | // if we rounded up: | |
1903 | if(str[std::string::size_type(number_of_digits - 1)] != '0') | |
1904 | { | |
1905 | ++my_exp; | |
1906 | str.erase(0, std::string::size_type(number_of_digits - 1)); | |
1907 | } | |
1908 | else | |
1909 | str.erase(0, std::string::size_type(number_of_digits)); | |
1910 | } | |
1911 | ||
1912 | if(isneg()) | |
1913 | str.insert(static_cast<std::string::size_type>(0), 1, '-'); | |
1914 | ||
1915 | boost::multiprecision::detail::format_float_string(str, my_exp, org_digits, f, this->iszero()); | |
1916 | return str; | |
1917 | } | |
1918 | ||
1919 | template <unsigned Digits10, class ExponentType, class Allocator> | |
1920 | bool cpp_dec_float<Digits10, ExponentType, Allocator>::rd_string(const char* const s) | |
1921 | { | |
1922 | #ifndef BOOST_NO_EXCEPTIONS | |
1923 | try{ | |
1924 | #endif | |
1925 | ||
1926 | std::string str(s); | |
1927 | ||
1928 | // TBD: Using several regular expressions may significantly reduce | |
1929 | // the code complexity (and perhaps the run-time) of rd_string(). | |
1930 | ||
1931 | // Get a possible exponent and remove it. | |
1932 | exp = static_cast<ExponentType>(0); | |
1933 | ||
1934 | std::size_t pos; | |
1935 | ||
1936 | if( ((pos = str.find('e')) != std::string::npos) | |
1937 | || ((pos = str.find('E')) != std::string::npos) | |
1938 | ) | |
1939 | { | |
1940 | // Remove the exponent part from the string. | |
1941 | exp = boost::lexical_cast<ExponentType>(static_cast<const char*>(str.c_str() + (pos + 1u))); | |
1942 | str = str.substr(static_cast<std::size_t>(0u), pos); | |
1943 | } | |
1944 | ||
1945 | // Get a possible +/- sign and remove it. | |
1946 | neg = false; | |
1947 | ||
1948 | if(str.size()) | |
1949 | { | |
1950 | if(str[0] == '-') | |
1951 | { | |
1952 | neg = true; | |
1953 | str.erase(0, 1); | |
1954 | } | |
1955 | else if(str[0] == '+') | |
1956 | { | |
1957 | str.erase(0, 1); | |
1958 | } | |
1959 | } | |
1960 | // | |
1961 | // Special cases for infinities and NaN's: | |
1962 | // | |
1963 | if((str == "inf") || (str == "INF") || (str == "infinity") || (str == "INFINITY")) | |
1964 | { | |
1965 | if(neg) | |
1966 | { | |
1967 | *this = this->inf(); | |
1968 | this->negate(); | |
1969 | } | |
1970 | else | |
1971 | *this = this->inf(); | |
1972 | return true; | |
1973 | } | |
1974 | if((str.size() >= 3) && ((str.substr(0, 3) == "nan") || (str.substr(0, 3) == "NAN") || (str.substr(0, 3) == "NaN"))) | |
1975 | { | |
1976 | *this = this->nan(); | |
1977 | return true; | |
1978 | } | |
1979 | ||
1980 | // Remove the leading zeros for all input types. | |
1981 | const std::string::iterator fwd_it_leading_zero = std::find_if(str.begin(), str.end(), char_is_nonzero_predicate); | |
1982 | ||
1983 | if(fwd_it_leading_zero != str.begin()) | |
1984 | { | |
1985 | if(fwd_it_leading_zero == str.end()) | |
1986 | { | |
1987 | // The string contains nothing but leading zeros. | |
1988 | // This string represents zero. | |
1989 | operator=(zero()); | |
1990 | return true; | |
1991 | } | |
1992 | else | |
1993 | { | |
1994 | str.erase(str.begin(), fwd_it_leading_zero); | |
1995 | } | |
1996 | } | |
1997 | ||
1998 | // Put the input string into the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form | |
1999 | // aaa.bbbbE+/-n, where aaa has 1...cpp_dec_float_elem_digits10, bbbb has an | |
2000 | // even multiple of cpp_dec_float_elem_digits10 which are possibly zero padded | |
2001 | // on the right-end, and n is a signed 64-bit integer which is an | |
2002 | // even multiple of cpp_dec_float_elem_digits10. | |
2003 | ||
2004 | // Find a possible decimal point. | |
2005 | pos = str.find(static_cast<char>('.')); | |
2006 | ||
2007 | if(pos != std::string::npos) | |
2008 | { | |
2009 | // Remove all trailing insignificant zeros. | |
2010 | const std::string::const_reverse_iterator rit_non_zero = std::find_if(str.rbegin(), str.rend(), char_is_nonzero_predicate); | |
2011 | ||
2012 | if(rit_non_zero != static_cast<std::string::const_reverse_iterator>(str.rbegin())) | |
2013 | { | |
2014 | const std::string::size_type ofs = str.length() - std::distance<std::string::const_reverse_iterator>(str.rbegin(), rit_non_zero); | |
2015 | str.erase(str.begin() + ofs, str.end()); | |
2016 | } | |
2017 | ||
2018 | // Check if the input is identically zero. | |
2019 | if(str == std::string(".")) | |
2020 | { | |
2021 | operator=(zero()); | |
2022 | return true; | |
2023 | } | |
2024 | ||
2025 | // Remove leading significant zeros just after the decimal point | |
2026 | // and adjust the exponent accordingly. | |
2027 | // Note that the while-loop operates only on strings of the form ".000abcd..." | |
2028 | // and peels away the zeros just after the decimal point. | |
2029 | if(str.at(static_cast<std::size_t>(0u)) == static_cast<char>('.')) | |
2030 | { | |
2031 | const std::string::iterator it_non_zero = std::find_if(str.begin() + 1u, str.end(), char_is_nonzero_predicate); | |
2032 | ||
2033 | std::size_t delta_exp = static_cast<std::size_t>(0u); | |
2034 | ||
2035 | if(str.at(static_cast<std::size_t>(1u)) == static_cast<char>('0')) | |
2036 | { | |
2037 | delta_exp = std::distance<std::string::const_iterator>(str.begin() + 1u, it_non_zero); | |
2038 | } | |
2039 | ||
2040 | // Bring one single digit into the mantissa and adjust the exponent accordingly. | |
2041 | str.erase(str.begin(), it_non_zero); | |
2042 | str.insert(static_cast<std::string::size_type>(1u), "."); | |
2043 | exp -= static_cast<ExponentType>(delta_exp + 1u); | |
2044 | } | |
2045 | } | |
2046 | else | |
2047 | { | |
2048 | // Input string has no decimal point: Append decimal point. | |
2049 | str.append("."); | |
2050 | } | |
2051 | ||
2052 | // Shift the decimal point such that the exponent is an even multiple of cpp_dec_float_elem_digits10. | |
2053 | std::size_t n_shift = static_cast<std::size_t>(0u); | |
2054 | const std::size_t n_exp_rem = static_cast<std::size_t>(exp % static_cast<ExponentType>(cpp_dec_float_elem_digits10)); | |
2055 | ||
2056 | if((exp % static_cast<ExponentType>(cpp_dec_float_elem_digits10)) != static_cast<ExponentType>(0)) | |
2057 | { | |
2058 | n_shift = ((exp < static_cast<ExponentType>(0)) | |
2059 | ? static_cast<std::size_t>(n_exp_rem + static_cast<std::size_t>(cpp_dec_float_elem_digits10)) | |
2060 | : static_cast<std::size_t>(n_exp_rem)); | |
2061 | } | |
2062 | ||
2063 | // Make sure that there are enough digits for the decimal point shift. | |
2064 | pos = str.find(static_cast<char>('.')); | |
2065 | ||
2066 | std::size_t pos_plus_one = static_cast<std::size_t>(pos + 1u); | |
2067 | ||
2068 | if((str.length() - pos_plus_one) < n_shift) | |
2069 | { | |
2070 | const std::size_t sz = static_cast<std::size_t>(n_shift - (str.length() - pos_plus_one)); | |
2071 | ||
2072 | str.append(std::string(sz, static_cast<char>('0'))); | |
2073 | } | |
2074 | ||
2075 | // Do the decimal point shift. | |
2076 | if(n_shift != static_cast<std::size_t>(0u)) | |
2077 | { | |
2078 | str.insert(static_cast<std::string::size_type>(pos_plus_one + n_shift), "."); | |
2079 | ||
2080 | str.erase(pos, static_cast<std::string::size_type>(1u)); | |
2081 | ||
2082 | exp -= static_cast<ExponentType>(n_shift); | |
2083 | } | |
2084 | ||
2085 | // Cut the size of the mantissa to <= cpp_dec_float_elem_digits10. | |
2086 | pos = str.find(static_cast<char>('.')); | |
2087 | pos_plus_one = static_cast<std::size_t>(pos + 1u); | |
2088 | ||
2089 | if(pos > static_cast<std::size_t>(cpp_dec_float_elem_digits10)) | |
2090 | { | |
2091 | const boost::int32_t n_pos = static_cast<boost::int32_t>(pos); | |
2092 | const boost::int32_t n_rem_is_zero = ((static_cast<boost::int32_t>(n_pos % cpp_dec_float_elem_digits10) == static_cast<boost::int32_t>(0)) ? static_cast<boost::int32_t>(1) : static_cast<boost::int32_t>(0)); | |
2093 | const boost::int32_t n = static_cast<boost::int32_t>(static_cast<boost::int32_t>(n_pos / cpp_dec_float_elem_digits10) - n_rem_is_zero); | |
2094 | ||
2095 | str.insert(static_cast<std::size_t>(static_cast<boost::int32_t>(n_pos - static_cast<boost::int32_t>(n * cpp_dec_float_elem_digits10))), "."); | |
2096 | ||
2097 | str.erase(pos_plus_one, static_cast<std::size_t>(1u)); | |
2098 | ||
2099 | exp += static_cast<ExponentType>(static_cast<ExponentType>(n) * static_cast<ExponentType>(cpp_dec_float_elem_digits10)); | |
2100 | } | |
2101 | ||
2102 | // Pad the decimal part such that its value is an even | |
2103 | // multiple of cpp_dec_float_elem_digits10. | |
2104 | pos = str.find(static_cast<char>('.')); | |
2105 | pos_plus_one = static_cast<std::size_t>(pos + 1u); | |
2106 | ||
2107 | const boost::int32_t n_dec = static_cast<boost::int32_t>(static_cast<boost::int32_t>(str.length() - 1u) - static_cast<boost::int32_t>(pos)); | |
2108 | const boost::int32_t n_rem = static_cast<boost::int32_t>(n_dec % cpp_dec_float_elem_digits10); | |
2109 | ||
2110 | boost::int32_t n_cnt = ((n_rem != static_cast<boost::int32_t>(0)) | |
2111 | ? static_cast<boost::int32_t>(cpp_dec_float_elem_digits10 - n_rem) | |
2112 | : static_cast<boost::int32_t>(0)); | |
2113 | ||
2114 | if(n_cnt != static_cast<boost::int32_t>(0)) | |
2115 | { | |
2116 | str.append(static_cast<std::size_t>(n_cnt), static_cast<char>('0')); | |
2117 | } | |
2118 | ||
2119 | // Truncate decimal part if it is too long. | |
2120 | const std::size_t max_dec = static_cast<std::size_t>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10); | |
2121 | ||
2122 | if(static_cast<std::size_t>(str.length() - pos) > max_dec) | |
2123 | { | |
2124 | str = str.substr(static_cast<std::size_t>(0u), | |
2125 | static_cast<std::size_t>(pos_plus_one + max_dec)); | |
2126 | } | |
2127 | ||
2128 | // Now the input string has the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form. | |
2129 | // (See the comment above.) | |
2130 | ||
2131 | // Set all the data elements to 0. | |
2132 | std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); | |
2133 | ||
2134 | // Extract the data. | |
2135 | ||
2136 | // First get the digits to the left of the decimal point... | |
2137 | data[0u] = boost::lexical_cast<boost::uint32_t>(str.substr(static_cast<std::size_t>(0u), pos)); | |
2138 | ||
2139 | // ...then get the remaining digits to the right of the decimal point. | |
2140 | const std::string::size_type i_end = ((str.length() - pos_plus_one) / static_cast<std::string::size_type>(cpp_dec_float_elem_digits10)); | |
2141 | ||
2142 | for(std::string::size_type i = static_cast<std::string::size_type>(0u); i < i_end; i++) | |
2143 | { | |
2144 | const std::string::const_iterator it = str.begin() | |
2145 | + pos_plus_one | |
2146 | + (i * static_cast<std::string::size_type>(cpp_dec_float_elem_digits10)); | |
2147 | ||
2148 | data[i + 1u] = boost::lexical_cast<boost::uint32_t>(std::string(it, it + static_cast<std::string::size_type>(cpp_dec_float_elem_digits10))); | |
2149 | } | |
2150 | ||
2151 | // Check for overflow... | |
2152 | if(exp > cpp_dec_float_max_exp10) | |
2153 | { | |
2154 | const bool b_result_is_neg = neg; | |
2155 | ||
2156 | *this = inf(); | |
2157 | if(b_result_is_neg) | |
2158 | negate(); | |
2159 | } | |
2160 | ||
2161 | // ...and check for underflow. | |
2162 | if(exp <= cpp_dec_float_min_exp10) | |
2163 | { | |
2164 | if(exp == cpp_dec_float_min_exp10) | |
2165 | { | |
2166 | // Check for identity with the minimum value. | |
2167 | cpp_dec_float<Digits10, ExponentType, Allocator> test = *this; | |
2168 | ||
2169 | test.exp = static_cast<ExponentType>(0); | |
2170 | ||
2171 | if(test.isone()) | |
2172 | { | |
2173 | *this = zero(); | |
2174 | } | |
2175 | } | |
2176 | else | |
2177 | { | |
2178 | *this = zero(); | |
2179 | } | |
2180 | } | |
2181 | ||
2182 | #ifndef BOOST_NO_EXCEPTIONS | |
2183 | } | |
2184 | catch(const bad_lexical_cast&) | |
2185 | { | |
2186 | // Rethrow with better error message: | |
2187 | std::string msg = "Unable to parse the string \""; | |
2188 | msg += s; | |
2189 | msg += "\" as a floating point value."; | |
2190 | throw std::runtime_error(msg); | |
2191 | } | |
2192 | #endif | |
2193 | return true; | |
2194 | } | |
2195 | ||
2196 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2197 | cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float(const double mantissa, const ExponentType exponent) | |
2198 | : data (), | |
2199 | exp (static_cast<ExponentType>(0)), | |
2200 | neg (false), | |
2201 | fpclass (cpp_dec_float_finite), | |
2202 | prec_elem(cpp_dec_float_elem_number) | |
2203 | { | |
2204 | // Create *this cpp_dec_float<Digits10, ExponentType, Allocator> from a given mantissa and exponent. | |
2205 | // Note: This constructor does not maintain the full precision of double. | |
2206 | ||
2207 | const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits<double>::min)() * (1.0 + std::numeric_limits<double>::epsilon()))); | |
2208 | ||
2209 | if(mantissa_is_iszero) | |
2210 | { | |
2211 | std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); | |
2212 | return; | |
2213 | } | |
2214 | ||
2215 | const bool b_neg = (mantissa < 0.0); | |
2216 | ||
2217 | double d = ((!b_neg) ? mantissa : -mantissa); | |
2218 | ExponentType e = exponent; | |
2219 | ||
2220 | while(d > 10.0) { d /= 10.0; ++e; } | |
2221 | while(d < 1.0) { d *= 10.0; --e; } | |
2222 | ||
2223 | boost::int32_t shift = static_cast<boost::int32_t>(e % static_cast<boost::int32_t>(cpp_dec_float_elem_digits10)); | |
2224 | ||
2225 | while(static_cast<boost::int32_t>(shift-- % cpp_dec_float_elem_digits10) != static_cast<boost::int32_t>(0)) | |
2226 | { | |
2227 | d *= 10.0; | |
2228 | --e; | |
2229 | } | |
2230 | ||
2231 | exp = e; | |
2232 | neg = b_neg; | |
2233 | ||
2234 | std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); | |
2235 | ||
2236 | static const boost::int32_t digit_ratio = static_cast<boost::int32_t>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) / static_cast<boost::int32_t>(cpp_dec_float_elem_digits10)); | |
2237 | static const boost::int32_t digit_loops = static_cast<boost::int32_t>(digit_ratio + static_cast<boost::int32_t>(2)); | |
2238 | ||
2239 | for(boost::int32_t i = static_cast<boost::int32_t>(0); i < digit_loops; i++) | |
2240 | { | |
2241 | boost::uint32_t n = static_cast<boost::uint32_t>(static_cast<boost::uint64_t>(d)); | |
2242 | data[i] = static_cast<boost::uint32_t>(n); | |
2243 | d -= static_cast<double>(n); | |
2244 | d *= static_cast<double>(cpp_dec_float_elem_mask); | |
2245 | } | |
2246 | } | |
2247 | ||
2248 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2249 | cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator= (long double a) | |
2250 | { | |
2251 | // Christopher Kormanyos's original code used a cast to boost::long_long_type here, but that fails | |
2252 | // when long double has more digits than a boost::long_long_type. | |
2253 | using std::frexp; | |
2254 | using std::ldexp; | |
2255 | using std::floor; | |
2256 | ||
2257 | if(a == 0) | |
2258 | return *this = zero(); | |
2259 | ||
2260 | if(a == 1) | |
2261 | return *this = one(); | |
2262 | ||
2263 | if((boost::math::isinf)(a)) | |
2264 | { | |
2265 | *this = inf(); | |
2266 | if(a < 0) | |
2267 | this->negate(); | |
2268 | return *this; | |
2269 | } | |
2270 | ||
2271 | if((boost::math::isnan)(a)) | |
2272 | return *this = nan(); | |
2273 | ||
2274 | int e; | |
2275 | long double f, term; | |
2276 | *this = zero(); | |
2277 | ||
2278 | f = frexp(a, &e); | |
2279 | // See https://svn.boost.org/trac/boost/ticket/10924 for an example of why this may go wrong: | |
2280 | BOOST_ASSERT((boost::math::isfinite)(f)); | |
2281 | ||
2282 | static const int shift = std::numeric_limits<int>::digits - 1; | |
2283 | ||
2284 | while(f) | |
2285 | { | |
2286 | // extract int sized bits from f: | |
2287 | f = ldexp(f, shift); | |
2288 | BOOST_ASSERT((boost::math::isfinite)(f)); | |
2289 | term = floor(f); | |
2290 | e -= shift; | |
2291 | *this *= pow2(shift); | |
2292 | if(term > 0) | |
2293 | add_unsigned_long_long(static_cast<unsigned>(term)); | |
2294 | else | |
2295 | sub_unsigned_long_long(static_cast<unsigned>(-term)); | |
2296 | f -= term; | |
2297 | } | |
2298 | ||
2299 | if(e != 0) | |
2300 | *this *= pow2(e); | |
2301 | ||
2302 | return *this; | |
2303 | } | |
2304 | ||
2305 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2306 | void cpp_dec_float<Digits10, ExponentType, Allocator>::from_unsigned_long_long(const boost::ulong_long_type u) | |
2307 | { | |
2308 | std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u)); | |
2309 | ||
2310 | exp = static_cast<ExponentType>(0); | |
2311 | neg = false; | |
2312 | fpclass = cpp_dec_float_finite; | |
2313 | prec_elem = cpp_dec_float_elem_number; | |
2314 | ||
2315 | std::size_t i =static_cast<std::size_t>(0u); | |
2316 | ||
2317 | boost::ulong_long_type uu = u; | |
2318 | ||
2319 | boost::uint32_t temp[(std::numeric_limits<boost::ulong_long_type>::digits10 / static_cast<int>(cpp_dec_float_elem_digits10)) + 3] = { static_cast<boost::uint32_t>(0u) }; | |
2320 | ||
2321 | while(uu != static_cast<boost::ulong_long_type>(0u)) | |
2322 | { | |
2323 | temp[i] = static_cast<boost::uint32_t>(uu % static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask)); | |
2324 | uu = static_cast<boost::ulong_long_type>(uu / static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask)); | |
2325 | ++i; | |
2326 | } | |
2327 | ||
2328 | if(i > static_cast<std::size_t>(1u)) | |
2329 | { | |
2330 | exp += static_cast<ExponentType>((i - 1u) * static_cast<std::size_t>(cpp_dec_float_elem_digits10)); | |
2331 | } | |
2332 | ||
2333 | std::reverse(temp, temp + i); | |
2334 | std::copy(temp, temp + (std::min)(i, static_cast<std::size_t>(cpp_dec_float_elem_number)), data.begin()); | |
2335 | } | |
2336 | ||
2337 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2338 | boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p) | |
2339 | { | |
2340 | // | |
2341 | // There is a limit on how many limbs this algorithm can handle without dropping digits | |
2342 | // due to overflow in the carry, it is: | |
2343 | // | |
2344 | // FLOOR( (2^64 - 1) / (10^8 * 10^8) ) == 1844 | |
2345 | // | |
2346 | BOOST_STATIC_ASSERT_MSG(cpp_dec_float_elem_number < 1800, "Too many limbs in the data type for the multiplication algorithm - unsupported precision in cpp_dec_float."); | |
2347 | ||
2348 | boost::uint64_t carry = static_cast<boost::uint64_t>(0u); | |
2349 | ||
2350 | for(boost::int32_t j = static_cast<boost::int32_t>(p - 1u); j >= static_cast<boost::int32_t>(0); j--) | |
2351 | { | |
2352 | boost::uint64_t sum = carry; | |
2353 | ||
2354 | for(boost::int32_t i = j; i >= static_cast<boost::int32_t>(0); i--) | |
2355 | { | |
2356 | sum += static_cast<boost::uint64_t>(u[j - i] * static_cast<boost::uint64_t>(v[i])); | |
2357 | } | |
2358 | ||
2359 | u[j] = static_cast<boost::uint32_t>(sum % static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); | |
2360 | carry = static_cast<boost::uint64_t>(sum / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); | |
2361 | } | |
2362 | ||
2363 | return static_cast<boost::uint32_t>(carry); | |
2364 | } | |
2365 | ||
2366 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2367 | boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) | |
2368 | { | |
2369 | boost::uint64_t carry = static_cast<boost::uint64_t>(0u); | |
2370 | ||
2371 | // Multiplication loop. | |
2372 | for(boost::int32_t j = p - 1; j >= static_cast<boost::int32_t>(0); j--) | |
2373 | { | |
2374 | const boost::uint64_t t = static_cast<boost::uint64_t>(carry + static_cast<boost::uint64_t>(u[j] * static_cast<boost::uint64_t>(n))); | |
2375 | carry = static_cast<boost::uint64_t>(t / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask)); | |
2376 | u[j] = static_cast<boost::uint32_t>(t - static_cast<boost::uint64_t>(static_cast<boost::uint32_t>(cpp_dec_float_elem_mask) * static_cast<boost::uint64_t>(carry))); | |
2377 | } | |
2378 | ||
2379 | return static_cast<boost::uint32_t>(carry); | |
2380 | } | |
2381 | ||
2382 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2383 | boost::uint32_t cpp_dec_float<Digits10, ExponentType, Allocator>::div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p) | |
2384 | { | |
2385 | boost::uint64_t prev = static_cast<boost::uint64_t>(0u); | |
2386 | ||
2387 | for(boost::int32_t j = static_cast<boost::int32_t>(0); j < p; j++) | |
2388 | { | |
2389 | const boost::uint64_t t = static_cast<boost::uint64_t>(u[j] + static_cast<boost::uint64_t>(prev * static_cast<boost::uint32_t>(cpp_dec_float_elem_mask))); | |
2390 | u[j] = static_cast<boost::uint32_t>(t / n); | |
2391 | prev = static_cast<boost::uint64_t>(t - static_cast<boost::uint64_t>(n * static_cast<boost::uint64_t>(u[j]))); | |
2392 | } | |
2393 | ||
2394 | return static_cast<boost::uint32_t>(prev); | |
2395 | } | |
2396 | ||
2397 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2398 | cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(const boost::long_long_type p) | |
2399 | { | |
2400 | // Create a static const table of p^2 for -128 < p < +128. | |
2401 | // Note: The size of this table must be odd-numbered and | |
2402 | // symmetric about 0. | |
2403 | init.do_nothing(); | |
2404 | static const boost::array<cpp_dec_float<Digits10, ExponentType, Allocator>, 255u> p2_data = | |
2405 | {{ | |
2406 | cpp_dec_float("5.877471754111437539843682686111228389093327783860437607543758531392086297273635864257812500000000000e-39"), | |
2407 | cpp_dec_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"), | |
2408 | cpp_dec_float("2.350988701644575015937473074444491355637331113544175043017503412556834518909454345703125000000000000e-38"), | |
2409 | cpp_dec_float("4.701977403289150031874946148888982711274662227088350086035006825113669037818908691406250000000000000e-38"), | |
2410 | cpp_dec_float("9.403954806578300063749892297777965422549324454176700172070013650227338075637817382812500000000000000e-38"), | |
2411 | cpp_dec_float("1.880790961315660012749978459555593084509864890835340034414002730045467615127563476562500000000000000e-37"), | |
2412 | cpp_dec_float("3.761581922631320025499956919111186169019729781670680068828005460090935230255126953125000000000000000e-37"), | |
2413 | cpp_dec_float("7.523163845262640050999913838222372338039459563341360137656010920181870460510253906250000000000000000e-37"), | |
2414 | cpp_dec_float("1.504632769052528010199982767644474467607891912668272027531202184036374092102050781250000000000000000e-36"), | |
2415 | cpp_dec_float("3.009265538105056020399965535288948935215783825336544055062404368072748184204101562500000000000000000e-36"), | |
2416 | cpp_dec_float("6.018531076210112040799931070577897870431567650673088110124808736145496368408203125000000000000000000e-36"), | |
2417 | cpp_dec_float("1.203706215242022408159986214115579574086313530134617622024961747229099273681640625000000000000000000e-35"), | |
2418 | cpp_dec_float("2.407412430484044816319972428231159148172627060269235244049923494458198547363281250000000000000000000e-35"), | |
2419 | cpp_dec_float("4.814824860968089632639944856462318296345254120538470488099846988916397094726562500000000000000000000e-35"), | |
2420 | cpp_dec_float("9.629649721936179265279889712924636592690508241076940976199693977832794189453125000000000000000000000e-35"), | |
2421 | cpp_dec_float("1.925929944387235853055977942584927318538101648215388195239938795566558837890625000000000000000000000e-34"), | |
2422 | cpp_dec_float("3.851859888774471706111955885169854637076203296430776390479877591133117675781250000000000000000000000e-34"), | |
2423 | cpp_dec_float("7.703719777548943412223911770339709274152406592861552780959755182266235351562500000000000000000000000e-34"), | |
2424 | cpp_dec_float("1.540743955509788682444782354067941854830481318572310556191951036453247070312500000000000000000000000e-33"), | |
2425 | cpp_dec_float("3.081487911019577364889564708135883709660962637144621112383902072906494140625000000000000000000000000e-33"), | |
2426 | cpp_dec_float("6.162975822039154729779129416271767419321925274289242224767804145812988281250000000000000000000000000e-33"), | |
2427 | cpp_dec_float("1.232595164407830945955825883254353483864385054857848444953560829162597656250000000000000000000000000e-32"), | |
2428 | cpp_dec_float("2.465190328815661891911651766508706967728770109715696889907121658325195312500000000000000000000000000e-32"), | |
2429 | cpp_dec_float("4.930380657631323783823303533017413935457540219431393779814243316650390625000000000000000000000000000e-32"), | |
2430 | cpp_dec_float("9.860761315262647567646607066034827870915080438862787559628486633300781250000000000000000000000000000e-32"), | |
2431 | cpp_dec_float("1.972152263052529513529321413206965574183016087772557511925697326660156250000000000000000000000000000e-31"), | |
2432 | cpp_dec_float("3.944304526105059027058642826413931148366032175545115023851394653320312500000000000000000000000000000e-31"), | |
2433 | cpp_dec_float("7.888609052210118054117285652827862296732064351090230047702789306640625000000000000000000000000000000e-31"), | |
2434 | cpp_dec_float("1.577721810442023610823457130565572459346412870218046009540557861328125000000000000000000000000000000e-30"), | |
2435 | cpp_dec_float("3.155443620884047221646914261131144918692825740436092019081115722656250000000000000000000000000000000e-30"), | |
2436 | cpp_dec_float("6.310887241768094443293828522262289837385651480872184038162231445312500000000000000000000000000000000e-30"), | |
2437 | cpp_dec_float("1.262177448353618888658765704452457967477130296174436807632446289062500000000000000000000000000000000e-29"), | |
2438 | cpp_dec_float("2.524354896707237777317531408904915934954260592348873615264892578125000000000000000000000000000000000e-29"), | |
2439 | cpp_dec_float("5.048709793414475554635062817809831869908521184697747230529785156250000000000000000000000000000000000e-29"), | |
2440 | cpp_dec_float("1.009741958682895110927012563561966373981704236939549446105957031250000000000000000000000000000000000e-28"), | |
2441 | cpp_dec_float("2.019483917365790221854025127123932747963408473879098892211914062500000000000000000000000000000000000e-28"), | |
2442 | cpp_dec_float("4.038967834731580443708050254247865495926816947758197784423828125000000000000000000000000000000000000e-28"), | |
2443 | cpp_dec_float("8.077935669463160887416100508495730991853633895516395568847656250000000000000000000000000000000000000e-28"), | |
2444 | cpp_dec_float("1.615587133892632177483220101699146198370726779103279113769531250000000000000000000000000000000000000e-27"), | |
2445 | cpp_dec_float("3.231174267785264354966440203398292396741453558206558227539062500000000000000000000000000000000000000e-27"), | |
2446 | cpp_dec_float("6.462348535570528709932880406796584793482907116413116455078125000000000000000000000000000000000000000e-27"), | |
2447 | cpp_dec_float("1.292469707114105741986576081359316958696581423282623291015625000000000000000000000000000000000000000e-26"), | |
2448 | cpp_dec_float("2.584939414228211483973152162718633917393162846565246582031250000000000000000000000000000000000000000e-26"), | |
2449 | cpp_dec_float("5.169878828456422967946304325437267834786325693130493164062500000000000000000000000000000000000000000e-26"), | |
2450 | cpp_dec_float("1.033975765691284593589260865087453566957265138626098632812500000000000000000000000000000000000000000e-25"), | |
2451 | cpp_dec_float("2.067951531382569187178521730174907133914530277252197265625000000000000000000000000000000000000000000e-25"), | |
2452 | cpp_dec_float("4.135903062765138374357043460349814267829060554504394531250000000000000000000000000000000000000000000e-25"), | |
2453 | cpp_dec_float("8.271806125530276748714086920699628535658121109008789062500000000000000000000000000000000000000000000e-25"), | |
2454 | cpp_dec_float("1.654361225106055349742817384139925707131624221801757812500000000000000000000000000000000000000000000e-24"), | |
2455 | cpp_dec_float("3.308722450212110699485634768279851414263248443603515625000000000000000000000000000000000000000000000e-24"), | |
2456 | cpp_dec_float("6.617444900424221398971269536559702828526496887207031250000000000000000000000000000000000000000000000e-24"), | |
2457 | cpp_dec_float("1.323488980084844279794253907311940565705299377441406250000000000000000000000000000000000000000000000e-23"), | |
2458 | cpp_dec_float("2.646977960169688559588507814623881131410598754882812500000000000000000000000000000000000000000000000e-23"), | |
2459 | cpp_dec_float("5.293955920339377119177015629247762262821197509765625000000000000000000000000000000000000000000000000e-23"), | |
2460 | cpp_dec_float("1.058791184067875423835403125849552452564239501953125000000000000000000000000000000000000000000000000e-22"), | |
2461 | cpp_dec_float("2.117582368135750847670806251699104905128479003906250000000000000000000000000000000000000000000000000e-22"), | |
2462 | cpp_dec_float("4.235164736271501695341612503398209810256958007812500000000000000000000000000000000000000000000000000e-22"), | |
2463 | cpp_dec_float("8.470329472543003390683225006796419620513916015625000000000000000000000000000000000000000000000000000e-22"), | |
2464 | cpp_dec_float("1.694065894508600678136645001359283924102783203125000000000000000000000000000000000000000000000000000e-21"), | |
2465 | cpp_dec_float("3.388131789017201356273290002718567848205566406250000000000000000000000000000000000000000000000000000e-21"), | |
2466 | cpp_dec_float("6.776263578034402712546580005437135696411132812500000000000000000000000000000000000000000000000000000e-21"), | |
2467 | cpp_dec_float("1.355252715606880542509316001087427139282226562500000000000000000000000000000000000000000000000000000e-20"), | |
2468 | cpp_dec_float("2.710505431213761085018632002174854278564453125000000000000000000000000000000000000000000000000000000e-20"), | |
2469 | cpp_dec_float("5.421010862427522170037264004349708557128906250000000000000000000000000000000000000000000000000000000e-20"), | |
2470 | cpp_dec_float("1.084202172485504434007452800869941711425781250000000000000000000000000000000000000000000000000000000e-19"), | |
2471 | cpp_dec_float("2.168404344971008868014905601739883422851562500000000000000000000000000000000000000000000000000000000e-19"), | |
2472 | cpp_dec_float("4.336808689942017736029811203479766845703125000000000000000000000000000000000000000000000000000000000e-19"), | |
2473 | cpp_dec_float("8.673617379884035472059622406959533691406250000000000000000000000000000000000000000000000000000000000e-19"), | |
2474 | cpp_dec_float("1.734723475976807094411924481391906738281250000000000000000000000000000000000000000000000000000000000e-18"), | |
2475 | cpp_dec_float("3.469446951953614188823848962783813476562500000000000000000000000000000000000000000000000000000000000e-18"), | |
2476 | cpp_dec_float("6.938893903907228377647697925567626953125000000000000000000000000000000000000000000000000000000000000e-18"), | |
2477 | cpp_dec_float("1.387778780781445675529539585113525390625000000000000000000000000000000000000000000000000000000000000e-17"), | |
2478 | cpp_dec_float("2.775557561562891351059079170227050781250000000000000000000000000000000000000000000000000000000000000e-17"), | |
2479 | cpp_dec_float("5.551115123125782702118158340454101562500000000000000000000000000000000000000000000000000000000000000e-17"), | |
2480 | cpp_dec_float("1.110223024625156540423631668090820312500000000000000000000000000000000000000000000000000000000000000e-16"), | |
2481 | cpp_dec_float("2.220446049250313080847263336181640625000000000000000000000000000000000000000000000000000000000000000e-16"), | |
2482 | cpp_dec_float("4.440892098500626161694526672363281250000000000000000000000000000000000000000000000000000000000000000e-16"), | |
2483 | cpp_dec_float("8.881784197001252323389053344726562500000000000000000000000000000000000000000000000000000000000000000e-16"), | |
2484 | cpp_dec_float("1.776356839400250464677810668945312500000000000000000000000000000000000000000000000000000000000000000e-15"), | |
2485 | cpp_dec_float("3.552713678800500929355621337890625000000000000000000000000000000000000000000000000000000000000000000e-15"), | |
2486 | cpp_dec_float("7.105427357601001858711242675781250000000000000000000000000000000000000000000000000000000000000000000e-15"), | |
2487 | cpp_dec_float("1.421085471520200371742248535156250000000000000000000000000000000000000000000000000000000000000000000e-14"), | |
2488 | cpp_dec_float("2.842170943040400743484497070312500000000000000000000000000000000000000000000000000000000000000000000e-14"), | |
2489 | cpp_dec_float("5.684341886080801486968994140625000000000000000000000000000000000000000000000000000000000000000000000e-14"), | |
2490 | cpp_dec_float("1.136868377216160297393798828125000000000000000000000000000000000000000000000000000000000000000000000e-13"), | |
2491 | cpp_dec_float("2.273736754432320594787597656250000000000000000000000000000000000000000000000000000000000000000000000e-13"), | |
2492 | cpp_dec_float("4.547473508864641189575195312500000000000000000000000000000000000000000000000000000000000000000000000e-13"), | |
2493 | cpp_dec_float("9.094947017729282379150390625000000000000000000000000000000000000000000000000000000000000000000000000e-13"), | |
2494 | cpp_dec_float("1.818989403545856475830078125000000000000000000000000000000000000000000000000000000000000000000000000e-12"), | |
2495 | cpp_dec_float("3.637978807091712951660156250000000000000000000000000000000000000000000000000000000000000000000000000e-12"), | |
2496 | cpp_dec_float("7.275957614183425903320312500000000000000000000000000000000000000000000000000000000000000000000000000e-12"), | |
2497 | cpp_dec_float("1.455191522836685180664062500000000000000000000000000000000000000000000000000000000000000000000000000e-11"), | |
2498 | cpp_dec_float("2.910383045673370361328125000000000000000000000000000000000000000000000000000000000000000000000000000e-11"), | |
2499 | cpp_dec_float("5.820766091346740722656250000000000000000000000000000000000000000000000000000000000000000000000000000e-11"), | |
2500 | cpp_dec_float("1.164153218269348144531250000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), | |
2501 | cpp_dec_float("2.328306436538696289062500000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), | |
2502 | cpp_dec_float("4.656612873077392578125000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), | |
2503 | cpp_dec_float("9.313225746154785156250000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"), | |
2504 | cpp_dec_float("1.862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), | |
2505 | cpp_dec_float("3.725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), | |
2506 | cpp_dec_float("7.450580596923828125000000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"), | |
2507 | cpp_dec_float("1.490116119384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), | |
2508 | cpp_dec_float("2.980232238769531250000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), | |
2509 | cpp_dec_float("5.960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"), | |
2510 | cpp_dec_float("1.192092895507812500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), | |
2511 | cpp_dec_float("2.384185791015625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), | |
2512 | cpp_dec_float("4.768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), | |
2513 | cpp_dec_float("9.536743164062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"), | |
2514 | cpp_dec_float("1.907348632812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), | |
2515 | cpp_dec_float("3.814697265625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), | |
2516 | cpp_dec_float("7.629394531250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"), | |
2517 | cpp_dec_float("0.000015258789062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2518 | cpp_dec_float("0.000030517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2519 | cpp_dec_float("0.000061035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2520 | cpp_dec_float("0.000122070312500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2521 | cpp_dec_float("0.000244140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2522 | cpp_dec_float("0.000488281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2523 | cpp_dec_float("0.000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2524 | cpp_dec_float("0.001953125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2525 | cpp_dec_float("0.003906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2526 | cpp_dec_float("0.007812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2527 | cpp_dec_float("0.01562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2528 | cpp_dec_float("0.03125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2529 | cpp_dec_float("0.06250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), | |
2530 | cpp_dec_float("0.125"), | |
2531 | cpp_dec_float("0.25"), | |
2532 | cpp_dec_float("0.5"), | |
2533 | one(), | |
2534 | two(), | |
2535 | cpp_dec_float(static_cast<boost::ulong_long_type>(4)), | |
2536 | cpp_dec_float(static_cast<boost::ulong_long_type>(8)), | |
2537 | cpp_dec_float(static_cast<boost::ulong_long_type>(16)), | |
2538 | cpp_dec_float(static_cast<boost::ulong_long_type>(32)), | |
2539 | cpp_dec_float(static_cast<boost::ulong_long_type>(64)), | |
2540 | cpp_dec_float(static_cast<boost::ulong_long_type>(128)), | |
2541 | cpp_dec_float(static_cast<boost::ulong_long_type>(256)), | |
2542 | cpp_dec_float(static_cast<boost::ulong_long_type>(512)), | |
2543 | cpp_dec_float(static_cast<boost::ulong_long_type>(1024)), | |
2544 | cpp_dec_float(static_cast<boost::ulong_long_type>(2048)), | |
2545 | cpp_dec_float(static_cast<boost::ulong_long_type>(4096)), | |
2546 | cpp_dec_float(static_cast<boost::ulong_long_type>(8192)), | |
2547 | cpp_dec_float(static_cast<boost::ulong_long_type>(16384)), | |
2548 | cpp_dec_float(static_cast<boost::ulong_long_type>(32768)), | |
2549 | cpp_dec_float(static_cast<boost::ulong_long_type>(65536)), | |
2550 | cpp_dec_float(static_cast<boost::ulong_long_type>(131072)), | |
2551 | cpp_dec_float(static_cast<boost::ulong_long_type>(262144)), | |
2552 | cpp_dec_float(static_cast<boost::ulong_long_type>(524288)), | |
2553 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 20u)), | |
2554 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 21u)), | |
2555 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 22u)), | |
2556 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 23u)), | |
2557 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 24u)), | |
2558 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 25u)), | |
2559 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 26u)), | |
2560 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 27u)), | |
2561 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 28u)), | |
2562 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 29u)), | |
2563 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 30u)), | |
2564 | cpp_dec_float(static_cast<boost::uint64_t>(1uL << 31u)), | |
2565 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 32u)), | |
2566 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 33u)), | |
2567 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 34u)), | |
2568 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 35u)), | |
2569 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 36u)), | |
2570 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 37u)), | |
2571 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 38u)), | |
2572 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 39u)), | |
2573 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 40u)), | |
2574 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 41u)), | |
2575 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 42u)), | |
2576 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 43u)), | |
2577 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 44u)), | |
2578 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 45u)), | |
2579 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 46u)), | |
2580 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 47u)), | |
2581 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 48u)), | |
2582 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 49u)), | |
2583 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 50u)), | |
2584 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 51u)), | |
2585 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 52u)), | |
2586 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 53u)), | |
2587 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 54u)), | |
2588 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 55u)), | |
2589 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 56u)), | |
2590 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 57u)), | |
2591 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 58u)), | |
2592 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 59u)), | |
2593 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 60u)), | |
2594 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 61u)), | |
2595 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 62u)), | |
2596 | cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 63u)), | |
2597 | cpp_dec_float("1.844674407370955161600000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), | |
2598 | cpp_dec_float("3.689348814741910323200000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), | |
2599 | cpp_dec_float("7.378697629483820646400000000000000000000000000000000000000000000000000000000000000000000000000000000e19"), | |
2600 | cpp_dec_float("1.475739525896764129280000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), | |
2601 | cpp_dec_float("2.951479051793528258560000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), | |
2602 | cpp_dec_float("5.902958103587056517120000000000000000000000000000000000000000000000000000000000000000000000000000000e20"), | |
2603 | cpp_dec_float("1.180591620717411303424000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), | |
2604 | cpp_dec_float("2.361183241434822606848000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), | |
2605 | cpp_dec_float("4.722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), | |
2606 | cpp_dec_float("9.444732965739290427392000000000000000000000000000000000000000000000000000000000000000000000000000000e21"), | |
2607 | cpp_dec_float("1.888946593147858085478400000000000000000000000000000000000000000000000000000000000000000000000000000e22"), | |
2608 | cpp_dec_float("3.777893186295716170956800000000000000000000000000000000000000000000000000000000000000000000000000000e22"), | |
2609 | cpp_dec_float("7.555786372591432341913600000000000000000000000000000000000000000000000000000000000000000000000000000e22"), | |
2610 | cpp_dec_float("1.511157274518286468382720000000000000000000000000000000000000000000000000000000000000000000000000000e23"), | |
2611 | cpp_dec_float("3.022314549036572936765440000000000000000000000000000000000000000000000000000000000000000000000000000e23"), | |
2612 | cpp_dec_float("6.044629098073145873530880000000000000000000000000000000000000000000000000000000000000000000000000000e23"), | |
2613 | cpp_dec_float("1.208925819614629174706176000000000000000000000000000000000000000000000000000000000000000000000000000e24"), | |
2614 | cpp_dec_float("2.417851639229258349412352000000000000000000000000000000000000000000000000000000000000000000000000000e24"), | |
2615 | cpp_dec_float("4.835703278458516698824704000000000000000000000000000000000000000000000000000000000000000000000000000e24"), | |
2616 | cpp_dec_float("9.671406556917033397649408000000000000000000000000000000000000000000000000000000000000000000000000000e24"), | |
2617 | cpp_dec_float("1.934281311383406679529881600000000000000000000000000000000000000000000000000000000000000000000000000e25"), | |
2618 | cpp_dec_float("3.868562622766813359059763200000000000000000000000000000000000000000000000000000000000000000000000000e25"), | |
2619 | cpp_dec_float("7.737125245533626718119526400000000000000000000000000000000000000000000000000000000000000000000000000e25"), | |
2620 | cpp_dec_float("1.547425049106725343623905280000000000000000000000000000000000000000000000000000000000000000000000000e26"), | |
2621 | cpp_dec_float("3.094850098213450687247810560000000000000000000000000000000000000000000000000000000000000000000000000e26"), | |
2622 | cpp_dec_float("6.189700196426901374495621120000000000000000000000000000000000000000000000000000000000000000000000000e26"), | |
2623 | cpp_dec_float("1.237940039285380274899124224000000000000000000000000000000000000000000000000000000000000000000000000e27"), | |
2624 | cpp_dec_float("2.475880078570760549798248448000000000000000000000000000000000000000000000000000000000000000000000000e27"), | |
2625 | cpp_dec_float("4.951760157141521099596496896000000000000000000000000000000000000000000000000000000000000000000000000e27"), | |
2626 | cpp_dec_float("9.903520314283042199192993792000000000000000000000000000000000000000000000000000000000000000000000000e27"), | |
2627 | cpp_dec_float("1.980704062856608439838598758400000000000000000000000000000000000000000000000000000000000000000000000e28"), | |
2628 | cpp_dec_float("3.961408125713216879677197516800000000000000000000000000000000000000000000000000000000000000000000000e28"), | |
2629 | cpp_dec_float("7.922816251426433759354395033600000000000000000000000000000000000000000000000000000000000000000000000e28"), | |
2630 | cpp_dec_float("1.584563250285286751870879006720000000000000000000000000000000000000000000000000000000000000000000000e29"), | |
2631 | cpp_dec_float("3.169126500570573503741758013440000000000000000000000000000000000000000000000000000000000000000000000e29"), | |
2632 | cpp_dec_float("6.338253001141147007483516026880000000000000000000000000000000000000000000000000000000000000000000000e29"), | |
2633 | cpp_dec_float("1.267650600228229401496703205376000000000000000000000000000000000000000000000000000000000000000000000e30"), | |
2634 | cpp_dec_float("2.535301200456458802993406410752000000000000000000000000000000000000000000000000000000000000000000000e30"), | |
2635 | cpp_dec_float("5.070602400912917605986812821504000000000000000000000000000000000000000000000000000000000000000000000e30"), | |
2636 | cpp_dec_float("1.014120480182583521197362564300800000000000000000000000000000000000000000000000000000000000000000000e31"), | |
2637 | cpp_dec_float("2.028240960365167042394725128601600000000000000000000000000000000000000000000000000000000000000000000e31"), | |
2638 | cpp_dec_float("4.056481920730334084789450257203200000000000000000000000000000000000000000000000000000000000000000000e31"), | |
2639 | cpp_dec_float("8.112963841460668169578900514406400000000000000000000000000000000000000000000000000000000000000000000e31"), | |
2640 | cpp_dec_float("1.622592768292133633915780102881280000000000000000000000000000000000000000000000000000000000000000000e32"), | |
2641 | cpp_dec_float("3.245185536584267267831560205762560000000000000000000000000000000000000000000000000000000000000000000e32"), | |
2642 | cpp_dec_float("6.490371073168534535663120411525120000000000000000000000000000000000000000000000000000000000000000000e32"), | |
2643 | cpp_dec_float("1.298074214633706907132624082305024000000000000000000000000000000000000000000000000000000000000000000e33"), | |
2644 | cpp_dec_float("2.596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000e33"), | |
2645 | cpp_dec_float("5.192296858534827628530496329220096000000000000000000000000000000000000000000000000000000000000000000e33"), | |
2646 | cpp_dec_float("1.038459371706965525706099265844019200000000000000000000000000000000000000000000000000000000000000000e34"), | |
2647 | cpp_dec_float("2.076918743413931051412198531688038400000000000000000000000000000000000000000000000000000000000000000e34"), | |
2648 | cpp_dec_float("4.153837486827862102824397063376076800000000000000000000000000000000000000000000000000000000000000000e34"), | |
2649 | cpp_dec_float("8.307674973655724205648794126752153600000000000000000000000000000000000000000000000000000000000000000e34"), | |
2650 | cpp_dec_float("1.661534994731144841129758825350430720000000000000000000000000000000000000000000000000000000000000000e35"), | |
2651 | cpp_dec_float("3.323069989462289682259517650700861440000000000000000000000000000000000000000000000000000000000000000e35"), | |
2652 | cpp_dec_float("6.646139978924579364519035301401722880000000000000000000000000000000000000000000000000000000000000000e35"), | |
2653 | cpp_dec_float("1.329227995784915872903807060280344576000000000000000000000000000000000000000000000000000000000000000e36"), | |
2654 | cpp_dec_float("2.658455991569831745807614120560689152000000000000000000000000000000000000000000000000000000000000000e36"), | |
2655 | cpp_dec_float("5.316911983139663491615228241121378304000000000000000000000000000000000000000000000000000000000000000e36"), | |
2656 | cpp_dec_float("1.063382396627932698323045648224275660800000000000000000000000000000000000000000000000000000000000000e37"), | |
2657 | cpp_dec_float("2.126764793255865396646091296448551321600000000000000000000000000000000000000000000000000000000000000e37"), | |
2658 | cpp_dec_float("4.253529586511730793292182592897102643200000000000000000000000000000000000000000000000000000000000000e37"), | |
2659 | cpp_dec_float("8.507059173023461586584365185794205286400000000000000000000000000000000000000000000000000000000000000e37"), | |
2660 | cpp_dec_float("1.701411834604692317316873037158841057280000000000000000000000000000000000000000000000000000000000000e38") | |
2661 | }}; | |
2662 | ||
2663 | if((p > static_cast<boost::long_long_type>(-128)) && (p < static_cast<boost::long_long_type>(+128))) | |
2664 | { | |
2665 | return p2_data[static_cast<std::size_t>(p + ((p2_data.size() - 1u) / 2u))]; | |
2666 | } | |
2667 | else | |
2668 | { | |
2669 | // Compute and return 2^p. | |
2670 | if(p < static_cast<boost::long_long_type>(0)) | |
2671 | { | |
2672 | return pow2(static_cast<boost::long_long_type>(-p)).calculate_inv(); | |
2673 | } | |
2674 | else | |
2675 | { | |
2676 | cpp_dec_float<Digits10, ExponentType, Allocator> t; | |
2677 | default_ops::detail::pow_imp(t, two(), p, mpl::true_()); | |
2678 | return t; | |
2679 | } | |
2680 | } | |
2681 | } | |
2682 | ||
2683 | ||
2684 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2685 | inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) | |
2686 | { | |
2687 | result += o; | |
2688 | } | |
2689 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2690 | inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) | |
2691 | { | |
2692 | result -= o; | |
2693 | } | |
2694 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2695 | inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) | |
2696 | { | |
2697 | result *= o; | |
2698 | } | |
2699 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2700 | inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o) | |
2701 | { | |
2702 | result /= o; | |
2703 | } | |
2704 | ||
2705 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2706 | inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o) | |
2707 | { | |
2708 | result.add_unsigned_long_long(o); | |
2709 | } | |
2710 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2711 | inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o) | |
2712 | { | |
2713 | result.sub_unsigned_long_long(o); | |
2714 | } | |
2715 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2716 | inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o) | |
2717 | { | |
2718 | result.mul_unsigned_long_long(o); | |
2719 | } | |
2720 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2721 | inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o) | |
2722 | { | |
2723 | result.div_unsigned_long_long(o); | |
2724 | } | |
2725 | ||
2726 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2727 | inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o) | |
2728 | { | |
2729 | if(o < 0) | |
2730 | result.sub_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); | |
2731 | else | |
2732 | result.add_unsigned_long_long(o); | |
2733 | } | |
2734 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2735 | inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o) | |
2736 | { | |
2737 | if(o < 0) | |
2738 | result.add_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); | |
2739 | else | |
2740 | result.sub_unsigned_long_long(o); | |
2741 | } | |
2742 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2743 | inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o) | |
2744 | { | |
2745 | if(o < 0) | |
2746 | { | |
2747 | result.mul_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); | |
2748 | result.negate(); | |
2749 | } | |
2750 | else | |
2751 | result.mul_unsigned_long_long(o); | |
2752 | } | |
2753 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2754 | inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o) | |
2755 | { | |
2756 | if(o < 0) | |
2757 | { | |
2758 | result.div_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o)); | |
2759 | result.negate(); | |
2760 | } | |
2761 | else | |
2762 | result.div_unsigned_long_long(o); | |
2763 | } | |
2764 | ||
2765 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2766 | inline void eval_convert_to(boost::ulong_long_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) | |
2767 | { | |
2768 | *result = val.extract_unsigned_long_long(); | |
2769 | } | |
2770 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2771 | inline void eval_convert_to(boost::long_long_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val) | |
2772 | { | |
2773 | *result = val.extract_signed_long_long(); | |
2774 | } | |
2775 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2776 | inline void eval_convert_to(long double* result, cpp_dec_float<Digits10, ExponentType, Allocator>& val) | |
2777 | { | |
2778 | *result = val.extract_long_double(); | |
2779 | } | |
2780 | ||
2781 | // | |
2782 | // Non member function support: | |
2783 | // | |
2784 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2785 | inline int eval_fpclassify(const cpp_dec_float<Digits10, ExponentType, Allocator>& x) | |
2786 | { | |
2787 | if((x.isinf)()) | |
2788 | return FP_INFINITE; | |
2789 | if((x.isnan)()) | |
2790 | return FP_NAN; | |
2791 | if(x.iszero()) | |
2792 | return FP_ZERO; | |
2793 | return FP_NORMAL; | |
2794 | } | |
2795 | ||
2796 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2797 | inline void eval_abs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) | |
2798 | { | |
2799 | result = x; | |
2800 | if(x.isneg()) | |
2801 | result.negate(); | |
2802 | } | |
2803 | ||
2804 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2805 | inline void eval_fabs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) | |
2806 | { | |
2807 | result = x; | |
2808 | if(x.isneg()) | |
2809 | result.negate(); | |
2810 | } | |
2811 | ||
2812 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2813 | inline void eval_sqrt(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) | |
2814 | { | |
2815 | result = x; | |
2816 | result.calculate_sqrt(); | |
2817 | } | |
2818 | ||
2819 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2820 | inline void eval_floor(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) | |
2821 | { | |
2822 | result = x; | |
2823 | if(!(x.isfinite)() || x.isint()) | |
2824 | { | |
2825 | return; | |
2826 | } | |
2827 | ||
2828 | if(x.isneg()) | |
2829 | result -= cpp_dec_float<Digits10, ExponentType, Allocator>::one(); | |
2830 | result = result.extract_integer_part(); | |
2831 | } | |
2832 | ||
2833 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2834 | inline void eval_ceil(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) | |
2835 | { | |
2836 | result = x; | |
2837 | if(!(x.isfinite)() || x.isint()) | |
2838 | { | |
2839 | return; | |
2840 | } | |
2841 | ||
2842 | if(!x.isneg()) | |
2843 | result += cpp_dec_float<Digits10, ExponentType, Allocator>::one(); | |
2844 | result = result.extract_integer_part(); | |
2845 | } | |
2846 | ||
2847 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2848 | inline void eval_trunc(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x) | |
2849 | { | |
2850 | if(!(x.isfinite)()) | |
2851 | { | |
2852 | result = boost::math::policies::raise_rounding_error("boost::multiprecision::trunc<%1%>(%1%)", 0, number<cpp_dec_float<Digits10, ExponentType, Allocator> >(x), number<cpp_dec_float<Digits10, ExponentType, Allocator> >(x), boost::math::policies::policy<>()).backend(); | |
2853 | return; | |
2854 | } | |
2855 | else if(x.isint()) | |
2856 | { | |
2857 | result = x; | |
2858 | return; | |
2859 | } | |
2860 | result = x.extract_integer_part(); | |
2861 | } | |
2862 | ||
2863 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2864 | inline ExponentType eval_ilogb(const cpp_dec_float<Digits10, ExponentType, Allocator>& val) | |
2865 | { | |
2866 | // Set result, to the exponent of val: | |
2867 | return val.order(); | |
2868 | } | |
2869 | template <unsigned Digits10, class ExponentType, class Allocator, class ArgType> | |
2870 | inline void eval_scalbn(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val, ArgType e_) | |
2871 | { | |
2872 | using default_ops::eval_multiply; | |
2873 | const ExponentType e = e_; | |
2874 | cpp_dec_float<Digits10, ExponentType, Allocator> t(1.0, e); | |
2875 | eval_multiply(result, val, t); | |
2876 | } | |
2877 | ||
2878 | template <unsigned Digits10, class ExponentType, class Allocator, class ArgType> | |
2879 | inline void eval_ldexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ArgType e) | |
2880 | { | |
2881 | const boost::long_long_type the_exp = static_cast<boost::long_long_type>(e); | |
2882 | ||
2883 | if((the_exp > (std::numeric_limits<ExponentType>::max)()) || (the_exp < (std::numeric_limits<ExponentType>::min)())) | |
2884 | BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Exponent value is out of range."))); | |
2885 | ||
2886 | result = x; | |
2887 | ||
2888 | if ((the_exp > static_cast<boost::long_long_type>(-std::numeric_limits<boost::long_long_type>::digits)) && (the_exp < static_cast<boost::long_long_type>(0))) | |
2889 | result.div_unsigned_long_long(1ULL << static_cast<boost::long_long_type>(-the_exp)); | |
2890 | else if((the_exp < static_cast<boost::long_long_type>( std::numeric_limits<boost::long_long_type>::digits)) && (the_exp > static_cast<boost::long_long_type>(0))) | |
2891 | result.mul_unsigned_long_long(1ULL << the_exp); | |
2892 | else if(the_exp != static_cast<boost::long_long_type>(0)) | |
2893 | result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(e); | |
2894 | } | |
2895 | ||
2896 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2897 | inline void eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ExponentType* e) | |
2898 | { | |
2899 | result = x; | |
2900 | if(result.isneg()) | |
2901 | result.negate(); | |
2902 | ||
2903 | if(result.iszero()) | |
2904 | { | |
2905 | *e = 0; | |
2906 | return; | |
2907 | } | |
2908 | ||
2909 | ExponentType t = result.order(); | |
2910 | BOOST_MP_USING_ABS | |
2911 | if(abs(t) < ((std::numeric_limits<ExponentType>::max)() / 1000)) | |
2912 | { | |
2913 | t *= 1000; | |
2914 | t /= 301; | |
2915 | } | |
2916 | else | |
2917 | { | |
2918 | t /= 301; | |
2919 | t *= 1000; | |
2920 | } | |
2921 | ||
2922 | result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t); | |
2923 | ||
2924 | if(result.iszero() || (result.isinf)() || (result.isnan)()) | |
2925 | { | |
2926 | // pow2 overflowed, slip the calculation up: | |
2927 | result = x; | |
2928 | if(result.isneg()) | |
2929 | result.negate(); | |
2930 | t /= 2; | |
2931 | result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t); | |
2932 | } | |
2933 | BOOST_MP_USING_ABS | |
2934 | if(abs(result.order()) > 5) | |
2935 | { | |
2936 | // If our first estimate doesn't get close enough then try recursion until we do: | |
2937 | ExponentType e2; | |
2938 | cpp_dec_float<Digits10, ExponentType, Allocator> r2; | |
2939 | eval_frexp(r2, result, &e2); | |
2940 | // overflow protection: | |
2941 | if((t > 0) && (e2 > 0) && (t > (std::numeric_limits<ExponentType>::max)() - e2)) | |
2942 | BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2.")); | |
2943 | if((t < 0) && (e2 < 0) && (t < (std::numeric_limits<ExponentType>::min)() - e2)) | |
2944 | BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2.")); | |
2945 | t += e2; | |
2946 | result = r2; | |
2947 | } | |
2948 | ||
2949 | while(result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::one()) >= 0) | |
2950 | { | |
2951 | result /= cpp_dec_float<Digits10, ExponentType, Allocator>::two(); | |
2952 | ++t; | |
2953 | } | |
2954 | while(result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::half()) < 0) | |
2955 | { | |
2956 | result *= cpp_dec_float<Digits10, ExponentType, Allocator>::two(); | |
2957 | --t; | |
2958 | } | |
2959 | *e = t; | |
2960 | if(x.isneg()) | |
2961 | result.negate(); | |
2962 | } | |
2963 | ||
2964 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2965 | inline typename disable_if<is_same<ExponentType, int> >::type eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, int* e) | |
2966 | { | |
2967 | ExponentType t; | |
2968 | eval_frexp(result, x, &t); | |
2969 | if((t > (std::numeric_limits<int>::max)()) || (t < (std::numeric_limits<int>::min)())) | |
2970 | BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is outside the range of an int")); | |
2971 | *e = static_cast<int>(t); | |
2972 | } | |
2973 | ||
2974 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2975 | inline bool eval_is_zero(const cpp_dec_float<Digits10, ExponentType, Allocator>& val) | |
2976 | { | |
2977 | return val.iszero(); | |
2978 | } | |
2979 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2980 | inline int eval_get_sign(const cpp_dec_float<Digits10, ExponentType, Allocator>& val) | |
2981 | { | |
2982 | return val.iszero() ? 0 : val.isneg() ? -1 : 1; | |
2983 | } | |
2984 | ||
2985 | template <unsigned Digits10, class ExponentType, class Allocator> | |
2986 | inline std::size_t hash_value(const cpp_dec_float<Digits10, ExponentType, Allocator>& val) | |
2987 | { | |
2988 | return val.hash(); | |
2989 | } | |
2990 | ||
2991 | } // namespace backends | |
2992 | ||
2993 | using boost::multiprecision::backends::cpp_dec_float; | |
2994 | ||
2995 | ||
2996 | typedef number<cpp_dec_float<50> > cpp_dec_float_50; | |
2997 | typedef number<cpp_dec_float<100> > cpp_dec_float_100; | |
2998 | ||
2999 | #ifdef BOOST_NO_SFINAE_EXPR | |
3000 | ||
3001 | namespace detail{ | |
3002 | ||
3003 | template<unsigned D1, class E1, class A1, unsigned D2, class E2, class A2> | |
3004 | struct is_explicitly_convertible<cpp_dec_float<D1, E1, A1>, cpp_dec_float<D2, E2, A2> > : public mpl::true_ {}; | |
3005 | ||
3006 | } | |
3007 | ||
3008 | #endif | |
3009 | ||
3010 | ||
3011 | }} | |
3012 | ||
3013 | namespace std | |
3014 | { | |
3015 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3016 | class numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> > | |
3017 | { | |
3018 | public: | |
3019 | BOOST_STATIC_CONSTEXPR bool is_specialized = true; | |
3020 | BOOST_STATIC_CONSTEXPR bool is_signed = true; | |
3021 | BOOST_STATIC_CONSTEXPR bool is_integer = false; | |
3022 | BOOST_STATIC_CONSTEXPR bool is_exact = false; | |
3023 | BOOST_STATIC_CONSTEXPR bool is_bounded = true; | |
3024 | BOOST_STATIC_CONSTEXPR bool is_modulo = false; | |
3025 | BOOST_STATIC_CONSTEXPR bool is_iec559 = false; | |
3026 | BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; | |
3027 | BOOST_STATIC_CONSTEXPR int digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; | |
3028 | BOOST_STATIC_CONSTEXPR int max_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_total_digits10; | |
3029 | BOOST_STATIC_CONSTEXPR ExponentType min_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp; // Type differs from int. | |
3030 | BOOST_STATIC_CONSTEXPR ExponentType min_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10; // Type differs from int. | |
3031 | BOOST_STATIC_CONSTEXPR ExponentType max_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp; // Type differs from int. | |
3032 | BOOST_STATIC_CONSTEXPR ExponentType max_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10; // Type differs from int. | |
3033 | BOOST_STATIC_CONSTEXPR int radix = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix; | |
3034 | BOOST_STATIC_CONSTEXPR std::float_round_style round_style = std::round_indeterminate; | |
3035 | BOOST_STATIC_CONSTEXPR bool has_infinity = true; | |
3036 | BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true; | |
3037 | BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false; | |
3038 | BOOST_STATIC_CONSTEXPR std::float_denorm_style has_denorm = std::denorm_absent; | |
3039 | BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false; | |
3040 | BOOST_STATIC_CONSTEXPR bool traps = false; | |
3041 | BOOST_STATIC_CONSTEXPR bool tinyness_before = false; | |
3042 | ||
3043 | BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> (min) () { return (boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::min)(); } | |
3044 | BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> (max) () { return (boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::max)(); } | |
3045 | BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> lowest () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); } | |
3046 | BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> epsilon () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::eps(); } | |
3047 | BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> round_error () { return 0.5L; } | |
3048 | BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> infinity () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::inf(); } | |
3049 | BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> quiet_NaN () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::nan(); } | |
3050 | BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> signaling_NaN() { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); } | |
3051 | BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> denorm_min () { return boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::zero(); } | |
3052 | }; | |
3053 | ||
3054 | #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION | |
3055 | ||
3056 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3057 | BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits; | |
3058 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3059 | BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits10; | |
3060 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3061 | BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_digits10; | |
3062 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3063 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_signed; | |
3064 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3065 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_integer; | |
3066 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3067 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_exact; | |
3068 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3069 | BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::radix; | |
3070 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3071 | BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent; | |
3072 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3073 | BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent10; | |
3074 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3075 | BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent; | |
3076 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3077 | BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent10; | |
3078 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3079 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_infinity; | |
3080 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3081 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_quiet_NaN; | |
3082 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3083 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_signaling_NaN; | |
3084 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3085 | BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm; | |
3086 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3087 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm_loss; | |
3088 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3089 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_iec559; | |
3090 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3091 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_bounded; | |
3092 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3093 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_modulo; | |
3094 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3095 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::traps; | |
3096 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3097 | BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::tinyness_before; | |
3098 | template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3099 | BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::round_style; | |
3100 | ||
3101 | #endif | |
3102 | } | |
3103 | ||
3104 | namespace boost{ namespace math{ | |
3105 | ||
3106 | namespace policies{ | |
3107 | ||
3108 | template <unsigned Digits10, class ExponentType, class Allocator, class Policy, boost::multiprecision::expression_template_option ExpressionTemplates> | |
3109 | struct precision< boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates>, Policy> | |
3110 | { | |
3111 | // Define a local copy of cpp_dec_float_digits10 because it might differ | |
3112 | // from the template parameter Digits10 for small or large digit counts. | |
3113 | static const boost::int32_t cpp_dec_float_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10; | |
3114 | ||
3115 | typedef typename Policy::precision_type precision_type; | |
3116 | typedef digits2<((cpp_dec_float_digits10 + 1LL) * 1000LL) / 301LL> digits_2; | |
3117 | typedef typename mpl::if_c< | |
3118 | ((digits_2::value <= precision_type::value) | |
3119 | || (Policy::precision_type::value <= 0)), | |
3120 | // Default case, full precision for RealType: | |
3121 | digits_2, | |
3122 | // User customized precision: | |
3123 | precision_type | |
3124 | >::type type; | |
3125 | }; | |
3126 | ||
3127 | } // namespace policies | |
3128 | ||
3129 | }} // namespaces boost::math | |
3130 | ||
3131 | #ifdef BOOST_MSVC | |
3132 | #pragma warning(pop) | |
3133 | #endif | |
3134 | ||
3135 | #endif |