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 #include <boost/multiprecision/detail/itos.hpp>
33
34 //
35 // Headers required for Boost.Math integration:
36 //
37 #include <boost/math/policies/policy.hpp>
38 //
39 // Some includes we need from Boost.Math, since we rely on that library to provide these functions:
40 //
41 #include <boost/math/special_functions/asinh.hpp>
42 #include <boost/math/special_functions/acosh.hpp>
43 #include <boost/math/special_functions/atanh.hpp>
44 #include <boost/math/special_functions/cbrt.hpp>
45 #include <boost/math/special_functions/expm1.hpp>
46 #include <boost/math/special_functions/gamma.hpp>
47
48 #ifdef BOOST_MSVC
49 #pragma warning(push)
50 #pragma warning(disable : 6326) // comparison of two constants
51 #endif
52
53 namespace boost {
54 namespace multiprecision {
55 namespace backends {
56
57 template <unsigned Digits10, class ExponentType = boost::int32_t, class Allocator = void>
58 class cpp_dec_float;
59
60 } // namespace backends
61
62 template <unsigned Digits10, class ExponentType, class Allocator>
63 struct number_category<backends::cpp_dec_float<Digits10, ExponentType, Allocator> > : public mpl::int_<number_kind_floating_point>
64 {};
65
66 namespace backends {
67
68 template <unsigned Digits10, class ExponentType, class Allocator>
69 class cpp_dec_float
70 {
71 private:
72 static const boost::int32_t cpp_dec_float_digits10_setting = Digits10;
73
74 // We need at least 16-bits in the exponent type to do anything sensible:
75 BOOST_STATIC_ASSERT_MSG(boost::is_signed<ExponentType>::value, "ExponentType must be a signed built in integer type.");
76 BOOST_STATIC_ASSERT_MSG(sizeof(ExponentType) > 1, "ExponentType is too small.");
77
78 public:
79 typedef mpl::list<boost::long_long_type> signed_types;
80 typedef mpl::list<boost::ulong_long_type> unsigned_types;
81 typedef mpl::list<double, long double> float_types;
82 typedef ExponentType exponent_type;
83
84 static const boost::int32_t cpp_dec_float_radix = 10L;
85 static const boost::int32_t cpp_dec_float_digits10_limit_lo = 9L;
86 static const boost::int32_t cpp_dec_float_digits10_limit_hi = boost::integer_traits<boost::int32_t>::const_max - 100;
87 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));
88 static const ExponentType cpp_dec_float_max_exp10 = (static_cast<ExponentType>(1) << (std::numeric_limits<ExponentType>::digits - 5));
89 static const ExponentType cpp_dec_float_min_exp10 = -cpp_dec_float_max_exp10;
90 static const ExponentType cpp_dec_float_max_exp = cpp_dec_float_max_exp10;
91 static const ExponentType cpp_dec_float_min_exp = cpp_dec_float_min_exp10;
92
93 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));
94
95 private:
96 static const boost::int32_t cpp_dec_float_elem_digits10 = 8L;
97 static const boost::int32_t cpp_dec_float_elem_mask = 100000000L;
98
99 BOOST_STATIC_ASSERT(0 == cpp_dec_float_max_exp10 % cpp_dec_float_elem_digits10);
100
101 // There are three guard limbs.
102 // 1) The first limb has 'play' from 1...8 decimal digits.
103 // 2) The last limb also has 'play' from 1...8 decimal digits.
104 // 3) One limb can get lost when justifying after multiply,
105 // as only half of the triangle is multiplied and a carry
106 // from below is missing.
107 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));
108
109 // The number of elements needed (with a minimum of two) plus three added guard limbs.
110 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);
111
112 public:
113 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);
114
115 private:
116 typedef enum enum_fpclass_type
117 {
118 cpp_dec_float_finite,
119 cpp_dec_float_inf,
120 cpp_dec_float_NaN
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> >::type array_type;
127 #else
128 typedef typename mpl::if_<is_void<Allocator>,
129 boost::array<boost::uint32_t, cpp_dec_float_elem_number>,
130 detail::dynamic_array<boost::uint32_t, cpp_dec_float_elem_number, Allocator> >::type array_type;
131 #endif
132
133 array_type data;
134 ExponentType exp;
135 bool neg;
136 fpclass_type fpclass;
137 boost::int32_t prec_elem;
138
139 //
140 // Special values constructor:
141 //
cpp_dec_float(fpclass_type c)142 cpp_dec_float(fpclass_type c) : data(),
143 exp(static_cast<ExponentType>(0)),
144 neg(false),
145 fpclass(c),
146 prec_elem(cpp_dec_float_elem_number) {}
147
148 //
149 // Static data initializer:
150 //
151 struct initializer
152 {
initializerboost::multiprecision::backends::cpp_dec_float::initializer153 initializer()
154 {
155 cpp_dec_float<Digits10, ExponentType, Allocator>::nan();
156 cpp_dec_float<Digits10, ExponentType, Allocator>::inf();
157 (cpp_dec_float<Digits10, ExponentType, Allocator>::min)();
158 (cpp_dec_float<Digits10, ExponentType, Allocator>::max)();
159 cpp_dec_float<Digits10, ExponentType, Allocator>::zero();
160 cpp_dec_float<Digits10, ExponentType, Allocator>::one();
161 cpp_dec_float<Digits10, ExponentType, Allocator>::two();
162 cpp_dec_float<Digits10, ExponentType, Allocator>::half();
163 cpp_dec_float<Digits10, ExponentType, Allocator>::double_min();
164 cpp_dec_float<Digits10, ExponentType, Allocator>::double_max();
165 //cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_max();
166 //cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_min();
167 cpp_dec_float<Digits10, ExponentType, Allocator>::long_long_max();
168 cpp_dec_float<Digits10, ExponentType, Allocator>::long_long_min();
169 cpp_dec_float<Digits10, ExponentType, Allocator>::ulong_long_max();
170 cpp_dec_float<Digits10, ExponentType, Allocator>::eps();
171 cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(0);
172 }
do_nothingboost::multiprecision::backends::cpp_dec_float::initializer173 void do_nothing() {}
174 };
175
176 static initializer init;
177
178 struct long_double_initializer
179 {
long_double_initializerboost::multiprecision::backends::cpp_dec_float::long_double_initializer180 long_double_initializer()
181 {
182 cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_max();
183 cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_min();
184 }
do_nothingboost::multiprecision::backends::cpp_dec_float::long_double_initializer185 void do_nothing() {}
186 };
187
188 static long_double_initializer linit;
189
190 public:
191 // Constructors
BOOST_MP_NOEXCEPT_IF(noexcept (array_type ()))192 cpp_dec_float() BOOST_MP_NOEXCEPT_IF(noexcept(array_type())) : data(),
193 exp(static_cast<ExponentType>(0)),
194 neg(false),
195 fpclass(cpp_dec_float_finite),
196 prec_elem(cpp_dec_float_elem_number) {}
197
cpp_dec_float(const char * s)198 cpp_dec_float(const char* s) : data(),
199 exp(static_cast<ExponentType>(0)),
200 neg(false),
201 fpclass(cpp_dec_float_finite),
202 prec_elem(cpp_dec_float_elem_number)
203 {
204 *this = s;
205 }
206
207 template <class I>
cpp_dec_float(I i,typename enable_if<is_unsigned<I>>::type * =0)208 cpp_dec_float(I i, typename enable_if<is_unsigned<I> >::type* = 0) : data(),
209 exp(static_cast<ExponentType>(0)),
210 neg(false),
211 fpclass(cpp_dec_float_finite),
212 prec_elem(cpp_dec_float_elem_number)
213 {
214 from_unsigned_long_long(i);
215 }
216
217 template <class I>
cpp_dec_float(I i,typename enable_if<is_signed<I>>::type * =0)218 cpp_dec_float(I i, typename enable_if<is_signed<I> >::type* = 0) : data(),
219 exp(static_cast<ExponentType>(0)),
220 neg(false),
221 fpclass(cpp_dec_float_finite),
222 prec_elem(cpp_dec_float_elem_number)
223 {
224 if (i < 0)
225 {
226 from_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(i));
227 negate();
228 }
229 else
230 from_unsigned_long_long(i);
231 }
232
BOOST_MP_NOEXCEPT_IF(noexcept (array_type (std::declval<const array_type &> ())))233 cpp_dec_float(const cpp_dec_float& f) BOOST_MP_NOEXCEPT_IF(noexcept(array_type(std::declval<const array_type&>()))) : data(f.data),
234 exp(f.exp),
235 neg(f.neg),
236 fpclass(f.fpclass),
237 prec_elem(f.prec_elem) {}
238
239 template <unsigned D, class ET, class A>
cpp_dec_float(const cpp_dec_float<D,ET,A> & f,typename enable_if_c<D<=Digits10>::type * =0)240 cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename enable_if_c<D <= Digits10>::type* = 0) : data(),
241 exp(f.exp),
242 neg(f.neg),
243 fpclass(static_cast<fpclass_type>(static_cast<int>(f.fpclass))),
244 prec_elem(cpp_dec_float_elem_number)
245 {
246 std::copy(f.data.begin(), f.data.begin() + f.prec_elem, data.begin());
247 }
248 template <unsigned D, class ET, class A>
cpp_dec_float(const cpp_dec_float<D,ET,A> & f,typename disable_if_c<D<=Digits10>::type * =0)249 explicit cpp_dec_float(const cpp_dec_float<D, ET, A>& f, typename disable_if_c<D <= Digits10>::type* = 0) : data(),
250 exp(f.exp),
251 neg(f.neg),
252 fpclass(static_cast<fpclass_type>(static_cast<int>(f.fpclass))),
253 prec_elem(cpp_dec_float_elem_number)
254 {
255 // TODO: this doesn't round!
256 std::copy(f.data.begin(), f.data.begin() + prec_elem, data.begin());
257 }
258
259 template <class F>
cpp_dec_float(const F val,typename enable_if_c<is_floating_point<F>::value &&!boost::is_same<F,__float128>::value>::type * =0)260 cpp_dec_float(const F val, typename enable_if_c<is_floating_point<F>::value
261 #ifdef BOOST_HAS_FLOAT128
262 && !boost::is_same<F, __float128>::value
263 #endif
264 >::type* = 0) : data(),
265 exp(static_cast<ExponentType>(0)),
266 neg(false),
267 fpclass(cpp_dec_float_finite),
268 prec_elem(cpp_dec_float_elem_number)
269 {
270 *this = val;
271 }
272
273 cpp_dec_float(const double mantissa, const ExponentType exponent);
274
hash() const275 std::size_t hash() const
276 {
277 std::size_t result = 0;
278 for (int i = 0; i < prec_elem; ++i)
279 boost::hash_combine(result, data[i]);
280 boost::hash_combine(result, exp);
281 boost::hash_combine(result, neg);
282 boost::hash_combine(result, fpclass);
283 return result;
284 }
285
286 // Specific special values.
nan()287 static const cpp_dec_float& nan()
288 {
289 static const cpp_dec_float val(cpp_dec_float_NaN);
290 init.do_nothing();
291 return val;
292 }
293
inf()294 static const cpp_dec_float& inf()
295 {
296 static const cpp_dec_float val(cpp_dec_float_inf);
297 init.do_nothing();
298 return val;
299 }
300
301 static const cpp_dec_float&(max)()
302 {
303 init.do_nothing();
304 static cpp_dec_float val_max = std::string("1.0e" + boost::multiprecision::detail::itos(cpp_dec_float_max_exp10)).c_str();
305 return val_max;
306 }
307
308 static const cpp_dec_float&(min)()
309 {
310 init.do_nothing();
311 static cpp_dec_float val_min = std::string("1.0e" + boost::multiprecision::detail::itos(cpp_dec_float_min_exp10)).c_str();
312 return val_min;
313 }
314
zero()315 static const cpp_dec_float& zero()
316 {
317 init.do_nothing();
318 static cpp_dec_float val(static_cast<boost::ulong_long_type>(0u));
319 return val;
320 }
321
one()322 static const cpp_dec_float& one()
323 {
324 init.do_nothing();
325 static cpp_dec_float val(static_cast<boost::ulong_long_type>(1u));
326 return val;
327 }
328
two()329 static const cpp_dec_float& two()
330 {
331 init.do_nothing();
332 static cpp_dec_float val(static_cast<boost::ulong_long_type>(2u));
333 return val;
334 }
335
half()336 static const cpp_dec_float& half()
337 {
338 init.do_nothing();
339 static cpp_dec_float val(0.5L);
340 return val;
341 }
342
double_min()343 static const cpp_dec_float& double_min()
344 {
345 init.do_nothing();
346 static cpp_dec_float val((std::numeric_limits<double>::min)());
347 return val;
348 }
349
double_max()350 static const cpp_dec_float& double_max()
351 {
352 init.do_nothing();
353 static cpp_dec_float val((std::numeric_limits<double>::max)());
354 return val;
355 }
356
long_double_min()357 static const cpp_dec_float& long_double_min()
358 {
359 linit.do_nothing();
360 #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
361 static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::min)()));
362 #else
363 static cpp_dec_float val((std::numeric_limits<long double>::min)());
364 #endif
365 return val;
366 }
367
long_double_max()368 static const cpp_dec_float& long_double_max()
369 {
370 linit.do_nothing();
371 #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
372 static cpp_dec_float val(static_cast<long double>((std::numeric_limits<double>::max)()));
373 #else
374 static cpp_dec_float val((std::numeric_limits<long double>::max)());
375 #endif
376 return val;
377 }
378
long_long_max()379 static const cpp_dec_float& long_long_max()
380 {
381 init.do_nothing();
382 static cpp_dec_float val((std::numeric_limits<boost::long_long_type>::max)());
383 return val;
384 }
385
long_long_min()386 static const cpp_dec_float& long_long_min()
387 {
388 init.do_nothing();
389 static cpp_dec_float val((std::numeric_limits<boost::long_long_type>::min)());
390 return val;
391 }
392
ulong_long_max()393 static const cpp_dec_float& ulong_long_max()
394 {
395 init.do_nothing();
396 static cpp_dec_float val((std::numeric_limits<boost::ulong_long_type>::max)());
397 return val;
398 }
399
eps()400 static const cpp_dec_float& eps()
401 {
402 init.do_nothing();
403 static cpp_dec_float val(1.0, 1 - static_cast<int>(cpp_dec_float_digits10));
404 return val;
405 }
406
407 // Basic operations.
operator =(const cpp_dec_float & v)408 cpp_dec_float& operator=(const cpp_dec_float& v) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<array_type&>() = std::declval<const array_type&>()))
409 {
410 data = v.data;
411 exp = v.exp;
412 neg = v.neg;
413 fpclass = v.fpclass;
414 prec_elem = v.prec_elem;
415 return *this;
416 }
417
418 template <unsigned D>
operator =(const cpp_dec_float<D> & f)419 cpp_dec_float& operator=(const cpp_dec_float<D>& f)
420 {
421 exp = f.exp;
422 neg = f.neg;
423 fpclass = static_cast<enum_fpclass_type>(static_cast<int>(f.fpclass));
424 unsigned elems = (std::min)(f.prec_elem, cpp_dec_float_elem_number);
425 std::copy(f.data.begin(), f.data.begin() + elems, data.begin());
426 std::fill(data.begin() + elems, data.end(), 0);
427 prec_elem = cpp_dec_float_elem_number;
428 return *this;
429 }
430
operator =(boost::long_long_type v)431 cpp_dec_float& operator=(boost::long_long_type v)
432 {
433 if (v < 0)
434 {
435 from_unsigned_long_long(1u - boost::ulong_long_type(v + 1)); // Avoid undefined behaviour in negation of minimum value for long long
436 negate();
437 }
438 else
439 from_unsigned_long_long(v);
440 return *this;
441 }
442
operator =(boost::ulong_long_type v)443 cpp_dec_float& operator=(boost::ulong_long_type v)
444 {
445 from_unsigned_long_long(v);
446 return *this;
447 }
448
449 template <class Float>
450 typename boost::enable_if_c<boost::is_floating_point<Float>::value, cpp_dec_float&>::type operator=(Float v);
451
operator =(const char * v)452 cpp_dec_float& operator=(const char* v)
453 {
454 rd_string(v);
455 return *this;
456 }
457
458 cpp_dec_float& operator+=(const cpp_dec_float& v);
459 cpp_dec_float& operator-=(const cpp_dec_float& v);
460 cpp_dec_float& operator*=(const cpp_dec_float& v);
461 cpp_dec_float& operator/=(const cpp_dec_float& v);
462
add_unsigned_long_long(const boost::ulong_long_type n)463 cpp_dec_float& add_unsigned_long_long(const boost::ulong_long_type n)
464 {
465 cpp_dec_float t;
466 t.from_unsigned_long_long(n);
467 return *this += t;
468 }
469
sub_unsigned_long_long(const boost::ulong_long_type n)470 cpp_dec_float& sub_unsigned_long_long(const boost::ulong_long_type n)
471 {
472 cpp_dec_float t;
473 t.from_unsigned_long_long(n);
474 return *this -= t;
475 }
476
477 cpp_dec_float& mul_unsigned_long_long(const boost::ulong_long_type n);
478 cpp_dec_float& div_unsigned_long_long(const boost::ulong_long_type n);
479
480 // Elementary primitives.
481 cpp_dec_float& calculate_inv();
482 cpp_dec_float& calculate_sqrt();
483
negate()484 void negate()
485 {
486 if (!iszero())
487 neg = !neg;
488 }
489
490 // Comparison functions
BOOST_PREVENT_MACRO_SUBSTITUTION() const491 bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_NaN); }
BOOST_PREVENT_MACRO_SUBSTITUTION() const492 bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_inf); }
BOOST_PREVENT_MACRO_SUBSTITUTION() const493 bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION() const { return (fpclass == cpp_dec_float_finite); }
494
iszero() const495 bool iszero() const
496 {
497 return ((fpclass == cpp_dec_float_finite) && (data[0u] == 0u));
498 }
499
500 bool isone() const;
501 bool isint() const;
isneg() const502 bool isneg() const { return neg; }
503
504 // Operators pre-increment and pre-decrement
operator ++()505 cpp_dec_float& operator++()
506 {
507 return *this += one();
508 }
509
operator --()510 cpp_dec_float& operator--()
511 {
512 return *this -= one();
513 }
514
515 std::string str(boost::intmax_t digits, std::ios_base::fmtflags f) const;
516
517 int compare(const cpp_dec_float& v) const;
518
519 template <class V>
compare(const V & v) const520 int compare(const V& v) const
521 {
522 cpp_dec_float<Digits10, ExponentType, Allocator> t;
523 t = v;
524 return compare(t);
525 }
526
swap(cpp_dec_float & v)527 void swap(cpp_dec_float& v)
528 {
529 data.swap(v.data);
530 std::swap(exp, v.exp);
531 std::swap(neg, v.neg);
532 std::swap(fpclass, v.fpclass);
533 std::swap(prec_elem, v.prec_elem);
534 }
535
536 double extract_double() const;
537 long double extract_long_double() const;
538 boost::long_long_type extract_signed_long_long() const;
539 boost::ulong_long_type extract_unsigned_long_long() const;
540 void extract_parts(double& mantissa, ExponentType& exponent) const;
541 cpp_dec_float extract_integer_part() const;
542
precision(const boost::int32_t prec_digits)543 void precision(const boost::int32_t prec_digits)
544 {
545 if (prec_digits >= cpp_dec_float_total_digits10)
546 {
547 prec_elem = cpp_dec_float_elem_number;
548 }
549 else
550 {
551 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) + static_cast<boost::int32_t>(((prec_digits % cpp_dec_float_elem_digits10) != 0) ? 1 : 0));
552
553 prec_elem = (std::min)(cpp_dec_float_elem_number, (std::max)(elems, static_cast<boost::int32_t>(2)));
554 }
555 }
556 static cpp_dec_float pow2(boost::long_long_type i);
order() const557 ExponentType order() const
558 {
559 const bool bo_order_is_zero = ((!(isfinite)()) || (data[0] == static_cast<boost::uint32_t>(0u)));
560 //
561 // Binary search to find the order of the leading term:
562 //
563 ExponentType prefix = 0;
564
565 if (data[0] >= 100000UL)
566 {
567 if (data[0] >= 10000000UL)
568 {
569 if (data[0] >= 100000000UL)
570 {
571 if (data[0] >= 1000000000UL)
572 prefix = 9;
573 else
574 prefix = 8;
575 }
576 else
577 prefix = 7;
578 }
579 else
580 {
581 if (data[0] >= 1000000UL)
582 prefix = 6;
583 else
584 prefix = 5;
585 }
586 }
587 else
588 {
589 if (data[0] >= 1000UL)
590 {
591 if (data[0] >= 10000UL)
592 prefix = 4;
593 else
594 prefix = 3;
595 }
596 else
597 {
598 if (data[0] >= 100)
599 prefix = 2;
600 else if (data[0] >= 10)
601 prefix = 1;
602 }
603 }
604
605 return (bo_order_is_zero ? static_cast<ExponentType>(0) : static_cast<ExponentType>(exp + prefix));
606 }
607
608 template <class Archive>
serialize(Archive & ar,const unsigned int)609 void serialize(Archive& ar, const unsigned int /*version*/)
610 {
611 for (unsigned i = 0; i < data.size(); ++i)
612 ar& boost::make_nvp("digit", data[i]);
613 ar& boost::make_nvp("exponent", exp);
614 ar& boost::make_nvp("sign", neg);
615 ar& boost::make_nvp("class-type", fpclass);
616 ar& boost::make_nvp("precision", prec_elem);
617 }
618
619 private:
data_elem_is_non_zero_predicate(const boost::uint32_t & d)620 static bool data_elem_is_non_zero_predicate(const boost::uint32_t& d) { return (d != static_cast<boost::uint32_t>(0u)); }
data_elem_is_non_nine_predicate(const boost::uint32_t & d)621 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)); }
char_is_nonzero_predicate(const char & c)622 static bool char_is_nonzero_predicate(const char& c) { return (c != static_cast<char>('0')); }
623
624 void from_unsigned_long_long(const boost::ulong_long_type u);
625
626 int cmp_data(const array_type& vd) const;
627
628 static boost::uint32_t mul_loop_uv(boost::uint32_t* const u, const boost::uint32_t* const v, const boost::int32_t p);
629 static boost::uint32_t mul_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p);
630 static boost::uint32_t div_loop_n(boost::uint32_t* const u, boost::uint32_t n, const boost::int32_t p);
631
632 bool rd_string(const char* const s);
633
634 template <unsigned D, class ET, class A>
635 friend class cpp_dec_float;
636 };
637
638 template <unsigned Digits10, class ExponentType, class Allocator>
639 typename cpp_dec_float<Digits10, ExponentType, Allocator>::initializer cpp_dec_float<Digits10, ExponentType, Allocator>::init;
640 template <unsigned Digits10, class ExponentType, class Allocator>
641 typename cpp_dec_float<Digits10, ExponentType, Allocator>::long_double_initializer cpp_dec_float<Digits10, ExponentType, Allocator>::linit;
642
643 template <unsigned Digits10, class ExponentType, class Allocator>
644 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix;
645 template <unsigned Digits10, class ExponentType, class Allocator>
646 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_setting;
647 template <unsigned Digits10, class ExponentType, class Allocator>
648 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_lo;
649 template <unsigned Digits10, class ExponentType, class Allocator>
650 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10_limit_hi;
651 template <unsigned Digits10, class ExponentType, class Allocator>
652 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
653 template <unsigned Digits10, class ExponentType, class Allocator>
654 const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp;
655 template <unsigned Digits10, class ExponentType, class Allocator>
656 const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp;
657 template <unsigned Digits10, class ExponentType, class Allocator>
658 const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10;
659 template <unsigned Digits10, class ExponentType, class Allocator>
660 const ExponentType cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10;
661 template <unsigned Digits10, class ExponentType, class Allocator>
662 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_digits10;
663 template <unsigned Digits10, class ExponentType, class Allocator>
664 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number_request;
665 template <unsigned Digits10, class ExponentType, class Allocator>
666 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_number;
667 template <unsigned Digits10, class ExponentType, class Allocator>
668 const boost::int32_t cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_elem_mask;
669
670 template <unsigned Digits10, class ExponentType, class Allocator>
operator +=(const cpp_dec_float<Digits10,ExponentType,Allocator> & v)671 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator+=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
672 {
673 if ((isnan)())
674 {
675 return *this;
676 }
677
678 if ((isinf)())
679 {
680 if ((v.isinf)() && (isneg() != v.isneg()))
681 {
682 *this = nan();
683 }
684 return *this;
685 }
686
687 if (iszero())
688 {
689 return operator=(v);
690 }
691
692 if ((v.isnan)() || (v.isinf)())
693 {
694 *this = v;
695 return *this;
696 }
697
698 // Get the offset for the add/sub operation.
699 static const ExponentType max_delta_exp = static_cast<ExponentType>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10);
700
701 const ExponentType ofs_exp = static_cast<ExponentType>(exp - v.exp);
702
703 // Check if the operation is out of range, requiring special handling.
704 if (v.iszero() || (ofs_exp > max_delta_exp))
705 {
706 // Result is *this unchanged since v is negligible compared to *this.
707 return *this;
708 }
709 else if (ofs_exp < -max_delta_exp)
710 {
711 // Result is *this = v since *this is negligible compared to v.
712 return operator=(v);
713 }
714
715 // Do the add/sub operation.
716
717 typename array_type::iterator p_u = data.begin();
718 typename array_type::const_iterator p_v = v.data.begin();
719 bool b_copy = false;
720 const boost::int32_t ofs = static_cast<boost::int32_t>(static_cast<boost::int32_t>(ofs_exp) / cpp_dec_float_elem_digits10);
721 array_type n_data;
722
723 if (neg == v.neg)
724 {
725 // Add v to *this, where the data array of either *this or v
726 // might have to be treated with a positive, negative or zero offset.
727 // The result is stored in *this. The data are added one element
728 // at a time, each element with carry.
729 if (ofs >= static_cast<boost::int32_t>(0))
730 {
731 std::copy(v.data.begin(), v.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_v = n_data.begin();
734 }
735 else
736 {
737 std::copy(data.begin(), data.end() - static_cast<size_t>(-ofs), n_data.begin() + static_cast<size_t>(-ofs));
738 std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(-ofs), static_cast<boost::uint32_t>(0u));
739 p_u = n_data.begin();
740 b_copy = true;
741 }
742
743 // Addition algorithm
744 boost::uint32_t carry = static_cast<boost::uint32_t>(0u);
745
746 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--)
747 {
748 boost::uint32_t t = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(p_u[j] + p_v[j]) + carry);
749 carry = t / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask);
750 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)));
751 }
752
753 if (b_copy)
754 {
755 data = n_data;
756 exp = v.exp;
757 }
758
759 // There needs to be a carry into the element -1 of the array data
760 if (carry != static_cast<boost::uint32_t>(0u))
761 {
762 std::copy_backward(data.begin(), data.end() - static_cast<std::size_t>(1u), data.end());
763 data[0] = carry;
764 exp += static_cast<ExponentType>(cpp_dec_float_elem_digits10);
765 }
766 }
767 else
768 {
769 // Subtract v from *this, where the data array of either *this or v
770 // might have to be treated with a positive, negative or zero offset.
771 if ((ofs > static_cast<boost::int32_t>(0)) || ((ofs == static_cast<boost::int32_t>(0)) && (cmp_data(v.data) > static_cast<boost::int32_t>(0))))
772 {
773 // In this case, |u| > |v| and ofs is positive.
774 // Copy the data of v, shifted down to a lower value
775 // into the data array m_n. Set the operand pointer p_v
776 // to point to the copied, shifted data m_n.
777 std::copy(v.data.begin(), v.data.end() - static_cast<size_t>(ofs), n_data.begin() + static_cast<size_t>(ofs));
778 std::fill(n_data.begin(), n_data.begin() + static_cast<size_t>(ofs), static_cast<boost::uint32_t>(0u));
779 p_v = n_data.begin();
780 }
781 else
782 {
783 if (ofs != static_cast<boost::int32_t>(0))
784 {
785 // In this case, |u| < |v| and ofs is negative.
786 // Shift the data of u down to a lower value.
787 std::copy_backward(data.begin(), data.end() - static_cast<size_t>(-ofs), data.end());
788 std::fill(data.begin(), data.begin() + static_cast<size_t>(-ofs), static_cast<boost::uint32_t>(0u));
789 }
790
791 // Copy the data of v into the data array n_data.
792 // Set the u-pointer p_u to point to m_n and the
793 // operand pointer p_v to point to the shifted
794 // data m_data.
795 n_data = v.data;
796 p_u = n_data.begin();
797 p_v = data.begin();
798 b_copy = true;
799 }
800
801 boost::int32_t j;
802
803 // Subtraction algorithm
804 boost::int32_t borrow = static_cast<boost::int32_t>(0);
805
806 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--)
807 {
808 boost::int32_t t = static_cast<boost::int32_t>(static_cast<boost::int32_t>(static_cast<boost::int32_t>(p_u[j]) - static_cast<boost::int32_t>(p_v[j])) - borrow);
809
810 // Underflow? Borrow?
811 if (t < static_cast<boost::int32_t>(0))
812 {
813 // Yes, underflow and borrow
814 t += static_cast<boost::int32_t>(cpp_dec_float_elem_mask);
815 borrow = static_cast<boost::int32_t>(1);
816 }
817 else
818 {
819 borrow = static_cast<boost::int32_t>(0);
820 }
821
822 p_u[j] = static_cast<boost::uint32_t>(static_cast<boost::uint32_t>(t) % static_cast<boost::uint32_t>(cpp_dec_float_elem_mask));
823 }
824
825 if (b_copy)
826 {
827 data = n_data;
828 exp = v.exp;
829 neg = v.neg;
830 }
831
832 // Is it necessary to justify the data?
833 const typename array_type::const_iterator first_nonzero_elem = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate);
834
835 if (first_nonzero_elem != data.begin())
836 {
837 if (first_nonzero_elem == data.end())
838 {
839 // This result of the subtraction is exactly zero.
840 // Reset the sign and the exponent.
841 neg = false;
842 exp = static_cast<ExponentType>(0);
843 }
844 else
845 {
846 // Justify the data
847 const std::size_t sj = static_cast<std::size_t>(std::distance<typename array_type::const_iterator>(data.begin(), first_nonzero_elem));
848
849 std::copy(data.begin() + static_cast<std::size_t>(sj), data.end(), data.begin());
850 std::fill(data.end() - sj, data.end(), static_cast<boost::uint32_t>(0u));
851
852 exp -= static_cast<ExponentType>(sj * static_cast<std::size_t>(cpp_dec_float_elem_digits10));
853 }
854 }
855 }
856
857 // Handle underflow.
858 if (iszero())
859 return (*this = zero());
860
861 // Check for potential overflow.
862 const bool b_result_might_overflow = (exp >= static_cast<ExponentType>(cpp_dec_float_max_exp10));
863
864 // Handle overflow.
865 if (b_result_might_overflow)
866 {
867 const bool b_result_is_neg = neg;
868 neg = false;
869
870 if (compare((cpp_dec_float::max)()) > 0)
871 *this = inf();
872
873 neg = b_result_is_neg;
874 }
875
876 return *this;
877 }
878
879 template <unsigned Digits10, class ExponentType, class Allocator>
operator -=(const cpp_dec_float<Digits10,ExponentType,Allocator> & v)880 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator-=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
881 {
882 // Use *this - v = -(-*this + v).
883 negate();
884 *this += v;
885 negate();
886 return *this;
887 }
888
889 template <unsigned Digits10, class ExponentType, class Allocator>
operator *=(const cpp_dec_float<Digits10,ExponentType,Allocator> & v)890 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator*=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
891 {
892 // Evaluate the sign of the result.
893 const bool b_result_is_neg = (neg != v.neg);
894
895 // Artificially set the sign of the result to be positive.
896 neg = false;
897
898 // Handle special cases like zero, inf and NaN.
899 const bool b_u_is_inf = (isinf)();
900 const bool b_v_is_inf = (v.isinf)();
901 const bool b_u_is_zero = iszero();
902 const bool b_v_is_zero = v.iszero();
903
904 if (((isnan)() || (v.isnan)()) || (b_u_is_inf && b_v_is_zero) || (b_v_is_inf && b_u_is_zero))
905 {
906 *this = nan();
907 return *this;
908 }
909
910 if (b_u_is_inf || b_v_is_inf)
911 {
912 *this = inf();
913 if (b_result_is_neg)
914 negate();
915 return *this;
916 }
917
918 if (b_u_is_zero || b_v_is_zero)
919 {
920 return *this = zero();
921 }
922
923 // Check for potential overflow or underflow.
924 const bool b_result_might_overflow = ((exp + v.exp) >= static_cast<ExponentType>(cpp_dec_float_max_exp10));
925 const bool b_result_might_underflow = ((exp + v.exp) <= static_cast<ExponentType>(cpp_dec_float_min_exp10));
926
927 // Set the exponent of the result.
928 exp += v.exp;
929
930 const boost::int32_t prec_mul = (std::min)(prec_elem, v.prec_elem);
931
932 const boost::uint32_t carry = mul_loop_uv(data.data(), v.data.data(), prec_mul);
933
934 // Handle a potential carry.
935 if (carry != static_cast<boost::uint32_t>(0u))
936 {
937 exp += cpp_dec_float_elem_digits10;
938
939 // Shift the result of the multiplication one element to the right...
940 std::copy_backward(data.begin(),
941 data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)),
942 data.begin() + static_cast<std::size_t>(prec_elem));
943
944 // ... And insert the carry.
945 data.front() = carry;
946 }
947
948 // Handle overflow.
949 if (b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0))
950 {
951 *this = inf();
952 }
953
954 // Handle underflow.
955 if (b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0))
956 {
957 *this = zero();
958
959 return *this;
960 }
961
962 // Set the sign of the result.
963 neg = b_result_is_neg;
964
965 return *this;
966 }
967
968 template <unsigned Digits10, class ExponentType, class Allocator>
operator /=(const cpp_dec_float<Digits10,ExponentType,Allocator> & v)969 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::operator/=(const cpp_dec_float<Digits10, ExponentType, Allocator>& v)
970 {
971 if (iszero())
972 {
973 if ((v.isnan)())
974 {
975 return *this = v;
976 }
977 else if (v.iszero())
978 {
979 return *this = nan();
980 }
981 }
982
983 const bool u_and_v_are_finite_and_identical = ((isfinite)() && (fpclass == v.fpclass) && (exp == v.exp) && (cmp_data(v.data) == static_cast<boost::int32_t>(0)));
984
985 if (u_and_v_are_finite_and_identical)
986 {
987 if (neg != v.neg)
988 {
989 *this = one();
990 negate();
991 }
992 else
993 *this = one();
994 return *this;
995 }
996 else
997 {
998 cpp_dec_float t(v);
999 t.calculate_inv();
1000 return operator*=(t);
1001 }
1002 }
1003
1004 template <unsigned Digits10, class ExponentType, class Allocator>
mul_unsigned_long_long(const boost::ulong_long_type n)1005 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::mul_unsigned_long_long(const boost::ulong_long_type n)
1006 {
1007 // Multiply *this with a constant boost::ulong_long_type.
1008
1009 // Evaluate the sign of the result.
1010 const bool b_neg = neg;
1011
1012 // Artificially set the sign of the result to be positive.
1013 neg = false;
1014
1015 // Handle special cases like zero, inf and NaN.
1016 const bool b_u_is_inf = (isinf)();
1017 const bool b_n_is_zero = (n == static_cast<boost::int32_t>(0));
1018
1019 if ((isnan)() || (b_u_is_inf && b_n_is_zero))
1020 {
1021 return (*this = nan());
1022 }
1023
1024 if (b_u_is_inf)
1025 {
1026 *this = inf();
1027 if (b_neg)
1028 negate();
1029 return *this;
1030 }
1031
1032 if (iszero() || b_n_is_zero)
1033 {
1034 // Multiplication by zero.
1035 return *this = zero();
1036 }
1037
1038 if (n >= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask))
1039 {
1040 neg = b_neg;
1041 cpp_dec_float t;
1042 t = n;
1043 return operator*=(t);
1044 }
1045
1046 if (n == static_cast<boost::ulong_long_type>(1u))
1047 {
1048 neg = b_neg;
1049 return *this;
1050 }
1051
1052 // Set up the multiplication loop.
1053 const boost::uint32_t nn = static_cast<boost::uint32_t>(n);
1054 const boost::uint32_t carry = mul_loop_n(data.data(), nn, prec_elem);
1055
1056 // Handle the carry and adjust the exponent.
1057 if (carry != static_cast<boost::uint32_t>(0u))
1058 {
1059 exp += static_cast<ExponentType>(cpp_dec_float_elem_digits10);
1060
1061 // Shift the result of the multiplication one element to the right.
1062 std::copy_backward(data.begin(),
1063 data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)),
1064 data.begin() + static_cast<std::size_t>(prec_elem));
1065
1066 data.front() = static_cast<boost::uint32_t>(carry);
1067 }
1068
1069 // Check for potential overflow.
1070 const bool b_result_might_overflow = (exp >= cpp_dec_float_max_exp10);
1071
1072 // Handle overflow.
1073 if (b_result_might_overflow && (compare((cpp_dec_float::max)()) > 0))
1074 {
1075 *this = inf();
1076 }
1077
1078 // Set the sign.
1079 neg = b_neg;
1080
1081 return *this;
1082 }
1083
1084 template <unsigned Digits10, class ExponentType, class Allocator>
div_unsigned_long_long(const boost::ulong_long_type n)1085 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::div_unsigned_long_long(const boost::ulong_long_type n)
1086 {
1087 // Divide *this by a constant boost::ulong_long_type.
1088
1089 // Evaluate the sign of the result.
1090 const bool b_neg = neg;
1091
1092 // Artificially set the sign of the result to be positive.
1093 neg = false;
1094
1095 // Handle special cases like zero, inf and NaN.
1096 if ((isnan)())
1097 {
1098 return *this;
1099 }
1100
1101 if ((isinf)())
1102 {
1103 *this = inf();
1104 if (b_neg)
1105 negate();
1106 return *this;
1107 }
1108
1109 if (n == static_cast<boost::ulong_long_type>(0u))
1110 {
1111 // Divide by 0.
1112 if (iszero())
1113 {
1114 *this = nan();
1115 return *this;
1116 }
1117 else
1118 {
1119 *this = inf();
1120 if (isneg())
1121 negate();
1122 return *this;
1123 }
1124 }
1125
1126 if (iszero())
1127 {
1128 return *this;
1129 }
1130
1131 if (n >= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask))
1132 {
1133 neg = b_neg;
1134 cpp_dec_float t;
1135 t = n;
1136 return operator/=(t);
1137 }
1138
1139 const boost::uint32_t nn = static_cast<boost::uint32_t>(n);
1140
1141 if (nn > static_cast<boost::uint32_t>(1u))
1142 {
1143 // Do the division loop.
1144 const boost::uint32_t prev = div_loop_n(data.data(), nn, prec_elem);
1145
1146 // Determine if one leading zero is in the result data.
1147 if (data[0] == static_cast<boost::uint32_t>(0u))
1148 {
1149 // Adjust the exponent
1150 exp -= static_cast<ExponentType>(cpp_dec_float_elem_digits10);
1151
1152 // Shift result of the division one element to the left.
1153 std::copy(data.begin() + static_cast<std::size_t>(1u),
1154 data.begin() + static_cast<std::size_t>(prec_elem - static_cast<boost::int32_t>(1)),
1155 data.begin());
1156
1157 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);
1158 }
1159 }
1160
1161 // Check for potential underflow.
1162 const bool b_result_might_underflow = (exp <= cpp_dec_float_min_exp10);
1163
1164 // Handle underflow.
1165 if (b_result_might_underflow && (compare((cpp_dec_float::min)()) < 0))
1166 return (*this = zero());
1167
1168 // Set the sign of the result.
1169 neg = b_neg;
1170
1171 return *this;
1172 }
1173
1174 template <unsigned Digits10, class ExponentType, class Allocator>
calculate_inv()1175 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_inv()
1176 {
1177 // Compute the inverse of *this.
1178 const bool b_neg = neg;
1179
1180 neg = false;
1181
1182 // Handle special cases like zero, inf and NaN.
1183 if (iszero())
1184 {
1185 *this = inf();
1186 if (b_neg)
1187 negate();
1188 return *this;
1189 }
1190
1191 if ((isnan)())
1192 {
1193 return *this;
1194 }
1195
1196 if ((isinf)())
1197 {
1198 return *this = zero();
1199 }
1200
1201 if (isone())
1202 {
1203 if (b_neg)
1204 negate();
1205 return *this;
1206 }
1207
1208 // Save the original *this.
1209 cpp_dec_float<Digits10, ExponentType, Allocator> x(*this);
1210
1211 // Generate the initial estimate using division.
1212 // Extract the mantissa and exponent for a "manual"
1213 // computation of the estimate.
1214 double dd;
1215 ExponentType ne;
1216 x.extract_parts(dd, ne);
1217
1218 // Do the inverse estimate using double precision estimates of mantissa and exponent.
1219 operator=(cpp_dec_float<Digits10, ExponentType, Allocator>(1.0 / dd, -ne));
1220
1221 // Compute the inverse of *this. Quadratically convergent Newton-Raphson iteration
1222 // is used. During the iterative steps, the precision of the calculation is limited
1223 // to the minimum required in order to minimize the run-time.
1224
1225 static const boost::int32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3;
1226
1227 for (boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= static_cast<boost::int32_t>(2))
1228 {
1229 // Adjust precision of the terms.
1230 precision(static_cast<boost::int32_t>((digits + 10) * static_cast<boost::int32_t>(2)));
1231 x.precision(static_cast<boost::int32_t>((digits + 10) * static_cast<boost::int32_t>(2)));
1232
1233 // Next iteration.
1234 cpp_dec_float t(*this);
1235 t *= x;
1236 t -= two();
1237 t.negate();
1238 *this *= t;
1239 }
1240
1241 neg = b_neg;
1242
1243 prec_elem = cpp_dec_float_elem_number;
1244
1245 return *this;
1246 }
1247
1248 template <unsigned Digits10, class ExponentType, class Allocator>
calculate_sqrt()1249 cpp_dec_float<Digits10, ExponentType, Allocator>& cpp_dec_float<Digits10, ExponentType, Allocator>::calculate_sqrt()
1250 {
1251 // Compute the square root of *this.
1252
1253 if ((isinf)() && !isneg())
1254 {
1255 return *this;
1256 }
1257
1258 if (isneg() || (!(isfinite)()))
1259 {
1260 *this = nan();
1261 errno = EDOM;
1262 return *this;
1263 }
1264
1265 if (iszero() || isone())
1266 {
1267 return *this;
1268 }
1269
1270 // Save the original *this.
1271 cpp_dec_float<Digits10, ExponentType, Allocator> x(*this);
1272
1273 // Generate the initial estimate using division.
1274 // Extract the mantissa and exponent for a "manual"
1275 // computation of the estimate.
1276 double dd;
1277 ExponentType ne;
1278 extract_parts(dd, ne);
1279
1280 // Force the exponent to be an even multiple of two.
1281 if ((ne % static_cast<ExponentType>(2)) != static_cast<ExponentType>(0))
1282 {
1283 ++ne;
1284 dd /= 10.0;
1285 }
1286
1287 // Setup the iteration.
1288 // Estimate the square root using simple manipulations.
1289 const double sqd = std::sqrt(dd);
1290
1291 *this = cpp_dec_float<Digits10, ExponentType, Allocator>(sqd, static_cast<ExponentType>(ne / static_cast<ExponentType>(2)));
1292
1293 // Estimate 1.0 / (2.0 * x0) using simple manipulations.
1294 cpp_dec_float<Digits10, ExponentType, Allocator> vi(0.5 / sqd, static_cast<ExponentType>(-ne / static_cast<ExponentType>(2)));
1295
1296 // Compute the square root of x. Coupled Newton iteration
1297 // as described in "Pi Unleashed" is used. During the
1298 // iterative steps, the precision of the calculation is
1299 // limited to the minimum required in order to minimize
1300 // the run-time.
1301 //
1302 // Book references:
1303 // https://doi.org/10.1007/978-3-642-56735-3
1304 // 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
1305
1306 static const boost::uint32_t double_digits10_minus_a_few = std::numeric_limits<double>::digits10 - 3;
1307
1308 for (boost::int32_t digits = double_digits10_minus_a_few; digits <= cpp_dec_float_total_digits10; digits *= 2u)
1309 {
1310 // Adjust precision of the terms.
1311 precision((digits + 10) * 2);
1312 vi.precision((digits + 10) * 2);
1313
1314 // Next iteration of vi
1315 cpp_dec_float t(*this);
1316 t *= vi;
1317 t.negate();
1318 t.mul_unsigned_long_long(2u);
1319 t += one();
1320 t *= vi;
1321 vi += t;
1322
1323 // Next iteration of *this
1324 t = *this;
1325 t *= *this;
1326 t.negate();
1327 t += x;
1328 t *= vi;
1329 *this += t;
1330 }
1331
1332 prec_elem = cpp_dec_float_elem_number;
1333
1334 return *this;
1335 }
1336
1337 template <unsigned Digits10, class ExponentType, class Allocator>
cmp_data(const array_type & vd) const1338 int cpp_dec_float<Digits10, ExponentType, Allocator>::cmp_data(const array_type& vd) const
1339 {
1340 // Compare the data of *this with those of v.
1341 // Return +1 for *this > v
1342 // 0 for *this = v
1343 // -1 for *this < v
1344
1345 const std::pair<typename array_type::const_iterator, typename array_type::const_iterator> mismatch_pair = std::mismatch(data.begin(), data.end(), vd.begin());
1346
1347 const bool is_equal = ((mismatch_pair.first == data.end()) && (mismatch_pair.second == vd.end()));
1348
1349 if (is_equal)
1350 {
1351 return 0;
1352 }
1353 else
1354 {
1355 return ((*mismatch_pair.first > *mismatch_pair.second) ? 1 : -1);
1356 }
1357 }
1358
1359 template <unsigned Digits10, class ExponentType, class Allocator>
compare(const cpp_dec_float & v) const1360 int cpp_dec_float<Digits10, ExponentType, Allocator>::compare(const cpp_dec_float& v) const
1361 {
1362 // Compare v with *this.
1363 // Return +1 for *this > v
1364 // 0 for *this = v
1365 // -1 for *this < v
1366
1367 // Handle all non-finite cases.
1368 if ((!(isfinite)()) || (!(v.isfinite)()))
1369 {
1370 // NaN can never equal NaN. Return an implementation-dependent
1371 // signed result. Also note that comparison of NaN with NaN
1372 // using operators greater-than or less-than is undefined.
1373 if ((isnan)() || (v.isnan)())
1374 {
1375 return ((isnan)() ? 1 : -1);
1376 }
1377
1378 if ((isinf)() && (v.isinf)())
1379 {
1380 // Both *this and v are infinite. They are equal if they have the same sign.
1381 // Otherwise, *this is less than v if and only if *this is negative.
1382 return ((neg == v.neg) ? 0 : (neg ? -1 : 1));
1383 }
1384
1385 if ((isinf)())
1386 {
1387 // *this is infinite, but v is finite.
1388 // So negative infinite *this is less than any finite v.
1389 // Whereas positive infinite *this is greater than any finite v.
1390 return (isneg() ? -1 : 1);
1391 }
1392 else
1393 {
1394 // *this is finite, and v is infinite.
1395 // So any finite *this is greater than negative infinite v.
1396 // Whereas any finite *this is less than positive infinite v.
1397 return (v.neg ? 1 : -1);
1398 }
1399 }
1400
1401 // And now handle all *finite* cases.
1402 if (iszero())
1403 {
1404 // The value of *this is zero and v is either zero or non-zero.
1405 return (v.iszero() ? 0
1406 : (v.neg ? 1 : -1));
1407 }
1408 else if (v.iszero())
1409 {
1410 // The value of v is zero and *this is non-zero.
1411 return (neg ? -1 : 1);
1412 }
1413 else
1414 {
1415 // Both *this and v are non-zero.
1416
1417 if (neg != v.neg)
1418 {
1419 // The signs are different.
1420 return (neg ? -1 : 1);
1421 }
1422 else if (exp != v.exp)
1423 {
1424 // The signs are the same and the exponents are different.
1425 const int val_cexpression = ((exp < v.exp) ? 1 : -1);
1426
1427 return (neg ? val_cexpression : -val_cexpression);
1428 }
1429 else
1430 {
1431 // The signs are the same and the exponents are the same.
1432 // Compare the data.
1433 const int val_cmp_data = cmp_data(v.data);
1434
1435 return ((!neg) ? val_cmp_data : -val_cmp_data);
1436 }
1437 }
1438 }
1439
1440 template <unsigned Digits10, class ExponentType, class Allocator>
isone() const1441 bool cpp_dec_float<Digits10, ExponentType, Allocator>::isone() const
1442 {
1443 // Check if the value of *this is identically 1 or very close to 1.
1444
1445 const bool not_negative_and_is_finite = ((!neg) && (isfinite)());
1446
1447 if (not_negative_and_is_finite)
1448 {
1449 if ((data[0u] == static_cast<boost::uint32_t>(1u)) && (exp == static_cast<ExponentType>(0)))
1450 {
1451 const typename array_type::const_iterator it_non_zero = std::find_if(data.begin(), data.end(), data_elem_is_non_zero_predicate);
1452 return (it_non_zero == data.end());
1453 }
1454 else if ((data[0u] == static_cast<boost::uint32_t>(cpp_dec_float_elem_mask - 1)) && (exp == static_cast<ExponentType>(-cpp_dec_float_elem_digits10)))
1455 {
1456 const typename array_type::const_iterator it_non_nine = std::find_if(data.begin(), data.end(), data_elem_is_non_nine_predicate);
1457 return (it_non_nine == data.end());
1458 }
1459 }
1460
1461 return false;
1462 }
1463
1464 template <unsigned Digits10, class ExponentType, class Allocator>
isint() const1465 bool cpp_dec_float<Digits10, ExponentType, Allocator>::isint() const
1466 {
1467 if (fpclass != cpp_dec_float_finite)
1468 {
1469 return false;
1470 }
1471
1472 if (iszero())
1473 {
1474 return true;
1475 }
1476
1477 if (exp < static_cast<ExponentType>(0))
1478 {
1479 return false;
1480 } // |*this| < 1.
1481
1482 const typename array_type::size_type offset_decimal_part = static_cast<typename array_type::size_type>(exp / cpp_dec_float_elem_digits10) + 1u;
1483
1484 if (offset_decimal_part >= static_cast<typename array_type::size_type>(cpp_dec_float_elem_number))
1485 {
1486 // The number is too large to resolve the integer part.
1487 // It considered to be a pure integer.
1488 return true;
1489 }
1490
1491 typename array_type::const_iterator it_non_zero = std::find_if(data.begin() + offset_decimal_part, data.end(), data_elem_is_non_zero_predicate);
1492
1493 return (it_non_zero == data.end());
1494 }
1495
1496 template <unsigned Digits10, class ExponentType, class Allocator>
extract_parts(double & mantissa,ExponentType & exponent) const1497 void cpp_dec_float<Digits10, ExponentType, Allocator>::extract_parts(double& mantissa, ExponentType& exponent) const
1498 {
1499 // Extract the approximate parts mantissa and base-10 exponent from the input cpp_dec_float<Digits10, ExponentType, Allocator> value x.
1500
1501 // Extracts the mantissa and exponent.
1502 exponent = exp;
1503
1504 boost::uint32_t p10 = static_cast<boost::uint32_t>(1u);
1505 boost::uint32_t test = data[0u];
1506
1507 for (;;)
1508 {
1509 test /= static_cast<boost::uint32_t>(10u);
1510
1511 if (test == static_cast<boost::uint32_t>(0u))
1512 {
1513 break;
1514 }
1515
1516 p10 *= static_cast<boost::uint32_t>(10u);
1517 ++exponent;
1518 }
1519
1520 // Establish the upper bound of limbs for extracting the double.
1521 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) + (static_cast<int>(static_cast<boost::int32_t>(std::numeric_limits<double>::digits10) % cpp_dec_float_elem_digits10) != 0 ? 1 : 0) + 1;
1522
1523 // And make sure this upper bound stays within bounds of the elems.
1524 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));
1525
1526 // Extract into the mantissa the first limb, extracted as a double.
1527 mantissa = static_cast<double>(data[0]);
1528 double scale = 1.0;
1529
1530 // Extract the rest of the mantissa piecewise from the limbs.
1531 for (std::size_t i = 1u; i < max_elem_extract_count; i++)
1532 {
1533 scale /= static_cast<double>(cpp_dec_float_elem_mask);
1534 mantissa += (static_cast<double>(data[i]) * scale);
1535 }
1536
1537 mantissa /= static_cast<double>(p10);
1538
1539 if (neg)
1540 {
1541 mantissa = -mantissa;
1542 }
1543 }
1544
1545 template <unsigned Digits10, class ExponentType, class Allocator>
extract_double() const1546 double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_double() const
1547 {
1548 // Returns the double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>.
1549
1550 // Check for non-normal cpp_dec_float<Digits10, ExponentType, Allocator>.
1551 if (!(isfinite)())
1552 {
1553 if ((isnan)())
1554 {
1555 return std::numeric_limits<double>::quiet_NaN();
1556 }
1557 else
1558 {
1559 return ((!neg) ? std::numeric_limits<double>::infinity()
1560 : -std::numeric_limits<double>::infinity());
1561 }
1562 }
1563
1564 cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this);
1565 if (xx.isneg())
1566 xx.negate();
1567
1568 // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero.
1569 if (iszero() || (xx.compare(double_min()) < 0))
1570 {
1571 return 0.0;
1572 }
1573
1574 // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double.
1575 if (xx.compare(double_max()) > 0)
1576 {
1577 return ((!neg) ? std::numeric_limits<double>::infinity()
1578 : -std::numeric_limits<double>::infinity());
1579 }
1580
1581 std::stringstream ss;
1582 ss.imbue(std::locale::classic());
1583
1584 ss << str(std::numeric_limits<double>::digits10 + (2 + 1), std::ios_base::scientific);
1585
1586 double d;
1587 ss >> d;
1588
1589 return d;
1590 }
1591
1592 template <unsigned Digits10, class ExponentType, class Allocator>
extract_long_double() const1593 long double cpp_dec_float<Digits10, ExponentType, Allocator>::extract_long_double() const
1594 {
1595 // Returns the long double conversion of a cpp_dec_float<Digits10, ExponentType, Allocator>.
1596
1597 // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is subnormal.
1598 if (!(isfinite)())
1599 {
1600 if ((isnan)())
1601 {
1602 return std::numeric_limits<long double>::quiet_NaN();
1603 }
1604 else
1605 {
1606 return ((!neg) ? std::numeric_limits<long double>::infinity()
1607 : -std::numeric_limits<long double>::infinity());
1608 }
1609 }
1610
1611 cpp_dec_float<Digits10, ExponentType, Allocator> xx(*this);
1612 if (xx.isneg())
1613 xx.negate();
1614
1615 // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> is zero.
1616 if (iszero() || (xx.compare(long_double_min()) < 0))
1617 {
1618 return static_cast<long double>(0.0);
1619 }
1620
1621 // Check if *this cpp_dec_float<Digits10, ExponentType, Allocator> exceeds the maximum of double.
1622 if (xx.compare(long_double_max()) > 0)
1623 {
1624 return ((!neg) ? std::numeric_limits<long double>::infinity()
1625 : -std::numeric_limits<long double>::infinity());
1626 }
1627
1628 std::stringstream ss;
1629 ss.imbue(std::locale::classic());
1630
1631 ss << str(std::numeric_limits<long double>::digits10 + (2 + 1), std::ios_base::scientific);
1632
1633 long double ld;
1634 ss >> ld;
1635
1636 return ld;
1637 }
1638
1639 template <unsigned Digits10, class ExponentType, class Allocator>
extract_signed_long_long() const1640 boost::long_long_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_signed_long_long() const
1641 {
1642 // Extracts a signed long long from *this.
1643 // If (x > maximum of long long) or (x < minimum of long long),
1644 // then the maximum or minimum of long long is returned accordingly.
1645
1646 if (exp < static_cast<ExponentType>(0))
1647 {
1648 return static_cast<boost::long_long_type>(0);
1649 }
1650
1651 const bool b_neg = isneg();
1652
1653 boost::ulong_long_type val;
1654
1655 if ((!b_neg) && (compare(long_long_max()) > 0))
1656 {
1657 return (std::numeric_limits<boost::long_long_type>::max)();
1658 }
1659 else if (b_neg && (compare(long_long_min()) < 0))
1660 {
1661 return (std::numeric_limits<boost::long_long_type>::min)();
1662 }
1663 else
1664 {
1665 // Extract the data into an boost::ulong_long_type value.
1666 cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part());
1667 if (xn.isneg())
1668 xn.negate();
1669
1670 val = static_cast<boost::ulong_long_type>(xn.data[0]);
1671
1672 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)));
1673
1674 for (boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++)
1675 {
1676 val *= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask);
1677 val += static_cast<boost::ulong_long_type>(xn.data[i]);
1678 }
1679 }
1680
1681 if (!b_neg)
1682 {
1683 return static_cast<boost::long_long_type>(val);
1684 }
1685 else
1686 {
1687 // This strange expression avoids a hardware trap in the corner case
1688 // that val is the most negative value permitted in boost::long_long_type.
1689 // See https://svn.boost.org/trac/boost/ticket/9740.
1690 //
1691 boost::long_long_type sval = static_cast<boost::long_long_type>(val - 1);
1692 sval = -sval;
1693 --sval;
1694 return sval;
1695 }
1696 }
1697
1698 template <unsigned Digits10, class ExponentType, class Allocator>
extract_unsigned_long_long() const1699 boost::ulong_long_type cpp_dec_float<Digits10, ExponentType, Allocator>::extract_unsigned_long_long() const
1700 {
1701 // Extracts an boost::ulong_long_type from *this.
1702 // If x exceeds the maximum of boost::ulong_long_type,
1703 // then the maximum of boost::ulong_long_type is returned.
1704 // If x is negative, then the boost::ulong_long_type cast of
1705 // the long long extracted value is returned.
1706
1707 if (isneg())
1708 {
1709 return static_cast<boost::ulong_long_type>(extract_signed_long_long());
1710 }
1711
1712 if (exp < static_cast<ExponentType>(0))
1713 {
1714 return static_cast<boost::ulong_long_type>(0u);
1715 }
1716
1717 const cpp_dec_float<Digits10, ExponentType, Allocator> xn(extract_integer_part());
1718
1719 boost::ulong_long_type val;
1720
1721 if (xn.compare(ulong_long_max()) > 0)
1722 {
1723 return (std::numeric_limits<boost::ulong_long_type>::max)();
1724 }
1725 else
1726 {
1727 // Extract the data into an boost::ulong_long_type value.
1728 val = static_cast<boost::ulong_long_type>(xn.data[0]);
1729
1730 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)));
1731
1732 for (boost::int32_t i = static_cast<boost::int32_t>(1); i <= imax; i++)
1733 {
1734 val *= static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask);
1735 val += static_cast<boost::ulong_long_type>(xn.data[i]);
1736 }
1737 }
1738
1739 return val;
1740 }
1741
1742 template <unsigned Digits10, class ExponentType, class Allocator>
extract_integer_part() const1743 cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::extract_integer_part() const
1744 {
1745 // Compute the signed integer part of x.
1746
1747 if (!(isfinite)())
1748 {
1749 return *this;
1750 }
1751
1752 if (exp < static_cast<ExponentType>(0))
1753 {
1754 // The absolute value of the number is smaller than 1.
1755 // Thus the integer part is zero.
1756 return zero();
1757 }
1758
1759 // Truncate the digits from the decimal part, including guard digits
1760 // that do not belong to the integer part.
1761
1762 // Make a local copy.
1763 cpp_dec_float<Digits10, ExponentType, Allocator> x = *this;
1764
1765 // Clear out the decimal portion
1766 const size_t first_clear = (static_cast<size_t>(x.exp) / static_cast<size_t>(cpp_dec_float_elem_digits10)) + 1u;
1767 const size_t last_clear = static_cast<size_t>(cpp_dec_float_elem_number);
1768
1769 if (first_clear < last_clear)
1770 std::fill(x.data.begin() + first_clear, x.data.begin() + last_clear, static_cast<boost::uint32_t>(0u));
1771
1772 return x;
1773 }
1774
1775 template <unsigned Digits10, class ExponentType, class Allocator>
str(boost::intmax_t number_of_digits,std::ios_base::fmtflags f) const1776 std::string cpp_dec_float<Digits10, ExponentType, Allocator>::str(boost::intmax_t number_of_digits, std::ios_base::fmtflags f) const
1777 {
1778 if ((this->isinf)())
1779 {
1780 if (this->isneg())
1781 return "-inf";
1782 else if (f & std::ios_base::showpos)
1783 return "+inf";
1784 else
1785 return "inf";
1786 }
1787 else if ((this->isnan)())
1788 {
1789 return "nan";
1790 }
1791
1792 std::string str;
1793 boost::intmax_t org_digits(number_of_digits);
1794 ExponentType my_exp = order();
1795
1796 if (number_of_digits == 0)
1797 number_of_digits = cpp_dec_float_total_digits10;
1798
1799 if (f & std::ios_base::fixed)
1800 {
1801 number_of_digits += my_exp + 1;
1802 }
1803 else if (f & std::ios_base::scientific)
1804 ++number_of_digits;
1805 // Determine the number of elements needed to provide the requested digits from cpp_dec_float<Digits10, ExponentType, Allocator>.
1806 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),
1807 static_cast<std::size_t>(cpp_dec_float_elem_number));
1808
1809 // Extract the remaining digits from cpp_dec_float<Digits10, ExponentType, Allocator> after the decimal point.
1810 std::stringstream ss;
1811 ss.imbue(std::locale::classic());
1812 ss << data[0];
1813 // Extract all of the digits from cpp_dec_float<Digits10, ExponentType, Allocator>, beginning with the first data element.
1814 for (std::size_t i = static_cast<std::size_t>(1u); i < number_of_elements; i++)
1815 {
1816 ss << std::setw(static_cast<std::streamsize>(cpp_dec_float_elem_digits10))
1817 << std::setfill(static_cast<char>('0'))
1818 << data[i];
1819 }
1820 str += ss.str();
1821
1822 bool have_leading_zeros = false;
1823
1824 if (number_of_digits == 0)
1825 {
1826 // We only get here if the output format is "fixed" and we just need to
1827 // round the first non-zero digit.
1828 number_of_digits -= my_exp + 1; // reset to original value
1829 str.insert(static_cast<std::string::size_type>(0), std::string::size_type(number_of_digits), '0');
1830 have_leading_zeros = true;
1831 }
1832
1833 if (number_of_digits < 0)
1834 {
1835 str = "0";
1836 if (isneg())
1837 str.insert(static_cast<std::string::size_type>(0), 1, '-');
1838 boost::multiprecision::detail::format_float_string(str, 0, number_of_digits - my_exp - 1, f, this->iszero());
1839 return str;
1840 }
1841 else
1842 {
1843 // Cut the output to the size of the precision.
1844 if (str.length() > static_cast<std::string::size_type>(number_of_digits))
1845 {
1846 // Get the digit after the last needed digit for rounding
1847 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'));
1848
1849 bool need_round_up = round >= 5u;
1850
1851 if (round == 5u)
1852 {
1853 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'));
1854 if ((ix & 1u) == 0)
1855 {
1856 // We have an even digit followed by a 5, so we might not actually need to round up
1857 // if all the remaining digits are zero:
1858 if (str.find_first_not_of('0', static_cast<std::string::size_type>(number_of_digits + 1)) == std::string::npos)
1859 {
1860 bool all_zeros = true;
1861 // No none-zero trailing digits in the string, now check whatever parts we didn't convert to the string:
1862 for (std::size_t i = number_of_elements; i < data.size(); i++)
1863 {
1864 if (data[i])
1865 {
1866 all_zeros = false;
1867 break;
1868 }
1869 }
1870 if (all_zeros)
1871 need_round_up = false; // tie break - round to even.
1872 }
1873 }
1874 }
1875
1876 // Truncate the string
1877 str.erase(static_cast<std::string::size_type>(number_of_digits));
1878
1879 if (need_round_up)
1880 {
1881 std::size_t ix = static_cast<std::size_t>(str.length() - 1u);
1882
1883 // Every trailing 9 must be rounded up
1884 while (ix && (static_cast<boost::int32_t>(str.at(ix)) - static_cast<boost::int32_t>('0') == static_cast<boost::int32_t>(9)))
1885 {
1886 str.at(ix) = static_cast<char>('0');
1887 --ix;
1888 }
1889
1890 if (!ix)
1891 {
1892 // There were nothing but trailing nines.
1893 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))
1894 {
1895 // Increment up to the next order and adjust exponent.
1896 str.at(ix) = static_cast<char>('1');
1897 ++my_exp;
1898 }
1899 else
1900 {
1901 // Round up this digit.
1902 ++str.at(ix);
1903 }
1904 }
1905 else
1906 {
1907 // Round up the last digit.
1908 ++str[ix];
1909 }
1910 }
1911 }
1912 }
1913
1914 if (have_leading_zeros)
1915 {
1916 // We need to take the zeros back out again, and correct the exponent
1917 // if we rounded up:
1918 if (str[std::string::size_type(number_of_digits - 1)] != '0')
1919 {
1920 ++my_exp;
1921 str.erase(0, std::string::size_type(number_of_digits - 1));
1922 }
1923 else
1924 str.erase(0, std::string::size_type(number_of_digits));
1925 }
1926
1927 if (isneg())
1928 str.insert(static_cast<std::string::size_type>(0), 1, '-');
1929
1930 boost::multiprecision::detail::format_float_string(str, my_exp, org_digits, f, this->iszero());
1931 return str;
1932 }
1933
1934 template <unsigned Digits10, class ExponentType, class Allocator>
rd_string(const char * const s)1935 bool cpp_dec_float<Digits10, ExponentType, Allocator>::rd_string(const char* const s)
1936 {
1937 #ifndef BOOST_NO_EXCEPTIONS
1938 try
1939 {
1940 #endif
1941
1942 std::string str(s);
1943
1944 // TBD: Using several regular expressions may significantly reduce
1945 // the code complexity (and perhaps the run-time) of rd_string().
1946
1947 // Get a possible exponent and remove it.
1948 exp = static_cast<ExponentType>(0);
1949
1950 std::size_t pos;
1951
1952 if (((pos = str.find('e')) != std::string::npos) || ((pos = str.find('E')) != std::string::npos))
1953 {
1954 // Remove the exponent part from the string.
1955 exp = boost::lexical_cast<ExponentType>(static_cast<const char*>(str.c_str() + (pos + 1u)));
1956 str = str.substr(static_cast<std::size_t>(0u), pos);
1957 }
1958
1959 // Get a possible +/- sign and remove it.
1960 neg = false;
1961
1962 if (str.size())
1963 {
1964 if (str[0] == '-')
1965 {
1966 neg = true;
1967 str.erase(0, 1);
1968 }
1969 else if (str[0] == '+')
1970 {
1971 str.erase(0, 1);
1972 }
1973 }
1974 //
1975 // Special cases for infinities and NaN's:
1976 //
1977 if ((str == "inf") || (str == "INF") || (str == "infinity") || (str == "INFINITY"))
1978 {
1979 if (neg)
1980 {
1981 *this = this->inf();
1982 this->negate();
1983 }
1984 else
1985 *this = this->inf();
1986 return true;
1987 }
1988 if ((str.size() >= 3) && ((str.substr(0, 3) == "nan") || (str.substr(0, 3) == "NAN") || (str.substr(0, 3) == "NaN")))
1989 {
1990 *this = this->nan();
1991 return true;
1992 }
1993
1994 // Remove the leading zeros for all input types.
1995 const std::string::iterator fwd_it_leading_zero = std::find_if(str.begin(), str.end(), char_is_nonzero_predicate);
1996
1997 if (fwd_it_leading_zero != str.begin())
1998 {
1999 if (fwd_it_leading_zero == str.end())
2000 {
2001 // The string contains nothing but leading zeros.
2002 // This string represents zero.
2003 operator=(zero());
2004 return true;
2005 }
2006 else
2007 {
2008 str.erase(str.begin(), fwd_it_leading_zero);
2009 }
2010 }
2011
2012 // Put the input string into the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form
2013 // aaa.bbbbE+/-n, where aaa has 1...cpp_dec_float_elem_digits10, bbbb has an
2014 // even multiple of cpp_dec_float_elem_digits10 which are possibly zero padded
2015 // on the right-end, and n is a signed 64-bit integer which is an
2016 // even multiple of cpp_dec_float_elem_digits10.
2017
2018 // Find a possible decimal point.
2019 pos = str.find(static_cast<char>('.'));
2020
2021 if (pos != std::string::npos)
2022 {
2023 // Remove all trailing insignificant zeros.
2024 const std::string::const_reverse_iterator rit_non_zero = std::find_if(str.rbegin(), str.rend(), char_is_nonzero_predicate);
2025
2026 if (rit_non_zero != static_cast<std::string::const_reverse_iterator>(str.rbegin()))
2027 {
2028 const std::string::size_type ofs = str.length() - std::distance<std::string::const_reverse_iterator>(str.rbegin(), rit_non_zero);
2029 str.erase(str.begin() + ofs, str.end());
2030 }
2031
2032 // Check if the input is identically zero.
2033 if (str == std::string("."))
2034 {
2035 operator=(zero());
2036 return true;
2037 }
2038
2039 // Remove leading significant zeros just after the decimal point
2040 // and adjust the exponent accordingly.
2041 // Note that the while-loop operates only on strings of the form ".000abcd..."
2042 // and peels away the zeros just after the decimal point.
2043 if (str.at(static_cast<std::size_t>(0u)) == static_cast<char>('.'))
2044 {
2045 const std::string::iterator it_non_zero = std::find_if(str.begin() + 1u, str.end(), char_is_nonzero_predicate);
2046
2047 std::size_t delta_exp = static_cast<std::size_t>(0u);
2048
2049 if (str.at(static_cast<std::size_t>(1u)) == static_cast<char>('0'))
2050 {
2051 delta_exp = std::distance<std::string::const_iterator>(str.begin() + 1u, it_non_zero);
2052 }
2053
2054 // Bring one single digit into the mantissa and adjust the exponent accordingly.
2055 str.erase(str.begin(), it_non_zero);
2056 str.insert(static_cast<std::string::size_type>(1u), ".");
2057 exp -= static_cast<ExponentType>(delta_exp + 1u);
2058 }
2059 }
2060 else
2061 {
2062 // Input string has no decimal point: Append decimal point.
2063 str.append(".");
2064 }
2065
2066 // Shift the decimal point such that the exponent is an even multiple of cpp_dec_float_elem_digits10.
2067 std::size_t n_shift = static_cast<std::size_t>(0u);
2068 const std::size_t n_exp_rem = static_cast<std::size_t>(exp % static_cast<ExponentType>(cpp_dec_float_elem_digits10));
2069
2070 if ((exp % static_cast<ExponentType>(cpp_dec_float_elem_digits10)) != static_cast<ExponentType>(0))
2071 {
2072 n_shift = ((exp < static_cast<ExponentType>(0))
2073 ? static_cast<std::size_t>(n_exp_rem + static_cast<std::size_t>(cpp_dec_float_elem_digits10))
2074 : static_cast<std::size_t>(n_exp_rem));
2075 }
2076
2077 // Make sure that there are enough digits for the decimal point shift.
2078 pos = str.find(static_cast<char>('.'));
2079
2080 std::size_t pos_plus_one = static_cast<std::size_t>(pos + 1u);
2081
2082 if ((str.length() - pos_plus_one) < n_shift)
2083 {
2084 const std::size_t sz = static_cast<std::size_t>(n_shift - (str.length() - pos_plus_one));
2085
2086 str.append(std::string(sz, static_cast<char>('0')));
2087 }
2088
2089 // Do the decimal point shift.
2090 if (n_shift != static_cast<std::size_t>(0u))
2091 {
2092 str.insert(static_cast<std::string::size_type>(pos_plus_one + n_shift), ".");
2093
2094 str.erase(pos, static_cast<std::string::size_type>(1u));
2095
2096 exp -= static_cast<ExponentType>(n_shift);
2097 }
2098
2099 // Cut the size of the mantissa to <= cpp_dec_float_elem_digits10.
2100 pos = str.find(static_cast<char>('.'));
2101 pos_plus_one = static_cast<std::size_t>(pos + 1u);
2102
2103 if (pos > static_cast<std::size_t>(cpp_dec_float_elem_digits10))
2104 {
2105 const boost::int32_t n_pos = static_cast<boost::int32_t>(pos);
2106 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));
2107 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);
2108
2109 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))), ".");
2110
2111 str.erase(pos_plus_one, static_cast<std::size_t>(1u));
2112
2113 exp += static_cast<ExponentType>(static_cast<ExponentType>(n) * static_cast<ExponentType>(cpp_dec_float_elem_digits10));
2114 }
2115
2116 // Pad the decimal part such that its value is an even
2117 // multiple of cpp_dec_float_elem_digits10.
2118 pos = str.find(static_cast<char>('.'));
2119 pos_plus_one = static_cast<std::size_t>(pos + 1u);
2120
2121 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));
2122 const boost::int32_t n_rem = static_cast<boost::int32_t>(n_dec % cpp_dec_float_elem_digits10);
2123
2124 boost::int32_t n_cnt = ((n_rem != static_cast<boost::int32_t>(0))
2125 ? static_cast<boost::int32_t>(cpp_dec_float_elem_digits10 - n_rem)
2126 : static_cast<boost::int32_t>(0));
2127
2128 if (n_cnt != static_cast<boost::int32_t>(0))
2129 {
2130 str.append(static_cast<std::size_t>(n_cnt), static_cast<char>('0'));
2131 }
2132
2133 // Truncate decimal part if it is too long.
2134 const std::size_t max_dec = static_cast<std::size_t>((cpp_dec_float_elem_number - 1) * cpp_dec_float_elem_digits10);
2135
2136 if (static_cast<std::size_t>(str.length() - pos) > max_dec)
2137 {
2138 str = str.substr(static_cast<std::size_t>(0u),
2139 static_cast<std::size_t>(pos_plus_one + max_dec));
2140 }
2141
2142 // Now the input string has the standard cpp_dec_float<Digits10, ExponentType, Allocator> input form.
2143 // (See the comment above.)
2144
2145 // Set all the data elements to 0.
2146 std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u));
2147
2148 // Extract the data.
2149
2150 // First get the digits to the left of the decimal point...
2151 data[0u] = boost::lexical_cast<boost::uint32_t>(str.substr(static_cast<std::size_t>(0u), pos));
2152
2153 // ...then get the remaining digits to the right of the decimal point.
2154 const std::string::size_type i_end = ((str.length() - pos_plus_one) / static_cast<std::string::size_type>(cpp_dec_float_elem_digits10));
2155
2156 for (std::string::size_type i = static_cast<std::string::size_type>(0u); i < i_end; i++)
2157 {
2158 const std::string::const_iterator it = str.begin() + pos_plus_one + (i * static_cast<std::string::size_type>(cpp_dec_float_elem_digits10));
2159
2160 data[i + 1u] = boost::lexical_cast<boost::uint32_t>(std::string(it, it + static_cast<std::string::size_type>(cpp_dec_float_elem_digits10)));
2161 }
2162
2163 // Check for overflow...
2164 if (exp > cpp_dec_float_max_exp10)
2165 {
2166 const bool b_result_is_neg = neg;
2167
2168 *this = inf();
2169 if (b_result_is_neg)
2170 negate();
2171 }
2172
2173 // ...and check for underflow.
2174 if (exp <= cpp_dec_float_min_exp10)
2175 {
2176 if (exp == cpp_dec_float_min_exp10)
2177 {
2178 // Check for identity with the minimum value.
2179 cpp_dec_float<Digits10, ExponentType, Allocator> test = *this;
2180
2181 test.exp = static_cast<ExponentType>(0);
2182
2183 if (test.isone())
2184 {
2185 *this = zero();
2186 }
2187 }
2188 else
2189 {
2190 *this = zero();
2191 }
2192 }
2193
2194 #ifndef BOOST_NO_EXCEPTIONS
2195 }
2196 catch (const bad_lexical_cast&)
2197 {
2198 // Rethrow with better error message:
2199 std::string msg = "Unable to parse the string \"";
2200 msg += s;
2201 msg += "\" as a floating point value.";
2202 throw std::runtime_error(msg);
2203 }
2204 #endif
2205 return true;
2206 }
2207
2208 template <unsigned Digits10, class ExponentType, class Allocator>
cpp_dec_float(const double mantissa,const ExponentType exponent)2209 cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float(const double mantissa, const ExponentType exponent)
2210 : data(),
2211 exp(static_cast<ExponentType>(0)),
2212 neg(false),
2213 fpclass(cpp_dec_float_finite),
2214 prec_elem(cpp_dec_float_elem_number)
2215 {
2216 // Create *this cpp_dec_float<Digits10, ExponentType, Allocator> from a given mantissa and exponent.
2217 // Note: This constructor does not maintain the full precision of double.
2218
2219 const bool mantissa_is_iszero = (::fabs(mantissa) < ((std::numeric_limits<double>::min)() * (1.0 + std::numeric_limits<double>::epsilon())));
2220
2221 if (mantissa_is_iszero)
2222 {
2223 std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u));
2224 return;
2225 }
2226
2227 const bool b_neg = (mantissa < 0.0);
2228
2229 double d = ((!b_neg) ? mantissa : -mantissa);
2230 ExponentType e = exponent;
2231
2232 while (d > 10.0)
2233 {
2234 d /= 10.0;
2235 ++e;
2236 }
2237 while (d < 1.0)
2238 {
2239 d *= 10.0;
2240 --e;
2241 }
2242
2243 boost::int32_t shift = static_cast<boost::int32_t>(e % static_cast<boost::int32_t>(cpp_dec_float_elem_digits10));
2244
2245 while (static_cast<boost::int32_t>(shift-- % cpp_dec_float_elem_digits10) != static_cast<boost::int32_t>(0))
2246 {
2247 d *= 10.0;
2248 --e;
2249 }
2250
2251 exp = e;
2252 neg = b_neg;
2253
2254 std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u));
2255
2256 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));
2257 static const boost::int32_t digit_loops = static_cast<boost::int32_t>(digit_ratio + static_cast<boost::int32_t>(2));
2258
2259 for (boost::int32_t i = static_cast<boost::int32_t>(0); i < digit_loops; i++)
2260 {
2261 boost::uint32_t n = static_cast<boost::uint32_t>(static_cast<boost::uint64_t>(d));
2262 data[i] = static_cast<boost::uint32_t>(n);
2263 d -= static_cast<double>(n);
2264 d *= static_cast<double>(cpp_dec_float_elem_mask);
2265 }
2266 }
2267
2268 template <unsigned Digits10, class ExponentType, class Allocator>
2269 template <class Float>
operator =(Float a)2270 typename boost::enable_if_c<boost::is_floating_point<Float>::value, cpp_dec_float<Digits10, ExponentType, Allocator>&>::type cpp_dec_float<Digits10, ExponentType, Allocator>::operator=(Float a)
2271 {
2272 // Christopher Kormanyos's original code used a cast to boost::long_long_type here, but that fails
2273 // when long double has more digits than a boost::long_long_type.
2274 using std::floor;
2275 using std::frexp;
2276 using std::ldexp;
2277
2278 if (a == 0)
2279 return *this = zero();
2280
2281 if (a == 1)
2282 return *this = one();
2283
2284 if ((boost::math::isinf)(a))
2285 {
2286 *this = inf();
2287 if (a < 0)
2288 this->negate();
2289 return *this;
2290 }
2291
2292 if ((boost::math::isnan)(a))
2293 return *this = nan();
2294
2295 int e;
2296 Float f, term;
2297 *this = zero();
2298
2299 f = frexp(a, &e);
2300 // See https://svn.boost.org/trac/boost/ticket/10924 for an example of why this may go wrong:
2301 BOOST_ASSERT((boost::math::isfinite)(f));
2302
2303 static const int shift = std::numeric_limits<int>::digits - 1;
2304
2305 while (f)
2306 {
2307 // extract int sized bits from f:
2308 f = ldexp(f, shift);
2309 BOOST_ASSERT((boost::math::isfinite)(f));
2310 term = floor(f);
2311 e -= shift;
2312 *this *= pow2(shift);
2313 if (term > 0)
2314 add_unsigned_long_long(static_cast<unsigned>(term));
2315 else
2316 sub_unsigned_long_long(static_cast<unsigned>(-term));
2317 f -= term;
2318 }
2319
2320 if (e != 0)
2321 *this *= pow2(e);
2322
2323 return *this;
2324 }
2325
2326 template <unsigned Digits10, class ExponentType, class Allocator>
from_unsigned_long_long(const boost::ulong_long_type u)2327 void cpp_dec_float<Digits10, ExponentType, Allocator>::from_unsigned_long_long(const boost::ulong_long_type u)
2328 {
2329 std::fill(data.begin(), data.end(), static_cast<boost::uint32_t>(0u));
2330
2331 exp = static_cast<ExponentType>(0);
2332 neg = false;
2333 fpclass = cpp_dec_float_finite;
2334 prec_elem = cpp_dec_float_elem_number;
2335
2336 if (u == 0)
2337 {
2338 return;
2339 }
2340
2341 std::size_t i = static_cast<std::size_t>(0u);
2342
2343 boost::ulong_long_type uu = u;
2344
2345 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)};
2346
2347 while (uu != static_cast<boost::ulong_long_type>(0u))
2348 {
2349 temp[i] = static_cast<boost::uint32_t>(uu % static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask));
2350 uu = static_cast<boost::ulong_long_type>(uu / static_cast<boost::ulong_long_type>(cpp_dec_float_elem_mask));
2351 ++i;
2352 }
2353
2354 if (i > static_cast<std::size_t>(1u))
2355 {
2356 exp += static_cast<ExponentType>((i - 1u) * static_cast<std::size_t>(cpp_dec_float_elem_digits10));
2357 }
2358
2359 std::reverse(temp, temp + i);
2360 std::copy(temp, temp + (std::min)(i, static_cast<std::size_t>(cpp_dec_float_elem_number)), data.begin());
2361 }
2362
2363 template <unsigned Digits10, class ExponentType, class Allocator>
mul_loop_uv(boost::uint32_t * const u,const boost::uint32_t * const v,const boost::int32_t p)2364 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)
2365 {
2366 //
2367 // There is a limit on how many limbs this algorithm can handle without dropping digits
2368 // due to overflow in the carry, it is:
2369 //
2370 // FLOOR( (2^64 - 1) / (10^8 * 10^8) ) == 1844
2371 //
2372 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.");
2373
2374 boost::uint64_t carry = static_cast<boost::uint64_t>(0u);
2375
2376 for (boost::int32_t j = static_cast<boost::int32_t>(p - 1u); j >= static_cast<boost::int32_t>(0); j--)
2377 {
2378 boost::uint64_t sum = carry;
2379
2380 for (boost::int32_t i = j; i >= static_cast<boost::int32_t>(0); i--)
2381 {
2382 sum += static_cast<boost::uint64_t>(u[j - i] * static_cast<boost::uint64_t>(v[i]));
2383 }
2384
2385 u[j] = static_cast<boost::uint32_t>(sum % static_cast<boost::uint32_t>(cpp_dec_float_elem_mask));
2386 carry = static_cast<boost::uint64_t>(sum / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask));
2387 }
2388
2389 return static_cast<boost::uint32_t>(carry);
2390 }
2391
2392 template <unsigned Digits10, class ExponentType, class Allocator>
mul_loop_n(boost::uint32_t * const u,boost::uint32_t n,const boost::int32_t p)2393 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)
2394 {
2395 boost::uint64_t carry = static_cast<boost::uint64_t>(0u);
2396
2397 // Multiplication loop.
2398 for (boost::int32_t j = p - 1; j >= static_cast<boost::int32_t>(0); j--)
2399 {
2400 const boost::uint64_t t = static_cast<boost::uint64_t>(carry + static_cast<boost::uint64_t>(u[j] * static_cast<boost::uint64_t>(n)));
2401 carry = static_cast<boost::uint64_t>(t / static_cast<boost::uint32_t>(cpp_dec_float_elem_mask));
2402 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)));
2403 }
2404
2405 return static_cast<boost::uint32_t>(carry);
2406 }
2407
2408 template <unsigned Digits10, class ExponentType, class Allocator>
div_loop_n(boost::uint32_t * const u,boost::uint32_t n,const boost::int32_t p)2409 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)
2410 {
2411 boost::uint64_t prev = static_cast<boost::uint64_t>(0u);
2412
2413 for (boost::int32_t j = static_cast<boost::int32_t>(0); j < p; j++)
2414 {
2415 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)));
2416 u[j] = static_cast<boost::uint32_t>(t / n);
2417 prev = static_cast<boost::uint64_t>(t - static_cast<boost::uint64_t>(n * static_cast<boost::uint64_t>(u[j])));
2418 }
2419
2420 return static_cast<boost::uint32_t>(prev);
2421 }
2422
2423 template <unsigned Digits10, class ExponentType, class Allocator>
pow2(const boost::long_long_type p)2424 cpp_dec_float<Digits10, ExponentType, Allocator> cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(const boost::long_long_type p)
2425 {
2426 // Create a static const table of p^2 for -128 < p < +128.
2427 // Note: The size of this table must be odd-numbered and
2428 // symmetric about 0.
2429 init.do_nothing();
2430 static const boost::array<cpp_dec_float<Digits10, ExponentType, Allocator>, 255u> p2_data =
2431 {{cpp_dec_float("5.877471754111437539843682686111228389093327783860437607543758531392086297273635864257812500000000000e-39"),
2432 cpp_dec_float("1.175494350822287507968736537222245677818665556772087521508751706278417259454727172851562500000000000e-38"),
2433 cpp_dec_float("2.350988701644575015937473074444491355637331113544175043017503412556834518909454345703125000000000000e-38"),
2434 cpp_dec_float("4.701977403289150031874946148888982711274662227088350086035006825113669037818908691406250000000000000e-38"),
2435 cpp_dec_float("9.403954806578300063749892297777965422549324454176700172070013650227338075637817382812500000000000000e-38"),
2436 cpp_dec_float("1.880790961315660012749978459555593084509864890835340034414002730045467615127563476562500000000000000e-37"),
2437 cpp_dec_float("3.761581922631320025499956919111186169019729781670680068828005460090935230255126953125000000000000000e-37"),
2438 cpp_dec_float("7.523163845262640050999913838222372338039459563341360137656010920181870460510253906250000000000000000e-37"),
2439 cpp_dec_float("1.504632769052528010199982767644474467607891912668272027531202184036374092102050781250000000000000000e-36"),
2440 cpp_dec_float("3.009265538105056020399965535288948935215783825336544055062404368072748184204101562500000000000000000e-36"),
2441 cpp_dec_float("6.018531076210112040799931070577897870431567650673088110124808736145496368408203125000000000000000000e-36"),
2442 cpp_dec_float("1.203706215242022408159986214115579574086313530134617622024961747229099273681640625000000000000000000e-35"),
2443 cpp_dec_float("2.407412430484044816319972428231159148172627060269235244049923494458198547363281250000000000000000000e-35"),
2444 cpp_dec_float("4.814824860968089632639944856462318296345254120538470488099846988916397094726562500000000000000000000e-35"),
2445 cpp_dec_float("9.629649721936179265279889712924636592690508241076940976199693977832794189453125000000000000000000000e-35"),
2446 cpp_dec_float("1.925929944387235853055977942584927318538101648215388195239938795566558837890625000000000000000000000e-34"),
2447 cpp_dec_float("3.851859888774471706111955885169854637076203296430776390479877591133117675781250000000000000000000000e-34"),
2448 cpp_dec_float("7.703719777548943412223911770339709274152406592861552780959755182266235351562500000000000000000000000e-34"),
2449 cpp_dec_float("1.540743955509788682444782354067941854830481318572310556191951036453247070312500000000000000000000000e-33"),
2450 cpp_dec_float("3.081487911019577364889564708135883709660962637144621112383902072906494140625000000000000000000000000e-33"),
2451 cpp_dec_float("6.162975822039154729779129416271767419321925274289242224767804145812988281250000000000000000000000000e-33"),
2452 cpp_dec_float("1.232595164407830945955825883254353483864385054857848444953560829162597656250000000000000000000000000e-32"),
2453 cpp_dec_float("2.465190328815661891911651766508706967728770109715696889907121658325195312500000000000000000000000000e-32"),
2454 cpp_dec_float("4.930380657631323783823303533017413935457540219431393779814243316650390625000000000000000000000000000e-32"),
2455 cpp_dec_float("9.860761315262647567646607066034827870915080438862787559628486633300781250000000000000000000000000000e-32"),
2456 cpp_dec_float("1.972152263052529513529321413206965574183016087772557511925697326660156250000000000000000000000000000e-31"),
2457 cpp_dec_float("3.944304526105059027058642826413931148366032175545115023851394653320312500000000000000000000000000000e-31"),
2458 cpp_dec_float("7.888609052210118054117285652827862296732064351090230047702789306640625000000000000000000000000000000e-31"),
2459 cpp_dec_float("1.577721810442023610823457130565572459346412870218046009540557861328125000000000000000000000000000000e-30"),
2460 cpp_dec_float("3.155443620884047221646914261131144918692825740436092019081115722656250000000000000000000000000000000e-30"),
2461 cpp_dec_float("6.310887241768094443293828522262289837385651480872184038162231445312500000000000000000000000000000000e-30"),
2462 cpp_dec_float("1.262177448353618888658765704452457967477130296174436807632446289062500000000000000000000000000000000e-29"),
2463 cpp_dec_float("2.524354896707237777317531408904915934954260592348873615264892578125000000000000000000000000000000000e-29"),
2464 cpp_dec_float("5.048709793414475554635062817809831869908521184697747230529785156250000000000000000000000000000000000e-29"),
2465 cpp_dec_float("1.009741958682895110927012563561966373981704236939549446105957031250000000000000000000000000000000000e-28"),
2466 cpp_dec_float("2.019483917365790221854025127123932747963408473879098892211914062500000000000000000000000000000000000e-28"),
2467 cpp_dec_float("4.038967834731580443708050254247865495926816947758197784423828125000000000000000000000000000000000000e-28"),
2468 cpp_dec_float("8.077935669463160887416100508495730991853633895516395568847656250000000000000000000000000000000000000e-28"),
2469 cpp_dec_float("1.615587133892632177483220101699146198370726779103279113769531250000000000000000000000000000000000000e-27"),
2470 cpp_dec_float("3.231174267785264354966440203398292396741453558206558227539062500000000000000000000000000000000000000e-27"),
2471 cpp_dec_float("6.462348535570528709932880406796584793482907116413116455078125000000000000000000000000000000000000000e-27"),
2472 cpp_dec_float("1.292469707114105741986576081359316958696581423282623291015625000000000000000000000000000000000000000e-26"),
2473 cpp_dec_float("2.584939414228211483973152162718633917393162846565246582031250000000000000000000000000000000000000000e-26"),
2474 cpp_dec_float("5.169878828456422967946304325437267834786325693130493164062500000000000000000000000000000000000000000e-26"),
2475 cpp_dec_float("1.033975765691284593589260865087453566957265138626098632812500000000000000000000000000000000000000000e-25"),
2476 cpp_dec_float("2.067951531382569187178521730174907133914530277252197265625000000000000000000000000000000000000000000e-25"),
2477 cpp_dec_float("4.135903062765138374357043460349814267829060554504394531250000000000000000000000000000000000000000000e-25"),
2478 cpp_dec_float("8.271806125530276748714086920699628535658121109008789062500000000000000000000000000000000000000000000e-25"),
2479 cpp_dec_float("1.654361225106055349742817384139925707131624221801757812500000000000000000000000000000000000000000000e-24"),
2480 cpp_dec_float("3.308722450212110699485634768279851414263248443603515625000000000000000000000000000000000000000000000e-24"),
2481 cpp_dec_float("6.617444900424221398971269536559702828526496887207031250000000000000000000000000000000000000000000000e-24"),
2482 cpp_dec_float("1.323488980084844279794253907311940565705299377441406250000000000000000000000000000000000000000000000e-23"),
2483 cpp_dec_float("2.646977960169688559588507814623881131410598754882812500000000000000000000000000000000000000000000000e-23"),
2484 cpp_dec_float("5.293955920339377119177015629247762262821197509765625000000000000000000000000000000000000000000000000e-23"),
2485 cpp_dec_float("1.058791184067875423835403125849552452564239501953125000000000000000000000000000000000000000000000000e-22"),
2486 cpp_dec_float("2.117582368135750847670806251699104905128479003906250000000000000000000000000000000000000000000000000e-22"),
2487 cpp_dec_float("4.235164736271501695341612503398209810256958007812500000000000000000000000000000000000000000000000000e-22"),
2488 cpp_dec_float("8.470329472543003390683225006796419620513916015625000000000000000000000000000000000000000000000000000e-22"),
2489 cpp_dec_float("1.694065894508600678136645001359283924102783203125000000000000000000000000000000000000000000000000000e-21"),
2490 cpp_dec_float("3.388131789017201356273290002718567848205566406250000000000000000000000000000000000000000000000000000e-21"),
2491 cpp_dec_float("6.776263578034402712546580005437135696411132812500000000000000000000000000000000000000000000000000000e-21"),
2492 cpp_dec_float("1.355252715606880542509316001087427139282226562500000000000000000000000000000000000000000000000000000e-20"),
2493 cpp_dec_float("2.710505431213761085018632002174854278564453125000000000000000000000000000000000000000000000000000000e-20"),
2494 cpp_dec_float("5.421010862427522170037264004349708557128906250000000000000000000000000000000000000000000000000000000e-20"),
2495 cpp_dec_float("1.084202172485504434007452800869941711425781250000000000000000000000000000000000000000000000000000000e-19"),
2496 cpp_dec_float("2.168404344971008868014905601739883422851562500000000000000000000000000000000000000000000000000000000e-19"),
2497 cpp_dec_float("4.336808689942017736029811203479766845703125000000000000000000000000000000000000000000000000000000000e-19"),
2498 cpp_dec_float("8.673617379884035472059622406959533691406250000000000000000000000000000000000000000000000000000000000e-19"),
2499 cpp_dec_float("1.734723475976807094411924481391906738281250000000000000000000000000000000000000000000000000000000000e-18"),
2500 cpp_dec_float("3.469446951953614188823848962783813476562500000000000000000000000000000000000000000000000000000000000e-18"),
2501 cpp_dec_float("6.938893903907228377647697925567626953125000000000000000000000000000000000000000000000000000000000000e-18"),
2502 cpp_dec_float("1.387778780781445675529539585113525390625000000000000000000000000000000000000000000000000000000000000e-17"),
2503 cpp_dec_float("2.775557561562891351059079170227050781250000000000000000000000000000000000000000000000000000000000000e-17"),
2504 cpp_dec_float("5.551115123125782702118158340454101562500000000000000000000000000000000000000000000000000000000000000e-17"),
2505 cpp_dec_float("1.110223024625156540423631668090820312500000000000000000000000000000000000000000000000000000000000000e-16"),
2506 cpp_dec_float("2.220446049250313080847263336181640625000000000000000000000000000000000000000000000000000000000000000e-16"),
2507 cpp_dec_float("4.440892098500626161694526672363281250000000000000000000000000000000000000000000000000000000000000000e-16"),
2508 cpp_dec_float("8.881784197001252323389053344726562500000000000000000000000000000000000000000000000000000000000000000e-16"),
2509 cpp_dec_float("1.776356839400250464677810668945312500000000000000000000000000000000000000000000000000000000000000000e-15"),
2510 cpp_dec_float("3.552713678800500929355621337890625000000000000000000000000000000000000000000000000000000000000000000e-15"),
2511 cpp_dec_float("7.105427357601001858711242675781250000000000000000000000000000000000000000000000000000000000000000000e-15"),
2512 cpp_dec_float("1.421085471520200371742248535156250000000000000000000000000000000000000000000000000000000000000000000e-14"),
2513 cpp_dec_float("2.842170943040400743484497070312500000000000000000000000000000000000000000000000000000000000000000000e-14"),
2514 cpp_dec_float("5.684341886080801486968994140625000000000000000000000000000000000000000000000000000000000000000000000e-14"),
2515 cpp_dec_float("1.136868377216160297393798828125000000000000000000000000000000000000000000000000000000000000000000000e-13"),
2516 cpp_dec_float("2.273736754432320594787597656250000000000000000000000000000000000000000000000000000000000000000000000e-13"),
2517 cpp_dec_float("4.547473508864641189575195312500000000000000000000000000000000000000000000000000000000000000000000000e-13"),
2518 cpp_dec_float("9.094947017729282379150390625000000000000000000000000000000000000000000000000000000000000000000000000e-13"),
2519 cpp_dec_float("1.818989403545856475830078125000000000000000000000000000000000000000000000000000000000000000000000000e-12"),
2520 cpp_dec_float("3.637978807091712951660156250000000000000000000000000000000000000000000000000000000000000000000000000e-12"),
2521 cpp_dec_float("7.275957614183425903320312500000000000000000000000000000000000000000000000000000000000000000000000000e-12"),
2522 cpp_dec_float("1.455191522836685180664062500000000000000000000000000000000000000000000000000000000000000000000000000e-11"),
2523 cpp_dec_float("2.910383045673370361328125000000000000000000000000000000000000000000000000000000000000000000000000000e-11"),
2524 cpp_dec_float("5.820766091346740722656250000000000000000000000000000000000000000000000000000000000000000000000000000e-11"),
2525 cpp_dec_float("1.164153218269348144531250000000000000000000000000000000000000000000000000000000000000000000000000000e-10"),
2526 cpp_dec_float("2.328306436538696289062500000000000000000000000000000000000000000000000000000000000000000000000000000e-10"),
2527 cpp_dec_float("4.656612873077392578125000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"),
2528 cpp_dec_float("9.313225746154785156250000000000000000000000000000000000000000000000000000000000000000000000000000000e-10"),
2529 cpp_dec_float("1.862645149230957031250000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"),
2530 cpp_dec_float("3.725290298461914062500000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"),
2531 cpp_dec_float("7.450580596923828125000000000000000000000000000000000000000000000000000000000000000000000000000000000e-9"),
2532 cpp_dec_float("1.490116119384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"),
2533 cpp_dec_float("2.980232238769531250000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"),
2534 cpp_dec_float("5.960464477539062500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-8"),
2535 cpp_dec_float("1.192092895507812500000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"),
2536 cpp_dec_float("2.384185791015625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"),
2537 cpp_dec_float("4.768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"),
2538 cpp_dec_float("9.536743164062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-7"),
2539 cpp_dec_float("1.907348632812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"),
2540 cpp_dec_float("3.814697265625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"),
2541 cpp_dec_float("7.629394531250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-6"),
2542 cpp_dec_float("0.000015258789062500000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2543 cpp_dec_float("0.000030517578125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2544 cpp_dec_float("0.000061035156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2545 cpp_dec_float("0.000122070312500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2546 cpp_dec_float("0.000244140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2547 cpp_dec_float("0.000488281250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2548 cpp_dec_float("0.000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2549 cpp_dec_float("0.001953125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2550 cpp_dec_float("0.003906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2551 cpp_dec_float("0.007812500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2552 cpp_dec_float("0.01562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2553 cpp_dec_float("0.03125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2554 cpp_dec_float("0.06250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"),
2555 cpp_dec_float("0.125"),
2556 cpp_dec_float("0.25"),
2557 cpp_dec_float("0.5"),
2558 one(),
2559 two(),
2560 cpp_dec_float(static_cast<boost::ulong_long_type>(4)),
2561 cpp_dec_float(static_cast<boost::ulong_long_type>(8)),
2562 cpp_dec_float(static_cast<boost::ulong_long_type>(16)),
2563 cpp_dec_float(static_cast<boost::ulong_long_type>(32)),
2564 cpp_dec_float(static_cast<boost::ulong_long_type>(64)),
2565 cpp_dec_float(static_cast<boost::ulong_long_type>(128)),
2566 cpp_dec_float(static_cast<boost::ulong_long_type>(256)),
2567 cpp_dec_float(static_cast<boost::ulong_long_type>(512)),
2568 cpp_dec_float(static_cast<boost::ulong_long_type>(1024)),
2569 cpp_dec_float(static_cast<boost::ulong_long_type>(2048)),
2570 cpp_dec_float(static_cast<boost::ulong_long_type>(4096)),
2571 cpp_dec_float(static_cast<boost::ulong_long_type>(8192)),
2572 cpp_dec_float(static_cast<boost::ulong_long_type>(16384)),
2573 cpp_dec_float(static_cast<boost::ulong_long_type>(32768)),
2574 cpp_dec_float(static_cast<boost::ulong_long_type>(65536)),
2575 cpp_dec_float(static_cast<boost::ulong_long_type>(131072)),
2576 cpp_dec_float(static_cast<boost::ulong_long_type>(262144)),
2577 cpp_dec_float(static_cast<boost::ulong_long_type>(524288)),
2578 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 20u)),
2579 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 21u)),
2580 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 22u)),
2581 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 23u)),
2582 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 24u)),
2583 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 25u)),
2584 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 26u)),
2585 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 27u)),
2586 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 28u)),
2587 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 29u)),
2588 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 30u)),
2589 cpp_dec_float(static_cast<boost::uint64_t>(1uL << 31u)),
2590 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 32u)),
2591 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 33u)),
2592 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 34u)),
2593 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 35u)),
2594 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 36u)),
2595 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 37u)),
2596 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 38u)),
2597 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 39u)),
2598 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 40u)),
2599 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 41u)),
2600 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 42u)),
2601 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 43u)),
2602 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 44u)),
2603 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 45u)),
2604 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 46u)),
2605 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 47u)),
2606 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 48u)),
2607 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 49u)),
2608 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 50u)),
2609 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 51u)),
2610 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 52u)),
2611 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 53u)),
2612 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 54u)),
2613 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 55u)),
2614 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 56u)),
2615 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 57u)),
2616 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 58u)),
2617 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 59u)),
2618 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 60u)),
2619 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 61u)),
2620 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 62u)),
2621 cpp_dec_float(static_cast<boost::uint64_t>(1uLL << 63u)),
2622 cpp_dec_float("1.844674407370955161600000000000000000000000000000000000000000000000000000000000000000000000000000000e19"),
2623 cpp_dec_float("3.689348814741910323200000000000000000000000000000000000000000000000000000000000000000000000000000000e19"),
2624 cpp_dec_float("7.378697629483820646400000000000000000000000000000000000000000000000000000000000000000000000000000000e19"),
2625 cpp_dec_float("1.475739525896764129280000000000000000000000000000000000000000000000000000000000000000000000000000000e20"),
2626 cpp_dec_float("2.951479051793528258560000000000000000000000000000000000000000000000000000000000000000000000000000000e20"),
2627 cpp_dec_float("5.902958103587056517120000000000000000000000000000000000000000000000000000000000000000000000000000000e20"),
2628 cpp_dec_float("1.180591620717411303424000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
2629 cpp_dec_float("2.361183241434822606848000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
2630 cpp_dec_float("4.722366482869645213696000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
2631 cpp_dec_float("9.444732965739290427392000000000000000000000000000000000000000000000000000000000000000000000000000000e21"),
2632 cpp_dec_float("1.888946593147858085478400000000000000000000000000000000000000000000000000000000000000000000000000000e22"),
2633 cpp_dec_float("3.777893186295716170956800000000000000000000000000000000000000000000000000000000000000000000000000000e22"),
2634 cpp_dec_float("7.555786372591432341913600000000000000000000000000000000000000000000000000000000000000000000000000000e22"),
2635 cpp_dec_float("1.511157274518286468382720000000000000000000000000000000000000000000000000000000000000000000000000000e23"),
2636 cpp_dec_float("3.022314549036572936765440000000000000000000000000000000000000000000000000000000000000000000000000000e23"),
2637 cpp_dec_float("6.044629098073145873530880000000000000000000000000000000000000000000000000000000000000000000000000000e23"),
2638 cpp_dec_float("1.208925819614629174706176000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
2639 cpp_dec_float("2.417851639229258349412352000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
2640 cpp_dec_float("4.835703278458516698824704000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
2641 cpp_dec_float("9.671406556917033397649408000000000000000000000000000000000000000000000000000000000000000000000000000e24"),
2642 cpp_dec_float("1.934281311383406679529881600000000000000000000000000000000000000000000000000000000000000000000000000e25"),
2643 cpp_dec_float("3.868562622766813359059763200000000000000000000000000000000000000000000000000000000000000000000000000e25"),
2644 cpp_dec_float("7.737125245533626718119526400000000000000000000000000000000000000000000000000000000000000000000000000e25"),
2645 cpp_dec_float("1.547425049106725343623905280000000000000000000000000000000000000000000000000000000000000000000000000e26"),
2646 cpp_dec_float("3.094850098213450687247810560000000000000000000000000000000000000000000000000000000000000000000000000e26"),
2647 cpp_dec_float("6.189700196426901374495621120000000000000000000000000000000000000000000000000000000000000000000000000e26"),
2648 cpp_dec_float("1.237940039285380274899124224000000000000000000000000000000000000000000000000000000000000000000000000e27"),
2649 cpp_dec_float("2.475880078570760549798248448000000000000000000000000000000000000000000000000000000000000000000000000e27"),
2650 cpp_dec_float("4.951760157141521099596496896000000000000000000000000000000000000000000000000000000000000000000000000e27"),
2651 cpp_dec_float("9.903520314283042199192993792000000000000000000000000000000000000000000000000000000000000000000000000e27"),
2652 cpp_dec_float("1.980704062856608439838598758400000000000000000000000000000000000000000000000000000000000000000000000e28"),
2653 cpp_dec_float("3.961408125713216879677197516800000000000000000000000000000000000000000000000000000000000000000000000e28"),
2654 cpp_dec_float("7.922816251426433759354395033600000000000000000000000000000000000000000000000000000000000000000000000e28"),
2655 cpp_dec_float("1.584563250285286751870879006720000000000000000000000000000000000000000000000000000000000000000000000e29"),
2656 cpp_dec_float("3.169126500570573503741758013440000000000000000000000000000000000000000000000000000000000000000000000e29"),
2657 cpp_dec_float("6.338253001141147007483516026880000000000000000000000000000000000000000000000000000000000000000000000e29"),
2658 cpp_dec_float("1.267650600228229401496703205376000000000000000000000000000000000000000000000000000000000000000000000e30"),
2659 cpp_dec_float("2.535301200456458802993406410752000000000000000000000000000000000000000000000000000000000000000000000e30"),
2660 cpp_dec_float("5.070602400912917605986812821504000000000000000000000000000000000000000000000000000000000000000000000e30"),
2661 cpp_dec_float("1.014120480182583521197362564300800000000000000000000000000000000000000000000000000000000000000000000e31"),
2662 cpp_dec_float("2.028240960365167042394725128601600000000000000000000000000000000000000000000000000000000000000000000e31"),
2663 cpp_dec_float("4.056481920730334084789450257203200000000000000000000000000000000000000000000000000000000000000000000e31"),
2664 cpp_dec_float("8.112963841460668169578900514406400000000000000000000000000000000000000000000000000000000000000000000e31"),
2665 cpp_dec_float("1.622592768292133633915780102881280000000000000000000000000000000000000000000000000000000000000000000e32"),
2666 cpp_dec_float("3.245185536584267267831560205762560000000000000000000000000000000000000000000000000000000000000000000e32"),
2667 cpp_dec_float("6.490371073168534535663120411525120000000000000000000000000000000000000000000000000000000000000000000e32"),
2668 cpp_dec_float("1.298074214633706907132624082305024000000000000000000000000000000000000000000000000000000000000000000e33"),
2669 cpp_dec_float("2.596148429267413814265248164610048000000000000000000000000000000000000000000000000000000000000000000e33"),
2670 cpp_dec_float("5.192296858534827628530496329220096000000000000000000000000000000000000000000000000000000000000000000e33"),
2671 cpp_dec_float("1.038459371706965525706099265844019200000000000000000000000000000000000000000000000000000000000000000e34"),
2672 cpp_dec_float("2.076918743413931051412198531688038400000000000000000000000000000000000000000000000000000000000000000e34"),
2673 cpp_dec_float("4.153837486827862102824397063376076800000000000000000000000000000000000000000000000000000000000000000e34"),
2674 cpp_dec_float("8.307674973655724205648794126752153600000000000000000000000000000000000000000000000000000000000000000e34"),
2675 cpp_dec_float("1.661534994731144841129758825350430720000000000000000000000000000000000000000000000000000000000000000e35"),
2676 cpp_dec_float("3.323069989462289682259517650700861440000000000000000000000000000000000000000000000000000000000000000e35"),
2677 cpp_dec_float("6.646139978924579364519035301401722880000000000000000000000000000000000000000000000000000000000000000e35"),
2678 cpp_dec_float("1.329227995784915872903807060280344576000000000000000000000000000000000000000000000000000000000000000e36"),
2679 cpp_dec_float("2.658455991569831745807614120560689152000000000000000000000000000000000000000000000000000000000000000e36"),
2680 cpp_dec_float("5.316911983139663491615228241121378304000000000000000000000000000000000000000000000000000000000000000e36"),
2681 cpp_dec_float("1.063382396627932698323045648224275660800000000000000000000000000000000000000000000000000000000000000e37"),
2682 cpp_dec_float("2.126764793255865396646091296448551321600000000000000000000000000000000000000000000000000000000000000e37"),
2683 cpp_dec_float("4.253529586511730793292182592897102643200000000000000000000000000000000000000000000000000000000000000e37"),
2684 cpp_dec_float("8.507059173023461586584365185794205286400000000000000000000000000000000000000000000000000000000000000e37"),
2685 cpp_dec_float("1.701411834604692317316873037158841057280000000000000000000000000000000000000000000000000000000000000e38")}};
2686
2687 if ((p > static_cast<boost::long_long_type>(-128)) && (p < static_cast<boost::long_long_type>(+128)))
2688 {
2689 return p2_data[static_cast<std::size_t>(p + ((p2_data.size() - 1u) / 2u))];
2690 }
2691 else
2692 {
2693 // Compute and return 2^p.
2694 if (p < static_cast<boost::long_long_type>(0))
2695 {
2696 return pow2(static_cast<boost::long_long_type>(-p)).calculate_inv();
2697 }
2698 else
2699 {
2700 cpp_dec_float<Digits10, ExponentType, Allocator> t;
2701 default_ops::detail::pow_imp(t, two(), p, mpl::true_());
2702 return t;
2703 }
2704 }
2705 }
2706
2707 template <unsigned Digits10, class ExponentType, class Allocator>
eval_add(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & o)2708 inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
2709 {
2710 result += o;
2711 }
2712 template <unsigned Digits10, class ExponentType, class Allocator>
eval_subtract(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & o)2713 inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
2714 {
2715 result -= o;
2716 }
2717 template <unsigned Digits10, class ExponentType, class Allocator>
eval_multiply(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & o)2718 inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
2719 {
2720 result *= o;
2721 }
2722 template <unsigned Digits10, class ExponentType, class Allocator>
eval_divide(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & o)2723 inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& o)
2724 {
2725 result /= o;
2726 }
2727
2728 template <unsigned Digits10, class ExponentType, class Allocator>
eval_add(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const boost::ulong_long_type & o)2729 inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o)
2730 {
2731 result.add_unsigned_long_long(o);
2732 }
2733 template <unsigned Digits10, class ExponentType, class Allocator>
eval_subtract(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const boost::ulong_long_type & o)2734 inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o)
2735 {
2736 result.sub_unsigned_long_long(o);
2737 }
2738 template <unsigned Digits10, class ExponentType, class Allocator>
eval_multiply(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const boost::ulong_long_type & o)2739 inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o)
2740 {
2741 result.mul_unsigned_long_long(o);
2742 }
2743 template <unsigned Digits10, class ExponentType, class Allocator>
eval_divide(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const boost::ulong_long_type & o)2744 inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const boost::ulong_long_type& o)
2745 {
2746 result.div_unsigned_long_long(o);
2747 }
2748
2749 template <unsigned Digits10, class ExponentType, class Allocator>
eval_add(cpp_dec_float<Digits10,ExponentType,Allocator> & result,boost::long_long_type o)2750 inline void eval_add(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o)
2751 {
2752 if (o < 0)
2753 result.sub_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
2754 else
2755 result.add_unsigned_long_long(o);
2756 }
2757 template <unsigned Digits10, class ExponentType, class Allocator>
eval_subtract(cpp_dec_float<Digits10,ExponentType,Allocator> & result,boost::long_long_type o)2758 inline void eval_subtract(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o)
2759 {
2760 if (o < 0)
2761 result.add_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
2762 else
2763 result.sub_unsigned_long_long(o);
2764 }
2765 template <unsigned Digits10, class ExponentType, class Allocator>
eval_multiply(cpp_dec_float<Digits10,ExponentType,Allocator> & result,boost::long_long_type o)2766 inline void eval_multiply(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o)
2767 {
2768 if (o < 0)
2769 {
2770 result.mul_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
2771 result.negate();
2772 }
2773 else
2774 result.mul_unsigned_long_long(o);
2775 }
2776 template <unsigned Digits10, class ExponentType, class Allocator>
eval_divide(cpp_dec_float<Digits10,ExponentType,Allocator> & result,boost::long_long_type o)2777 inline void eval_divide(cpp_dec_float<Digits10, ExponentType, Allocator>& result, boost::long_long_type o)
2778 {
2779 if (o < 0)
2780 {
2781 result.div_unsigned_long_long(boost::multiprecision::detail::unsigned_abs(o));
2782 result.negate();
2783 }
2784 else
2785 result.div_unsigned_long_long(o);
2786 }
2787
2788 template <unsigned Digits10, class ExponentType, class Allocator>
eval_convert_to(boost::ulong_long_type * result,const cpp_dec_float<Digits10,ExponentType,Allocator> & val)2789 inline void eval_convert_to(boost::ulong_long_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
2790 {
2791 *result = val.extract_unsigned_long_long();
2792 }
2793 template <unsigned Digits10, class ExponentType, class Allocator>
eval_convert_to(boost::long_long_type * result,const cpp_dec_float<Digits10,ExponentType,Allocator> & val)2794 inline void eval_convert_to(boost::long_long_type* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
2795 {
2796 *result = val.extract_signed_long_long();
2797 }
2798 template <unsigned Digits10, class ExponentType, class Allocator>
eval_convert_to(long double * result,const cpp_dec_float<Digits10,ExponentType,Allocator> & val)2799 inline void eval_convert_to(long double* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
2800 {
2801 *result = val.extract_long_double();
2802 }
2803 template <unsigned Digits10, class ExponentType, class Allocator>
eval_convert_to(double * result,const cpp_dec_float<Digits10,ExponentType,Allocator> & val)2804 inline void eval_convert_to(double* result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
2805 {
2806 *result = val.extract_double();
2807 }
2808
2809 //
2810 // Non member function support:
2811 //
2812 template <unsigned Digits10, class ExponentType, class Allocator>
eval_fpclassify(const cpp_dec_float<Digits10,ExponentType,Allocator> & x)2813 inline int eval_fpclassify(const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2814 {
2815 if ((x.isinf)())
2816 return FP_INFINITE;
2817 if ((x.isnan)())
2818 return FP_NAN;
2819 if (x.iszero())
2820 return FP_ZERO;
2821 return FP_NORMAL;
2822 }
2823
2824 template <unsigned Digits10, class ExponentType, class Allocator>
eval_abs(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & x)2825 inline void eval_abs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2826 {
2827 result = x;
2828 if (x.isneg())
2829 result.negate();
2830 }
2831
2832 template <unsigned Digits10, class ExponentType, class Allocator>
eval_fabs(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & x)2833 inline void eval_fabs(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2834 {
2835 result = x;
2836 if (x.isneg())
2837 result.negate();
2838 }
2839
2840 template <unsigned Digits10, class ExponentType, class Allocator>
eval_sqrt(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & x)2841 inline void eval_sqrt(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2842 {
2843 result = x;
2844 result.calculate_sqrt();
2845 }
2846
2847 template <unsigned Digits10, class ExponentType, class Allocator>
eval_floor(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & x)2848 inline void eval_floor(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2849 {
2850 result = x;
2851 if (!(x.isfinite)() || x.isint())
2852 {
2853 if ((x.isnan)())
2854 errno = EDOM;
2855 return;
2856 }
2857
2858 if (x.isneg())
2859 result -= cpp_dec_float<Digits10, ExponentType, Allocator>::one();
2860 result = result.extract_integer_part();
2861 }
2862
2863 template <unsigned Digits10, class ExponentType, class Allocator>
eval_ceil(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & x)2864 inline void eval_ceil(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2865 {
2866 result = x;
2867 if (!(x.isfinite)() || x.isint())
2868 {
2869 if ((x.isnan)())
2870 errno = EDOM;
2871 return;
2872 }
2873
2874 if (!x.isneg())
2875 result += cpp_dec_float<Digits10, ExponentType, Allocator>::one();
2876 result = result.extract_integer_part();
2877 }
2878
2879 template <unsigned Digits10, class ExponentType, class Allocator>
eval_trunc(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & x)2880 inline void eval_trunc(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x)
2881 {
2882 if (x.isint() || !(x.isfinite)())
2883 {
2884 result = x;
2885 if ((x.isnan)())
2886 errno = EDOM;
2887 return;
2888 }
2889 result = x.extract_integer_part();
2890 }
2891
2892 template <unsigned Digits10, class ExponentType, class Allocator>
eval_ilogb(const cpp_dec_float<Digits10,ExponentType,Allocator> & val)2893 inline ExponentType eval_ilogb(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
2894 {
2895 if (val.iszero())
2896 return (std::numeric_limits<ExponentType>::min)();
2897 if ((val.isinf)())
2898 return INT_MAX;
2899 if ((val.isnan)())
2900 #ifdef FP_ILOGBNAN
2901 return FP_ILOGBNAN;
2902 #else
2903 return INT_MAX;
2904 #endif
2905 // Set result, to the exponent of val:
2906 return val.order();
2907 }
2908 template <unsigned Digits10, class ExponentType, class Allocator, class ArgType>
eval_scalbn(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & val,ArgType e_)2909 inline void eval_scalbn(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& val, ArgType e_)
2910 {
2911 using default_ops::eval_multiply;
2912 const ExponentType e = static_cast<ExponentType>(e_);
2913 cpp_dec_float<Digits10, ExponentType, Allocator> t(1.0, e);
2914 eval_multiply(result, val, t);
2915 }
2916
2917 template <unsigned Digits10, class ExponentType, class Allocator, class ArgType>
eval_ldexp(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & x,ArgType e)2918 inline void eval_ldexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ArgType e)
2919 {
2920 const boost::long_long_type the_exp = static_cast<boost::long_long_type>(e);
2921
2922 if ((the_exp > (std::numeric_limits<ExponentType>::max)()) || (the_exp < (std::numeric_limits<ExponentType>::min)()))
2923 BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Exponent value is out of range.")));
2924
2925 result = x;
2926
2927 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)))
2928 result.div_unsigned_long_long(1ULL << static_cast<boost::long_long_type>(-the_exp));
2929 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)))
2930 result.mul_unsigned_long_long(1ULL << the_exp);
2931 else if (the_exp != static_cast<boost::long_long_type>(0))
2932 result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(e);
2933 }
2934
2935 template <unsigned Digits10, class ExponentType, class Allocator>
eval_frexp(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & x,ExponentType * e)2936 inline void eval_frexp(cpp_dec_float<Digits10, ExponentType, Allocator>& result, const cpp_dec_float<Digits10, ExponentType, Allocator>& x, ExponentType* e)
2937 {
2938 result = x;
2939
2940 if (result.iszero() || (result.isinf)() || (result.isnan)())
2941 {
2942 *e = 0;
2943 return;
2944 }
2945
2946 if (result.isneg())
2947 result.negate();
2948
2949 ExponentType t = result.order();
2950 BOOST_MP_USING_ABS
2951 if (abs(t) < ((std::numeric_limits<ExponentType>::max)() / 1000))
2952 {
2953 t *= 1000;
2954 t /= 301;
2955 }
2956 else
2957 {
2958 t /= 301;
2959 t *= 1000;
2960 }
2961
2962 result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t);
2963
2964 if (result.iszero() || (result.isinf)() || (result.isnan)())
2965 {
2966 // pow2 overflowed, slip the calculation up:
2967 result = x;
2968 if (result.isneg())
2969 result.negate();
2970 t /= 2;
2971 result *= cpp_dec_float<Digits10, ExponentType, Allocator>::pow2(-t);
2972 }
2973 BOOST_MP_USING_ABS
2974 if (abs(result.order()) > 5)
2975 {
2976 // If our first estimate doesn't get close enough then try recursion until we do:
2977 ExponentType e2;
2978 cpp_dec_float<Digits10, ExponentType, Allocator> r2;
2979 eval_frexp(r2, result, &e2);
2980 // overflow protection:
2981 if ((t > 0) && (e2 > 0) && (t > (std::numeric_limits<ExponentType>::max)() - e2))
2982 BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2."));
2983 if ((t < 0) && (e2 < 0) && (t < (std::numeric_limits<ExponentType>::min)() - e2))
2984 BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is too large to be represented as a power of 2."));
2985 t += e2;
2986 result = r2;
2987 }
2988
2989 while (result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::one()) >= 0)
2990 {
2991 result /= cpp_dec_float<Digits10, ExponentType, Allocator>::two();
2992 ++t;
2993 }
2994 while (result.compare(cpp_dec_float<Digits10, ExponentType, Allocator>::half()) < 0)
2995 {
2996 result *= cpp_dec_float<Digits10, ExponentType, Allocator>::two();
2997 --t;
2998 }
2999 *e = t;
3000 if (x.isneg())
3001 result.negate();
3002 }
3003
3004 template <unsigned Digits10, class ExponentType, class Allocator>
eval_frexp(cpp_dec_float<Digits10,ExponentType,Allocator> & result,const cpp_dec_float<Digits10,ExponentType,Allocator> & x,int * e)3005 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)
3006 {
3007 ExponentType t;
3008 eval_frexp(result, x, &t);
3009 if ((t > (std::numeric_limits<int>::max)()) || (t < (std::numeric_limits<int>::min)()))
3010 BOOST_THROW_EXCEPTION(std::runtime_error("Exponent is outside the range of an int"));
3011 *e = static_cast<int>(t);
3012 }
3013
3014 template <unsigned Digits10, class ExponentType, class Allocator>
eval_is_zero(const cpp_dec_float<Digits10,ExponentType,Allocator> & val)3015 inline bool eval_is_zero(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
3016 {
3017 return val.iszero();
3018 }
3019 template <unsigned Digits10, class ExponentType, class Allocator>
eval_get_sign(const cpp_dec_float<Digits10,ExponentType,Allocator> & val)3020 inline int eval_get_sign(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
3021 {
3022 return val.iszero() ? 0 : val.isneg() ? -1 : 1;
3023 }
3024
3025 template <unsigned Digits10, class ExponentType, class Allocator>
hash_value(const cpp_dec_float<Digits10,ExponentType,Allocator> & val)3026 inline std::size_t hash_value(const cpp_dec_float<Digits10, ExponentType, Allocator>& val)
3027 {
3028 return val.hash();
3029 }
3030
3031 } // namespace backends
3032
3033 using boost::multiprecision::backends::cpp_dec_float;
3034
3035 typedef number<cpp_dec_float<50> > cpp_dec_float_50;
3036 typedef number<cpp_dec_float<100> > cpp_dec_float_100;
3037
3038 #ifdef BOOST_NO_SFINAE_EXPR
3039
3040 namespace detail {
3041
3042 template <unsigned D1, class E1, class A1, unsigned D2, class E2, class A2>
3043 struct is_explicitly_convertible<cpp_dec_float<D1, E1, A1>, cpp_dec_float<D2, E2, A2> > : public mpl::true_
3044 {};
3045
3046 } // namespace detail
3047
3048 #endif
3049
3050 }} // namespace boost::multiprecision
3051
3052 namespace std {
3053 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3054 class numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >
3055 {
3056 public:
3057 BOOST_STATIC_CONSTEXPR bool is_specialized = true;
3058 BOOST_STATIC_CONSTEXPR bool is_signed = true;
3059 BOOST_STATIC_CONSTEXPR bool is_integer = false;
3060 BOOST_STATIC_CONSTEXPR bool is_exact = false;
3061 BOOST_STATIC_CONSTEXPR bool is_bounded = true;
3062 BOOST_STATIC_CONSTEXPR bool is_modulo = false;
3063 BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
3064 BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
3065 BOOST_STATIC_CONSTEXPR int digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
3066 BOOST_STATIC_CONSTEXPR int max_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_total_digits10;
3067 BOOST_STATIC_CONSTEXPR ExponentType min_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp; // Type differs from int.
3068 BOOST_STATIC_CONSTEXPR ExponentType min_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_min_exp10; // Type differs from int.
3069 BOOST_STATIC_CONSTEXPR ExponentType max_exponent = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp; // Type differs from int.
3070 BOOST_STATIC_CONSTEXPR ExponentType max_exponent10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_max_exp10; // Type differs from int.
3071 BOOST_STATIC_CONSTEXPR int radix = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_radix;
3072 BOOST_STATIC_CONSTEXPR std::float_round_style round_style = std::round_indeterminate;
3073 BOOST_STATIC_CONSTEXPR bool has_infinity = true;
3074 BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true;
3075 BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
3076 BOOST_STATIC_CONSTEXPR std::float_denorm_style has_denorm = std::denorm_absent;
3077 BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
3078 BOOST_STATIC_CONSTEXPR bool traps = false;
3079 BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
3080
3081 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)(); }
3082 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)(); }
lowest()3083 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(); }
epsilon()3084 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(); }
round_error()3085 BOOST_STATIC_CONSTEXPR boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> round_error() { return 0.5L; }
infinity()3086 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(); }
quiet_NaN()3087 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(); }
signaling_NaN()3088 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(); }
denorm_min()3089 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(); }
3090 };
3091
3092 #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
3093
3094 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3095 BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits;
3096 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3097 BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::digits10;
3098 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3099 BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_digits10;
3100 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3101 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_signed;
3102 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3103 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_integer;
3104 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3105 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_exact;
3106 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3107 BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::radix;
3108 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3109 BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent;
3110 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3111 BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::min_exponent10;
3112 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3113 BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent;
3114 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3115 BOOST_CONSTEXPR_OR_CONST ExponentType numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::max_exponent10;
3116 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3117 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_infinity;
3118 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3119 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_quiet_NaN;
3120 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3121 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_signaling_NaN;
3122 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3123 BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm;
3124 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3125 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::has_denorm_loss;
3126 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3127 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_iec559;
3128 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3129 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_bounded;
3130 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3131 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::is_modulo;
3132 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3133 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::traps;
3134 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3135 BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::tinyness_before;
3136 template <unsigned Digits10, class ExponentType, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
3137 BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates> >::round_style;
3138
3139 #endif
3140 } // namespace std
3141
3142 namespace boost {
3143 namespace math {
3144
3145 namespace policies {
3146
3147 template <unsigned Digits10, class ExponentType, class Allocator, class Policy, boost::multiprecision::expression_template_option ExpressionTemplates>
3148 struct precision<boost::multiprecision::number<boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>, ExpressionTemplates>, Policy>
3149 {
3150 // Define a local copy of cpp_dec_float_digits10 because it might differ
3151 // from the template parameter Digits10 for small or large digit counts.
3152 static const boost::int32_t cpp_dec_float_digits10 = boost::multiprecision::cpp_dec_float<Digits10, ExponentType, Allocator>::cpp_dec_float_digits10;
3153
3154 typedef typename Policy::precision_type precision_type;
3155 typedef digits2<((cpp_dec_float_digits10 + 1LL) * 1000LL) / 301LL> digits_2;
3156 typedef typename mpl::if_c<
3157 ((digits_2::value <= precision_type::value) || (Policy::precision_type::value <= 0)),
3158 // Default case, full precision for RealType:
3159 digits_2,
3160 // User customized precision:
3161 precision_type>::type type;
3162 };
3163
3164 }
3165
3166 }} // namespace boost::math::policies
3167
3168 #ifdef BOOST_MSVC
3169 #pragma warning(pop)
3170 #endif
3171
3172 #endif
3173