1 // Copyright John Maddock 2016
2 // Copyright Christopher Kormanyos 2016.
3 // Copyright Paul A. Bristow 2016.
4
5 // Use, modification and distribution are subject to the
6 // Boost Software License, Version 1.0. (See accompanying file
7 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
8
9 // Contains Quickbook snippets as C++ comments - do not remove.
10
11 // http://gcc.gnu.org/onlinedocs/libquadmath/ GCC Quad-Precision Math Library
12 // https://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format
13
14 // https://gcc.gnu.org/onlinedocs/gcc/C_002b_002b-Dialect-Options.html#C_002b_002b-Dialect-Options GNU 3.5 Options Controlling C++ Dialect
15 // https://gcc.gnu.org/onlinedocs/gcc/C-Dialect-Options.html#C-Dialect-Options 3.4 Options Controlling C Dialect
16
17 //[float128_includes_1
18
19 #include <boost/cstdfloat.hpp> // For float_64_t, float128_t. Must be first include!
20 //#include <boost/config.hpp>
21 #include <boost/multiprecision/float128.hpp>
22 #include <boost/math/special_functions.hpp> // For gamma function.
23 #include <boost/math/constants/constants.hpp> // For constants pi, e ...
24 #include <typeinfo> //
25
26 #include <cmath> // for pow function.
27
28 // #include <quadmath.h>
29 // C:\program files\gcc-6-win64\lib\gcc\x86_64-w64-mingw32\6.1.1\include\quadmath.h
30
31 // i:\modular-boost\boost\multiprecision\float128.hpp|210| undefined reference to `quadmath_snprintf'.
32
33 //] [/float128_includes_1]
34
35 //[float128_dialect_1
36 /*`To make float128 available it is vital to get the dialect and options on the command line correct.
37
38 Quad type is forbidden by all the strict C++ standards, so using or adding -std=c++11 and later standards will prevent its use.
39 so explicitly use -std=gnu++11, 1y, 14, 17, or 1z or ...
40
41 For GCC 6.1.1, for example, the default is if no C++ language dialect options are given, is -std=gnu++14.
42
43 See https://gcc.gnu.org/onlinedocs/gcc/C-Dialect-Options.html#C-Dialect-Options
44 https://gcc.gnu.org/onlinedocs/gcc/Standards.html#Standards 2 Language Standards Supported by GCC
45
46 g++.exe -Wall -fexceptions -std=gnu++17 -g -fext-numeric-literals -fpermissive -lquadmath
47 -II:\modular-boost\libs\math\include -Ii:\modular-boost -c J:\Cpp\float128\float128\float128_example.cpp -o obj\Debug\float128_example.o
48
49 Requires GCC linker option -lquadmath
50
51 If this is missing, then get errors like:
52
53 \modular-boost\boost\multiprecision\float128.hpp|210|undefined reference to `quadmath_snprintf'|
54 \modular-boost\boost\multiprecision\float128.hpp|351|undefined reference to `sqrtq'|
55
56 Requires compile option
57
58 -fext-numeric-literals
59
60 If missing, then get errors like:
61
62 \modular-boost\libs\math\include/boost/math/cstdfloat/cstdfloat_types.hpp:229:43: error: unable to find numeric literal operator 'operator""Q'
63
64 A successful build log was:
65
66 g++.exe -Wall -std=c++11 -fexceptions -std=gnu++17 -g -fext-numeric-literals -II:\modular-boost\libs\math\include -Ii:\modular-boost -c J:\Cpp\float128\float128\float128_example.cpp -o obj\Debug\float128_example.o
67 g++.exe -o bin\Debug\float128.exe obj\Debug\float128_example.o -lquadmath
68 */
69
70 //] [/float128_dialect_1]
71
show_versions(std::string title)72 void show_versions(std::string title)
73 {
74 std::cout << title << std::endl;
75
76 std::cout << "Platform: " << BOOST_PLATFORM << '\n'
77 << "Compiler: " << BOOST_COMPILER << '\n'
78 << "STL : " << BOOST_STDLIB << '\n'
79 << "Boost : " << BOOST_VERSION / 100000 << "."
80 << BOOST_VERSION / 100 % 1000 << "."
81 << BOOST_VERSION % 100
82 << std::endl;
83 #ifdef _MSC_VER
84 std::cout << "_MSC_FULL_VER = " << _MSC_FULL_VER << std::endl; // VS 2015 190023026
85 #if defined _M_IX86
86 std::cout << "(x86)" << std::endl;
87 #endif
88 #if defined _M_X64
89 std::cout << " (x64)" << std::endl;
90 #endif
91 #if defined _M_IA64
92 std::cout << " (Itanium)" << std::endl;
93 #endif
94 // Something very wrong if more than one is defined (so show them in all just in case)!
95 #endif // _MSC_VER
96 #ifdef __GNUC__
97 //PRINT_MACRO(__GNUC__);
98 //PRINT_MACRO(__GNUC_MINOR__);
99 //PRINT_MACRO(__GNUC_PATCH__);
100 std::cout << "GCC " << __VERSION__ << std::endl;
101 //PRINT_MACRO(LONG_MAX);
102 #endif // __GNUC__
103 return;
104 } // void show_version(std::string title)
105
main()106 int main()
107 {
108 try
109 {
110
111 //[float128_example_3
112 // Always use try'n'catch blocks to ensure any error messages are displayed.
113 //`Ensure that all possibly significant digits (17) including trailing zeros are shown.
114
115 std::cout.precision(std::numeric_limits<boost::float64_t>::max_digits10);
116 std::cout.setf(std::ios::showpoint); // Show all significant trailing zeros.
117 //] [/ float128_example_3]
118
119 #ifdef BOOST_FLOAT128_C
120 std::cout << "Floating-point type boost::float128_t is available." << std::endl;
121 std::cout << " std::numeric_limits<boost::float128_t>::digits10 == "
122 << std::numeric_limits<boost::float128_t>::digits10 << std::endl;
123 std::cout << " std::numeric_limits<boost::float128_t>::max_digits10 == "
124 << std::numeric_limits<boost::float128_t>::max_digits10 << std::endl;
125 #else
126 std::cout << "Floating-point type boost::float128_t is NOT available." << std::endl;
127 #endif
128
129 show_versions("");
130
131 using boost::multiprecision::float128; // Wraps, for example, __float128 or _Quad.
132 // or
133 //using namespace boost::multiprecision;
134
135 std::cout.precision(std::numeric_limits<float128>::max_digits10); // Show all potentially meaningful digits.
136 std::cout.setf(std::ios::showpoint); // Show all significant trailing zeros.
137
138 // float128 pi0 = boost::math::constants::pi(); // Compile fails - need to specify a type for the constant!
139
140 float128 pi1 = boost::math::constants::pi<float128>(); // Returns a constant of type float128.
141 std::cout << sqrt(pi1) << std::endl; // 1.77245385090551602729816748334114514
142
143 float128 pi2 = boost::math::constants::pi<__float128>(); // Constant of type __float128 gets converted to float128 on the assignment.
144 std::cout << sqrt(pi2) << std::endl; // 1.77245385090551602729816748334114514
145
146 // DIY decimal digit literal constant, with suffix Q.
147 float128 pi3 = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348Q;
148 std::cout << sqrt(pi3) << std::endl; // 1.77245385090551602729816748334114514
149
150 // Compare to ready-rolled sqrt(pi) constant from Boost.Math:
151 std::cout << boost::math::constants::root_pi<float128>() << std::endl; // 1.77245385090551602729816748334114514
152
153 // DIY decimal digit literal constant, without suffix Q, suffering seventeen silent digits loss of precision!
154 float128 pi4 = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348;
155 std::cout << sqrt(pi4) << std::endl; // 1.77245385090551599275151910313924857
156
157 // float128 variables constructed from a quad-type literal can be declared constexpr if required:
158
159 #ifndef BOOST_NO_CXX11_CONSTEXPR
160 constexpr float128 pi_constexpr = 3.1415926535897932384626433832795028841971693993751058Q;
161 #endif
162 std::cout << pi_constexpr << std::endl; // 3.14159265358979323846264338327950280
163
164 // But sadly functions like sqrt are not yet available constexpr for float128.
165
166 // constexpr float128 root_pi_constexpr = sqrt(pi_constexpr); // Fails - not constexpr (yet).
167 // constexpr float128 root_pi_constexpr = std::sqrt(pi_constexpr); // Fails - no known conversion for argument 1 from 'const float128'.
168 // constexpr float128 root_pi_constexpr = sqrt(pi_constexpr); // Call to non-constexpr
169 // constexpr float128 root_pi_constexpr = boost::math::constants::root_pi(); // Missing type for constant.
170
171 // Best current way to get a constexpr is to use a Boost.Math constant if one is available.
172 constexpr float128 root_pi_constexpr = boost::math::constants::root_pi<float128>();
173 std::cout << root_pi_constexpr << std::endl; // 1.77245385090551602729816748334114514
174
175 // Note that casts within the sqrt call are NOT NEEDED (nor allowed),
176 // since all the variables are the correct type to begin with.
177 // std::cout << sqrt<float128>(pi3) << std::endl;
178 // But note examples of catastrophic (but hard to see) loss of precision below.
179
180 // Note also that the library functions, here sqrt, is NOT defined using std::sqrt,
181 // so that the correct overload is found using Argument Dependent LookUp (ADL).
182
183 float128 ee = boost::math::constants::e<float128>();
184 std::cout << ee << std::endl; // 2.71828182845904523536028747135266231
185
186 float128 e1 = exp(1.Q); // Note argument to exp is type float128.
187 std::cout << e1 << std::endl; // 2.71828182845904523536028747135266231
188
189 // Beware - it is all too easy to silently get a much lower precision by mistake.
190
191 float128 e1d = exp(1.); // Caution - only double 17 decimal digits precision!
192 std::cout << e1d << std::endl; // 2.71828182845904509079559829842764884
193
194 float128 e1i = exp(1); // Caution int promoted to double so only 17 decimal digits precision!
195 std::cout << e1i << std::endl; // 2.71828182845904509079559829842764884
196
197 float f1 = 1.F;
198 float128 e1f = exp(f1); // Caution float so only 6 decimal digits precision out of 36!
199 std::cout << e1f << std::endl; // 2.71828174591064453125000000000000000
200
201 // In all these cases you get what you asked for and not what you expected or wanted.
202
203 // Casting is essential if you start with a lower precision type.
204
205 float128 e1q = exp(static_cast<float128>(f1)); // Full 36 decimal digits precision!
206 std::cout << e1q << std::endl; // 2.71828182845904523536028747135266231
207
208 float128 e1qc = exp((float128)f1); // Full 36 decimal digits precision!
209 std::cout << e1qc << std::endl; // 2.71828182845904523536028747135266231
210
211 float128 e1qcc = exp(float128(f1)); // Full 36 decimal digits precision!
212 std::cout << e1qcc << std::endl; // 2.71828182845904523536028747135266231
213
214 //float128 e1q = exp<float128>(1.); // Compile fails.
215 // std::cout << e1q << std::endl; //
216
217 // http://en.cppreference.com/w/cpp/language/typeid
218 // The name()is implementation-dependent mangled, and may not be able to be output.
219 // The example showing output using one of the implementations where type_info::name prints full type names;
220 // filter through c++filt -t if using gcc or similar.
221
222 //[float128_type_info
223 const std::type_info& tifu128 = typeid(__float128); // OK.
224 //std::cout << tifu128.name() << std::endl; // On GCC, aborts (because not printable string).
225 //std::cout << typeid(__float128).name() << std::endl; // Aborts -
226 // string name cannot be output.
227
228 const std::type_info& tif128 = typeid(float128); // OK.
229 std::cout << tif128.name() << std::endl; // OK.
230 std::cout << typeid(float128).name() << std::endl; // OK.
231
232 const std::type_info& tpi = typeid(pi1); // OK using GCC 6.1.1.
233 // (from GCC 5 according to http://gcc.gnu.org/bugzilla/show_bug.cgi?id=43622)
234 std::cout << tpi.name() << std::endl; // OK, Output implementation-dependent mangled name:
235
236 // N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
237
238 //] [/float128_type_info]
239
240 }
241 catch (std::exception ex)
242 { // Display details about why any exceptions are thrown.
243 std::cout << "Thrown exception " << ex.what() << std::endl;
244 }
245 } // int main()
246
247 /*
248 [float128_output
249
250 -std=c++11 or -std=c++17 don't work
251
252 Floating-point type boost::float128_t is NOT available.
253
254 Platform: Win32
255 Compiler: GNU C++ version 6.1.1 20160609
256 STL : GNU libstdc++ version 20160609
257 Boost : 1.62.0
258 GCC 6.1.1 20160609
259
260
261 Added -fext-numeric-literals to
262
263 -std=gnu++11 -fext-numeric-literals -lquadmath
264
265 Floating-point type boost::float128_t is available.
266 std::numeric_limits<boost::float128_t>::digits10 == 33
267 std::numeric_limits<boost::float128_t>::max_digits10 == 36
268
269 Platform: Win32
270 Compiler: GNU C++ version 6.1.1 20160609
271 STL : GNU libstdc++ version 20160609
272 Boost : 1.62.0
273 GCC 6.1.1 20160609
274 1.77245385090551602729816748334114514
275 1.77245385090551602729816748334114514
276 1.77245385090551602729816748334114514
277 1.77245385090551602729816748334114514
278 N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
279 N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
280 N5boost14multiprecision6numberINS0_8backends16float128_backendELNS0_26expression_template_optionE0EEE
281
282 Process returned 0 (0x0) execution time : 0.033 s
283 Press any key to continue.
284
285
286
287 //] [/float128_output]
288
289 */
290