60 lines
2.1 KiB
Plaintext
60 lines
2.1 KiB
Plaintext
[/
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Copyright 2021 John Maddock.
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Copyright 2021 Paul A. Bristow.
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Copyright 2021 Christopher Kormanyos.
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt).
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]
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[section:floatbuiltinctor Construction from Specific Values Without Precision Loss]
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Construction of multiprecision types from built-in floating-point types
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can lead to potentially unexpected, yet correct, results.
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Consider, for instance constructing an instance of `cpp_dec_float_50`
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from the literal built-in floating-point `double` value 11.1.
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#include <iomanip>
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#include <iostream>
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#include <limits>
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#include <boost/multiprecision/cpp_dec_float.hpp>
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int main()
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{
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using my_dec_100 = boost::multiprecision::cpp_dec_float_50;
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const my_dec_100 f11(11.1);
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// On a system with 64-bit double:
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// 11.09999999999999964472863211994990706443786621093750
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std::cout << std::setprecision(std::numeric_limits<my_dec_100>::digits10)
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<< std::fixed
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<< f11
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<< std::endl;
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}
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In this example, the system has a 64-bit built in `double` representation.
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The variable `f11` is initialized with the literal
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`double` value 11.1. Recall that built-in floating-point representations
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are based on successive binary fractional approximations.
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These are, in fact, very close approximations.
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But they are approximations nonetheless, having their built-in finite precision.
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For this reason,
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the full multiple precision value of the `double` approximation
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of 11.1 is given by the large value shown above. Observations show
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us that the value is reliable up to the approximate 15 decimal
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digit precision of built-in 64-bit `double` on this system.
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If the exact value of 11.1 is desired
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(within the wider precision of the multiprecision type),
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then construction from literal string or from a rational
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integral construction/division sequence should be used.
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const my_dec_100 f11_str("11.1");
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const my_dec_100 f11_n (my_dec_100(111) / 10);
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[endsect] [/section:floatbuiltinctor Construction from Built-In Floats]
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