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* Update Jamfile.v2 * Update introduction.qbk * Update tutorial.qbk * Update tutorial_cpp_int.qbk * Update tutorial_gmp_int.qbk * Update tutorial_tommath.qbk * Update integer_examples.cpp * Update tutorial_cpp_bin_float.qbk * Update tutorial_cpp_dec_float.qbk * Update tutorial_gmp_float.qbk * Update tutorial_mpfr_float.qbk * Update tutorial_float128.qbk * Update tutorial_float_builtin_ctor.qbk * Update big_seventh.cpp * Update tutorial_float_eg.qbk * Update floating_point_examples.cpp * Update mpfr_precision.cpp * Update gauss_laguerre_quadrature.cpp * Update tutorial_interval_mpfi.qbk * Update tutorial_cpp_complex.qbk * Update tutorial_mpc_complex.qbk * Update tutorial_float128_complex.qbk * Update tutorial_complex_adaptor.qbk * Update tutorial_rational.qbk * Update tutorial_tommath_rational.qbk * Update tutorial_logged_adaptor.qbk * Update tutorial_debug_adaptor.qbk * Update tutorial_visualizers.qbk * Update tutorial_fwd.qbk * Update tutorial_conversions.qbk * Update tutorial_random.qbk * Update random_snips.cpp * Update tutorial_constexpr.qbk * Update tutorial_import_export.qbk * Update cpp_int_import_export.cpp * Update tutorial_mixed_precision.qbk * Update tutorial_variable_precision.qbk * Update scoped_precision_example.cpp * Update tutorial_numeric_limits.qbk * Update tutorial_numeric_limits.qbk * Update numeric_limits_snips.cpp * Update numeric_limits_snips.cpp * Update tutorial_numeric_limits.qbk * Update numeric_limits_snips.cpp * Update numeric_limits_snips.cpp * Update tutorial_io.qbk * Update reference_number.qbk * Update reference_cpp_bin_float.qbk * Update reference_cpp_double_fp_backend.qbk * Update reference_internal_support.qbk * Update reference_backend_requirements.qbk * Update performance.qbk * Update performance_overhead.qbk * Update performance_real_world.qbk * Update performance_integer_real_world.qbk * Update performance_rational_real_world.qbk * Update reference_number.qbk * Update tutorial_numeric_limits.qbk * Update reference_backend_requirements.qbk
73 lines
2.9 KiB
Plaintext
73 lines
2.9 KiB
Plaintext
[/
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Copyright 2011 - 2020 John Maddock.
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Copyright 2013 - 2019 Paul A. Bristow.
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Copyright 2013 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:perf Performance Comparison]
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In the beginning of the project and throughout,
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many performance analyses, counts of multiprecision-operations-per-second
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and the like have been performed.
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Some of these are already listed in the ensuing sections.
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We will now provide some general notes on performance, valid
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for all of the multiprecision backends, before the detailed
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benchmarks of the following sections.
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The header-only, library-independent Boost-licenses integer
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and floating-point backends including
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__cpp_int for multiprecision integers,
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__cpp_bin_float and __cpp_dec_float for multiprecision floating-point types
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are significantly slower than the world's fastest implementations
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generally agreed to be found in GMP/MPIR, MPFR and MPC (which are based on GMP).
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Complex types __cpp_complex that are synthesized from these types
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share similar relative performances.
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The backends which effectively wrap GMP/MPIR and MPFR
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retain the superior performance of the low-level big-number engines.
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When these are used (in association with at least some level of optimization)
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they achieve and retain the expected low-level performances.
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At low digit counts, however, it is noted that the performances of __cpp_int,
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__cpp_bin_float and __cpp_dec_float can actually meet or exceed
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those encountered for GMP/MPIR, MPFR, etc. The reason for this
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is because stack allocation and/or the use of fast container
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storage can actually out-perform the allocation mechanisms in
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GMP/MPIR, which dominate run-time costs at low digit counts.
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As digit counts rise above about 50 or so, however,
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GMP/MPIR performance steadily increases,
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and simultaneously increases beyond (in relation to)
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the performances of the Boost-licensed, self-written backends.
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At around a few hundred to several thousands of digits,
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factors of about two through five are observed,
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whereby GMP/MPIR-based calculations are (performance-wise)
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superior ones.
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At a few thousand decimal digits, the upper end of
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the Boost backends is reached. At the moment,
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advanced big-number multiplication schemes in the
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Boost-licensed, self-written backends is limited
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to school multiplication and Karatsuba multiplication.
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Higher-orders of Toom-Cook and FFT-based multiplication
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are not (yet) implemented. So it is not yet
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feasible to perform mega-digit calculations
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with the Boost-licensed, self-written backends,
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whereas these are readily possible with
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the GMP/MPIR and MPRF based backends.
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[include performance_overhead.qbk]
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[include performance_real_world.qbk]
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[include performance_integer_real_world.qbk]
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[include performance_rational_real_world.qbk]
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[include performance_float.qbk]
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[include performance_integer.qbk]
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[include performance_rational.qbk]
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[endsect]
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