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Merge pull request #268 from stillwater-sc/v3.49
non-saturating small cfloats using a block arithmetic abstraction
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@@ -2,7 +2,7 @@ name: CMake | |
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| on: | ||
| push: | ||
| branches: [ main ] | ||
| branches: [ v3.49 ] | ||
| pull_request: | ||
| branches: [ main ] | ||
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| file (GLOB SOURCES "./*.cpp") | ||
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| compile_all("true" "adaptive" "Applications/Oracles/Floating Point Arithmetic" "${SOURCES}") |
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| // double-double.cpp: experiments with double-double floating-point arithmetic | ||
| // | ||
| // Copyright (C) 2017-2021 Stillwater Supercomputing, Inc. | ||
| // | ||
| // This file is part of the universal numbers project, which is released under an MIT Open Source license. | ||
| #include <universal/utility/directives.hpp> | ||
| #include <limits> | ||
| #include <utility> | ||
| #if (__cplusplus == 202003L) || (_MSVC_LANG == 202003L) | ||
| #include <numbers> // high-precision numbers | ||
| #endif | ||
| #include <universal/utility/number_system_properties.hpp> //minmax_range etc. for native types | ||
| #include <universal/common/numeric_limits_utility.hpp> | ||
| #include <universal/verification/performance_runner.hpp> | ||
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| // select the number systems we would like to compare | ||
| #include <universal/number/fixpnt/fixpnt.hpp> | ||
| #include <universal/number/areal/areal.hpp> | ||
| #include <universal/number/cfloat/cfloat.hpp> | ||
| #include <universal/number/posit/posit.hpp> | ||
| #include <universal/number/lns/lns.hpp> | ||
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| /* | ||
| Definition of FAITHFUL arithmetic | ||
| For a t-digit number a and b, and op element {+,-,*,/}, let c = a op b exactly. | ||
| Suppose x and y are consecutive t-digit floating-point numbers with the same | ||
| sign as c such at |x| <= |c| < |y|. Then the floating-point arithmetic is | ||
| called faithful if fl(a op b) = x whenever c = x and fl(a op b) is either x or y | ||
| whenever c != x. | ||
| */ | ||
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| int main() | ||
| try { | ||
| using namespace sw::universal; | ||
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| std::cout << "Experiments with double-double floating-point arithmetic\n"; | ||
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| std::streamsize precision = std::cout.precision(); | ||
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| std::cout << std::setprecision(precision); | ||
| std::cout << std::endl; | ||
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| return EXIT_SUCCESS; | ||
| } | ||
| catch (char const* msg) { | ||
| std::cerr << "Caught ad-hoc exception: " << msg << std::endl; | ||
| return EXIT_FAILURE; | ||
| } | ||
| catch (const sw::universal::universal_arithmetic_exception& err) { | ||
| std::cerr << "Caught unexpected universal arithmetic exception: " << err.what() << std::endl; | ||
| return EXIT_FAILURE; | ||
| } | ||
| catch (const sw::universal::universal_internal_exception& err) { | ||
| std::cerr << "Caught unexpected universal internal exception: " << err.what() << std::endl; | ||
| return EXIT_FAILURE; | ||
| } | ||
| catch (std::runtime_error& err) { | ||
| std::cerr << "Caught unexpected runtime error: " << err.what() << std::endl; | ||
| return EXIT_FAILURE; | ||
| } | ||
| catch (...) { | ||
| std::cerr << "Caught unknown exception" << std::endl; | ||
| return EXIT_FAILURE; | ||
| } |
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| // priest.cpp: experiments with Douglas Priest arbitrary precision floating-point arithmetic | ||
| // | ||
| // Copyright (C) 2017-2021 Stillwater Supercomputing, Inc. | ||
| // | ||
| // This file is part of the universal numbers project, which is released under an MIT Open Source license. | ||
| #include <universal/utility/directives.hpp> | ||
| #include <limits> | ||
| #include <utility> | ||
| #if (__cplusplus == 202003L) || (_MSVC_LANG == 202003L) | ||
| #include <numbers> // high-precision numbers | ||
| #endif | ||
| #include <universal/utility/number_system_properties.hpp> //minmax_range etc. for native types | ||
| #include <universal/common/numeric_limits_utility.hpp> | ||
| #include <universal/verification/performance_runner.hpp> | ||
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| // select the number systems we would like to compare | ||
| #include <universal/number/fixpnt/fixpnt.hpp> | ||
| #include <universal/number/areal/areal.hpp> | ||
| #include <universal/number/cfloat/cfloat.hpp> | ||
| #include <universal/number/posit/posit.hpp> | ||
| #include <universal/number/lns/lns.hpp> | ||
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| /* | ||
| Definition of FAITHFUL arithmetic | ||
| For a t-digit number a and b, and op element {+,-,*,/}, let c = a op b exactly. | ||
| Suppose x and y are consecutive t-digit floating-point numbers with the same | ||
| sign as c such at |x| <= |c| < |y|. Then the floating-point arithmetic is | ||
| called faithful if fl(a op b) = x whenever c = x and fl(a op b) is either x or y | ||
| whenever c != x. | ||
| */ | ||
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| template<typename Real> | ||
| std::pair<Real, Real> SumErr(Real a, Real b) { | ||
| Real c, d, e, f, g, h; | ||
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| if (abs(a) < abs(b)) std::swap(a, b); | ||
| c = a + b; | ||
| e = c - a; | ||
| g = c - e; | ||
| h = g - a; | ||
| f = b - h; | ||
| d = f - e; | ||
| if (d + e != f) { | ||
| c = a, d = b; | ||
| } | ||
| return std::pair(c, d); | ||
| } | ||
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| template<typename Real> | ||
| std::pair<Real, Real> SumErrCorollary2(Real a, Real b) { | ||
| Real c, d, e; | ||
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| if (abs(a) < abs(b)) std::swap(a, b); | ||
| c = a + b; | ||
| e = c - a; | ||
| d = b - e; | ||
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| return std::pair(c, d); | ||
| } | ||
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| template<typename Real> | ||
| void TestSumErr() { | ||
| using namespace sw::universal; | ||
| using Float = sw::universal::cfloat<32, 8, uint32_t>; | ||
| Float fa, fb; | ||
| Real a, b, c, d; | ||
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| fa = 1.0f; | ||
| ++fa; | ||
| fb = 1.0f; | ||
| --fb; | ||
| a = float(fa); | ||
| b = float(fb); | ||
| auto result = SumErr(a, b); | ||
| c = result.first; | ||
| d = result.second; | ||
| std::cout << c << " + " << d << " = " << a << " + " << b << '\n'; | ||
| std::cout << to_binary(c) << " : " << to_binary(a + b) << '\n'; | ||
| std::cout << to_binary(d) << '\n'; | ||
| std::cout << "a : " << to_binary(a) << '\n'; | ||
| std::cout << "b : " << to_binary(b) << '\n'; | ||
| std::cout << "c : " << to_binary(c) << '\n'; | ||
| std::cout << "d : " << to_binary(d) << '\n'; | ||
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| std::cout << "Corollary2: simplified\n"; | ||
| result = SumErrCorollary2(a, b); | ||
| c = result.first; | ||
| d = result.second; | ||
| std::cout << c << " + " << d << " = " << a << " + " << b << '\n'; | ||
| std::cout << to_binary(c) << " : " << to_binary(a + b) << '\n'; | ||
| std::cout << to_binary(d) << '\n'; | ||
| std::cout << "a : " << to_binary(a) << '\n'; | ||
| std::cout << "b : " << to_binary(b) << '\n'; | ||
| std::cout << "c : " << to_binary(c) << '\n'; | ||
| std::cout << "d : " << to_binary(d) << '\n'; | ||
| } | ||
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| template<typename Real> | ||
| std::pair<Real, Real> split(Real x, unsigned k) { | ||
| using namespace sw::universal; | ||
| unsigned t = ieee754_parameter<Real>::fbits; | ||
| Real a_k = static_cast<Real>((1ull << (t - k)) + 1); | ||
| Real y = a_k * x; | ||
| Real z = y - x; | ||
| Real xp = y - z; | ||
| Real xpp = x - xp; | ||
| return std::pair(xp, xpp); | ||
| } | ||
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| int main() | ||
| try { | ||
| using namespace sw::universal; | ||
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| std::cout << "Douglas Priest arbitrary precision arithmetic experiments\n"; | ||
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| using Sngle = float; | ||
| using Longd = long double; | ||
| using Fixed = fixpnt<32,16>; | ||
| using Posit = posit<32,2>; | ||
| using Float = cfloat<32, 8, uint32_t>; | ||
| using Areal = areal<32, 8, uint32_t>; | ||
| using Lns = lns<32, uint32_t>; | ||
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| std::streamsize precision = std::cout.precision(); | ||
| std::cout << std::setprecision(std::numeric_limits<Longd>::max_digits10); | ||
| std::cout << "float digits of precision : " << std::numeric_limits<float>::max_digits10 << '\n'; | ||
| std::cout << "double digits of precision : " << std::numeric_limits<double>::max_digits10 << '\n'; | ||
| std::cout << "long double digits of precision : " << std::numeric_limits<Longd>::max_digits10 << '\n'; | ||
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| TestSumErr<float>(); | ||
| TestSumErr<double>(); | ||
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| std::cout << "\nSplitting of a floating-point value\n"; | ||
| Float fa{ 1.875f + 0.0625f + 0.03125f }; | ||
| ++fa; | ||
| float x = float(fa); | ||
| for (unsigned k = 1; k < 10; ++k) { | ||
| auto xs = split(x, k); | ||
| float xp = xs.first; | ||
| float xpp = xs.second; | ||
| std::cout << "x : " << to_binary(x) << " : " << x << '\n'; | ||
| std::cout << "x' : " << to_binary(xp) << " : " << xp << '\n'; | ||
| std::cout << "x'' : " << to_binary(xpp) << " : " << xpp << '\n'; | ||
| } | ||
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| std::cout << std::setprecision(precision); | ||
| std::cout << std::endl; | ||
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| return EXIT_SUCCESS; | ||
| } | ||
| catch (char const* msg) { | ||
| std::cerr << "Caught ad-hoc exception: " << msg << std::endl; | ||
| return EXIT_FAILURE; | ||
| } | ||
| catch (const sw::universal::universal_arithmetic_exception& err) { | ||
| std::cerr << "Caught unexpected universal arithmetic exception: " << err.what() << std::endl; | ||
| return EXIT_FAILURE; | ||
| } | ||
| catch (const sw::universal::universal_internal_exception& err) { | ||
| std::cerr << "Caught unexpected universal internal exception: " << err.what() << std::endl; | ||
| return EXIT_FAILURE; | ||
| } | ||
| catch (std::runtime_error& err) { | ||
| std::cerr << "Caught unexpected runtime error: " << err.what() << std::endl; | ||
| return EXIT_FAILURE; | ||
| } | ||
| catch (...) { | ||
| std::cerr << "Caught unknown exception" << std::endl; | ||
| return EXIT_FAILURE; | ||
| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,3 +1,3 @@ | ||
| file (GLOB SOURCES "./*.cpp") | ||
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| compile_all("true" "blas" "Applications/Basic Linear Algebra" "${SOURCES}") | ||
| compile_all("true" "blas" "Applications/Reproducibility/Basic Linear Algebra" "${SOURCES}") |
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