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adding the Kahan Challenge to the application mix
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| // harmonic_series.cpp: experiments with mixed-precision representations of the Harmonic Series | ||
| // | ||
| // Copyright (C) 2017 Stillwater Supercomputing, Inc. | ||
| // SPDX-License-Identifier: MIT | ||
| // | ||
| // This file is part of the UNIVERSAL project, which is released under an MIT Open Source license. | ||
| #include <universal/utility/directives.hpp> | ||
| #include <iostream> | ||
| #include <iomanip> | ||
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| #include <universal/number/posit/posit.hpp> | ||
| #include <universal/number/cfloat/cfloat.hpp> | ||
| #include <universal/number/dd/dd.hpp> | ||
| #include <universal/number/qd/qd.hpp> | ||
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| namespace sw { | ||
| namespace universal { | ||
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| template<typename Scalar> | ||
| Scalar E(Scalar z, bool verbose = false) { | ||
| using std::exp; | ||
| if (z == Scalar(0.0)) return Scalar(1.0); | ||
| Scalar e_of_z = exp(z); | ||
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| Scalar numerator = e_of_z - Scalar(1.0); | ||
| if (verbose) { | ||
| std::cout << "exp(" << z << ") = " << to_binary(e_of_z) << " : " << e_of_z << '\n'; | ||
| std::cout << "numerator = " << to_binary(numerator) << " : " << numerator << '\n'; | ||
| std::cout << "E(" << z << ") = " << to_binary(numerator / z) << " : " << numerator / z << '\n'; | ||
| } | ||
| return numerator / z; | ||
| } | ||
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| /// <summary> | ||
| /// sample the E function in the interval [-1.0, 1.0] | ||
| /// </summary> | ||
| /// <typeparam name="Scalar"></typeparam> | ||
| /// <param name="samples">nr of samples in the interval</param> | ||
| template<typename Scalar> | ||
| void sampleE(int samples) { | ||
| Scalar x{ -1.0 }; | ||
| Scalar dx = Scalar(2.0) / Scalar(samples); | ||
| for (int i = 0; i < samples; ++i) { | ||
| std::cout << std::setw(10) << i << " : " << x << " : " << E(x) << '\n'; | ||
| x += dx; | ||
| } | ||
| } | ||
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| template<typename Scalar> | ||
| Scalar Q(Scalar x, bool verbose = false) { | ||
| using std::sqrt, std::abs; | ||
| Scalar xsquare = x * x; | ||
| Scalar xsquare_plus_one = xsquare + Scalar(1.0); | ||
| Scalar sqrt_of_xsquare_plus_one = sqrt(xsquare_plus_one); | ||
| Scalar xplus = x + sqrt_of_xsquare_plus_one; | ||
| Scalar xminus = x - sqrt_of_xsquare_plus_one; | ||
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| Scalar abs_xminus = abs(xminus); | ||
| Scalar one_over_xplus = Scalar(1.0) / xplus; | ||
| Scalar q_of_x = abs_xminus - one_over_xplus; | ||
| if (verbose) { | ||
| std::cout << "1st term : " << to_binary(abs_xminus) << " : " << abs_xminus << '\n'; | ||
| std::cout << "2nd term : " << to_binary(one_over_xplus) << " : " << one_over_xplus << '\n'; | ||
| std::cout << "function : " << to_binary(q_of_x) << " : " << q_of_x << '\n'; | ||
| } | ||
| return q_of_x; | ||
| } | ||
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| /// <summary> | ||
| /// sample the Q function in the interval [-1.0, 1.0] | ||
| /// </summary> | ||
| /// <typeparam name="Scalar"></typeparam> | ||
| /// <param name="samples">nr of samples in the interval</param> | ||
| template<typename Scalar> | ||
| void sampleQ(int samples) { | ||
| Scalar x{ -1.0 }; | ||
| Scalar dx = Scalar(2.0) / Scalar(samples); | ||
| for (int i = 0; i < samples; ++i) { | ||
| std::cout << std::setw(10) << i << " : " << x << " : " << Q(x) << '\n'; | ||
| x += dx; | ||
| } | ||
| } | ||
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| template<typename Scalar> | ||
| Scalar H(Scalar x, bool verbose = false) { | ||
| Scalar q_of_x = Q(x, verbose); | ||
| Scalar qx_squared = q_of_x * q_of_x; | ||
| Scalar e_of_qx_squared = E(qx_squared, verbose); | ||
| if (verbose) { | ||
| std::cout << "Q(" << x << ") = " << to_binary(q_of_x) << " : " << q_of_x << '\n'; | ||
| std::cout << "Q(x)*Q(x) = " << to_binary(qx_squared) << " : " << qx_squared << '\n'; | ||
| std::cout << "E(Q^2) = " << to_binary(e_of_qx_squared) << " : " << e_of_qx_squared << '\n'; | ||
| } | ||
| return e_of_qx_squared; | ||
| } | ||
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| /// <summary> | ||
| /// sample the H function in the interval [-1.0, 1.0] | ||
| /// </summary> | ||
| /// <typeparam name="Scalar"></typeparam> | ||
| /// <param name="samples">nr of samples in the interval</param> | ||
| template<typename Scalar> | ||
| void sampleH(int samples) { | ||
| Scalar x{ -1.0 }; | ||
| Scalar dx = Scalar(2.0) / Scalar(samples); | ||
| for (int i = 0; i < samples; ++i) { | ||
| std::cout << std::setw(10) << i << " : " << x << " : " << H(x) << '\n'; | ||
| x += dx; | ||
| } | ||
| } | ||
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| template<typename Scalar> | ||
| void eval_H_at(Scalar x) { | ||
| std::cout << "H(" << x << ") = " << H(x) << '\n'; | ||
| } | ||
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| template<typename Scalar> | ||
| void sample_set() { | ||
| Scalar x{ 0.0 }; | ||
| std::cout << "Scalar = " << type_tag(x) << '\n'; | ||
| eval_H_at(Scalar(1.0f)); | ||
| eval_H_at(Scalar(15.0f)); | ||
| eval_H_at(Scalar(9999.0f)); | ||
| std::cout << '\n'; | ||
| } | ||
| } | ||
| } | ||
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| int main() | ||
| try { | ||
| using namespace sw::universal; | ||
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| //sampleE<float>(10); | ||
| //sampleQ<float>(10); | ||
| //sampleH<float>(10); | ||
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| sample_set<float>(); | ||
| sample_set<double>(); | ||
| sample_set<cfloat<128, 11>>(); | ||
| sample_set<cfloat<128, 11, std::uint32_t, true>>(); | ||
| sample_set<dd>(); | ||
| sample_set<qd>(); | ||
| sample_set<posit<256, 2>>(); | ||
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| // Question: why does double-double work, but cfloat<128.11,subnormals> not work? | ||
| std::cout << "Question: why does double-double work, but cfloat<128.11,subnormals> not work?\n"; | ||
| H(cfloat < 128, 11, std::uint32_t, true>{ 15.0f }, true); | ||
| H(dd{ 15.0f }, true); | ||
| } | ||
| catch(...) { | ||
| } | ||
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