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/*
**************************************************************
* C++ Mathematical Expression Toolkit Library *
* *
* Simple Example 10 *
* Author: Arash Partow (1999-2024) *
* URL: https://www.partow.net/programming/exprtk/index.html *
* *
* Copyright notice: *
* Free use of the Mathematical Expression Toolkit Library is *
* permitted under the guidelines and in accordance with the *
* most current version of the MIT License. *
* https://www.opensource.org/licenses/MIT *
* SPDX-License-Identifier: MIT *
* *
**************************************************************
*/
#include <cmath>
#include <cstdio>
#include <string>
#include "exprtk.hpp"
template <typename T>
void newton_sqrt()
{
typedef exprtk::symbol_table<T> symbol_table_t;
typedef exprtk::expression<T> expression_t;
typedef exprtk::parser<T> parser_t;
typedef exprtk::function_compositor<T> compositor_t;
typedef typename compositor_t::function function_t;
T x = T(0);
symbol_table_t symbol_table;
symbol_table.add_constants();
symbol_table.add_variable("x",x);
compositor_t compositor(symbol_table);
compositor.add(
function_t("newton_sqrt")
.var("x")
.expression
(
" switch "
" { "
" case x < 0 : null; "
" case x == 0 : 0; "
" case x == 1 : 1; "
" default: "
" { "
" var z := 100; "
" var sqrt_x := x / 2; "
" repeat "
" if (equal(sqrt_x^2, x)) "
" break[sqrt_x]; "
" else "
" sqrt_x := (1 / 2) * (sqrt_x + (x / sqrt_x)); "
" until ((z -= 1) <= 0); "
" }; "
" } "
));
const std::string expression_str = "newton_sqrt(x)";
expression_t expression;
expression.register_symbol_table(symbol_table);
parser_t parser;
parser.compile(expression_str,expression);
for (std::size_t i = 0; i < 1000; ++i)
{
x = static_cast<T>(i);
const T result = expression.value();
const T real = std::sqrt(x);
const T error = std::abs(result - real);
printf("sqrt(%03d) - Result: %15.13f\tReal: %15.13f\tError: %18.16f\n",
static_cast<unsigned int>(i),
result,
real,
error);
}
}
int main()
{
newton_sqrt<double>();
return 0;
}
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