More modernization

code_snippets/chapter12/chapter12.sh

@@ -1,6 +1,6 @@
 #!/usr/bin/env bash
 #
-#  Copyright Christopher Kormanyos 2023.
+#  Copyright Christopher Kormanyos 2023 - 2025.
 #  Distributed under the Boost Software License,
 #  Version 1.0. (See accompanying file LICENSE_1_0.txt
 #  or copy at http://www.boost.org/LICENSE_1_0.txt)
@@ -24,28 +24,44 @@ rm -f ./bin/*.*
 
 echo build snippets with GCC=$GCC STD=$STD
 
-$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_01-001_sinc_function.cpp         -o ./bin/chapter12_01-001_sinc_function.exe
-$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_04-001_ellint_1.cpp              -o ./bin/chapter12_04-001_ellint_1.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_01-001_area_of_circle.cpp        -o ./bin/chapter12_01-001_area_of_circle.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_01-002_sinc_function.cpp         -o ./bin/chapter12_01-002_sinc_function.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_02-001_numbers_pi.cpp            -o ./bin/chapter12_02-001_numbers_pi.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_02-002_area_of_circle.cpp        -o ./bin/chapter12_02-002_area_of_circle.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_02-003_zeta_three.cpp            -o ./bin/chapter12_02-003_zeta_three.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_03-001_elem_func_sin.cpp         -o ./bin/chapter12_03-001_elem_func_sin.exe
 $GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_04-001_tgamma.cpp                -o ./bin/chapter12_04-001_tgamma.exe
-$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_04-002_euler_gamma_approx.cpp    -o ./bin/chapter12_04-002_euler_gamma_approx.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_04-002_cyl_bessel_j.cpp          -o ./bin/chapter12_04-002_cyl_bessel_j.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_04-003_ellint_1.cpp              -o ./bin/chapter12_04-003_ellint_1.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_04-004_euler_gamma_approx.cpp    -o ./bin/chapter12_04-004_euler_gamma_approx.exe
 $GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_05-001_complex.cpp               -o ./bin/chapter12_05-001_complex.exe
-$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_05-002_complex_sinc_function.cpp -o ./bin/chapter12_05-002_complex_sinc_function.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_05-002_complex.cpp               -o ./bin/chapter12_05-002_complex.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_05-003_complex.cpp               -o ./bin/chapter12_05-003_complex.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_05-004_complex_sinc_function.cpp -o ./bin/chapter12_05-004_complex_sinc_function.exe
 $GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_06-001_constexpr_sine.cpp        -o ./bin/chapter12_06-001_constexpr_sine.exe
-$GCC -std=c++11 -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_06-002_constexpr_exp.cpp         -o ./bin/chapter12_06-002_constexpr_exp.exe
-$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_07-001_area_of_a_circle.cpp      -o ./bin/chapter12_07-001_area_of_a_circle.exe
-$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_07-002_derivative.cpp            -o ./bin/chapter12_07-002_derivative.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_07-001_derivative.cpp            -o ./bin/chapter12_07-001_derivative.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_07-002_deriv_quadratic.cpp       -o ./bin/chapter12_07-002_deriv_quadratic.exe
+$GCC -std=$STD  -Wall -Wextra -Wpedantic -Werror -O3 -m64 -fsanitize=address -fsanitize=shift -fsanitize=shift-exponent -fsanitize=shift-base -fsanitize=integer-divide-by-zero -fsanitize=null -fsanitize=signed-integer-overflow -fsanitize=bounds -fsanitize=alignment -fsanitize=float-divide-by-zero -fsanitize=float-cast-overflow -fsanitize=enum ./chapter12_07-003_integral_j2.cpp           -o ./bin/chapter12_07-003_integral_j2.exe
 
 ls -la \
-./bin/chapter12_01-001_sinc_function.exe            \
-./bin/chapter12_04-001_ellint_1.exe                 \
+./bin/chapter12_01-001_area_of_circle.exe           \
+./bin/chapter12_01-002_sinc_function.exe            \
+./bin/chapter12_02-001_numbers_pi.exe               \
+./bin/chapter12_02-002_area_of_circle.exe           \
+./bin/chapter12_02-003_zeta_three.exe               \
+./bin/chapter12_03-001_elem_func_sin.exe            \
 ./bin/chapter12_04-001_tgamma.exe                   \
-./bin/chapter12_04-002_euler_gamma_approx.exe       \
+./bin/chapter12_04-002_cyl_bessel_j.exe             \
+./bin/chapter12_04-003_ellint_1.exe                 \
+./bin/chapter12_04-004_euler_gamma_approx.exe       \
 ./bin/chapter12_05-001_complex.exe                  \
-./bin/chapter12_05-002_complex_sinc_function.exe    \
+./bin/chapter12_05-002_complex.exe                  \
+./bin/chapter12_05-003_complex.exe                  \
+./bin/chapter12_05-004_complex_sinc_function.exe    \
 ./bin/chapter12_06-001_constexpr_sine.exe           \
-./bin/chapter12_06-002_constexpr_exp.exe            \
-./bin/chapter12_07-001_area_of_a_circle.exe         \
-./bin/chapter12_07-002_derivative.exe
+./bin/chapter12_07-001_derivative.exe               \
+./bin/chapter12_07-002_deriv_quadratic.exe          \
+./bin/chapter12_07-003_integral_j2.exe
 
 result_ls=$?
 

code_snippets/chapter12/chapter12_01-001_area_of_circle.cpp

@@ -0,0 +1,33 @@
+///////////////////////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2025.
+//  Distributed under the Boost Software License,
+//  Version 1.0. (See accompanying file LICENSE_1_0.txt
+//  or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+
+// chapter12_01-001_area_of_circle.cpp
+
+#include <cmath>
+#include <format>
+#include <limits>
+#include <iomanip>
+#include <iostream>
+#include <numbers>
+#include <sstream>
+
+constexpr auto area_of_a_circle(float r) -> float
+{
+  return (std::numbers::pi_v<float> * r) * r;
+}
+
+auto main() -> int;
+
+auto main() -> int
+{
+  std::stringstream strm { };
+
+  strm << "area_of_a_circle(0.5F): " << std::fixed << std::setprecision(std::numeric_limits<float>::digits10) << area_of_a_circle(0.5F) << '\n';
+  strm << "area_of_a_circle(1.5F): " << std::fixed << std::setprecision(std::numeric_limits<float>::digits10) << area_of_a_circle(1.5F) << '\n';
+
+  std::cout << strm.str() << std::endl;
+}

code_snippets/chapter12/chapter12_01-001_sinc_function.cpp → code_snippets/chapter12/chapter12_01-002_sinc_function.cpp

@@ -1,18 +1,19 @@
 ///////////////////////////////////////////////////////////////////////////////
-//  Copyright Christopher Kormanyos 2017 - 2018.
+//  Copyright Christopher Kormanyos 2025.
 //  Distributed under the Boost Software License,
 //  Version 1.0. (See accompanying file LICENSE_1_0.txt
 //  or copy at http://www.boost.org/LICENSE_1_0.txt)
 //
 
-// chapter12_01-001_sinc_function.cpp
+// chapter12_01-002_sinc_function.cpp
 
 #include <cmath>
+#include <limits>
 #include <iomanip>
 #include <iostream>
-#include <limits>
+#include <sstream>
 
-float sinc(const float& x)
+auto sinc(const float& x) -> float
 {
   if(std::fabs(x) <
      std::numeric_limits<float>::epsilon())
@@ -36,20 +37,19 @@ float sinc(const float& x)
   }
 }
 
-int main()
+auto main() -> int;
+
+auto main() -> int
 {
-  // 1
-  std::cout << std::setprecision(std::numeric_limits<float>::digits10)
-            << sinc(1.0E-10F)
-            << std::endl;
-
-  // 0.999904
-  std::cout << std::setprecision(std::numeric_limits<float>::digits10)
-            << sinc(0.024F)
-            << std::endl;
-
-  // 0.664997
-  std::cout << std::setprecision(std::numeric_limits<float>::digits10)
-            << sinc(1.5F)
-            << std::endl;
+  std::stringstream strm { };
+
+  // N[Sin[1/64]/(1/64), 12]
+  // N[Sin[1/8]/(1/8), 12]
+  // N[Sin[5/4]/(5/4), 12]
+
+  strm << "sinc(0.015625F): " << std::fixed << std::setprecision(std::numeric_limits<float>::digits10) << sinc(0.0078125F) << '\n';
+  strm << "sinc(0.125F)   : " << std::fixed << std::setprecision(std::numeric_limits<float>::digits10) << sinc(0.125F) << '\n';
+  strm << "sinc(1.25F)    : " << std::fixed << std::setprecision(std::numeric_limits<float>::digits10) << sinc(1.25F) << '\n';
+
+  std::cout << strm.str() << std::endl;
 }

code_snippets/chapter12/chapter12_02-001_numbers_pi.cpp

@@ -0,0 +1,29 @@
+///////////////////////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2025.
+//  Distributed under the Boost Software License,
+//  Version 1.0. (See accompanying file LICENSE_1_0.txt
+//  or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+
+// chapter12_02-001_numbers_pi.cpp
+
+#include <limits>
+#include <iomanip>
+#include <iostream>
+#include <numbers>
+#include <sstream>
+
+auto main() -> int;
+
+auto main() -> int
+{
+  std::stringstream strm { };
+
+  constexpr float  pi_f = std::numbers::pi_v<float>;
+  constexpr double pi_d = std::numbers::pi_v<double>;
+
+  strm << "pi_f: " << std::fixed << std::setprecision(std::numeric_limits<float>::digits10) << pi_f << '\n';
+  strm << "pi_d: " << std::fixed << std::setprecision(std::numeric_limits<double>::digits10) << pi_d << '\n';
+
+  std::cout << strm.str() << std::endl;
+}

code_snippets/chapter12/chapter12_02-002_area_of_circle.cpp

@@ -0,0 +1,35 @@
+///////////////////////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2025.
+//  Distributed under the Boost Software License,
+//  Version 1.0. (See accompanying file LICENSE_1_0.txt
+//  or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+
+// chapter12_02-002_area_of_circle.cpp
+
+#include <cmath>
+#include <concepts>
+#include <limits>
+#include <iomanip>
+#include <iostream>
+#include <numbers>
+#include <sstream>
+
+template<typename T>
+requires std::floating_point<T>
+constexpr auto area_of_a_circle(T r) -> T
+{
+  return (std::numbers::pi_v<T> * r) * r;
+}
+
+auto main() -> int;
+
+auto main() -> int
+{
+  std::stringstream strm { };
+
+  strm << "area_of_a_circle(0.5F): " << std::fixed << std::setprecision(std::numeric_limits<float>::digits10)  << area_of_a_circle(0.5F) << '\n';
+  strm << "area_of_a_circle(1.5) : " << std::fixed << std::setprecision(std::numeric_limits<double>::digits10) << area_of_a_circle(1.5)  << '\n';
+
+  std::cout << strm.str() << std::endl;
+}

code_snippets/chapter12/chapter12_02-003_zeta_three.cpp

@@ -0,0 +1,36 @@
+///////////////////////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2025.
+//  Distributed under the Boost Software License,
+//  Version 1.0. (See accompanying file LICENSE_1_0.txt
+//  or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+
+// chapter12_02-003_zeta_three.cpp
+
+#include <concepts>
+#include <limits>
+#include <iomanip>
+#include <iostream>
+#include <numbers>
+#include <sstream>
+
+template<typename T>
+requires std::floating_point<T>
+constexpr T zeta_three_v =
+  T(1.2020569031'5959428539'9738161511'4499907650L);
+
+auto main() -> int;
+
+auto main() -> int
+{
+  std::stringstream strm { };
+
+  constexpr float  z3_f = zeta_three_v<float>;
+  constexpr double z3_d = zeta_three_v<double>;
+
+  strm << "z3_f: " << std::fixed << std::setprecision(std::numeric_limits<float>::digits10)  << z3_f << '\n';
+  strm << "z3_d: " << std::fixed << std::setprecision(std::numeric_limits<double>::digits10) << z3_d << '\n';
+
+  std::cout << strm.str() << std::endl;
+}
+

code_snippets/chapter12/chapter12_03-001_elem_func_sin.cpp

@@ -0,0 +1,27 @@
+///////////////////////////////////////////////////////////////////////////////
+//  Copyright Christopher Kormanyos 2025.
+//  Distributed under the Boost Software License,
+//  Version 1.0. (See accompanying file LICENSE_1_0.txt
+//  or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+
+// chapter12_03-001_elem_func_sin.cpp
+
+#include <cmath>
+#include <limits>
+#include <iomanip>
+#include <iostream>
+#include <sstream>
+
+auto main() -> int;
+
+auto main() -> int
+{
+  std::stringstream strm { };
+
+  const float s { std::sin(1.23F) };
+
+  strm << "s: " << std::fixed << std::setprecision(std::numeric_limits<float>::digits10) << s << '\n';
+
+  std::cout << strm.str() << std::endl;
+}