src/functions.f90

   1 ! Copyright 2019 Wojciech Kosior
   2
   3 ! This is free and unencumbered software released into the public domain.
   4
   5 ! Anyone is free to copy, modify, publish, use, compile, sell, or
   6 ! distribute this software, either in source code form or as a compiled
   7 ! binary, for any purpose, commercial or non-commercial, and by any
   8 ! means.
   9
  10 ! In jurisdictions that recognize copyright laws, the author or authors
  11 ! of this software dedicate any and all copyright interest in the
  12 ! software to the public domain. We make this dedication for the benefit
  13 ! of the public at large and to the detriment of our heirs and
  14 ! successors. We intend this dedication to be an overt act of
  15 ! relinquishment in perpetuity of all present and future rights to this
  16 ! software under copyright law.
  17
  18 ! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  19 ! EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  20 ! MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
  21 ! IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
  22 ! OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
  23 ! ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
  24 ! OTHER DEALINGS IN THE SOFTWARE.
  25
  26 ! For more information, please refer to <http://unlicense.org/>
  27
  28 MODULE functions
  29
  30   real(kind=8), private, parameter :: poly_coeffs(11) =            &
  31        [-11.0, 15.6, -4.6, 22.5, 8.1, 5.1, -0.3, -8.0, 0.0, -9.9, 2.2]
  32
  33   INTERFACE
  34      FUNCTION analytical_integral(ibeg, iend) result(y)
  35        real(kind=8), intent(in) :: ibeg, iend
  36        real(kind=8) :: y
  37      END FUNCTION analytical_integral
  38   END INTERFACE
  39
  40 CONTAINS
  41
  42   FUNCTION my_exp(x) result(y)
  43     real(kind=8), intent(in) :: x
  44     real(kind=8) :: y
  45     y = exp(x)
  46   END FUNCTION my_exp
  47
  48   FUNCTION my_sin(x) result(y)
  49     real(kind=8), intent(in) :: x
  50     real(kind=8) :: y
  51     y = sin(x)
  52   END FUNCTION my_sin
  53
  54   FUNCTION my_poly(x) result(y)
  55     real(kind=8), intent(in) :: x
  56     real(kind=8) :: y
  57     integer(kind=4) :: i
  58     y = sum(poly_coeffs(:) * [1.0_8, (x ** [(i, i = 1, 10)])])
  59   END FUNCTION my_poly
  60
  61   FUNCTION my_exp_int(ibeg, iend) result(y)
  62     real(kind=8), intent(in) :: ibeg, iend
  63     real(kind=8) :: y
  64     y = exp(iend) - exp(ibeg)
  65   END FUNCTION my_exp_int
  66
  67   FUNCTION my_sin_int(ibeg, iend) result(y)
  68     real(kind=8), intent(in) :: ibeg, iend
  69     real(kind=8) :: y
  70     y = -cos(iend) + cos(ibeg)
  71   END FUNCTION my_sin_int
  72
  73   FUNCTION my_poly_int_indefinite(x) result(y)
  74     real(kind=8), intent(in) :: x
  75     real(kind=8) :: y
  76     integer(kind=4) :: i, j
  77     y = sum(poly_coeffs(:) * (1 / real([(j, j = 1, 11)])) *        &
  78          (x ** [(i, i = 1, 11)]))
  79   END FUNCTION my_poly_int_indefinite
  80
  81   FUNCTION my_poly_int(ibeg, iend) result(y)
  82     real(kind=8), intent(in) :: ibeg, iend
  83     real(kind=8) :: y
  84     y = my_poly_int_indefinite(iend) - my_poly_int_indefinite(ibeg)
  85   END FUNCTION my_poly_int
  86
  87 END MODULE functions