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       1             : !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
       2             : !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
       3             : !!!!                                                                                                                            !!!!
       4             : !!!!    ParaMonte: Parallel Monte Carlo and Machine Learning Library.                                                           !!!!
       5             : !!!!                                                                                                                            !!!!
       6             : !!!!    Copyright (C) 2012-present, The Computational Data Science Lab                                                          !!!!
       7             : !!!!                                                                                                                            !!!!
       8             : !!!!    This file is part of the ParaMonte library.                                                                             !!!!
       9             : !!!!                                                                                                                            !!!!
      10             : !!!!    LICENSE                                                                                                                 !!!!
      11             : !!!!                                                                                                                            !!!!
      12             : !!!!       https://github.com/cdslaborg/paramonte/blob/main/LICENSE.md                                                          !!!!
      13             : !!!!                                                                                                                            !!!!
      14             : !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
      15             : !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
      16             : 
      17             : !>  \brief
      18             : !>  This include file contains implementations of the procedures in module [pm_mathSqrt](@ref pm_mathSqrt).
      19             : !>
      20             : !>  \finmain
      21             : !>
      22             : !>  \author
      23             : !>  \FatemehBagheri, Sunday 11:23 PM, September 19, 2021, Dallas, TX
      24             : 
      25             : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      26             : 
      27             : #if     !getSqrt_ENABLED
      28             : #error  "Unrecognized interface."
      29             : #endif
      30             : #if     Bin_ENABLED || Def_ENABLED
      31             :         integer(IKC) :: middle, upper
      32             :         integer(IKC) , parameter :: maxIntSqrt = floor(sqrt(real(huge(0_IKC), RKB)), IKC)
      33          47 :         CHECK_ASSERTION(__LINE__, 0_IKC <= posint, SK_"@getSqrt(): The condition `0 <= posint` must hold. posint = "//getStr(posint))
      34          47 :         upper = min(maxIntSqrt, posint) + 1_IKC ! Avoid possible overflow.
      35           0 :         intSqrt = 0_IKC
      36             :         do
      37         480 :             if (upper - intSqrt == 1_IKC) return
      38         433 :             middle = (intSqrt + upper) / 2_IKC
      39           0 :             if (middle * middle <= posint) then
      40           0 :                 intSqrt = middle
      41             :             else
      42           0 :                 upper = middle
      43             :             end if
      44             :         end do
      45             : #elif   Lin_ENABLED
      46             :         ! linear search, ascending, using addition.
      47             :         ! (intSqrt + 1)^2 = intSqrt^2 + 2L + 1 = intSqrt^2 + 1 + \sum _{i = 1}^intSqrt 2
      48             :         integer(IKC) :: a, d
      49             :         integer(IKC) , parameter :: huge_IKC = huge(0_IKC)
      50          11 :         CHECK_ASSERTION(__LINE__, 0_IKC <= posint, SK_"@getSqrt(): The condition `0 <= posint` must hold. posint = "//getStr(posint))
      51           0 :         intSqrt = 0_IKC
      52           0 :         a = 1_IKC
      53           0 :         d = 3_IKC
      54          19 :         do
      55          30 :             if (posint < a) return
      56          19 :             if (huge_IKC - a < d) return
      57          19 :             a = a + d ! (a + 1_IKC) ** 2_IKC
      58          19 :             d = d + 2_IKC
      59          19 :             intSqrt = intSqrt + 1_IKC
      60             :         end do
      61             : #else
      62             :         !%%%%%%%%%%%%%%%%%%%%%%%%
      63             : #error  "Unrecognized interface."
      64             :         !%%%%%%%%%%%%%%%%%%%%%%%%
      65             : #endif