sqrt$m (2) --- calculate square root                     04/27/83


          | _C_a_l_l_i_n_g _I_n_f_o_r_m_a_t_i_o_n

          |      longreal function sqrt$m (x)
          |      real x

          |      Library: vswtmath (Subsystem mathematical library)


          | _F_u_n_c_t_i_o_n

          |      This function calculates the square root of a floating point
          |      value.   Attempts to take the square root of negative values
          |      will result in an error.  The default return  in  this  case
          |      will  be  the  square  root  of  the  absolute  value of the
          |      argument.  All other arguments are in range and return valid
          |      results.  The  condition  SWT_MATH_ERROR$  is  signalled  if
          |      there  is  an argument error.  An on-unit can be established
          |      to deal with this error; the SWT  Math  Library  contains  a
          |      default handler named 'err$m' which the user may utilize.

          |      This  function  is  intended  to serve as a single precision
          |      function although it returns a double precision result.  The
          |      function has been coded so that any value returned will  not
          |      overflow  or  underflow  a  single  precision floating point
          |      value.  The double precision register  overlaps  the  single
          |      precision register so it is possible to declare and use this
          |      function as simply a "real" function.


          | _I_m_p_l_e_m_e_n_t_a_t_i_o_n

          |      The  algorithm  involved  is based on Newton's approximation
          |      method with an initial  multiplicative  approximation.   The
          |      argument  is  scaled to within the range [0.5, 2.0) and then
          |      the algorithm is iterated to a solution.  Adapted  from  the
          |      algorithm   given  in  the  book  _S_o_f_t_w_a_r_e  _M_a_n_u_a_l  _f_o_r  _t_h_e
          |      _E_l_e_m_e_n_t_a_r_y _F_u_n_c_t_i_o_n_s by William Waite and William Cody,  Jr.
          |      (Prentice-Hall, 1980).


          | _C_a_l_l_s

          |      Primos signl$


          | _S_e_e _A_l_s_o

          |      dsqt$m (2), err$m (2),
          |      _S_W_T _M_a_t_h _L_i_b_r_a_r_y _U_s_e_r_'_s _G_u_i_d_e









            sqrt$m (2)                    - 1 -                    sqrt$m (2)