LaTeX3: \fp_pow:Nn giving wrong results

Question

I want to draw the square-root from a rational number using the l3fp package. As the package does not provide an sqrt function, I played with \fp_pow:Nn. Unfortunately, I could only get the correct result for $\sqrt{4}$:

\documentclass{article}
\usepackage{expl3}

\begin{document}

\ExplSyntaxOn

\fp_set:Nn\a_fp{0.04}
\fp_pow:Nn\a_fp{0.5}
\fp_use:N\a_fp\par    %wrong

\fp_set:Nn\a_fp{4.0}
\fp_pow:Nn\a_fp{0.5}
\fp_use:N\a_fp\par    %ok

\fp_set:Nn\a_fp{9.0}
\fp_pow:Nn\a_fp{0.5}
\fp_use:N\a_fp\par    %wrong

\fp_set:Nn\a_fp{16.0}
\fp_pow:Nn\a_fp{0.5}
\fp_use:N\a_fp\par    %wrong

\ExplSyntaxOff

\end{document}

Answer 1

As Joseph said, the code is quite intricate. The bug should be fixed in the SVN (and probably in the next week or so on CTAN with the next update of expl3).

If you cannot wait, you can also redefine the offending function \fp_pow_aux_iv:. Only the end changes, but the function is massive.

\cs_set_protected_nopar:Npn \fp_pow_aux_iv:
  {
    \group_begin:
      \l_fp_input_a_integer_int  \l_fp_input_b_integer_int
      \l_fp_input_a_decimal_int  \l_fp_input_b_decimal_int
      \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
      \fp_ln_internal:
      \cs_set_protected_nopar:Npx \fp_tmp:w
        {
          \group_end:
          \exp_not:N \l_fp_input_b_sign_int
            \int_use:N \l_fp_output_sign_int \scan_stop:
          \exp_not:N \l_fp_input_b_integer_int
            \int_use:N \l_fp_output_integer_int \scan_stop:
          \exp_not:N \l_fp_input_b_decimal_int
            \int_use:N \l_fp_output_decimal_int \scan_stop:
          \exp_not:N \l_fp_input_b_extended_int
            \int_use:N \l_fp_output_extended_int \scan_stop:
          \exp_not:N \l_fp_input_b_exponent_int
            \int_use:N \l_fp_output_exponent_int \scan_stop:
        }
    \fp_tmp:w
    \l_fp_input_a_extended_int  \c_zero
    \fp_mul:NNNNNNNNN
      \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
        \l_fp_input_a_extended_int
      \l_fp_input_b_integer_int \l_fp_input_b_decimal_int
        \l_fp_input_b_extended_int
      \l_fp_output_integer_int \l_fp_output_decimal_int
        \l_fp_output_extended_int
    \l_fp_output_exponent_int
      \int_eval:w
        \l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int
      \scan_stop:
    \fp_extended_normalise_output:
    \tex_multiply:D \l_fp_input_a_sign_int \l_fp_input_b_sign_int
    \l_fp_input_a_integer_int  \l_fp_output_integer_int
    \l_fp_input_a_decimal_int  \l_fp_output_decimal_int
    \l_fp_input_a_extended_int \l_fp_output_extended_int
    \l_fp_input_a_exponent_int \l_fp_output_exponent_int
    \l_fp_output_integer_int  \c_zero
    \l_fp_output_decimal_int  \c_zero
    \l_fp_output_extended_int \c_zero
    \l_fp_output_exponent_int \c_zero
    \cs_set_eq:NN \fp_exp_const:Nx \use_none:nn
    \fp_exp_internal:
  }

Answer 2

Interestingly enough

\fp_set:Nn\a_fp{0.04}
\fp_ln:Nn\a_fp{\a_fp}
\fp_div:Nn\a_fp{2}
\fp_exp:Nn\a_fp{\a_fp}
\fp_use:N\a_fp\par

prints 0.2000000010, but using 4 as argument prints 1.999999999.

After \fp_set:Nn\a_fp{0.04} and \fp_pow:Nn\a_fp{0.5}, \fp_show:N\a_fp shows +2.624477407e0. When used with 4 it shows +2.000000000e0. When used with 400 it says "Number too big"!

Note: my version of l3fp.sty is l3fp.dtx 2201 2011-03-19 17:16:13Z