Re^3: [OT] Function to do x**y for |y|<1 w/o ** operator.

[syphilis]

He has log, but not exp.

Perhaps there's also something helpful in Math::BigFloat's _pow() sub:

  # Taylor:       |   u    u^2    u^3         |
  # x ** y  = 1 + |  --- + --- + ----- + ...  |
  #               |_  1    1*2   1*2*3       _|

where (I gather)

u = y * ln x

Cheers,
Rob

[BrowserUk]

Here's the Taylor series version, but it converges much less quickly and achieved less accuracy (at least for very small x):

#! perl -slw
use strict;

our $N //= 32;

sub myExp2 {
    my $x = shift;
    my( $r, $top, $bot ) = ( 1, $x, 1 );
    $r += $top / $bot, $top *= $x, $bot *= $_ for 2 .. $N;
    $r;
}
printf "%30.20g : %30.20g \n", exp( $_ ), myExp2( $_ ) #, myExp2( $_ )
+ - exp( $_ )
    for map log( 10**$_ ), -10 .. 10;

__END__
C:\test>exp -N=227
       9.9999999999999965e-011 :       -9.2662709999185665e-008
       1.0000000000000007e-009 :       -8.6393006494132869e-009
        9.999999999999982e-009 :        1.1100933780704416e-008
       9.9999999999999943e-008 :        9.9888569074918635e-008
       1.0000000000000004e-006 :        1.0000228347576172e-006
       9.9999999999999974e-006 :        1.0000001331927489e-005
        0.00010000000000000009 :         0.00010000000018884082
         0.0010000000000000002 :          0.0010000000000062366
          0.010000000000000005 :          0.0099999999999984095
           0.10000000000000002 :           0.099999999999999867
                             1 :                              1
            10.000000000000002 :             10.000000000000004
            100.00000000000004 :                            100
            999.99999999999977 :             999.99999999999955
            10000.000000000009 :             10000.000000000007
            100000.00000000001 :             100000.00000000004
            999999.99999999953 :             999999.99999999977
            10000000.000000006 :             10000000.000000009
            100000000.00000018 :             100000000.00000022
            999999999.99999928 :             999999999.99999964
            10000000000.000004 :             10000000000.000002

Try going higher with the iterations and things turn to #inf.