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

by BrowserUk (Pope)
on Feb 19, 2013 at 19:06 UTC ( #1019646=note: print w/ replies, xml ) Need Help??


in reply to [OT] Function to do x**y for |y|<1 w/o ** operator.

Does he have log and exp available?

print exp( log( 100 ) *.5 );; 10 print exp( log( 1000 ) *.3333333333333333333333 );; 10

Ie.

sub pow{ exp( log( $_[0] ) * $_[1] ) };; printf "%2d : %20.17f\n", $_, pow( 10**$_, 1/$_ ) for 1 .. 20;; 1 : 10.00000000000000200 2 : 10.00000000000000200 3 : 9.99999999999999820 4 : 10.00000000000000200 5 : 10.00000000000000200 6 : 9.99999999999999820 7 : 9.99999999999999820 8 : 10.00000000000000200 9 : 9.99999999999999820 10 : 10.00000000000000200 11 : 10.00000000000000200 12 : 9.99999999999999820 13 : 10.00000000000000200 14 : 9.99999999999999820 15 : 9.99999999999999820 16 : 10.00000000000000200 17 : 10.00000000000000200 18 : 9.99999999999999820 19 : 10.00000000000000200 20 : 10.00000000000000200 printf "%2d : %20.17f\n", $_, pow( 12345**$_, 1/$_ ) for 1 .. 20;; 1 : 12345.00000000000500000 2 : 12345.00000000000500000 3 : 12345.00000000000500000 4 : 12345.00000000000500000 5 : 12345.00000000000500000 6 : 12345.00000000000500000 7 : 12345.00000000000500000 8 : 12345.00000000000500000 9 : 12345.00000000000500000 10 : 12345.00000000000500000 11 : 12345.00000000000500000 12 : 12345.00000000000500000 13 : 12345.00000000000500000 14 : 12345.00000000000500000 15 : 12344.99999999998400000 16 : 12345.00000000000500000 17 : 12344.99999999998400000 18 : 12345.00000000000500000 19 : 12344.99999999998400000 20 : 12345.00000000000500000

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.


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Re^2: [OT] Function to do x**y for |y|<1 w/o ** operator.
by swampyankee (Parson) on Feb 19, 2013 at 19:18 UTC

    He has log, but not exp.


    Information about American English usage here and here. Floating point issues? Please read this before posting. — emc

      If you don't need fast or accurate:

      #! perl -slw use strict; sub myExp{ my $e = 1 + ( shift() / 10000000 ); my $r = $e; $r *= $e for 2 .. 10000000; $r; } printf "%30.20g : %30.20g\n", exp( $_ ), myExp( $_ ) for map log( 10**$_ ), -10 .. 10; __END__ C:\test>exp 9.9999999999999965e-011 : 9.9997349036884958e-011 1.0000000000000007e-009 : 9.9997852777366009e-010 9.999999999999982e-009 : 9.9998303391048947e-009 9.9999999999999943e-008 : 9.9998700988200641e-008 1.0000000000000004e-006 : 9.9999045679358269e-007 9.9999999999999974e-006 : 9.9999337241854084e-006 0.00010000000000000009 : 9.9999575897369183e-005 0.0010000000000000002 : 0.00099999761423453593 0.010000000000000005 : 0.0099999893930861859 0.10000000000000002 : 0.099999973530420908 1 : 1 10.000000000000002 : 9.9999973561653093 100.00000000000004 : 99.999893882330838 999.99999999999977 : 999.99761406302275 10000.000000000009 : 9999.9575911775646 100000.00000000001 : 99999.337176962814 999999.99999999953 : 999990.45646420098 10000000.000000006 : 9999870.1098560225 100000000.00000018 : 99998303.311974689 999999999.99999928 : 999978527.31280696 10000000000.000004 : 9999734913.5273266

      With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.

        Can I post a link to your code? It's on cosmoquest.org, which used to be the Bad Astronomy & Universe Today forum.


        Information about American English usage here and here. Floating point issues? Please read this before posting. — emc

      Update:Changed constants for slightly greater accuracy for the sake of another couple of iterations.

      Here's a somewhat more accurate, and much faster version:

      #! perl -slw use strict; sub myExp{ my $e = 1 + ( shift() / 4294967296 ); $e *= $e for 1 .. 32; $e; } printf "%30.20g : %30.20g\n", exp( $_ ), myExp( $_ ) for map log( 10**$_ ), -10 .. 10; __END__ C:\test>exp 9.9999999999999965e-011 : 1.0000000285332257e-010 1.0000000000000007e-009 : 1.0000000829163549e-009 9.999999999999982e-009 : 1.0000002130576865e-008 9.9999999999999943e-008 : 9.9999976329917627e-008 1.0000000000000004e-006 : 9.9999969112813618e-007 9.9999999999999974e-006 : 9.9999977582604716e-006 0.00010000000000000009 : 9.999998681099902e-005 0.0010000000000000002 : 0.00099999984556405617 0.010000000000000005 : 0.0099999993405499293 0.10000000000000002 : 0.099999996702749588 1 : 1 10.000000000000002 : 9.9999952742988558 100.00000000000004 : 100.00000084944983 999.99999999999977 : 999.99959325720954 10000.000000000009 : 10000.000169889967 100000.00000000001 : 99999.966690555739 999999.99999999953 : 1000000.1401405634 10000000.000000006 : 9999996.1589527112 100000000.00000018 : 100000003.39779937 999999999.99999928 : 999999662.81900096 10000000000.000004 : 10000002874.419859

      With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.
      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

        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.


        With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority".
        In the absence of evidence, opinion is indistinguishable from prejudice.
        He has log, but not exp.

      Seriously. What kind of brain-dead platform has one but not the other. That's truly ridiculous.

      Alex / talexb / Toronto

      "Groklaw is the open-source mentality applied to legal research" ~ Linus Torvalds

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