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

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
[download]

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
[download]

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.

Comment on Re: [OT] Function to do xy for \|y\|<1 w/o operator. Select or Download Code

Replies are listed 'Best First'.
Re^2: [OT] Function to do xy 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	[reply]
Re^3: [OT] Function to do xy for \|y\|<1 w/o operator. by BrowserUk (Patriarch) on Feb 19, 2013 at 20:08 UTC
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 [download] 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.	[reply] [d/l]
Re^3: [OT] Function to do xy for \|y\|<1 w/o operator. by BrowserUk (Patriarch) on Feb 19, 2013 at 19:47 UTC
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 [download] 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.	[reply] [d/l]
Re^4: [OT] Function to do xy for \|y\|<1 w/o operator. by swampyankee (Parson) on Feb 19, 2013 at 21:44 UTC
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	[reply]
Re^5: [OT] Function to do xy for \|y\|<1 w/o operator. by BrowserUk (Patriarch) on Feb 20, 2013 at 01:34 UTC
Re^6: [OT] Function to do xy for \|y\|<1 w/o operator. by swampyankee (Parson) on Feb 20, 2013 at 02:40 UTC
Re^3: [OT] Function to do xy for \|y\|<1 w/o operator. by syphilis (Archbishop) on Feb 20, 2013 at 02:23 UTC
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 12 123 _\|` [download] where (I gather) `u = y ln x` [download] Cheers, Rob	[reply] [d/l] [select]
Re^4: [OT] Function to do xy for \|y\|<1 w/o operator. by BrowserUk (Patriarch) on Feb 20, 2013 at 02:49 UTC
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 [download] 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.	[reply] [d/l]
Re^3: [OT] Function to do xy for \|y\|<1 w/o operator. by talexb (Chancellor) on Feb 20, 2013 at 15:25 UTC
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	[reply]

In Section Seekers of Perl Wisdom

Replies are listed 'Best First'.
Re^2: [OT] Function to do xy 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	[reply]
Re^3: [OT] Function to do xy for \|y\|<1 w/o operator. by BrowserUk (Patriarch) on Feb 19, 2013 at 20:08 UTC
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 [download] 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.	[reply] [d/l]
Re^3: [OT] Function to do xy for \|y\|<1 w/o operator. by BrowserUk (Patriarch) on Feb 19, 2013 at 19:47 UTC
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 [download] 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.	[reply] [d/l]
Re^4: [OT] Function to do xy for \|y\|<1 w/o operator. by swampyankee (Parson) on Feb 19, 2013 at 21:44 UTC
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	[reply]
Re^5: [OT] Function to do xy for \|y\|<1 w/o operator. by BrowserUk (Patriarch) on Feb 20, 2013 at 01:34 UTC
Re^6: [OT] Function to do xy for \|y\|<1 w/o operator. by swampyankee (Parson) on Feb 20, 2013 at 02:40 UTC
Re^3: [OT] Function to do xy for \|y\|<1 w/o operator. by syphilis (Archbishop) on Feb 20, 2013 at 02:23 UTC
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 12 123 _\|` [download] where (I gather) `u = y ln x` [download] Cheers, Rob	[reply] [d/l] [select]
Re^4: [OT] Function to do xy for \|y\|<1 w/o operator. by BrowserUk (Patriarch) on Feb 20, 2013 at 02:49 UTC
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 [download] 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.	[reply] [d/l]
Re^3: [OT] Function to do xy for \|y\|<1 w/o operator. by talexb (Chancellor) on Feb 20, 2013 at 15:25 UTC
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	[reply]