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Re: Re: What is the fastest pure-Perl implementation of XXX?
by TimToady (Parson) on Mar 30, 2004 at 22:07 UTC
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I don't think throwing 170 scalars onto the stack every time in order to pick one is going to be as good as using an existing array. | [reply] |
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Good point. Updated.
Examine what is said, not who speaks.
"Efficiency is intelligent laziness." -David Dunham
"Think for yourself!" - Abigail
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[d/l] |
Re: Re: What is the fastest pure-Perl implementation of XXX?
by TimToady (Parson) on Mar 30, 2004 at 23:26 UTC
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Um, nope, just the same. Now you're just calling the FACTORIALS subroutine to put 170 scalars on the stack. The ()[] construct is always going to do that. You have to use @foo[] or $foo->[] to access an existing array. Which you have to have constructed using some variant of @foo = (0,1,etc) or $foo = [0, 1, etc.]. And you have to arrange to do that only once (generally outside the routine, but it can be done inside if you're tricksie), or you're still in the same boat of constructing your list at run time. | [reply]
[d/l]
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use constant FACTORIALS => [ qw[
0 1 2 6 24 120 720 5040 40320 362880 3628800 39916800 479001600 6
+227020800
87178291200 1307674368000 20922789888000 355687428096000 64023737
+05728000
1.21645100408832e+017 2.43290200817664e+018 5.109094217170944e+01
+9
1.124000727777608e+021 2.585201673888498e+022 6.204484017332394e+
+023
1.551121004333099e+025 4.032914611266057e+026 1.088886945041835e+
+028
3.048883446117138e+029 8.841761993739701e+030 2.65252859812191e+0
+32
8.222838654177922e+033 2.631308369336935e+035 8.683317618811886e+
+036
2.952327990396041e+038 1.033314796638614e+040 3.719933267899012e+
+041
1.376375309122634e+043 5.23022617466601e+044 2.039788208119744e+0
+46
8.159152832478977e+047 3.34525266131638e+049 1.40500611775288e+05
+1
6.041526306337383e+052 2.658271574788449e+054 1.196222208654802e+
+056
5.502622159812089e+057 2.586232415111682e+059 1.241391559253607e+
+061
6.082818640342675e+062 3.041409320171338e+064 1.551118753287382e+
+066
8.065817517094388e+067 4.274883284060026e+069 2.308436973392414e+
+071
1.269640335365828e+073 7.109985878048635e+074 4.052691950487722e+
+076
2.350561331282879e+078 1.386831185456899e+080 8.320987112741392e+
+081
5.075802138772248e+083 3.146997326038794e+085 1.98260831540444e+0
+87
1.268869321858842e+089 8.247650592082472e+090 5.443449390774431e+
+092
3.647111091818868e+094 2.480035542436831e+096 1.711224524281413e+
+098
1.197857166996989e+100 8.504785885678622e+101 6.123445837688608e+
+103
4.470115461512683e+105 3.307885441519386e+107 2.480914081139539e+
+109
1.88549470166605e+111 1.451830920282858e+113 1.13242811782063e+11
+5
8.946182130782973e+116 7.156945704626378e+118 5.797126020747366e+
+120
4.75364333701284e+122 3.945523969720657e+124 3.314240134565352e+1
+26
2.817104114380549e+128 2.422709538367272e+130 2.107757298379527e+
+132
1.854826422573984e+134 1.650795516090845e+136 1.485715964481761e+
+138
1.352001527678402e+140 1.24384140546413e+142 1.156772507081641e+1
+44
1.087366156656742e+146 1.032997848823905e+148 9.916779348709491e+
+149
9.619275968248206e+151 9.426890448883242e+153 9.33262154439441e+1
+55
9.33262154439441e+157 9.425947759838354e+159 9.614466715035121e+1
+61
9.902900716486175e+163 1.029901674514562e+166 1.08139675824029e+1
+68
1.146280563734708e+170 1.226520203196137e+172 1.324641819451828e+
+174
1.443859583202493e+176 1.588245541522742e+178 1.762952551090244e+
+180
1.974506857221073e+182 2.231192748659812e+184 2.543559733472186e+
+186
2.925093693493014e+188 3.393108684451897e+190 3.969937160808719e+
+192
4.684525849754288e+194 5.574585761207603e+196 6.689502913449124e+
+198
8.09429852527344e+200 9.875044200833598e+202 1.214630436702533e+2
+05
1.50614174151114e+207 1.882677176888925e+209 2.372173242880046e+2
+11
3.012660018457658e+213 3.856204823625803e+215 4.974504222477286e+
+217
6.466855489220472e+219 8.471580690878817e+221 1.118248651196004e+
+224
1.487270706090685e+226 1.992942746161518e+228 2.69047270731805e+2
+30
3.659042881952547e+232 5.01288874827499e+234 6.917786472619486e+2
+36
9.615723196941086e+238 1.346201247571752e+241 1.89814375907617e+2
+43
2.695364137888161e+245 3.854370717180071e+247 5.550293832739301e+
+249
8.047926057471987e+251 1.17499720439091e+254 1.727245890454638e+2
+56
2.556323917872864e+258 3.808922637630567e+260 5.713383956445851e+
+262
8.627209774233235e+264 1.311335885683452e+267 2.006343905095681e+
+269
3.089769613847349e+271 4.789142901463391e+273 7.471062926282891e+
+275
1.172956879426414e+278 1.853271869493734e+280 2.946702272495037e+
+282
4.714723635992059e+284 7.590705053947215e+286 1.229694218739449e+
+289
2.004401576545302e+291 3.287218585534295e+293 5.423910666131586e+
+295
9.003691705778433e+297 1.503616514864998e+300 2.526075744973197e+
+302
4.269068009004703e+304 7.257415615307994e+306
] ];
sub factorial{ $_[ 0 ] < 171 ? FACTORIALS->[ $_[ 0 ] ] : '#INF'; }
Examine what is said, not who speaks.
"Efficiency is intelligent laziness." -David Dunham
"Think for yourself!" - Abigail
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[d/l] |
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Nothing wrong with this. There are way too few factorials that can actually be expressed by Perl...
Perhaps a better question would be to see how well fibonacci or some other function can be sped up, but that too has an answer ...closed form of fibonacci is well known.
Bottom line, for simple math problems, the best answer is always to cheat. This is what calculators do with factorials (and sines and cosines and many other things), and for good reason! Where they don't cheat, they may use simple approximations (taylor's series, etc). But hey, I don't work for Texas Instruments, I just repeat what I am told :)
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Re: Re: What is the fastest pure-Perl implementation of XXX?
by I0 (Priest) on Mar 31, 2004 at 09:44 UTC
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Only by definition and because it's useful. 0! can just as easily be defined as 0, with different results.
------
We are the carpenters and bricklayers of the Information Age.
Then there are Damian modules.... *sigh* ... that's not about being less-lazy -- that's about being on some really good drugs -- you know, there is no spoon. - flyingmoose
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To the extent that "factorial" is an arbitrary function, you can define it any way that you like. This is trivially obvious, but not very useful.
But you will have a very hard time finding any mathematician who agrees that it either makes sense or is useful to define 0! as anything other than 1. I can think of a half-dozen reasons to make it 1. None to call it 0. If you did find such an odd mathematician, I guarantee that it won't be someone in combinatorics (which is the field of math where factorial tends to come up the most).
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