in reply to Re: Re: What is the fastest pure-Perl implementation of XXX?
in thread What is the fastest pure-Perl implementation of XXX?

Maybe?

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'; }

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Examine what is said, not who speaks.
"Efficiency is intelligent laziness." -David Dunham
"Think for yourself!" - Abigail

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Re: Re: Re: Re: What is the fastest pure-Perl implementation of XXX?
by flyingmoose (Priest) on Mar 31, 2004 at 02:39 UTC
    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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