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RE: Simplify a module

• To: mathgroup at smc.vnet.net
• Subject: [mg39487] RE: Simplify a module
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Wed, 19 Feb 2003 04:42:05 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Bobby,

dcalc4[ein_] := 
  Block[{a1, a2, a3, 
      e = ein}, {T1, M1, T2, M2, T3, M3} = {2, 392, 3, 147, 47, 24};
    Evaluate[sw /@ mytab];
    Mod[a1*T1*M1 + a2*T2*M2 + a3*T3*M3, 1176]]

does it. BTW, 

sw[{{a_, base_}, seq_}] := (a = 
      Switch[Mod[e, base], Evaluate[Sequence @@ seq], _, 0])

Evaluate[a] is not needed after destructuring.


Nonetheless, I'd not recommend this solution neither my dcalc2, as I
hopefully have made clear in my first posting, more so something like in my
PS, as e.g.
 
ct1 = ctab[[All, 1, 2]];  (* get rid of hard-wired names *)
ct2 = ctab[[All, 2]];     (* I'd not flatten this *)
ct3 = {2, 3, 47};         (* perhaps better Transpose[{ct3,ct4}] ? *)
ct4 = {392, 147, 24};

dcalc3x[e_] := 
  Mod[#, 1176] &[
    MapThread[
        Switch[Mod[e, #1], 
            Evaluate[Apply[Sequence, #2, {0, 1}]],
            _, 0 ] &, {ct1, ct2}].(ct3*ct4)]

Now rework ct1,...,ct4 into a single structure and supply this as a second
parameter to dcalc.

--
Hartmut Wolf


>-----Original Message-----
>From: Dr Bob [mailto:drbob at bigfoot.com]
To: mathgroup at smc.vnet.net
>Sent: Tuesday, February 18, 2003 6:10 PM
>To: Wolf, Hartmut; mathgroup at smc.vnet.net
>Subject: [mg39487] Re:  Simplify a module
>
>
>Here's a marginally simpler solution:
>
>Cases[Hold[
>      If[Mod[e, 3] == 1, a1 = 1]; If[Mod[e, 3] == 2, a1 = 2];
>      If[Mod[e, 8] == 1, a2 = 1];
>      If[Mod[e, 8] == 3, a2 = 3]; If[Mod[e, 8] == 5, a2 = 5];
>      If[Mod[e, 8] == 7, a2 = 7];
>      If[Mod[e, 49] == 1, a3 = 1]; If[Mod[e, 49] == 2, a3 = 25];
>      If[Mod[e, 49] == 3, a3 = 33]; If[Mod[e, 49] == 4, a3 = 37];
>      If[Mod[e, 49] == 5, a3 = 10]; If[Mod[e, 49] == 6, a3 = 41];
>      If[Mod[e, 49] == 8, a3 = 43]; If[Mod[e, 49] == 9, a3 = 11];
>      If[Mod[e, 49] == 10, a3 = 5]; If[Mod[e, 49] == 11, a3 = 9];
>      If[Mod[e, 49] == 12, a3 = 45]; If[Mod[e, 49] == 13, a3 = 34];
>      If[Mod[e, 49] == 15, a3 = 36]; If[Mod[e, 49] == 16, a3 = 46];
>      If[Mod[e, 49] == 17, a3 = 26]; If[Mod[e, 49] == 18, a3 = 30];
>      If[Mod[e, 49] == 19, a3 = 31]; If[Mod[e, 49] == 20, a3 = 27];
>      If[Mod[e, 49] == 22, a3 = 29]; If[Mod[e, 49] == 23, a3 = 32];
>      If[Mod[e, 49] == 24, a3 = 47]; If[Mod[e, 49] == 25, a3 = 2];
>      If[Mod[e, 49] == 26, a3 = 17]; If[Mod[e, 49] == 27, a3 = 20];
>      If[Mod[e, 49] == 29, a3 = 22]; If[Mod[e, 49] == 30, a3 = 18];
>      If[Mod[e, 49] == 31, a3 = 19]; If[Mod[e, 49] == 32, a3 = 23];
>      If[Mod[e, 49] == 33, a3 = 3]; If[Mod[e, 49] == 34, a3 = 13];
>      If[Mod[e, 49] == 36, a3 = 15]; If[Mod[e, 49] == 37, a3 = 4];
>      If[Mod[e, 49] == 38, a3 = 40]; If[Mod[e, 49] == 39, a3 = 44];
>      If[Mod[e, 49] == 40, a3 = 38]; If[Mod[e, 49] == 41, a3 = 6];
>      If[Mod[e, 49] == 43, a3 = 8]; If[Mod[e, 49] == 44, a3 = 39];
>      If[Mod[e, 49] == 45, a3 = 12]; If[Mod[e, 49] == 46, a3 = 16];
>      If[Mod[e, 49] == 47, a3 = 24]; If[Mod[e, 49] == 48, a3 = 48];],
>      If[
>         Mod[_, g_] == h_, ax_ = k_] :> {ax, g, h, k}, Infinity];
>split = Split[%, #1[[1]] === #2[[1]] &];
>mytab = {#[[1, {1, 2}]], Flatten[#[[All, {3, 4}]]]} & /@ split;
>dcalc3[e_] := Block[{a1, a2, a3}, {T1, M1, T2, M2, T3, M3} = 
>{2, 392, 3, 
>147, 47, 24};
>    (Evaluate[#[[1, 1]]] = Switch[Mod[e, #[[
>    1, 2]]], Evaluate[Sequence @@ #[[2]]], _, 0]) & /@ mytab;
>    Mod[a1*T1*M1 + a2*T2*M2 + a3*T3*M3, 1176]]
>
>dcalc3@# == dcalc2@# & /@ Range[1176];
>And @@ %
>
>True
>
>Could someone explain why something like the following doesn't 
>work?  I've 
>tried several versions and haven't been able to use a named 
>function like 
>sw in place of the identical in-line function.
>
>sw[{{a_, base_}, seq_}] := (Evaluate[a] = Switch[Mod[e, base], 
>Evaluate[Sequence @@ seq], _, 0])
>dcalc4[e_] := Block[{a1, a2,
>         a3}, {T1, M1, T2, M2, T3, M3} = {2, 392, 3, 147, 47, 24};
>    Evaluate[sw /@ mytab];
>    Mod[a1*T1*M1 + a2*T2*M2 + a3*T3*M3, 1176]]
>
>Bobby
>
>On Mon, 17 Feb 2003 18:17:34 -0500 (EST), Wolf, Hartmut 
><Hartmut.Wolf@t- 
>systems.com> wrote:
>
>>
>>> -----Original Message-----
>>> From: flip [mailto:flip_alpha at safebunch.com]
To: mathgroup at smc.vnet.net
>> To: mathgroup at smc.vnet.net
>>> Sent: Sunday, February 16, 2003 12:14 PM
>>> To: mathgroup at smc.vnet.net
>>> Subject: [mg39487]  Simplify a module
>>>
>>>
>>> Hi All,
>>>
>>> Can someone recommend a simplification to this module (just 
>a bunch of 
>>> if
>>> checks).
>>>
>>> It was specified to be done that way (and I know how to 
>sove the problem
>>> using PowerMod in one step, so please bear with me here).
>>>
>>> Thanks, Flip
>>>
>>> (* to email me remove "_alpha" *)
>>>
>>> Anyway, here goes.
>>>
>>> dcalc[ein_] := Module[{e = ein, a1 = 0, a2 = 0, a3 = 0},
>>> {T1, M1, T2, M2, T3, M3} = {2, 392, 3, 147, 47, 24};
>>> If[Mod[e, 3] == 1, a1 = 1]; If[Mod[e, 3] == 2, a1 = 2];
>>> If[Mod[e, 8] == 1, a2 = 1];
>>> If[Mod[e, 8] == 3, a2 = 3]; If[Mod[e, 8] == 5, a2 = 5];
>>> If[Mod[e, 8] == 7, a2 = 7];
>>> If[Mod[e, 49] == 1, a3 = 1]; If[Mod[e, 49] == 2, a3 = 25];
>>> If[Mod[e, 49] == 3, a3 = 33]; If[Mod[e, 49] == 4, a3 = 37];
>>> If[Mod[e, 49] == 5, a3 = 10]; If[Mod[e, 49] == 6, a3 = 41];
>>> If[Mod[e, 49] == 8, a3 = 43]; If[Mod[e, 49] == 9, a3 = 11];
>>> If[Mod[e, 49] == 10, a3 = 5]; If[Mod[e, 49] == 11, a3 = 9];
>>> If[Mod[e, 49] == 12, a3 = 45]; If[Mod[e, 49] == 13, a3 = 34];
>>> If[Mod[e, 49] == 15, a3 = 36]; If[Mod[e, 49] == 16, a3 = 46];
>>> If[Mod[e, 49] == 17, a3 = 26]; If[Mod[e, 49] == 18, a3 = 30];
>>> If[Mod[e, 49] == 19, a3 = 31]; If[Mod[e, 49] == 20, a3 = 27];
>>> If[Mod[e, 49] == 22, a3 = 29]; If[Mod[e, 49] == 23, a3 = 32];
>>> If[Mod[e, 49] == 24, a3 = 47]; If[Mod[e, 49] == 25, a3 = 2];
>>> If[Mod[e, 49] == 26, a3 = 17]; If[Mod[e, 49] == 27, a3 = 20];
>>> If[Mod[e, 49] == 29, a3 = 22]; If[Mod[e, 49] == 30, a3 = 18];
>>> If[Mod[e, 49] == 31, a3 = 19]; If[Mod[e, 49] == 32, a3 = 23];
>>> If[Mod[e, 49] == 33, a3 = 3]; If[Mod[e, 49] == 34, a3 = 13];
>>> If[Mod[e, 49] == 36, a3 = 15]; If[Mod[e, 49] == 37, a3 = 4];
>>> If[Mod[e, 49] == 38, a3 = 40]; If[Mod[e, 49] == 39, a3 = 44];
>>> If[Mod[e, 49] == 40, a3 = 38]; If[Mod[e, 49] == 41, a3 = 6];
>>> If[Mod[e, 49] == 43, a3 = 8]; If[Mod[e, 49] == 44, a3 = 39];
>>> If[Mod[e, 49] == 45, a3 = 12]; If[Mod[e, 49] == 46, a3 = 16];
>>> If[Mod[e, 49] == 47, a3 = 24]; If[Mod[e, 49] == 48, a3 = 48];
>>> Return[Mod[a1*T1*M1 + a2*T2*M2 + a3*T3*M3, 1176]]]
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>> Flip,
>>
>> to "simplify" your module, resort to metaprogramming, i.e. 
>write another
>> program that constructs that module from data you supply 
>from a table.
>>
>> The following is a somewhat foolish example, just to show 
>the idea. To 
>> begin with, I cut out part of your coding...
>>
>> In[2]:=
>> Cases[Hold[If[Mod[e, 3] == 1, a1 = 1]; If[Mod[e, 3] == 2, a1 = 2];
>> If[Mod[e, 8] == 1, a2 = 1];
>> ......,and so on......
>> If[Mod[e, 49] == 47, a3 = 24]; If[Mod[e, 49] == 48, a3 = 48];],
>> If[Mod[_, g_] == h_, ax_ = k_] :> {ax, g, h, k}, Infinity];
>>
>> ...to extract your data
>>
>> In[3]:= Split[%, #1[[1]] === #2[[1]] &];
>>
>> ...group, and transform it to a handy structure
>>
>> In[4]:= ctab = {#[[1, {1, 2}]], #[[All, {3, 4}]]} & /@ %;
>>
>>
>> Of course in future you'll just start with ctab, or 
>something similar.
>>
>>
>>
>> In[5]:= dcalc2[e_] := Block[{a1, a2, a3}, {T1, M1, T2, M2, 
>T3, M3} = {2, 
>> 392, 3, 147, 47, 24};
>> (Evaluate[#[[1, 1]]] = Switch[Mod[e, #[[1, 2]]], 
>Evaluate[Apply[Sequence, 
>> #[[2, All]], {0, 1}]], _, 0 ]) & /@ ctab;
>> Mod[a1*T1*M1 + a2*T2*M2 + a3*T3*M3, 1176]]
>>
>> In[6]:= d100 = dcalc /@ Range[100];
>> In[7]:= d100x = dcalc2 /@ Range[100];
>> In[8]:= d100 == d100x
>> Out[8]= True
>>
>> As said, just to get an idea; this is not a suggestion as 
>how to code it,
>> don't use the hard-wired symbols a1, a2, a3 between ctab and dcalc2
>> (generate them as needed) or thread, avoid global T1, M2, etc. Your
>> exercise.
>>
>> --
>> Hartmut
>>
>>
>> PS, perhaps something like
>>
>> dcalc3[e_] := Mod[Plus @@ MapThread[
>> Switch[Mod[e, #1[[1, 2]]], Evaluate[Apply[Sequence, #1[[2, 
>All]], {0, 
>> 1}]],
>> _, 0 ]*#2*#3 &, {ctab, {2, 3, 47}, {392, 147, 24}}], 1176]
>>
>> (a1, etc. not used)
>>
>>
>>
>
>
>
>-- 
>majort at cox-internet.com
>Bobby R. Treat
>

• Follow-Ups:
  • Re: RE: Simplify a module
    • From: Dr Bob <drbob@bigfoot.com>