Can anyone make heads or tales of this spigot algorithm code Pitiny.c

Question

This C program is just 143 characters long!

But it “decompresses” into the first 10,000 digits of Pi.

//  Created by cheeseMan on 30/11/13.

long a[35014],b,c=35014,d,e,f=1e4,g,h;

int main(int argc, const char * argv[])

{
    for(;(b=c-=14);

        h=printf("%04ld",e+d/f))

        for(e=d%=f;(g=--b*2);d/=g)
            d=d*b+f*(h?a[b]:f/5), a[b]=d%--g;
}

I was doing some research on loss-less compression algorithms, still no luck yet, when I came across this pitiny.c.

The weird thing is that it compiles successfully no errors or bugs, but like i said i cannot make heads or tales of the code, even its syntax. I just would like to know whats going on? what is it doing exactly?

Answer 1

Update

This program is a purposely obfuscated implementation of a spigot algorithm for the Digits of Pi from the book Pi - Unleashed and we can find the original version on page 37 of the book which is as follows:

a[52514],b,c=52514,d,e,f=1e4,g,h;main(){for(;b=c-=14;h=printf("%04d", e+d/f))for(e=d%=f;g=--b*2;d/=g)d=db+f(h?a[b]:f/5),a[b]=d%--g;}

the paper Unbounded Spigot Algorithms for the Digits of Pi does a good job in explaining the algorithm. Basically it is an implementation of this expansion:

Original

The reason it was designed this way other than to make the code impossible to comprehend and impress people escapes me but we can break down what is going on, first here:

long a[35014],b,c=35014,d,e,f=1e4,g,h;

the variables are static since they are global so all variables not explicitly initialized will be initialized to 0. Next we have an outer for loop:

for(;(b=c-=14); h=printf("%04ld",e+d/f)
    ^ ^         ^
    1 2         3

1. Is an empty initialization and it also a null statement.
2. Is subtracting 14 from c and assigning the value back to c and also assigning the same value to b. This loop will execute 2500 times since 35014/14 is 2501 and on the 2501th iteration the result will 0 and thus false and the loop will stop.
3. h is being assigned the result of printf which is the number of characters printed. What is being printed out is the result of e+d/f and always at least 4 digits and zero padded due to 04 in the format specifier.

Now we have an inner for loop:

for(e=d%=f;(g=--b*2);d/=g)
    ^       ^        ^
    1       2        3

1. Initializes e and d to d modulus f.
2. Due to operator precedence does a pre-decrement of b and multiples that by 2 and assigns the result to g
3. d is being divided by g and assigned the result.

Finally the body of the inner for loop:

d=d*b+f*(h?a[b]:f/5), a[b]=d%--g;
          ^         ^
          1         2

uses both the conditional operator in 1 and comma operator in 2. So we could at least split this into:

d    = d*b+f*(h?a[b]:f/5) ; // (1)
a[b] = d%--g;               // (2)

(1) can further be broken down into:

long tmp =  h ? a[b] : f/5 ;  // conditional operator
d = (d * b) + f * tmp;

The conditional operator only matters during the first iteration since h is intialized to 0 but will never be 0 again afterwards since it is always assigned a non-zero value in the outer for loop, so other then the first time h will be assigned a[b].

(2) will again due to precedence pre-decrement g first and then evaluate d modulus the result and assign that to a[b].

Answer 2

It can be written as

long a[35014];
long b;
long c=35014;
long d;
long e;
long f=1e4;
long g;
long h;

int main(int argc, const char * argv[])
{
    for(; (b=c-=14); h=printf("%04ld",e+d/f)) {
        for(e=d%=f; (g=--b*2); d/=g) {
            d = (d * b) + f * ( h ? a[b] : f/5);
            a[b] = d % --g;
        }
    }
}

In other words it's double for loop

Answer 3

Just for grins:
"Calculate" Pi to 10,000 digits
Here is a "simplified" version. "Simplified" meaning breaking up the multiple operators, using the results of assignment statements and for loops. Missing are meaningful names.

(this was verified against the results of the original code.

void simplier() {
    long a[35014];
    long b = 0;
    long c = 35000;
    long d = 0;
    long e = 0;
    long f = 10000;
    long g = 0;
    long h = 0;
    long i = 0;

    while (c) {
        d %= f;
        e  = d;
        b  = c-1;
        g  = b*2;

        while(g) {
            g -= 1;
            i  = h ? a[b] : f/5;
            d  = (d*b) + (f*i);
            a[b] = d % g;
            d /= g;
            b -= 1;
            g  = b*2;
        }

        printf("%04ld", e+d/f);
        h  = 1;
        c -= 14;
    }
}

Runtimes:

Original time: 1.110
Simplier time: 1.138

Of course most of the time is in the formatting and printing.

Output:

31415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416948685558484063534220722258284886481584560285060168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288797108931456691368672287489405601015033086179286809208747609178249385890097149096759852613655497818931297848216829989487226588048575640142704775551323796414515237462343645428584447952658678210511413547357395231134271661021359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435064302184531910484810053706146806749192781911979399520614196634287544406437451237181921799983910159195618146751426912397489409071864942319615679452080951465502252316038819301420937621378559566389377870830390697920773467221825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539057962685610055081066587969981635747363840525714591028970641401109712062804390397595156771577004203378699360072305587631763594218731251471205329281918261861258673215791984148488291644706095752706957220917567116722910981690915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398315019701651511685171437657618351556508849099898599823873455283316355076479185358932261854896321329330898570642046752590709154814165498594616371802709819943099244889575712828905923233260972997120844335732654893823911932597463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100449293215160842444859637669838952286847831235526582131449576857262433441893039686426243410773226978028073189154411010446823252716201052652272111660396665573092547110557853763466820653109896526918620564769312570586356620185581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318586769751456614068007002378776591344017127494704205622305389945613140711270004078547332699390814546646458807972708266830634328587856983052358089330657574067954571637752542021149557615814002501262285941302164715509792592309907965473761255176567513575178296664547791745011299614890304639947132962107340437518957359614589019389713111790429782856475032031986915140287080859904801094121472213179476477726224142548545403321571853061422881375850430633217518297986622371721591607716692547487389866549494501146540628433663937900397692656721463853067360965712091807638327166416274888800786925602902284721040317211860820419000422966171196377921337575114959501566049631862947265473642523081770367515906735023507283540567040386743513622224771589150495309844489333096340878076932599397805419341447377441842631298608099888687413260472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