// System to calculate digits of pi. // ftp://rtfm.mit.edu/pub/usenet/sci.math/sci.math_FAQ%3A_Digits_or_Pi // // This uses Ramanujan's equation for pi, which converges very rapidly. // It adds approximately 8 decimal places for each iteration through the loop. // Most of the class is for caching so repeated calls are efficient. // Users should use the Pi.getPi[] method which performs caching. use root.frink class Pi { // This is a cache of digits of pi keyed by digits. class var cachedPiDict = new dict // This is a cache of digits of sqrt[K3] keyed by digits. class var cachedK3Dict = new dict // The number of digits in the biggest cached value. class var biggestCachedDigitsPi = -1 // The number of digits in the biggest cached value. class var biggestCachedDigitsK3 = -1 // The biggest calculated cached value of pi. class var biggestCachePi = undef // The biggest calculated cached root of k3 class var biggestCacheK3 = undef // get pi to the specified number of digits, with caching class getPi[digits] := { digits = ceil[digits] cachedVal = cachedPiDict@digits if cachedVal != undef return cachedVal else // Must generate it if digits <= biggestCachedDigitsPi { prevPrec = getPrecision[] try { setPrecision[digits] val = 1. * biggestCachePi // Generate from cached value cachedPiDict@digits = val return val } finally setPrecision[prevPrec] } else { // Generate whole thing val = calculatePi[digits] cachedPiDict@digits = val biggestCachePi = val biggestCachedDigitsPi = digits return val } } // Calculate pi to the specified number of digits. // You shouldn't call this method directly, but rather call getPi[digits] // which does caching. class calculatePi[digits] := { k1 = 545140134 k2 = 13591409 k3 = 640320 k4 = 100100025 k5 = 327843840 k6 = 53360 dn = 8 k4 k5 s=0 mypi = 0 prevPrec = getPrecision[] try { setPrecision[digits+3] err = 10^(-digits-1) //println["Err is \$err"] n = 0 do { term = (-1)^n ((6n)! (k2 + n k1)) / ((n!)^3 (3n)! dn^n) s = s + term // if (n mod 100 == 0) // print["\$n..."] n = n + 1 } while (abs[term] > err) //println["Used \$n terms"] //println["Taking root"] sqrk = getRootK3[digits+3] mypi = k6 / s sqrk setPrecision[digits] return mypi * 1. } finally setPrecision[prevPrec] } // get the root of k3 to the specified number of digits, with caching. class getRootK3[digits] := { digits = ceil[digits] cachedVal = cachedK3Dict@digits if cachedVal != undef return cachedVal else // Must generate it if digits <= biggestCachedDigitsK3 { prevPrec = getPrecision[] try { setPrecision[digits] val = 1. * biggestCacheK3 // Generate from cached value cachedK3Dict@digits = val return val } finally setPrecision[prevPrec] } else { // Generate whole thing val = sqrt[640320, digits] cachedK3Dict@digits = val biggestCacheK3 = val biggestCachedDigitsK3 = digits return val } } } //start = now[] //println[Pi.getPi[10000]] //end = now[] //println["Total time: " + (end-start)] //println[Pi.getPi[40]] //println[Pi.getPi[5000]] // pifull = 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875546873115956286388235378759375195778185778053217122680661300192787661119590921642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151557485724245415069595082953311686172785588907509838175463746493931925506040092770167113900984882401285836160356370766010471018194295559619894676783744944825537977472684710404753464620804668425906949129331367702898915210475216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992458631503028618297455570674983850549458858692699569092721079750930295532116534498720275596023648066549911988183479775356636980742654252786255181841757467289097777279380008164706001614524919217321721477235014144197356854816136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179049460165346680498862723279178608578438382796797668145410095388378636095068006422512520511739298489608412848862694560424196528502221066118630674427862203919494504712371378696095636437191728746776465757396241389086583264599581339047802759009946576407895126946839835259570982582262052248940772671947826848260147699090264013639443745530506820349625245174939965143142980919065925093722169646151570985838741059788595977297549893016175392846813826868386894277415599185592524595395943104997252468084598727364469584865383673622262609912460805124388439045124413654976278079771569143599770012961608944169486855584840635342207222582848864815845602850601684273945226746767889525213852254995466672782398645659611635488623057745649803559363456817432411251507606947945109659609402522887971089314566913686722874894056010150330861792868092087476091782493858900971490967598526136554978189312978482168299894872265880485756401427047755513237964145152374623436454285844479526586782105114135473573952311342716610213596953623144295248493718711014576540359027993440374200731057853906219838744780847848968332144571386875194350643021845319104848100537061468067491927