March 2014 update
This commit is contained in:
Ingy döt Net
parent
09687c4926
commit
a25938f123
1846 changed files with 21876 additions and 5203 deletions
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@ -1,17 +1,22 @@
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import std.stdio, std.mathspecial;
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import std.stdio, std.math, std.mathspecial;
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real myGamma(in real x) pure nothrow {
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real taylorGamma(in real x) pure nothrow {
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static immutable real[30] table = [
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1.00000000000000000000, 0.57721566490153286061, -0.65587807152025388108,
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-0.04200263503409523553, 0.16653861138229148950, -0.04219773455554433675,
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-0.00962197152787697356, 0.00721894324666309954, -0.00116516759185906511,
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-0.00021524167411495097, 0.00012805028238811619, -0.00002013485478078824,
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-0.00000125049348214267, 0.00000113302723198170, -0.00000020563384169776,
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0.00000000611609510448, 0.00000000500200764447, -0.00000000118127457049,
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0.00000000010434267117, 0.00000000000778226344, -0.00000000000369680562,
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0.00000000000051003703, -0.00000000000002058326, -0.00000000000000534812,
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0.00000000000000122678, -0.00000000000000011813, 0.00000000000000000119,
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0.00000000000000000141, -0.00000000000000000023, 0.00000000000000000002];
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0x1p+0, 0x1.2788cfc6fb618f4cp-1,
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-0x1.4fcf4026afa2dcecp-1, -0x1.5815e8fa27047c8cp-5,
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0x1.5512320b43fbe5dep-3, -0x1.59af103c340927bep-5,
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-0x1.3b4af28483e214e4p-7, 0x1.d919c527f60b195ap-8,
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-0x1.317112ce3a2a7bd2p-10, -0x1.c364fe6f1563ce9cp-13,
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0x1.0c8a78cd9f9d1a78p-13, -0x1.51ce8af47eabdfdcp-16,
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-0x1.4fad41fc34fbb2p-20, 0x1.302509dbc0de2c82p-20,
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-0x1.b9986666c225d1d4p-23, 0x1.a44b7ba22d628acap-28,
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0x1.57bc3fc384333fb2p-28, -0x1.44b4cedca388f7c6p-30,
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0x1.cae7675c18606c6p-34, 0x1.11d065bfaf06745ap-37,
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-0x1.0423bac8ca3faaa4p-38, 0x1.1f20151323cd0392p-41,
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-0x1.72cb88ea5ae6e778p-46, -0x1.815f72a05f16f348p-48,
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0x1.6198491a83bccbep-50, -0x1.10613dde57a88bd6p-53,
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0x1.5e3fee81de0e9c84p-60, 0x1.a0dc770fb8a499b6p-60,
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-0x1.0f635344a29e9f8ep-62, 0x1.43d79a4b90ce8044p-66];
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immutable real y = x - 1.0L;
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real sm = table[$ - 1];
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@ -20,9 +25,38 @@ real myGamma(in real x) pure nothrow {
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return 1.0L / sm;
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}
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real lanczosGamma(real z) pure nothrow {
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// Coefficients used by the GNU Scientific Library.
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// http://en.wikipedia.org/wiki/Lanczos_approximation
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enum g = 7;
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static immutable real[9] table =
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[ 0.99999_99999_99809_93,
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676.52036_81218_851,
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-1259.13921_67224_028,
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771.32342_87776_5313,
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-176.61502_91621_4059,
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12.50734_32786_86905,
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-0.13857_10952_65720_12,
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9.98436_95780_19571_6e-6,
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1.50563_27351_49311_6e-7];
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// Reflection formula.
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if (z < 0.5L) {
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return PI / (sin(PI * z) * lanczosGamma(1 - z));
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} else {
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z -= 1;
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real x = table[0];
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foreach (immutable i; 1 .. g + 2)
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x += table[i] / (z + i);
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immutable real t = z + g + 0.5L;
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return sqrt(2 * PI) * t ^^ (z + 0.5L) * exp(-t) * x;
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}
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}
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void main() {
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foreach (immutable i; 1 .. 11) {
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immutable real x = i / 3.0L;
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writefln("%f: %20.19e %20.19e", x, myGamma(x), gamma(x));
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writefln("%f: %20.19e %20.19e %20.19e", x,
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x.taylorGamma, x.lanczosGamma, x.gamma);
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}
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}
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15
Task/Gamma-function/Forth/gamma-function.fth
Normal file
15
Task/Gamma-function/Forth/gamma-function.fth
Normal file
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@ -0,0 +1,15 @@
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8 constant (gamma-shift)
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: (mortici) ( f1 -- f2)
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-1 s>f f+ 1 s>f
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fover 271828183e-8 f* 12 s>f f* f/
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fover 271828183e-8 f/ f+
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fover f** fswap
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628318530e-8 f* fsqrt f* \ 2*pi
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;
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: gamma ( f1 -- f2)
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fdup f0< >r fdup f0= r> or abort" Gamma less or equal to zero"
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fdup (gamma-shift) s>f f+ (mortici) fswap
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1 s>f (gamma-shift) 0 do fover i s>f f+ f* loop fswap fdrop f/
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;
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44
Task/Gamma-function/Limbo/gamma-function.limbo
Normal file
44
Task/Gamma-function/Limbo/gamma-function.limbo
Normal file
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@ -0,0 +1,44 @@
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implement Lanczos7;
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include "sys.m"; sys: Sys;
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include "draw.m";
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include "math.m"; math: Math;
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lgamma, exp, pow, sqrt: import math;
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Lanczos7: module {
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init: fn(nil: ref Draw->Context, nil: list of string);
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};
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init(nil: ref Draw->Context, nil: list of string)
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{
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sys = load Sys Sys->PATH;
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math = load Math Math->PATH;
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# We ignore some floating point exceptions:
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math->FPcontrol(0, Math->OVFL|Math->UNFL);
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ns : list of real = -0.5 :: 0.1 :: 0.5 :: 1.0 :: 1.5 :: 2.0 :: 3.0 :: 10.0 :: 140.0 :: 170.0 :: nil;
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sys->print("%5s %24s %24s\n", "x", "math->lgamma", "lanczos7");
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while(ns != nil) {
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x := hd ns;
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ns = tl ns;
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# math->lgamma returns a tuple.
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(i, r) := lgamma(x);
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g := real i * exp(r);
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sys->print("%5.1f %24.16g %24.16g\n", x, g, lanczos7(x));
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}
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}
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lanczos7(z: real): real
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{
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t := z + 6.5;
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x := 0.99999999999980993 +
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676.5203681218851/z -
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1259.1392167224028/(z+1.0) +
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771.32342877765313/(z+2.0) -
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176.61502916214059/(z+3.0) +
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12.507343278686905/(z+4.0) -
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0.13857109526572012/(z+5.0) +
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9.9843695780195716e-6/(z+6.0) +
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1.5056327351493116e-7/(z+7.0);
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return sqrt(2.0) * sqrt(Math->Pi) * pow(t, z - 0.5) * exp(-t) * x;
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}
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@ -1,18 +1,51 @@
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sub Γ($x) {
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1 / <
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0.00000_00000_00000_00002 -0.00000_00000_00000_00023 0.00000_00000_00000_00141
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0.00000_00000_00000_00119 -0.00000_00000_00000_11813 0.00000_00000_00001_22678
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-0.00000_00000_00005_34812 -0.00000_00000_00020_58326 0.00000_00000_00510_03703
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-0.00000_00000_03696_80562 0.00000_00000_07782_26344 0.00000_00001_04342_67117
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-0.00000_00011_81274_57049 0.00000_00050_02007_64447 0.00000_00061_16095_10448
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-0.00000_02056_33841_69776 0.00000_11330_27231_98170 -0.00000_12504_93482_14267
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-0.00002_01348_54780_78824 0.00012_80502_82388_11619 -0.00021_52416_74114_95097
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-0.00116_51675_91859_06511 0.00721_89432_46663_09954 -0.00962_19715_27876_97356
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-0.04219_77345_55544_33675 0.16653_86113_82291_48950 -0.04200_26350_34095_23553
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-0.65587_80715_20253_88108 0.57721_56649_01532_86061 1.00000_00000_00000_00000
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>.reduce: * *($x-1) + *
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sub Γ(\z, :$method = 'lanczos') {
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given $method {
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when 'lanczos' {
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constant g = 9;
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z < .5 ?? pi/ sin(pi * z) / Γ(1 - z, :$method) !!
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sqrt(2*pi) *
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(z + g - 1/2)**(z - 1/2) *
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exp(-(z + g - 1/2)) *
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[+] <
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1.000000000000000174663
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5716.400188274341379136
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-14815.30426768413909044
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14291.49277657478554025
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-6348.160217641458813289
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1301.608286058321874105
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-108.1767053514369634679
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2.605696505611755827729
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-0.7423452510201416151527e-2
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0.5384136432509564062961e-7
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-0.4023533141268236372067e-8
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> Z* 1, map 1/(z + *), 0..*
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}
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when 'stirling' {
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z < 10 ?? Γ(z + 1, :$method) / z !!
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sqrt(2*pi*z)*(z/e + 1/(12*z*e))**z / z
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}
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when 'taylor' {
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z > 3/2 ?? (z - 1)*Γ(z - 1, :$method) !!
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z < 1/2 ?? Γ(z + 1, :$method)/z !!
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1 / <
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0.00000_00000_00000_00002 -0.00000_00000_00000_00023 0.00000_00000_00000_00141
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0.00000_00000_00000_00119 -0.00000_00000_00000_11813 0.00000_00000_00001_22678
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-0.00000_00000_00005_34812 -0.00000_00000_00020_58326 0.00000_00000_00510_03703
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-0.00000_00000_03696_80562 0.00000_00000_07782_26344 0.00000_00001_04342_67117
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-0.00000_00011_81274_57049 0.00000_00050_02007_64447 0.00000_00061_16095_10448
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-0.00000_02056_33841_69776 0.00000_11330_27231_98170 -0.00000_12504_93482_14267
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-0.00002_01348_54780_78824 0.00012_80502_82388_11619 -0.00021_52416_74114_95097
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-0.00116_51675_91859_06511 0.00721_89432_46663_09954 -0.00962_19715_27876_97356
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-0.04219_77345_55544_33675 0.16653_86113_82291_48950 -0.04200_26350_34095_23553
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-0.65587_80715_20253_88108 0.57721_56649_01532_86061 1.00000_00000_00000_00000
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>.reduce: * *(z-1) + *
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}
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default { die "unknow method '$method'" }
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}
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}
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for 1/3, 2/3 ... 10/3 {
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printf "Γ(%.5f) ≈ %.14f\n", $_, Γ($_);
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for <lanczos taylor stirling> -> $method {
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# a bug in fmt forces us to round numbers before displaying them
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say "{$method.fmt("%10s")}: ",
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map { Γ($_, :$method).round(1e-12).fmt("%.12f") }, (1/3, 2/3 ... 10/3);
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}
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@ -1,44 +1,61 @@
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my @coeff = reverse <DATA>;
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use strict;
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use warnings;
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use constant pi => 4*atan2(1, 1);
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use constant e => exp(1);
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sub Gamma {
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my $x = shift;
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my $s;
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$s = $s*($x-1) + $_ for @coeff;
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return 1 / $s;
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my $z = shift;
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my $method = shift // 'lanczos';
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if ($method eq 'lanczos') {
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use constant g => 9;
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$z < .5 ? pi / sin(pi * $z) / Gamma(1 - $z, $method) :
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sqrt(2* pi) *
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($z + g - .5)**($z - .5) *
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exp(-($z + g - .5)) *
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do {
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my @coeff = qw{
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1.000000000000000174663
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5716.400188274341379136
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-14815.30426768413909044
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14291.49277657478554025
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-6348.160217641458813289
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1301.608286058321874105
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-108.1767053514369634679
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2.605696505611755827729
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-0.7423452510201416151527e-2
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0.5384136432509564062961e-7
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-0.4023533141268236372067e-8
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};
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my ($sum, $i) = (shift(@coeff), 0);
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$sum += $_ / ($z + $i++) for @coeff;
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$sum;
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}
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} elsif ($method eq 'taylor') {
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$z < .5 ? Gamma($z+1, $method)/$z :
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$z > 1.5 ? ($z-1)*Gamma($z-1, $method) :
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do {
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my $s = 0; ($s *= $z-1) += $_ for qw{
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0.00000000000000000002 -0.00000000000000000023 0.00000000000000000141
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0.00000000000000000119 -0.00000000000000011813 0.00000000000000122678
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-0.00000000000000534812 -0.00000000000002058326 0.00000000000051003703
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-0.00000000000369680562 0.00000000000778226344 0.00000000010434267117
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-0.00000000118127457049 0.00000000500200764447 0.00000000611609510448
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-0.00000020563384169776 0.00000113302723198170 -0.00000125049348214267
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-0.00002013485478078824 0.00012805028238811619 -0.00021524167411495097
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-0.00116516759185906511 0.00721894324666309954 -0.00962197152787697356
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-0.04219773455554433675 0.16653861138229148950 -0.04200263503409523553
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-0.65587807152025388108 0.57721566490153286061 1.00000000000000000000
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}; 1/$s;
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}
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} elsif ($method eq 'stirling') {
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no warnings qw(recursion);
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$z < 100 ? Gamma($z + 1, $method)/$z :
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sqrt(2*pi*$z)*($z/e + 1/(12*e*$z))**$z / $z;
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} else { die "unknown method '$method'" }
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}
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for (1 .. 10) {
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$_ /= 3;
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printf "Gamma(%.5f) ≈ %.14e\n", $_, Gamma($_);
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for my $method (qw(lanczos taylor stirling)) {
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printf "%10s: ", $method;
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print join(' ', map { sprintf "%.12f", Gamma($_/3, $method) } 1 .. 10);
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print "\n";
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}
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__DATA__
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1.00000000000000000000
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0.57721566490153286061
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-0.65587807152025388108
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-0.04200263503409523553
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0.16653861138229148950
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-0.04219773455554433675
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-0.00962197152787697356
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0.00721894324666309954
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-0.00116516759185906511
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-0.00021524167411495097
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0.00012805028238811619
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-0.00002013485478078824
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-0.00000125049348214267
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0.00000113302723198170
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-0.00000020563384169776
|
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0.00000000611609510448
|
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0.00000000500200764447
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||||
-0.00000000118127457049
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0.00000000010434267117
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||||
0.00000000000778226344
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-0.00000000000369680562
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0.00000000000051003703
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-0.00000000000002058326
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||||
-0.00000000000000534812
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0.00000000000000122678
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||||
-0.00000000000000011813
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0.00000000000000000119
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0.00000000000000000141
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-0.00000000000000000023
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0.00000000000000000002
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|
|
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@ -1,70 +1,68 @@
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/*REXX pgm calculates GAMMA using Taylor series coefficients, ≈80 digits*/
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/*The GAMMA function symbol is the Greek cap letter: Γ */
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numeric digits 82 /*able to use extended precision.*/
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parse arg y . /*allow specification of Γ arg.*/
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/*either show a range or a */
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do j=word(y 1,1) to word(y 9,1) /* single gamma value(s). */
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say 'gamma('j") =" gamma(j) /*compute gamma of J and display.*/
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end /*j*/
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exit /*stick a fork in it, we're done.*/
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/*The GAMMA function symbol is the Greek capital letter: Γ */
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numeric digits 84 /*able to use extended precision.*/
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parse arg y z . /*allow specification of Γ arg.*/
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/*either show a range or a ··· */
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do j=word(y 1,1) to word(z y 9,1) /* ··· single gamma value(s). */
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say 'gamma('j") =" gamma(j) /*compute gamma of J and display.*/
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end /*j*/
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exit /*stick a fork in it, we're done.*/
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/*───────────────────────────────────GAMMA subroutine=──────────────────*/
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gamma: procedure; parse arg x; xm=x-1; sum=0
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#.1= 1 /*#.2 is the Euler-Mascheroni constant.*/
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/*coefficients thanks to: Arne Fransén and Staffan Wrigge.*/
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#.2= 0.57721566490153286060651209008240243104215933593992359880576723488486772677766467
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#.3=-0.65587807152025388107701951514539048127976638047858434729236244568387083835372210
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#.4=-0.04200263503409523552900393487542981871139450040110609352206581297618009687597599
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#.5= 0.16653861138229148950170079510210523571778150224717434057046890317899386605647425
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#.6=-0.04219773455554433674820830128918739130165268418982248637691887327545901118558900
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#.7=-0.00962197152787697356211492167234819897536294225211300210513886262731167351446074
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#.8= 0.00721894324666309954239501034044657270990480088023831800109478117362259497415854
|
||||
#.9=-0.00116516759185906511211397108401838866680933379538405744340750527562002584816653
|
||||
#.10=-0.00021524167411495097281572996305364780647824192337833875035026748908563946371678
|
||||
#.11= 0.00012805028238811618615319862632816432339489209969367721490054583804120355204347
|
||||
#.12=-0.00002013485478078823865568939142102181838229483329797911526116267090822918618897
|
||||
#.13=-0.00000125049348214267065734535947383309224232265562115395981534992315749121245561
|
||||
#.14= 0.00000113302723198169588237412962033074494332400483862107565429550539546040842730
|
||||
#.15=-0.00000020563384169776071034501541300205728365125790262933794534683172533245680371
|
||||
#.16= 0.00000000611609510448141581786249868285534286727586571971232086732402927723507435
|
||||
#.17= 0.00000000500200764446922293005566504805999130304461274249448171895337887737472132
|
||||
#.18=-0.00000000118127457048702014458812656543650557773875950493258759096189263169643391
|
||||
#.19= 0.00000000010434267116911005104915403323122501914007098231258121210871073927347588
|
||||
#.20= 0.00000000000778226343990507125404993731136077722606808618139293881943550732692987
|
||||
#.21=-0.00000000000369680561864220570818781587808576623657096345136099513648454655443000
|
||||
#.22= 0.00000000000051003702874544759790154813228632318027268860697076321173501048565735
|
||||
#.23=-0.00000000000002058326053566506783222429544855237419746091080810147188058196444349
|
||||
#.24=-0.00000000000000534812253942301798237001731872793994898971547812068211168095493211
|
||||
#.25= 0.00000000000000122677862823826079015889384662242242816545575045632136601135999606
|
||||
#.26=-0.00000000000000011812593016974587695137645868422978312115572918048478798375081233
|
||||
#.27= 0.00000000000000000118669225475160033257977724292867407108849407966482711074006109
|
||||
#.28= 0.00000000000000000141238065531803178155580394756670903708635075033452562564122263
|
||||
#.29=-0.00000000000000000022987456844353702065924785806336992602845059314190367014889830
|
||||
#.30= 0.00000000000000000001714406321927337433383963370267257066812656062517433174649858
|
||||
#.31= 0.00000000000000000000013373517304936931148647813951222680228750594717618947898583
|
||||
#.32=-0.00000000000000000000020542335517666727893250253513557337960820379352387364127301
|
||||
#.33= 0.00000000000000000000002736030048607999844831509904330982014865311695836363370165
|
||||
#.34=-0.00000000000000000000000173235644591051663905742845156477979906974910879499841377
|
||||
#.35=-0.00000000000000000000000002360619024499287287343450735427531007926413552145370486
|
||||
#.36= 0.00000000000000000000000001864982941717294430718413161878666898945868429073668232
|
||||
#.37=-0.00000000000000000000000000221809562420719720439971691362686037973177950067567580
|
||||
#.38= 0.00000000000000000000000000012977819749479936688244144863305941656194998646391332
|
||||
#.39= 0.00000000000000000000000000000118069747496652840622274541550997151855968463784158
|
||||
#.40=-0.00000000000000000000000000000112458434927708809029365467426143951211941179558301
|
||||
#.41= 0.00000000000000000000000000000012770851751408662039902066777511246477487720656005
|
||||
#.42=-0.00000000000000000000000000000000739145116961514082346128933010855282371056899245
|
||||
#.43= 0.00000000000000000000000000000000001134750257554215760954165259469306393008612196
|
||||
#.44= 0.00000000000000000000000000000000004639134641058722029944804907952228463057968680
|
||||
#.45=-0.00000000000000000000000000000000000534733681843919887507741819670989332090488591
|
||||
#.46= 0.00000000000000000000000000000000000032079959236133526228612372790827943910901464
|
||||
#.47=-0.00000000000000000000000000000000000000444582973655075688210159035212464363740144
|
||||
#.48=-0.00000000000000000000000000000000000000131117451888198871290105849438992219023663
|
||||
#.49= 0.00000000000000000000000000000000000000016470333525438138868182593279063941453996
|
||||
#.50=-0.00000000000000000000000000000000000000001056233178503581218600561071538285049997
|
||||
#.51= 0.00000000000000000000000000000000000000000026784429826430494783549630718908519485
|
||||
#.52= 0.00000000000000000000000000000000000000000002424715494851782689673032938370921241
|
||||
/*coefficients thanks to: Arne Fransén and Staffan Wrigge.*/
|
||||
#.1 = 1 /* [↓] #.2 is the Euler-Mascheroni constant.*/
|
||||
#.2 = 0.57721566490153286060651209008240243104215933593992359880576723488486772677766467
|
||||
#.3 = -0.65587807152025388107701951514539048127976638047858434729236244568387083835372210
|
||||
#.4 = -0.04200263503409523552900393487542981871139450040110609352206581297618009687597599
|
||||
#.5 = 0.16653861138229148950170079510210523571778150224717434057046890317899386605647425
|
||||
#.6 = -0.04219773455554433674820830128918739130165268418982248637691887327545901118558900
|
||||
#.7 = -0.00962197152787697356211492167234819897536294225211300210513886262731167351446074
|
||||
#.8 = 0.00721894324666309954239501034044657270990480088023831800109478117362259497415854
|
||||
#.9 = -0.00116516759185906511211397108401838866680933379538405744340750527562002584816653
|
||||
#.10 = -0.00021524167411495097281572996305364780647824192337833875035026748908563946371678
|
||||
#.11 = 0.00012805028238811618615319862632816432339489209969367721490054583804120355204347
|
||||
#.12 = -0.00002013485478078823865568939142102181838229483329797911526116267090822918618897
|
||||
#.13 = -0.00000125049348214267065734535947383309224232265562115395981534992315749121245561
|
||||
#.14 = 0.00000113302723198169588237412962033074494332400483862107565429550539546040842730
|
||||
#.15 = -0.00000020563384169776071034501541300205728365125790262933794534683172533245680371
|
||||
#.16 = 0.00000000611609510448141581786249868285534286727586571971232086732402927723507435
|
||||
#.17 = 0.00000000500200764446922293005566504805999130304461274249448171895337887737472132
|
||||
#.18 = -0.00000000118127457048702014458812656543650557773875950493258759096189263169643391
|
||||
#.19 = 0.00000000010434267116911005104915403323122501914007098231258121210871073927347588
|
||||
#.20 = 0.00000000000778226343990507125404993731136077722606808618139293881943550732692987
|
||||
#.21 = -0.00000000000369680561864220570818781587808576623657096345136099513648454655443000
|
||||
#.22 = 0.00000000000051003702874544759790154813228632318027268860697076321173501048565735
|
||||
#.23 = -0.00000000000002058326053566506783222429544855237419746091080810147188058196444349
|
||||
#.24 = -0.00000000000000534812253942301798237001731872793994898971547812068211168095493211
|
||||
#.25 = 0.00000000000000122677862823826079015889384662242242816545575045632136601135999606
|
||||
#.26 = -0.00000000000000011812593016974587695137645868422978312115572918048478798375081233
|
||||
#.27 = 0.00000000000000000118669225475160033257977724292867407108849407966482711074006109
|
||||
#.28 = 0.00000000000000000141238065531803178155580394756670903708635075033452562564122263
|
||||
#.29 = -0.00000000000000000022987456844353702065924785806336992602845059314190367014889830
|
||||
#.30 = 0.00000000000000000001714406321927337433383963370267257066812656062517433174649858
|
||||
#.31 = 0.00000000000000000000013373517304936931148647813951222680228750594717618947898583
|
||||
#.32 = -0.00000000000000000000020542335517666727893250253513557337960820379352387364127301
|
||||
#.33 = 0.00000000000000000000002736030048607999844831509904330982014865311695836363370165
|
||||
#.34 = -0.00000000000000000000000173235644591051663905742845156477979906974910879499841377
|
||||
#.35 = -0.00000000000000000000000002360619024499287287343450735427531007926413552145370486
|
||||
#.36 = 0.00000000000000000000000001864982941717294430718413161878666898945868429073668232
|
||||
#.37 = -0.00000000000000000000000000221809562420719720439971691362686037973177950067567580
|
||||
#.38 = 0.00000000000000000000000000012977819749479936688244144863305941656194998646391332
|
||||
#.39 = 0.00000000000000000000000000000118069747496652840622274541550997151855968463784158
|
||||
#.40 = -0.00000000000000000000000000000112458434927708809029365467426143951211941179558301
|
||||
#.41 = 0.00000000000000000000000000000012770851751408662039902066777511246477487720656005
|
||||
#.42 = -0.00000000000000000000000000000000739145116961514082346128933010855282371056899245
|
||||
#.43 = 0.00000000000000000000000000000000001134750257554215760954165259469306393008612196
|
||||
#.44 = 0.00000000000000000000000000000000004639134641058722029944804907952228463057968680
|
||||
#.45 = -0.00000000000000000000000000000000000534733681843919887507741819670989332090488591
|
||||
#.46 = 0.00000000000000000000000000000000000032079959236133526228612372790827943910901464
|
||||
#.47 = -0.00000000000000000000000000000000000000444582973655075688210159035212464363740144
|
||||
#.48 = -0.00000000000000000000000000000000000000131117451888198871290105849438992219023663
|
||||
#.49 = 0.00000000000000000000000000000000000000016470333525438138868182593279063941453996
|
||||
#.50 = -0.00000000000000000000000000000000000000001056233178503581218600561071538285049997
|
||||
#.51 = 0.00000000000000000000000000000000000000000026784429826430494783549630718908519485
|
||||
#.52 = 0.00000000000000000000000000000000000000000002424715494851782689673032938370921241
|
||||
do j=52 by -1 to 1
|
||||
sum = sum * xm + #.j
|
||||
end /*j*/
|
||||
end /*j*/
|
||||
return 1/sum
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue