aparler/RosettaCodeData
1
0
Fork 0
Code Issues 12 Pull requests 3 Projects Releases Packages Wiki Activity Actions

Data commit

Browse source
This commit is contained in:
Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
199093 changed files with 3378972 additions and 0 deletions
Download patch file Download diff file Expand all files Collapse all files

81
Task/Eulers-constant-0.5772.../XPL0/eulers-constant-0.5772....xpl0 Normal file
View file

@ -0,0 +1,81 @@
\*********************************************
\Subject: Comparing five methods for
\ computing Euler's constant 0.5772...
\---------------------------------------------
include xpllib; \for Print
define Epsilon = 1e-6;
real A, B, H, N2, R, U, V, S(2), B2;
int K, K2, M, N;
[Print("From the definition, error 3e-10\n");
N:= 400; H:= 1.;
for K:= 2 to N do
H:= H + 1.0/float(K);
\Faster convergence: Negoi, 1997
A:= Ln(float(N) + 0.5 + 1.0/(24.*float(N)));
Print("Hn %1.16f\n", H);
Print("gamma %1.16f\nK = %d\n\n", H-A, N);
Print("Sweeney, 1963, error 3e-10\n");
N:= 21; S(0):= 0.; S(1):= float(N);
R:= float(N); K:= 1;
repeat
K:= K+1;
R:= R * float(N) / float(K);
S(K&1):= S(K&1) + R/float(K);
until R <= Epsilon;
Print("gamma %1.16f\nK = %d\n\n", S(1)-S(0)-Ln(float(N)), K);
Print("Bailey, 1988\n");
N:= 5; A:= 1.; H:= 1.;
N2:= Pow(2., float(N));
R:= 1.; K:= 1;
repeat
K:= K+1;
R:= R * N2 / float(K);
H:= H + 1.0/float(K);
B:= A; A:= A + R*H;
until abs(B-A) <= Epsilon;
A:= A * N2 / Exp(N2);
Print("gamma %1.16f\nK = %d\n\n", A-float(N)*Ln(2.), K);
Print("Brent-McMillan, 1980\n");
N:= 13; A:= -Ln(float(N));
B:= 1.; U:= A; V:= B;
N2:= float(N*N); K2:= 0; K:= 0;
repeat
K2:= K2 + 2*K + 1;
K:= K+1;
A:= A * N2 / float(K);
B:= B * N2 / float(K2);
A:= (A + B) / float(K);
U:= U + A;
V:= V + B;
until abs(A) <= Epsilon;
Print("gamma %1.16f\nK = %d\n\n", U/V, K);
Print("How Euler did it in 1735\n");
\Bernoulli numbers with even indices
B2:= [1.0, 1.0/6., -1.0/30., 1.0/42., -1.0/30.,
5.0/66., -691.0/2730., 7.0/6., -3617.0/510., 43867.0/798.];
M:= 7; N:= 10;
\Nth harmonic number
H:= 1.;
for K:= 2 to N do
H:= H + 1.0/float(K);
Print("Hn %1.16f\n", H);
H:= H - Ln(float(N));
Print(" -ln %1.16f\n", H);
\Expansion C:= -digamma(1)
A:= -1.0 / (2.*float(N));
N2:= float(N*N);
R:= 1.;
for K:= 1 to M do [
R:= R * N2;
A:= A + B2(K)/(2.*float(K)*R);
];
Print("err %1.16f\ngamma %1.16f\nK = %d", A, H+A, N+M);
Print("\n\nC = 0.57721566490153286...\n");
]