The source files need the many.h header file, C24 need gauss.h too, and C22 needs the intlib library from Laurent Fousse (not yet available).
The given timings were obtained on harif.cs.ru.nl, a mono-processor AMD Opteron 144 machine running Debian GNU/Linux "sid" unstable i386 (32 bit mode), which has 4GB of RAM. We used gmp-4.1.4, mpfr-20050920 (cvs version from 20 Sep 2005), and mpfi-1.3.3 (adapted to mpfr-cvs). The methods used in the different programs are explained here. We recall here the rule to find the ``optimal'' parameter N: "find the N closest to the default value so that the cpu time fits between 2 seconds and 2 minutes".
| Problem | Parameter (initial value) | Output | Results | |||
|---|---|---|---|---|---|---|
| C01 | sin (tan (cos (1)) | N (=4) | The first 10N decimal digits after the decimal point | 17.8s for N=5, using c01.c | ||
| C02 | sqrt (e/pi) | N (=5) | The first 10N decimal digits after the decimal point | 32.0s for N=6, using c02.c | ||
| C03 | sin((e+1)^3) | N (=4) | The first 10N decimal digits after the decimal point | 9.1s for N=5 using c03.c | ||
| C04 | exp (pi * sqrt(2011)) | N (=4) | The first 10N decimal digits after the decimal point | 11.6s for N=5 using c04.c | ||
| C05 | exp (exp (exp (1/2))) | N (=4) | The first 10N decimal digits after the decimal point | 5.1s for N=5 using c05a.c | ||
| C06 | arctanh(1-arctanh(1-arctanh(1-arctanh(1/pi)))) | N (=4) | The first 10N decimal digits after the decimal point | 8.2s for N=5 using c06.c | ||
| C07 | pi^1000 | N (=4) | The first 10N decimal digits after the decimal point | 24.8s for N=6 using c07a.c | ||
| C08 | sin(6(6^6)) | N (=4) | The first 10N decimal digits after the decimal point | 8.7s for N=5 using c08a.c | ||
| C09 | sin(10*arctan(tanh(pi*(2011^(1/2))/3))) | N (=4) | The first 10N decimal digits after the decimal point | 33.1s for N=5 using c09.c | ||
| C10 | (7+2^(1/5)-5*(8^(1/5)))^(1/3) + 4^(1/5)-2^(1/5) | N (=4) | The first 10N decimal digits after the decimal point | 4.1s for N=5 using c10.c | ||
| C11 | tan(2^(1/2))+arctanh(sin(1)) | N (=4) | The first 10N decimal digits after the decimal point | 24.2s for N=5 using c11.c | ||
| C12 | arcsin(1/e^2) + arcsinh(e^2) | N (=4) | The first 10N decimal digits after the decimal point | 8.5s for N=5 using c12.c | ||
| C13 | The logistic map: x0=.5, xn+1=3.999*xn*(1-xn) | N (=4) | The first 10N digits after the decimal point of x10N | 9.1s for N=4 using c13.c | ||
| C14 | a0=14/3, a1=5, a2=184/35, a(n+2)= 114 - (1463 - (6390 - (9000/an-1))/an)/an+1 | N (=2) | The first 10N digits after the decimal point of a(10N+2). | 40.4s for N=2 using c14tmp.c | ||
| C15 | h(n) = 1/n + 1/(n+1) +...+ 1/n^2 | N (=4) | The first 10N digits after the decimal point of h(10N+1). | 7.2s for N=4 using c15a.c | ||
| C16 | f(i)= (Pi^2)/6 - (13/8+(1/(8*27))(34/8+(8/(8*125))(...((21*i-8)/8+((i^3)/(8*(2i+1)^3)))))) | N (=4) | The first 10N digits after the decimal point of f(10N) | 0.9s for N=4, 129.0s for N=5 using c16.c | ||
| C17 | S= -4*Zeta(2) - 2*Zeta(3) + 4*Zeta(2)*Zeta(3) + 2*Zeta(5) | N (=4) | The first 10N decimal digits after the decimal point of S | 115.5s for N=5 using c17best.c | ||
| C18 | Catalan G = Sum{n=0}{\infty}(-1)^i/(2i+1)^2 | N (=4) | The first 10N decimal digits after the decimal point of G | 8.1s for N=5 using c18.c | ||
| C19 | an=n^3+1, L= Sum{n=1}{\infty} (1/7)^(an) | N (=4) | The first 10N digits after the decimal point of L | 3.4s for N=6 using c19.c | ||
| C20 | X = sin(2*pi/17) | N (=4) | The 10Nth element of the regular continued fraction of X | 4.3s for N=5 using c20b.c | ||
| C21 | Equation exp(cos(x)) = x | N (=4) | The first 10N digits after the decimal point of x | 14.8s for N=5 using c21.c | ||
| C22 | J = integral(sin(sin(sin(x)))), x=0..1 | N (=3) | The first 10N digits after the decimal point of J | 26.1s for N=3 using c22.c with n=218, m=26 | ||
| C23 |
M1=Inverse of the 10N*10N Hankel matrix X
where Xij=1/fib(i+j-1) (i,j>0) fib(k)=((1+sqrt(5))^k-(1-sqrt(5))^k)/(2^k*sqrt(5)) |
N (=2) | The first 10 decimal digits of the element (10N -1,10N -3) of the matrix | 18.5s for N=7 using c23-c.c | ||
| C24 | M2=Inverse of I10N+X (sum of the identity and the 10Nx10N Hankel matrix X) where X is defined as in C23 | N (=2) | The first 10 decimal digits of the element (10N -1,10N) of the matrix | 0.2s for N=2, 172.8s for N=3 using c24.c |