load("c:\\dfw5\\math\\elliptbf2.mac")$

/* Use numerical checks from Numerical Algorithms 10(1995)13-26.
B.C. Carlson Numerical computation of real or complex elliptic integrals
page 22 3. Numerical checks */

mrf:bfloat([[1,2,0,1.3110287771461],
[%i,-%i,0,1.8540746773014],
[0.5,1,0,1.8540746773014],
[%i-1,%i,0,0.79612586584234-%i*(1.2138566698365)],
[2,3,4,0.58408284167715],[%i,-%i,2,1.0441445654064],
[%i-1,%i,1-%i,0.93912050218619-%i*(0.53296252018635)]]);

fpprec:20;
bferrtol:1.b-6;
maxn:16;

bfrf(mrf[5][1],mrf[5][2],mrf[5][3])-mrf[5][4];

rf(x,y,z):=romberg (u/SQRT((u^2*(x+1)-2*u*x+x)*(u^2*(y+1)-2*u*y+y)*(u^2*(z+1)-2*u*z+z)),u,0,1);

bfloat(rf(mrf[5][1],mrf[5][2],mrf[5][3])-mrf[5][4]);