File: [local] / OpenXM_contrib2 / asir2000 / lib / const (download)
Revision 1.1.1.1 (vendor branch), Fri Dec 3 07:39:11 1999 UTC (24 years, 10 months ago) by noro
Branch: NORO
CVS Tags: RELEASE_20000124, RELEASE_1_1_2, ASIR2000 Changes since 1.1: +0 -0
lines
Imported asir2000 as OpenXM_contrib2/asir2000.
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/* $OpenXM: OpenXM_contrib2/asir2000/lib/const,v 1.1.1.1 1999/12/03 07:39:11 noro Exp $ */
def cat(D) {
tstart;
for ( S = T = P = idiv(10^D,2), I = 1, J = 3; T; I++, J += 2 ) {
P = idiv(P*I,J); T = idiv(T*I+P,J); S += T;
}
tstop;
return S;
}
def e(D,N)
{
for ( F = 1, S = 1, I = 1; I <= N; I++ ) {
S = S*I + 1;
F *= I;
}
T = red(S/F);
return idiv(nm(T)*10^D,dn(T));
}
def at0(X,D)
{
for ( S = T = idiv(D,X), I = 1, Y = X^2, Sgn = -1;
T;
I += 2, Sgn *= -1 ) {
T = idiv(T*I,Y*(I+2)); S += (Sgn*T);
}
return S;
}
def pi(D)
{
tstart; Y = 10^D; X = 16*at0(5,Y)-4*at0(239,Y); tstop;
return X;
}
def at1(M,D) {
for (N = 1, SGN = 1, MM = M*M, A = 0, XN = idiv(D,M);
XN;
N += 2, XN = idiv(XN,MM), SGN *= -1)
A += (SGN*idiv(XN,N));
return A;
}
def pi1(D) {
tstart; Y = 10^D; X = 16*at1(5,Y)-4*at1(239,Y); tstop;
return X;
}
def pi2(D) {
tstart; Y = 10^D;
X = 48*at1(49,Y)+128*at1(57,Y)-20*at1(239,Y)+48*at1(110443,Y);
tstop;
return X;
}
def bn(N)
{
B = newvect(N+1); C = c2(N+1);
for ( I = 1, B[0] = 1; I <= N; I++ ) {
for ( D = C[I+1], J = 0, S = 0; J < I; J++ )
S += D[J]*B[J];
B[I] = red(-S/(I+1));
}
return [B,C];
}
def bp(N,B,C,V)
{
for ( I = 0, S = 0; I <= N; I++ )
S += C[I]*B[N-I]*V^I;
return S;
}
/*
* sum(N) = 1^N+2^N+...+n^N
*/
def sum(N)
{
L = bn(N+1);
R = car(L); C = car(cdr(L));
S = bp(N+1,R,C[N+1],n);
return red((subst(S,n,n+1)-subst(S,n,1))/(N+1));
}
def c(N,I)
{
for ( M = 1, J = 0; J < I; J++ )
M *= N-J;
return red(M/f(I));
}
def c1(N)
{
A = newvect(N+1); B = newvect(N+1); A[0] = 1;
for ( K = 1; K <= N; K++ ) {
B[0] = B[K] = 1;
for ( J = 1; J < K; J++ ) B[J] = A[J-1]+A[J];
T = A; A = B; B = T;
}
return A;
}
def c2(N)
{
A = newvect(N+1); A[0] = B = newvect(1); B[0] = 1;
for ( K = 1; K <= N; K++ ) {
A[K] = B = newvect(K+1); B[0] = B[K] = 1;
for ( P = A[K-1], J = 1; J < K; J++ )
B[J] = P[J-1]+P[J];
}
return A;
}
def f(N)
{
for ( I = 1, M = 1; I <= N; I++ )
M *= I;
return M;
}
def sumd(N,M)
{
for ( I = 1, S = 0; I <= M; I++ )
S += I^N;
return S;
}
#if 0
def sqrt(A,N) {
for ( I = 0, X = 1, B = A; I < N; I++, B *= 100, X *= 10 ) {
while ( 1 ) {
T = idiv(idiv(B,X) + X,2);
/*
if ((Y = T - X)== 0)
if ( B == X^2) return (X/(10^I));
else break;
else if ( (Y == 1) || (Y == -1) ) break;
*/
if ( ( (Y = T - X) == 0 ) || (Y == 1) || (Y == -1) ) break;
X = T;
}
}
return (X/(10^I));
}
#endif
def sqrt(A) {
for ( J = 0, T = A; T >= 2^27; J++ ) {
T = idiv(T,2^27)+1;
}
for ( I = 0; T >= 2; I++ ) {
S = idiv(T,2);
if ( T = S+S )
T = S;
else
T = S+1;
}
X = (2^27)^idiv(J,2)*2^idiv(I,2);
while ( 1 ) {
if ( (Y=X^2) < A )
X += X;
else if ( Y == A )
return X;
else
break;
}
while ( 1 )
if ( (Y = X^2) <= A )
return X;
else
X = idiv(A + Y,2*X);
}
end$