![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to const CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM_contrib2 / asir2000 / lib|
Return to const CVS log | Up to [local] / OpenXM_contrib2 / asir2000 / lib |
1.1 ! noro 1: /* $OpenXM: OpenXM/src/asir99/lib/const,v 1.1.1.1 1999/11/10 08:12:30 noro Exp $ */
! 2: def cat(D) {
! 3: tstart;
! 4: for ( S = T = P = idiv(10^D,2), I = 1, J = 3; T; I++, J += 2 ) {
! 5: P = idiv(P*I,J); T = idiv(T*I+P,J); S += T;
! 6: }
! 7: tstop;
! 8: return S;
! 9: }
! 10:
! 11: def e(D,N)
! 12: {
! 13: for ( F = 1, S = 1, I = 1; I <= N; I++ ) {
! 14: S = S*I + 1;
! 15: F *= I;
! 16: }
! 17: T = red(S/F);
! 18: return idiv(nm(T)*10^D,dn(T));
! 19: }
! 20:
! 21: def at0(X,D)
! 22: {
! 23: for ( S = T = idiv(D,X), I = 1, Y = X^2, Sgn = -1;
! 24: T;
! 25: I += 2, Sgn *= -1 ) {
! 26: T = idiv(T*I,Y*(I+2)); S += (Sgn*T);
! 27: }
! 28: return S;
! 29: }
! 30:
! 31: def pi(D)
! 32: {
! 33: tstart; Y = 10^D; X = 16*at0(5,Y)-4*at0(239,Y); tstop;
! 34: return X;
! 35: }
! 36:
! 37: def at1(M,D) {
! 38: for (N = 1, SGN = 1, MM = M*M, A = 0, XN = idiv(D,M);
! 39: XN;
! 40: N += 2, XN = idiv(XN,MM), SGN *= -1)
! 41: A += (SGN*idiv(XN,N));
! 42: return A;
! 43: }
! 44:
! 45: def pi1(D) {
! 46: tstart; Y = 10^D; X = 16*at1(5,Y)-4*at1(239,Y); tstop;
! 47: return X;
! 48: }
! 49:
! 50: def pi2(D) {
! 51: tstart; Y = 10^D;
! 52: X = 48*at1(49,Y)+128*at1(57,Y)-20*at1(239,Y)+48*at1(110443,Y);
! 53: tstop;
! 54: return X;
! 55: }
! 56:
! 57:
! 58: def bn(N)
! 59: {
! 60: B = newvect(N+1); C = c2(N+1);
! 61: for ( I = 1, B[0] = 1; I <= N; I++ ) {
! 62: for ( D = C[I+1], J = 0, S = 0; J < I; J++ )
! 63: S += D[J]*B[J];
! 64: B[I] = red(-S/(I+1));
! 65: }
! 66: return [B,C];
! 67: }
! 68:
! 69: def bp(N,B,C,V)
! 70: {
! 71: for ( I = 0, S = 0; I <= N; I++ )
! 72: S += C[I]*B[N-I]*V^I;
! 73: return S;
! 74: }
! 75:
! 76: /*
! 77: * sum(N) = 1^N+2^N+...+n^N
! 78: */
! 79:
! 80: def sum(N)
! 81: {
! 82: L = bn(N+1);
! 83: R = car(L); C = car(cdr(L));
! 84: S = bp(N+1,R,C[N+1],n);
! 85: return red((subst(S,n,n+1)-subst(S,n,1))/(N+1));
! 86: }
! 87:
! 88: def c(N,I)
! 89: {
! 90: for ( M = 1, J = 0; J < I; J++ )
! 91: M *= N-J;
! 92: return red(M/f(I));
! 93: }
! 94:
! 95: def c1(N)
! 96: {
! 97: A = newvect(N+1); B = newvect(N+1); A[0] = 1;
! 98: for ( K = 1; K <= N; K++ ) {
! 99: B[0] = B[K] = 1;
! 100: for ( J = 1; J < K; J++ ) B[J] = A[J-1]+A[J];
! 101: T = A; A = B; B = T;
! 102: }
! 103: return A;
! 104: }
! 105:
! 106: def c2(N)
! 107: {
! 108: A = newvect(N+1); A[0] = B = newvect(1); B[0] = 1;
! 109: for ( K = 1; K <= N; K++ ) {
! 110: A[K] = B = newvect(K+1); B[0] = B[K] = 1;
! 111: for ( P = A[K-1], J = 1; J < K; J++ )
! 112: B[J] = P[J-1]+P[J];
! 113: }
! 114: return A;
! 115: }
! 116:
! 117: def f(N)
! 118: {
! 119: for ( I = 1, M = 1; I <= N; I++ )
! 120: M *= I;
! 121: return M;
! 122: }
! 123:
! 124: def sumd(N,M)
! 125: {
! 126: for ( I = 1, S = 0; I <= M; I++ )
! 127: S += I^N;
! 128: return S;
! 129: }
! 130:
! 131: #if 0
! 132: def sqrt(A,N) {
! 133: for ( I = 0, X = 1, B = A; I < N; I++, B *= 100, X *= 10 ) {
! 134: while ( 1 ) {
! 135: T = idiv(idiv(B,X) + X,2);
! 136: /*
! 137: if ((Y = T - X)== 0)
! 138: if ( B == X^2) return (X/(10^I));
! 139: else break;
! 140: else if ( (Y == 1) || (Y == -1) ) break;
! 141: */
! 142: if ( ( (Y = T - X) == 0 ) || (Y == 1) || (Y == -1) ) break;
! 143: X = T;
! 144: }
! 145: }
! 146: return (X/(10^I));
! 147: }
! 148: #endif
! 149:
! 150: def sqrt(A) {
! 151: for ( J = 0, T = A; T >= 2^27; J++ ) {
! 152: T = idiv(T,2^27)+1;
! 153: }
! 154: for ( I = 0; T >= 2; I++ ) {
! 155: S = idiv(T,2);
! 156: if ( T = S+S )
! 157: T = S;
! 158: else
! 159: T = S+1;
! 160: }
! 161: X = (2^27)^idiv(J,2)*2^idiv(I,2);
! 162: while ( 1 ) {
! 163: if ( (Y=X^2) < A )
! 164: X += X;
! 165: else if ( Y == A )
! 166: return X;
! 167: else
! 168: break;
! 169: }
! 170: while ( 1 )
! 171: if ( (Y = X^2) <= A )
! 172: return X;
! 173: else
! 174: X = idiv(A + Y,2*X);
! 175: }
! 176: end$