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1.1 ! noro 1: /* $OpenXM: OpenXM/src/asir99/lib/num,v 1.1.1.1 1999/11/10 08:12:30 noro Exp $ */
! 2: /* factorial */
! 3:
! 4: def f(N)
! 5: {
! 6: for ( I = 1, M = 1; I <= N; I++ )
! 7: M *= I;
! 8: return M;
! 9: }
! 10:
! 11: /* factorial by recursion */
! 12:
! 13: def recf(X) {
! 14: if ( X == 0 )
! 15: return ( 1 );
! 16: else
! 17: return ( X * recf(X-1) );
! 18: }
! 19:
! 20: /* Catalan's constant */
! 21:
! 22: def cat(D) {
! 23: tstart;
! 24: for ( S = T = P = idiv(10^D,2), I = 1, J = 3; T; I++, J += 2 ) {
! 25: P = idiv(P*I,J); T = idiv(T*I+P,J); S += T;
! 26: }
! 27: tstop;
! 28: return S;
! 29: }
! 30:
! 31: /* Napier's constant */
! 32:
! 33: def e(D,N)
! 34: {
! 35: for ( F = 1, S = 1, I = 1; I <= N; I++ ) {
! 36: S = S*I + 1;
! 37: F *= I;
! 38: }
! 39: T = red(S/F);
! 40: return idiv(nm(T)*10^D,dn(T));
! 41: }
! 42:
! 43: /* atan */
! 44:
! 45: def at0(X,D)
! 46: {
! 47: for ( S = T = idiv(D,X), I = 1, Y = X^2, Sgn = -1;
! 48: T;
! 49: I += 2, Sgn *= -1 ) {
! 50: T = idiv(T*I,Y*(I+2)); S += (Sgn*T);
! 51: }
! 52: return S;
! 53: }
! 54:
! 55: /* pi */
! 56:
! 57: def pi(D)
! 58: {
! 59: tstart; Y = 10^D; X = 16*at0(5,Y)-4*at0(239,Y); tstop;
! 60: return X;
! 61: }
! 62:
! 63: def at1(M,D) {
! 64: for (N = 1, SGN = 1, MM = M*M, A = 0, XN = idiv(D,M);
! 65: XN;
! 66: N += 2, XN = idiv(XN,MM), SGN *= -1)
! 67: A += (SGN*idiv(XN,N));
! 68: return A;
! 69: }
! 70:
! 71: def pi1(D) {
! 72: tstart; Y = 10^D; X = 16*at1(5,Y)-4*at1(239,Y); tstop;
! 73: return X;
! 74: }
! 75:
! 76: def pi2(D) {
! 77: tstart; Y = 10^D;
! 78: X = 48*at1(49,Y)+128*at1(57,Y)-20*at1(239,Y)+48*at1(110443,Y);
! 79: tstop;
! 80: return X;
! 81: }
! 82:
! 83: /* Bernoulli number */
! 84: def bn(N)
! 85: {
! 86: B = newvect(N+1); C = c2(N+1);
! 87: for ( I = 1, B[0] = 1; I <= N; I++ ) {
! 88: for ( D = C[I+1], J = 0, S = 0; J < I; J++ )
! 89: S += D[J]*B[J];
! 90: B[I] = red(-S/(I+1));
! 91: }
! 92: return [B,C];
! 93: }
! 94:
! 95: def bp(N,B,C,V)
! 96: {
! 97: for ( I = 0, S = 0; I <= N; I++ )
! 98: S += C[I]*B[N-I]*V^I;
! 99: return S;
! 100: }
! 101:
! 102: /*
! 103: * sum(N) = 1^N+2^N+...+n^N
! 104: */
! 105:
! 106: def sum(N)
! 107: {
! 108: L = bn(N+1);
! 109: R = car(L); C = car(cdr(L));
! 110: S = bp(N+1,R,C[N+1],n);
! 111: return red((subst(S,n,n+1)-subst(S,n,1))/(N+1));
! 112: }
! 113:
! 114: /* nCi */
! 115:
! 116: def c(N,I)
! 117: {
! 118: for ( M = 1, J = 0; J < I; J++ )
! 119: M *= N-J;
! 120: return red(M/f(I));
! 121: }
! 122:
! 123: def c1(N)
! 124: {
! 125: A = newvect(N+1); B = newvect(N+1); A[0] = 1;
! 126: for ( K = 1; K <= N; K++ ) {
! 127: B[0] = B[K] = 1;
! 128: for ( J = 1; J < K; J++ ) B[J] = A[J-1]+A[J];
! 129: T = A; A = B; B = T;
! 130: }
! 131: return A;
! 132: }
! 133:
! 134: def c2(N)
! 135: {
! 136: A = newvect(N+1); A[0] = B = newvect(1); B[0] = 1;
! 137: for ( K = 1; K <= N; K++ ) {
! 138: A[K] = B = newvect(K+1); B[0] = B[K] = 1;
! 139: for ( P = A[K-1], J = 1; J < K; J++ )
! 140: B[J] = P[J-1]+P[J];
! 141: }
! 142: return A;
! 143: }
! 144:
! 145: def sumd(N,M)
! 146: {
! 147: for ( I = 1, S = 0; I <= M; I++ )
! 148: S += I^N;
! 149: return S;
! 150: }
! 151:
! 152: #if 0
! 153: def sqrt(A,N) {
! 154: for ( I = 0, X = 1, B = A; I < N; I++, B *= 100, X *= 10 ) {
! 155: while ( 1 ) {
! 156: T = idiv(idiv(B,X) + X,2);
! 157: /*
! 158: if ((Y = T - X)== 0)
! 159: if ( B == X^2) return (X/(10^I));
! 160: else break;
! 161: else if ( (Y == 1) || (Y == -1) ) break;
! 162: */
! 163: if ( ( (Y = T - X) == 0 ) || (Y == 1) || (Y == -1) ) break;
! 164: X = T;
! 165: }
! 166: }
! 167: return (X/(10^I));
! 168: }
! 169: #endif
! 170:
! 171: def sqrt(A) {
! 172: for ( J = 0, T = A; T >= 2^27; J++ ) {
! 173: T = idiv(T,2^27)+1;
! 174: }
! 175: for ( I = 0; T >= 2; I++ ) {
! 176: S = idiv(T,2);
! 177: if ( T = S+S )
! 178: T = S;
! 179: else
! 180: T = S+1;
! 181: }
! 182: X = (2^27)^idiv(J,2)*2^idiv(I,2);
! 183: while ( 1 ) {
! 184: if ( (Y=X^2) < A )
! 185: X += X;
! 186: else if ( Y == A )
! 187: return X;
! 188: else
! 189: break;
! 190: }
! 191: while ( 1 )
! 192: if ( (Y = X^2) <= A )
! 193: return X;
! 194: else
! 195: X = idiv(A + Y,2*X);
! 196: }
! 197:
! 198: /* internal -> hexadecimal */
! 199:
! 200: def hex(N) {
! 201: C = newvect(6,["a","b","c","d","e","f"]);
! 202: for ( I = 0, T = 1; T < N; T *= 16, I++ );
! 203: B = newvect(I+1);
! 204: for ( I = 0; N >= 16; I++ ) {
! 205: B[I] = irem(N,16);
! 206: N = idiv(N,16);
! 207: }
! 208: B[I] = N;
! 209: for ( ; I >= 0; I-- )
! 210: if ( (T = B[I]) < 10 )
! 211: print(T,0);
! 212: else
! 213: print(C[B[I]-10],0);
! 214: print("");
! 215: }
! 216:
! 217: /* internal -> binary */
! 218:
! 219: def bin(N) {
! 220: for ( I = 0, T = 1; T < N; T *= 2, I++ );
! 221: B = newvect(I+1);
! 222: for ( I = 0; N >= 2; I++ ) {
! 223: B[I] = irem(N,2);
! 224: N = idiv(N,2);
! 225: }
! 226: B[I] = N;
! 227: for ( ; I >= 0; I-- ) {
! 228: if ( B[I] )
! 229: print("1",0);
! 230: else
! 231: print("0",0);
! 232: }
! 233: print("");
! 234: }
! 235: end$