Annotation of OpenXM_contrib2/asir2000/lib/const, Revision 1.3
1.2 noro 1: /*
2: * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
3: * All rights reserved.
4: *
5: * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
6: * non-exclusive and royalty-free license to use, copy, modify and
7: * redistribute, solely for non-commercial and non-profit purposes, the
8: * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
9: * conditions of this Agreement. For the avoidance of doubt, you acquire
10: * only a limited right to use the SOFTWARE hereunder, and FLL or any
11: * third party developer retains all rights, including but not limited to
12: * copyrights, in and to the SOFTWARE.
13: *
14: * (1) FLL does not grant you a license in any way for commercial
15: * purposes. You may use the SOFTWARE only for non-commercial and
16: * non-profit purposes only, such as academic, research and internal
17: * business use.
18: * (2) The SOFTWARE is protected by the Copyright Law of Japan and
19: * international copyright treaties. If you make copies of the SOFTWARE,
20: * with or without modification, as permitted hereunder, you shall affix
21: * to all such copies of the SOFTWARE the above copyright notice.
22: * (3) An explicit reference to this SOFTWARE and its copyright owner
23: * shall be made on your publication or presentation in any form of the
24: * results obtained by use of the SOFTWARE.
25: * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
1.3 ! noro 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.2 noro 27: * for such modification or the source code of the modified part of the
28: * SOFTWARE.
29: *
30: * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
31: * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
32: * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
33: * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
43: * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
44: * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
45: * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
46: * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
47: *
1.3 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/lib/const,v 1.2 2000/08/21 08:31:41 noro Exp $
1.2 noro 49: */
1.1 noro 50: def cat(D) {
51: tstart;
52: for ( S = T = P = idiv(10^D,2), I = 1, J = 3; T; I++, J += 2 ) {
53: P = idiv(P*I,J); T = idiv(T*I+P,J); S += T;
54: }
55: tstop;
56: return S;
57: }
58:
59: def e(D,N)
60: {
61: for ( F = 1, S = 1, I = 1; I <= N; I++ ) {
62: S = S*I + 1;
63: F *= I;
64: }
65: T = red(S/F);
66: return idiv(nm(T)*10^D,dn(T));
67: }
68:
69: def at0(X,D)
70: {
71: for ( S = T = idiv(D,X), I = 1, Y = X^2, Sgn = -1;
72: T;
73: I += 2, Sgn *= -1 ) {
74: T = idiv(T*I,Y*(I+2)); S += (Sgn*T);
75: }
76: return S;
77: }
78:
79: def pi(D)
80: {
81: tstart; Y = 10^D; X = 16*at0(5,Y)-4*at0(239,Y); tstop;
82: return X;
83: }
84:
85: def at1(M,D) {
86: for (N = 1, SGN = 1, MM = M*M, A = 0, XN = idiv(D,M);
87: XN;
88: N += 2, XN = idiv(XN,MM), SGN *= -1)
89: A += (SGN*idiv(XN,N));
90: return A;
91: }
92:
93: def pi1(D) {
94: tstart; Y = 10^D; X = 16*at1(5,Y)-4*at1(239,Y); tstop;
95: return X;
96: }
97:
98: def pi2(D) {
99: tstart; Y = 10^D;
100: X = 48*at1(49,Y)+128*at1(57,Y)-20*at1(239,Y)+48*at1(110443,Y);
101: tstop;
102: return X;
103: }
104:
105:
106: def bn(N)
107: {
108: B = newvect(N+1); C = c2(N+1);
109: for ( I = 1, B[0] = 1; I <= N; I++ ) {
110: for ( D = C[I+1], J = 0, S = 0; J < I; J++ )
111: S += D[J]*B[J];
112: B[I] = red(-S/(I+1));
113: }
114: return [B,C];
115: }
116:
117: def bp(N,B,C,V)
118: {
119: for ( I = 0, S = 0; I <= N; I++ )
120: S += C[I]*B[N-I]*V^I;
121: return S;
122: }
123:
124: /*
125: * sum(N) = 1^N+2^N+...+n^N
126: */
127:
128: def sum(N)
129: {
130: L = bn(N+1);
131: R = car(L); C = car(cdr(L));
132: S = bp(N+1,R,C[N+1],n);
133: return red((subst(S,n,n+1)-subst(S,n,1))/(N+1));
134: }
135:
136: def c(N,I)
137: {
138: for ( M = 1, J = 0; J < I; J++ )
139: M *= N-J;
140: return red(M/f(I));
141: }
142:
143: def c1(N)
144: {
145: A = newvect(N+1); B = newvect(N+1); A[0] = 1;
146: for ( K = 1; K <= N; K++ ) {
147: B[0] = B[K] = 1;
148: for ( J = 1; J < K; J++ ) B[J] = A[J-1]+A[J];
149: T = A; A = B; B = T;
150: }
151: return A;
152: }
153:
154: def c2(N)
155: {
156: A = newvect(N+1); A[0] = B = newvect(1); B[0] = 1;
157: for ( K = 1; K <= N; K++ ) {
158: A[K] = B = newvect(K+1); B[0] = B[K] = 1;
159: for ( P = A[K-1], J = 1; J < K; J++ )
160: B[J] = P[J-1]+P[J];
161: }
162: return A;
163: }
164:
165: def f(N)
166: {
167: for ( I = 1, M = 1; I <= N; I++ )
168: M *= I;
169: return M;
170: }
171:
172: def sumd(N,M)
173: {
174: for ( I = 1, S = 0; I <= M; I++ )
175: S += I^N;
176: return S;
177: }
178:
179: #if 0
180: def sqrt(A,N) {
181: for ( I = 0, X = 1, B = A; I < N; I++, B *= 100, X *= 10 ) {
182: while ( 1 ) {
183: T = idiv(idiv(B,X) + X,2);
184: /*
185: if ((Y = T - X)== 0)
186: if ( B == X^2) return (X/(10^I));
187: else break;
188: else if ( (Y == 1) || (Y == -1) ) break;
189: */
190: if ( ( (Y = T - X) == 0 ) || (Y == 1) || (Y == -1) ) break;
191: X = T;
192: }
193: }
194: return (X/(10^I));
195: }
196: #endif
197:
198: def sqrt(A) {
199: for ( J = 0, T = A; T >= 2^27; J++ ) {
200: T = idiv(T,2^27)+1;
201: }
202: for ( I = 0; T >= 2; I++ ) {
203: S = idiv(T,2);
204: if ( T = S+S )
205: T = S;
206: else
207: T = S+1;
208: }
209: X = (2^27)^idiv(J,2)*2^idiv(I,2);
210: while ( 1 ) {
211: if ( (Y=X^2) < A )
212: X += X;
213: else if ( Y == A )
214: return X;
215: else
216: break;
217: }
218: while ( 1 )
219: if ( (Y = X^2) <= A )
220: return X;
221: else
222: X = idiv(A + Y,2*X);
223: }
224: end$
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