Annotation of OpenXM_contrib2/asir2000/lib/num, 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/num,v 1.2 2000/08/21 08:31:41 noro Exp $
1.2 noro 49: */
1.1 noro 50: /* factorial */
51:
52: def f(N)
53: {
54: for ( I = 1, M = 1; I <= N; I++ )
55: M *= I;
56: return M;
57: }
58:
59: /* factorial by recursion */
60:
61: def recf(X) {
62: if ( X == 0 )
63: return ( 1 );
64: else
65: return ( X * recf(X-1) );
66: }
67:
68: /* Catalan's constant */
69:
70: def cat(D) {
71: tstart;
72: for ( S = T = P = idiv(10^D,2), I = 1, J = 3; T; I++, J += 2 ) {
73: P = idiv(P*I,J); T = idiv(T*I+P,J); S += T;
74: }
75: tstop;
76: return S;
77: }
78:
79: /* Napier's constant */
80:
81: def e(D,N)
82: {
83: for ( F = 1, S = 1, I = 1; I <= N; I++ ) {
84: S = S*I + 1;
85: F *= I;
86: }
87: T = red(S/F);
88: return idiv(nm(T)*10^D,dn(T));
89: }
90:
91: /* atan */
92:
93: def at0(X,D)
94: {
95: for ( S = T = idiv(D,X), I = 1, Y = X^2, Sgn = -1;
96: T;
97: I += 2, Sgn *= -1 ) {
98: T = idiv(T*I,Y*(I+2)); S += (Sgn*T);
99: }
100: return S;
101: }
102:
103: /* pi */
104:
105: def pi(D)
106: {
107: tstart; Y = 10^D; X = 16*at0(5,Y)-4*at0(239,Y); tstop;
108: return X;
109: }
110:
111: def at1(M,D) {
112: for (N = 1, SGN = 1, MM = M*M, A = 0, XN = idiv(D,M);
113: XN;
114: N += 2, XN = idiv(XN,MM), SGN *= -1)
115: A += (SGN*idiv(XN,N));
116: return A;
117: }
118:
119: def pi1(D) {
120: tstart; Y = 10^D; X = 16*at1(5,Y)-4*at1(239,Y); tstop;
121: return X;
122: }
123:
124: def pi2(D) {
125: tstart; Y = 10^D;
126: X = 48*at1(49,Y)+128*at1(57,Y)-20*at1(239,Y)+48*at1(110443,Y);
127: tstop;
128: return X;
129: }
130:
131: /* Bernoulli number */
132: def bn(N)
133: {
134: B = newvect(N+1); C = c2(N+1);
135: for ( I = 1, B[0] = 1; I <= N; I++ ) {
136: for ( D = C[I+1], J = 0, S = 0; J < I; J++ )
137: S += D[J]*B[J];
138: B[I] = red(-S/(I+1));
139: }
140: return [B,C];
141: }
142:
143: def bp(N,B,C,V)
144: {
145: for ( I = 0, S = 0; I <= N; I++ )
146: S += C[I]*B[N-I]*V^I;
147: return S;
148: }
149:
150: /*
151: * sum(N) = 1^N+2^N+...+n^N
152: */
153:
154: def sum(N)
155: {
156: L = bn(N+1);
157: R = car(L); C = car(cdr(L));
158: S = bp(N+1,R,C[N+1],n);
159: return red((subst(S,n,n+1)-subst(S,n,1))/(N+1));
160: }
161:
162: /* nCi */
163:
164: def c(N,I)
165: {
166: for ( M = 1, J = 0; J < I; J++ )
167: M *= N-J;
168: return red(M/f(I));
169: }
170:
171: def c1(N)
172: {
173: A = newvect(N+1); B = newvect(N+1); A[0] = 1;
174: for ( K = 1; K <= N; K++ ) {
175: B[0] = B[K] = 1;
176: for ( J = 1; J < K; J++ ) B[J] = A[J-1]+A[J];
177: T = A; A = B; B = T;
178: }
179: return A;
180: }
181:
182: def c2(N)
183: {
184: A = newvect(N+1); A[0] = B = newvect(1); B[0] = 1;
185: for ( K = 1; K <= N; K++ ) {
186: A[K] = B = newvect(K+1); B[0] = B[K] = 1;
187: for ( P = A[K-1], J = 1; J < K; J++ )
188: B[J] = P[J-1]+P[J];
189: }
190: return A;
191: }
192:
193: def sumd(N,M)
194: {
195: for ( I = 1, S = 0; I <= M; I++ )
196: S += I^N;
197: return S;
198: }
199:
200: #if 0
201: def sqrt(A,N) {
202: for ( I = 0, X = 1, B = A; I < N; I++, B *= 100, X *= 10 ) {
203: while ( 1 ) {
204: T = idiv(idiv(B,X) + X,2);
205: /*
206: if ((Y = T - X)== 0)
207: if ( B == X^2) return (X/(10^I));
208: else break;
209: else if ( (Y == 1) || (Y == -1) ) break;
210: */
211: if ( ( (Y = T - X) == 0 ) || (Y == 1) || (Y == -1) ) break;
212: X = T;
213: }
214: }
215: return (X/(10^I));
216: }
217: #endif
218:
219: def sqrt(A) {
220: for ( J = 0, T = A; T >= 2^27; J++ ) {
221: T = idiv(T,2^27)+1;
222: }
223: for ( I = 0; T >= 2; I++ ) {
224: S = idiv(T,2);
225: if ( T = S+S )
226: T = S;
227: else
228: T = S+1;
229: }
230: X = (2^27)^idiv(J,2)*2^idiv(I,2);
231: while ( 1 ) {
232: if ( (Y=X^2) < A )
233: X += X;
234: else if ( Y == A )
235: return X;
236: else
237: break;
238: }
239: while ( 1 )
240: if ( (Y = X^2) <= A )
241: return X;
242: else
243: X = idiv(A + Y,2*X);
244: }
245:
246: /* internal -> hexadecimal */
247:
248: def hex(N) {
249: C = newvect(6,["a","b","c","d","e","f"]);
250: for ( I = 0, T = 1; T < N; T *= 16, I++ );
251: B = newvect(I+1);
252: for ( I = 0; N >= 16; I++ ) {
253: B[I] = irem(N,16);
254: N = idiv(N,16);
255: }
256: B[I] = N;
257: for ( ; I >= 0; I-- )
258: if ( (T = B[I]) < 10 )
259: print(T,0);
260: else
261: print(C[B[I]-10],0);
262: print("");
263: }
264:
265: /* internal -> binary */
266:
267: def bin(N) {
268: for ( I = 0, T = 1; T < N; T *= 2, I++ );
269: B = newvect(I+1);
270: for ( I = 0; N >= 2; I++ ) {
271: B[I] = irem(N,2);
272: N = idiv(N,2);
273: }
274: B[I] = N;
275: for ( ; I >= 0; I-- ) {
276: if ( B[I] )
277: print("1",0);
278: else
279: print("0",0);
280: }
281: print("");
282: }
283: end$
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to num CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM_contrib2 / asir2000 / lib