Annotation of OpenXM_contrib2/asir2018/lib/num, Revision 1.1
1.1 ! 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
! 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
! 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: *
! 48: * $OpenXM$
! 49: */
! 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$
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