Annotation of OpenXM_contrib2/asir2000/fft/dft.c, Revision 1.4
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'
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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: *
1.4 ! ohara 48: * $OpenXM: OpenXM_contrib2/asir2000/fft/dft.c,v 1.3 2000/08/22 05:04:12 noro Exp $
1.2 noro 49: */
1.1 noro 50: /*
51: * store arith modulus
52: * -------------------------------------------------------
53: * IEEE: float (23+1) <-> double (52+1) 24 bits
54: * int (32) <-> double (52+1) 26 bits
55: * 370: float (24) <-> double (56) 24/25 bits
56: * int (32) <-> double (56) 28 bits
57: */
58:
59:
60: #include "dft.h"
61:
62:
63: /*
64: #define C_DFT_FORE C_DFTfore
65: #define C_DFT_BACK C_DFTback
66: #define C_PREP_ALPHA C_prep_alpha
67: */
68:
69:
70: /*****************************************************/
71:
72: void C_DFT_FORE( in, nin, i1, K, powa,
73: #ifdef POWA_STRIDE
74: a1,
75: #endif
76: out, o1, P, Pinv, wk )
77: ModNum in[], powa[], out[], wk[];
78: ModNum P;
79: int nin, i1, K, o1;
80: #ifdef POWA_STRIDE
81: int a1;
82: #endif
83: double Pinv;
84: /*
85: * Let N = 2^K, and \alpha be a primitive N-th root of 1.
86: * out[0:N-1][o1] = DFT of in[0:nin-1][i1] using \alpha modulo P.
87: * The powers \alpha (to the degrees upto N/2=2^{K-1} at least) are given in powa[*],
88: * (or powa[a1**]).
89: * nin <= N assumed.
90: * wk[] must have 2^K entries at least.
91: */
92: {
93: int istep, ostep, i, j, k, idist, odist, n, Ndiv2n, K_k,
94: #ifndef OPT
95: K_k_1,
96: #endif
97: #ifdef POWA_STRIDE
98: aj,
99: #endif
100: inwk;
101: int idistwk, idistout, iostep, oostep;
102: ModNum *qi, *qo, *qis, *qos, a, t0, tn;
103:
104: /*
105: * for k = K-1, ..., 0 do the following:
106: *
107: * Out[2^{K-k}*i + j] <= t0 + \alpha^{2^k * j} * tn;
108: * Out[2^{K-k}*i + j + 2^{K-k-1}] <= t0 - \alpha^{2^k * j} * tn;
109: *
110: * where t0 = In[2^{K-k-1}*i + j] and
111: * tn = In[2^{K-k-1}*i + j + 2^{K-1}],
112: * for 0 <= i < 2^k and 0 <= j < 2^{K-k-1}.
113: *
114: */
115: /* In the following, n = 2^k and Ndiv2n = 2^{K-k-1}.
116: */
117: n = 1 << (k = K - 1);
118: idistwk = n, idistout = o1 << k;
119: /* when k = K-1, Out[2*i] <= In[i] + In[i+2^{K-1}],
120: * and Out[2*i+1] <= In[i] - In[i+2^{K-1}], for 0 <= i < 2^{K-1}.
121: */
122: if ( k&1 ) qo = wk, ostep = 2, inwk = 1, odist = 1;
123: else qo = out, ostep = o1 << 1, inwk = 0, odist = o1;
124: qi = in;
125: /**/
126: if ( nin <= n ) {
127: for ( i = nin; i > 0; i--, qi += i1, qo += ostep ) qo[0] = qo[odist] = qi[0];
128: for ( i = n - nin; i > 0; i--, qo += ostep ) qo[0] = qo[odist] = 0;
129: } else {
130: idist = i1 << k; /* distance = 2^{K-1} */
131: for ( j = i = nin - n; i > 0; i--, qi += i1, qo += ostep ) {
132: t0 = qi[0], tn = qi[idist];
133: if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0;
134: else {
135: qo[0] = AplusBmodP( t0, tn, P );
136: qo[odist] = A_BmodP( t0, tn, P );
137: }
138: }
139: for ( i = n - j; i > 0; i--, qi += i1, qo += ostep )
140: qo[0] = qo[odist] = qi[0];
141: }
142: /******/
143: #ifndef J_INNER
144: for ( K_k = 1, Ndiv2n = 1; --k > 0; inwk = 1 - inwk ) {
145: #ifndef OPT
146: K_k = (K_k_1 = K_k) + 1;
147: #endif
148: n >>= 1; /* == 2^k */
149: Ndiv2n <<= 1; /* == 2^{K-k-1} */
150: if ( inwk )
151: qi = wk, qo = out, iostep = 1, oostep = o1, idist = idistwk;
152: else
153: qi = out, qo = wk, iostep = o1, oostep = 1, idist = idistout;
154: qis = qi, qos = qo;
155: /**/
156: istep = ostep; /* = iostep << K_k_1; */
157: #ifndef OPT
158: ostep = oostep << K_k;
159: odist = oostep << K_k_1;
160: #else
161: odist = oostep << K_k;
162: ++K_k;
163: ostep = oostep << K_k;
164: #endif /* OPT */
165: /* j = 0 */
166: for ( i = n; i-- > 0; qi += istep, qo += ostep ) {
167: t0 = qi[0], tn = qi[idist];
168: if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0;
169: else {
170: qo[0] = AplusBmodP( t0, tn, P );
171: qo[odist] = A_BmodP( t0, tn, P );
172: }
173: }
174: /**/
175: #ifdef POWA_STRIDE
176: for ( aj = a1, j = 1; j < Ndiv2n; aj += a1, j++ ) {
177: a = powa[aj << k];
178: #else
179: for ( j = 1; j < Ndiv2n; j++ ) {
180: a = powa[j << k];
181: #endif
182: qi = (qis += iostep), qo = (qos += oostep);
183: for ( i = 0; i < n; i++, qi += istep, qo += ostep ) {
184: t0 = qi[0], tn = qi[idist];
185: if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0;
186: else {
187: AxBmodP( tn, ModNum, tn, a, P, Pinv );
188: qo[0] = AplusBmodP( t0, tn, P );
189: qo[odist] = A_BmodP( t0, tn, P );
190: }
191: }
192: }
193: }
194: /*
195: * When k = 0, for i = 0 (0 <= i < 2^0=1) and 0 <= j < 2^{K-1},
196: * Out[j] <= t0 + \alpha^{j}*tn and Out[j+2^{K-1}] <= t0 - \alpha^{j}*tn,
197: * where t0 = In[j] and tn = In[j + 2^{K-1}].
198: */
199: qi = wk, qo = out, idist = idistwk, odist = idistout;
200: /* == 2^{K-1}, == o1 << (K-1) */
201: t0 = qi[0], tn = qi[idist];
202: if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0;
203: else {
204: qo[0] = AplusBmodP( t0, tn, P );
205: qo[odist] = A_BmodP( t0, tn, P );
206: }
207: #ifdef POWA_STRIDE
208: for ( k = o1, aj = a1, j = 1; j < idist; aj += a1, j++ ) {
209: #else
210: for ( k = o1, j = 1; j < idist; j++ ) {
211: #endif
212: qi++, qo += k;
213: t0 = qi[0], tn = qi[idist];
214: if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0;
215: else {
216: #ifdef POWA_STRIDE
217: a = powa[aj];
218: #else
219: a = powa[j];
220: #endif
221: AxBmodP( tn, ModNum, tn, a, P, Pinv );
222: qo[0] = AplusBmodP( t0, tn, P );
223: qo[odist] = A_BmodP( t0, tn, P );
224: }
225: }
226: #else
227: for ( K_k = 1, Ndiv2n = 1; --k >= 0; inwk = 1 - inwk ) {
228: #ifndef OPT
229: K_k = (K_k_1 = K_k) + 1;
230: #endif
231: n >>= 1; /* == 2^k */
232: Ndiv2n <<= 1; /* == 2^{K-k-1} */
233: if ( inwk ) qi = wk, qo = out, istep = 1, ostep = o1, idist = idistwk;
234: else qi = out, qo = wk, istep = o1, ostep = 1, idist = idistout;
235: qis = qi, qos = qo;
236: /**/
237: iostep = oostep; /* = istep << K_k_1; */
238: #ifndef OPT
239: oostep = ostep << K_k;
240: odist = ostep << K_k_1;
241: #else
242: odist = ostep << K_k;
243: ++K_k;
244: oostep = ostep << K_k;
245: #endif /* OPT */
246: for ( i = n; i-- > 0; qis += iostep, qos += oostep ) {
247: /* j = 0 */
248: t0 = qis[0], tn = qis[idist];
249: if ( tn == (ModNum)0 ) qos[0] = qos[odist] = t0;
250: else {
251: qos[0] = AplusBmodP( t0, tn, P );
252: qos[odist] = A_BmodP( t0, tn, P );
253: }
254: #ifdef POWA_STRIDE
255: for ( aj = a1, j = 1, qi = qis, qo = qos; j < Ndiv2n; aj += a1, j++ ) {
256: #else
257: for ( j = 1, qi = qis, qo = qos; j < Ndiv2n; j++ ) {
258: #endif
259: qi += istep, qo += ostep;
260: t0 = qi[0], tn = qi[idist];
261: if ( tn == (ModNum)0 ) qo[0] = qo[odist] = t0;
262: else {
263: #ifdef POWA_STRIDE
264: a = powa[aj << k];
265: #else
266: a = powa[j << k];
267: #endif
268: AxBmodP( tn, ModNum, tn, a, P, Pinv );
269: qo[0] = AplusBmodP( t0, tn, P );
270: qo[odist] = A_BmodP( t0, tn, P );
271: }
272: }
273: }
274: }
275: #endif
276: }
277:
278: /*********************************************************************
279: *
280: * NOTE:
281: * (1) Let \alpha be a primitive N-th root of unity modulo P,
282: * where N is even,
283: * and t be an integer s.t. 0 <= t < N/2.
284: * Then, 1/\alpha^t is given by (- \alpha^s) with s = N/2 - t.
285: *
286: * (2) Let P be a prime s.t. P = 2^n*Q + 1, where Q is an odd integer.
287: * Then, for 0 < s <= n, 2^{-s} \equiv - 2^{n-s}*Q \bmod P,
288: * because 1 \equiv - 2^n*Q \bmod P.
289: *
290: **********************************************************************/
291:
292: void C_DFT_BACK( in, N, i1, log2N, powa,
293: #ifdef POWA_STRIDE
294: a1,
295: #endif
296: out, o1, osi, nout, Ninv, P, Pinv, wk )
297: ModNum in[], powa[], out[], wk[];
298: int N, log2N, osi, nout, i1, o1;
299: #ifdef POWA_STRIDE
300: int a1;
301: #endif
302: ModNum P, Ninv;
303: double Pinv;
304: /*
305: * Let K denote log2N. Let N = 2^K, and \alpha be a primitive N-th root of 1.
306: * This routine computes the inverse discrete-Fourier transform of in[0:N-1][i1]
307: * using \alpha^{-1} modulo P, and store the `nout' transformed data from the
308: * `osi'-th in out[0:nout-1][o1]. 0 <= osi < N-1 and 0 < nout <= N.
309: * The powers of \alpha (to the degrees upto N/2=2^{K-1} at least) are given in powa[*] (or powa[a1* *]).
310: * The area wk[] is used to contain the intermediate transformed data, and thus,
311: * must have 2*N entries at least. Notice that `out' cannot be used because
312: * its space amount (`nout') may not be sufficient for this purpose.
313: */
314: {
315: int i, j, k, n, is, os, istep, ostep, idist, inwk, halfN;
316: #ifdef POWA_STRIDE
317: int aj, halfNa;
318: #endif
319: ModNum *qi, *qo, *qis, *qos, a, t0, tn, tt;
320:
321: /*
322: * for k = K-1, ..., 0 do the following:
323: *
324: * Out[2^{K-k}*i + j] <= t0 + \alpha^{- 2^k * j} * tn;
325: * = t0 - \alpha^{N/2 - 2^k * j}*tn;
326: * Out[2^{K-k}*i + j + 2^{K-k-1}] <= t0 - \alpha^{- 2^k * j} * tn;
327: * = t0 + \alpha^{N/2 - 2^k * j}*tn;
328: *
329: * where t0 = In[2^{K-k-1}*i + j] and
330: * tn = In[2^{K-k-1}*i + j + 2^{K-1}],
331: * for 0 <= i < 2^k and 0 <= j < 2^{K-k-1}.
332: *
333: */
334: if ( log2N == 1 ) {
335: /* K = 1, k = 0, 0 <= i < 1, 0 <= j < 1.
336: * Out[0] <= t0 + tn, Out[1] <= t0 - tn,
337: * where t0 = In[0] and Tn = In[1].
338: */
339: t0 = in[0], tn = in[i1];
340: if ( osi == 0 ) {
341: /* out[0] = (t0 + tn)*Ninv; */
342: tt = tn == (ModNum)0 ? t0 : AplusBmodP( t0, tn, P );
343: if ( tt != (ModNum)0 ) {
344: AxBmodP( tt, ModNum, tt, Ninv, P, Pinv );
345: }
346: out[0] = tt;
347: i = 1;
348: } else i = 0;
349: /**/
350: if ( osi + nout >= 2 ) {
351: /* out[osi == 0 ? 1 : 0] = (t0 - tn)*Ninv; */
352: tt = tn == (ModNum)0 ? t0 : A_BmodP( t0, tn, P );
353: if ( tt != (ModNum)0 ) {
354: AxBmodP( tt, ModNum, tt, Ninv, P, Pinv );
355: }
356: out[i] = tt;
357: }
358: return;
359: }
360: /****/
361: halfN = n = 1 << (k = log2N - 1); /* == 2^{K-1} */
362: #ifdef POWA_STRIDE
363: halfNa = a1 << k;
364: #endif
365: /*
366: * when k = K-1,
367: * Out[2*i] <= t0 + tn, and Out[2*i+1] <= t0 - tn,
368: * where t0 = In[i] and tn = In[i+2^{K-1}],
369: * for 0 <= i < 2^{K-1}.
370: */
371: qi = in, istep = i1, idist = i1 << k, qo = wk, inwk = 0;
372: for ( i = n; i-- > 0; qi += istep, qo += 2 ) {
373: t0 = qi[0], tn = qi[idist];
374: if ( tn == (ModNum)0 ) qo[0] = qo[1] = t0;
375: else {
376: qo[0] = AplusBmodP( t0, tn, P );
377: qo[1] = A_BmodP( t0, tn, P );
378: }
379: }
380: #ifdef EBUG
381: fprintf( stderr, "::: DFT^{-1} ::: after the first step\n" );
382: for ( qo = wk, i = 0; i < N; i++ ) {
383: if ( (i%5) == 0 ) fprintf( stderr, "\t" );
384: fprintf( stderr, "%10d,", (int)wk[i] );
385: if ( (i%5) == 4 ) fprintf( stderr, "\n" );
386: }
387: if ( (i%5) != 0 ) fprintf( stderr, "\n" );
388: #endif
389: /**/
390: idist = halfN;
391: for ( ostep = 2; --k > 0; inwk = 1 - inwk ) {
392: n >>= 1;
393: istep = ostep; /* == 2^{K-k-1} */
394: ostep <<= 1; /* == 2^{K-k} */
395: if ( inwk ) qi = &wk[N], qo = wk;
396: else qi = wk, qo = &wk[N];
397: qis = qi, qos = qo;
398: /*
399: * for j = 0,
400: * Out[2^{K-k}*i] <= t0 + tn, and Out[2^{K-k}*i + 2^{K-k-1}] <= t0 - tn,
401: * where t0 = In[2^{K-k-1}*i] and tn = In[2^{K-k-1}*i + 2^{K-1}].
402: */
403: for ( i = n, is = os = 0; i-- > 0; qi += istep, qo += ostep ) {
404: t0 = qi[0], tn = qi[idist];
405: if ( tn == (ModNum)0 ) qo[0] = qo[istep] = t0;
406: else {
407: qo[0] = AplusBmodP( t0, tn, P );
408: qo[istep] = A_BmodP( t0, tn, P );
409: }
410: }
411: #ifdef POWA_STRIDE
412: for ( aj = a1, j = 1; j < istep; aj += a1, j++ ) {
413: /*** a = P - powa[halfNa - (aj << k)]; ***/
414: a = powa[halfNa - (aj << k)];
415: #else
416: for ( j = 1; j < istep; j++ ) {
417: /*** a = P - powa[halfN - (j << k)]; ***/
418: a = powa[halfN - (j << k)];
419: #endif
420: qi = ++qis, qo = ++qos;
421: for ( i = n; i-- > 0; qi += istep, qo += ostep ) {
422: t0 = qi[0], tn = qi[idist];
423: if ( tn == (ModNum)0 ) qo[0] = qo[istep] = t0;
424: else {
425: AxBmodP( tn, ModNum, tn, a, P, Pinv );
426: /*** qo[0] = AplusBmodP( t0, tn, P ); ***/
427: /*** qo[istep] = A_BmodP( t0, tn, P ); ***/
428: qo[0] = A_BmodP( t0, tn, P );
429: qo[istep] = AplusBmodP( t0, tn, P );
430: }
431: }
432: }
433: }
434: #if 0
435: final:
436: #endif
437: /*
438: * The final step of k = 0. i can take only the value 0.
439: *
440: * Out[j] <= t0 + \alpha^{-j} * tn;
441: * Out[j + 2^{K-1}] <= t0 - \alpha^{-j} * tn;
442: *
443: * where t0 = In[j] and tn = In[j + 2^{K-1}],
444: * for 0 <= j < 2^{K-1}.
445: *
446: */
447: qo = out, qi = &wk[inwk ? N : 0];
448: if ( (n = osi + nout) > N ) nout = (n = N) - osi; /* true nout */
449: if ( (k = nout - halfN) <= 0 ) { /* no overlap, i.e., no +- */
450: if ( osi <= 0 ) {
451: t0 = qi[0], tn = qi[idist];
452: if ( tn != (ModNum)0 ) t0 = AplusBmodP( t0, tn, P );
453: if ( t0 == (ModNum)0 ) qo[0] = t0;
454: else {
455: AxBmodP( qo[0], ModNum, t0, Ninv, P, Pinv );
456: }
457: #ifdef POWA_STRIDE
458: aj = a1;
459: #endif
460: j = 1, k = n, i = 0, qo += o1;
461: } else {
462: j = osi;
463: #ifdef POWA_STRIDE
464: aj = osi*a1;
465: #endif
466: if ( n <= halfN ) i = 0, k = n; /* lower only */
467: else if ( j == halfN ) goto L_halfN; /* start with j = N/2 */
468: else if ( j > halfN ) goto L_upper; /* upper only */
469: else i = n - halfN + 1, k = halfN; /* we have lower, and i upper */
470: }
471: } else {
472: os = o1*halfN;
473: #ifdef EBUG
474: fprintf( stderr, "::::: DFT^{-1} ::: os=%d*%d=%d\n", o1, halfN, os );
475: #endif
476: if ( osi <= 0 ) {
477: t0 = qi[0], tn = qi[idist];
478: if ( tn == (ModNum)0 ) {
479: if ( t0 == (ModNum)0 ) tt = t0;
480: else { AxBmodP( tt, ModNum, t0, Ninv, P, Pinv ); }
481: qo[0] = qo[os] = tt;
482: } else {
483: tt = AplusBmodP( t0, tn, P );
484: if ( tt == (ModNum)0 ) qo[0] = tt;
485: else { AxBmodP( qo[0], ModNum, tt, Ninv, P, Pinv ); }
486: tt = A_BmodP( t0, tn, P );
487: if ( tt == (ModNum)0 ) qo[os] = tt;
488: else { AxBmodP( qo[os], ModNum, tt, Ninv, P, Pinv ); }
489: }
490: #ifdef EBUG
491: fprintf( stderr, "::::: DFT^{-1} ::: [0]=%d, [%d]=%d\n", (int)qo[0], os, (int)qo[os] );
492: #endif
493: #ifdef POWA_STRIDE
494: j = 1, aj = a1, n = halfN, i = 0, qo += o1, k--;
495: } else j = osi, aj = osi*a1, i = (n -= k) - halfN;
496: /**/
497: for ( ; k-- > 0; aj += a1, j++, qo += o1 ) {
498: #else
499: j = 1, n = halfN, i = 0, qo += o1, k--;
500: } else j = osi, i = (n -= k) - halfN;
501: /**/
502: for ( ; k-- > 0; j++, qo += o1 ) {
503: #endif
504: t0 = qi[j], tn = qi[j+idist];
505: if ( tn == (ModNum)0 ) {
506: if ( t0 != (ModNum)0 ) {
507: AxBmodP( t0, ModNum, t0, Ninv, P, Pinv );
508: }
509: qo[0] = qo[os] = t0;
510: } else {
511: #ifdef POWA_STRIDE
512: /*** a = P - powa[halfNa - aj]; ***/
513: a = powa[halfNa - aj];
514: #else
515: /*** a = P - powa[halfN - j]; ***/
516: a = powa[halfN - j];
517: #endif
518: AxBmodP( tn, ModNum, tn, a, P, Pinv );
519: /*** tt = AplusBmodP( t0, tn, P ); ***/
520: tt = A_BmodP( t0, tn, P );
521: if ( tt == (ModNum)0 ) qo[0] = tt;
522: else { AxBmodP( qo[0], ModNum, tt, Ninv, P, Pinv ); }
523: /*** tt = A_BmodP( t0, tn, P ); ***/
524: tt = AplusBmodP( t0, tn, P );
525: if ( tt == (ModNum)0 ) qo[os] = tt;
526: else { AxBmodP( qo[os], ModNum, tt, Ninv, P, Pinv ); }
527: }
528: }
529: k = halfN;
530: }
531: /*
532: * At this point, k is an upper limit < N/2 for j, i is the number of j's
533: * > N/2, and n is the real upper limit of j.
534: */
535: #ifdef POWA_STRIDE
536: for ( ; j < k; aj += a1, j++, qo += o1 ) {
537: #else
538: for ( ; j < k; j++, qo += o1 ) {
539: #endif
540: t0 = qi[j], tn = qi[j+idist];
541: if ( tn == (ModNum)0 ) {
542: if ( t0 == (ModNum)0 ) qo[0] = t0;
543: else { AxBmodP( qo[0], ModNum, t0, Ninv, P, Pinv ); }
544: } else {
545: #ifdef POWA_STRIDE
546: a = P - powa[halfNa - aj];
547: #else
548: a = P - powa[halfN - j];
549: #endif
550: AxBplusCmodP( tt, ModNum, tn, a, t0, P, Pinv );
551: if ( tt == (ModNum)0 ) qo[0] = tt;
552: else { AxBmodP( qo[0], ModNum, tt, Ninv, P, Pinv ); }
553: }
554: }
555: if ( i <= 0 ) return;
556: /**/
557: L_halfN:
558: t0 = qi[0], tn = qi[idist];
559: tt = tn == (ModNum)0 ? t0 : A_BmodP( t0, tn, P );
560: if ( tt == (ModNum)0 ) qo[0] = tt;
561: else { AxBmodP( qo[0], ModNum, tt, Ninv, P, Pinv ); }
562: qo += o1, j++;
563: /**/
564: L_upper:
565: #ifdef POWA_STRIDE
566: for ( n -= halfN, aj = a1, j = 1; j < n; aj += a1, j++, qo += o1 ) {
567: #else
568: for ( n -= halfN, j = 1; j < n; j++, qo += o1 ) {
569: #endif
570: t0 = qi[j], tn = qi[j+idist];
571: if ( tn == (ModNum)0 ) {
572: if ( t0 == (ModNum)0 ) qo[0] = t0;
573: else { AxBmodP( qo[0], ModNum, t0, Ninv, P, Pinv ); }
574: } else {
575: #ifdef POWA_STRIDE
576: a = powa[halfNa - aj];
577: #else
578: a = powa[halfN - j];
579: #endif
580: AxBplusCmodP( tt, ModNum, tn, a, t0, P, Pinv );
581: if ( tt == (ModNum)0 ) qo[0] = tt;
582: else { AxBmodP( qo[0], ModNum, tt, Ninv, P, Pinv ); }
583: }
584: }
585: }
586:
1.4 ! ohara 587: #if defined(USE_FLOAT)
1.1 noro 588: void C_PREP_ALPHA( r, log2ord, log2k, n, tbl, P, Pinv )
589: ModNum r, tbl[], P;
590: int log2ord, log2k, n;
591: double Pinv;
592: /*
593: * Let K and k denote log2ord and log2k, respectively.
594: * Let r be a primitive (2^K)-th root of unity in Z/(P), where P is a prime.
595: * Compute a = r^{2^{K-k}}, a primitive (2^k)-th root of unity, and
596: * its powers to the degrees upto n in tbl[*].
597: */
598: {
599: int i;
600: ModNum *q;
601: double t, w, dp = (double) P;
602:
603: for ( w = (double) r, i = log2ord - log2k; i > 0; i-- ) {
604: w *= w;
605: if ( w < dp ) continue;
606: w -= (dp*(double)((int) (w*Pinv)));
607: }
608: tbl[0] = 1;
609: tbl[1] = (ModNum)(t = w);
610: for ( q = &tbl[2], i = n - 1; i > 0; i-- ) {
611: t *= w;
612: if ( t >= dp ) t -= (dp*(double)((int) (t*Pinv)));
613: *q++ = t;
614: }
615: }
616: #else
617:
618: void C_PREP_ALPHA( r, log2ord, log2k, n, tbl, P, Pinv )
619: ModNum r, tbl[], P;
620: int log2ord, log2k, n;
621: double Pinv;
622: /*
623: * Let K and k denote log2ord and log2k, respectively.
624: * Let r be a primitive (2^K)-th root of unity in Z/(P), where P is a prime.
625: * Compute a = r^{2^{K-k}}, a primitive (2^k)-th root of unity, and
626: * its powers to the degrees upto n in tbl[*].
627: */
628: {
629: int i;
630: ModNum *q;
631: ModNum t, w, s;
632:
633: for ( w = r, i = log2ord - log2k; i > 0; i-- ) {
634: AxBmodP( t, ModNum, w, w, P, Pinv );
635: w = t;
636: }
637: tbl[0] = 1;
638: tbl[1] = (ModNum)(t = w);
639: for ( q = &tbl[2], i = n - 1; i > 0; i-- ) {
640: AxBmodP( s, ModNum, t, w, P, Pinv );
641: t = s;
642: *q++ = t;
643: }
644: }
645: #endif
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