1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
|
* fortran version of *dgpfa3* -
* radix-3 section of self-sorting, in-place
* generalized PFA
*
*-------------------------------------------------------------------
*
subroutine dgpfa3f(a,b,trigs,inc,jump,n,mm,lot,isign)
double precision a(*), b(*), trigs(*)
integer inc, jump, n, mm, lot, isign
double precision s, c1, t1, t2, t3, u1, u2, u3, co1, co2
double precision si1, si2, aja, ajb, ajc, bjb, bjc, bja, ajd, bjd
double precision aje, ajf, ajh, bje, bjf, bjh, aji, ajg, bji, bjg
data sin60/0.866025403784437d+0/
data lvr/128/
*
* ***************************************************************
* * *
* * N.B. LVR = LENGTH OF VECTOR REGISTERS, SET TO 128 FOR C90. *
* * RESET TO 64 FOR OTHER CRAY MACHINES, OR TO ANY LARGE VALUE *
* * (GREATER THAN OR EQUAL TO LOT) FOR A SCALAR COMPUTER. *
* * *
* ***************************************************************
*
n3 = 3**mm
inq = n/n3
jstepx = (n3-n) * inc
ninc = n * inc
ink = inc * inq
mu = mod(inq,3)
if (isign.eq.-1) mu = 3-mu
m = mm
mh = (m+1)/2
s = dfloat(isign)
c1 = sin60
if (mu.eq.2) c1 = -c1
*
nblox = 1 + (lot-1)/lvr
left = lot
s = dfloat(isign)
istart = 1
*
* loop on blocks of lvr transforms
* --------------------------------
do 500 nb = 1 , nblox
*
if (left.le.lvr) then
nvex = left
else if (left.lt.(2*lvr)) then
nvex = left/2
nvex = nvex + mod(nvex,2)
else
nvex = lvr
endif
left = left - nvex
*
la = 1
*
* loop on type I radix-3 passes
* -----------------------------
do 160 ipass = 1 , mh
jstep = (n*inc) / (3*la)
jstepl = jstep - ninc
*
* k = 0 loop (no twiddle factors)
* -------------------------------
do 120 jjj = 0 , (n-1)*inc , 3*jstep
ja = istart + jjj
*
* "transverse" loop
* -----------------
do 115 nu = 1 , inq
jb = ja + jstepl
if (jb.lt.istart) jb = jb + ninc
jc = jb + jstepl
if (jc.lt.istart) jc = jc + ninc
j = 0
*
* loop across transforms
* ----------------------
cdir$ ivdep, shortloop
do 110 l = 1 , nvex
ajb = a(jb+j)
ajc = a(jc+j)
t1 = ajb + ajc
aja = a(ja+j)
t2 = aja - 0.5 * t1
t3 = c1 * ( ajb - ajc )
bjb = b(jb+j)
bjc = b(jc+j)
u1 = bjb + bjc
bja = b(ja+j)
u2 = bja - 0.5 * u1
u3 = c1 * ( bjb - bjc )
a(ja+j) = aja + t1
b(ja+j) = bja + u1
a(jb+j) = t2 - u3
b(jb+j) = u2 + t3
a(jc+j) = t2 + u3
b(jc+j) = u2 - t3
j = j + jump
110 continue
ja = ja + jstepx
if (ja.lt.istart) ja = ja + ninc
115 continue
120 continue
*
* finished if n3 = 3
* ------------------
if (n3.eq.3) go to 490
kk = 2 * la
*
* loop on nonzero k
* -----------------
do 150 k = ink , jstep-ink , ink
co1 = trigs(kk+1)
si1 = s*trigs(kk+2)
co2 = trigs(2*kk+1)
si2 = s*trigs(2*kk+2)
*
* loop along transform
* --------------------
do 140 jjj = k , (n-1)*inc , 3*jstep
ja = istart + jjj
*
* "transverse" loop
* -----------------
do 135 nu = 1 , inq
jb = ja + jstepl
if (jb.lt.istart) jb = jb + ninc
jc = jb + jstepl
if (jc.lt.istart) jc = jc + ninc
j = 0
*
* loop across transforms
* ----------------------
cdir$ ivdep,shortloop
do 130 l = 1 , nvex
ajb = a(jb+j)
ajc = a(jc+j)
t1 = ajb + ajc
aja = a(ja+j)
t2 = aja - 0.5 * t1
t3 = c1 * ( ajb - ajc )
bjb = b(jb+j)
bjc = b(jc+j)
u1 = bjb + bjc
bja = b(ja+j)
u2 = bja - 0.5 * u1
u3 = c1 * ( bjb - bjc )
a(ja+j) = aja + t1
b(ja+j) = bja + u1
a(jb+j) = co1*(t2-u3) - si1*(u2+t3)
b(jb+j) = si1*(t2-u3) + co1*(u2+t3)
a(jc+j) = co2*(t2+u3) - si2*(u2-t3)
b(jc+j) = si2*(t2+u3) + co2*(u2-t3)
j = j + jump
130 continue
*-----( end of loop across transforms )
ja = ja + jstepx
if (ja.lt.istart) ja = ja + ninc
135 continue
140 continue
*-----( end of loop along transforms )
kk = kk + 2*la
150 continue
*-----( end of loop on nonzero k )
la = 3*la
160 continue
*-----( end of loop on type I radix-3 passes)
*
* loop on type II radix-3 passes
* ------------------------------
400 continue
*
do 480 ipass = mh+1 , m
jstep = (n*inc) / (3*la)
jstepl = jstep - ninc
laincl = la*ink - ninc
*
* k=0 loop (no twiddle factors)
* -----------------------------
do 430 ll = 0 , (la-1)*ink , 3*jstep
*
do 420 jjj = ll , (n-1)*inc , 3*la*ink
ja = istart + jjj
*
* "transverse" loop
* -----------------
do 415 nu = 1 , inq
jb = ja + jstepl
if (jb.lt.istart) jb = jb + ninc
jc = jb + jstepl
if (jc.lt.istart) jc = jc + ninc
jd = ja + laincl
if (jd.lt.istart) jd = jd + ninc
je = jd + jstepl
if (je.lt.istart) je = je + ninc
jf = je + jstepl
if (jf.lt.istart) jf = jf + ninc
jg = jd + laincl
if (jg.lt.istart) jg = jg + ninc
jh = jg + jstepl
if (jh.lt.istart) jh = jh + ninc
ji = jh + jstepl
if (ji.lt.istart) ji = ji + ninc
j = 0
*
* loop across transforms
* ----------------------
cdir$ ivdep, shortloop
do 410 l = 1 , nvex
ajb = a(jb+j)
ajc = a(jc+j)
t1 = ajb + ajc
aja = a(ja+j)
t2 = aja - 0.5 * t1
t3 = c1 * ( ajb - ajc )
ajd = a(jd+j)
ajb = ajd
bjb = b(jb+j)
bjc = b(jc+j)
u1 = bjb + bjc
bja = b(ja+j)
u2 = bja - 0.5 * u1
u3 = c1 * ( bjb - bjc )
bjd = b(jd+j)
bjb = bjd
a(ja+j) = aja + t1
b(ja+j) = bja + u1
a(jd+j) = t2 - u3
b(jd+j) = u2 + t3
ajc = t2 + u3
bjc = u2 - t3
*----------------------
aje = a(je+j)
ajf = a(jf+j)
t1 = aje + ajf
t2 = ajb - 0.5 * t1
t3 = c1 * ( aje - ajf )
ajh = a(jh+j)
ajf = ajh
bje = b(je+j)
bjf = b(jf+j)
u1 = bje + bjf
u2 = bjb - 0.5 * u1
u3 = c1 * ( bje - bjf )
bjh = b(jh+j)
bjf = bjh
a(jb+j) = ajb + t1
b(jb+j) = bjb + u1
a(je+j) = t2 - u3
b(je+j) = u2 + t3
a(jh+j) = t2 + u3
b(jh+j) = u2 - t3
*----------------------
aji = a(ji+j)
t1 = ajf + aji
ajg = a(jg+j)
t2 = ajg - 0.5 * t1
t3 = c1 * ( ajf - aji )
t1 = ajg + t1
a(jg+j) = ajc
bji = b(ji+j)
u1 = bjf + bji
bjg = b(jg+j)
u2 = bjg - 0.5 * u1
u3 = c1 * ( bjf - bji )
u1 = bjg + u1
b(jg+j) = bjc
a(jc+j) = t1
b(jc+j) = u1
a(jf+j) = t2 - u3
b(jf+j) = u2 + t3
a(ji+j) = t2 + u3
b(ji+j) = u2 - t3
j = j + jump
410 continue
*-----( end of loop across transforms )
ja = ja + jstepx
if (ja.lt.istart) ja = ja + ninc
415 continue
420 continue
430 continue
*-----( end of double loop for k=0 )
*
* finished if last pass
* ---------------------
if (ipass.eq.m) go to 490
*
kk = 2*la
*
* loop on nonzero k
* -----------------
do 470 k = ink , jstep-ink , ink
co1 = trigs(kk+1)
si1 = s*trigs(kk+2)
co2 = trigs(2*kk+1)
si2 = s*trigs(2*kk+2)
*
* double loop along first transform in block
* ------------------------------------------
do 460 ll = k , (la-1)*ink , 3*jstep
*
do 450 jjj = ll , (n-1)*inc , 3*la*ink
ja = istart + jjj
*
* "transverse" loop
* -----------------
do 445 nu = 1 , inq
jb = ja + jstepl
if (jb.lt.istart) jb = jb + ninc
jc = jb + jstepl
if (jc.lt.istart) jc = jc + ninc
jd = ja + laincl
if (jd.lt.istart) jd = jd + ninc
je = jd + jstepl
if (je.lt.istart) je = je + ninc
jf = je + jstepl
if (jf.lt.istart) jf = jf + ninc
jg = jd + laincl
if (jg.lt.istart) jg = jg + ninc
jh = jg + jstepl
if (jh.lt.istart) jh = jh + ninc
ji = jh + jstepl
if (ji.lt.istart) ji = ji + ninc
j = 0
*
* loop across transforms
* ----------------------
cdir$ ivdep, shortloop
do 440 l = 1 , nvex
ajb = a(jb+j)
ajc = a(jc+j)
t1 = ajb + ajc
aja = a(ja+j)
t2 = aja - 0.5 * t1
t3 = c1 * ( ajb - ajc )
ajd = a(jd+j)
ajb = ajd
bjb = b(jb+j)
bjc = b(jc+j)
u1 = bjb + bjc
bja = b(ja+j)
u2 = bja - 0.5 * u1
u3 = c1 * ( bjb - bjc )
bjd = b(jd+j)
bjb = bjd
a(ja+j) = aja + t1
b(ja+j) = bja + u1
a(jd+j) = co1*(t2-u3) - si1*(u2+t3)
b(jd+j) = si1*(t2-u3) + co1*(u2+t3)
ajc = co2*(t2+u3) - si2*(u2-t3)
bjc = si2*(t2+u3) + co2*(u2-t3)
*----------------------
aje = a(je+j)
ajf = a(jf+j)
t1 = aje + ajf
t2 = ajb - 0.5 * t1
t3 = c1 * ( aje - ajf )
ajh = a(jh+j)
ajf = ajh
bje = b(je+j)
bjf = b(jf+j)
u1 = bje + bjf
u2 = bjb - 0.5 * u1
u3 = c1 * ( bje - bjf )
bjh = b(jh+j)
bjf = bjh
a(jb+j) = ajb + t1
b(jb+j) = bjb + u1
a(je+j) = co1*(t2-u3) - si1*(u2+t3)
b(je+j) = si1*(t2-u3) + co1*(u2+t3)
a(jh+j) = co2*(t2+u3) - si2*(u2-t3)
b(jh+j) = si2*(t2+u3) + co2*(u2-t3)
*----------------------
aji = a(ji+j)
t1 = ajf + aji
ajg = a(jg+j)
t2 = ajg - 0.5 * t1
t3 = c1 * ( ajf - aji )
t1 = ajg + t1
a(jg+j) = ajc
bji = b(ji+j)
u1 = bjf + bji
bjg = b(jg+j)
u2 = bjg - 0.5 * u1
u3 = c1 * ( bjf - bji )
u1 = bjg + u1
b(jg+j) = bjc
a(jc+j) = t1
b(jc+j) = u1
a(jf+j) = co1*(t2-u3) - si1*(u2+t3)
b(jf+j) = si1*(t2-u3) + co1*(u2+t3)
a(ji+j) = co2*(t2+u3) - si2*(u2-t3)
b(ji+j) = si2*(t2+u3) + co2*(u2-t3)
j = j + jump
440 continue
*-----(end of loop across transforms)
ja = ja + jstepx
if (ja.lt.istart) ja = ja + ninc
445 continue
450 continue
460 continue
*-----( end of double loop for this k )
kk = kk + 2*la
470 continue
*-----( end of loop over values of k )
la = 3*la
480 continue
*-----( end of loop on type II radix-3 passes )
*-----( nvex transforms completed)
490 continue
istart = istart + nvex * jump
500 continue
*-----( end of loop on blocks of transforms )
*
return
end
|
