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|
* fortran version of *dgpfa2* -
* radix-2 section of self-sorting, in-place, generalized pfa
* central radix-2 and radix-8 passes included
* so that transform length can be any power of 2
*
*-------------------------------------------------------------------
*
subroutine dgpfa2f(a,b,trigs,inc,jump,n,mm,lot,isign)
double precision a(*), b(*), trigs(*)
integer inc, jump, n, mm, lot, isign
double precision s, ss, c1, c2, c3, t0, t1, t2, t3, u0, u1, u2, u3
double precision co1, co2, co3, co4, co5, co6, co7
double precision si1, si2, si3, si4, si5, si6, si7
double precision aja, ajb, ajc, ajd, bja, bjc, bjb, bjd
double precision aje, ajg, ajf, ajh, bje, bjg, bjf, bjh, aji
double precision bjm, ajj, bjj, ajk, ajl, bji, bjk
double precision ajo, bjl, bjo, ajm, ajn, ajp, bjn, bjp
data lvr/1024/
*
* ***************************************************************
* * *
* * 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. *
* * *
* ***************************************************************
*
n2 = 2**mm
inq = n/n2
jstepx = (n2-n) * inc
ninc = n * inc
ink = inc * inq
*
m2 = 0
m8 = 0
if (mod(mm,2).eq.0) then
m = mm/2
else if (mod(mm,4).eq.1) then
m = (mm-1)/2
m2 = 1
else if (mod(mm,4).eq.3) then
m = (mm-3)/2
m8 = 1
endif
mh = (m+1)/2
*
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-4 passes
* -----------------------------
mu = mod(inq,4)
if (isign.eq.-1) mu = 4 - mu
ss = 1.0
if (mu.eq.3) ss = -1.0
*
if (mh.eq.0) go to 200
*
do 160 ipass = 1 , mh
jstep = (n*inc) / (4*la)
jstepl = jstep - ninc
*
* k = 0 loop (no twiddle factors)
* -------------------------------
do 120 jjj = 0 , (n-1)*inc , 4*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
jd = jc + jstepl
if (jd.lt.istart) jd = jd + ninc
j = 0
*
* loop across transforms
* ----------------------
cdir$ ivdep, shortloop
do 110 l = 1 , nvex
aja = a(ja+j)
ajc = a(jc+j)
t0 = aja + ajc
t2 = aja - ajc
ajb = a(jb+j)
ajd = a(jd+j)
t1 = ajb + ajd
t3 = ss * ( ajb - ajd )
bja = b(ja+j)
bjc = b(jc+j)
u0 = bja + bjc
u2 = bja - bjc
bjb = b(jb+j)
bjd = b(jd+j)
u1 = bjb + bjd
u3 = ss * ( bjb - bjd )
a(ja+j) = t0 + t1
a(jc+j) = t0 - t1
b(ja+j) = u0 + u1
b(jc+j) = u0 - u1
a(jb+j) = t2 - u3
a(jd+j) = t2 + u3
b(jb+j) = u2 + t3
b(jd+j) = u2 - t3
j = j + jump
110 continue
ja = ja + jstepx
if (ja.lt.istart) ja = ja + ninc
115 continue
120 continue
*
* finished if n2 = 4
* ------------------
if (n2.eq.4) 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)
co3 = trigs(3*kk+1)
si3 = s*trigs(3*kk+2)
*
* loop along transform
* --------------------
do 140 jjj = k , (n-1)*inc , 4*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
jd = jc + jstepl
if (jd.lt.istart) jd = jd + ninc
j = 0
*
* loop across transforms
* ----------------------
cdir$ ivdep,shortloop
do 130 l = 1 , nvex
aja = a(ja+j)
ajc = a(jc+j)
t0 = aja + ajc
t2 = aja - ajc
ajb = a(jb+j)
ajd = a(jd+j)
t1 = ajb + ajd
t3 = ss * ( ajb - ajd )
bja = b(ja+j)
bjc = b(jc+j)
u0 = bja + bjc
u2 = bja - bjc
bjb = b(jb+j)
bjd = b(jd+j)
u1 = bjb + bjd
u3 = ss * ( bjb - bjd )
a(ja+j) = t0 + t1
b(ja+j) = u0 + u1
a(jb+j) = co1*(t2-u3) - si1*(u2+t3)
b(jb+j) = si1*(t2-u3) + co1*(u2+t3)
a(jc+j) = co2*(t0-t1) - si2*(u0-u1)
b(jc+j) = si2*(t0-t1) + co2*(u0-u1)
a(jd+j) = co3*(t2+u3) - si3*(u2-t3)
b(jd+j) = si3*(t2+u3) + co3*(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 = 4*la
160 continue
*-----( end of loop on type I radix-4 passes)
*
* central radix-2 pass
* --------------------
200 continue
if (m2.eq.0) go to 300
*
jstep = (n*inc) / (2*la)
jstepl = jstep - ninc
*
* k=0 loop (no twiddle factors)
* -----------------------------
do 220 jjj = 0 , (n-1)*inc , 2*jstep
ja = istart + jjj
*
* "transverse" loop
* -----------------
do 215 nu = 1 , inq
jb = ja + jstepl
if (jb.lt.istart) jb = jb + ninc
j = 0
*
* loop across transforms
* ----------------------
cdir$ ivdep, shortloop
do 210 l = 1 , nvex
aja = a(ja+j)
ajb = a(jb+j)
t0 = aja - ajb
a(ja+j) = aja + ajb
a(jb+j) = t0
bja = b(ja+j)
bjb = b(jb+j)
u0 = bja - bjb
b(ja+j) = bja + bjb
b(jb+j) = u0
j = j + jump
210 continue
*-----(end of loop across transforms)
ja = ja + jstepx
if (ja.lt.istart) ja = ja + ninc
215 continue
220 continue
*
* finished if n2=2
* ----------------
if (n2.eq.2) go to 490
*
kk = 2 * la
*
* loop on nonzero k
* -----------------
do 260 k = ink , jstep - ink , ink
co1 = trigs(kk+1)
si1 = s*trigs(kk+2)
*
* loop along transforms
* ---------------------
do 250 jjj = k , (n-1)*inc , 2*jstep
ja = istart + jjj
*
* "transverse" loop
* -----------------
do 245 nu = 1 , inq
jb = ja + jstepl
if (jb.lt.istart) jb = jb + ninc
j = 0
*
* loop across transforms
* ----------------------
if (kk.eq.n2/2) then
cdir$ ivdep, shortloop
do 230 l = 1 , nvex
aja = a(ja+j)
ajb = a(jb+j)
t0 = ss * ( aja - ajb )
a(ja+j) = aja + ajb
bjb = b(jb+j)
bja = b(ja+j)
a(jb+j) = ss * ( bjb - bja )
b(ja+j) = bja + bjb
b(jb+j) = t0
j = j + jump
230 continue
*
else
*
cdir$ ivdep, shortloop
do 240 l = 1 , nvex
aja = a(ja+j)
ajb = a(jb+j)
t0 = aja - ajb
a(ja+j) = aja + ajb
bja = b(ja+j)
bjb = b(jb+j)
u0 = bja - bjb
b(ja+j) = bja + bjb
a(jb+j) = co1*t0 - si1*u0
b(jb+j) = si1*t0 + co1*u0
j = j + jump
240 continue
*
endif
*
*-----(end of loop across transforms)
ja = ja + jstepx
if (ja.lt.istart) ja = ja + ninc
245 continue
250 continue
*-----(end of loop along transforms)
kk = kk + 2 * la
260 continue
*-----(end of loop on nonzero k)
*-----(end of radix-2 pass)
*
la = 2 * la
go to 400
*
* central radix-8 pass
* --------------------
300 continue
if (m8.eq.0) go to 400
jstep = (n*inc) / (8*la)
jstepl = jstep - ninc
mu = mod(inq,8)
if (isign.eq.-1) mu = 8 - mu
c1 = 1.0
if (mu.eq.3.or.mu.eq.7) c1 = -1.0
c2 = sqrt(0.5)
if (mu.eq.3.or.mu.eq.5) c2 = -c2
c3 = c1 * c2
*
* stage 1
* -------
do 320 k = 0 , jstep - ink , ink
do 315 jjj = k , (n-1)*inc , 8*jstep
ja = istart + jjj
*
* "transverse" loop
* -----------------
do 312 nu = 1 , inq
jb = ja + jstepl
if (jb.lt.istart) jb = jb + ninc
jc = jb + jstepl
if (jc.lt.istart) jc = jc + ninc
jd = jc + jstepl
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 = jf + jstepl
if (jg.lt.istart) jg = jg + ninc
jh = jg + jstepl
if (jh.lt.istart) jh = jh + ninc
j = 0
cdir$ ivdep, shortloop
do 310 l = 1 , nvex
aja = a(ja+j)
aje = a(je+j)
t0 = aja - aje
a(ja+j) = aja + aje
ajc = a(jc+j)
ajg = a(jg+j)
t1 = c1 * ( ajc - ajg )
a(je+j) = ajc + ajg
ajb = a(jb+j)
ajf = a(jf+j)
t2 = ajb - ajf
a(jc+j) = ajb + ajf
ajd = a(jd+j)
ajh = a(jh+j)
t3 = ajd - ajh
a(jg+j) = ajd + ajh
a(jb+j) = t0
a(jf+j) = t1
a(jd+j) = c2 * ( t2 - t3 )
a(jh+j) = c3 * ( t2 + t3 )
bja = b(ja+j)
bje = b(je+j)
u0 = bja - bje
b(ja+j) = bja + bje
bjc = b(jc+j)
bjg = b(jg+j)
u1 = c1 * ( bjc - bjg )
b(je+j) = bjc + bjg
bjb = b(jb+j)
bjf = b(jf+j)
u2 = bjb - bjf
b(jc+j) = bjb + bjf
bjd = b(jd+j)
bjh = b(jh+j)
u3 = bjd - bjh
b(jg+j) = bjd + bjh
b(jb+j) = u0
b(jf+j) = u1
b(jd+j) = c2 * ( u2 - u3 )
b(jh+j) = c3 * ( u2 + u3 )
j = j + jump
310 continue
ja = ja + jstepx
if (ja.lt.istart) ja = ja + ninc
312 continue
315 continue
320 continue
*
* stage 2
* -------
*
* k=0 (no twiddle factors)
* ------------------------
do 330 jjj = 0 , (n-1)*inc , 8*jstep
ja = istart + jjj
*
* "transverse" loop
* -----------------
do 328 nu = 1 , inq
jb = ja + jstepl
if (jb.lt.istart) jb = jb + ninc
jc = jb + jstepl
if (jc.lt.istart) jc = jc + ninc
jd = jc + jstepl
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 = jf + jstepl
if (jg.lt.istart) jg = jg + ninc
jh = jg + jstepl
if (jh.lt.istart) jh = jh + ninc
j = 0
cdir$ ivdep, shortloop
do 325 l = 1 , nvex
aja = a(ja+j)
aje = a(je+j)
t0 = aja + aje
t2 = aja - aje
ajc = a(jc+j)
ajg = a(jg+j)
t1 = ajc + ajg
t3 = c1 * ( ajc - ajg )
bja = b(ja+j)
bje = b(je+j)
u0 = bja + bje
u2 = bja - bje
bjc = b(jc+j)
bjg = b(jg+j)
u1 = bjc + bjg
u3 = c1 * ( bjc - bjg )
a(ja+j) = t0 + t1
a(je+j) = t0 - t1
b(ja+j) = u0 + u1
b(je+j) = u0 - u1
a(jc+j) = t2 - u3
a(jg+j) = t2 + u3
b(jc+j) = u2 + t3
b(jg+j) = u2 - t3
ajb = a(jb+j)
ajd = a(jd+j)
t0 = ajb + ajd
t2 = ajb - ajd
ajf = a(jf+j)
ajh = a(jh+j)
t1 = ajf - ajh
t3 = ajf + ajh
bjb = b(jb+j)
bjd = b(jd+j)
u0 = bjb + bjd
u2 = bjb - bjd
bjf = b(jf+j)
bjh = b(jh+j)
u1 = bjf - bjh
u3 = bjf + bjh
a(jb+j) = t0 - u3
a(jh+j) = t0 + u3
b(jb+j) = u0 + t3
b(jh+j) = u0 - t3
a(jd+j) = t2 + u1
a(jf+j) = t2 - u1
b(jd+j) = u2 - t1
b(jf+j) = u2 + t1
j = j + jump
325 continue
ja = ja + jstepx
if (ja.lt.istart) ja = ja + ninc
328 continue
330 continue
*
if (n2.eq.8) go to 490
*
* loop on nonzero k
* -----------------
kk = 2 * la
*
do 350 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)
co3 = trigs(3*kk+1)
si3 = s * trigs(3*kk+2)
co4 = trigs(4*kk+1)
si4 = s * trigs(4*kk+2)
co5 = trigs(5*kk+1)
si5 = s * trigs(5*kk+2)
co6 = trigs(6*kk+1)
si6 = s * trigs(6*kk+2)
co7 = trigs(7*kk+1)
si7 = s * trigs(7*kk+2)
*
do 345 jjj = k , (n-1)*inc , 8*jstep
ja = istart + jjj
*
* "transverse" loop
* -----------------
do 342 nu = 1 , inq
jb = ja + jstepl
if (jb.lt.istart) jb = jb + ninc
jc = jb + jstepl
if (jc.lt.istart) jc = jc + ninc
jd = jc + jstepl
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 = jf + jstepl
if (jg.lt.istart) jg = jg + ninc
jh = jg + jstepl
if (jh.lt.istart) jh = jh + ninc
j = 0
cdir$ ivdep, shortloop
do 340 l = 1 , nvex
aja = a(ja+j)
aje = a(je+j)
t0 = aja + aje
t2 = aja - aje
ajc = a(jc+j)
ajg = a(jg+j)
t1 = ajc + ajg
t3 = c1 * ( ajc - ajg )
bja = b(ja+j)
bje = b(je+j)
u0 = bja + bje
u2 = bja - bje
bjc = b(jc+j)
bjg = b(jg+j)
u1 = bjc + bjg
u3 = c1 * ( bjc - bjg )
a(ja+j) = t0 + t1
b(ja+j) = u0 + u1
a(je+j) = co4*(t0-t1) - si4*(u0-u1)
b(je+j) = si4*(t0-t1) + co4*(u0-u1)
a(jc+j) = co2*(t2-u3) - si2*(u2+t3)
b(jc+j) = si2*(t2-u3) + co2*(u2+t3)
a(jg+j) = co6*(t2+u3) - si6*(u2-t3)
b(jg+j) = si6*(t2+u3) + co6*(u2-t3)
ajb = a(jb+j)
ajd = a(jd+j)
t0 = ajb + ajd
t2 = ajb - ajd
ajf = a(jf+j)
ajh = a(jh+j)
t1 = ajf - ajh
t3 = ajf + ajh
bjb = b(jb+j)
bjd = b(jd+j)
u0 = bjb + bjd
u2 = bjb - bjd
bjf = b(jf+j)
bjh = b(jh+j)
u1 = bjf - bjh
u3 = bjf + bjh
a(jb+j) = co1*(t0-u3) - si1*(u0+t3)
b(jb+j) = si1*(t0-u3) + co1*(u0+t3)
a(jh+j) = co7*(t0+u3) - si7*(u0-t3)
b(jh+j) = si7*(t0+u3) + co7*(u0-t3)
a(jd+j) = co3*(t2+u1) - si3*(u2-t1)
b(jd+j) = si3*(t2+u1) + co3*(u2-t1)
a(jf+j) = co5*(t2-u1) - si5*(u2+t1)
b(jf+j) = si5*(t2-u1) + co5*(u2+t1)
j = j + jump
340 continue
ja = ja + jstepx
if (ja.lt.istart) ja = ja + ninc
342 continue
345 continue
kk = kk + 2 * la
350 continue
*
la = 8 * la
*
* loop on type II radix-4 passes
* ------------------------------
400 continue
mu = mod(inq,4)
if (isign.eq.-1) mu = 4 - mu
ss = 1.0
if (mu.eq.3) ss = -1.0
*
do 480 ipass = mh+1 , m
jstep = (n*inc) / (4*la)
jstepl = jstep - ninc
laincl = la * ink - ninc
*
* k=0 loop (no twiddle factors)
* -----------------------------
do 430 ll = 0 , (la-1)*ink , 4*jstep
*
do 420 jjj = ll , (n-1)*inc , 4*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 = jc + jstepl
if (jd.lt.istart) jd = jd + ninc
je = ja + laincl
if (je.lt.istart) je = je + ninc
jf = je + jstepl
if (jf.lt.istart) jf = jf + ninc
jg = jf + jstepl
if (jg.lt.istart) jg = jg + ninc
jh = jg + jstepl
if (jh.lt.istart) jh = jh + ninc
ji = je + laincl
if (ji.lt.istart) ji = ji + ninc
jj = ji + jstepl
if (jj.lt.istart) jj = jj + ninc
jk = jj + jstepl
if (jk.lt.istart) jk = jk + ninc
jl = jk + jstepl
if (jl.lt.istart) jl = jl + ninc
jm = ji + laincl
if (jm.lt.istart) jm = jm + ninc
jn = jm + jstepl
if (jn.lt.istart) jn = jn + ninc
jo = jn + jstepl
if (jo.lt.istart) jo = jo + ninc
jp = jo + jstepl
if (jp.lt.istart) jp = jp + ninc
j = 0
*
* loop across transforms
* ----------------------
cdir$ ivdep, shortloop
do 410 l = 1 , nvex
aja = a(ja+j)
ajc = a(jc+j)
t0 = aja + ajc
t2 = aja - ajc
ajb = a(jb+j)
ajd = a(jd+j)
t1 = ajb + ajd
t3 = ss * ( ajb - ajd )
aji = a(ji+j)
ajc = aji
bja = b(ja+j)
bjc = b(jc+j)
u0 = bja + bjc
u2 = bja - bjc
bjb = b(jb+j)
bjd = b(jd+j)
u1 = bjb + bjd
u3 = ss * ( bjb - bjd )
aje = a(je+j)
ajb = aje
a(ja+j) = t0 + t1
a(ji+j) = t0 - t1
b(ja+j) = u0 + u1
bjc = u0 - u1
bjm = b(jm+j)
bjd = bjm
a(je+j) = t2 - u3
ajd = t2 + u3
bjb = u2 + t3
b(jm+j) = u2 - t3
*----------------------
ajg = a(jg+j)
t0 = ajb + ajg
t2 = ajb - ajg
ajf = a(jf+j)
ajh = a(jh+j)
t1 = ajf + ajh
t3 = ss * ( ajf - ajh )
ajj = a(jj+j)
ajg = ajj
bje = b(je+j)
bjg = b(jg+j)
u0 = bje + bjg
u2 = bje - bjg
bjf = b(jf+j)
bjh = b(jh+j)
u1 = bjf + bjh
u3 = ss * ( bjf - bjh )
b(je+j) = bjb
a(jb+j) = t0 + t1
a(jj+j) = t0 - t1
bjj = b(jj+j)
bjg = bjj
b(jb+j) = u0 + u1
b(jj+j) = u0 - u1
a(jf+j) = t2 - u3
ajh = t2 + u3
b(jf+j) = u2 + t3
bjh = u2 - t3
*----------------------
ajk = a(jk+j)
t0 = ajc + ajk
t2 = ajc - ajk
ajl = a(jl+j)
t1 = ajg + ajl
t3 = ss * ( ajg - ajl )
bji = b(ji+j)
bjk = b(jk+j)
u0 = bji + bjk
u2 = bji - bjk
ajo = a(jo+j)
ajl = ajo
bjl = b(jl+j)
u1 = bjg + bjl
u3 = ss * ( bjg - bjl )
b(ji+j) = bjc
a(jc+j) = t0 + t1
a(jk+j) = t0 - t1
bjo = b(jo+j)
bjl = bjo
b(jc+j) = u0 + u1
b(jk+j) = u0 - u1
a(jg+j) = t2 - u3
a(jo+j) = t2 + u3
b(jg+j) = u2 + t3
b(jo+j) = u2 - t3
*----------------------
ajm = a(jm+j)
t0 = ajm + ajl
t2 = ajm - ajl
ajn = a(jn+j)
ajp = a(jp+j)
t1 = ajn + ajp
t3 = ss * ( ajn - ajp )
a(jm+j) = ajd
u0 = bjd + bjl
u2 = bjd - bjl
bjn = b(jn+j)
bjp = b(jp+j)
u1 = bjn + bjp
u3 = ss * ( bjn - bjp )
a(jn+j) = ajh
a(jd+j) = t0 + t1
a(jl+j) = t0 - t1
b(jd+j) = u0 + u1
b(jl+j) = u0 - u1
b(jn+j) = bjh
a(jh+j) = t2 - u3
a(jp+j) = t2 + u3
b(jh+j) = u2 + t3
b(jp+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)
co3 = trigs(3*kk+1)
si3 = s*trigs(3*kk+2)
*
* double loop along first transform in block
* ------------------------------------------
do 460 ll = k , (la-1)*ink , 4*jstep
*
do 450 jjj = ll , (n-1)*inc , 4*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 = jc + jstepl
if (jd.lt.istart) jd = jd + ninc
je = ja + laincl
if (je.lt.istart) je = je + ninc
jf = je + jstepl
if (jf.lt.istart) jf = jf + ninc
jg = jf + jstepl
if (jg.lt.istart) jg = jg + ninc
jh = jg + jstepl
if (jh.lt.istart) jh = jh + ninc
ji = je + laincl
if (ji.lt.istart) ji = ji + ninc
jj = ji + jstepl
if (jj.lt.istart) jj = jj + ninc
jk = jj + jstepl
if (jk.lt.istart) jk = jk + ninc
jl = jk + jstepl
if (jl.lt.istart) jl = jl + ninc
jm = ji + laincl
if (jm.lt.istart) jm = jm + ninc
jn = jm + jstepl
if (jn.lt.istart) jn = jn + ninc
jo = jn + jstepl
if (jo.lt.istart) jo = jo + ninc
jp = jo + jstepl
if (jp.lt.istart) jp = jp + ninc
j = 0
*
* loop across transforms
* ----------------------
cdir$ ivdep, shortloop
do 440 l = 1 , nvex
aja = a(ja+j)
ajc = a(jc+j)
t0 = aja + ajc
t2 = aja - ajc
ajb = a(jb+j)
ajd = a(jd+j)
t1 = ajb + ajd
t3 = ss * ( ajb - ajd )
aji = a(ji+j)
ajc = aji
bja = b(ja+j)
bjc = b(jc+j)
u0 = bja + bjc
u2 = bja - bjc
bjb = b(jb+j)
bjd = b(jd+j)
u1 = bjb + bjd
u3 = ss * ( bjb - bjd )
aje = a(je+j)
ajb = aje
a(ja+j) = t0 + t1
b(ja+j) = u0 + u1
a(je+j) = co1*(t2-u3) - si1*(u2+t3)
bjb = si1*(t2-u3) + co1*(u2+t3)
bjm = b(jm+j)
bjd = bjm
a(ji+j) = co2*(t0-t1) - si2*(u0-u1)
bjc = si2*(t0-t1) + co2*(u0-u1)
ajd = co3*(t2+u3) - si3*(u2-t3)
b(jm+j) = si3*(t2+u3) + co3*(u2-t3)
*----------------------------------------
ajg = a(jg+j)
t0 = ajb + ajg
t2 = ajb - ajg
ajf = a(jf+j)
ajh = a(jh+j)
t1 = ajf + ajh
t3 = ss * ( ajf - ajh )
ajj = a(jj+j)
ajg = ajj
bje = b(je+j)
bjg = b(jg+j)
u0 = bje + bjg
u2 = bje - bjg
bjf = b(jf+j)
bjh = b(jh+j)
u1 = bjf + bjh
u3 = ss * ( bjf - bjh )
b(je+j) = bjb
a(jb+j) = t0 + t1
b(jb+j) = u0 + u1
bjj = b(jj+j)
bjg = bjj
a(jf+j) = co1*(t2-u3) - si1*(u2+t3)
b(jf+j) = si1*(t2-u3) + co1*(u2+t3)
a(jj+j) = co2*(t0-t1) - si2*(u0-u1)
b(jj+j) = si2*(t0-t1) + co2*(u0-u1)
ajh = co3*(t2+u3) - si3*(u2-t3)
bjh = si3*(t2+u3) + co3*(u2-t3)
*----------------------------------------
ajk = a(jk+j)
t0 = ajc + ajk
t2 = ajc - ajk
ajl = a(jl+j)
t1 = ajg + ajl
t3 = ss * ( ajg - ajl )
bji = b(ji+j)
bjk = b(jk+j)
u0 = bji + bjk
u2 = bji - bjk
ajo = a(jo+j)
ajl = ajo
bjl = b(jl+j)
u1 = bjg + bjl
u3 = ss * ( bjg - bjl )
b(ji+j) = bjc
a(jc+j) = t0 + t1
b(jc+j) = u0 + u1
bjo = b(jo+j)
bjl = bjo
a(jg+j) = co1*(t2-u3) - si1*(u2+t3)
b(jg+j) = si1*(t2-u3) + co1*(u2+t3)
a(jk+j) = co2*(t0-t1) - si2*(u0-u1)
b(jk+j) = si2*(t0-t1) + co2*(u0-u1)
a(jo+j) = co3*(t2+u3) - si3*(u2-t3)
b(jo+j) = si3*(t2+u3) + co3*(u2-t3)
*----------------------------------------
ajm = a(jm+j)
t0 = ajm + ajl
t2 = ajm - ajl
ajn = a(jn+j)
ajp = a(jp+j)
t1 = ajn + ajp
t3 = ss * ( ajn - ajp )
a(jm+j) = ajd
u0 = bjd + bjl
u2 = bjd - bjl
a(jn+j) = ajh
bjn = b(jn+j)
bjp = b(jp+j)
u1 = bjn + bjp
u3 = ss * ( bjn - bjp )
b(jn+j) = bjh
a(jd+j) = t0 + t1
b(jd+j) = u0 + u1
a(jh+j) = co1*(t2-u3) - si1*(u2+t3)
b(jh+j) = si1*(t2-u3) + co1*(u2+t3)
a(jl+j) = co2*(t0-t1) - si2*(u0-u1)
b(jl+j) = si2*(t0-t1) + co2*(u0-u1)
a(jp+j) = co3*(t2+u3) - si3*(u2-t3)
b(jp+j) = si3*(t2+u3) + co3*(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 = 4*la
480 continue
*-----( end of loop on type II radix-4 passes )
*-----( nvex transforms completed)
490 continue
istart = istart + nvex * jump
500 continue
*-----( end of loop on blocks of transforms )
*
return
end
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