trunk/blas/dnrm2.f

C  dnrm2.f
C  is freely available from netlib. It is not subject to any GNU License
C  set by the authors of the ASCEND math programming system.
C  $Date: 1996/04/30 18:14:07 $ $Revision: 1.1.1.1 $
C
      double precision function dnrm2 ( n, dx, incx)
      integer          next
      double precision   dx(*), cutlo, cuthi, hitest, sum, xmax,zero,one
      data   zero, one /0.0d0, 1.0d0/
c
c     euclidean norm of the n-vector stored in dx() with storage
c     increment incx .
c     if    n .le. 0 return with result = 0.
c     if n .ge. 1 then incx must be .ge. 1
c
c           c.l.lawson, 1978 jan 08
c
c     four phase method     using two built-in constants that are
c     hopefully applicable to all machines.
c         cutlo = maximum of  dsqrt(u/eps)  over all known machines.
c         cuthi = minimum of  dsqrt(v)      over all known machines.
c     where
c         eps = smallest no. such that eps + 1. .gt. 1.
c         u   = smallest positive no.   (underflow limit)
c         v   = largest  no.            (overflow  limit)
c
c     brief outline of algorithm..
c
c     phase 1    scans zero components.
c     move to phase 2 when a component is nonzero and .le. cutlo
c     move to phase 3 when a component is .gt. cutlo
c     move to phase 4 when a component is .ge. cuthi/m
c     where m = n for x() real and m = 2*n for complex.
c
c     values for cutlo and cuthi..
c     from the environmental parameters listed in the imsl converter
c     document the limiting values are as follows..
c     cutlo, s.p.   u/eps = 2**(-102) for  honeywell.  close seconds are
c                   univac and dec at 2**(-103)
c                   thus cutlo = 2**(-51) = 4.44089e-16
c     cuthi, s.p.   v = 2**127 for univac, honeywell, and dec.
c                   thus cuthi = 2**(63.5) = 1.30438e19
c     cutlo, d.p.   u/eps = 2**(-67) for honeywell and dec.
c                   thus cutlo = 2**(-33.5) = 8.23181d-11
c     cuthi, d.p.   same as s.p.  cuthi = 1.30438d19
c     data cutlo, cuthi / 8.232d-11,  1.304d19 /
c     data cutlo, cuthi / 4.441e-16,  1.304e19 /
      data cutlo, cuthi / 8.232d-11,  1.304d19 /
c
      if(n .gt. 0) go to 10
         dnrm2  = zero
         go to 300
c
   10 assign 30 to next
      sum = zero
      nn = n * incx
c                                                 begin main loop
      i = 1
   20    go to next,(30, 50, 70, 110)
   30 if( dabs(dx(i)) .gt. cutlo) go to 85
      assign 50 to next
      xmax = zero
c
c                        phase 1.  sum is zero
c
   50 if( dx(i) .eq. zero) go to 200
      if( dabs(dx(i)) .gt. cutlo) go to 85
c
c                                prepare for phase 2.
      assign 70 to next
      go to 105
c
c                                prepare for phase 4.
c
  100 i = j
      assign 110 to next
      sum = (sum / dx(i)) / dx(i)
  105 xmax = dabs(dx(i))
      go to 115
c
c                   phase 2.  sum is small.
c                             scale to avoid destructive underflow.
c
   70 if( dabs(dx(i)) .gt. cutlo ) go to 75
c
c                     common code for phases 2 and 4.
c                     in phase 4 sum is large.  scale to avoid overflow.
c
  110 if( dabs(dx(i)) .le. xmax ) go to 115
         sum = one + sum * (xmax / dx(i))**2
         xmax = dabs(dx(i))
         go to 200
c
  115 sum = sum + (dx(i)/xmax)**2
      go to 200
c
c
c                  prepare for phase 3.
c
   75 sum = (sum * xmax) * xmax
c
c
c     for real or d.p. set hitest = cuthi/n
c     for complex      set hitest = cuthi/(2*n)
c
   85 hitest = cuthi/float( n )
c
c                   phase 3.  sum is mid-range.  no scaling.
c
      do 95 j =i,nn,incx
      if(dabs(dx(j)) .ge. hitest) go to 100
   95    sum = sum + dx(j)**2
      dnrm2 = dsqrt( sum )
      go to 300
c
  200 continue
      i = i + incx
      if ( i .le. nn ) go to 20
c
c              end of main loop.
c
c              compute square root and adjust for scaling.
c
      dnrm2 = xmax * dsqrt(sum)
  300 continue
      return
      end

1	C dnrm2.f
2	C is freely available from netlib. It is not subject to any GNU License
3	C set by the authors of the ASCEND math programming system.
4	C $Date: 1996/04/30 18:14:07 $ $Revision: 1.1.1.1 $
5	C
6	double precision function dnrm2 ( n, dx, incx)
7	integer next
8	double precision dx(*), cutlo, cuthi, hitest, sum, xmax,zero,one
9	data zero, one /0.0d0, 1.0d0/
10	c
11	c euclidean norm of the n-vector stored in dx() with storage
12	c increment incx .
13	c if n .le. 0 return with result = 0.
14	c if n .ge. 1 then incx must be .ge. 1
15	c
16	c c.l.lawson, 1978 jan 08
17	c
18	c four phase method using two built-in constants that are
19	c hopefully applicable to all machines.
20	c cutlo = maximum of dsqrt(u/eps) over all known machines.
21	c cuthi = minimum of dsqrt(v) over all known machines.
22	c where
23	c eps = smallest no. such that eps + 1. .gt. 1.
24	c u = smallest positive no. (underflow limit)
25	c v = largest no. (overflow limit)
26	c
27	c brief outline of algorithm..
28	c
29	c phase 1 scans zero components.
30	c move to phase 2 when a component is nonzero and .le. cutlo
31	c move to phase 3 when a component is .gt. cutlo
32	c move to phase 4 when a component is .ge. cuthi/m
33	c where m = n for x() real and m = 2*n for complex.
34	c
35	c values for cutlo and cuthi..
36	c from the environmental parameters listed in the imsl converter
37	c document the limiting values are as follows..
38	c cutlo, s.p. u/eps = 2**(-102) for honeywell. close seconds are
39	c univac and dec at 2**(-103)
40	c thus cutlo = 2**(-51) = 4.44089e-16
41	c cuthi, s.p. v = 2**127 for univac, honeywell, and dec.
42	c thus cuthi = 2**(63.5) = 1.30438e19
43	c cutlo, d.p. u/eps = 2**(-67) for honeywell and dec.
44	c thus cutlo = 2**(-33.5) = 8.23181d-11
45	c cuthi, d.p. same as s.p. cuthi = 1.30438d19
46	c data cutlo, cuthi / 8.232d-11, 1.304d19 /
47	c data cutlo, cuthi / 4.441e-16, 1.304e19 /
48	data cutlo, cuthi / 8.232d-11, 1.304d19 /
49	c
50	if(n .gt. 0) go to 10
51	dnrm2 = zero
52	go to 300
53	c
54	10 assign 30 to next
55	sum = zero
56	nn = n * incx
57	c begin main loop
58	i = 1
59	20 go to next,(30, 50, 70, 110)
60	30 if( dabs(dx(i)) .gt. cutlo) go to 85
61	assign 50 to next
62	xmax = zero
63	c
64	c phase 1. sum is zero
65	c
66	50 if( dx(i) .eq. zero) go to 200
67	if( dabs(dx(i)) .gt. cutlo) go to 85
68	c
69	c prepare for phase 2.
70	assign 70 to next
71	go to 105
72	c
73	c prepare for phase 4.
74	c
75	100 i = j
76	assign 110 to next
77	sum = (sum / dx(i)) / dx(i)
78	105 xmax = dabs(dx(i))
79	go to 115
80	c
81	c phase 2. sum is small.
82	c scale to avoid destructive underflow.
83	c
84	70 if( dabs(dx(i)) .gt. cutlo ) go to 75
85	c
86	c common code for phases 2 and 4.
87	c in phase 4 sum is large. scale to avoid overflow.
88	c
89	110 if( dabs(dx(i)) .le. xmax ) go to 115
90	sum = one + sum * (xmax / dx(i))**2
91	xmax = dabs(dx(i))
92	go to 200
93	c
94	115 sum = sum + (dx(i)/xmax)**2
95	go to 200
96	c
97	c
98	c prepare for phase 3.
99	c
100	75 sum = (sum * xmax) * xmax
101	c
102	c
103	c for real or d.p. set hitest = cuthi/n
104	c for complex set hitest = cuthi/(2*n)
105	c
106	85 hitest = cuthi/float( n )
107	c
108	c phase 3. sum is mid-range. no scaling.
109	c
110	do 95 j =i,nn,incx
111	if(dabs(dx(j)) .ge. hitest) go to 100
112	95 sum = sum + dx(j)**2
113	dnrm2 = dsqrt( sum )
114	go to 300
115	c
116	200 continue
117	i = i + incx
118	if ( i .le. nn ) go to 20
119	c
120	c end of main loop.
121	c
122	c compute square root and adjust for scaling.
123	c
124	dnrm2 = xmax * dsqrt(sum)
125	300 continue
126	return
127	end
128