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