double precision function dznrm2( n, zx, incx) logical imag, scale integer next double precision cutlo, cuthi, hitest, sum, xmax, absx, zero, one double complex zx(1) double precision dreal,dimag double complex zdumr,zdumi dreal(zdumr) = zdumr dimag(zdumi) = (0.0d0,-1.0d0)*zdumi data zero, one /0.0d0, 1.0d0/ c c unitary norm of the complex n-vector stored in zx() 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 sqrt(u/eps) over all known machines. c cuthi = minimum of sqrt(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 dznrm2 = zero go to 300 c 10 assign 30 to next sum = zero nn = n * incx c begin main loop do 210 i=1,nn,incx absx = dabs(dreal(zx(i))) imag = .false. go to next,(30, 50, 70, 90, 110) 30 if( absx .gt. cutlo) go to 85 assign 50 to next scale = .false. c c phase 1. sum is zero c 50 if( absx .eq. zero) go to 200 if( absx .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 assign 110 to next sum = (sum / absx) / absx 105 scale = .true. xmax = absx go to 115 c c phase 2. sum is small. c scale to avoid destructive underflow. c 70 if( absx .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( absx .le. xmax ) go to 115 sum = one + sum * (xmax / absx)**2 xmax = absx go to 200 c 115 sum = sum + (absx/xmax)**2 go to 200 c c c prepare for phase 3. c 75 sum = (sum * xmax) * xmax c 85 assign 90 to next scale = .false. c c for real or d.p. set hitest = cuthi/n c for complex set hitest = cuthi/(2*n) c hitest = cuthi/float( n ) c c phase 3. sum is mid-range. no scaling. c 90 if(absx .ge. hitest) go to 100 sum = sum + absx**2 200 continue c control selection of real and imaginary parts. c if(imag) go to 210 absx = dabs(dimag(zx(i))) imag = .true. go to next,( 50, 70, 90, 110 ) c 210 continue c c end of main loop. c compute square root and adjust for scaling. c dznrm2 = dsqrt(sum) if(scale) dznrm2 = dznrm2 * xmax 300 continue return end