# SLATEC Routines --- DNRM2 ---

Note: this is a BLAS routine and is not in libslatec.a

```*DECK DNRM2
DOUBLE PRECISION FUNCTION DNRM2 (N, DX, INCX)
C***BEGIN PROLOGUE  DNRM2
C***PURPOSE  Compute the Euclidean length (L2 norm) of a vector.
C***LIBRARY   SLATEC (BLAS)
C***CATEGORY  D1A3B
C***TYPE      DOUBLE PRECISION (SNRM2-S, DNRM2-D, SCNRM2-C)
C***KEYWORDS  BLAS, EUCLIDEAN LENGTH, EUCLIDEAN NORM, L2,
C             LINEAR ALGEBRA, UNITARY, VECTOR
C***AUTHOR  Lawson, C. L., (JPL)
C           Hanson, R. J., (SNLA)
C           Kincaid, D. R., (U. of Texas)
C           Krogh, F. T., (JPL)
C***DESCRIPTION
C
C                B L A S  Subprogram
C    Description of parameters
C
C     --Input--
C        N  number of elements in input vector(s)
C       DX  double precision vector with N elements
C     INCX  storage spacing between elements of DX
C
C     --Output--
C    DNRM2  double precision result (zero if N .LE. 0)
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     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/
C
C***REFERENCES  C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T.
C                 Krogh, Basic linear algebra subprograms for Fortran
C                 usage, Algorithm No. 539, Transactions on Mathematical
C                 Software 5, 3 (September 1979), pp. 308-323.
C***ROUTINES CALLED  (NONE)
C***REVISION HISTORY  (YYMMDD)
C   791001  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   890831  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   920501  Reformatted the REFERENCES section.  (WRB)
C***END PROLOGUE  DNRM2
```