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