      REAL FUNCTION SCNRM2( N, CX, INCX)
      LOGICAL IMAG, SCALE
      INTEGER          NEXT
      REAL         CUTLO, CUTHI, HITEST, SUM, XMAX, ABSX, ZERO, ONE
      COMPLEX      CX(1)
      DATA         ZERO, ONE /0.0E0, 1.0E0/
C
C     UNITARY NORM OF THE COMPLEX N-VECTOR STORED IN CX() 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 / 4.441E-16,  1.304E19 /
C
      IF(N .GT. 0) GO TO 10
         SCNRM2  = 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 = ABS(REAL(CX(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 )
      HITEST = HITEST * 0.5
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 = ABS(AIMAG(CX(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
      SCNRM2 = SQRT(SUM)
      IF(SCALE) SCNRM2 = SCNRM2 * XMAX
  300 CONTINUE
      RETURN
      END
