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- *DECK DCBRT
- DOUBLE PRECISION FUNCTION DCBRT (X)
- C***BEGIN PROLOGUE DCBRT
- C***PURPOSE Compute the cube root.
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C2
- C***TYPE DOUBLE PRECISION (CBRT-S, DCBRT-D, CCBRT-C)
- C***KEYWORDS CUBE ROOT, ELEMENTARY FUNCTIONS, FNLIB, ROOTS
- C***AUTHOR Fullerton, W., (LANL)
- C***DESCRIPTION
- C
- C DCBRT(X) calculates the double precision cube root for
- C double precision argument X.
- C
- C***REFERENCES (NONE)
- C***ROUTINES CALLED D1MACH, D9PAK, D9UPAK
- C***REVISION HISTORY (YYMMDD)
- C 770601 DATE WRITTEN
- C 890531 Changed all specific intrinsics to generic. (WRB)
- C 890531 REVISION DATE from Version 3.2
- C 891214 Prologue converted to Version 4.0 format. (BAB)
- C***END PROLOGUE DCBRT
- DOUBLE PRECISION X, CBRT2(5), Y, CBRTSQ, D9PAK, D1MACH
- SAVE CBRT2, NITER
- DATA CBRT2(1) / 0.6299605249 4743658238 3605303639 11 D0 /
- DATA CBRT2(2) / 0.7937005259 8409973737 5852819636 15 D0 /
- DATA CBRT2(3) / 1.0 D0 /
- DATA CBRT2(4) / 1.2599210498 9487316476 7210607278 23 D0 /
- DATA CBRT2(5) / 1.5874010519 6819947475 1705639272 31 D0 /
- DATA NITER / 0 /
- C***FIRST EXECUTABLE STATEMENT DCBRT
- IF (NITER.EQ.0) NITER = 1.443*LOG(-.106*LOG(0.1*REAL(D1MACH(3)))
- 1 ) + 1.0
- C
- DCBRT = 0.D0
- IF (X.EQ.0.D0) RETURN
- C
- CALL D9UPAK (ABS(X), Y, N)
- IXPNT = N/3
- IREM = N - 3*IXPNT + 3
- C
- C THE APPROXIMATION BELOW IS A GENERALIZED CHEBYSHEV SERIES CONVERTED
- C TO POLYNOMIAL FORM. THE APPROX IS NEARLY BEST IN THE SENSE OF
- C RELATIVE ERROR WITH 4.085 DIGITS ACCURACY.
- C
- Z = Y
- DCBRT = .439581E0 + Z*(.928549E0 + Z*(-.512653E0 + Z*.144586E0))
- C
- DO 10 ITER=1,NITER
- CBRTSQ = DCBRT*DCBRT
- DCBRT = DCBRT + (Y-DCBRT*CBRTSQ)/(3.D0*CBRTSQ)
- 10 CONTINUE
- C
- DCBRT = D9PAK (CBRT2(IREM)*SIGN(DCBRT,X), IXPNT)
- RETURN
- C
- END
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