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- *DECK CBRT
- FUNCTION CBRT (X)
- C***BEGIN PROLOGUE CBRT
- C***PURPOSE Compute the cube root.
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C2
- C***TYPE SINGLE PRECISION (CBRT-S, DCBRT-D, CCBRT-C)
- C***KEYWORDS CUBE ROOT, ELEMENTARY FUNCTIONS, FNLIB, ROOTS
- C***AUTHOR Fullerton, W., (LANL)
- C***DESCRIPTION
- C
- C CBRT(X) calculates the cube root of X.
- C
- C***REFERENCES (NONE)
- C***ROUTINES CALLED R1MACH, R9PAK, R9UPAK
- 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 CBRT
- DIMENSION CBRT2(5)
- SAVE CBRT2, NITER
- DATA CBRT2(1) / 0.6299605249 4743658E0 /
- DATA CBRT2(2) / 0.7937005259 8409974E0 /
- DATA CBRT2(3) / 1.0E0 /
- DATA CBRT2(4) / 1.2599210498 9487316E0 /
- DATA CBRT2(5) / 1.5874010519 6819947E0 /
- DATA NITER / 0 /
- C***FIRST EXECUTABLE STATEMENT CBRT
- IF (NITER.EQ.0) NITER = 1.443*LOG(-.106*LOG(0.1*R1MACH(3))) + 1.
- C
- CBRT = 0.0
- IF (X.EQ.0.) RETURN
- C
- CALL R9UPAK (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
- CBRT = .439581E0 + Y*(.928549E0 + Y*(-.512653E0 + Y*.144586E0))
- C
- DO 10 ITER=1,NITER
- CBRTSQ = CBRT*CBRT
- CBRT = CBRT + (Y-CBRT*CBRTSQ)/(3.0*CBRTSQ)
- 10 CONTINUE
- C
- CBRT = R9PAK (CBRT2(IREM)*SIGN(CBRT,X), IXPNT)
- RETURN
- C
- END
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