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54 lines
1.6 KiB
Fortran
54 lines
1.6 KiB
Fortran
*DECK CBRT
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FUNCTION CBRT (X)
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C***BEGIN PROLOGUE CBRT
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C***PURPOSE Compute the cube root.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C2
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C***TYPE SINGLE PRECISION (CBRT-S, DCBRT-D, CCBRT-C)
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C***KEYWORDS CUBE ROOT, ELEMENTARY FUNCTIONS, FNLIB, ROOTS
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C***AUTHOR Fullerton, W., (LANL)
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C***DESCRIPTION
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C
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C CBRT(X) calculates the cube root of X.
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED R1MACH, R9PAK, R9UPAK
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C***REVISION HISTORY (YYMMDD)
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C 770601 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890531 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C***END PROLOGUE CBRT
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DIMENSION CBRT2(5)
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SAVE CBRT2, NITER
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DATA CBRT2(1) / 0.6299605249 4743658E0 /
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DATA CBRT2(2) / 0.7937005259 8409974E0 /
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DATA CBRT2(3) / 1.0E0 /
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DATA CBRT2(4) / 1.2599210498 9487316E0 /
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DATA CBRT2(5) / 1.5874010519 6819947E0 /
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DATA NITER / 0 /
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C***FIRST EXECUTABLE STATEMENT CBRT
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IF (NITER.EQ.0) NITER = 1.443*LOG(-.106*LOG(0.1*R1MACH(3))) + 1.
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C
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CBRT = 0.0
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IF (X.EQ.0.) RETURN
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C
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CALL R9UPAK (ABS(X), Y, N)
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IXPNT = N/3
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IREM = N - 3*IXPNT + 3
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C
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C THE APPROXIMATION BELOW IS A GENERALIZED CHEBYSHEV SERIES CONVERTED
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C TO POLYNOMIAL FORM. THE APPROX IS NEARLY BEST IN THE SENSE OF
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C RELATIVE ERROR WITH 4.085 DIGITS ACCURACY.
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C
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CBRT = .439581E0 + Y*(.928549E0 + Y*(-.512653E0 + Y*.144586E0))
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C
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DO 10 ITER=1,NITER
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CBRTSQ = CBRT*CBRT
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CBRT = CBRT + (Y-CBRT*CBRTSQ)/(3.0*CBRTSQ)
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10 CONTINUE
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C
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CBRT = R9PAK (CBRT2(IREM)*SIGN(CBRT,X), IXPNT)
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RETURN
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C
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END
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