*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