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C *******************************************************************
C ** THIS FORTRAN CODE IS INTENDED TO ILLUSTRATE POINTS MADE IN **
C ** THE TEXT. TO OUR KNOWLEDGE IT WORKS CORRECTLY. HOWEVER IT IS **
C ** THE RESPONSIBILITY OF THE USER TO TEST IT, IF IT IS USED IN A **
C ** RESEARCH APPLICATION. **
C *******************************************************************
C *******************************************************************
C ** FICHE F.18 **
C ** FUNCTION TO COMPUTE SQUARE ROOT FASTER THAN FORTRAN SQRT. **
C *******************************************************************
REAL FUNCTION SSQRT ( XSQ )
C *******************************************************************
C ** FUNCTION TO COMPUTE SQUARE ROOT FASTER THAN FORTRAN SQRT. **
C ** **
C ** THIS FUNCTION RETURNS THE SQUARE ROOT OF A REAL NUMBER XSQ **
C ** WITH 0.1 < XSQ < 1.0. THE METHOD USES A POLYNOMIAL **
C ** APPROXIMATION FOLLOWED BY NEWTON-RAPHSON ITERATION. **
C ** **
C ** REFERENCES: **
C ** **
C ** SINGER, CCP5 QUARTERLY, 8, 47, 1983. **
C ** POWLES, CCP5 QUARTERLY, 11, 39, 1984. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** REAL XSQ THE NUMBER WHOSE SQUARE ROOT IS REQUIRED **
C ** REAL X THE SQUARE ROOT **
C ** REAL C0,C1,C2,C3 COEFFICIENTS IN THE POLYNOMIAL APPROX. **
C *******************************************************************
REAL XSQ
REAL X
REAL C0, C1, C2, C3
PARAMETER ( C0 = 0.188030699, C1 = 1.48359853 )
PARAMETER ( C2 = -1.0979059 , C3 = 0.430357353 )
C *******************************************************************
C ** POLYNOMIAL APPROXIMATION TO X **
X = C0 + XSQ * ( C1 + XSQ * ( C2 + XSQ * C3 ) )
C ** ITERATION OF APPROXIMATION **
X = X + 0.5 * ( XSQ / X - X )
X = X + 0.5 * ( XSQ / X - X )
SSQRT = X + 0.5 * ( XSQ / X - X )
RETURN
END
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