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Silverfrost Fortran 95 subroutine to compute Nth Root of X
NROOT is a REAL*8 function in
sttstcs.dll
(called by subroutine GEOMEAN in the same .dll). It
has been tested for X up to 9536, and is callable by D,
Pascal, and FORTRAN.
Iteratively computes and returns
Data Table
Algorithm term
FORTRAN variable
Description
A
X (REAL*8); passed by reference parameter; if calling from a D procedure,
define as a double in the calling D procedure
Variable to take the root of
a[i]
A1 (REAL*8)
Previous guess of root
a[i+1]
A2 (REAL*8) (returned to calling procedure through ROOTN)
Current guess of root
n
N (INTEGER*2); passed by reference parameter
Root Index; root to be taken (inverse exponent)
Source Code1
C X**(1/N)
REAL*8 FUNCTION NROOT (X, N) RESULT (ROOTN)
REAL*8 X, ROOTN, T2, A1, A2, D
REAL T1, EPS
INTEGER*2 N, N2, I
PARAMETER (EPS=0.000005)
ROOTN = X
IF ((N.EQ.1).OR.(N.LE.-1)) GO TO 100
IF (N.EQ.0) THEN
ROOTN = 1
GO TO 100
ENDIF
I = 0
A1 = SQRT(SQRT(X)) !Begin Seed the nth root
IF (X.GT.448000) THEN !to prevent overflow for large X
A1 = SQRT(A1) !and reduce number of iterations
ENDIF
IF (X.GT.(1.0D70)) THEN
A1 = SQRT(A1)
ENDIF
IF (X.GT.(1.0D99)) THEN
A1 = SQRT(A1)
ENDIF
IF (X.GT.(1.0D199)) THEN
A1 = SQRT(A1)
ENDIF
IF (N.GT.25) THEN
A1 = SQRT(A1)
ENDIF !End Seed the nth root
N2 = N - 1
T1 = 1.0/FLOAT(N)
C PRINT
FORTRAN Statements
FUNCTION
Subprogram type (FUNCTION or SUBROUTINE) declaration; FUNCTION
statement prefixed with
data type (REAL, INTEGER, etc) of returned variable
NROOT
Function name
RESULT
specifies variable whose value is to be returned to calling procedure
REAL*8
8 byte floating point variable declaration - same as double in D
REAL
4 byte floating point variable - same as float in D
INTEGER*2
2 byte Integer, same as short in D
PARAMETER
Attribute Declaration - constant part of expression
.EQ.
logical = (or ==)
.LE.
logical <= (or !>)
.OR.
logical or (same as ||)
.GT.
logical >
1.0D70
Double Precision (or REAL*8) constant,
1.0 * 1070 (1 followed by 70 zeroes)
SQRT()
Square root library function - returns the square root of its passed
argument
FLOAT()
casts an Integer argument into a Real
GO TO
transfer statement; jump to statement with label
10
100
statement label
CONTINUE
“Dummy” statement
pass control to next statement in normal control flow
used in connection with DO loops as the final statement of
loop range
RETURN
return control to calling program
END
END FUNCTION
end of subroutine or function
1. Download includes fixes to take odd roots of negative numbers, exit
with zero for even root of negative number.
Source file also includes
REAL*8 FUNCTION RPOWER (X, P) RESULT (R). Using natural logarithms,
raises X to real power P. Initial tests (called by
Object Pascal) have been successful.
Thanks to Scientific Psychic for the square root HTML code,
gmplib.org for the algorithm
