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223 lines
6.4 KiB
223 lines
6.4 KiB
/* slagtf.f -- translated by f2c (version 20061008). |
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You must link the resulting object file with libf2c: |
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on Microsoft Windows system, link with libf2c.lib; |
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
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or, if you install libf2c.a in a standard place, with -lf2c -lm |
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-- in that order, at the end of the command line, as in |
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cc *.o -lf2c -lm |
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
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http://www.netlib.org/f2c/libf2c.zip |
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*/ |
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#include "clapack.h" |
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/* Subroutine */ int slagtf_(integer *n, real *a, real *lambda, real *b, real |
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*c__, real *tol, real *d__, integer *in, integer *info) |
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{ |
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/* System generated locals */ |
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integer i__1; |
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real r__1, r__2; |
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/* Local variables */ |
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integer k; |
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real tl, eps, piv1, piv2, temp, mult, scale1, scale2; |
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extern doublereal slamch_(char *); |
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extern /* Subroutine */ int xerbla_(char *, integer *); |
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/* -- LAPACK routine (version 3.2) -- */ |
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
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/* November 2006 */ |
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/* .. Scalar Arguments .. */ |
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/* .. */ |
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/* .. Array Arguments .. */ |
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/* .. */ |
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/* Purpose */ |
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/* ======= */ |
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/* SLAGTF factorizes the matrix (T - lambda*I), where T is an n by n */ |
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/* tridiagonal matrix and lambda is a scalar, as */ |
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/* T - lambda*I = PLU, */ |
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/* where P is a permutation matrix, L is a unit lower tridiagonal matrix */ |
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/* with at most one non-zero sub-diagonal elements per column and U is */ |
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/* an upper triangular matrix with at most two non-zero super-diagonal */ |
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/* elements per column. */ |
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/* The factorization is obtained by Gaussian elimination with partial */ |
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/* pivoting and implicit row scaling. */ |
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/* The parameter LAMBDA is included in the routine so that SLAGTF may */ |
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/* be used, in conjunction with SLAGTS, to obtain eigenvectors of T by */ |
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/* inverse iteration. */ |
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/* Arguments */ |
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/* ========= */ |
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/* N (input) INTEGER */ |
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/* The order of the matrix T. */ |
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/* A (input/output) REAL array, dimension (N) */ |
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/* On entry, A must contain the diagonal elements of T. */ |
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/* On exit, A is overwritten by the n diagonal elements of the */ |
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/* upper triangular matrix U of the factorization of T. */ |
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/* LAMBDA (input) REAL */ |
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/* On entry, the scalar lambda. */ |
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/* B (input/output) REAL array, dimension (N-1) */ |
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/* On entry, B must contain the (n-1) super-diagonal elements of */ |
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/* T. */ |
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/* On exit, B is overwritten by the (n-1) super-diagonal */ |
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/* elements of the matrix U of the factorization of T. */ |
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/* C (input/output) REAL array, dimension (N-1) */ |
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/* On entry, C must contain the (n-1) sub-diagonal elements of */ |
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/* T. */ |
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/* On exit, C is overwritten by the (n-1) sub-diagonal elements */ |
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/* of the matrix L of the factorization of T. */ |
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/* TOL (input) REAL */ |
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/* On entry, a relative tolerance used to indicate whether or */ |
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/* not the matrix (T - lambda*I) is nearly singular. TOL should */ |
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/* normally be chose as approximately the largest relative error */ |
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/* in the elements of T. For example, if the elements of T are */ |
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/* correct to about 4 significant figures, then TOL should be */ |
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/* set to about 5*10**(-4). If TOL is supplied as less than eps, */ |
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/* where eps is the relative machine precision, then the value */ |
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/* eps is used in place of TOL. */ |
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/* D (output) REAL array, dimension (N-2) */ |
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/* On exit, D is overwritten by the (n-2) second super-diagonal */ |
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/* elements of the matrix U of the factorization of T. */ |
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/* IN (output) INTEGER array, dimension (N) */ |
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/* On exit, IN contains details of the permutation matrix P. If */ |
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/* an interchange occurred at the kth step of the elimination, */ |
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/* then IN(k) = 1, otherwise IN(k) = 0. The element IN(n) */ |
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/* returns the smallest positive integer j such that */ |
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/* abs( u(j,j) ).le. norm( (T - lambda*I)(j) )*TOL, */ |
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/* where norm( A(j) ) denotes the sum of the absolute values of */ |
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/* the jth row of the matrix A. If no such j exists then IN(n) */ |
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/* is returned as zero. If IN(n) is returned as positive, then a */ |
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/* diagonal element of U is small, indicating that */ |
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/* (T - lambda*I) is singular or nearly singular, */ |
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/* INFO (output) INTEGER */ |
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/* = 0 : successful exit */ |
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/* .lt. 0: if INFO = -k, the kth argument had an illegal value */ |
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/* ===================================================================== */ |
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/* .. Parameters .. */ |
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/* .. */ |
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/* .. Local Scalars .. */ |
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/* .. */ |
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/* .. Intrinsic Functions .. */ |
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/* .. */ |
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/* .. External Functions .. */ |
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/* .. */ |
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/* .. External Subroutines .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Parameter adjustments */ |
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--in; |
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--d__; |
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--c__; |
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--b; |
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--a; |
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/* Function Body */ |
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*info = 0; |
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if (*n < 0) { |
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*info = -1; |
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i__1 = -(*info); |
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xerbla_("SLAGTF", &i__1); |
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return 0; |
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} |
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if (*n == 0) { |
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return 0; |
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} |
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a[1] -= *lambda; |
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in[*n] = 0; |
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if (*n == 1) { |
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if (a[1] == 0.f) { |
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in[1] = 1; |
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} |
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return 0; |
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} |
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eps = slamch_("Epsilon"); |
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tl = dmax(*tol,eps); |
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scale1 = dabs(a[1]) + dabs(b[1]); |
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i__1 = *n - 1; |
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for (k = 1; k <= i__1; ++k) { |
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a[k + 1] -= *lambda; |
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scale2 = (r__1 = c__[k], dabs(r__1)) + (r__2 = a[k + 1], dabs(r__2)); |
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if (k < *n - 1) { |
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scale2 += (r__1 = b[k + 1], dabs(r__1)); |
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} |
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if (a[k] == 0.f) { |
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piv1 = 0.f; |
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} else { |
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piv1 = (r__1 = a[k], dabs(r__1)) / scale1; |
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} |
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if (c__[k] == 0.f) { |
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in[k] = 0; |
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piv2 = 0.f; |
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scale1 = scale2; |
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if (k < *n - 1) { |
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d__[k] = 0.f; |
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} |
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} else { |
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piv2 = (r__1 = c__[k], dabs(r__1)) / scale2; |
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if (piv2 <= piv1) { |
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in[k] = 0; |
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scale1 = scale2; |
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c__[k] /= a[k]; |
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a[k + 1] -= c__[k] * b[k]; |
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if (k < *n - 1) { |
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d__[k] = 0.f; |
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} |
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} else { |
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in[k] = 1; |
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mult = a[k] / c__[k]; |
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a[k] = c__[k]; |
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temp = a[k + 1]; |
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a[k + 1] = b[k] - mult * temp; |
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if (k < *n - 1) { |
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d__[k] = b[k + 1]; |
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b[k + 1] = -mult * d__[k]; |
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} |
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b[k] = temp; |
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c__[k] = mult; |
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} |
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} |
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if (dmax(piv1,piv2) <= tl && in[*n] == 0) { |
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in[*n] = k; |
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} |
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/* L10: */ |
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} |
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if ((r__1 = a[*n], dabs(r__1)) <= scale1 * tl && in[*n] == 0) { |
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in[*n] = *n; |
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} |
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return 0; |
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/* End of SLAGTF */ |
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} /* slagtf_ */
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