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NAME SLAS2 - compute the singular values of the 2-by-2 matrix [ F G ] [ 0 H ] SYNOPSIS SUBROUTINE SLAS2( F, G, H, SSMIN, SSMAX ) REAL F, G, H, SSMAX, SSMIN PURPOSE SLAS2 computes the singular values of the 2-by-2 matrix [ F G ] [ 0 H ]. On return, SSMIN is the smaller singular value and SSMAX is the larger singular value. ARGUMENTS F (input) REAL The (1,1) entry of the 2-by-2 matrix. G (input) REAL The (1,2) entry of the 2-by-2 matrix. H (input) REAL The (2,2) entry of the 2-by-2 matrix. SSMIN (output) REAL The smaller singular value. SSMAX (output) REAL The larger singular value. FURTHER DETAILS Barring over/underflow, all output quantities are correct to within a few units in the last place (ulps), even in the absence of a guard digit in addition/subtraction. In IEEE arithmetic, the code works correctly if one matrix entry is infinite. Overflow will not occur unless the largest singular value itself overflows, or is within a few ulps of overflow. (On machines with partial overflow, like the Cray, overflow may occur if the largest singular value is within a factor of 2 of overflow.) Underflow is harmless if underflow is gradual. Otherwise, results may correspond to a matrix modified by perturbations of size near the underflow threshold.