SLAZQ3(3) for deflation, computes a shift (TAU) and calls dqds

## SYNOPSIS

SUBROUTINE SLAZQ3(
I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, DN2, TAU )

LOGICAL IEEE

INTEGER I0, ITER, N0, NDIV, NFAIL, PP, TTYPE

REAL DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, QMAX, SIGMA, TAU

REAL Z( * )

## PURPOSE

SLAZQ3 checks for deflation, computes a shift (TAU) and calls dqds. In case of failure it changes shifts, and tries again until output is positive.

## ARGUMENTS

I0 (input) INTEGER
First index.
N0 (input) INTEGER
Last index.
Z (input) REAL array, dimension ( 4*N )
Z holds the qd array.
PP (input) INTEGER
PP=0 for ping, PP=1 for pong.
DMIN (output) REAL
Minimum value of d.
SIGMA (output) REAL
Sum of shifts used in current segment.
DESIG (input/output) REAL
Lower order part of SIGMA
QMAX (input) REAL
Maximum value of q.
NFAIL (output) INTEGER
Number of times shift was too big.
ITER (output) INTEGER
Number of iterations.
NDIV (output) INTEGER
Number of divisions.
IEEE (input) LOGICAL
Flag for IEEE or non IEEE arithmetic (passed to SLASQ5).
TTYPE (input/output) INTEGER
Shift type. TTYPE is passed as an argument in order to save its value between calls to SLAZQ3
DMIN1 (input/output) REAL
DMIN2 (input/output) REAL DN (input/output) REAL DN1 (input/output) REAL DN2 (input/output) REAL TAU (input/output) REAL These are passed as arguments in order to save their values between calls to SLAZQ3

This is a thread safe version of SLASQ3, which passes TTYPE, DMIN1, DMIN2, DN, DN1. DN2 and TAU through the argument list in place of declaring them in a SAVE statment.