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subroutine quad(a, b1, c, sr, si, lr, li)
c calculate the zeros of the quadratic a*z**2+b1*z+c.
c the quadratic formula, modified to avoid
c overflow, is used to find the larger zero if the
c zeros are real and both zeros are complex
c the smaller real zero is found directly from the
c product of the zero c/a.
double precision a, b1, c, sr, si, lr, li, b,
* d, e
if (a.ne.0.0d+0) go to 20
sr = 0.0d+0
if (b1.ne.0.0d+0) sr = -c/b1
lr = 0.0d+0
10 si = 0.0d+0
li = 0.0d+0
return
20 if (c.ne.0.0d+0) go to 30
sr = 0.0d+0
lr = -b1/a
go to 10
c compute discriminant avoiding overflow
30 b = b1/2.0d+0
if (abs(b).lt.abs(c)) go to 40
e = 1.0d+0 - (a/b)*(c/b)
d = sqrt(abs(e))*abs(b)
go to 50
40 e = a
if (c.lt.0.0d+0) e = -a
e = b*(b/abs(c)) - e
d = sqrt(abs(e))*sqrt(abs(c))
50 if (e.lt.0.0d+0) go to 60
c real zeros
if (b.ge.0.0d+0) d = -d
lr = (-b+d)/a
sr = 0.0d+0
if (lr.ne.0.0d+0) sr = (c/lr)/a
go to 10
c complex conjugate zeros
60 sr = -b/a
lr = sr
si = abs(d/a)
li = -si
return
end
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