"to_digits: nonpositive leading digit" message and incorrect solutions with double double and quad double precision

[bryangingechen]

Using macairM1_phcv24p.tar.gz from v2.4.88:

with the following input file,

5 5
- 4e+0*x4^2 + x0^2 + x3^2 + x2^2 + x1^2;
x0;
x1;
x2;
x3-1;

Running phc -b input output0 results in output0 which contains (among other things) the following:

THE SOLUTIONS :

2 5
===========================================================================
solution 1 :    start residual :  2.220E-16   #iterations : 1   success
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x4 : -5.00000000000000E-01   0.00000000000000E+00
 x0 :  0.00000000000000E+00   0.00000000000000E+00
 x3 :  1.00000000000000E+00   0.00000000000000E+00
 x2 :  0.00000000000000E+00   0.00000000000000E+00
 x1 :  0.00000000000000E+00   0.00000000000000E+00
== err :  2.699E-78 = rco :  3.623E-01 = res :  0.000E+00 = real regular ==
solution 2 :    start residual :  2.220E-16   #iterations : 1   success
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x4 :  5.00000000000000E-01   0.00000000000000E+00
 x0 :  0.00000000000000E+00   0.00000000000000E+00
 x3 :  1.00000000000000E+00   0.00000000000000E+00
 x2 :  0.00000000000000E+00   0.00000000000000E+00
 x1 :  0.00000000000000E+00   0.00000000000000E+00
== err :  2.699E-78 = rco :  3.623E-01 = res :  0.000E+00 = real regular ==

(This is expected.)

However, when running phc -b2 input output2:

to_digits: nonpositive leading digit

Is printed to the console many times, and output2 contains the following:

THE SOLUTIONS :
2 5
===========================================================================
solution 1 :    start residual : 1.220E-35   #iterations : 0   success
t : 1.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
m : 1
the solution for t :
 x4 : 0.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
 x0 : 0.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
 x3 : 0.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
 x2 : 0.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
 x1 : 0.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
== err : 0.000E+00 = rco : 0.000E+00 = res : 0.000E+00 = real regular ==
solution 2 :    start residual : 1.220E-35   #iterations : 0   success
t : 1.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
m : 2
the solution for t :
 x4 : 0.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
 x0 : 0.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
 x3 : 0.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
 x2 : 0.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
 x1 : 0.00000000000000000000000000000000E+00  0.00000000000000000000000000000000E+00
== err : 0.000E+00 = rco : 0.000E+00 = res : 0.000E+00 = real regular ==

Clearly something went wrong here.

Running phc -b4 input outpu4 yields similar results as in the -b2 case.

The full files input, output0, output2 and output4 can be viewed here.

[janverschelde]

Thanks for reporting this problem. It may be due to a mishandled underflow.