Mathematical Concerns

This article is intended to capture and preserve recent investigation effort related to mathematical difficulties that produce values of infinity and NaN.

Captured from Slack discussion:

Tracing where NaN comes from in compression spring eqnset.js when OD_Free = 0.4 and Wire_Dia = 0.2

Line 19
x[o.Spring_Index] = x[o.Mean_Dia] / p[o.Wire_Dia];
= 1.0

Line 21
kc = (4.0 * x[o.Spring_Index] - 1.0) / (4.0 * x[o.Spring_Index] - 4.0);
= infinity

line 23
ks = kc + 0.615 / x[o.Spring_Index];
= infinity

line 52
s_f = ks * 8.0 * x[o.Mean_Dia] / (Math.PI * p[o.Wire_Dia] * p[o.Wire_Dia] * p[o.Wire_Dia]);
= infinity

line 54, 55
x[o.Stress_1] = s_f * p[o.Force_1];
x[o.Stress_2] = s_f * p[o.Force_2];
= infinity

line 88
stress_rng = (x[o.Stress_2] - x[o.Stress_1]) / 2.0;
= NaN

line 90
x[o.FS_CycleLife] = x[o.Stress_Lim_Stat] /
(kc * stress_rng * (x[o.Stress_Lim_Stat] - se2) / se2 + stress_avg);
= NaN

Conclusion:
Doing math involving multiple infinities gets NaN which then propagates.

Javascript specification

This specification provides detail on the exact operations that produce values of infinity and NaN.

See:
Javascript specification

See also:

Github issue #870 Add eqnset tests for pathological cases

Philosophy / point of view

A situation where the equations produce a value of infinity is undesirable.
A situation where the equations produce a value of NaN is much worse.