(35S) - Quadratic root finder -- high performance

[Jeff_Kearns]

(05-30-2014 02:29 AM)Douglas De Boer Wrote:  The goal of this program is to handle all types of cases with accuracy, both real and complex, including cases that challenge the accuracy and range limits of the calculator.

I haven't entered the 123 line program yet, however it would be interesting if you could compare its performance with this 95 line "Cadillac" Quadratic Solver by the late Palmer O. Hanson Jr. for the HP-35s.

It solves the following 8 cases correctly:

Case 1:

a = 1E-13 b = -2 c = 1

R1 = 2E13 R2 = 0.5

Case 2:

a = 654,323 b = -1,308,644 c = 654,321

R1 = 1 R2 = 0.999996943...

Case 3:

a = 11,713 b = -1,470,492 c = 46,152,709

Re = 62.77179203... ; Im = 8.5375E-05

Case 4:

a = 80,841 b = -1,975,288 c = 12,066,163

Re = 12.21711755... ; Im = 0.001374514...

Case 5:

a = 4,877,361,379 b = -9,754,525,226 c = 4,877,163,849

Re = 0.999979750 ; Im = 2.8995463E-10

Case 6:

a = 1 b = -222,223 c = 12,193,329,370

R1 = 123,458 ; R2 = 98765

Case 7:

a = 11,111,119 b = -22,222,222 c = 11,111,103

R1 = 1 ; R2 = 0.999998560001

Case 8::

a = 8,441,600 b = -22,222,222 c = 14,624,809

Re = 1.31623282316 Im = ± 1.05290400129E-6

Regards,

Jeff K