HP 15c User Manual
Page 177
Appendix: Accuracy of Numerical Calculations
177
Keystrokes
Display
l÷V
071-45,10,25
v
072- 36
”
073- 16
l0
074- 45 0
lV
075- 45 25
÷
076- 10
®
077- 34
´V
078- 42 25
v
079- 36
|(
080- 43 33
´V
081- 42 25
|n
082- 43 32
|¥
This program's accuracy is phenomenal: better than nine significant digits even for the
imaginary parts of nearly indistinguishable complex roots (as when c = 4,877,163,849 and
b = 4,877,262,613 and a = 4,877,361,379); if the roots are integers, real or complex, and if
a = 1, then the roots are calculated exactly (as when c = 1,219,332,937×10
1
, b = 111,111.5,
and a = 1). But the program is costly; it uses more than twice as much memory for both
program and data as does subroutine "A", and much more time, to achieve nine significant
digits of accuracy instead of five in a few cases that can hardly ever matter−simply because
the quadratic's coefficients can hardly ever be calculated exactly. If any coefficient c, b, or a
is uncertain by as much as one unit in its 10th significant digit, then subroutine "B" is
overkill. Subroutine "B" is like Grandmother's expensive chinaware, reserved for special
occasions, leaving subroutine "A" for everyday use.