round #4: calculation domains
i noticed that different types of calculator give up at different points
on the domain of scientific functions.
for periodic functions the domain limit is either arbitrary (eg 1440) or
governed by the accuracy of performing mod(x, m) for large x. consequently, part
of the test is to see how much accuracy is achieved near the manufacturers
domain limit. for details of this problem see, the
secret life of the mod function.
actual values:
sin(999999999 radians) = -.410137277280044
sin(1e9) = .5458434494486996
sin(1e8) = .9316390271097260
sin(1e30) = -0.0901169019121380
| calculator |
sin, cos & tan (radians) |
result |
accuracy |
sinh, cosh & tanh |
asinh(x) & acosh(x) |
x! |
| sharp el-512 |
174532925.2 (pi/180*1e10) |
sin(1e8) = .931691228 |
5.60e-5 |
230.258 |
<1e50 |
69 |
| sharp el-531p |
174532925.2 (pi/180*1e10) |
sin(1e8) = .931641418 |
2.57e-6 |
230.258 |
<1e50 |
69 |
| sharp el-9900 |
174532925.2
(pi/180)*1e10 |
sin(1e8) = 0.93163923 |
2.18e-7 |
230.258 |
<1e50 |
69.5 |
| casio fx-992v |
15707963267 (5*pi*1e9) |
sin(999999999)=-.4101331034 |
1.05e-5 |
230.258 |
<5e99 |
69 |
| casio fx-19, fx-29, fx-39 & fx-120 |
25.13 (1440*pi/180) |
sin(25) = -0.1323516 |
|
NA |
NA |
69
NA for fx-19 & fx-29 |
| casio fx-101 |
25.13 |
sin(25) = -0.13235168 |
|
NA |
NA |
NA |
| casio fx-85m, fx-920 |
25.13 |
sin(25) = -.1323517 |
|
230.258 |
<5e99 |
69 |
| casio fx-350 |
25.13 |
sin(25) = -.1323517 |
|
230 (sinh) |
<5e99 |
69 |
| casio fx-3500p |
25.13 |
sin(25) = -.13235175 |
|
230.258 |
<5e99 |
69 |
| casio fx-100 |
25.13 |
sin(25) = -.132351752 |
|
NA |
NA |
69 |
| casio fx-4800p |
157079632
(pi/2*1e8) |
sin(1e8)=.9316391026 |
8.1e-8 |
230.258 |
<5e99 |
69 |
| casio fx-991es |
157079632
(pi/2*1e8) |
sin(1e8)=.9316391026 |
8.1e-8 |
230.258 |
<5e99 |
69 |
| casio fx-50f |
157079632
(pi/2*1e8) |
sin(1e8)=.931747567 |
1.17e-4 |
230.258 |
<5e99 |
69 |
| ti-52 |
785398163
(pi/4*1e9) |
sin(1e8)=.931641418 |
2.57e-6 |
230.258 |
<1e50 |
69 |
| ti-30x iiB |
999999999 |
sin(999999999) = -.410197301 |
1.46e-4 |
230.258 |
<5e99 |
69 |
| ti-30 |
1.74e98 |
sin(1e8) = 0.93169 |
5.60e-5 |
NA |
NA |
NA |
| ti-89 |
9.99e12 |
sin(999999999) = -.410139240195 |
4.79e-6 |
2302 |
9.99e999 |
449 |
| ti-51-iii |
9.99e99 |
sin(1e30)=9.622851e-01 |
completely wrong |
227.95 |
<1e50 |
69 |
| commodore sr4148r & 1540 |
9.99e99 |
sin(999999999) = -.413098193 |
7.22e-3 |
NA |
NA |
NA |
| hp15c |
9.99e99 |
sin(999999999) = -.4101973005 |
1.46e-4 |
230.951 |
9.99e99 |
69.95 |
| hp30s, hp9g |
785398163 (pi/180*4.5e10) |
sin(1e8) = .931639027 |
0 |
230.258 |
<5e99 |
69 |
| hp48gx |
9.99e499 |
sin(999999999) = -.41013727728 |
0 |
1151.98 |
9.99e499 |
253.1 |
| hp20s |
9.99e499 |
sin(1e3) = -9.10311968e-2 |
1.01e-2 |
1151.98 |
9.99e499 |
253 |
| hp32sii |
9.99e499 |
sin(1e30) = -9.10311968e-2 |
1.01e-2 |
1151.98 |
9.99e499 |
253.1 |
comments
- the hp32sii does really well due to its extra exponent capacity, but
pushed to 1e30 gets only 2 digits correct.
- the hp30s, although accurate is not as good in the domain test as other hp
machines, but at least it stops the trig domain before it starts to go
wrong.
- the ti89 finds the full integer up to 299!, thereafter goes scientific to
1e1000, it could do better in the trig domain though.
- above numbers like 9.99 actually mean 9.999999 etc can be accommodated in
practice.
- the hp20s is slow for n! even though it only supports integers.
- the fx-350 sinh(x) function stops at 230 (but not cosh and tanh). this
could be a bug.
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