Re: which calculators use the improved log/exp algorithms Message #11 Posted by Mike Morrow on 6 Sept 2009, 12:36 p.m., in response to message #10 by Eric Smith
I've always found these differences in results for the same calculation to be interesting. Here are three examples that puzzle me a bit. Each is a 2500iteration Savage Benchmark, where the "perfect" numerical result would be 2500.
HP25
01 RAD
02 STO 0
03 0
04 STO 1
05 RCL 1
06 1
07 +
08 SQRT
09 X^2
10 LN
11 e^X
12 ATAN
13 TAN
14 STO 1
15 RCL 0
16 1
17 
18 STO 0
19 X=0?
20 GTO 22
21 GTO 05
22 RCL 1
23 DEG
24 GTO 00
Enter 2500 and press R/S
Result = 2499.079996 after 5940 seconds.
HP67
01 LBL B
02 RAD
03 ST I
04 0
05 LBL 1
06 1
07 +
08 SQRT
09 X^2
10 LN
11 e^X
12 ATAN
13 TAN
14 DSZ I
15 GTO 1
16 DEG
17 RTN
Enter 2500 and press B
Result = 2499.976148 after 5840 seconds
HP34C
01 LBL B
02 RAD
03 STO I
04 0
05 LBL 1
06 1
07 +
08 SQRT
09 X^2
10 LN
11 e^X
12 ATAN
13 TAN
14 DSE I
15 GTO 1
16 DEG
17 RTN
Enter 2500 and press B
Result = 2499.969898 after 7530 seconds
The HP41CX after 3210 seconds and the HP15C after 5840 seconds produce numerical results identical to the HP34C.
SUMMARY (Result and time in seconds)
HP25____2499.079996____5940
HP67____2499.976148____5840
HP34C___2499.969898____7530
HP41CX__2499.969898____3210
HP15C___2499.969898____5840
The benchmark does not use the Y^X function, so other differences must exist in the numerical algorithms of the HP25 and the later models.
Suprisingly, the HP67 result differs slightly from that of all the later preSaturn calculators. However, if the benchmark is run for less than 1500 iterations, the HP67's result is identical to the later calculators!
I don't have a working HP19C to check results for the 19C/29C models, but I'd bet they show the same strange effect as the HP67.
Edited: 6 Sept 2009, 12:53 p.m.
