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 2500-iteration Savage Benchmark, where the "perfect" numerical result would be 2500.
HP-25
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.
HP-67
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
HP-34C
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 HP-41CX after 3210 seconds and the HP-15C after 5840 seconds produce numerical results identical to the HP-34C.
SUMMARY (Result and time in seconds)
HP-25____2499.079996____5940
HP-67____2499.976148____5840
HP-34C___2499.969898____7530
HP-41CX__2499.969898____3210
HP-15C___2499.969898____5840
The benchmark does not use the Y^X function, so other differences must exist in the numerical algorithms of the HP-25 and the later models.
Suprisingly, the HP-67 result differs slightly from that of all the later pre-Saturn calculators. However, if the benchmark is run for less than 1500 iterations, the HP-67's result is identical to the later calculators!
I don't have a working HP-19C to check results for the 19C/29C models, but I'd bet they show the same strange effect as the HP-67.
Edited: 6 Sept 2009, 12:53 p.m.
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