HP71B Integral Questions

[J-F Garnier]

Yes, this is the basic idea, I believe.

I found in the HP71 and HP75 user manuals a significant difference in the way IBOUND is computed in the two machines.
This is a simple description, but still helps:
HP71: Convergence is determined using J(k) defined as the kth approximation to the integral of |F| over the same interval of integration.
HP75: Convergence is determined using J(k) defined as the kth approximation to the integral of 10^(int(log|F|)) over the same interval of integration.
In both cases, these estimations are compared to the series of integral extrapolations |I(k,j) - I(k,j-1)| < E.J(k) as you described above, using the user-supplied E value.

Computing 10^(int(log|F|)) may look strange and complicate, but it is not with BCD numbers especially in asm: 10^(int(log|F|)) just means to set the mantissa to 1 and the sign to +, just keeping the exponent. I believe the benefit is to save memory locations, it may come from the original code on the 34C/15C/41C that were quite memory-limited.
From this description, the error estimation is using the weighted samples, before any extrapolation.

This explains the IBOUND results and the difference between the HP71 and HP75, for instance:
HP71:
P=?1e-5
IA( 127 ) = 62563050744 , IBOUND=625265.300862 .
the weighted sample sum was 62526530086, slightly different from the extrapolated value returned by INTEGRAL.

HP75:
P=?1e-3
IA( 127 ) = 62563050559 , IBOUND=21501195.6588
the weighted sample sum (using all mantissa=1) was 21501195659, significantly smaller than the value returned by INTEGRAL.

J-F