WP-34S (Prime Number Test) question

[Barry Mead]

I looked into how the Prime? test works, and essentially it takes
the integer part of the X register IP(X) then tests that value for
primality. If instead it took the RND(X) before doing the primality test then numbers with tiny rounding errors would still
accurately indicate the expected primality.

For example if you take the number 79 and divide it by 3 then multiply it by 3, you get a number with a tiny rounding error
in the 16th digit. On the display (even fix 11, or all 11) it appears to be 79 exactly. If you display the whole number with
(f <) it shows 78.99999999999999.

So the primality test (h test prime?) clips it down to 78 and shows false. If the RND(X) were applied to the number prior to testing for
primality, then the result will always reflect the primality of the
number shown on the display. What do you think?

Edited: 20 Oct 2013, 3:06 p.m.

[Dieter]

All numerical functions always work with the exact, unrounded argument in (usually) X. And I think it's fine this way.

Consider your example with the 78,99999999999999 that is displayed as 79 since you do not see the last four digits. Now subtract 79 from this. Should the 34s display zero? Of course it shouldn't. And that's why it shouldn't claim 78,99999999999999 is prime either, or maybe even INT(x) = 79 just because that's what you see in the display.

Dieter

[Barry Mead]

That is not exactly true. For instance the Even? and Odd? tests
show false for numbers like 78.1 and 79.1, although the underlying
integer 78 and 79 are Even and Odd respectively. These tests distinguish between whole numbers and fractional numbers, but the Prime number test does not, and when it converts a non-whole to an integer it does it in a way that is less representative of the displayed number than it could be. In my humble opinion.

[Dieter]

Quote:

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For instance the Even? and Odd? tests show false for numbers like 78.1 and 79.1, although the underlying integer 78 and 79 are Even and Odd respectively

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Yes, that's the way these functions are supposed to work. Take a look at the manual (IOP):

EVEN?    Checks if x is integer and even

ODD?     Checks if x is integer and odd

Thus any non-integer will return "false" here.

Compare this with what the manual states for the PRIME? function:

PRIME?   Checks if the absolute value of the integer part of x is prime.

That's why 78,9999... tests false. The integer part of x is 78, and 78 is not prime.

So PRIME? tests if the integer part of x (!) is prime, while ODD? and EVEN? first test if x is an integer at all, and only if it is, they test if this integer is odd resp. even.

So yes, you are right: not all functions work on the full-precision value of X. Some ignore the sign and fractional part of X, such as the PRIME? function. But they do not round to the next integer either.

Dieter

Edited: 20 Oct 2013, 5:32 p.m.