Exception in floor(tanh(91))

[Georgi Guninski]

hi,

floor(tanh(91))

ValueError: cannot compute floor(sinh(91)/cosh(91)) using 256 bits of precision

gp('floor(tanh(91))')
1

[dmo...@deductivepress.ca]

The ValueError is correct -- the quantity is so close to 1 that numerics cannot tell whether the floor is 0 or 1.  You could report a bug to gp, though, because the correct answer is 0, not 1.

[Georgi Guninski]

When I try to extract digits of tanh(91) via floor, I still get error

sage: floor(10^4*tanh(91))
ValueError

sage: gp('floor(10^4*tanh(91))')
10000


gp computes it both ways :)

sage: gp.default('realprecision',10^5)
0
sage: gp('floor(tanh(91))')
0

[Vincent Delecroix]

The following is the proper way to extract digits

sage: tanh(91).numerical_approx(digits=10)
1.000000000
sage: tanh(91).numerical_approx(digits=100)
0.9999999999999999999999999999999999999999999999999999999999999999999999999999998182667935304138503930

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[Nils Bruin]

On Friday 9 February 2024 at 08:16:03 UTC-8 Georgi Guninski wrote:

When I try to extract digits of tanh(91) via floor, I still get error

sage: floor(10^4*tanh(91))
ValueError

The sage code doesn't use gp for this. The error you're encountering happens in

sage.functions.other._eval_floor_ceil

and it happens because the system tries to evaluate the expression using interval arithmetic. It iteratively increases the precision until it find an interval that doesn't straddle an integer or it gives up after a set number of trials. You're hitting that second condition. You don't make it easier by multiplying by 10^4. In fact, you make it harder: you now need more digits to get the interval to not include an integer.

Without more information, this code basically has to give up after a fixed number of tries: it could be evaluating an expression that actually does evaluate to 1. In that case, no amount of increased precision will result in an interval that doesn't contain an integer. It's a well-known problem in numerical approximation: discontinuous functions are basically not computable in that model.

 

gp computes it both ways :)

sage: gp.default('realprecision',10^5)
0
sage: gp('floor(tanh(91))')
0

so does sage if you tell it to use the same approach gp uses:

 sage: tanh(91).n(30).floor()
1
sage: tanh(91).n(300).floor()
0