Summation on HP 42S
09-25-2018, 05:28 PM (This post was last modified: 10-22-2019 12:29 PM by Albert Chan.)
Post: #22
 Albert Chan Senior Member Posts: 2,004 Joined: Jul 2018
RE: Summation on HP 42S
Hi, Frido Bohn

For reference, 1000! ~ 4.023872600770937735437024339230039857194E+2567

To avoid overflow, sum log10 of the integers.
A straight sum will loses a few significant digits.

>>> from math import *
>>> n = 1001
>>> frac = lambda x: x - int(x)
>>> sum(log10(i) for i in xrange(2, n))
2567.6046442221304
>>> 10 ** frac(_)
4.0238726007486756

If error terms is collected, result is 1000X more accurate

>>> sum = error = 0
>>> for i in xrange(2, n):
... ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ v = log10(i)
... ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ old = sum
... ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ sum += v
... ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ error += v - (sum - old) ### collect what is not added to sum
...
>>> sum, error
(2567.6046442221304, 2.4005242238445135e-12)
>>> 10 ** (frac(sum) + error)
4.0238726007709165

Update: we could collect powers of 10, without log10()

lua> p, e = 1, 0
lua> for x = 1, 500, 2 do
﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ p = x * (x+1) * (1000-x) * (1001-x) * p
﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ if p > 1e200 then e=e+300; p=p*1e-300 end
﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ end
lua>
lua> p, '* 10^' .. e
4.0238726007709384e+167 * 10^2400
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 Messages In This Thread Summation on HP 42S - lrdheat - 09-23-2018, 06:14 PM RE: Summation on HP 42S - Didier Lachieze - 09-23-2018, 06:28 PM RE: Summation on HP 42S - lrdheat - 09-23-2018, 06:41 PM RE: Summation on HP 42S - lrdheat - 09-23-2018, 06:51 PM RE: Summation on HP 42S - ijabbott - 09-23-2018, 07:40 PM RE: Summation on HP 42S - burkhard - 09-25-2018, 12:58 PM RE: Summation on HP 42S - John Keith - 09-25-2018, 04:15 PM RE: Summation on HP 42S - Thomas Klemm - 09-23-2018, 08:29 PM RE: Summation on HP 42S - lrdheat - 09-23-2018, 09:25 PM RE: Summation on HP 42S - Didier Lachieze - 09-23-2018, 10:03 PM RE: Summation on HP 42S - lrdheat - 09-23-2018, 10:02 PM RE: Summation on HP 42S - lrdheat - 09-23-2018, 10:37 PM RE: Summation on HP 42S - Thomas Klemm - 09-24-2018, 12:56 AM RE: Summation on HP 42S - Albert Chan - 09-24-2018, 11:56 AM RE: Summation on HP 42S - Thomas Klemm - 09-24-2018, 01:17 AM RE: Summation on HP 42S - Thomas Klemm - 09-24-2018, 01:52 PM RE: Summation on HP 42S - Albert Chan - 09-24-2018, 04:20 PM RE: Summation on HP 42S - pier4r - 09-24-2018, 01:55 PM RE: Summation on HP 42S - Frido Bohn - 09-25-2018, 01:59 PM RE: Summation on HP 42S - Dieter - 09-25-2018, 04:47 PM RE: Summation on HP 42S - Frido Bohn - 09-26-2018, 10:10 AM RE: Summation on HP 42S - Albert Chan - 09-26-2018, 03:13 PM RE: Summation on HP 42S - Albert Chan - 09-25-2018 05:28 PM RE: Summation on HP 42S - lrdheat - 09-25-2018, 05:17 PM RE: Summation on HP 42S - lrdheat - 09-25-2018, 05:28 PM RE: Summation on HP 42S - Albert Chan - 09-25-2018, 07:17 PM RE: Summation on HP 42S - Valentin Albillo - 09-25-2018, 08:01 PM RE: Summation on HP 42S - Albert Chan - 09-25-2018, 08:59 PM RE: Summation on HP 42S - Gerson W. Barbosa - 09-26-2018, 12:36 PM RE: Summation on HP 42S - Albert Chan - 09-26-2018, 01:23 PM RE: Summation on HP 42S - Gerson W. Barbosa - 09-26-2018, 01:54 PM RE: Summation on HP 42S - pier4r - 09-26-2018, 04:09 PM RE: Summation on HP 42S - Thomas Klemm - 09-27-2018, 03:47 AM RE: Summation on HP 42S - Ángel Martin - 09-27-2018, 05:27 AM RE: Summation on HP 42S - pier4r - 09-27-2018, 10:37 PM RE: Summation on HP 42S - Thomas Okken - 09-28-2018, 12:33 AM RE: Summation on HP 42S - pier4r - 09-28-2018, 01:40 PM RE: Summation on HP 42S - ijabbott - 09-28-2018, 11:20 PM RE: Summation on HP 42S - Albert Chan - 09-29-2018, 12:51 AM RE: Summation on HP 42S - Valentin Albillo - 09-29-2018, 01:15 AM RE: Summation on HP 42S - Thomas Okken - 09-29-2018, 01:24 AM RE: Summation on HP 42S - ijabbott - 09-29-2018, 11:58 AM RE: Summation on HP 42S - Albert Chan - 09-29-2018, 12:49 PM RE: Summation on HP 42S - Thomas Okken - 09-29-2018, 01:50 PM RE: Summation on HP 42S - ijabbott - 09-29-2018, 04:06 PM RE: Summation on HP 42S - Thomas Okken - 09-29-2018, 06:15 PM RE: Summation on HP 42S - ijabbott - 09-29-2018, 09:10 PM RE: Summation on HP 42S - Thomas Okken - 09-29-2018, 09:33 PM RE: Summation on HP 42S - Albert Chan - 09-30-2018, 03:03 PM RE: Summation on HP 42S - ijabbott - 09-30-2018, 05:28 PM RE: Summation on HP 42S - brickviking - 10-01-2018, 08:40 AM RE: Summation on HP 42S - pier4r - 09-29-2018, 05:59 PM RE: Summation on HP 42S - Thomas Okken - 09-29-2018, 08:59 PM

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