Calculating e^x-1 on classic HPs
02-04-2019, 07:28 PM
Post: #40
 Albert Chan Senior Member Posts: 1,246 Joined: Jul 2018
RE: Calculating e^x-1 on classic HPs
Quote:expm1(x) = (u-1) - (ln(u) - x) * u, where u = exp(x), rounded

log1p( x ) = ln(u) - ((u-1) - x) / u, where u = 1+x, rounded

A really short prove of above formulas: If z ≈ x, f(x) ≈ f(z) + (x-z) * f'(z)

expm1(x) = expm1(z) + (x-z) * exp(z)
log1p(x) = log1p(z) + (x-z) * 1/(1+z)

Let z = ln(exp(x)), rounded for expm1 eqn, and z = (1+x)-1, rounded for log1p, we get the quoted formulas.
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 Messages In This Thread Calculating e^x-1 on classic HPs - Dieter - 01-11-2016, 10:20 PM RE: Calculating e^x-1 on classic HPs - Thomas Klemm - 01-12-2016, 01:41 AM RE: Calculating e^x-1 on classic HPs - Dieter - 01-12-2016, 06:12 PM RE: Calculating e^x-1 on classic HPs - Claudio L. - 01-12-2016, 05:13 AM RE: Calculating e^x-1 on classic HPs - Dieter - 01-12-2016, 02:02 PM RE: Calculating e^x-1 on classic HPs - ElectroDuende - 01-12-2016, 03:34 PM RE: Calculating e^x-1 on classic HPs - Dieter - 01-12-2016, 06:30 PM RE: Calculating e^x-1 on classic HPs - Claudio L. - 01-12-2016, 09:44 PM RE: Calculating e^x-1 on classic HPs - Dieter - 01-12-2016, 08:16 PM RE: Calculating e^x-1 on classic HPs - Gerson W. Barbosa - 01-13-2016, 03:46 PM RE: Calculating e^x-1 on classic HPs - Dieter - 01-13-2016, 06:43 PM RE: Calculating e^x-1 on classic HPs - Gerson W. Barbosa - 01-14-2016, 02:47 AM RE: Calculating e^x-1 on classic HPs - Dieter - 01-14-2016, 01:44 PM RE: Calculating e^x-1 on classic HPs - Gerson W. Barbosa - 01-14-2016, 03:30 PM RE: Calculating e^x-1 on classic HPs - Gerson W. Barbosa - 01-14-2016, 06:50 PM RE: Calculating e^x-1 on classic HPs - Dieter - 01-14-2016, 07:38 PM RE: Calculating e^x-1 on classic HPs - Gerson W. Barbosa - 01-14-2016, 07:50 PM RE: Calculating e^x-1 on classic HPs - Albert Chan - 02-02-2019, 07:32 PM RE: Calculating e^x-1 on classic HPs - Dieter - 02-03-2019, 06:46 PM RE: Calculating e^x-1 on classic HPs - Paul Dale - 01-14-2016, 07:20 AM RE: Calculating e^x-1 on classic HPs - Dieter - 01-14-2016, 01:48 PM RE: Calculating e^x-1 on classic HPs - emece67 - 01-14-2016, 03:55 PM RE: Calculating e^x-1 on classic HPs - Dieter - 01-14-2016, 06:42 PM RE: Calculating e^x-1 on classic HPs - emece67 - 01-14-2016, 09:14 PM RE: Calculating e^x-1 on classic HPs - Dieter - 01-14-2016, 09:55 PM RE: Calculating e^x-1 on classic HPs - Paul Dale - 01-15-2016, 01:19 AM RE: Calculating e^x-1 on classic HPs - Dieter - 01-15-2016, 02:00 PM RE: Calculating e^x-1 on classic HPs - matthiaspaul - 01-15-2016, 10:10 AM RE: Calculating e^x-1 on classic HPs - Gerson W. Barbosa - 01-15-2016, 06:07 PM RE: Calculating e^x-1 on classic HPs - Dieter - 01-15-2016, 06:46 PM RE: Calculating e^x-1 on classic HPs - Gerson W. Barbosa - 01-15-2016, 10:45 PM RE: Calculating e^x-1 on classic HPs - Dieter - 01-16-2016, 08:19 AM RE: Calculating e^x-1 on classic HPs - Gerson W. Barbosa - 01-16-2016, 12:40 PM RE: Calculating e^x-1 on classic HPs - Dieter - 01-16-2016, 01:32 PM RE: Calculating e^x-1 on classic HPs - Albert Chan - 02-02-2019, 07:22 PM RE: Calculating e^x-1 on classic HPs - Paul Dale - 01-14-2016, 09:22 PM RE: Calculating e^x-1 on classic HPs - Dieter - 01-14-2016, 09:49 PM RE: Calculating e^x-1 on classic HPs - Paul Dale - 01-15-2016, 01:15 AM RE: Calculating e^x-1 on classic HPs - Albert Chan - 02-03-2019, 08:28 PM RE: Calculating e^x-1 on classic HPs - Albert Chan - 02-04-2019 07:28 PM RE: Calculating e^x-1 on classic HPs - Dieter - 02-04-2019, 07:59 PM

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