POORMANLOG (v0.06, 2021/04/21)
==============================
poormanlog.tex provides (expandable) macros \PMLogZ and \PMPowTen
for computing base 10 logarithms and powers of 10 with a bit less
than 9 digits of (fixed point) precision.
It can be used with TeX (\input poormanlog) and has a LaTeX interface
(\usepackage{poormanlog}).
Regarding TeX, it requires the e-TeX \numexpr primitive, thus etex
or pdftex or other binaries with the e-TeX extensions are required.
Changes
-------
- v0.04 (2019/02/17): initial release. The package has no
dependencies and alongside two macros \PMLogZ and \PMPowTen
also provides some specific additions to xint.
- v0.05 (2019/04/22): the additions/patches to xint originally
provided by poormanlog.tex got moved into xint 1.3f itself.
Thus, poormanlog now reduces to only two macros
\PMLogZ and \PMPowTen. It can be imported by other macro
files with no danger of conflicting with future releases of
xint in case of concurrent usage.
- v0.06 (2021/04/21): documentation update (warning?) regarding
\PMLogZ{999999999} output being surprisingly 000000000.
Files
-----
poormanlog.tex
poormanlog.sty
README
\PMLogZ{#1} computes base-10 logarithms:
----------------------------------------
expansion: the argument is submitted to f-expansion and the macro
itself expands fully in two steps.
input: #1 must be (or f-expands to) a mantissa ddddddddd with exactly
nine digits, standing for D = d.dddddddd, 1 <= D < 10
output: nine digits xxxxxxxxx standing for X = 0.xxxxxxxxx such that
log10(D) is about X
CAUTION: for #1=999999999, the macro outputs 000000000,
which are the fractional digits of the correct rounding
1.000000000 of log10(9.99999999)=0.9999999995657...
As outputting 999999999 to represent log10(0.999999999) is not
completely satisfactory either, it is better to work out one's
own alternate wrapper of "\the\numexpr\PML@#1." as the latter
produces exceptionally 1000000000 with ten digits for
#1=999999999, and it is actually as simple to test the
exceptional case on this ten digit output than on input.
Please refer to source code and check how \PMLogZ is built on
top of \PML@ output and design own user variant: in place of
the gobble in the \PMLogZ one only needs to test if first
digit is 2 to identify the special case.
precision: It seems from testing that absolute error is not much
more than 1 unit in the last (*fixed point*) place,
and result differs from rounded mathematical value of
log10(D) by at most 1 unit in the last place.
(*attention estimate not rigorously proven*).
\PMPowTen{#1} computes fractional powers of 10:
-----------------------------------------------
expansion: the argument is submitted to f-expansion and the macro
itself expands fully in two steps.
input: #1 must be (f-expands to) exactly nine digits xxxxxxxxx, standing
for X = 0.xxxxxxxxx
output: nine digits ddddddddd, such that D = d.dddddddd is about 10^X
The first digit of output is never zero (i.e. 1 <= D < 10)
precision: It seems from testing that absolute error is less than
2 units in the last place, and result D differs from
rounded mathematical value of 10^X by at most 2 units in
the last place.
(*attention estimate not rigorously proven*).
LICENSE
-------
Copyright (C) 2019-2021, Jean-Francois Burnol.
This Work may be distributed and/or modified under the conditions of the
LaTeX Project Public License version 1.3c. This version of this license
is in
and version 1.3 or later is part of all distributions of LaTeX version
2005/12/01 or later.
This Work has the LPPL maintenance status `author-maintained'.
The Author of this Work is Jean-Francois Burnol.
This Work consists of files poormanlog.tex, poormanlog.sty and this
README.