# Directory `macros/generic/poormanlog`

POORMANLOG (0.07, 2022/05/25) ============================= 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 ------- - 0.04 (2019/02/17): initial release. The package has no dependencies and alongside two macros \PMLogZ and \PMPowTen also provides some specific additions to xint. - 0.05 (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. - 0.06 (2021/04/21): documentation update (warning?) regarding \PMLogZ{999999999} output being surprisingly 000000000. - 0.07 (2022/05/25): (again cosmetic changes) * add a % at end of the \ProvidesPackage line in poormanlog.sty * release 0.06 modified only the README and forgot to update the version strings in poormanlog.sty and in poormanlog.tex 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) 2019-2022, 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 <http://www.latex-project.org/lppl/lppl-1-3c.txt> 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.

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## poormanlog – Logarithms and powers with (almost) 9 digits

This small package (usable with Plain e-TeX, LaTeX, or others) with no dependencies provides two fast expandable macros computing logarithms in base 10 and fractional powers of 10.

They handle arguments of 9 digit tokens which stand for either
`1 <= d.dddddddd < 10` (for the log) or
`0.xxxxxxxxx` (for powers of 10). They achieve a
precision of 1ulp for the logarithm and 2ulp for
fractional powers of ten.

Extension to other numerical ranges has to be done by user, via own macros or some math engine.

The xintexpr package (at 1.3f) imports the poormanlog macros as core constituents of its log10(), pow10(), log(), exp() and pow() functions.

Package | poormanlog |

Version | 0.07 2022-05-25 |

Licenses | The LaTeX Project Public License 1.3c |

Copyright | 2019–2022 Jean-François Burnol |

Maintainer | Jean-François Burnol |

Contained in | TeX Live as poormanlog MiKTeX as poormanlog |

Topics | Calculation |