Hi guys...
I am working on limited basic set of maths routines for ksh93 that can be sourced as . ./ksh_math.sh and I am gobsmacked by its capabilities.
Although some big guns may already know this, I didn't, and ksh93 is easily able to do floating point numbers to floating point powers and floating point roots.
WWOOWW!!
It is so simple to get the floating point NTH root of a floating point number, within limits of ksh93's floating point precision and rounding capabilities.
I started it earlier today and this is how far I have gotten:
Code:
#!/bin/ksh
# ksh_math.sh
# Basic Math extensions.
# CONSTANTS.
PI=3.14159265358979323
e=2.71828182845904523
# NTH ROOT of a positive floating point number.
# Called as:
# NthRoot NUMBER NTHROOT PRECISION
# ALL POSITIVE VALUES.
# NUMBER and NTHROOT can be floating point, PRECISION is an integer from 1 to 16.
# Returns NTHROOT as a variable.
NthRoot()
{
NUMBER=$1
NTHROOT=$2
PRECISION=$3
if [ "$PRECISION" = "" ] || [ $PRECISION -lt 1 ]
then
PRECISION=5
fi
NTHROOT=$( printf "%.${PRECISION}f" "$(( ${NUMBER}**(1.0/${NTHROOT}) ))" )
}
# SQUARE ROOT of a positive floating point number.
# Called as:
# Sqrt NUMBER PRECISION
# ALL POSITIVE VALUES.
# NUMBER can be floating point, PRECISION is an integer from 1 to 16.
# Returns SQRT as a variable.
Sqrt()
{
NUMBER=$1
NTHROOT=2.0
PRECISION=$2
NthRoot $NUMBER $NTHROOT $PRECISION
SQRT=$NTHROOT
}
Sqrt 813.7173 10
echo ""
echo "Floating Point Square Root:"
echo "KSH93 FP maths routines = $SQRT."
echo "From Google calculator = 28.5257304902."
echo ""
echo "Floating Point Number And Nth Root:"
NthRoot 10.5 12.3 11
echo "KSH93 FP maths routines = $NTHROOT."
echo "From Google calculator = 1.21066369814."
echo ""
Results so far on OSX 10.13.6, default bash terminal calling ksh from the script:
Code:
Last login: Mon Oct 15 16:59:39 on ttys000
AMIGA:amiga~> cd Desktop/Code/Shell
AMIGA:amiga~/Desktop/Code/Shell> ./ksh_math.sh
Floating Point Square Root:
KSH93 FP maths routines = 28.5257304902.
From Google calculator = 28.5257304902.
Floating Point Number And Nth Root:
KSH93 FP maths routines = 1.21066369814.
From Google calculator = 1.21066369814.
AMIGA:amiga~/Desktop/Code/Shell> _
Will be working on basic TRIG functions next.
Enjoy...
I am working on limited basic set of maths routines for ksh93 that can be sourced as . ./ksh_math.sh
Notice that the Korn shell doesn't need that: There is a variable FPATH, which works quite like PATH, but for functions: You set it to a (list of) directory/ies and every function not yet defined will be searched there. It is possible to build "libraries" that way by collecting functions into a certain directory.
In fact i use this feature heavily in my scripts. Here is my "standard script template":
Code:
#! /bin/ksh
# ------------------------------------------------------------------------------
# script-template template for scripts
# ------------------------------------------------------------------------------
# Author.....:
# last update: 2000 00 00 by:
# ------------------------------------------------------------------------------
# Revision Log:
# - 0.xx 2000 00 00 Original Creation
# - <keyword here>
#
# ------------------------------------------------------------------------------
# Usage:
#
#
# Example:
#
# Prerequisites:
#
# ------------------------------------------------------------------------------
# Documentation:
#
# Parameters:
# returns:
# ------------------------------------------------------------------------------
# known bugs:
#
# none
# ------------------------------------------------------------------------------
# ................................(C) 2000 ... .................................
# ------------------------------------------------------------------------------
if [ -z "$DEVELOP" ] ; then # set environment
. /usr/local/lib/ksh/f_env
else
. ~/lib/f_env
fi
# local variables
typeset chUsageShort="usage: $0 [-(?|h)] | [-V] [-S]"
typeset achUsageLong[0]="$chUsageShort"
typeset achUsageLong[1]=" "
typeset achUsageLong[2]="Where means"
typeset achUsageLong[3]=" -?|h[elp] display this help"
typeset achUsageLong[4]=" -V verbose, fulldebug mode"
typeset achUsageLong[5]=" -S simulation mode, cmds only displayed"
typeset chProgBase="${chProgName##*/}" # ^= basename $0
typeset chOpt=""
while getopts ":hVS" chOpt ; do # process commandline
case "$chOpt" in
h) # display help
f_usage full
;;
"?")
if [ "$chOpt" == "?" -a "$OPTARG" == "?" ] ; then
f_usage full
else
f_die 1 "unknown option -${OPTARG}"
fi
;;
V) # fulldebug mode
export chFullDebug='set -xv'
;;
S) # simulation mode
SIMULATE='print -'
;;
esac
done
<your code here>
# -- EOF template.sh
where f_usage and f_env are functions in this library. Here is f_env:
Code:
# ------------------------------------------------------------------------------
# f_env() set the environment to a defined state
# ------------------------------------------------------------------------------
# Author.....: Wolf Machowitsch
# last update: 2001 08 08 by: Wolf Machowitsch
# ------------------------------------------------------------------------------
# Revision Log:
# - 0.99 1999 01 21 Original Creation
# -
#
# - 1.00 1999 03 12 Production release
# Reviewed version. chFullDebug can now be set via
# the commandline outside the script too. However,
# in this case the value of $chFullDebug is not
# checked for validity.
# -
#
# - 1.01 1999 04 18 Developers switch
# f_env now scans the environment for a variable
# $DEVELOP. If it is non-null, then FPATH is not
# set to "/usr/local/lib/ksh" but to "~/lib".
# This way it is possible to test new developments
# for the library before migrating them to the
# production environment.
#
# - 1.10 1999 05 01 bugfix version: system environment used
# /etc/environment is now parsed in in f_env().
# Not to do this would leave variables like ODMDIR
# unset. Some AIX processes rely on this.
#
# - 1.20 1999 05 10 Log- and Error-file
# support added for error- and logfile as used in
# the f_Cmd*-functions.
#
# - 1.30 2000 03 07 User- and Host-information
# to support the automated mailing facility some
# info about effective UID, hostname, etc. is
# retrieved.
#
#
# - 1.40 2001 05 23 Linux ready
# the 'uname' command is now used to find out the
# OS we're running. Accordingly either /etc/profile
# or /etc/environment is sourced in and a variable
# is set.
#
# - 1.41 2001 08 08 bugfix
# since in Linux '/bin' is not a link to '/usr/bin'
# (like in AIX) '/bin' is now included in the path.
#
# - 1.50 2015 09 24 HMC-List
# added a list of known HMCs to use for f_GetHostList()
#
# ------------------------------------------------------------------------------
# Usage:
# f_env() is to be PARSED into the scripts environment. The following
# piece of code shows how to use it.
#
# Example:
# #!/bin/ksh
# # example script for using f_env()
# . /usr/local/lib/ksh/f_env
# # ---- here goes the rest of your code -----
# exit
#
# Prerequisites:
# ------------------------------------------------------------------------------
# Documentation:
# f_env() is intended to be used at the beginning of scripts to make
# the environment always the same for every script instead of being
# dependant of the environment the developer has set in his shell.
# To use this script it has to be PARSED rather than called as a
# function.
#
# Parameters: void
# returns: void
# ------------------------------------------------------------------------------
# known bugs:
#
# none
# ------------------------------------------------------------------------------
# ......................(C) 99 Wolf Machowitsch ................................
# ------------------------------------------------------------------------------
if [ -z "$NEVER_USE_THIS_VAR" ] ; then # are we called recursively ?
unset ENV # clear the environment
#---------------------------------------------------- set basic environment
typeset -x OS=$(uname -a | cut -d' ' -f1) # find out the OS
# read in standard environment
case "$OS" in
AIX)
. /etc/environment
;;
Linux)
. /etc/profile
;;
*)
. /etc/environment
;;
esac
# set default TERM variable
case "$OS" in
AIX)
TERMDEF="$(termdef)"
;;
Linux)
TERMDEF="$TERM"
;;
*)
TERMDEF="$TERM"
;;
esac
typeset -x TERM=${TERMDEF:-'wyse60'} # set default TERM variable
typeset -x LANG=C # default language environment
typeset -x EDITOR=vi # what else ? ;-))
typeset -x VISUAL=$EDITOR
typeset -x PATH="/usr/bin" # set the path
PATH="$PATH:/bin"
PATH="$PATH:/etc"
PATH="$PATH:/usr/sbin"
PATH="$PATH:/usr/ucb"
PATH="$PATH:/sbin"
PATH="$PATH:/usr/bin/X11"
PATH="$PATH:/usr/local/bin" # tools, home for scripts
PATH="$PATH:/usr/local/sbin" # -"-
typeset -x chTmpDir="" # path for temporary files
#---------------------------------------------------- debugging stuff
if [ -z "$chFullDebug" ] ; then # debug switch
typeset -x chFullDebug=""
else
typeset -x chFullDebug # export if already set
fi
typeset -x SIMULATE='' # set to 'print' for
# simulation mode
typeset -x TRACE='' # set to 'on' for trace mode
if [ -z "$DEVELOP" ] ; then
typeset -x FPATH="/usr/local/lib/ksh" # set fnc path for fnc lib
FPATH="$FPATH:/usr/local/bin"
FPATH="$FPATH:/usr/local/sbin"
else
typeset -x FPATH=~/lib # for lib development
fi
#---------------------------------------------------- global constants
typeset -x chProgName="$0" # const. for main program name
typeset -x chUsageShort="" # short usage message
typeset -x achUsageLong[0]="" # long usage message (line)
if [ -z "$fLogFile" ] ; then # log file
if [ $(f_ImRoot ; print $?) -eq 0 ] ; then
typeset -x fLogFile='/usr/local/log/system.log'
else
typeset -x fLogFile=~/system.log
fi
else
typeset -x fLogFile
fi
if [ -z "$fErrFile" ] ; then # error file
if [ $(f_ImRoot ; print $?) -eq 0 ] ; then
typeset -x fErrFile='/usr/local/log/system.err'
else
typeset -x fErrFile=~/system.err
fi
else
typeset -x fErrFile
fi
#---------------------------------------------------- automated mail
typeset -x chUser=$(id -nur)
#-------------------------------------------------- site dependent includes
# HP Open View at xxx
typeset -x AlertSW='OV' # alerting software
typeset -x AlertCmd='/usr/lpp/OV/bin/opcmsg' # for f_Alert()
typeset -x AlertApp='' # are defined in the script
typeset -x AlertObj=''
# HMC list for xxx
typeset -x CachHMC[1]="xxx-f-hmc1"
typeset -x CachHMC[2]="xxx-f-hmc2"
typeset -x CachHMC[3]="xxx-f-hmc3"
typeset -x CachHMC[4]="xxx-f-hmc4"
#-------------------------------------------------- reentrancy protection
typeset -x NEVER_USE_THIS_VAR="KILROY_WAS_HERE"
fi
# --- EOF f_env
Notice that there is a variable "DEVELOP": set it to any value and the script will use not the library in /usr/local/lib/ksh but the one in ~/lib. This way you can have a personal copy of the lib and tinker with it without affecting other scripts using the same functions. Also notice that i have some logging functions which all write to a continuous log defined here (/usr/local/log/system.log and /usr/local/log/system.err).
If you are interested i can eventually publish more functions from my library.
@Corona: ksh93 is a widely used shell. In every AIX version since 5L it is included (as ksh93) and in most Linux distributions it is part of the installable base. AIX uses a ksh88 (as ksh and as sh) as the default shell since AIX 4 (about 1997).
Bakunin, why not using logger to log ?
On first glance, looks like the script(s) should stay portable, perhaps a bit shorter.
First, i tried hard to make the whole thing as independent from it surroundings as possible. Up to now, the library has worked on Linux (SLES, RHEL, centOS, Fedora, OpenVZ), Solaris, HP-Ux, and AIX while being developed mainly on AIX. It also works on both ksh88 and ksh93 and the most part of it even on bash. Introducing logger as a prerequisite would hurt that goal.
Second: i am terminally lazy! When i started the library aobunt 20 years ago logging was one of the first things i implemented. Since it worked (and worked well, for my purposes) i never got around to change it.
@bakunin
I like the template idea and will use it when I am happy with the results.
@all the viewers
In the code are two attempts at creating SINE(X).
The first uses ANGLE in degrees and this is my choice at the moment because:
1: The results are consistent to 8 decimal places to the Google calculator values. (NOTE: printf rounds at the 8th decimal place.)
2: Number 1: gives the correct result irrespective of ANGLEs greater than 360 degrees.
However...
3: The RADIAN method is good enough for the first quadrant but creeping errors start to begin beyond that due to PRECISION and rounding.
4: For RADIAN values greater than 2*PI these creeping errors become large and when greater than 6*PI even 5 decimal places is not good enough.
The RADIAN version is commented out along with test code so experimenters can see these anomalies for themselves.
Code:
# SINE(angle) in degrees.
# Called as:
# Sin ANGLE
# Where ANGLE is any positive floating point value.
# Returns SIN as a variable to 8 decimal places.
# Google sin(degrees) values for first quadrant.
#
# 0 0.00000000000
# 15 0.25881904510
# 30 0.50000000000
# 45 0.70710678118
# 60 0.86602540378
# 75 0.96592582628
# 90 1.00000000000
Sin()
{
# SIN fixed to 8 decimal places.
ANGLE=$1
while [ $ANGLE -gt 360.0 ]
do
ANGLE=$(( $ANGLE-360.0 ))
done
if [ $ANGLE -ge 360.0 ]
then
ANGLE=0.0
fi
if [ $ANGLE -gt 270.0 ]
then
ANGLE=$(( $ANGLE-360.0 ))
fi
if [ $ANGLE -gt 180.0 ]
then
ANGLE=$(( -($ANGLE-180.0) ))
fi
if [ $ANGLE -gt 90.0 ]
then
ANGLE=$(( 180.0-$ANGLE ))
fi
Radian $ANGLE
SIN=$(( $RADIAN-(($RADIAN**3)/6.0)+(($RADIAN**5)/120.0)-(($RADIAN**7)/5040.0)+(($RADIAN**9)/362880.0)-(($RADIAN**11)/39916800.0)+(($RADIAN**13)/6227020800.0) ))
SIN=$( printf "%.8f" "$SIN" )
}
#Sin(radians).
#{
# RADIAN=$1
# while [ $RADIAN -gt $(( 2*$PI )) ]
# do
# RADIAN=$(( $RADIAN-2*$PI ))
# done
# if [ $RADIAN -ge $(( 2*$PI )) ]
# then
# RADIAN=0.0
# fi
# if [ $RADIAN -gt $(( (3*PI)/4 )) ]
# then
# RADIAN=$(( $RADIAN-2*PI ))
# fi
# if [ $RADIAN -gt $PI ]
# then
# RADIAN=$(( -($RADIAN-$PI) ))
# fi
# if [ $RADIAN -gt $(( $PI/2 )) ]
# then
# RADIAN=$(( $PI-$RADIAN ))
# fi
# SIN=$(( $RADIAN-(($RADIAN**3)/6.0)+(($RADIAN**5)/120.0)-(($RADIAN**7)/5040.0)+(($RADIAN**9)/362880.0)-(($RADIAN**11)/39916800.0)+(($RADIAN**13)/6227020800.0) ))
#}
# COSINE(x)
# Called as:
# Cos RADIANS
# Returns COS as a variable.
Cos()
{
:
}
# ANGLE to RADIAN.
# Called as:
# Radian ANGLE
# Returns RADIAN as a variable.
Radian()
{
ANGLE=$1
RADIAN=$(( ($ANGLE*$PI)/180.0 ))
}
# RADIAN to ANGLE.
# Called as:
# Angle RADIAN
# Returns ANGLE as a variable.
Angle()
{
RADIAN=$1
ANGLE=$(( ($RADIAN*180.0)/$PI ))
}
# **********************************
# Test radians.
#for x in $( seq 0 $(( $PI/12 )) $(( 6*PI )) )
#do
# Sin x
# printf "%u -> %.8f\n" "$x" "$SIN"
#done
# Test degrees.
for x in $( seq 0.0 15.0 360.0 )
do
Sin x
echo "$x -> $SIN"
done
# **********************************
(( )) replaces [ ] for integer mathematics, especially float
The && construct will tremendously reduce redundancy here
You should use typeset to declare a local variable, otherwise you're unintentionally stomping on each other's ANGLE all the time
You should not be using global variables for all communication
You can make that giant equation one short loop
Not everything needs to be a function, many things are shorter and more readable as the single value they are
A bit more sanitization for negative input values
Code:
#!/bin/ksh
e=2.71828182845904523
PI=3.14159265358979323
TORADIANS=$(( PI/180.0 )) # Correction for degrees to radians
TODEGREES=$(( 180.0/PI )) # Correction for radians to degrees
# SIN fixed to 8 decimal places.
Sin()
{
typeset ANGLE var # Tell KSH ANGLE is local
typeset SIN var # Also local
ANGLE="$1"
SIN=0.0
while (( ANGLE < 0.0 ))
do
(( ANGLE += 360 ))
done
while (( ANGLE >= 360.0 )) # Too bad KSH doesn't have fmod
do
(( ANGLE -= 360.0 ))
done
(( ANGLE > 270.0 )) && (( ANGLE -= 360 ))
(( ANGLE > 180.0 )) && ANGLE=$((-(ANGLE-180)))
(( ANGLE > 90.0 )) && ANGLE=$(( 180 - ANGLE ))
(( ANGLE *= TORADIANS )) # Convert to radians
# Series coefficients, for the sum of A to the $1 divided by $2 for each pair
# Sets $1=1, $2=1.0, $3=3, $4=-6.0, etc
set -- 1 1.0 \
3 -6.0 \
5 120.0 \
7 -5040.0 \
9 362880.0 \
11 -39916800 \
13 6227020800.0
while [ "$#" -gt 0 ]
do
# We DO need $ here since $1, $2, etc are special
(( SIN += (ANGLE**$1)/$2 ))
shift 2 # Discard the first two arguments
done
printf "%.8f\n" "$SIN"
}
# Test degrees.
for x in $( seq 0.0 15.0 360.0 )
do
printf "%d\t" $x
Sin $x
done
Last edited by Corona688; 10-18-2018 at 01:43 PM..
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