#!/usr/bin/bc

# bc integer functions I've found useful

# while systems programming in the unix environment.

# License: LGPLv2

# Author:

# http://www.pixelbeat.org/

# Notes:

# I only use bc when python is not available.

# Personally I have this file in ~/bin/bc so

# that I can just invoke bc as normal and have these

# extra functions available.

# Changes:

# V0.1, 11 Apr 2007, Initial release

define min(x,y) {

if (x<y) return x

return y

}

define max(x,y) {

if (x>y) return x

return y

}

define abs(x) {

if (x<0) return -x

return x

}

/* take integer part */

define int(x) {

auto old_scale /* variables global by default */

old_scale=scale /* scale is global */

scale=0; ret=x/1

scale=old_scale

return ret

}

/* round to nearest integer */

define round(x) {

if (x<0) x-=.5 else x+=.5

return int(x)

}

/* smallest integer >= arg */

define ceil(x) {

auto intx

intx=int(x)

if (intx<x) intx+=1

return intx

}

/* largest integer <= arg */

define floor(x) {

return -ceil(-x)

}

/* round x to previous multiple of y */

define round_down(x,y) {

return y*floor(x/y)

}

/* round x to next multiple of y */

define round_up(x,y) {

return y*ceil(x/y)

}

/* round x to nearest multiple of y */

define round_to(x,y) {

return y*round(x/y)

}

/* Greatest Common Divisor or Highest Common Factor of x and y */

/* Note when people say Lowest Common Denominator they usually mean this */

define gcd(x,y) {

if (y==0) return x

return gcd(y,x%y) /* anything that divides into x and y also divides into the remainder of x/y */

}

/* Lowest Common Multiple of x and y */

/* Lowest Common Denominator of fractions is LCM of the denominators */

define lcm(x,y) {

return (x*y/gcd(x,y))

}