mathc.html

Shall高级编程

> using a <I
CLASS="FIRSTTERM"
>here
	        document</I
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CLASS="PROGRAMLISTING"
>   1&nbsp;#!/bin/bash
   2&nbsp;# Invoking 'bc' using command substitution
   3&nbsp;# in combination with a 'here document'.
   4&nbsp;
   5&nbsp;
   6&nbsp;var1=`bc &#60;&#60; EOF
   7&nbsp;18.33 * 19.78
   8&nbsp;EOF
   9&nbsp;`
  10&nbsp;echo $var1       # 362.56
  11&nbsp;
  12&nbsp;
  13&nbsp;#  $( ... ) notation also works.
  14&nbsp;v1=23.53
  15&nbsp;v2=17.881
  16&nbsp;v3=83.501
  17&nbsp;v4=171.63
  18&nbsp;
  19&nbsp;var2=$(bc &#60;&#60; EOF
  20&nbsp;scale = 4
  21&nbsp;a = ( $v1 + $v2 )
  22&nbsp;b = ( $v3 * $v4 )
  23&nbsp;a * b + 15.35
  24&nbsp;EOF
  25&nbsp;)
  26&nbsp;echo $var2       # 593487.8452
  27&nbsp;
  28&nbsp;
  29&nbsp;var3=$(bc -l &#60;&#60; EOF
  30&nbsp;scale = 9
  31&nbsp;s ( 1.7 )
  32&nbsp;EOF
  33&nbsp;)
  34&nbsp;# Returns the sine of 1.7 radians.
  35&nbsp;# The "-l" option calls the 'bc' math library.
  36&nbsp;echo $var3       # .991664810
  37&nbsp;
  38&nbsp;
  39&nbsp;# Now, try it in a function...
  40&nbsp;hypotenuse ()    # Calculate hypotenuse of a right triangle.
  41&nbsp;{                # c = sqrt( a^2 + b^2 )
  42&nbsp;hyp=$(bc -l &#60;&#60; EOF
  43&nbsp;scale = 9
  44&nbsp;sqrt ( $1 * $1 + $2 * $2 )
  45&nbsp;EOF
  46&nbsp;)
  47&nbsp;# Can't directly return floating point values from a Bash function.
  48&nbsp;# But, can echo-and-capture:
  49&nbsp;echo "$hyp"
  50&nbsp;}
  51&nbsp;
  52&nbsp;hyp=$(hypotenuse 3.68 7.31)
  53&nbsp;echo "hypotenuse = $hyp"    # 8.184039344
  54&nbsp;
  55&nbsp;
  56&nbsp;exit 0</PRE
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><P
><A
NAME="CANNONREF"
></A
></P
><DIV
CLASS="EXAMPLE"
><HR><A
NAME="CANNON"
></A
><P
><B
>Example 15-48. Calculating PI</B
></P
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><PRE
CLASS="PROGRAMLISTING"
>   1&nbsp;#!/bin/bash
   2&nbsp;# cannon.sh: Approximating PI by firing cannonballs.
   3&nbsp;
   4&nbsp;# This is a very simple instance of a "Monte Carlo" simulation:
   5&nbsp;#+ a mathematical model of a real-life event,
   6&nbsp;#+ using pseudorandom numbers to emulate random chance.
   7&nbsp;
   8&nbsp;#  Consider a perfectly square plot of land, 10000 units on a side.
   9&nbsp;#  This land has a perfectly circular lake in its center,
  10&nbsp;#+ with a diameter of 10000 units.
  11&nbsp;#  The plot is actually mostly water, except for land in the four corners.
  12&nbsp;#  (Think of it as a square with an inscribed circle.)
  13&nbsp;#
  14&nbsp;#  We will fire iron cannonballs from an old-style cannon
  15&nbsp;#+ at the square.
  16&nbsp;#  All the shots impact somewhere on the square,
  17&nbsp;#+ either in the lake or on the dry corners.
  18&nbsp;#  Since the lake takes up most of the area,
  19&nbsp;#+ most of the shots will SPLASH! into the water.
  20&nbsp;#  Just a few shots will THUD! into solid ground
  21&nbsp;#+ in the four corners of the square.
  22&nbsp;#
  23&nbsp;#  If we take enough random, unaimed shots at the square,
  24&nbsp;#+ Then the ratio of SPLASHES to total shots will approximate
  25&nbsp;#+ the value of PI/4.
  26&nbsp;#
  27&nbsp;#  The reason for this is that the cannon is actually shooting
  28&nbsp;#+ only at the upper right-hand quadrant of the square,
  29&nbsp;#+ i.e., Quadrant I of the Cartesian coordinate plane.
  30&nbsp;#  (The previous explanation was a simplification.)
  31&nbsp;#
  32&nbsp;#  Theoretically, the more shots taken, the better the fit.
  33&nbsp;#  However, a shell script, as opposed to a compiled language
  34&nbsp;#+ with floating-point math built in, requires a few compromises.
  35&nbsp;#  This tends to lower the accuracy of the simulation, of course.
  36&nbsp;
  37&nbsp;
  38&nbsp;DIMENSION=10000  # Length of each side of the plot.
  39&nbsp;                 # Also sets ceiling for random integers generated.
  40&nbsp;
  41&nbsp;MAXSHOTS=1000    # Fire this many shots.
  42&nbsp;                 # 10000 or more would be better, but would take too long.
  43&nbsp;PMULTIPLIER=4.0  # Scaling factor to approximate PI.
  44&nbsp;
  45&nbsp;get_random ()
  46&nbsp;{
  47&nbsp;SEED=$(head -n 1 /dev/urandom | od -N 1 | awk '{ print $2 }')
  48&nbsp;RANDOM=$SEED                                  #  From "seeding-random.sh"
  49&nbsp;                                              #+ example script.
  50&nbsp;let "rnum = $RANDOM % $DIMENSION"             #  Range less than 10000.
  51&nbsp;echo $rnum
  52&nbsp;}
  53&nbsp;
  54&nbsp;distance=        # Declare global variable.
  55&nbsp;hypotenuse ()    # Calculate hypotenuse of a right triangle.
  56&nbsp;{                # From "alt-bc.sh" example.
  57&nbsp;distance=$(bc -l &#60;&#60; EOF
  58&nbsp;scale = 0
  59&nbsp;sqrt ( $1 * $1 + $2 * $2 )
  60&nbsp;EOF
  61&nbsp;)
  62&nbsp;#  Setting "scale" to zero rounds down result to integer value,
  63&nbsp;#+ a necessary compromise in this script.
  64&nbsp;#  This diminshes the accuracy of the simulation, unfortunately.
  65&nbsp;}
  66&nbsp;
  67&nbsp;
  68&nbsp;# main() {
  69&nbsp;
  70&nbsp;# Initialize variables.
  71&nbsp;shots=0
  72&nbsp;splashes=0
  73&nbsp;thuds=0
  74&nbsp;Pi=0
  75&nbsp;
  76&nbsp;while [ "$shots" -lt  "$MAXSHOTS" ]           # Main loop.
  77&nbsp;do
  78&nbsp;
  79&nbsp;  xCoord=$(get_random)                        # Get random X and Y coords.
  80&nbsp;  yCoord=$(get_random)
  81&nbsp;  hypotenuse $xCoord $yCoord                  #  Hypotenuse of right-triangle =
  82&nbsp;                                              #+ distance.
  83&nbsp;  ((shots++))
  84&nbsp;
  85&nbsp;  printf "#%4d   " $shots
  86&nbsp;  printf "Xc = %4d  " $xCoord
  87&nbsp;  printf "Yc = %4d  " $yCoord
  88&nbsp;  printf "Distance = %5d  " $distance         #  Distance from 
  89&nbsp;                                              #+ center of lake --
  90&nbsp;                                              #  the "origin" --
  91&nbsp;                                              #+ coordinate (0,0).
  92&nbsp;
  93&nbsp;  if [ "$distance" -le "$DIMENSION" ]
  94&nbsp;  then
  95&nbsp;    echo -n "SPLASH!  "
  96&nbsp;    ((splashes++))
  97&nbsp;  else
  98&nbsp;    echo -n "THUD!    "
  99&nbsp;    ((thuds++))
 100&nbsp;  fi
 101&nbsp;
 102&nbsp;  Pi=$(echo "scale=9; $PMULTIPLIER*$splashes/$shots" | bc)
 103&nbsp;  # Multiply ratio by 4.0.
 104&nbsp;  echo -n "PI ~ $Pi"
 105&nbsp;  echo
 106&nbsp;
 107&nbsp;done
 108&nbsp;
 109&nbsp;echo
 110&nbsp;echo "After $shots shots, PI looks like approximately $Pi."
 111&nbsp;# Tends to run a bit high . . . 
 112&nbsp;# Probably due to round-off error and imperfect randomness of $RANDOM.
 113&nbsp;echo
 114&nbsp;
 115&nbsp;# }
 116&nbsp;
 117&nbsp;exit 0
 118&nbsp;
 119&nbsp;#  One might well wonder whether a shell script is appropriate for
 120&nbsp;#+ an application as complex and computation-intensive as a simulation.
 121&nbsp;#
 122&nbsp;#  There are at least two justifications.
 123&nbsp;#  1) As a proof of concept: to show it can be done.
 124&nbsp;#  2) To prototype and test the algorithms before rewriting
 125&nbsp;#+    it in a compiled high-level language.</PRE
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></DD
><DT
><A
NAME="DCREF"
></A
><B
CLASS="COMMAND"
>dc</B
></DT
><DD
><P
>The <B
CLASS="COMMAND"
>dc</B
> (<B
CLASS="COMMAND"
>d</B
>esk
	    <B
CLASS="COMMAND"
>c</B
>alculator) utility is stack-oriented
	      and uses RPN (<SPAN
CLASS="QUOTE"
>"Reverse Polish Notation"</SPAN
>). Like
	      <B
CLASS="COMMAND"
>bc</B
>, it has much of the power of a
	      programming language.</P
><P
>Most persons avoid <B
CLASS="COMMAND"
>dc</B
>, since it
	        requires non-intuitive RPN input. Yet, it has its uses.</P
><DIV
CLASS="EXAMPLE"
><HR><A
NAME="HEXCONVERT"
></A
><P
><B
>Example 15-49. Converting a decimal number to hexadecimal</B
></P
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><PRE
CLASS="PROGRAMLISTING"
>   1&nbsp;#!/bin/bash
   2&nbsp;# hexconvert.sh: Convert a decimal number to hexadecimal.
   3&nbsp;
   4&nbsp;E_NOARGS=65 # Command-line arg missing.
   5&nbsp;BASE=16     # Hexadecimal.
   6&nbsp;
   7&nbsp;if [ -z "$1" ]
   8&nbsp;then
   9&nbsp;  echo "Usage: $0 number"
  10&nbsp;  exit $E_NOARGS
  11&nbsp;  # Need a command line argument.
  12&nbsp;fi
  13&nbsp;# Exercise: add argument validity checking.
  14&nbsp;
  15&nbsp;
  16&nbsp;hexcvt ()
  17&nbsp;{
  18&nbsp;if [ -z "$1" ]
  19&nbsp;then
  20&nbsp;  echo 0
  21&nbsp;  return    # "Return" 0 if no arg passed to function.
  22&nbsp;fi
  23&nbsp;
  24&nbsp;echo ""$1" "$BASE" o p" | dc
  25&nbsp;#                 "o" sets radix (numerical base) of output.
  26&nbsp;#                   "p" prints the top of stack.
  27&nbsp;# See 'man dc' for other options.
  28&nbsp;return
  29&nbsp;}
  30&nbsp;
  31&nbsp;hexcvt "$1"
  32&nbsp;
  33&nbsp;exit 0</PRE
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><HR></DIV
><P
>Studying the <I
CLASS="FIRSTTERM"
>info</I
> page for
		<B
CLASS="COMMAND"
>dc</B
> is a painful path to understanding its
		intricacies. There seems to be a small, select group of
		<SPAN
CLASS="emphasis"
><I
CLASS="EMPHASIS"
>dc wizards</I
></SPAN
> who delight in showing off
		their mastery of this powerful, but arcane utility.</P
><P
>	      <TABLE
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WIDTH="90%"
><TR
><TD
><PRE
CLASS="SCREEN"
> <TT
CLASS="PROMPT"
>bash$ </TT
><TT
CLASS="USERINPUT"
><B
>echo "16i[q]sa[ln0=aln100%Pln100/snlbx]sbA0D68736142snlbxq" | dc"</B
></TT
>
 <TT
CLASS="COMPUTEROUTPUT"
>Bash</TT
>
 	      </PRE
></TD
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>
	  </P
><DIV
CLASS="EXAMPLE"
><HR><A
NAME="FACTR"
></A
><P
><B
>Example 15-50. Factoring</B
></P
><TABLE
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><TD
><PRE
CLASS="PROGRAMLISTING"
>   1&nbsp;#!/bin/bash
   2&nbsp;# factr.sh: Factor a number
   3&nbsp;
   4&nbsp;MIN=2       # Will not work for number smaller than this.
   5&nbsp;E_NOARGS=65
   6&nbsp;E_TOOSMALL=66
   7&nbsp;
   8&nbsp;if [ -z $1 ]
   9&nbsp;then
  10&nbsp;  echo "Usage: $0 number"
  11&nbsp;  exit $E_NOARGS
  12&nbsp;fi
  13&nbsp;
  14&nbsp;if [ "$1" -lt "$MIN" ]
  15&nbsp;then
  16&nbsp;  echo "Number to factor must be $MIN or greater."
  17&nbsp;  exit $E_TOOSMALL
  18&nbsp;fi  
  19&nbsp;
  20&nbsp;# Exercise: Add type checking (to reject non-integer arg).
  21&nbsp;
  22&nbsp;echo "Factors of $1:"
  23&nbsp;# -------------------------------------------------------------------------------
  24&nbsp;echo "$1[p]s2[lip/dli%0=1dvsr]s12sid2%0=13sidvsr[dli%0=1lrli2+dsi!&#62;.]ds.xd1&#60;2"|dc
  25&nbsp;# -------------------------------------------------------------------------------
  26&nbsp;# Above line of code written by Michel Charpentier &#60;[e-mail]&#62;.
  27&nbsp;# Used in ABS Guide with permission (thanks!).
  28&nbsp;
  29&nbsp; exit 0</PRE
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><HR></DIV
></DD
><DT
><A
NAME="AWKMATH"
></A
><B
CLASS="COMMAND"
>awk</B
></DT
><DD
><P
>Yet another way of doing floating point math in
	      a script is using <A
HREF="awk.html#AWKREF"
>awk's</A
>
	      built-in math functions in a <A
HREF="wrapper.html#SHWRAPPER"
>shell
	      wrapper</A
>.</P
><DIV
CLASS="EXAMPLE"
><HR><A
NAME="HYPOT"
></A
><P
><B
>Example 15-51. Calculating the hypotenuse of a triangle</B
></P
><TABLE
BORDER="0"
BGCOLOR="#E0E0E0"
WIDTH="90%"
><TR
><TD
><PRE
CLASS="PROGRAMLISTING"
>   1&nbsp;#!/bin/bash
   2&nbsp;# hypotenuse.sh: Returns the "hypotenuse" of a right triangle.
   3&nbsp;#                (square root of sum of squares of the "legs")
   4&nbsp;
   5&nbsp;ARGS=2                # Script needs sides of triangle passed.
   6&nbsp;E_BADARGS=65          # Wrong number of arguments.
   7&nbsp;
   8&nbsp;if [ $# -ne "$ARGS" ] # Test number of arguments to script.
   9&nbsp;then
  10&nbsp;  echo "Usage: `basename $0` side_1 side_2"
  11&nbsp;  exit $E_BADARGS
  12&nbsp;fi
  13&nbsp;
  14&nbsp;
  15&nbsp;AWKSCRIPT=' { printf( "%3.7f\n", sqrt($1*$1 + $2*$2) ) } '
  16&nbsp;#             command(s) / parameters passed to awk
  17&nbsp;
  18&nbsp;
  19&nbsp;# Now, pipe the parameters to awk.
  20&nbsp;    echo -n "Hypotenuse of $1 and $2 = "
  21&nbsp;    echo $1 $2 | awk "$AWKSCRIPT"
  22&nbsp;#   ^^^^^^^^^^^^
  23&nbsp;# An echo-and-pipe is an easy way of passing shell parameters to awk.
  24&nbsp;
  25&nbsp;exit 0
  26&nbsp;
  27&nbsp;# Exercise: Rewrite this script using 'bc' rather than awk.
  28&nbsp;#           Which method is more intuitive?</PRE
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