1 | .\"
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2 | .\" bc.1 - the *roff document processor source for the bc manual
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3 | .\"
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4 | .\" This file is part of bc written for MINIX.
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5 | .\" Copyright (C) 1991, 1992 Free Software Foundation, Inc.
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6 | .\"
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7 | .\" This program is free software; you can redistribute it and/or modify
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8 | .\" it under the terms of the GNU General Public License as published by
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9 | .\" the Free Software Foundation; either version 2 of the License , or
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10 | .\" (at your option) any later version.
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11 | .\"
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12 | .\" This program is distributed in the hope that it will be useful,
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13 | .\" but WITHOUT ANY WARRANTY; without even the implied warranty of
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14 | .\" MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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15 | .\" GNU General Public License for more details.
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16 | .\"
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17 | .\" You should have received a copy of the GNU General Public License
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18 | .\" along with this program; see the file COPYING. If not, write to
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19 | .\" the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
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20 | .\"
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21 | .\" You may contact the author by:
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22 | .\" e-mail: phil@cs.wwu.edu
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23 | .\" us-mail: Philip A. Nelson
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24 | .\" Computer Science Department, 9062
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25 | .\" Western Washington University
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26 | .\" Bellingham, WA 98226-9062
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27 | .\"
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28 | .\"
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29 | .TH bc 1 .\" "Command Manual" v1.02 "Feb 3, 1992"
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30 | .SH NAME
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31 | bc - An arbitrary precision calculator language
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32 | .SH SYNTAX
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33 | \fBbc\fR [ \fB-lws\fR ] [ \fI file ...\fR ]
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34 | .SH VERSION
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35 | This man page documents GNU bc version 1.02.
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36 | .SH DESCRIPTION
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37 | \fBbc\fR is a language that supports arbitrary precision numbers
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38 | with interactive execution of statements. There are some similarities
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39 | in the syntax to the C programming language.
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40 | A standard math library is available by command line option.
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41 | If requested, the math library is defined before processing any files.
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42 | \fBbc\fR starts by processing code from all the files listed
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43 | on the command line in the order listed. After all files have been
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44 | processed, \fBbc\fR reads from the standard input. All code is
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45 | executed as it is read. (If a file contains a command to halt the
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46 | processor, \fBbc\fR will never read from the standard input.)
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47 | .PP
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48 | This version of \fBbc\fR contains several extensions beyond
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49 | traditional \fBbc\fR implementations and the POSIX draft standard.
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50 | Command line options can cause these extensions to print a warning
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51 | or to be rejected. This
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52 | document describes the language accepted by this processor.
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53 | Extensions will be identified as such.
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54 | .SS OPTIONS
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55 | .IP -l
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56 | Define the standard math library.
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57 | .IP -w
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58 | Give warnings for extensions to POSIX \fBbc\fR.
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59 | .IP -s
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60 | Process exactly the POSIX \fBbc\fR language.
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61 | .SS NUMBERS
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62 | The most basic element in \fBbc\fR is the number. Numbers are
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63 | arbitrary precision numbers. This precision is both in the integer
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64 | part and the fractional part. All numbers are represented internally
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65 | in decimal and all computation is done in decimal. (This version
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66 | truncates results from divide and multiply operations.) There are two
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67 | attributes of numbers, the length and the scale. The length is the
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68 | total number of significant decimal digits in a number and the scale
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69 | is the total number of decimal digits after the decimal point. For
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70 | example:
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71 | .nf
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72 | .RS
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73 | .000001 has a length of 6 and scale of 6.
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74 | 1935.000 has a length of 7 and a scale of 3.
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75 | .RE
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76 | .fi
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77 | .SS VARIABLES
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78 | Numbers are stored in two types of variables, simple variables and
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79 | arrays. Both simple variables and array variables are named. Names
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80 | begin with a letter followed by any number of letters, digits and
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81 | underscores. All letters must be lower case. (Full alpha-numeric
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82 | names are an extension. In POSIX \fBbc\fR all names are a single
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83 | lower case letter.) The type of variable is clear by the context
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84 | because all array variable names will be followed by brackets ([]).
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85 | .PP
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86 | There are four special variables, \fBscale, ibase, obase,\fR and
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87 | \fBlast\fR. \fBscale\fR defines how some operations use digits after the
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88 | decimal point. The default value of \fBscale\fR is 0. \fBibase\fR
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89 | and \fBobase\fR define the conversion base for input and output
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90 | numbers. The default for both input and output is base 10.
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91 | \fBlast\fR (an extension) is a variable that has the value of the last
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92 | printed number. These will be discussed in further detail where
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93 | appropriate. All of these variables may have values assigned to them
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94 | as well as used in expressions.
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95 | .SS COMMENTS
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96 | Comments in \fBbc\fR start with the characters \fB/*\fR and end with
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97 | the characters \fB*/\fR. Comments may start anywhere and appear as a
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98 | single space in the input. (This causes comments to delimit other
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99 | input items. For example, a comment can not be found in the middle of
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100 | a variable name.) Comments include any newlines (end of line) between
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101 | the start and the end of the comment.
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102 | .SS EXPRESSIONS
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103 | The numbers are manipulated by expressions and statements. Since
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104 | the language was designed to be interactive, statements and expressions
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105 | are executed as soon as possible. There is no "main" program. Instead,
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106 | code is executed as it is encountered. (Functions, discussed in
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107 | detail later, are defined when encountered.)
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108 | .PP
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109 | A simple expression is just a constant. \fBbc\fR converts constants
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110 | into internal decimal numbers using the current input base, specified
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111 | by the variable \fBibase\fR. (There is an exception in functions.)
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112 | The legal values of \fBibase\fR are 2 through 16 (F). Assigning a
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113 | value outside this range to \fBibase\fR will result in a value of 2
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114 | or 16. Input numbers may contain the characters 0-9 and A-F. (Note:
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115 | They must be capitals. Lower case letters are variable names.)
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116 | Single digit numbers always have the value of the digit regardless of
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117 | the value of \fBibase\fR. (i.e. A = 10.) For multi-digit numbers,
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118 | \fBbc\fR changes all input digits greater or equal to ibase to the
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119 | value of \fBibase\fR-1. This makes the number \fBFFF\fR always be
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120 | the largest 3 digit number of the input base.
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121 | .PP
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122 | Full expressions are similar to many other high level languages.
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123 | Since there is only one kind of number, there are no rules for mixing
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124 | types. Instead, there are rules on the scale of expressions. Every
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125 | expression has a scale. This is derived from the scale of original
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126 | numbers, the operation performed and in many cases, the value of the
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127 | variable \fBscale\fR. Legal values of the variable \fBscale\fR are
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128 | 0 to the maximum number representable by a C integer.
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129 | .PP
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130 | In the following descriptions of legal expressions, "expr" refers to a
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131 | complete expression and "var" refers to a simple or an array variable.
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132 | A simple variable is just a
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133 | .RS
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134 | \fIname\fR
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135 | .RE
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136 | and an array variable is specified as
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137 | .RS
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138 | \fIname\fR[\fIexpr\fR]
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139 | .RE
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140 | Unless specifically
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141 | mentioned the scale of the result is the maximum scale of the
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142 | expressions involved.
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143 | .IP "- expr"
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144 | The result is the negation of the expression.
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145 | .IP "++ var"
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146 | The variable is incremented by one and the new value is the result of
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147 | the expression.
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148 | .IP "-- var"
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149 | The variable
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150 | is decremented by one and the new value is the result of the
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151 | expression.
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152 | .IP "var ++"
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153 | The result of the expression is the value of
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154 | the variable and then the variable is incremented by one.
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155 | .IP "var --"
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156 | The result of the expression is the value of the variable and then
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157 | the variable is decremented by one.
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158 | .IP "expr + expr"
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159 | The result of the expression is the sum of the two expressions.
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160 | .IP "expr - expr"
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161 | The result of the expression is the difference of the two expressions.
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162 | .IP "expr * expr"
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163 | The result of the expression is the product of the two expressions.
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164 | .IP "expr / expr"
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165 | The result of the expression is the quotient of the two expressions.
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166 | The scale of the result is the value of the variable \fBscale\fR.
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167 | .IP "expr % expr"
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168 | The result of the expression is the "remainder" and it is computed in the
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169 | following way. To compute a%b, first a/b is computed to \fBscale\fR
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170 | digits. That result is used to compute a-(a/b)*b to the scale of the
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171 | maximum of \fBscale\fR+scale(b) and scale(a). If \fBscale\fR is set
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172 | to zero and both expressions are integers this expression is the
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173 | integer remainder function.
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174 | .IP "expr ^ expr"
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175 | The result of the expression is the value of the first raised to the
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176 | second. The second expression must be an integer. (If the second
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177 | expression is not an integer, a warning is generated and the
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178 | expression is truncated to get an integer value.) The scale of the
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179 | result is \fBscale\fR if the exponent is negative. If the exponent
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180 | is positive the scale of the result is the minimum of the scale of the
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181 | first expression times the value of the exponent and the maximum of
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182 | \fBscale\fR and the scale of the first expression. (e.g. scale(a^b)
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183 | = min(scale(a)*b, max( \fBscale,\fR scale(a))).) It should be noted
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184 | that expr^0 will always return the value of 1.
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185 | .IP "( expr )"
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186 | This alters the standard precedence to force the evaluation of the
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187 | expression.
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188 | .IP "var = expr"
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189 | The variable is assigned the value of the expression.
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190 | .IP "var <op>= expr"
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191 | This is equivalent to "var = var <op> expr" with the exception that
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192 | the "var" part is evaluated only once. This can make a difference if
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193 | "var" is an array.
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194 | .PP
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195 | Relational expressions are a special kind of expression
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196 | that always evaluate to 0 or 1, 0 if the relation is false and 1 if
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197 | the relation is true. These may appear in any legal expression.
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198 | (POSIX bc requires that relational expressions are used only in if,
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199 | while, and for statements and that only one relational test may be
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200 | done in them.) The relational operators are
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201 | .IP "expr1 < expr2"
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202 | The result is 1 if expr1 is strictly less than expr2.
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203 | .IP "expr1 <= expr2"
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204 | The result is 1 if expr1 is less than or equal to expr2.
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205 | .IP "expr1 > expr2"
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206 | The result is 1 if expr1 is strictly greater than expr2.
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207 | .IP "expr1 >= expr2"
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208 | The result is 1 if expr1 is greater than or equal to expr2.
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209 | .IP "expr1 == expr2"
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210 | The result is 1 if expr1 is equal to expr2.
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211 | .IP "expr1 != expr2"
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212 | The result is 1 if expr1 is not equal to expr2.
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213 | .PP
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214 | Boolean operations are also legal. (POSIX \fBbc\fR does NOT have
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215 | boolean operations). The result of all boolean operations are 0 and 1
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216 | (for false and true) as in relational expressions. The boolean
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217 | operators are:
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218 | .IP "!expr"
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219 | The result is 1 if expr is 0.
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220 | .IP "expr && expr"
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221 | The result is 1 if both expressions are non-zero.
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222 | .IP "expr || expr"
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223 | The result is 1 if either expression is non-zero.
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224 | .PP
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225 | The expression precedence is as follows: (lowest to highest)
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226 | .nf
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227 | .RS
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228 | || operator, left associative
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229 | && operator, left associative
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230 | ! operator, nonassociative
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231 | Relational operators, left associative
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232 | Assignment operator, right associative
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233 | + and - operators, left associative
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234 | *, / and % operators, left associative
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235 | ^ operator, right associative
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236 | unary - operator, nonassociative
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237 | ++ and -- operators, nonassociative
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238 | .RE
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239 | .fi
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240 | .PP
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241 | This precedence was chosen so that POSIX compliant \fBbc\fR programs
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242 | will run correctly. This will cause the use of the relational and
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243 | logical operators to have some unusual behavior when used with
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244 | assignment expressions. Consider the expression:
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245 | .RS
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246 | a = 3 < 5
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247 | .RE
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248 | .PP
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249 | Most C programmers would assume this would assign the result of "3 <
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250 | 5" (the value 1) to the variable "a". What this does in \fBbc\fR is
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251 | assign the value 3 to the variable "a" and then compare 3 to 5. It is
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252 | best to use parenthesis when using relational and logical operators
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253 | with the assignment operators.
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254 | .PP
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255 | There are a few more special expressions that are provided in \fBbc\fR.
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256 | These have to do with user defined functions and standard
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257 | functions. They all appear as "\fIname\fB(\fIparameters\fB)\fR".
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258 | See the section on functions for user defined functions. The standard
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259 | functions are:
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260 | .IP "length ( expression )"
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261 | The value of the length function is the number of significant digits in the
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262 | expression.
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263 | .IP "read ( )"
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264 | The read function (an extension) will read a number from the standard
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265 | input, regardless of where the function occurs. Beware, this can
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266 | cause problems with the mixing of data and program in the standard input.
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267 | The best use for this function is in a previously written program that
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268 | needs input from the user, but never allows program code to be input
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269 | from the user. The value of the read function is the number read from
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270 | the standard input using the current value of the variable
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271 | \fBibase\fR for the conversion base.
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272 | .IP "scale ( expression )"
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273 | The value of the scale function is the number of digits after the decimal
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274 | point in the expression.
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275 | .IP "sqrt ( expression )"
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276 | The value of the sqrt function is the square root of the expression. If
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277 | the expression is negative, a run time error is generated.
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278 | .SS STATEMENTS
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279 | Statements (as in most algebraic languages) provide the sequencing of
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280 | expression evaluation. In \fBbc\fR statements are executed "as soon
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281 | as possible." Execution happens when a newline in encountered and
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282 | there is one or more complete statements. Due to this immediate
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283 | execution, newlines are very important in \fBbc\fR. In fact, both a
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284 | semicolon and a newline are used as statement separators. An
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285 | improperly placed newline will cause a syntax error. Because newlines
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286 | are statement separators, it is possible to hide a newline by using
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287 | the backslash character. The sequence "\e<nl>", where <nl> is the
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288 | newline appears to \fBbc\fR as whitespace instead of a newline. A
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289 | statement list is a series of statements separated by semicolons and
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290 | newlines. The following is a list of \fBbc\fR statements and what
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291 | they do: (Things enclosed in brackets ([]) are optional parts of the
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292 | statement.)
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293 | .IP "expression"
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294 | This statement does one of two things. If the expression starts with
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295 | "<variable> <assignment> ...", it is considered to be an assignment
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296 | statement. If the expression is not an assignment statement, the
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297 | expression is evaluated and printed to the output. After the number
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298 | is printed, a newline is printed. For example, "a=1" is an assignment
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299 | statement and "(a=1)" is an expression that has an embedded
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300 | assignment. All numbers that are printed are printed in the base
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301 | specified by the variable \fBobase\fR. The legal values for \fB
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302 | obase\fR are 2 through BC_BASE_MAX. (See the section LIMITS.) For
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303 | bases 2 through 16, the usual method of writing numbers is used. For
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304 | bases greater than 16, \fBbc\fR uses a multi-character digit method
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305 | of printing the numbers where each higher base digit is printed as a
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306 | base 10 number. The multi-character digits are separated by spaces.
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307 | Each digit contains the number of characters required to represent the
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308 | base ten value of "obase-1". Since numbers are of arbitrary
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309 | precision, some numbers may not be printable on a single output line.
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310 | These long numbers will be split across lines using the "\e" as the
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311 | last character on a line. The maximum number of characters printed
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312 | per line is 70. Due to the interactive nature of \fBbc\fR printing
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313 | a number cause the side effect of assigning the printed value the the
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314 | special variable \fBlast\fR. This allows the user to recover the
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315 | last value printed without having to retype the expression that
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316 | printed the number. Assigning to \fBlast\fR is legal and will
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317 | overwrite the last printed value with the assigned value. The newly
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318 | assigned value will remain until the next number is printed or another
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319 | value is assigned to \fBlast\fR.
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320 | .IP "string"
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321 | The string is printed to the output. Strings start with a double quote
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322 | character and contain all characters until the next double quote character.
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323 | All characters are take literally, including any newline. No newline
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324 | character is printed after the string.
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325 | .IP "\fBprint\fR list"
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326 | The print statement (an extension) provides another method of output.
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327 | The "list" is a list of strings and expressions separated by commas.
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328 | Each string or expression is printed in the order of the list. No
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329 | terminating newline is printed. Expressions are evaluated and their
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330 | value is printed and assigned the the variable \fBlast\fR. Strings
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331 | in the print statement are printed to the output and may contain
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332 | special characters. Special characters start with the backslash
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333 | character (\e). The special characters recognized by \fBbc\fR are
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334 | "b" (bell), "f" (form feed), "n" (newline), "r" (carriage return), "t"
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335 | (tab), and "\e" (backslash). Any other character following the
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336 | backslash will be ignored. This still does not allow the double quote
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337 | character to be part of any string.
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338 | .IP "{ statement_list }"
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339 | This is the compound statement. It allows multiple statements to be
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340 | grouped together for execution.
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341 | .IP "\fBif\fR ( expression ) \fBthen\fR statement1 [\fBelse\fR statement2]"
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342 | The if statement evaluates the expression and executes statement1 or
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343 | statement2 depending on the value of the expression. If the expression
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344 | is non-zero, statement1 is executed. If statement2 is present and
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345 | the value of the expression is 0, then statement2 is executed. (The
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346 | else clause is an extension.)
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347 | .IP "\fBwhile\fR ( expression ) statement"
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348 | The while statement will execute the statement while the expression
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349 | is non-zero. It evaluates the expression before each execution of
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350 | the statement. Termination of the loop is caused by a zero
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351 | expression value or the execution of a break statement.
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352 | .IP "\fBfor\fR ( [expression1] ; [expression2] ; [expression3] ) statement"
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353 | The for statement controls repeated execution of the statement.
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354 | Expression1 is evaluated before the loop. Expression2 is evaluated
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355 | before each execution of the statement. If it is non-zero, the statement
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356 | is evaluated. If it is zero, the loop is terminated. After each
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357 | execution of the statement, expression3 is evaluated before the reevaluation
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358 | of expression2. If expression1 or expression3 are missing, nothing is
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359 | evaluated at the point they would be evaluated.
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360 | If expression2 is missing, it is the same as substituting
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361 | the value 1 for expression2. (The optional expressions are an
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362 | extension. POSIX \fBbc\fR requires all three expressions.)
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363 | The following is equivalent code for the for statement:
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364 | .nf
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365 | .RS
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366 | expression1;
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367 | while (expression2) {
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368 | statement;
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369 | expression3;
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370 | }
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371 | .RE
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372 | .fi
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373 | .IP "\fBbreak\fR"
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374 | This statement causes a forced exit of the most recent enclosing while
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375 | statement or for statement.
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376 | .IP "\fBcontinue\fR"
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377 | The continue statement (an extension) causes the most recent enclosing
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378 | for statement to start the next iteration.
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379 | .IP "\fBhalt\fR"
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380 | The halt statement (an extension) is an executed statement that causes
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381 | the \fBbc\fR processor to quit only when it is executed. For example,
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382 | "if (0 == 1) halt" will not cause \fBbc\fR to terminate because the halt is
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383 | not executed.
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384 | .IP "\fBreturn\fR"
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385 | Return the value 0 from a function. (See the section on functions.)
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386 | .IP "\fBreturn\fR ( expression )"
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387 | Return the value of the expression from a function. (See the section on
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388 | functions.)
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---|
389 | .SS PSEUDO STATEMENTS
|
---|
390 | These statements are not statements in the traditional sense. They are
|
---|
391 | not executed statements. Their function is performed at "compile" time.
|
---|
392 | .IP "\fBlimits\fR"
|
---|
393 | Print the local limits enforced by the local version of \fBbc\fR. This
|
---|
394 | is an extension.
|
---|
395 | .IP "\fBquit\fR"
|
---|
396 | When the quit statement is read, the \fBbc\fR processor
|
---|
397 | is terminated, regardless of where the quit statement is found. For
|
---|
398 | example, "if (0 == 1) quit" will cause \fBbc\fR to terminate.
|
---|
399 | .IP "\fBwarranty\fR"
|
---|
400 | Print a longer warranty notice. This is an extension.
|
---|
401 | .SS FUNCTIONS
|
---|
402 | Functions provide a method of defining a computation that can be executed
|
---|
403 | later. Functions in
|
---|
404 | .B bc
|
---|
405 | always compute a value and return it to the caller. Function definitions
|
---|
406 | are "dynamic" in the sense that a function is undefined until a definition
|
---|
407 | is encountered in the input. That definition is then used until another
|
---|
408 | definition function for the same name is encountered. The new definition
|
---|
409 | then replaces the older definition. A function is defined as follows:
|
---|
410 | .nf
|
---|
411 | .RS
|
---|
412 | \fBdefine \fIname \fB( \fIparameters \fB) { \fInewline
|
---|
413 | \fI auto_list statement_list \fB}\fR
|
---|
414 | .RE
|
---|
415 | .fi
|
---|
416 | A function call is just an expression of the form
|
---|
417 | "\fIname\fB(\fIparameters\fB)\fR".
|
---|
418 | .PP
|
---|
419 | Parameters are numbers or arrays (an extension). In the function definition,
|
---|
420 | zero or more parameters are defined by listing their names separated by
|
---|
421 | commas. Numbers are only call by value parameters. Arrays are only
|
---|
422 | call by variable. Arrays are specified in the parameter definition by
|
---|
423 | the notation "\fIname\fB[]\fR". In the function call, actual parameters
|
---|
424 | are full expressions for number parameters. The same notation is used
|
---|
425 | for passing arrays as for defining array parameters. The named array is
|
---|
426 | passed by variable to the function. Since function definitions are dynamic,
|
---|
427 | parameter numbers and types are checked when a function is called. Any
|
---|
428 | mismatch in number or types of parameters will cause a runtime error.
|
---|
429 | A runtime error will also occur for the call to an undefined function.
|
---|
430 | .PP
|
---|
431 | The \fIauto_list\fR is an optional list of variables that are for
|
---|
432 | "local" use. The syntax of the auto list (if present) is "\fBauto
|
---|
433 | \fIname\fR, ... ;". (The semicolon is optional.) Each \fIname\fR is
|
---|
434 | the name of an auto variable. Arrays may be specified by using the
|
---|
435 | same notation as used in parameters. These variables have their
|
---|
436 | values pushed onto a stack at the start of the function. The
|
---|
437 | variables are then initialized to zero and used throughout the
|
---|
438 | execution of the function. At function exit, these variables are
|
---|
439 | popped so that the original value (at the time of the function call)
|
---|
440 | of these variables are restored. The parameters are really auto
|
---|
441 | variables that are initialized to a value provided in the function
|
---|
442 | call. Auto variables are different than traditional local variables
|
---|
443 | in the fact that if function A calls function B, B may access function
|
---|
444 | A's auto variables by just using the same name, unless function B has
|
---|
445 | called them auto variables. Due to the fact that auto variables and
|
---|
446 | parameters are pushed onto a stack, \fBbc\fR supports recursive functions.
|
---|
447 | .PP
|
---|
448 | The function body is a list of \fBbc\fR statements. Again, statements
|
---|
449 | are separated by semicolons or newlines. Return statements cause the
|
---|
450 | termination of a function and the return of a value. There are two
|
---|
451 | versions of the return statement. The first form, "\fBreturn\fR", returns
|
---|
452 | the value 0 to the calling expression. The second form,
|
---|
453 | "\fBreturn ( \fIexpression \fB)\fR", computes the value of the expression
|
---|
454 | and returns that value to the calling expression. There is an implied
|
---|
455 | "\fBreturn (0)\fR" at the end of every function. This allows a function
|
---|
456 | to terminate and return 0 without an explicit return statement.
|
---|
457 | .PP
|
---|
458 | Functions also change the usage of the variable \fBibase\fR. All
|
---|
459 | constants in the function body will be converted using the value of
|
---|
460 | \fBibase\fR at the time of the function call. Changes of \fBibase\fR
|
---|
461 | will be ignored during the execution of the function except for the
|
---|
462 | standard function \fBread\fR, which will always use the current value
|
---|
463 | of \fBibase\fR for conversion of numbers.
|
---|
464 | .SS MATH LIBRARY
|
---|
465 | If \fBbc\fR is invoked with the \fB-l\fR option, a math library is preloaded
|
---|
466 | and the default scale is set to 20. The math functions will calculate their
|
---|
467 | results to the scale set at the time of their call.
|
---|
468 | The math library defines the following functions:
|
---|
469 | .IP "s (\fIx\fR)"
|
---|
470 | The sine of x in radians.
|
---|
471 | .IP "c (\fIx\fR)"
|
---|
472 | The cosine of x in radians.
|
---|
473 | .IP "a (\fIx\fR)"
|
---|
474 | The arctangent of x.
|
---|
475 | .IP "l (\fIx\fR)"
|
---|
476 | The natural logarithm of x.
|
---|
477 | .IP "e (\fIx\fR)"
|
---|
478 | The exponential function of raising e to the value x.
|
---|
479 | .IP "j (\fIn,x\fR)"
|
---|
480 | The bessel function of integer order n of x.
|
---|
481 | .SS EXAMPLES
|
---|
482 | In /bin/sh, the following will assign the value of "pi" to the shell
|
---|
483 | variable \fBpi\fR.
|
---|
484 | .RS
|
---|
485 | \fB
|
---|
486 | pi=$(echo "scale=10; 4*a(1)" | bc -l)
|
---|
487 | \fR
|
---|
488 | .RE
|
---|
489 | .PP
|
---|
490 | The following is the definition of the exponential function used in the
|
---|
491 | math library. This function is written in POSIX \fBbc\fR.
|
---|
492 | .nf
|
---|
493 | .RS
|
---|
494 | \fB
|
---|
495 | scale = 20
|
---|
496 |
|
---|
497 | /* Uses the fact that e^x = (e^(x/2))^2
|
---|
498 | When x is small enough, we use the series:
|
---|
499 | e^x = 1 + x + x^2/2! + x^3/3! + ...
|
---|
500 | */
|
---|
501 |
|
---|
502 | define e(x) {
|
---|
503 | auto a, d, e, f, i, m, v, z
|
---|
504 |
|
---|
505 | /* Check the sign of x. */
|
---|
506 | if (x<0) {
|
---|
507 | m = 1
|
---|
508 | x = -x
|
---|
509 | }
|
---|
510 |
|
---|
511 | /* Precondition x. */
|
---|
512 | z = scale;
|
---|
513 | scale = 4 + z + .44*x;
|
---|
514 | while (x > 1) {
|
---|
515 | f += 1;
|
---|
516 | x /= 2;
|
---|
517 | }
|
---|
518 |
|
---|
519 | /* Initialize the variables. */
|
---|
520 | v = 1+x
|
---|
521 | a = x
|
---|
522 | d = 1
|
---|
523 |
|
---|
524 | for (i=2; 1; i++) {
|
---|
525 | e = (a *= x) / (d *= i)
|
---|
526 | if (e == 0) {
|
---|
527 | if (f>0) while (f--) v = v*v;
|
---|
528 | scale = z
|
---|
529 | if (m) return (1/v);
|
---|
530 | return (v/1);
|
---|
531 | }
|
---|
532 | v += e
|
---|
533 | }
|
---|
534 | }
|
---|
535 | \fR
|
---|
536 | .RE
|
---|
537 | .fi
|
---|
538 | .PP
|
---|
539 | The following is code that uses the extended features of \fBbc\fR to
|
---|
540 | implement a simple program for calculating checkbook balances. This
|
---|
541 | program is best kept in a file so that it can be used many times
|
---|
542 | without having to retype it at every use.
|
---|
543 | .nf
|
---|
544 | .RS
|
---|
545 | \fB
|
---|
546 | scale=2
|
---|
547 | print "\enCheck book program!\en"
|
---|
548 | print " Remember, deposits are negative transactions.\en"
|
---|
549 | print " Exit by a 0 transaction.\en\en"
|
---|
550 |
|
---|
551 | print "Initial balance? "; bal = read()
|
---|
552 | bal /= 1
|
---|
553 | print "\en"
|
---|
554 | while (1) {
|
---|
555 | "current balance = "; bal
|
---|
556 | "transaction? "; trans = read()
|
---|
557 | if (trans == 0) break;
|
---|
558 | bal -= trans
|
---|
559 | bal /= 1
|
---|
560 | }
|
---|
561 | quit
|
---|
562 | \fR
|
---|
563 | .RE
|
---|
564 | .fi
|
---|
565 | .PP
|
---|
566 | The following is the definition of the recursive factorial function.
|
---|
567 | .nf
|
---|
568 | .RS
|
---|
569 | \fB
|
---|
570 | define f (x) {
|
---|
571 | if (x <= 1) return (1);
|
---|
572 | return (f(x-1) * x);
|
---|
573 | }
|
---|
574 | \fR
|
---|
575 | .RE
|
---|
576 | .fi
|
---|
577 | .SS DIFFERENCES
|
---|
578 | This version of
|
---|
579 | .B bc
|
---|
580 | was implemented from the POSIX P1003.2/D11 draft and contains
|
---|
581 | several differences and extensions relative to the draft and
|
---|
582 | traditional implementations.
|
---|
583 | It is not implemented in the traditional way using
|
---|
584 | .I dc(1).
|
---|
585 | This version is a single process which parses and runs a byte code
|
---|
586 | translation of the program. There is an "undocumented" option (-c)
|
---|
587 | that causes the program to output the byte code to
|
---|
588 | the standard output instead of running it. It was mainly used for
|
---|
589 | debugging the parser and preparing the math library.
|
---|
590 | .PP
|
---|
591 | A major source of differences is
|
---|
592 | extensions, where a feature is extended to add more functionality and
|
---|
593 | additions, where new features are added.
|
---|
594 | The following is the list of differences and extensions.
|
---|
595 | .IP LANG 11n
|
---|
596 | This version does not conform to the POSIX standard in the processing
|
---|
597 | of the LANG environment variable and all environment variables starting
|
---|
598 | with LC_.
|
---|
599 | .IP names
|
---|
600 | Traditional and POSIX
|
---|
601 | .B bc
|
---|
602 | have single letter names for functions, variables and arrays. They have
|
---|
603 | been extended to be multi-character names that start with a letter and
|
---|
604 | may contain letters, numbers and the underscore character.
|
---|
605 | .IP Strings
|
---|
606 | Strings are not allowed to contain NUL characters. POSIX says all characters
|
---|
607 | must be included in strings.
|
---|
608 | .IP last
|
---|
609 | POSIX \fBbc\fR does not have a \fBlast\fR variable. Some implementations
|
---|
610 | of \fBbc\fR use the period (.) in a similar way.
|
---|
611 | .IP comparisons
|
---|
612 | POSIX \fBbc\fR allows comparisons only in the if statement, the while
|
---|
613 | statement, and the second expression of the for statement. Also, only
|
---|
614 | one relational operation is allowed in each of those statements.
|
---|
615 | .IP "if statement, else clause"
|
---|
616 | POSIX \fBbc\fR does not have an else clause.
|
---|
617 | .IP "for statement"
|
---|
618 | POSIX \fBbc\fR requires all expressions to be present in the for statement.
|
---|
619 | .IP "&&, ||, !"
|
---|
620 | POSIX \fBbc\fR does not have the logical operators.
|
---|
621 | .IP "read function"
|
---|
622 | POSIX \fBbc\fR does not have a read function.
|
---|
623 | .IP "print statement"
|
---|
624 | POSIX \fBbc\fR does not have a print statement .
|
---|
625 | .IP "continue statement"
|
---|
626 | POSIX \fBbc\fR does not have a continue statement.
|
---|
627 | .IP "array parameters"
|
---|
628 | POSIX \fBbc\fR does not have array parameters. Other implementations
|
---|
629 | of \fBbc\fR may have call by value array parameters.
|
---|
630 | .IP "=+, =-, =*, =/, =%, =^"
|
---|
631 | POSIX \fBbc\fR does not require these "old style" assignment operators to
|
---|
632 | be defined. This version may allow these "old style" assignments. Use
|
---|
633 | the limits statement to see if the installed version supports them. If
|
---|
634 | it does support the "old style" assignment operators, the statement
|
---|
635 | "a =- 1" will decrement \fBa\fR by 1 instead of setting \fBa\fR to the
|
---|
636 | value -1.
|
---|
637 | .IP "spaces in numbers"
|
---|
638 | Other implementations of \fBbc\fR allow spaces in numbers. For example,
|
---|
639 | "x=1 3" would assign the value 13 to the variable x. The same statement
|
---|
640 | would cause a syntax error in this version of \fBbc\fR.
|
---|
641 | .IP "errors and execution"
|
---|
642 | This implementation varies from other implementations in terms of what
|
---|
643 | code will be executed when syntax and other errors are found in the
|
---|
644 | program. If a syntax error is found in a function definition, error
|
---|
645 | recovery tries to find the beginning of a statement and continue to
|
---|
646 | parse the function. Once a syntax error is found in the function, the
|
---|
647 | function will not be callable and becomes undefined.
|
---|
648 | Syntax errors in the interactive execution code will invalidate the
|
---|
649 | current execution block. The execution block is terminated by an
|
---|
650 | end of line that appears after a complete sequence of statements.
|
---|
651 | For example,
|
---|
652 | .nf
|
---|
653 | .RS
|
---|
654 | a = 1
|
---|
655 | b = 2
|
---|
656 | .RE
|
---|
657 | .fi
|
---|
658 | has two execution blocks and
|
---|
659 | .nf
|
---|
660 | .RS
|
---|
661 | { a = 1
|
---|
662 | b = 2 }
|
---|
663 | .RE
|
---|
664 | .fi
|
---|
665 | has one execution block. Any runtime error will terminate the execution
|
---|
666 | of the current execution block. A runtime warning will not terminate the
|
---|
667 | current execution block.
|
---|
668 | .IP "Interrupts"
|
---|
669 | During an interactive session, the SIGINT signal (usually generated by
|
---|
670 | the control-C character from the terminal) will cause execution of the
|
---|
671 | current execution block to be interrupted. It will display a "runtime"
|
---|
672 | error indicating which function was interrupted. After all runtime
|
---|
673 | structures have been cleaned up, a message will be printed to notify the
|
---|
674 | user that \fBbc\fR is ready for more input. All previously defined functions
|
---|
675 | remain defined and the value of all non-auto variables are the value at
|
---|
676 | the point of interruption. All auto variables and function parameters
|
---|
677 | are removed during the
|
---|
678 | clean up process. During a non-interactive
|
---|
679 | session, the SIGINT signal will terminate the entire run of \fBbc\fR.
|
---|
680 | .SS LIMITS
|
---|
681 | The following are the limits currently in place for this
|
---|
682 | .B bc
|
---|
683 | processor. Some of them may have been changed by an installation.
|
---|
684 | Use the limits statement to see the actual values.
|
---|
685 | .IP BC_BASE_MAX
|
---|
686 | The maximum output base is currently set at 999. The maximum input base
|
---|
687 | is 16.
|
---|
688 | .IP BC_DIM_MAX
|
---|
689 | This is currently an arbitrary limit of 65535 as distributed. Your
|
---|
690 | installation may be different.
|
---|
691 | .IP BC_SCALE_MAX
|
---|
692 | The number of digits after the decimal point is limited to INT_MAX digits.
|
---|
693 | Also, the number of digits before the decimal point is limited to INT_MAX
|
---|
694 | digits.
|
---|
695 | .IP BC_STRING_MAX
|
---|
696 | The limit on the number of characters in a string is INT_MAX characters.
|
---|
697 | .IP exponent
|
---|
698 | The value of the exponent in the raise operation (^) is limited to LONG_MAX.
|
---|
699 | .IP multiply
|
---|
700 | The multiply routine may yield incorrect results if a number
|
---|
701 | has more than LONG_MAX / 90 total digits. For 32 bit longs, this number is
|
---|
702 | 23,860,929 digits.
|
---|
703 | .IP "code size"
|
---|
704 | Each function and the "main" program are limited to 10240 bytes of
|
---|
705 | compiled byte code each. This limit (BC_MAX_SEGS) can be easily changed
|
---|
706 | to have more than 10 segments of 1024 bytes.
|
---|
707 | .IP "variable names"
|
---|
708 | The current limit on the number of unique names is 32767 for each of
|
---|
709 | simple variables, arrays and functions.
|
---|
710 | .SH FILES
|
---|
711 | In most installations, \fBbc\fR is completely self-contained.
|
---|
712 | Where executable size is of importance or the C compiler does
|
---|
713 | not deal with very long strings, \fBbc\fR will read
|
---|
714 | the standard math library from the file /usr/local/lib/libmath.b.
|
---|
715 | (The actual location may vary. It may be /lib/libmath.b.)
|
---|
716 | .SH DIAGNOSTICS
|
---|
717 | If any file on the command line can not be opened, \fBbc\fR will report
|
---|
718 | that the file is unavailable and terminate. Also, there are compile
|
---|
719 | and run time diagnostics that should be self-explanatory.
|
---|
720 | .SH BUGS
|
---|
721 | Error recovery is not very good yet.
|
---|
722 | .SH AUTHOR
|
---|
723 | .nf
|
---|
724 | Philip A. Nelson
|
---|
725 | phil@cs.wwu.edu
|
---|
726 | .fi
|
---|
727 | .SH ACKNOWLEDGEMENTS
|
---|
728 | The author would like to thank Steve Sommars (sesv@iwtsf.att.com) for
|
---|
729 | his extensive help in testing the implementation. Many great suggestions
|
---|
730 | were given. This is a much better product due to his involvement.
|
---|