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<h1 id="operators">Operators</h1>
<p>우선순위가 높은 것부터 낮은 순서입니다.</p>
<table>
<thead>
<tr>
<th>Operators</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><strong>( . . . )</strong></td>
<td>Grouping.</td>
</tr>
<tr>
<td><strong><code>$</code></strong></td>
<td>Field reference.</td>
</tr>
<tr>
<td><strong><code>++</code> <code>--</code></strong></td>
<td>Increment and decrement (prefix and postfix).</td>
</tr>
<tr>
<td><strong><code>^</code></strong> <b><code>**</code></b></td>
<td>Power. (right to left)</td>
</tr>
<tr>
<td><strong><code>+</code> <code>-</code> <code>!</code></strong></td>
<td>Unary plus, minus, logical NOT.</td>
</tr>
<tr>
<td><strong><code>*</code> <code>/</code> <code>%</code></strong></td>
<td>Multiply, divide and modulus (remainder).</td>
</tr>
<tr>
<td><strong><code>+</code> <code>-</code></strong></td>
<td>Add and subtract.</td>
</tr>
<tr>
<td>nothing</td>
<td>String concatenation.</td>
</tr>
<tr>
<td><strong><code><</code> <code><=</code> <code>==</code> <code>!=</code> <code>></code> <code>>=</code> <code>>></code></strong> <b><code>| |&</code></b></td>
<td>Relational and redirection.</td>
</tr>
<tr>
<td><strong><code>~</code> <code>!~</code></strong></td>
<td>Matching, nonmatching.</td>
</tr>
<tr>
<td><strong><code>in</code></strong></td>
<td>Array membership.</td>
</tr>
<tr>
<td><strong><code>&&</code></strong></td>
<td>Logical AND.</td>
</tr>
<tr>
<td><b><code>||</code></b></td>
<td>Logical OR.</td>
</tr>
<tr>
<td><strong><code>?:</code></strong></td>
<td>Conditional. (right to left)</td>
</tr>
<tr>
<td><strong><code>=</code> <code>+=</code> <code>-=</code> <code>*=</code> <code>/=</code> <code>%=</code> <code>^=</code></strong> <b><code>**=</code></b></td>
<td>Assignment.</td>
</tr>
</tbody>
</table>
<blockquote>
<p>The <code>|&</code>, <code>**</code>, and <code>**=</code> operators are not specified by POSIX. For maximum portability, do not use them. </p>
</blockquote>
<pre><code class="lang-bash"><span class="hljs-comment"># '^=' 는 power 대입 연산자</span>
$ awk <span class="hljs-string">'BEGIN { aa = 3; aa ^= 2; print aa }'</span>
<span class="hljs-number">9</span>
</code></pre>
<h4 id="-연산자는-변수와의-사이에-공백이-올-수-있습니다"><code>++</code> <code>--</code> 연산자는 변수와의 사이에 공백이 올 수 있습니다.</h4>
<pre><code class="lang-bash">$ awk <span class="hljs-string">'BEGIN { n = 1; print ++ n; print n }'</span>
<span class="hljs-number">2</span>
<span class="hljs-number">2</span>
$ awk <span class="hljs-string">'BEGIN { n = 1; print n ++; print n }'</span>
<span class="hljs-number">1</span>
<span class="hljs-number">2</span>
</code></pre>
<p>따라서 다음과 같은 경우 결과가 <code>123</code> 이 되지 않습니다.
왜냐하면 두 번째와 같이 해석되기 때문입니다.</p>
<pre><code class="lang-bash">$ awk <span class="hljs-string">'BEGIN { n = 12; x = 2; r = n ++x; print r }'</span>
<span class="hljs-number">122</span>
$ awk <span class="hljs-string">'BEGIN { n = 12; x = 2; r = (n ++)x; print r }'</span>
<span class="hljs-number">122</span>
$ awk <span class="hljs-string">'BEGIN { n = 12; x = 2; r = n ++x; print n }'</span>
<span class="hljs-number">13</span>
</code></pre>
<p><code>r</code> 값이 <code>123</code> 이 되게 하려면 다음과 같이 해야 합니다.</p>
<pre><code class="lang-bash">$ awk <span class="hljs-string">'BEGIN { n = 12; x = 2; r = n (++x); print r }'</span>
<span class="hljs-number">123</span>
$ gawk <span class="hljs-string">'BEGIN { n = 12; x = 2; r = (n) ++x; print r }'</span>
<span class="hljs-number">123</span>
$ gawk <span class="hljs-string">'BEGIN { n = 12; x = 2; r = n "" ++x; print r }'</span>
<span class="hljs-number">123</span>
</code></pre>
<p><a name="quiz"></a></p>
<h1 id="quiz">Quiz</h1>
<p><code>7 + 3 * (5 - 2) + 4</code> 와 같은 사칙연산 수식을 라인 단위로 입력받아
연산 결과를 출력하는 것입니다. 덧셈, 뺄셈보다는 곱셈, 나눗셈을 먼저 계산해야 하고
괄호가 있을 경우 제일 먼저 계산해야 합니다.
여기서는 stack 을 활용하는 후위 표기법을 사용했습니다.
자세한 설명은 <a href="https://jamanbbo.tistory.com/53" target="_blank">쏭이님의 홈페이지</a> 를 참고하세요.</p>
<blockquote>
<p>후위 표기법 (postfix notation) 은 <a href="https://ko.wikipedia.org/wiki/%EC%97%AD%ED%8F%B4%EB%9E%80%EB%93%9C_%ED%91%9C%EA%B8%B0%EB%B2%95" target="_blank">역폴란드 표기법</a> (RPN, Reverse Polish Notation)
이라고도 하는데 연산자를 연산 대상의 뒤에 쓰는 표기법입니다.
이 방식은 수식을 계산할 때 특별한 변환 없이, 수식을 앞에서부터 읽어 나가면서 stack 에 저장하면 된다는 장점이 있다. </p>
</blockquote>
<pre><code class="lang-bash">$ ./parse.sh <<< <span class="hljs-string">'1 + 2 * 3'</span>
<span class="hljs-number">7</span>
$ cat file <span class="hljs-comment"># 수식은 공백 없이 붙여 쓸 수 있습니다.</span>
<span class="hljs-number">1</span> + <span class="hljs-number">2</span> * <span class="hljs-number">3</span> + <span class="hljs-number">4</span>
( <span class="hljs-number">1</span> + <span class="hljs-number">2</span> ) * <span class="hljs-number">3</span> + <span class="hljs-number">4</span>
<span class="hljs-number">7</span>+<span class="hljs-number">3</span>*(<span class="hljs-number">5</span>-<span class="hljs-number">2</span>)+<span class="hljs-number">4</span>
- - <span class="hljs-number">3</span> - + - - <span class="hljs-number">4</span> + <span class="hljs-number">5</span>
-<span class="hljs-number">3</span> - ( -<span class="hljs-number">4</span> + <span class="hljs-number">5</span> )
<span class="hljs-number">3</span> - -( -<span class="hljs-number">10</span> + -<span class="hljs-number">2</span> )
<span class="hljs-number">3</span> - -(-( -<span class="hljs-number">10</span> + -<span class="hljs-number">2</span> ))
<span class="hljs-number">3</span> + -( -<span class="hljs-number">10</span> - -(<span class="hljs-number">3</span>) + -( <span class="hljs-number">3</span> - ( -<span class="hljs-number">10</span> + -<span class="hljs-number">2</span> ) + -<span class="hljs-number">2</span> ))
$ ./parse.sh file <span class="hljs-comment"># 또는 cat file | ./parse.sh</span>
<span class="hljs-number">11</span>
<span class="hljs-number">13</span>
<span class="hljs-number">20</span>
<span class="hljs-number">4</span>
-<span class="hljs-number">4</span>
-<span class="hljs-number">9</span>
<span class="hljs-number">15</span>
<span class="hljs-number">23</span>
</code></pre>
<blockquote>
<ol>
<li><p>사용되는 연산자 우선순위는 <code>(</code> < <code>+</code> <code>-</code> < <code>*</code> <code>/</code> 입니다. </p>
</li>
<li><p>현재 연산자가 ostack 의 top 에 있는 연산자 보다 우선순위가 높아질 때까지 pop 해서
calc 하고 우선순위가 높아졌다면 ostack 에 push 합니다. </p>
</li>
<li><p><code>- 3 - ( - 4 - + - 5 )</code> 에서 숫자 앞에 있는 <code>- 3</code>, <code>- 4</code>, <code>+ - 5</code> 연산자는 두 개의
operand 를 이용해 연산하는 binary 연산자가 아니고 unary 연산자 이므로 ostack 에
push 하지 않고 number 에 부호를 설정해서 rstack 에 push 합니다.
( unary 연산자 위치에 <code>*</code> <code>/</code> 가 오는것은 오류 입니다. )</p>
</li>
<li><p><code>3 - - ( -10 + -2 )</code> 와 같이 괄호 앞에 있는 unary 연산자는 괄호가 닫힐때 최종 결과값에
부호를 설정해야 합니다. 괄호는 nesting 될수 있으므로 ustack 을 이용해 <code>"("</code> 에서
부호값을 저장하고 <code>")"</code> 에서 rstack 에서 결과값을 pop 해서 부호를 설정합니다.</p>
</li>
</ol>
</blockquote>
<pre><code class="lang-bash"><span class="hljs-comment">#!/usr/bin/env -S gawk -f</span>
<span class="hljs-comment"># stack 은 세 개를 사용합니다. ostack 에는 operator 와 괄호가 들어가고</span>
<span class="hljs-comment"># rstack 에는 operand 가 들어가고 calc 계산 결과가 저장됩니다.</span>
<span class="hljs-comment"># ustack 은 "(" 괄호 앞의 부호를 저장하는데 사용됩니다.</span>
BEGIN { FS=<span class="hljs-string">""</span>; token[<span class="hljs-number">0</span>][<span class="hljs-number">0</span>]; ostack[<span class="hljs-number">0</span>]; rstack[<span class="hljs-number">0</span>]; ustack[<span class="hljs-number">0</span>] }
{
idx = <span class="hljs-number">0</span>
tokenize() <span class="hljs-comment"># 라인 별로 tokenize 를 해서</span>
<span class="hljs-built_in">print</span> parse() <span class="hljs-comment"># 연산 결과를 출력합니다.</span>
delete token <span class="hljs-comment"># 다음 입력 라인을 위한 초기화 </span>
}
<span class="hljs-keyword">function</span> parse( i, len, op, pk, val, unary, unary_p) {
unary = unary_p = <span class="hljs-number">1</span> <span class="hljs-comment"># unary 연산자 부호 설정을 위한 변수. _p 는 괄호용</span>
len = length(token)
<span class="hljs-keyword">for</span> (i=<span class="hljs-number">0</span>; i < len; i++) {
switch ( token[i][<span class="hljs-string">"type"</span>] ) {
<span class="hljs-keyword">case</span> <span class="hljs-string">"number"</span> :
<span class="hljs-comment"># unary 값으로 부호를 설정해서 rstack 에 push 합니다.</span>
push(rstack, unary * token[i][<span class="hljs-string">"value"</span>])
unary = <span class="hljs-number">1</span> <span class="hljs-comment"># push 후에는 값을 1 로 reset</span>
<span class="hljs-built_in">break</span>
<span class="hljs-keyword">case</span> <span class="hljs-string">"operator"</span> :
op = token[i][<span class="hljs-string">"value"</span>]
<span class="hljs-comment"># 현재 연산자 바로 이전 token 이 ")" 와 "number" 가 아니면 unary 연산자</span>
<span class="hljs-keyword">if</span> (token[i-<span class="hljs-number">1</span>][<span class="hljs-string">"value"</span>] != <span class="hljs-string">")"</span> && token[i-<span class="hljs-number">1</span>][<span class="hljs-string">"type"</span>] != <span class="hljs-string">"number"</span>)
{
<span class="hljs-comment"># unary 연산자 자리에 * or / 가 오면 오류</span>
<span class="hljs-keyword">if</span> ( op ~ /*|\// ) error( <span class="hljs-string">"* or / on unary operator"</span> )
<span class="hljs-keyword">if</span> ( token[i+<span class="hljs-number">1</span>][<span class="hljs-string">"value"</span>] == <span class="hljs-string">"("</span>) { <span class="hljs-comment"># 바로 다음 token 이 "(" 이면</span>
unary_p = unary * (op <span class="hljs-number">1</span>) <span class="hljs-comment"># 괄호를 위한 unary_p 변수를 </span>
unary = <span class="hljs-number">1</span> <span class="hljs-comment"># 설정하고 unary 변수는 reset</span>
} <span class="hljs-keyword">else</span> unary *= (op <span class="hljs-number">1</span>) <span class="hljs-comment"># 이외는 unary 변수를 설정 </span>
<span class="hljs-built_in">break</span>
}
pk = peek(ostack) <span class="hljs-comment"># ostack 의 top 항목을 조회해서</span>
<span class="hljs-keyword">if</span> ( pk == <span class="hljs-string">""</span> || pk == <span class="hljs-string">"("</span> ) <span class="hljs-comment"># 항목이 empty 이거나 "(" 일 경우</span>
{ push(ostack, op); <span class="hljs-built_in">break</span> } <span class="hljs-comment"># 연산자를 ostack 에 push 합니다. </span>
<span class="hljs-keyword">if</span> ( op == <span class="hljs-string">"*"</span> || op == <span class="hljs-string">"/"</span> ) { <span class="hljs-comment"># 현재 연산자가 "*" or "/" 이면</span>
<span class="hljs-keyword">while</span>( peek(ostack) ~ /*|\// ) <span class="hljs-comment"># 같은 우선순위 연산자를 꺼내어</span>
calc( pop(ostack)) <span class="hljs-comment"># calc 하고 완료되면 현재</span>
push(ostack, op) <span class="hljs-comment"># 연산자를 ostack 에 push 합니다</span>
<span class="hljs-built_in">break</span>
}
<span class="hljs-comment"># 그외 현재 연산자가 "+" or "-" 일 경우 우선순위가 더 낮은 "(" 가</span>
<span class="hljs-comment"># ostack 의 top 이 될때까지 꺼내어 calc 하고 현재 연산자를 push 합니다.</span>
<span class="hljs-keyword">while</span>( peek(ostack) != <span class="hljs-string">"("</span> && slen(ostack) > <span class="hljs-number">0</span> )
calc( pop(ostack))
push( ostack, op)
<span class="hljs-built_in">break</span>
<span class="hljs-keyword">case</span> <span class="hljs-string">"parenthesis"</span> :
val = token[i][<span class="hljs-string">"value"</span>]
<span class="hljs-keyword">if</span> ( val == <span class="hljs-string">"("</span> ) { <span class="hljs-comment"># "(" 를 만나면 ostack 에 push 하고</span>
push(ostack, val) <span class="hljs-comment"># 괄호를 위한 부호 설정을 위해</span>
push(ustack, unary_p) <span class="hljs-comment"># ustack 에 unary_p 를 push 하고</span>
unary_p = <span class="hljs-number">1</span> <span class="hljs-comment"># 완료되면 1 로 reset 합니다.</span>
} <span class="hljs-keyword">else</span> { <span class="hljs-comment"># ")"</span>
<span class="hljs-keyword">while</span> (val = pop(ostack)) { <span class="hljs-comment"># ")" 를 만나면</span>
<span class="hljs-keyword">if</span> ( val == <span class="hljs-string">"("</span> ) <span class="hljs-built_in">break</span> <span class="hljs-comment"># "(" 가 나올때 까지 연산자를</span>
<span class="hljs-keyword">else</span> calc(val) <span class="hljs-comment"># pop 해서 calc 합니다.</span>
}
<span class="hljs-keyword">if</span> ( val != <span class="hljs-string">"("</span> ) error( <span class="hljs-string">"parentheses missmatch. more ')'"</span> )
<span class="hljs-comment"># ustack 에 저장해 놓은 부호값을 최종 결과값에 적용합니다. </span>
push(rstack, pop(ustack) * pop(rstack))
}
}
}
len = slen(ostack) <span class="hljs-comment"># ostack 에 연산자가 남아 있을경우 </span>
<span class="hljs-keyword">for</span> (i = <span class="hljs-number">1</span>; i <= len; i++) { <span class="hljs-comment"># pop 해서 calc 합니다.</span>
val = pop(ostack) <span class="hljs-comment"># "(" 가 남아 있다는 것은 ")" 가 모자란것</span>
<span class="hljs-keyword">if</span> ( val == <span class="hljs-string">"("</span> ) error( <span class="hljs-string">"parentheses missmatch. less ')'"</span> )
calc( val )
}
<span class="hljs-built_in">return</span> pop(rstack) <span class="hljs-comment"># ostack 에 있는 모든 연산자가 calc 되고 난후에는</span>
<span class="hljs-comment"># rstack 에는 최종 결과만 남아있게 됩니다.</span>
}
<span class="hljs-keyword">function</span> calc(op, num1, num2, res) {
num1 = pop(rstack) <span class="hljs-comment"># rstack 에서 두개의 operand 를 pop 해서</span>
num2 = pop(rstack) <span class="hljs-comment"># 인수로 전달된 op 연산자와 연산을 하고</span>
switch (op) {
<span class="hljs-keyword">case</span> <span class="hljs-string">"+"</span> : res = num2 + num1; <span class="hljs-built_in">break</span>
<span class="hljs-keyword">case</span> <span class="hljs-string">"-"</span> : res = num2 - num1; <span class="hljs-built_in">break</span>
<span class="hljs-keyword">case</span> <span class="hljs-string">"*"</span> : res = num2 * num1; <span class="hljs-built_in">break</span>
<span class="hljs-keyword">case</span> <span class="hljs-string">"/"</span> :
<span class="hljs-keyword">if</span> (num1 == <span class="hljs-number">0</span> ) error( <span class="hljs-string">"division by zero"</span> )
res = num2 / num1
}
push(rstack, res) <span class="hljs-comment"># 결과를 다시 rstack 으로 push 합니다.</span>
}
<span class="hljs-keyword">function</span> error (str) {
<span class="hljs-built_in">print</span> <span class="hljs-string">"ERROR: "</span> str > <span class="hljs-string">"/dev/stderr"</span>
<span class="hljs-built_in">exit</span> <span class="hljs-number">1</span>
}
<span class="hljs-comment">############ tokenize ############</span>
<span class="hljs-keyword">function</span> tokenize ( i, num) {
<span class="hljs-keyword">for</span> (i = <span class="hljs-number">1</span>; i <= NF; i++) {
switch (<span class="hljs-variable">$i</span>) {
<span class="hljs-keyword">case</span> <span class="hljs-string">"+"</span> : <span class="hljs-keyword">case</span> <span class="hljs-string">"-"</span> :
<span class="hljs-keyword">case</span> <span class="hljs-string">"*"</span> : <span class="hljs-keyword">case</span> <span class="hljs-string">"/"</span> :
token[idx][<span class="hljs-string">"type"</span>] = <span class="hljs-string">"operator"</span>
token[idx++][<span class="hljs-string">"value"</span>] = <span class="hljs-variable">$i</span>
<span class="hljs-built_in">break</span>
<span class="hljs-keyword">case</span> <span class="hljs-string">"("</span> : <span class="hljs-keyword">case</span> <span class="hljs-string">")"</span> :
token[idx][<span class="hljs-string">"type"</span>] = <span class="hljs-string">"parenthesis"</span>
token[idx++][<span class="hljs-string">"value"</span>] = <span class="hljs-variable">$i</span>
<span class="hljs-built_in">break</span>
<span class="hljs-keyword">case</span> /[<span class="hljs-number">0</span>-<span class="hljs-number">9</span>.]/ :
<span class="hljs-keyword">while</span> ( <span class="hljs-variable">$i</span> ~ /[<span class="hljs-number">0</span>-<span class="hljs-number">9</span>.]/ ) num = num $(i++)
token[idx][<span class="hljs-string">"type"</span>] = <span class="hljs-string">"number"</span>
token[idx++][<span class="hljs-string">"value"</span>] = num
num=<span class="hljs-string">""</span>; i--
<span class="hljs-built_in">break</span>
<span class="hljs-keyword">case</span> /[ \t]/ :
<span class="hljs-built_in">break</span>
default :
error( <span class="hljs-string">"tokenize : '"</span> <span class="hljs-variable">$i</span> <span class="hljs-string">"'"</span>)
}
}
}
<span class="hljs-comment">############ stack ############</span>
<span class="hljs-keyword">function</span> push(arr, val) {
arr[ length(arr) ] = val
}
<span class="hljs-keyword">function</span> pop (arr, len, ret) {
len = length(arr)
<span class="hljs-keyword">if</span> ( len > <span class="hljs-number">1</span> ) {
ret = arr[ len - <span class="hljs-number">1</span> ]
delete arr[ len - <span class="hljs-number">1</span> ]
}
<span class="hljs-built_in">return</span> ret
}
<span class="hljs-keyword">function</span> peek (arr, len, ret) {
len = length(arr)
<span class="hljs-keyword">if</span> ( len > <span class="hljs-number">1</span> )
ret = arr[ len - <span class="hljs-number">1</span> ]
<span class="hljs-built_in">return</span> ret
}
<span class="hljs-keyword">function</span> slen(arr) {
<span class="hljs-built_in">return</span> length(arr) - <span class="hljs-number">1</span>
}
</code></pre>
<h1 id="2-">2 .</h1>
<p>이번에는 사칙연산에 더해서 <code>%</code> <code>^</code> 연산자도 추가하는 것입니다.
<code>%</code> 연산자는 우선순위가 <code>*</code> <code>/</code> 와 같기 때문에 간단히 추가할 수 있지만,
<code>^</code> 연산자의 경우는 우선순위가 <code>*</code> <code>/</code> 보다 높습니다.
또한 unary 연산자보다도 높기 때문에 다음과 같은 결과가 되어야 합니다.</p>