任意精度の計算機 dcを使いこなせるようになりたい

man dcで確認できるマニュアルを読破してdcコマンドを完全に使いこなせるようにしたいと思います。
書き始め記事です。

dc(1)                       General Commands Manual                      dc(1)

NAME
       dc - an arbitrary precision calculator

SYNOPSIS
       dc [-V] [--version] [-h] [--help]
          [-e scriptexpression] [--expression=scriptexpression]
          [-f scriptfile] [--file=scriptfile]
          [file ...]

任意精度の計算機ってことですが、なぜdcって名前か分かりません。
使いそうなオプションは、-eと-fですね。

DESCRIPTION
       dc  is a reverse-polish desk calculator which supports unlimited preci‐
       sion arithmetic.  It also allows you to define and call  macros.   Nor‐
       mally  dc  reads  from the standard input; if any command arguments are
       given to it, they are filenames, and dc reads and executes the contents
       of  the files before reading from standard input.  All normal output is
       to standard output; all error output is to standard error.

       A reverse-polish calculator stores numbers on a stack.  Entering a num‐
       ber  pushes  it  on the stack.  Arithmetic operations pop arguments off
       the stack and push the results.

       To enter a number in dc, type the digits (using upper  case  letters  A
       through  F as "digits" when working with input bases greater than ten),
       with an optional decimal point.  Exponential notation is not supported.
       To  enter a negative number, begin the number with ``_''.  ``-'' cannot
       be used for this, as it is a binary operator for  subtraction  instead.
       To  enter  two numbers in succession, separate them with spaces or new‐
       lines.  These have no meaning as commands.

任意精度の逆ポーランド表記の電卓で、マクロも使えてしまう。いかにもすごい電卓っぽいですね。
標準入力が使えるようです。
ちょっと確認してみます。

takk~$ echo 10p | dc
10
takk~$

スタックに10を積んで、スタックの一番を、pコマンドで表示してみました。
10が表示されましたね。

足し算をしてみます。

takk~$ echo 10 20 +p | dc
30
takk~$

これは面白いですねえ。

では、man dcのマニュアルにしたがってオプションを確認していきます。

OPTIONS
       dc may be invoked with the following command-line options:

       -V

       --version
              Print out the version of dc that is being run  and  a  copyright
              notice, then exit.

バージョン表示ですね。ロングオプションの方も、ショートと同じなので省略しまs。

takk~$ dc -V
dc (GNU bc 1.07.1) 1.4.1

Copyright 1994, 1997, 1998, 2000, 2001, 2003-2006, 2008, 2010, 2012-2017 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE,
to the extent permitted by law.

次は、ヘルプです。


       -h

       --help Print a usage message briefly summarizing these command-line op‐
              tions and the bug-reporting address, then exit.

こちらもショートオプションだけ確認します。

takk~$ dc -h
Usage: dc [OPTION] [file ...]
  -e, --expression=EXPR    evaluate expression
  -f, --file=FILE          evaluate contents of file
  -h, --help               display this help and exit
  -V, --version            output version information and exit

Email bug reports to:  bug-dc@gnu.org .
takk~$

ふむふむ。忘れなさそうなオプションだけが表示されるヘルプですねえ。
次は-eオプション。スクリプト指定といえば、たいてい-eですね。

       -e script

       --expression=script
              Add the commands in script to the set  of  commands  to  be  run
              while processing the input.

スクリプトを直接指定できるんですね。

takk~$ dc -e '10 20 +p'
30
takk~$

標準入力とどちらか打ち込みが楽でしょうか。

takk~$ dc <<< '10 20 +p'
30
takk~$

ビミョーなところです。

       -f script-file

       --file=script-file
              Add the commands contained in the file script-file to the set of
              commands to be run while processing the input.

スクリプトファイルが使えるとのこと。
使ってみます。

takk~$ cat a.txt
10
20
+
p
takk~$ dc -f a.txt
30
takk~$

スクリプトファイルだと、後から計算式を見直すのに効率がよさそうです。

       If any command-line parameters remain after processing the above, these
       parameters are interpreted as the names of input files to be processed.
       A file name of - refers to the standard input stream.  The standard in‐
       put will processed if no script files or expressions are specified.

すでに使い方が分かってたので先走りましたが、ここに使い方が書いてありますね。

では各オプションです。

Printing Commands
      p      Prints  the  value on the top of the stack, without altering the
             stack.  A newline is printed after the value.

変更せずにスタックの一番上の値を表示だけしてくれます。

takk~$ dc <<< '10 20 30 ppp'
30
30
30
takk~$

pを3回実行しても、スタックを更新しないので、同じ値が3回表示されました。

      n      Prints the value on the top of the stack, popping  it  off,  and
             does not print a newline after.

次はスタックを取り出して表示するコマンドです。

takk~$ dc <<< '10 20 30 nnn'
302010takk~$

スタックの一番上から順に取り出して表示されました。改行は表示されません。

      P      Pops  off  the value on top of the stack.  If it it a string, it
             is simply printed without a trailing newline.  Otherwise it is a
             number, and the integer portion of its absolute value is printed
             out as  a  "base  (UCHAR_MAX+1)"  byte  stream.   Assuming  that
             (UCHAR_MAX+1)  is  256  (as  it  is  on most machines with 8-bit
             bytes),      the      sequence      KSK0k1/_1Ss      [ls*]Sxd0>x
             [256~Ssd0<x]dsxxsx[q]Sq[Lsd0>qaPlxx]  dsxxsx0sqLqsxLxLK+k  could
             also accomplish this function.  (Much of the complexity  of  the
             above  native-dc  code  is due to the ~ computing the characters
             backwards, and the desire to ensure that all registers  wind  up
             back in their original states.)

文字列は、文字列は[]で囲みます。Pで文字列を表示すると改行されません。
takk~$ dc <<< '[HELLO] P'
HELLOtakk~$
      f      Prints  the  entire  contents of the stack without altering any‐
             thing.  This is a good command to use if you are lost or want to
             figure out what the effect of some command has been.

全スタックを表示するコマンドですね。

takk~$ dc <<< '10 20 30 f'
30
20
10
takk~$
Arithmetic
      +      Pops two values off the stack, adds them, and pushes the result.
             The precision of the result is determined only by the values  of
             the arguments, and is enough to be exact.

一番上と二つ目のスタックを加算してくれるコマンドです。

takk~$ dc <<< '10 20 30 +f'
50
10
takk~$

加算された20と30が消えて、計算結果である50がスタックの一番上に積まれました。

次は減算です。

      -      Pops  two values, subtracts the first one popped from the second
             one popped, and pushes the result.

5 – 3を計算してみます。

takk~$ dc <<< '5 3 -p'
2
takk~$

次は乗算。

      *      Pops two values, multiplies them, and pushes  the  result.   The
             number  of  fraction digits in the result depends on the current
             precision value and the number of fraction digits in the two ar‐
             guments.

11 * 20です。

takk~$ dc <<< '11 20 *p'
220
takk~$

除算です。

      /      Pops  two  values,  divides the second one popped from the first
             one popped, and pushes the result.  The number of fraction  dig‐
             its is specified by the precision value.

30 ÷ 2です。

takk~$ dc <<< '30 2 /p'
15
takk~$

次は、余を求めます。

      %      Pops two values, computes the remainder of the division that the
             / command would do, and pushes that.  The value computed is  the
             same as that computed by the sequence Sd dld/ Ld*- .

5÷3の余りです。

takk~$ dc <<< '5 3 %p'
2
takk~$

商と余を同時に求めます。

      ~      Pops  two  values,  divides the second one popped from the first
             one popped.  The quotient is pushed first, and the remainder  is
             pushed next.  The number of fraction digits used in the division
             is specified by the precision value.  (The sequence  SdSn  lnld/
             LnLd% could also accomplish this function, with slightly differ‐
             ent error checking.)

20 ÷ 3を実行してみます。

takk~$ dc <<< '20 3 ~f'
2
6
takk~$

一番上のスタックが余、二つ目に商が格納されます。
次は指数計算です。

      ^      Pops two values and exponentiates, using the first value  popped
             as the exponent and the second popped as the base.  The fraction
             part of the exponent is ignored.  The precision value  specifies
             the number of fraction digits in the result.

一番上のスタックが指数で、二つ目が底になります。
2の8乗を計算してみます。

takk~$ dc <<<'2 8 ^p'
256
takk~$
      |      Pops  three  values  and computes a modular exponentiation.  The
             first value popped is used as the reduction modulus; this  value
             must be a non-zero number, and should be an integer.  The second
             popped is used as the exponent; this value must be  a  non-nega‐
             tive  number,  and  any fractional part of this exponent will be
             ignored.  The third value popped is the base which gets exponen‐
             tiated,  which should be an integer.  For small integers this is
             like the sequence Sm^Lm%, but, unlike ^, this command will  work
             with arbitrarily large exponents.

冪剰余(べきじょうよ)ですね。
一番上が法、二番目が冪指数、三番目が底です。
13の2乗を5で割った余を求めてみます。

takk~$ dc <<<'13 2 5 |p'
4
takk~$
     v       Pops  one value, computes its square root, and pushes that.  The
             maximum of the precision value and the precision of the argument
             is  used  to  determine the number of fraction digits in the re‐
             sult.

平方根です。9と25と36それぞれの平方根を求めます。

takk~$ dc <<<'9vp 25vp 36vp'
3
5
6
takk~$

結果が無理数となる場合はどうでしょうか。
2の平方根を求めてみます。

takk~$ dc <<<'2vp'
1
takk~$

1.4142…とはならずに、1が返りました。

             Most arithmetic operations are affected  by  the  ``precision  value'',
             which  you  can set with the k command.  The default precision value is
             zero, which means that all arithmetic except for addition and  subtrac‐
             tion produces integer results.

kコマンドで精度を変えられるが、初期精度は整数になっているようです(k=0)。
さきほどの2の平方根の結果も、精度を変更すれば小数点以下が返ってくるということですね。

takk~$ dc <<<'5k 2vp'
1.41421
takk~$

次はスタック制御です。

Stack Control
       c      Clears the stack, rendering it empty.

       d      Duplicates  the  value  on the top of the stack, pushing another
              copy of it.  Thus, ``4d*p'' computes 4 squared and prints it.

       r      Reverses the order of (swaps) the top two values on  the  stack.
              (This can also be accomplished with the sequence SaSbLaLb.)

       R      Pops  the  top-of-stack as an integer n.  Cyclically rotates the
              top n items on the updated stack.  If n is  positive,  then  the
              rotation direction will make the topmost element the second-from
              top; if n is negative, then the rotation will make  the  topmost
              element  the  n-th  element from the top.  If the stack depth is
              less than n, then the entire stack is rotated (in the  appropri‐
              ate direction), without any error being reported.
Registers
       dc provides at least 256 memory registers, each named by a single char‐
       acter.  You can store a number or a string in a register  and  retrieve
       it later.

       sr     Pop  the value off the top of the stack and store it into regis‐
              ter r.

       lr     Copy the value in register r and push it onto  the  stack.   The
              value  0  is  retrieved  if the register is uninitialized.  This
              does not alter the contents of r.

       Each register also contains its own stack.  The current register  value
       is the top of the register's stack.

       Sr     Pop  the  value off the top of the (main) stack and push it onto
              the stack of register r.  The previous value of the register be‐
              comes inaccessible.

       Lr     Pop the value off the top of register r's stack and push it onto
              the main stack.  The previous value in register  r's  stack,  if
              any, is now accessible via the lr command.
Parameters
       dc  has three parameters that control its operation: the precision, the
       input radix, and the output radix.  The precision specifies the  number
       of fraction digits to keep in the result of most arithmetic operations.
       The input radix controls the interpretation of numbers  typed  in;  all
       numbers typed in use this radix.  The output radix is used for printing
       numbers.

       The input and output radices are separate parameters; you can make them
       unequal, which can be useful or confusing.  The input radix must be be‐
       tween 2 and 16 inclusive.  The output radix must be at  least  2.   The
       precision must be zero or greater.  The precision is always measured in
       decimal digits, regardless of the current input or output radix.

       i      Pops the value off the top of the stack and uses it to  set  the
              input radix.

       o      Pops  the  value off the top of the stack and uses it to set the
              output radix.

       k      Pops the value off the top of the stack and uses it to  set  the
              precision.

       I      Pushes the current input radix on the stack.

       O      Pushes the current output radix on the stack.

       K      Pushes the current precision on the stack.
Strings
        dc  has  a limited ability to operate on strings as well as on numbers;
        the only things you can do with strings are print them and execute them
        as macros (which means that the contents of the string are processed as
        dc commands).  All registers and the stack can hold strings, and dc al‐
        ways knows whether any given object is a string or a number.  Some com‐
        mands such as arithmetic operations demand  numbers  as  arguments  and
        print errors if given strings.  Other commands can accept either a num‐
        ber or a string; for example, the  p  command  can  accept  either  and
        prints the object according to its type.

        [characters]
               Makes a string containing characters (contained between balanced
               [ and ] characters), and pushes it on the stack.   For  example,
               [foo]P prints the characters foo (with no newline).

        a      The  top-of-stack  is popped.  If it was a number, then the low-
               order byte of this number is converted into a string and  pushed
               onto  the  stack.   Otherwise the top-of-stack was a string, and
               the first character of that string is pushed back.

        x      Pops a value off the stack and executes it as a macro.  Normally
               it  should  be  a string; if it is a number, it is simply pushed
               back onto the stack.  For example, [1p]x executes the  macro  1p
               which pushes 1 on the stack and prints 1 on a separate line.

        Macros  are  most  often  stored in registers; [1p]sa stores a macro to
        print 1 into register a, and lax invokes this macro.

        >r     Pops two values off the stack and compares  them  assuming  they
               are  numbers, executing the contents of register r as a macro if
               the original top-of-stack is greater.  Thus, 1 2>a  will  invoke
               register a's contents and 2 1>a will not.

        !>r    Similar  but  invokes  the macro if the original top-of-stack is
               not greater than (less than or equal to) what was the second-to-
               top.

        <r     Similar  but  invokes  the macro if the original top-of-stack is
               less.

       !<r    Similar but invokes the macro if the  original  top-of-stack  is
              not less than (greater than or equal to) what was the second-to-
              top.

       =r     Similar but invokes the macro if  the  two  numbers  popped  are
              equal.

       !=r    Similar  but invokes the macro if the two numbers popped are not
              equal.

       ?      Reads a line from the terminal and executes  it.   This  command
              allows a macro to request input from the user.

       q      exits from a macro and also from the macro which invoked it.  If
              called from the top level, or from a macro which was called  di‐
              rectly from the top level, the q command will cause dc to exit.

       Q      Pops  a  value off the stack and uses it as a count of levels of
              macro execution to be exited.  Thus, 3Q exits three levels.  The
              Q command will never cause dc to exit.
Status Inquiry
       Z      Pops  a  value  off  the stack, calculates the number of decimal
              digits it has (or number of characters, if it is a  string)  and
              pushes  that  number.  The digit count for a number does not in‐
              clude any leading zeros, even if those appear to  the  right  of
              the radix point.

       X      Pops  a  value  off the stack, calculates the number of fraction
              digits it has, and pushes that number.  For a string, the  value
              pushed is 0.

       z      Pushes  the  current  stack  depth: the number of objects on the
              stack before the execution of the z command.
Miscellaneous
       !      Will run the rest of the line as a system  command.   Note  that
              parsing  of  the  !<, !=, and !> commands take precedence, so if
              you want to run a command starting with <, =, or > you will need
              to add a space after the !.

       #      Will interpret the rest of the line as a comment.

       :r     Will  pop  the top two values off of the stack.  The old second-
              to-top value will be stored in the array r, indexed by  the  old
              top-of-stack value.

       ;r     Pops  the top-of-stack and uses it as an index into the array r.
              The selected value is then pushed onto the stack.

       Note that each stacked instance of a register has its own array associ‐
       ated with it.  Thus 1 0:a 0Sa 2 0:a La 0;ap will print 1, because the 2
       was stored in an instance of 0:a that was later popped.
       FILES
              ~/.dcrc        The commands in this file will be executed  when  dc  is
                             first run.

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