-
Notifications
You must be signed in to change notification settings - Fork 31
/
dc.1.md.in
1593 lines (1074 loc) · 57.5 KB
/
dc.1.md.in
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!---
SPDX-License-Identifier: BSD-2-Clause
Copyright (c) 2018-2024 Gavin D. Howard and contributors.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this
list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
-->
# Name
dc - arbitrary-precision decimal reverse-Polish notation calculator
# SYNOPSIS
{{ A H N HN }}
**dc** [**-cChiPRvVx**] [**-\-version**] [**-\-help**] [**-\-digit-clamp**] [**-\-no-digit-clamp**] [**-\-interactive**] [**-\-no-prompt**] [**-\-no-read-prompt**] [**-\-extended-register**] [**-e** *expr*] [**-\-expression**=*expr*...] [**-f** *file*...] [**-\-file**=*file*...] [*file*...] [**-I** *ibase*] [**-\-ibase**=*ibase*] [**-O** *obase*] [**-\-obase**=*obase*] [**-S** *scale*] [**-\-scale**=*scale*] [**-E** *seed*] [**-\-seed**=*seed*]
{{ end }}
{{ E EH EN EHN }}
**dc** [**-cChiPRvVx**] [**-\-version**] [**-\-help**] [**-\-digit-clamp**] [**-\-no-digit-clamp**] [**-\-interactive**] [**-\-no-prompt**] [**-\-no-read-prompt**] [**-\-extended-register**] [**-e** *expr*] [**-\-expression**=*expr*...] [**-f** *file*...] [**-\-file**=*file*...] [*file*...]
{{ end }}
# DESCRIPTION
dc(1) is an arbitrary-precision calculator. It uses a stack (reverse Polish
notation) to store numbers and results of computations. Arithmetic operations
pop arguments off of the stack and push the results.
If no files are given on the command-line, then dc(1) reads from **stdin** (see
the **STDIN** section). Otherwise, those files are processed, and dc(1) will
then exit.
If a user wants to set up a standard environment, they can use **DC_ENV_ARGS**
(see the **ENVIRONMENT VARIABLES** section). For example, if a user wants the
**scale** always set to **10**, they can set **DC_ENV_ARGS** to **-e 10k**, and
this dc(1) will always start with a **scale** of **10**.
# OPTIONS
The following are the options that dc(1) accepts.
**-C**, **-\-no-digit-clamp**
: Disables clamping of digits greater than or equal to the current **ibase**
when parsing numbers.
This means that the value added to a number from a digit is always that
digit's value multiplied by the value of ibase raised to the power of the
digit's position, which starts from 0 at the least significant digit.
If this and/or the **-c** or **-\-digit-clamp** options are given multiple
times, the last one given is used.
This option overrides the **DC_DIGIT_CLAMP** environment variable (see the
**ENVIRONMENT VARIABLES** section) and the default, which can be queried
with the **-h** or **-\-help** options.
This is a **non-portable extension**.
**-c**, **-\-digit-clamp**
: Enables clamping of digits greater than or equal to the current **ibase**
when parsing numbers.
This means that digits that the value added to a number from a digit that is
greater than or equal to the ibase is the value of ibase minus 1 all
multiplied by the value of ibase raised to the power of the digit's
position, which starts from 0 at the least significant digit.
If this and/or the **-C** or **-\-no-digit-clamp** options are given
multiple times, the last one given is used.
This option overrides the **DC_DIGIT_CLAMP** environment variable (see the
**ENVIRONMENT VARIABLES** section) and the default, which can be queried
with the **-h** or **-\-help** options.
This is a **non-portable extension**.
{{ A H N HN }}
**-E** *seed*, **-\-seed**=*seed*
: Sets the builtin variable **seed** to the value *seed* assuming that *seed*
is in base 10. It is a fatal error if *seed* is not a valid number.
If multiple instances of this option are given, the last is used.
This is a **non-portable extension**.
{{ end }}
**-e** *expr*, **-\-expression**=*expr*
: Evaluates *expr*. If multiple expressions are given, they are evaluated in
order. If files are given as well (see below), the expressions and files are
evaluated in the order given. This means that if a file is given before an
expression, the file is read in and evaluated first.
If this option is given on the command-line (i.e., not in **DC_ENV_ARGS**,
see the **ENVIRONMENT VARIABLES** section), then after processing all
expressions and files, dc(1) will exit, unless **-** (**stdin**) was given
as an argument at least once to **-f** or **-\-file**, whether on the
command-line or in **DC_ENV_ARGS**. However, if any other **-e**,
**-\-expression**, **-f**, or **-\-file** arguments are given after **-f-**
or equivalent is given, dc(1) will give a fatal error and exit.
This is a **non-portable extension**.
**-f** *file*, **-\-file**=*file*
: Reads in *file* and evaluates it, line by line, as though it were read
through **stdin**. If expressions are also given (see above), the
expressions are evaluated in the order given.
If this option is given on the command-line (i.e., not in **DC_ENV_ARGS**,
see the **ENVIRONMENT VARIABLES** section), then after processing all
expressions and files, dc(1) will exit, unless **-** (**stdin**) was given
as an argument at least once to **-f** or **-\-file**. However, if any other
**-e**, **-\-expression**, **-f**, or **-\-file** arguments are given after
**-f-** or equivalent is given, dc(1) will give a fatal error and exit.
This is a **non-portable extension**.
**-h**, **-\-help**
: Prints a usage message and exits.
**-I** *ibase*, **-\-ibase**=*ibase*
: Sets the builtin variable **ibase** to the value *ibase* assuming that
*ibase* is in base 10. It is a fatal error if *ibase* is not a valid number.
If multiple instances of this option are given, the last is used.
This is a **non-portable extension**.
**-i**, **-\-interactive**
: Forces interactive mode. (See the **INTERACTIVE MODE** section.)
This is a **non-portable extension**.
**-L**, **-\-no-line-length**
: Disables line length checking and prints numbers without backslashes and
newlines. In other words, this option sets **BC_LINE_LENGTH** to **0** (see
the **ENVIRONMENT VARIABLES** section).
This is a **non-portable extension**.
**-O** *obase*, **-\-obase**=*obase*
: Sets the builtin variable **obase** to the value *obase* assuming that
*obase* is in base 10. It is a fatal error if *obase* is not a valid number.
If multiple instances of this option are given, the last is used.
This is a **non-portable extension**.
**-P**, **-\-no-prompt**
: Disables the prompt in TTY mode. (The prompt is only enabled in TTY mode.
See the **TTY MODE** section.) This is mostly for those users that do not
want a prompt or are not used to having them in dc(1). Most of those users
would want to put this option in **DC_ENV_ARGS**.
These options override the **DC_PROMPT** and **DC_TTY_MODE** environment
variables (see the **ENVIRONMENT VARIABLES** section).
This is a **non-portable extension**.
**-R**, **-\-no-read-prompt**
: Disables the read prompt in TTY mode. (The read prompt is only enabled in
TTY mode. See the **TTY MODE** section.) This is mostly for those users that
do not want a read prompt or are not used to having them in dc(1). Most of
those users would want to put this option in **BC_ENV_ARGS** (see the
**ENVIRONMENT VARIABLES** section). This option is also useful in hash bang
lines of dc(1) scripts that prompt for user input.
This option does not disable the regular prompt because the read prompt is
only used when the **?** command is used.
These options *do* override the **DC_PROMPT** and **DC_TTY_MODE**
environment variables (see the **ENVIRONMENT VARIABLES** section), but only
for the read prompt.
This is a **non-portable extension**.
**-S** *scale*, **-\-scale**=*scale*
: Sets the builtin variable **scale** to the value *scale* assuming that
*scale* is in base 10. It is a fatal error if *scale* is not a valid number.
If multiple instances of this option are given, the last is used.
This is a **non-portable extension**.
**-v**, **-V**, **-\-version**
: Print the version information (copyright header) and exits.
**-x** **-\-extended-register**
: Enables extended register mode. See the *Extended Register Mode* subsection
of the **REGISTERS** section for more information.
This is a **non-portable extension**.
**-z**, **-\-leading-zeroes**
: Makes dc(1) print all numbers greater than **-1** and less than **1**, and
not equal to **0**, with a leading zero.
This is a **non-portable extension**.
All long options are **non-portable extensions**.
# STDIN
If no files are given on the command-line and no files or expressions are given
by the **-f**, **-\-file**, **-e**, or **-\-expression** options, then dc(1)
reads from **stdin**.
However, there is a caveat to this.
First, **stdin** is evaluated a line at a time. The only exception to this is if
a string has been finished, but not ended. This means that, except for escaped
brackets, all brackets must be balanced before dc(1) parses and executes.
# STDOUT
Any non-error output is written to **stdout**. In addition, if history (see the
**HISTORY** section) and the prompt (see the **TTY MODE** section) are enabled,
both are output to **stdout**.
**Note**: Unlike other dc(1) implementations, this dc(1) will issue a fatal
error (see the **EXIT STATUS** section) if it cannot write to **stdout**, so if
**stdout** is closed, as in **dc <file> >&-**, it will quit with an error. This
is done so that dc(1) can report problems when **stdout** is redirected to a
file.
If there are scripts that depend on the behavior of other dc(1) implementations,
it is recommended that those scripts be changed to redirect **stdout** to
**/dev/null**.
# STDERR
Any error output is written to **stderr**.
**Note**: Unlike other dc(1) implementations, this dc(1) will issue a fatal
error (see the **EXIT STATUS** section) if it cannot write to **stderr**, so if
**stderr** is closed, as in **dc <file> 2>&-**, it will quit with an error. This
is done so that dc(1) can exit with an error code when **stderr** is redirected
to a file.
If there are scripts that depend on the behavior of other dc(1) implementations,
it is recommended that those scripts be changed to redirect **stderr** to
**/dev/null**.
# SYNTAX
Each item in the input source code, either a number (see the **NUMBERS**
section) or a command (see the **COMMANDS** section), is processed and executed,
in order. Input is processed immediately when entered.
**ibase** is a register (see the **REGISTERS** section) that determines how to
interpret constant numbers. It is the "input" base, or the number base used for
interpreting input numbers. **ibase** is initially **10**. The max allowable
value for **ibase** is **16**. The min allowable value for **ibase** is **2**.
The max allowable value for **ibase** can be queried in dc(1) programs with the
**T** command.
**obase** is a register (see the **REGISTERS** section) that determines how to
output results. It is the "output" base, or the number base used for outputting
numbers. **obase** is initially **10**. The max allowable value for **obase** is
**DC_BASE_MAX** and can be queried with the **U** command. The min allowable
{{ A H N HN }}
value for **obase** is **0**. If **obase** is **0**, values are output in
scientific notation, and if **obase** is **1**, values are output in engineering
notation. Otherwise, values are output in the specified base.
Outputting in scientific and engineering notations are **non-portable
extensions**.
{{ end }}
{{ E EH EN EHN }}
value for **obase** is **2**. Values are output in the specified base.
{{ end }}
The *scale* of an expression is the number of digits in the result of the
expression right of the decimal point, and **scale** is a register (see the
**REGISTERS** section) that sets the precision of any operations (with
exceptions). **scale** is initially **0**. **scale** cannot be negative. The max
allowable value for **scale** can be queried in dc(1) programs with the **V**
command.
{{ A H N HN }}
**seed** is a register containing the current seed for the pseudo-random number
generator. If the current value of **seed** is queried and stored, then if it is
assigned to **seed** later, the pseudo-random number generator is guaranteed to
produce the same sequence of pseudo-random numbers that were generated after the
value of **seed** was first queried.
Multiple values assigned to **seed** can produce the same sequence of
pseudo-random numbers. Likewise, when a value is assigned to **seed**, it is not
guaranteed that querying **seed** immediately after will return the same value.
In addition, the value of **seed** will change after any call to the **'**
command or the **"** command that does not get receive a value of **0** or
**1**. The maximum integer returned by the **'** command can be queried with the
**W** command.
**Note**: The values returned by the pseudo-random number generator with the
**'** and **"** commands are guaranteed to **NOT** be cryptographically secure.
This is a consequence of using a seeded pseudo-random number generator. However,
they *are* guaranteed to be reproducible with identical **seed** values. This
means that the pseudo-random values from dc(1) should only be used where a
reproducible stream of pseudo-random numbers is *ESSENTIAL*. In any other case,
use a non-seeded pseudo-random number generator.
The pseudo-random number generator, **seed**, and all associated operations are
**non-portable extensions**.
{{ end }}
## Comments
Comments go from **#** until, and not including, the next newline. This is a
**non-portable extension**.
# NUMBERS
Numbers are strings made up of digits, uppercase letters up to **F**, and at
most **1** period for a radix. Numbers can have up to **DC_NUM_MAX** digits.
Uppercase letters are equal to **9** plus their position in the alphabet (i.e.,
**A** equals **10**, or **9+1**).
If a digit or letter makes no sense with the current value of **ibase** (i.e.,
they are greater than or equal to the current value of **ibase**), then the
behavior depends on the existence of the **-c**/**-\-digit-clamp** or
**-C**/**-\-no-digit-clamp** options (see the **OPTIONS** section), the
existence and setting of the **DC_DIGIT_CLAMP** environment variable (see the
**ENVIRONMENT VARIABLES** section), or the default, which can be queried with
the **-h**/**-\-help** option.
If clamping is off, then digits or letters that are greater than or equal to the
current value of **ibase** are not changed. Instead, their given value is
multiplied by the appropriate power of **ibase** and added into the number. This
means that, with an **ibase** of **3**, the number **AB** is equal to
**3\^1\*A+3\^0\*B**, which is **3** times **10** plus **11**, or **41**.
If clamping is on, then digits or letters that are greater than or equal to the
current value of **ibase** are set to the value of the highest valid digit in
**ibase** before being multiplied by the appropriate power of **ibase** and
added into the number. This means that, with an **ibase** of **3**, the number
**AB** is equal to **3\^1\*2+3\^0\*2**, which is **3** times **2** plus **2**,
or **8**.
There is one exception to clamping: single-character numbers (i.e., **A**
alone). Such numbers are never clamped and always take the value they would have
in the highest possible **ibase**. This means that **A** alone always equals
decimal **10** and **Z** alone always equals decimal **35**. This behavior is
mandated by the standard for bc(1) (see the STANDARDS section) and is meant to
provide an easy way to set the current **ibase** (with the **i** command)
regardless of the current value of **ibase**.
If clamping is on, and the clamped value of a character is needed, use a leading
zero, i.e., for **A**, use **0A**.
{{ A H N HN }}
In addition, dc(1) accepts numbers in scientific notation. These have the form
**\<number\>e\<integer\>**. The exponent (the portion after the **e**) must be
an integer. An example is **1.89237e9**, which is equal to **1892370000**.
Negative exponents are also allowed, so **4.2890e_3** is equal to **0.0042890**.
**WARNING**: Both the number and the exponent in scientific notation are
interpreted according to the current **ibase**, but the number is still
multiplied by **10\^exponent** regardless of the current **ibase**. For example,
if **ibase** is **16** and dc(1) is given the number string **FFeA**, the
resulting decimal number will be **2550000000000**, and if dc(1) is given the
number string **10e_4**, the resulting decimal number will be **0.0016**.
Accepting input as scientific notation is a **non-portable extension**.
{{ end }}
# COMMANDS
The valid commands are listed below.
## Printing
These commands are used for printing.
{{ A H N HN }}
Note that both scientific notation and engineering notation are available for
printing numbers. Scientific notation is activated by assigning **0** to
**obase** using **0o**, and engineering notation is activated by assigning **1**
to **obase** using **1o**. To deactivate them, just assign a different value to
**obase**.
Printing numbers in scientific notation and/or engineering notation is a
**non-portable extension**.
{{ end }}
**p**
: Prints the value on top of the stack, whether number or string, and prints a
newline after.
This does not alter the stack.
**n**
: Prints the value on top of the stack, whether number or string, and pops it
off of the stack.
**P**
: Pops a value off the stack.
If the value is a number, it is truncated and the absolute value of the
result is printed as though **obase** is **256** and each digit is
interpreted as an 8-bit ASCII character, making it a byte stream.
If the value is a string, it is printed without a trailing newline.
This is a **non-portable extension**.
**f**
: Prints the entire contents of the stack, in order from newest to oldest,
without altering anything.
Users should use this command when they get lost.
## Arithmetic
These are the commands used for arithmetic.
**+**
: The top two values are popped off the stack, added, and the result is pushed
onto the stack. The *scale* of the result is equal to the max *scale* of
both operands.
**-**
: The top two values are popped off the stack, subtracted, and the result is
pushed onto the stack. The *scale* of the result is equal to the max
*scale* of both operands.
**\***
: The top two values are popped off the stack, multiplied, and the result is
pushed onto the stack. If **a** is the *scale* of the first expression and
**b** is the *scale* of the second expression, the *scale* of the result
is equal to **min(a+b,max(scale,a,b))** where **min()** and **max()** return
the obvious values.
**/**
: The top two values are popped off the stack, divided, and the result is
pushed onto the stack. The *scale* of the result is equal to **scale**.
The first value popped off of the stack must be non-zero.
**%**
: The top two values are popped off the stack, remaindered, and the result is
pushed onto the stack.
Remaindering is equivalent to 1) Computing **a/b** to current **scale**, and
2) Using the result of step 1 to calculate **a-(a/b)\*b** to *scale*
**max(scale+scale(b),scale(a))**.
The first value popped off of the stack must be non-zero.
**~**
: The top two values are popped off the stack, divided and remaindered, and
the results (divided first, remainder second) are pushed onto the stack.
This is equivalent to **x y / x y %** except that **x** and **y** are only
evaluated once.
The first value popped off of the stack must be non-zero.
This is a **non-portable extension**.
**\^**
: The top two values are popped off the stack, the second is raised to the
power of the first, and the result is pushed onto the stack. The *scale* of
the result is equal to **scale**.
The first value popped off of the stack must be an integer, and if that
value is negative, the second value popped off of the stack must be
non-zero.
**v**
: The top value is popped off the stack, its square root is computed, and the
result is pushed onto the stack. The *scale* of the result is equal to
**scale**.
The value popped off of the stack must be non-negative.
**\_**
: If this command *immediately* precedes a number (i.e., no spaces or other
commands), then that number is input as a negative number.
Otherwise, the top value on the stack is popped and copied, and the copy is
negated and pushed onto the stack. This behavior without a number is a
**non-portable extension**.
**b**
: The top value is popped off the stack, and if it is zero, it is pushed back
onto the stack. Otherwise, its absolute value is pushed onto the stack.
This is a **non-portable extension**.
**|**
: The top three values are popped off the stack, a modular exponentiation is
computed, and the result is pushed onto the stack.
The first value popped is used as the reduction modulus and must be an
integer and non-zero. The second value popped is used as the exponent and
must be an integer and non-negative. The third value popped is the base and
must be an integer.
This is a **non-portable extension**.
{{ A H N HN }}
**\$**
: The top value is popped off the stack and copied, and the copy is truncated
and pushed onto the stack.
This is a **non-portable extension**.
**\@**
: The top two values are popped off the stack, and the precision of the second
is set to the value of the first, whether by truncation or extension.
The first value popped off of the stack must be an integer and non-negative.
This is a **non-portable extension**.
**H**
: The top two values are popped off the stack, and the second is shifted left
(radix shifted right) to the value of the first.
The first value popped off of the stack must be an integer and non-negative.
This is a **non-portable extension**.
**h**
: The top two values are popped off the stack, and the second is shifted right
(radix shifted left) to the value of the first.
The first value popped off of the stack must be an integer and non-negative.
This is a **non-portable extension**.
{{ end }}
**G**
: The top two values are popped off of the stack, they are compared, and a
**1** is pushed if they are equal, or **0** otherwise.
This is a **non-portable extension**.
**N**
: The top value is popped off of the stack, and if it a **0**, a **1** is
pushed; otherwise, a **0** is pushed.
This is a **non-portable extension**.
**(**
: The top two values are popped off of the stack, they are compared, and a
**1** is pushed if the first is less than the second, or **0** otherwise.
This is a **non-portable extension**.
**{**
: The top two values are popped off of the stack, they are compared, and a
**1** is pushed if the first is less than or equal to the second, or **0**
otherwise.
This is a **non-portable extension**.
**)**
: The top two values are popped off of the stack, they are compared, and a
**1** is pushed if the first is greater than the second, or **0** otherwise.
This is a **non-portable extension**.
**}**
: The top two values are popped off of the stack, they are compared, and a
**1** is pushed if the first is greater than or equal to the second, or
**0** otherwise.
This is a **non-portable extension**.
**M**
: The top two values are popped off of the stack. If they are both non-zero, a
**1** is pushed onto the stack. If either of them is zero, or both of them
are, then a **0** is pushed onto the stack.
This is like the **&&** operator in bc(1), and it is *not* a short-circuit
operator.
This is a **non-portable extension**.
**m**
: The top two values are popped off of the stack. If at least one of them is
non-zero, a **1** is pushed onto the stack. If both of them are zero, then a
**0** is pushed onto the stack.
This is like the **||** operator in bc(1), and it is *not* a short-circuit
operator.
This is a **non-portable extension**.
{{ A H N HN }}
## Pseudo-Random Number Generator
dc(1) has a built-in pseudo-random number generator. These commands query the
pseudo-random number generator. (See Parameters for more information about the
**seed** value that controls the pseudo-random number generator.)
The pseudo-random number generator is guaranteed to **NOT** be
cryptographically secure.
**'**
: Generates an integer between 0 and **DC_RAND_MAX**, inclusive (see the
**LIMITS** section).
The generated integer is made as unbiased as possible, subject to the
limitations of the pseudo-random number generator.
This is a **non-portable extension**.
**"**
: Pops a value off of the stack, which is used as an **exclusive** upper bound
on the integer that will be generated. If the bound is negative or is a
non-integer, an error is raised, and dc(1) resets (see the **RESET**
section) while **seed** remains unchanged. If the bound is larger than
**DC_RAND_MAX**, the higher bound is honored by generating several
pseudo-random integers, multiplying them by appropriate powers of
**DC_RAND_MAX+1**, and adding them together. Thus, the size of integer that
can be generated with this command is unbounded. Using this command will
change the value of **seed**, unless the operand is **0** or **1**. In that
case, **0** is pushed onto the stack, and **seed** is *not* changed.
The generated integer is made as unbiased as possible, subject to the
limitations of the pseudo-random number generator.
This is a **non-portable extension**.
{{ end }}
## Stack Control
These commands control the stack.
**c**
: Removes all items from ("clears") the stack.
**d**
: Copies the item on top of the stack ("duplicates") and pushes the copy onto
the stack.
**r**
: Swaps ("reverses") the two top items on the stack.
**R**
: Pops ("removes") the top value from the stack.
## Register Control
These commands control registers (see the **REGISTERS** section).
**s**_r_
: Pops the value off the top of the stack and stores it into register *r*.
**l**_r_
: Copies the value in register *r* and pushes it onto the stack. This does not
alter the contents of *r*.
**S**_r_
: Pops the value off the top of the (main) stack and pushes it onto the stack
of register *r*. The previous value of the register becomes inaccessible.
**L**_r_
: Pops the value off the top of the stack for register *r* and push it onto
the main stack. The previous value in the stack for register *r*, if any, is
now accessible via the **l**_r_ command.
## Parameters
{{ A H N HN }}
These commands control the values of **ibase**, **obase**, **scale**, and
**seed**. Also see the **SYNTAX** section.
{{ end }}
{{ E EH EN EHN }}
These commands control the values of **ibase**, **obase**, and **scale**. Also
see the **SYNTAX** section.
{{ end }}
**i**
: Pops the value off of the top of the stack and uses it to set **ibase**,
which must be between **2** and **16**, inclusive.
If the value on top of the stack has any *scale*, the *scale* is ignored.
**o**
: Pops the value off of the top of the stack and uses it to set **obase**,
{{ A H N HN }}
which must be between **0** and **DC_BASE_MAX**, inclusive (see the
**LIMITS** section and the **NUMBERS** section).
{{ end }}
{{ E EH EN EHN }}
which must be between **2** and **DC_BASE_MAX**, inclusive (see the
**LIMITS** section).
{{ end }}
If the value on top of the stack has any *scale*, the *scale* is ignored.
**k**
: Pops the value off of the top of the stack and uses it to set **scale**,
which must be non-negative.
If the value on top of the stack has any *scale*, the *scale* is ignored.
{{ A H N HN }}
**j**
: Pops the value off of the top of the stack and uses it to set **seed**. The
meaning of **seed** is dependent on the current pseudo-random number
generator but is guaranteed to not change except for new major versions.
The *scale* and sign of the value may be significant.
If a previously used **seed** value is used again, the pseudo-random number
generator is guaranteed to produce the same sequence of pseudo-random
numbers as it did when the **seed** value was previously used.
The exact value assigned to **seed** is not guaranteed to be returned if the
**J** command is used. However, if **seed** *does* return a different value,
both values, when assigned to **seed**, are guaranteed to produce the same
sequence of pseudo-random numbers. This means that certain values assigned
to **seed** will not produce unique sequences of pseudo-random numbers.
There is no limit to the length (number of significant decimal digits) or
*scale* of the value that can be assigned to **seed**.
This is a **non-portable extension**.
{{ end }}
**I**
: Pushes the current value of **ibase** onto the main stack.
**O**
: Pushes the current value of **obase** onto the main stack.
**K**
: Pushes the current value of **scale** onto the main stack.
{{ A H N HN }}
**J**
: Pushes the current value of **seed** onto the main stack.
This is a **non-portable extension**.
{{ end }}
**T**
: Pushes the maximum allowable value of **ibase** onto the main stack.
This is a **non-portable extension**.
**U**
: Pushes the maximum allowable value of **obase** onto the main stack.
This is a **non-portable extension**.
**V**
: Pushes the maximum allowable value of **scale** onto the main stack.
This is a **non-portable extension**.
{{ A H N HN }}
**W**
: Pushes the maximum (inclusive) integer that can be generated with the **'**
pseudo-random number generator command.
This is a **non-portable extension**.
{{ end }}
## Strings
The following commands control strings.
dc(1) can work with both numbers and strings, and registers (see the
**REGISTERS** section) can hold both strings and numbers. dc(1) always knows
whether the contents of a register are a string or a number.
While arithmetic operations have to have numbers, and will print an error if
given a string, other commands accept strings.
Strings can also be executed as macros. For example, if the string **[1pR]** is
executed as a macro, then the code **1pR** is executed, meaning that the **1**
will be printed with a newline after and then popped from the stack.
**\[**_characters_**\]**
: Makes a string containing *characters* and pushes it onto the stack.
If there are brackets (**\[** and **\]**) in the string, then they must be
balanced. Unbalanced brackets can be escaped using a backslash (**\\**)
character.
If there is a backslash character in the string, the character after it
(even another backslash) is put into the string verbatim, but the (first)
backslash is not.
**a**
: The value on top of the stack is popped.
If it is a number, it is truncated and its absolute value is taken. The
result mod **256** is calculated. If that result is **0**, push an empty
string; otherwise, push a one-character string where the character is the
result of the mod interpreted as an ASCII character.
If it is a string, then a new string is made. If the original string is
empty, the new string is empty. If it is not, then the first character of
the original string is used to create the new string as a one-character
string. The new string is then pushed onto the stack.
This is a **non-portable extension**.
**x**
: Pops a value off of the top of the stack.
If it is a number, it is pushed back onto the stack.
If it is a string, it is executed as a macro.
This behavior is the norm whenever a macro is executed, whether by this
command or by the conditional execution commands below.
**\>**_r_
: Pops two values off of the stack that must be numbers and compares them. If
the first value is greater than the second, then the contents of register
*r* are executed.
For example, **0 1>a** will execute the contents of register **a**, and
**1 0>a** will not.
If either or both of the values are not numbers, dc(1) will raise an error
and reset (see the **RESET** section).
**>**_r_**e**_s_
: Like the above, but will execute register *s* if the comparison fails.
If either or both of the values are not numbers, dc(1) will raise an error
and reset (see the **RESET** section).
This is a **non-portable extension**.
**!\>**_r_
: Pops two values off of the stack that must be numbers and compares them. If
the first value is not greater than the second (less than or equal to), then
the contents of register *r* are executed.
If either or both of the values are not numbers, dc(1) will raise an error
and reset (see the **RESET** section).
**!\>**_r_**e**_s_
: Like the above, but will execute register *s* if the comparison fails.
If either or both of the values are not numbers, dc(1) will raise an error
and reset (see the **RESET** section).
This is a **non-portable extension**.
**\<**_r_
: Pops two values off of the stack that must be numbers and compares them. If
the first value is less than the second, then the contents of register *r*
are executed.
If either or both of the values are not numbers, dc(1) will raise an error
and reset (see the **RESET** section).
**\<**_r_**e**_s_
: Like the above, but will execute register *s* if the comparison fails.
If either or both of the values are not numbers, dc(1) will raise an error
and reset (see the **RESET** section).
This is a **non-portable extension**.
**!\<**_r_
: Pops two values off of the stack that must be numbers and compares them. If
the first value is not less than the second (greater than or equal to), then
the contents of register *r* are executed.
If either or both of the values are not numbers, dc(1) will raise an error
and reset (see the **RESET** section).
**!\<**_r_**e**_s_
: Like the above, but will execute register *s* if the comparison fails.
If either or both of the values are not numbers, dc(1) will raise an error
and reset (see the **RESET** section).
This is a **non-portable extension**.
**=**_r_
: Pops two values off of the stack that must be numbers and compares them. If
the first value is equal to the second, then the contents of register *r*
are executed.
If either or both of the values are not numbers, dc(1) will raise an error
and reset (see the **RESET** section).
**=**_r_**e**_s_
: Like the above, but will execute register *s* if the comparison fails.
If either or both of the values are not numbers, dc(1) will raise an error
and reset (see the **RESET** section).
This is a **non-portable extension**.
**!=**_r_
: Pops two values off of the stack that must be numbers and compares them. If
the first value is not equal to the second, then the contents of register
*r* are executed.