1<!--- 2 3SPDX-License-Identifier: BSD-2-Clause 4 5Copyright (c) 2018-2023 Gavin D. Howard and contributors. 6 7Redistribution and use in source and binary forms, with or without 8modification, are permitted provided that the following conditions are met: 9 10* Redistributions of source code must retain the above copyright notice, this 11 list of conditions and the following disclaimer. 12 13* Redistributions in binary form must reproduce the above copyright notice, 14 this list of conditions and the following disclaimer in the documentation 15 and/or other materials provided with the distribution. 16 17THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 18AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE 21LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 22CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 23SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 24INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 25CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 26ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 27POSSIBILITY OF SUCH DAMAGE. 28 29--> 30 31# NAME 32 33bc - arbitrary-precision decimal arithmetic language and calculator 34 35# SYNOPSIS 36 37**bc** [**-cCghilPqRsvVw**] [**-\-digit-clamp**] [**-\-no-digit-clamp**] [**-\-global-stacks**] [**-\-help**] [**-\-interactive**] [**-\-mathlib**] [**-\-no-prompt**] [**-\-no-read-prompt**] [**-\-quiet**] [**-\-standard**] [**-\-warn**] [**-\-version**] [**-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*] 38 39# DESCRIPTION 40 41bc(1) is an interactive processor for a language first standardized in 1991 by 42POSIX. (See the **STANDARDS** section.) The language provides unlimited 43precision decimal arithmetic and is somewhat C-like, but there are differences. 44Such differences will be noted in this document. 45 46After parsing and handling options, this bc(1) reads any files given on the 47command line and executes them before reading from **stdin**. 48 49This bc(1) is a drop-in replacement for *any* bc(1), including (and 50especially) the GNU bc(1). It also has many extensions and extra features beyond 51other implementations. 52 53**Note**: If running this bc(1) on *any* script meant for another bc(1) gives a 54parse error, it is probably because a word this bc(1) reserves as a keyword is 55used as the name of a function, variable, or array. To fix that, use the 56command-line option **-r** *keyword*, where *keyword* is the keyword that is 57used as a name in the script. For more information, see the **OPTIONS** section. 58 59If parsing scripts meant for other bc(1) implementations still does not work, 60that is a bug and should be reported. See the **BUGS** section. 61 62# OPTIONS 63 64The following are the options that bc(1) accepts. 65 66**-C**, **-\-no-digit-clamp** 67 68: Disables clamping of digits greater than or equal to the current **ibase** 69 when parsing numbers. 70 71 This means that the value added to a number from a digit is always that 72 digit's value multiplied by the value of ibase raised to the power of the 73 digit's position, which starts from 0 at the least significant digit. 74 75 If this and/or the **-c** or **-\-digit-clamp** options are given multiple 76 times, the last one given is used. 77 78 This option overrides the **BC_DIGIT_CLAMP** environment variable (see the 79 **ENVIRONMENT VARIABLES** section) and the default, which can be queried 80 with the **-h** or **-\-help** options. 81 82 This is a **non-portable extension**. 83 84**-c**, **-\-digit-clamp** 85 86: Enables clamping of digits greater than or equal to the current **ibase** 87 when parsing numbers. 88 89 This means that digits that the value added to a number from a digit that is 90 greater than or equal to the ibase is the value of ibase minus 1 all 91 multiplied by the value of ibase raised to the power of the digit's 92 position, which starts from 0 at the least significant digit. 93 94 If this and/or the **-C** or **-\-no-digit-clamp** options are given 95 multiple times, the last one given is used. 96 97 This option overrides the **BC_DIGIT_CLAMP** environment variable (see the 98 **ENVIRONMENT VARIABLES** section) and the default, which can be queried 99 with the **-h** or **-\-help** options. 100 101 This is a **non-portable extension**. 102 103**-E** *seed*, **-\-seed**=*seed* 104 105: Sets the builtin variable **seed** to the value *seed* assuming that *seed* 106 is in base 10. It is a fatal error if *seed* is not a valid number. 107 108 If multiple instances of this option are given, the last is used. 109 110 This is a **non-portable extension**. 111 112**-e** *expr*, **-\-expression**=*expr* 113 114: Evaluates *expr*. If multiple expressions are given, they are evaluated in 115 order. If files are given as well (see the **-f** and **-\-file** options), 116 the expressions and files are evaluated in the order given. This means that 117 if a file is given before an expression, the file is read in and evaluated 118 first. 119 120 If this option is given on the command-line (i.e., not in **BC_ENV_ARGS**, 121 see the **ENVIRONMENT VARIABLES** section), then after processing all 122 expressions and files, bc(1) will exit, unless **-** (**stdin**) was given 123 as an argument at least once to **-f** or **-\-file**, whether on the 124 command-line or in **BC_ENV_ARGS**. However, if any other **-e**, 125 **-\-expression**, **-f**, or **-\-file** arguments are given after **-f-** 126 or equivalent is given, bc(1) will give a fatal error and exit. 127 128 This is a **non-portable extension**. 129 130**-f** *file*, **-\-file**=*file* 131 132: Reads in *file* and evaluates it, line by line, as though it were read 133 through **stdin**. If expressions are also given (see the **-e** and 134 **-\-expression** options), the expressions are evaluated in the order 135 given. 136 137 If this option is given on the command-line (i.e., not in **BC_ENV_ARGS**, 138 see the **ENVIRONMENT VARIABLES** section), then after processing all 139 expressions and files, bc(1) will exit, unless **-** (**stdin**) was given 140 as an argument at least once to **-f** or **-\-file**. However, if any other 141 **-e**, **-\-expression**, **-f**, or **-\-file** arguments are given after 142 **-f-** or equivalent is given, bc(1) will give a fatal error and exit. 143 144 This is a **non-portable extension**. 145 146**-g**, **-\-global-stacks** 147 148: Turns the globals **ibase**, **obase**, **scale**, and **seed** into stacks. 149 150 This has the effect that a copy of the current value of all four are pushed 151 onto a stack for every function call, as well as popped when every function 152 returns. This means that functions can assign to any and all of those 153 globals without worrying that the change will affect other functions. 154 Thus, a hypothetical function named **output(x,b)** that simply printed 155 **x** in base **b** could be written like this: 156 157 define void output(x, b) { 158 obase=b 159 x 160 } 161 162 instead of like this: 163 164 define void output(x, b) { 165 auto c 166 c=obase 167 obase=b 168 x 169 obase=c 170 } 171 172 This makes writing functions much easier. 173 174 (**Note**: the function **output(x,b)** exists in the extended math library. 175 See the **LIBRARY** section.) 176 177 However, since using this flag means that functions cannot set **ibase**, 178 **obase**, **scale**, or **seed** globally, functions that are made to do so 179 cannot work anymore. There are two possible use cases for that, and each has 180 a solution. 181 182 First, if a function is called on startup to turn bc(1) into a number 183 converter, it is possible to replace that capability with various shell 184 aliases. Examples: 185 186 alias d2o="bc -e ibase=A -e obase=8" 187 alias h2b="bc -e ibase=G -e obase=2" 188 189 Second, if the purpose of a function is to set **ibase**, **obase**, 190 **scale**, or **seed** globally for any other purpose, it could be split 191 into one to four functions (based on how many globals it sets) and each of 192 those functions could return the desired value for a global. 193 194 For functions that set **seed**, the value assigned to **seed** is not 195 propagated to parent functions. This means that the sequence of 196 pseudo-random numbers that they see will not be the same sequence of 197 pseudo-random numbers that any parent sees. This is only the case once 198 **seed** has been set. 199 200 If a function desires to not affect the sequence of pseudo-random numbers 201 of its parents, but wants to use the same **seed**, it can use the following 202 line: 203 204 seed = seed 205 206 If the behavior of this option is desired for every run of bc(1), then users 207 could make sure to define **BC_ENV_ARGS** and include this option (see the 208 **ENVIRONMENT VARIABLES** section for more details). 209 210 If **-s**, **-w**, or any equivalents are used, this option is ignored. 211 212 This is a **non-portable extension**. 213 214**-h**, **-\-help** 215 216: Prints a usage message and exits. 217 218**-I** *ibase*, **-\-ibase**=*ibase* 219 220: Sets the builtin variable **ibase** to the value *ibase* assuming that 221 *ibase* is in base 10. It is a fatal error if *ibase* is not a valid number. 222 223 If multiple instances of this option are given, the last is used. 224 225 This is a **non-portable extension**. 226 227**-i**, **-\-interactive** 228 229: Forces interactive mode. (See the **INTERACTIVE MODE** section.) 230 231 This is a **non-portable extension**. 232 233**-L**, **-\-no-line-length** 234 235: Disables line length checking and prints numbers without backslashes and 236 newlines. In other words, this option sets **BC_LINE_LENGTH** to **0** (see 237 the **ENVIRONMENT VARIABLES** section). 238 239 This is a **non-portable extension**. 240 241**-l**, **-\-mathlib** 242 243: Sets **scale** (see the **SYNTAX** section) to **20** and loads the included 244 math library and the extended math library before running any code, 245 including any expressions or files specified on the command line. 246 247 To learn what is in the libraries, see the **LIBRARY** section. 248 249**-O** *obase*, **-\-obase**=*obase* 250 251: Sets the builtin variable **obase** to the value *obase* assuming that 252 *obase* is in base 10. It is a fatal error if *obase* is not a valid number. 253 254 If multiple instances of this option are given, the last is used. 255 256 This is a **non-portable extension**. 257 258**-P**, **-\-no-prompt** 259 260: Disables the prompt in TTY mode. (The prompt is only enabled in TTY mode. 261 See the **TTY MODE** section.) This is mostly for those users that do not 262 want a prompt or are not used to having them in bc(1). Most of those users 263 would want to put this option in **BC_ENV_ARGS** (see the 264 **ENVIRONMENT VARIABLES** section). 265 266 These options override the **BC_PROMPT** and **BC_TTY_MODE** environment 267 variables (see the **ENVIRONMENT VARIABLES** section). 268 269 This is a **non-portable extension**. 270 271**-q**, **-\-quiet** 272 273: This option is for compatibility with the GNU bc(1) 274 (https://www.gnu.org/software/bc/); it is a no-op. Without this option, GNU 275 bc(1) prints a copyright header. This bc(1) only prints the copyright header 276 if one or more of the **-v**, **-V**, or **-\-version** options are given 277 unless the **BC_BANNER** environment variable is set and contains a non-zero 278 integer or if this bc(1) was built with the header displayed by default. If 279 *any* of that is the case, then this option *does* prevent bc(1) from 280 printing the header. 281 282 This is a **non-portable extension**. 283 284**-R**, **-\-no-read-prompt** 285 286: Disables the read prompt in TTY mode. (The read prompt is only enabled in 287 TTY mode. See the **TTY MODE** section.) This is mostly for those users that 288 do not want a read prompt or are not used to having them in bc(1). Most of 289 those users would want to put this option in **BC_ENV_ARGS** (see the 290 **ENVIRONMENT VARIABLES** section). This option is also useful in hash bang 291 lines of bc(1) scripts that prompt for user input. 292 293 This option does not disable the regular prompt because the read prompt is 294 only used when the **read()** built-in function is called. 295 296 These options *do* override the **BC_PROMPT** and **BC_TTY_MODE** 297 environment variables (see the **ENVIRONMENT VARIABLES** section), but only 298 for the read prompt. 299 300 This is a **non-portable extension**. 301 302**-r** *keyword*, **-\-redefine**=*keyword* 303 304: Redefines *keyword* in order to allow it to be used as a function, variable, 305 or array name. This is useful when this bc(1) gives parse errors when 306 parsing scripts meant for other bc(1) implementations. 307 308 The keywords this bc(1) allows to be redefined are: 309 310 * **abs** 311 * **asciify** 312 * **continue** 313 * **divmod** 314 * **else** 315 * **halt** 316 * **irand** 317 * **last** 318 * **limits** 319 * **maxibase** 320 * **maxobase** 321 * **maxrand** 322 * **maxscale** 323 * **modexp** 324 * **print** 325 * **rand** 326 * **read** 327 * **seed** 328 * **stream** 329 330 If any of those keywords are used as a function, variable, or array name in 331 a script, use this option with the keyword as the argument. If multiple are 332 used, use this option for all of them; it can be used multiple times. 333 334 Keywords are *not* redefined when parsing the builtin math library (see the 335 **LIBRARY** section). 336 337 It is a fatal error to redefine keywords mandated by the POSIX standard (see 338 the **STANDARDS** section). It is a fatal error to attempt to redefine words 339 that this bc(1) does not reserve as keywords. 340 341**-S** *scale*, **-\-scale**=*scale* 342 343: Sets the builtin variable **scale** to the value *scale* assuming that 344 *scale* is in base 10. It is a fatal error if *scale* is not a valid number. 345 346 If multiple instances of this option are given, the last is used. 347 348 This is a **non-portable extension**. 349 350**-s**, **-\-standard** 351 352: Process exactly the language defined by the standard (see the **STANDARDS** 353 section) and error if any extensions are used. 354 355 This is a **non-portable extension**. 356 357**-v**, **-V**, **-\-version** 358 359: Print the version information (copyright header) and exits. 360 361 This is a **non-portable extension**. 362 363**-w**, **-\-warn** 364 365: Like **-s** and **-\-standard**, except that warnings (and not errors) are 366 printed for non-standard extensions and execution continues normally. 367 368 This is a **non-portable extension**. 369 370**-z**, **-\-leading-zeroes** 371 372: Makes bc(1) print all numbers greater than **-1** and less than **1**, and 373 not equal to **0**, with a leading zero. 374 375 This can be set for individual numbers with the **plz(x)**, **plznl(x)**, 376 **pnlz(x)**, and **pnlznl(x)** functions in the extended math library (see 377 the **LIBRARY** section). 378 379 This is a **non-portable extension**. 380 381All long options are **non-portable extensions**. 382 383# STDIN 384 385If no files or expressions are given by the **-f**, **-\-file**, **-e**, or 386**-\-expression** options, then bc(1) reads from **stdin**. 387 388However, there are a few caveats to this. 389 390First, **stdin** is evaluated a line at a time. The only exception to this is if 391the parse cannot complete. That means that starting a string without ending it 392or starting a function, **if** statement, or loop without ending it will also 393cause bc(1) to not execute. 394 395Second, after an **if** statement, bc(1) doesn't know if an **else** statement 396will follow, so it will not execute until it knows there will not be an **else** 397statement. 398 399# STDOUT 400 401Any non-error output is written to **stdout**. In addition, if history (see the 402**HISTORY** section) and the prompt (see the **TTY MODE** section) are enabled, 403both are output to **stdout**. 404 405**Note**: Unlike other bc(1) implementations, this bc(1) will issue a fatal 406error (see the **EXIT STATUS** section) if it cannot write to **stdout**, so if 407**stdout** is closed, as in **bc <file> >&-**, it will quit with an error. This 408is done so that bc(1) can report problems when **stdout** is redirected to a 409file. 410 411If there are scripts that depend on the behavior of other bc(1) implementations, 412it is recommended that those scripts be changed to redirect **stdout** to 413**/dev/null**. 414 415# STDERR 416 417Any error output is written to **stderr**. 418 419**Note**: Unlike other bc(1) implementations, this bc(1) will issue a fatal 420error (see the **EXIT STATUS** section) if it cannot write to **stderr**, so if 421**stderr** is closed, as in **bc <file> 2>&-**, it will quit with an error. This 422is done so that bc(1) can exit with an error code when **stderr** is redirected 423to a file. 424 425If there are scripts that depend on the behavior of other bc(1) implementations, 426it is recommended that those scripts be changed to redirect **stderr** to 427**/dev/null**. 428 429# SYNTAX 430 431The syntax for bc(1) programs is mostly C-like, with some differences. This 432bc(1) follows the POSIX standard (see the **STANDARDS** section), which is a 433much more thorough resource for the language this bc(1) accepts. This section is 434meant to be a summary and a listing of all the extensions to the standard. 435 436In the sections below, **E** means expression, **S** means statement, and **I** 437means identifier. 438 439Identifiers (**I**) start with a lowercase letter and can be followed by any 440number (up to **BC_NAME_MAX-1**) of lowercase letters (**a-z**), digits 441(**0-9**), and underscores (**\_**). The regex is **\[a-z\]\[a-z0-9\_\]\***. 442Identifiers with more than one character (letter) are a 443**non-portable extension**. 444 445**ibase** is a global variable determining how to interpret constant numbers. It 446is the "input" base, or the number base used for interpreting input numbers. 447**ibase** is initially **10**. If the **-s** (**-\-standard**) and **-w** 448(**-\-warn**) flags were not given on the command line, the max allowable value 449for **ibase** is **36**. Otherwise, it is **16**. The min allowable value for 450**ibase** is **2**. The max allowable value for **ibase** can be queried in 451bc(1) programs with the **maxibase()** built-in function. 452 453**obase** is a global variable determining how to output results. It is the 454"output" base, or the number base used for outputting numbers. **obase** is 455initially **10**. The max allowable value for **obase** is **BC_BASE_MAX** and 456can be queried in bc(1) programs with the **maxobase()** built-in function. The 457min allowable value for **obase** is **0**. If **obase** is **0**, values are 458output in scientific notation, and if **obase** is **1**, values are output in 459engineering notation. Otherwise, values are output in the specified base. 460 461Outputting in scientific and engineering notations are **non-portable 462extensions**. 463 464The *scale* of an expression is the number of digits in the result of the 465expression right of the decimal point, and **scale** is a global variable that 466sets the precision of any operations, with exceptions. **scale** is initially 467**0**. **scale** cannot be negative. The max allowable value for **scale** is 468**BC_SCALE_MAX** and can be queried in bc(1) programs with the **maxscale()** 469built-in function. 470 471bc(1) has both *global* variables and *local* variables. All *local* 472variables are local to the function; they are parameters or are introduced in 473the **auto** list of a function (see the **FUNCTIONS** section). If a variable 474is accessed which is not a parameter or in the **auto** list, it is assumed to 475be *global*. If a parent function has a *local* variable version of a variable 476that a child function considers *global*, the value of that *global* variable in 477the child function is the value of the variable in the parent function, not the 478value of the actual *global* variable. 479 480All of the above applies to arrays as well. 481 482The value of a statement that is an expression (i.e., any of the named 483expressions or operands) is printed unless the lowest precedence operator is an 484assignment operator *and* the expression is notsurrounded by parentheses. 485 486The value that is printed is also assigned to the special variable **last**. A 487single dot (**.**) may also be used as a synonym for **last**. These are 488**non-portable extensions**. 489 490Either semicolons or newlines may separate statements. 491 492## Comments 493 494There are two kinds of comments: 495 4961. Block comments are enclosed in **/\*** and **\*/**. 4972. Line comments go from **#** until, and not including, the next newline. This 498 is a **non-portable extension**. 499 500## Named Expressions 501 502The following are named expressions in bc(1): 503 5041. Variables: **I** 5052. Array Elements: **I[E]** 5063. **ibase** 5074. **obase** 5085. **scale** 5096. **seed** 5107. **last** or a single dot (**.**) 511 512Numbers 6 and 7 are **non-portable extensions**. 513 514The meaning of **seed** is dependent on the current pseudo-random number 515generator but is guaranteed to not change except for new major versions. 516 517The *scale* and sign of the value may be significant. 518 519If a previously used **seed** value is assigned to **seed** and used again, the 520pseudo-random number generator is guaranteed to produce the same sequence of 521pseudo-random numbers as it did when the **seed** value was previously used. 522 523The exact value assigned to **seed** is not guaranteed to be returned if 524**seed** is queried again immediately. However, if **seed** *does* return a 525different value, both values, when assigned to **seed**, are guaranteed to 526produce the same sequence of pseudo-random numbers. This means that certain 527values assigned to **seed** will *not* produce unique sequences of pseudo-random 528numbers. The value of **seed** will change after any use of the **rand()** and 529**irand(E)** operands (see the *Operands* subsection below), except if the 530parameter passed to **irand(E)** is **0**, **1**, or negative. 531 532There is no limit to the length (number of significant decimal digits) or 533*scale* of the value that can be assigned to **seed**. 534 535Variables and arrays do not interfere; users can have arrays named the same as 536variables. This also applies to functions (see the **FUNCTIONS** section), so a 537user can have a variable, array, and function that all have the same name, and 538they will not shadow each other, whether inside of functions or not. 539 540Named expressions are required as the operand of **increment**/**decrement** 541operators and as the left side of **assignment** operators (see the *Operators* 542subsection). 543 544## Operands 545 546The following are valid operands in bc(1): 547 5481. Numbers (see the *Numbers* subsection below). 5492. Array indices (**I[E]**). 5503. **(E)**: The value of **E** (used to change precedence). 5514. **sqrt(E)**: The square root of **E**. **E** must be non-negative. 5525. **length(E)**: The number of significant decimal digits in **E**. Returns 553 **1** for **0** with no decimal places. If given a string, the length of the 554 string is returned. Passing a string to **length(E)** is a **non-portable 555 extension**. 5566. **length(I[])**: The number of elements in the array **I**. This is a 557 **non-portable extension**. 5587. **scale(E)**: The *scale* of **E**. 5598. **abs(E)**: The absolute value of **E**. This is a **non-portable 560 extension**. 5619. **is_number(E)**: **1** if the given argument is a number, **0** if it is a 562 string. This is a **non-portable extension**. 56310. **is_string(E)**: **1** if the given argument is a string, **0** if it is a 564 number. This is a **non-portable extension**. 56511. **modexp(E, E, E)**: Modular exponentiation, where the first expression is 566 the base, the second is the exponent, and the third is the modulus. All 567 three values must be integers. The second argument must be non-negative. The 568 third argument must be non-zero. This is a **non-portable extension**. 56911. **divmod(E, E, I[])**: Division and modulus in one operation. This is for 570 optimization. The first expression is the dividend, and the second is the 571 divisor, which must be non-zero. The return value is the quotient, and the 572 modulus is stored in index **0** of the provided array (the last argument). 573 This is a **non-portable extension**. 57412. **asciify(E)**: If **E** is a string, returns a string that is the first 575 letter of its argument. If it is a number, calculates the number mod **256** 576 and returns that number as a one-character string. This is a **non-portable 577 extension**. 57813. **asciify(I[])**: A string that is made up of the characters that would 579 result from running **asciify(E)** on each element of the array identified 580 by the argument. This allows creating multi-character strings and storing 581 them. This is a **non-portable extension**. 58214. **I()**, **I(E)**, **I(E, E)**, and so on, where **I** is an identifier for 583 a non-**void** function (see the *Void Functions* subsection of the 584 **FUNCTIONS** section). The **E** argument(s) may also be arrays of the form 585 **I[]**, which will automatically be turned into array references (see the 586 *Array References* subsection of the **FUNCTIONS** section) if the 587 corresponding parameter in the function definition is an array reference. 58815. **read()**: Reads a line from **stdin** and uses that as an expression. The 589 result of that expression is the result of the **read()** operand. This is a 590 **non-portable extension**. 59116. **maxibase()**: The max allowable **ibase**. This is a **non-portable 592 extension**. 59317. **maxobase()**: The max allowable **obase**. This is a **non-portable 594 extension**. 59518. **maxscale()**: The max allowable **scale**. This is a **non-portable 596 extension**. 59719. **line_length()**: The line length set with **BC_LINE_LENGTH** (see the 598 **ENVIRONMENT VARIABLES** section). This is a **non-portable extension**. 59920. **global_stacks()**: **0** if global stacks are not enabled with the **-g** 600 or **-\-global-stacks** options, non-zero otherwise. See the **OPTIONS** 601 section. This is a **non-portable extension**. 60221. **leading_zero()**: **0** if leading zeroes are not enabled with the **-z** 603 or **--leading-zeroes** options, non-zero otherwise. See the **OPTIONS** 604 section. This is a **non-portable extension**. 60522. **rand()**: A pseudo-random integer between **0** (inclusive) and 606 **BC_RAND_MAX** (inclusive). Using this operand will change the value of 607 **seed**. This is a **non-portable extension**. 60823. **irand(E)**: A pseudo-random integer between **0** (inclusive) and the 609 value of **E** (exclusive). If **E** is negative or is a non-integer 610 (**E**'s *scale* is not **0**), an error is raised, and bc(1) resets (see 611 the **RESET** section) while **seed** remains unchanged. If **E** is larger 612 than **BC_RAND_MAX**, the higher bound is honored by generating several 613 pseudo-random integers, multiplying them by appropriate powers of 614 **BC_RAND_MAX+1**, and adding them together. Thus, the size of integer that 615 can be generated with this operand is unbounded. Using this operand will 616 change the value of **seed**, unless the value of **E** is **0** or **1**. 617 In that case, **0** is returned, and **seed** is *not* changed. This is a 618 **non-portable extension**. 61924. **maxrand()**: The max integer returned by **rand()**. This is a 620 **non-portable extension**. 621 622The integers generated by **rand()** and **irand(E)** are guaranteed to be as 623unbiased as possible, subject to the limitations of the pseudo-random number 624generator. 625 626**Note**: The values returned by the pseudo-random number generator with 627**rand()** and **irand(E)** are guaranteed to *NOT* be cryptographically secure. 628This is a consequence of using a seeded pseudo-random number generator. However, 629they *are* guaranteed to be reproducible with identical **seed** values. This 630means that the pseudo-random values from bc(1) should only be used where a 631reproducible stream of pseudo-random numbers is *ESSENTIAL*. In any other case, 632use a non-seeded pseudo-random number generator. 633 634## Numbers 635 636Numbers are strings made up of digits, uppercase letters, and at most **1** 637period for a radix. Numbers can have up to **BC_NUM_MAX** digits. Uppercase 638letters are equal to **9** plus their position in the alphabet, starting from 639**1** (i.e., **A** equals **10**, or **9+1**). 640 641If a digit or letter makes no sense with the current value of **ibase** (i.e., 642they are greater than or equal to the current value of **ibase**), then the 643behavior depends on the existence of the **-c**/**-\-digit-clamp** or 644**-C**/**-\-no-digit-clamp** options (see the **OPTIONS** section), the 645existence and setting of the **BC_DIGIT_CLAMP** environment variable (see the 646**ENVIRONMENT VARIABLES** section), or the default, which can be queried with 647the **-h**/**-\-help** option. 648 649If clamping is off, then digits or letters that are greater than or equal to the 650current value of **ibase** are not changed. Instead, their given value is 651multiplied by the appropriate power of **ibase** and added into the number. This 652means that, with an **ibase** of **3**, the number **AB** is equal to 653**3\^1\*A+3\^0\*B**, which is **3** times **10** plus **11**, or **41**. 654 655If clamping is on, then digits or letters that are greater than or equal to the 656current value of **ibase** are set to the value of the highest valid digit in 657**ibase** before being multiplied by the appropriate power of **ibase** and 658added into the number. This means that, with an **ibase** of **3**, the number 659**AB** is equal to **3\^1\*2+3\^0\*2**, which is **3** times **2** plus **2**, 660or **8**. 661 662There is one exception to clamping: single-character numbers (i.e., **A** 663alone). Such numbers are never clamped and always take the value they would have 664in the highest possible **ibase**. This means that **A** alone always equals 665decimal **10** and **Z** alone always equals decimal **35**. This behavior is 666mandated by the standard (see the STANDARDS section) and is meant to provide an 667easy way to set the current **ibase** (with the **i** command) regardless of the 668current value of **ibase**. 669 670If clamping is on, and the clamped value of a character is needed, use a leading 671zero, i.e., for **A**, use **0A**. 672 673In addition, bc(1) accepts numbers in scientific notation. These have the form 674**\<number\>e\<integer\>**. The exponent (the portion after the **e**) must be 675an integer. An example is **1.89237e9**, which is equal to **1892370000**. 676Negative exponents are also allowed, so **4.2890e-3** is equal to **0.0042890**. 677 678Using scientific notation is an error or warning if the **-s** or **-w**, 679respectively, command-line options (or equivalents) are given. 680 681**WARNING**: Both the number and the exponent in scientific notation are 682interpreted according to the current **ibase**, but the number is still 683multiplied by **10\^exponent** regardless of the current **ibase**. For example, 684if **ibase** is **16** and bc(1) is given the number string **FFeA**, the 685resulting decimal number will be **2550000000000**, and if bc(1) is given the 686number string **10e-4**, the resulting decimal number will be **0.0016**. 687 688Accepting input as scientific notation is a **non-portable extension**. 689 690## Operators 691 692The following arithmetic and logical operators can be used. They are listed in 693order of decreasing precedence. Operators in the same group have the same 694precedence. 695 696**++** **-\-** 697 698: Type: Prefix and Postfix 699 700 Associativity: None 701 702 Description: **increment**, **decrement** 703 704**-** **!** 705 706: Type: Prefix 707 708 Associativity: None 709 710 Description: **negation**, **boolean not** 711 712**\$** 713 714: Type: Postfix 715 716 Associativity: None 717 718 Description: **truncation** 719 720**\@** 721 722: Type: Binary 723 724 Associativity: Right 725 726 Description: **set precision** 727 728**\^** 729 730: Type: Binary 731 732 Associativity: Right 733 734 Description: **power** 735 736**\*** **/** **%** 737 738: Type: Binary 739 740 Associativity: Left 741 742 Description: **multiply**, **divide**, **modulus** 743 744**+** **-** 745 746: Type: Binary 747 748 Associativity: Left 749 750 Description: **add**, **subtract** 751 752**\<\<** **\>\>** 753 754: Type: Binary 755 756 Associativity: Left 757 758 Description: **shift left**, **shift right** 759 760**=** **\<\<=** **\>\>=** **+=** **-=** **\*=** **/=** **%=** **\^=** **\@=** 761 762: Type: Binary 763 764 Associativity: Right 765 766 Description: **assignment** 767 768**==** **\<=** **\>=** **!=** **\<** **\>** 769 770: Type: Binary 771 772 Associativity: Left 773 774 Description: **relational** 775 776**&&** 777 778: Type: Binary 779 780 Associativity: Left 781 782 Description: **boolean and** 783 784**||** 785 786: Type: Binary 787 788 Associativity: Left 789 790 Description: **boolean or** 791 792The operators will be described in more detail below. 793 794**++** **-\-** 795 796: The prefix and postfix **increment** and **decrement** operators behave 797 exactly like they would in C. They require a named expression (see the 798 *Named Expressions* subsection) as an operand. 799 800 The prefix versions of these operators are more efficient; use them where 801 possible. 802 803**-** 804 805: The **negation** operator returns **0** if a user attempts to negate any 806 expression with the value **0**. Otherwise, a copy of the expression with 807 its sign flipped is returned. 808 809**!** 810 811: The **boolean not** operator returns **1** if the expression is **0**, or 812 **0** otherwise. 813 814 This is a **non-portable extension**. 815 816**\$** 817 818: The **truncation** operator returns a copy of the given expression with all 819 of its *scale* removed. 820 821 This is a **non-portable extension**. 822 823**\@** 824 825: The **set precision** operator takes two expressions and returns a copy of 826 the first with its *scale* equal to the value of the second expression. That 827 could either mean that the number is returned without change (if the 828 *scale* of the first expression matches the value of the second 829 expression), extended (if it is less), or truncated (if it is more). 830 831 The second expression must be an integer (no *scale*) and non-negative. 832 833 This is a **non-portable extension**. 834 835**\^** 836 837: The **power** operator (not the **exclusive or** operator, as it would be in 838 C) takes two expressions and raises the first to the power of the value of 839 the second. The *scale* of the result is equal to **scale**. 840 841 The second expression must be an integer (no *scale*), and if it is 842 negative, the first value must be non-zero. 843 844**\*** 845 846: The **multiply** operator takes two expressions, multiplies them, and 847 returns the product. If **a** is the *scale* of the first expression and 848 **b** is the *scale* of the second expression, the *scale* of the result is 849 equal to **min(a+b,max(scale,a,b))** where **min()** and **max()** return 850 the obvious values. 851 852**/** 853 854: The **divide** operator takes two expressions, divides them, and returns the 855 quotient. The *scale* of the result shall be the value of **scale**. 856 857 The second expression must be non-zero. 858 859**%** 860 861: The **modulus** operator takes two expressions, **a** and **b**, and 862 evaluates them by 1) Computing **a/b** to current **scale** and 2) Using the 863 result of step 1 to calculate **a-(a/b)\*b** to *scale* 864 **max(scale+scale(b),scale(a))**. 865 866 The second expression must be non-zero. 867 868**+** 869 870: The **add** operator takes two expressions, **a** and **b**, and returns the 871 sum, with a *scale* equal to the max of the *scale*s of **a** and **b**. 872 873**-** 874 875: The **subtract** operator takes two expressions, **a** and **b**, and 876 returns the difference, with a *scale* equal to the max of the *scale*s of 877 **a** and **b**. 878 879**\<\<** 880 881: The **left shift** operator takes two expressions, **a** and **b**, and 882 returns a copy of the value of **a** with its decimal point moved **b** 883 places to the right. 884 885 The second expression must be an integer (no *scale*) and non-negative. 886 887 This is a **non-portable extension**. 888 889**\>\>** 890 891: The **right shift** operator takes two expressions, **a** and **b**, and 892 returns a copy of the value of **a** with its decimal point moved **b** 893 places to the left. 894 895 The second expression must be an integer (no *scale*) and non-negative. 896 897 This is a **non-portable extension**. 898 899**=** **\<\<=** **\>\>=** **+=** **-=** **\*=** **/=** **%=** **\^=** **\@=** 900 901: The **assignment** operators take two expressions, **a** and **b** where 902 **a** is a named expression (see the *Named Expressions* subsection). 903 904 For **=**, **b** is copied and the result is assigned to **a**. For all 905 others, **a** and **b** are applied as operands to the corresponding 906 arithmetic operator and the result is assigned to **a**. 907 908 The **assignment** operators that correspond to operators that are 909 extensions are themselves **non-portable extensions**. 910 911**==** **\<=** **\>=** **!=** **\<** **\>** 912 913: The **relational** operators compare two expressions, **a** and **b**, and 914 if the relation holds, according to C language semantics, the result is 915 **1**. Otherwise, it is **0**. 916 917 Note that unlike in C, these operators have a lower precedence than the 918 **assignment** operators, which means that **a=b\>c** is interpreted as 919 **(a=b)\>c**. 920 921 Also, unlike the standard (see the **STANDARDS** section) requires, these 922 operators can appear anywhere any other expressions can be used. This 923 allowance is a **non-portable extension**. 924 925**&&** 926 927: The **boolean and** operator takes two expressions and returns **1** if both 928 expressions are non-zero, **0** otherwise. 929 930 This is *not* a short-circuit operator. 931 932 This is a **non-portable extension**. 933 934**||** 935 936: The **boolean or** operator takes two expressions and returns **1** if one 937 of the expressions is non-zero, **0** otherwise. 938 939 This is *not* a short-circuit operator. 940 941 This is a **non-portable extension**. 942 943## Statements 944 945The following items are statements: 946 9471. **E** 9482. **{** **S** **;** ... **;** **S** **}** 9493. **if** **(** **E** **)** **S** 9504. **if** **(** **E** **)** **S** **else** **S** 9515. **while** **(** **E** **)** **S** 9526. **for** **(** **E** **;** **E** **;** **E** **)** **S** 9537. An empty statement 9548. **break** 9559. **continue** 95610. **quit** 95711. **halt** 95812. **limits** 95913. A string of characters, enclosed in double quotes 96014. **print** **E** **,** ... **,** **E** 96115. **stream** **E** **,** ... **,** **E** 96216. **I()**, **I(E)**, **I(E, E)**, and so on, where **I** is an identifier for 963 a **void** function (see the *Void Functions* subsection of the 964 **FUNCTIONS** section). The **E** argument(s) may also be arrays of the form 965 **I[]**, which will automatically be turned into array references (see the 966 *Array References* subsection of the **FUNCTIONS** section) if the 967 corresponding parameter in the function definition is an array reference. 968 969Numbers 4, 9, 11, 12, 14, 15, and 16 are **non-portable extensions**. 970 971Also, as a **non-portable extension**, any or all of the expressions in the 972header of a for loop may be omitted. If the condition (second expression) is 973omitted, it is assumed to be a constant **1**. 974 975The **break** statement causes a loop to stop iterating and resume execution 976immediately following a loop. This is only allowed in loops. 977 978The **continue** statement causes a loop iteration to stop early and returns to 979the start of the loop, including testing the loop condition. This is only 980allowed in loops. 981 982The **if** **else** statement does the same thing as in C. 983 984The **quit** statement causes bc(1) to quit, even if it is on a branch that will 985not be executed (it is a compile-time command). 986 987**Warning**: The behavior of this bc(1) on **quit** is slightly different from 988other bc(1) implementations. Other bc(1) implementations will exit as soon as 989they finish parsing the line that a **quit** command is on. This bc(1) will 990execute any completed and executable statements that occur before the **quit** 991statement before exiting. 992 993In other words, for the bc(1) code below: 994 995 for (i = 0; i < 3; ++i) i; quit 996 997Other bc(1) implementations will print nothing, and this bc(1) will print **0**, 998**1**, and **2** on successive lines before exiting. 999 1000The **halt** statement causes bc(1) to quit, if it is executed. (Unlike **quit** 1001if it is on a branch of an **if** statement that is not executed, bc(1) does not 1002quit.) 1003 1004The **limits** statement prints the limits that this bc(1) is subject to. This 1005is like the **quit** statement in that it is a compile-time command. 1006 1007An expression by itself is evaluated and printed, followed by a newline. 1008 1009Both scientific notation and engineering notation are available for printing the 1010results of expressions. Scientific notation is activated by assigning **0** to 1011**obase**, and engineering notation is activated by assigning **1** to 1012**obase**. To deactivate them, just assign a different value to **obase**. 1013 1014Scientific notation and engineering notation are disabled if bc(1) is run with 1015either the **-s** or **-w** command-line options (or equivalents). 1016 1017Printing numbers in scientific notation and/or engineering notation is a 1018**non-portable extension**. 1019 1020## Strings 1021 1022If strings appear as a statement by themselves, they are printed without a 1023trailing newline. 1024 1025In addition to appearing as a lone statement by themselves, strings can be 1026assigned to variables and array elements. They can also be passed to functions 1027in variable parameters. 1028 1029If any statement that expects a string is given a variable that had a string 1030assigned to it, the statement acts as though it had received a string. 1031 1032If any math operation is attempted on a string or a variable or array element 1033that has been assigned a string, an error is raised, and bc(1) resets (see the 1034**RESET** section). 1035 1036Assigning strings to variables and array elements and passing them to functions 1037are **non-portable extensions**. 1038 1039## Print Statement 1040 1041The "expressions" in a **print** statement may also be strings. If they are, there 1042are backslash escape sequences that are interpreted specially. What those 1043sequences are, and what they cause to be printed, are shown below: 1044 1045**\\a**: **\\a** 1046 1047**\\b**: **\\b** 1048 1049**\\\\**: **\\** 1050 1051**\\e**: **\\** 1052 1053**\\f**: **\\f** 1054 1055**\\n**: **\\n** 1056 1057**\\q**: **"** 1058 1059**\\r**: **\\r** 1060 1061**\\t**: **\\t** 1062 1063Any other character following a backslash causes the backslash and character to 1064be printed as-is. 1065 1066Any non-string expression in a print statement shall be assigned to **last**, 1067like any other expression that is printed. 1068 1069## Stream Statement 1070 1071The "expressions in a **stream** statement may also be strings. 1072 1073If a **stream** statement is given a string, it prints the string as though the 1074string had appeared as its own statement. In other words, the **stream** 1075statement prints strings normally, without a newline. 1076 1077If a **stream** statement is given a number, a copy of it is truncated and its 1078absolute value is calculated. The result is then printed as though **obase** is 1079**256** and each digit is interpreted as an 8-bit ASCII character, making it a 1080byte stream. 1081 1082## Order of Evaluation 1083 1084All expressions in a statment are evaluated left to right, except as necessary 1085to maintain order of operations. This means, for example, assuming that **i** is 1086equal to **0**, in the expression 1087 1088 a[i++] = i++ 1089 1090the first (or 0th) element of **a** is set to **1**, and **i** is equal to **2** 1091at the end of the expression. 1092 1093This includes function arguments. Thus, assuming **i** is equal to **0**, this 1094means that in the expression 1095 1096 x(i++, i++) 1097 1098the first argument passed to **x()** is **0**, and the second argument is **1**, 1099while **i** is equal to **2** before the function starts executing. 1100 1101# FUNCTIONS 1102 1103Function definitions are as follows: 1104 1105``` 1106define I(I,...,I){ 1107 auto I,...,I 1108 S;...;S 1109 return(E) 1110} 1111``` 1112 1113Any **I** in the parameter list or **auto** list may be replaced with **I[]** to 1114make a parameter or **auto** var an array, and any **I** in the parameter list 1115may be replaced with **\*I[]** to make a parameter an array reference. Callers 1116of functions that take array references should not put an asterisk in the call; 1117they must be called with just **I[]** like normal array parameters and will be 1118automatically converted into references. 1119 1120As a **non-portable extension**, the opening brace of a **define** statement may 1121appear on the next line. 1122 1123As a **non-portable extension**, the return statement may also be in one of the 1124following forms: 1125 11261. **return** 11272. **return** **(** **)** 11283. **return** **E** 1129 1130The first two, or not specifying a **return** statement, is equivalent to 1131**return (0)**, unless the function is a **void** function (see the *Void 1132Functions* subsection below). 1133 1134## Void Functions 1135 1136Functions can also be **void** functions, defined as follows: 1137 1138``` 1139define void I(I,...,I){ 1140 auto I,...,I 1141 S;...;S 1142 return 1143} 1144``` 1145 1146They can only be used as standalone expressions, where such an expression would 1147be printed alone, except in a print statement. 1148 1149Void functions can only use the first two **return** statements listed above. 1150They can also omit the return statement entirely. 1151 1152The word "void" is not treated as a keyword; it is still possible to have 1153variables, arrays, and functions named **void**. The word "void" is only 1154treated specially right after the **define** keyword. 1155 1156This is a **non-portable extension**. 1157 1158## Array References 1159 1160For any array in the parameter list, if the array is declared in the form 1161 1162``` 1163*I[] 1164``` 1165 1166it is a **reference**. Any changes to the array in the function are reflected, 1167when the function returns, to the array that was passed in. 1168 1169Other than this, all function arguments are passed by value. 1170 1171This is a **non-portable extension**. 1172 1173# LIBRARY 1174 1175All of the functions below, including the functions in the extended math 1176library (see the *Extended Library* subsection below), are available when the 1177**-l** or **-\-mathlib** command-line flags are given, except that the extended 1178math library is not available when the **-s** option, the **-w** option, or 1179equivalents are given. 1180 1181## Standard Library 1182 1183The standard (see the **STANDARDS** section) defines the following functions for 1184the math library: 1185 1186**s(x)** 1187 1188: Returns the sine of **x**, which is assumed to be in radians. 1189 1190 This is a transcendental function (see the *Transcendental Functions* 1191 subsection below). 1192 1193**c(x)** 1194 1195: Returns the cosine of **x**, which is assumed to be in radians. 1196 1197 This is a transcendental function (see the *Transcendental Functions* 1198 subsection below). 1199 1200**a(x)** 1201 1202: Returns the arctangent of **x**, in radians. 1203 1204 This is a transcendental function (see the *Transcendental Functions* 1205 subsection below). 1206 1207**l(x)** 1208 1209: Returns the natural logarithm of **x**. 1210 1211 This is a transcendental function (see the *Transcendental Functions* 1212 subsection below). 1213 1214**e(x)** 1215 1216: Returns the mathematical constant **e** raised to the power of **x**. 1217 1218 This is a transcendental function (see the *Transcendental Functions* 1219 subsection below). 1220 1221**j(x, n)** 1222 1223: Returns the bessel integer order **n** (truncated) of **x**. 1224 1225 This is a transcendental function (see the *Transcendental Functions* 1226 subsection below). 1227 1228## Extended Library 1229 1230The extended library is *not* loaded when the **-s**/**-\-standard** or 1231**-w**/**-\-warn** options are given since they are not part of the library 1232defined by the standard (see the **STANDARDS** section). 1233 1234The extended library is a **non-portable extension**. 1235 1236**p(x, y)** 1237 1238: Calculates **x** to the power of **y**, even if **y** is not an integer, and 1239 returns the result to the current **scale**. 1240 1241 It is an error if **y** is negative and **x** is **0**. 1242 1243 This is a transcendental function (see the *Transcendental Functions* 1244 subsection below). 1245 1246**r(x, p)** 1247 1248: Returns **x** rounded to **p** decimal places according to the rounding mode 1249 round half away from **0** 1250 (https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero). 1251 1252**ceil(x, p)** 1253 1254: Returns **x** rounded to **p** decimal places according to the rounding mode 1255 round away from **0** 1256 (https://en.wikipedia.org/wiki/Rounding#Rounding_away_from_zero). 1257 1258**f(x)** 1259 1260: Returns the factorial of the truncated absolute value of **x**. 1261 1262**perm(n, k)** 1263 1264: Returns the permutation of the truncated absolute value of **n** of the 1265 truncated absolute value of **k**, if **k \<= n**. If not, it returns **0**. 1266 1267**comb(n, k)** 1268 1269: Returns the combination of the truncated absolute value of **n** of the 1270 truncated absolute value of **k**, if **k \<= n**. If not, it returns **0**. 1271 1272**l2(x)** 1273 1274: Returns the logarithm base **2** of **x**. 1275 1276 This is a transcendental function (see the *Transcendental Functions* 1277 subsection below). 1278 1279**l10(x)** 1280 1281: Returns the logarithm base **10** of **x**. 1282 1283 This is a transcendental function (see the *Transcendental Functions* 1284 subsection below). 1285 1286**log(x, b)** 1287 1288: Returns the logarithm base **b** of **x**. 1289 1290 This is a transcendental function (see the *Transcendental Functions* 1291 subsection below). 1292 1293**cbrt(x)** 1294 1295: Returns the cube root of **x**. 1296 1297**root(x, n)** 1298 1299: Calculates the truncated value of **n**, **r**, and returns the **r**th root 1300 of **x** to the current **scale**. 1301 1302 If **r** is **0** or negative, this raises an error and causes bc(1) to 1303 reset (see the **RESET** section). It also raises an error and causes bc(1) 1304 to reset if **r** is even and **x** is negative. 1305 1306**gcd(a, b)** 1307 1308: Returns the greatest common divisor (factor) of the truncated absolute value 1309 of **a** and the truncated absolute value of **b**. 1310 1311**lcm(a, b)** 1312 1313: Returns the least common multiple of the truncated absolute value of **a** 1314 and the truncated absolute value of **b**. 1315 1316**pi(p)** 1317 1318: Returns **pi** to **p** decimal places. 1319 1320 This is a transcendental function (see the *Transcendental Functions* 1321 subsection below). 1322 1323**t(x)** 1324 1325: Returns the tangent of **x**, which is assumed to be in radians. 1326 1327 This is a transcendental function (see the *Transcendental Functions* 1328 subsection below). 1329 1330**a2(y, x)** 1331 1332: Returns the arctangent of **y/x**, in radians. If both **y** and **x** are 1333 equal to **0**, it raises an error and causes bc(1) to reset (see the 1334 **RESET** section). Otherwise, if **x** is greater than **0**, it returns 1335 **a(y/x)**. If **x** is less than **0**, and **y** is greater than or equal 1336 to **0**, it returns **a(y/x)+pi**. If **x** is less than **0**, and **y** 1337 is less than **0**, it returns **a(y/x)-pi**. If **x** is equal to **0**, 1338 and **y** is greater than **0**, it returns **pi/2**. If **x** is equal to 1339 **0**, and **y** is less than **0**, it returns **-pi/2**. 1340 1341 This function is the same as the **atan2()** function in many programming 1342 languages. 1343 1344 This is a transcendental function (see the *Transcendental Functions* 1345 subsection below). 1346 1347**sin(x)** 1348 1349: Returns the sine of **x**, which is assumed to be in radians. 1350 1351 This is an alias of **s(x)**. 1352 1353 This is a transcendental function (see the *Transcendental Functions* 1354 subsection below). 1355 1356**cos(x)** 1357 1358: Returns the cosine of **x**, which is assumed to be in radians. 1359 1360 This is an alias of **c(x)**. 1361 1362 This is a transcendental function (see the *Transcendental Functions* 1363 subsection below). 1364 1365**tan(x)** 1366 1367: Returns the tangent of **x**, which is assumed to be in radians. 1368 1369 If **x** is equal to **1** or **-1**, this raises an error and causes bc(1) 1370 to reset (see the **RESET** section). 1371 1372 This is an alias of **t(x)**. 1373 1374 This is a transcendental function (see the *Transcendental Functions* 1375 subsection below). 1376 1377**atan(x)** 1378 1379: Returns the arctangent of **x**, in radians. 1380 1381 This is an alias of **a(x)**. 1382 1383 This is a transcendental function (see the *Transcendental Functions* 1384 subsection below). 1385 1386**atan2(y, x)** 1387 1388: Returns the arctangent of **y/x**, in radians. If both **y** and **x** are 1389 equal to **0**, it raises an error and causes bc(1) to reset (see the 1390 **RESET** section). Otherwise, if **x** is greater than **0**, it returns 1391 **a(y/x)**. If **x** is less than **0**, and **y** is greater than or equal 1392 to **0**, it returns **a(y/x)+pi**. If **x** is less than **0**, and **y** 1393 is less than **0**, it returns **a(y/x)-pi**. If **x** is equal to **0**, 1394 and **y** is greater than **0**, it returns **pi/2**. If **x** is equal to 1395 **0**, and **y** is less than **0**, it returns **-pi/2**. 1396 1397 This function is the same as the **atan2()** function in many programming 1398 languages. 1399 1400 This is an alias of **a2(y, x)**. 1401 1402 This is a transcendental function (see the *Transcendental Functions* 1403 subsection below). 1404 1405**r2d(x)** 1406 1407: Converts **x** from radians to degrees and returns the result. 1408 1409 This is a transcendental function (see the *Transcendental Functions* 1410 subsection below). 1411 1412**d2r(x)** 1413 1414: Converts **x** from degrees to radians and returns the result. 1415 1416 This is a transcendental function (see the *Transcendental Functions* 1417 subsection below). 1418 1419**frand(p)** 1420 1421: Generates a pseudo-random number between **0** (inclusive) and **1** 1422 (exclusive) with the number of decimal digits after the decimal point equal 1423 to the truncated absolute value of **p**. If **p** is not **0**, then 1424 calling this function will change the value of **seed**. If **p** is **0**, 1425 then **0** is returned, and **seed** is *not* changed. 1426 1427**ifrand(i, p)** 1428 1429: Generates a pseudo-random number that is between **0** (inclusive) and the 1430 truncated absolute value of **i** (exclusive) with the number of decimal 1431 digits after the decimal point equal to the truncated absolute value of 1432 **p**. If the absolute value of **i** is greater than or equal to **2**, and 1433 **p** is not **0**, then calling this function will change the value of 1434 **seed**; otherwise, **0** is returned and **seed** is not changed. 1435 1436**srand(x)** 1437 1438: Returns **x** with its sign flipped with probability **0.5**. In other 1439 words, it randomizes the sign of **x**. 1440 1441**brand()** 1442 1443: Returns a random boolean value (either **0** or **1**). 1444 1445**band(a, b)** 1446 1447: Takes the truncated absolute value of both **a** and **b** and calculates 1448 and returns the result of the bitwise **and** operation between them. 1449 1450 If you want to use signed two's complement arguments, use **s2u(x)** to 1451 convert. 1452 1453**bor(a, b)** 1454 1455: Takes the truncated absolute value of both **a** and **b** and calculates 1456 and returns the result of the bitwise **or** operation between them. 1457 1458 If you want to use signed two's complement arguments, use **s2u(x)** to 1459 convert. 1460 1461**bxor(a, b)** 1462 1463: Takes the truncated absolute value of both **a** and **b** and calculates 1464 and returns the result of the bitwise **xor** operation between them. 1465 1466 If you want to use signed two's complement arguments, use **s2u(x)** to 1467 convert. 1468 1469**bshl(a, b)** 1470 1471: Takes the truncated absolute value of both **a** and **b** and calculates 1472 and returns the result of **a** bit-shifted left by **b** places. 1473 1474 If you want to use signed two's complement arguments, use **s2u(x)** to 1475 convert. 1476 1477**bshr(a, b)** 1478 1479: Takes the truncated absolute value of both **a** and **b** and calculates 1480 and returns the truncated result of **a** bit-shifted right by **b** places. 1481 1482 If you want to use signed two's complement arguments, use **s2u(x)** to 1483 convert. 1484 1485**bnotn(x, n)** 1486 1487: Takes the truncated absolute value of **x** and does a bitwise not as though 1488 it has the same number of bytes as the truncated absolute value of **n**. 1489 1490 If you want to a use signed two's complement argument, use **s2u(x)** to 1491 convert. 1492 1493**bnot8(x)** 1494 1495: Does a bitwise not of the truncated absolute value of **x** as though it has 1496 **8** binary digits (1 unsigned byte). 1497 1498 If you want to a use signed two's complement argument, use **s2u(x)** to 1499 convert. 1500 1501**bnot16(x)** 1502 1503: Does a bitwise not of the truncated absolute value of **x** as though it has 1504 **16** binary digits (2 unsigned bytes). 1505 1506 If you want to a use signed two's complement argument, use **s2u(x)** to 1507 convert. 1508 1509**bnot32(x)** 1510 1511: Does a bitwise not of the truncated absolute value of **x** as though it has 1512 **32** binary digits (4 unsigned bytes). 1513 1514 If you want to a use signed two's complement argument, use **s2u(x)** to 1515 convert. 1516 1517**bnot64(x)** 1518 1519: Does a bitwise not of the truncated absolute value of **x** as though it has 1520 **64** binary digits (8 unsigned bytes). 1521 1522 If you want to a use signed two's complement argument, use **s2u(x)** to 1523 convert. 1524 1525**bnot(x)** 1526 1527: Does a bitwise not of the truncated absolute value of **x** as though it has 1528 the minimum number of power of two unsigned bytes. 1529 1530 If you want to a use signed two's complement argument, use **s2u(x)** to 1531 convert. 1532 1533**brevn(x, n)** 1534 1535: Runs a bit reversal on the truncated absolute value of **x** as though it 1536 has the same number of 8-bit bytes as the truncated absolute value of **n**. 1537 1538 If you want to a use signed two's complement argument, use **s2u(x)** to 1539 convert. 1540 1541**brev8(x)** 1542 1543: Runs a bit reversal on the truncated absolute value of **x** as though it 1544 has 8 binary digits (1 unsigned byte). 1545 1546 If you want to a use signed two's complement argument, use **s2u(x)** to 1547 convert. 1548 1549**brev16(x)** 1550 1551: Runs a bit reversal on the truncated absolute value of **x** as though it 1552 has 16 binary digits (2 unsigned bytes). 1553 1554 If you want to a use signed two's complement argument, use **s2u(x)** to 1555 convert. 1556 1557**brev32(x)** 1558 1559: Runs a bit reversal on the truncated absolute value of **x** as though it 1560 has 32 binary digits (4 unsigned bytes). 1561 1562 If you want to a use signed two's complement argument, use **s2u(x)** to 1563 convert. 1564 1565**brev64(x)** 1566 1567: Runs a bit reversal on the truncated absolute value of **x** as though it 1568 has 64 binary digits (8 unsigned bytes). 1569 1570 If you want to a use signed two's complement argument, use **s2u(x)** to 1571 convert. 1572 1573**brev(x)** 1574 1575: Runs a bit reversal on the truncated absolute value of **x** as though it 1576 has the minimum number of power of two unsigned bytes. 1577 1578 If you want to a use signed two's complement argument, use **s2u(x)** to 1579 convert. 1580 1581**broln(x, p, n)** 1582 1583: Does a left bitwise rotatation of the truncated absolute value of **x**, as 1584 though it has the same number of unsigned 8-bit bytes as the truncated 1585 absolute value of **n**, by the number of places equal to the truncated 1586 absolute value of **p** modded by the **2** to the power of the number of 1587 binary digits in **n** 8-bit bytes. 1588 1589 If you want to a use signed two's complement argument, use **s2u(x)** to 1590 convert. 1591 1592**brol8(x, p)** 1593 1594: Does a left bitwise rotatation of the truncated absolute value of **x**, as 1595 though it has **8** binary digits (**1** unsigned byte), by the number of 1596 places equal to the truncated absolute value of **p** modded by **2** to the 1597 power of **8**. 1598 1599 If you want to a use signed two's complement argument, use **s2u(x)** to 1600 convert. 1601 1602**brol16(x, p)** 1603 1604: Does a left bitwise rotatation of the truncated absolute value of **x**, as 1605 though it has **16** binary digits (**2** unsigned bytes), by the number of 1606 places equal to the truncated absolute value of **p** modded by **2** to the 1607 power of **16**. 1608 1609 If you want to a use signed two's complement argument, use **s2u(x)** to 1610 convert. 1611 1612**brol32(x, p)** 1613 1614: Does a left bitwise rotatation of the truncated absolute value of **x**, as 1615 though it has **32** binary digits (**2** unsigned bytes), by the number of 1616 places equal to the truncated absolute value of **p** modded by **2** to the 1617 power of **32**. 1618 1619 If you want to a use signed two's complement argument, use **s2u(x)** to 1620 convert. 1621 1622**brol64(x, p)** 1623 1624: Does a left bitwise rotatation of the truncated absolute value of **x**, as 1625 though it has **64** binary digits (**2** unsigned bytes), by the number of 1626 places equal to the truncated absolute value of **p** modded by **2** to the 1627 power of **64**. 1628 1629 If you want to a use signed two's complement argument, use **s2u(x)** to 1630 convert. 1631 1632**brol(x, p)** 1633 1634: Does a left bitwise rotatation of the truncated absolute value of **x**, as 1635 though it has the minimum number of power of two unsigned 8-bit bytes, by 1636 the number of places equal to the truncated absolute value of **p** modded 1637 by 2 to the power of the number of binary digits in the minimum number of 1638 8-bit bytes. 1639 1640 If you want to a use signed two's complement argument, use **s2u(x)** to 1641 convert. 1642 1643**brorn(x, p, n)** 1644 1645: Does a right bitwise rotatation of the truncated absolute value of **x**, as 1646 though it has the same number of unsigned 8-bit bytes as the truncated 1647 absolute value of **n**, by the number of places equal to the truncated 1648 absolute value of **p** modded by the **2** to the power of the number of 1649 binary digits in **n** 8-bit bytes. 1650 1651 If you want to a use signed two's complement argument, use **s2u(x)** to 1652 convert. 1653 1654**bror8(x, p)** 1655 1656: Does a right bitwise rotatation of the truncated absolute value of **x**, as 1657 though it has **8** binary digits (**1** unsigned byte), by the number of 1658 places equal to the truncated absolute value of **p** modded by **2** to the 1659 power of **8**. 1660 1661 If you want to a use signed two's complement argument, use **s2u(x)** to 1662 convert. 1663 1664**bror16(x, p)** 1665 1666: Does a right bitwise rotatation of the truncated absolute value of **x**, as 1667 though it has **16** binary digits (**2** unsigned bytes), by the number of 1668 places equal to the truncated absolute value of **p** modded by **2** to the 1669 power of **16**. 1670 1671 If you want to a use signed two's complement argument, use **s2u(x)** to 1672 convert. 1673 1674**bror32(x, p)** 1675 1676: Does a right bitwise rotatation of the truncated absolute value of **x**, as 1677 though it has **32** binary digits (**2** unsigned bytes), by the number of 1678 places equal to the truncated absolute value of **p** modded by **2** to the 1679 power of **32**. 1680 1681 If you want to a use signed two's complement argument, use **s2u(x)** to 1682 convert. 1683 1684**bror64(x, p)** 1685 1686: Does a right bitwise rotatation of the truncated absolute value of **x**, as 1687 though it has **64** binary digits (**2** unsigned bytes), by the number of 1688 places equal to the truncated absolute value of **p** modded by **2** to the 1689 power of **64**. 1690 1691 If you want to a use signed two's complement argument, use **s2u(x)** to 1692 convert. 1693 1694**bror(x, p)** 1695 1696: Does a right bitwise rotatation of the truncated absolute value of **x**, as 1697 though it has the minimum number of power of two unsigned 8-bit bytes, by 1698 the number of places equal to the truncated absolute value of **p** modded 1699 by 2 to the power of the number of binary digits in the minimum number of 1700 8-bit bytes. 1701 1702 If you want to a use signed two's complement argument, use **s2u(x)** to 1703 convert. 1704 1705**bmodn(x, n)** 1706 1707: Returns the modulus of the truncated absolute value of **x** by **2** to the 1708 power of the multiplication of the truncated absolute value of **n** and 1709 **8**. 1710 1711 If you want to a use signed two's complement argument, use **s2u(x)** to 1712 convert. 1713 1714**bmod8(x, n)** 1715 1716: Returns the modulus of the truncated absolute value of **x** by **2** to the 1717 power of **8**. 1718 1719 If you want to a use signed two's complement argument, use **s2u(x)** to 1720 convert. 1721 1722**bmod16(x, n)** 1723 1724: Returns the modulus of the truncated absolute value of **x** by **2** to the 1725 power of **16**. 1726 1727 If you want to a use signed two's complement argument, use **s2u(x)** to 1728 convert. 1729 1730**bmod32(x, n)** 1731 1732: Returns the modulus of the truncated absolute value of **x** by **2** to the 1733 power of **32**. 1734 1735 If you want to a use signed two's complement argument, use **s2u(x)** to 1736 convert. 1737 1738**bmod64(x, n)** 1739 1740: Returns the modulus of the truncated absolute value of **x** by **2** to the 1741 power of **64**. 1742 1743 If you want to a use signed two's complement argument, use **s2u(x)** to 1744 convert. 1745 1746**bunrev(t)** 1747 1748: Assumes **t** is a bitwise-reversed number with an extra set bit one place 1749 more significant than the real most significant bit (which was the least 1750 significant bit in the original number). This number is reversed and 1751 returned without the extra set bit. 1752 1753 This function is used to implement other bitwise functions; it is not meant 1754 to be used by users, but it can be. 1755 1756**plz(x)** 1757 1758: If **x** is not equal to **0** and greater that **-1** and less than **1**, 1759 it is printed with a leading zero, regardless of the use of the **-z** 1760 option (see the **OPTIONS** section) and without a trailing newline. 1761 1762 Otherwise, **x** is printed normally, without a trailing newline. 1763 1764**plznl(x)** 1765 1766: If **x** is not equal to **0** and greater that **-1** and less than **1**, 1767 it is printed with a leading zero, regardless of the use of the **-z** 1768 option (see the **OPTIONS** section) and with a trailing newline. 1769 1770 Otherwise, **x** is printed normally, with a trailing newline. 1771 1772**pnlz(x)** 1773 1774: If **x** is not equal to **0** and greater that **-1** and less than **1**, 1775 it is printed without a leading zero, regardless of the use of the **-z** 1776 option (see the **OPTIONS** section) and without a trailing newline. 1777 1778 Otherwise, **x** is printed normally, without a trailing newline. 1779 1780**pnlznl(x)** 1781 1782: If **x** is not equal to **0** and greater that **-1** and less than **1**, 1783 it is printed without a leading zero, regardless of the use of the **-z** 1784 option (see the **OPTIONS** section) and with a trailing newline. 1785 1786 Otherwise, **x** is printed normally, with a trailing newline. 1787 1788**ubytes(x)** 1789 1790: Returns the numbers of unsigned integer bytes required to hold the truncated 1791 absolute value of **x**. 1792 1793**sbytes(x)** 1794 1795: Returns the numbers of signed, two's-complement integer bytes required to 1796 hold the truncated value of **x**. 1797 1798**s2u(x)** 1799 1800: Returns **x** if it is non-negative. If it *is* negative, then it calculates 1801 what **x** would be as a 2's-complement signed integer and returns the 1802 non-negative integer that would have the same representation in binary. 1803 1804**s2un(x,n)** 1805 1806: Returns **x** if it is non-negative. If it *is* negative, then it calculates 1807 what **x** would be as a 2's-complement signed integer with **n** bytes and 1808 returns the non-negative integer that would have the same representation in 1809 binary. If **x** cannot fit into **n** 2's-complement signed bytes, it is 1810 truncated to fit. 1811 1812**hex(x)** 1813 1814: Outputs the hexadecimal (base **16**) representation of **x**. 1815 1816 This is a **void** function (see the *Void Functions* subsection of the 1817 **FUNCTIONS** section). 1818 1819**binary(x)** 1820 1821: Outputs the binary (base **2**) representation of **x**. 1822 1823 This is a **void** function (see the *Void Functions* subsection of the 1824 **FUNCTIONS** section). 1825 1826**output(x, b)** 1827 1828: Outputs the base **b** representation of **x**. 1829 1830 This is a **void** function (see the *Void Functions* subsection of the 1831 **FUNCTIONS** section). 1832 1833**uint(x)** 1834 1835: Outputs the representation, in binary and hexadecimal, of **x** as an 1836 unsigned integer in as few power of two bytes as possible. Both outputs are 1837 split into bytes separated by spaces. 1838 1839 If **x** is not an integer or is negative, an error message is printed 1840 instead, but bc(1) is not reset (see the **RESET** section). 1841 1842 This is a **void** function (see the *Void Functions* subsection of the 1843 **FUNCTIONS** section). 1844 1845**int(x)** 1846 1847: Outputs the representation, in binary and hexadecimal, of **x** as a signed, 1848 two's-complement integer in as few power of two bytes as possible. Both 1849 outputs are split into bytes separated by spaces. 1850 1851 If **x** is not an integer, an error message is printed instead, but bc(1) 1852 is not reset (see the **RESET** section). 1853 1854 This is a **void** function (see the *Void Functions* subsection of the 1855 **FUNCTIONS** section). 1856 1857**uintn(x, n)** 1858 1859: Outputs the representation, in binary and hexadecimal, of **x** as an 1860 unsigned integer in **n** bytes. Both outputs are split into bytes separated 1861 by spaces. 1862 1863 If **x** is not an integer, is negative, or cannot fit into **n** bytes, an 1864 error message is printed instead, but bc(1) is not reset (see the **RESET** 1865 section). 1866 1867 This is a **void** function (see the *Void Functions* subsection of the 1868 **FUNCTIONS** section). 1869 1870**intn(x, n)** 1871 1872: Outputs the representation, in binary and hexadecimal, of **x** as a signed, 1873 two's-complement integer in **n** bytes. Both outputs are split into bytes 1874 separated by spaces. 1875 1876 If **x** is not an integer or cannot fit into **n** bytes, an error message 1877 is printed instead, but bc(1) is not reset (see the **RESET** section). 1878 1879 This is a **void** function (see the *Void Functions* subsection of the 1880 **FUNCTIONS** section). 1881 1882**uint8(x)** 1883 1884: Outputs the representation, in binary and hexadecimal, of **x** as an 1885 unsigned integer in **1** byte. Both outputs are split into bytes separated 1886 by spaces. 1887 1888 If **x** is not an integer, is negative, or cannot fit into **1** byte, an 1889 error message is printed instead, but bc(1) is not reset (see the **RESET** 1890 section). 1891 1892 This is a **void** function (see the *Void Functions* subsection of the 1893 **FUNCTIONS** section). 1894 1895**int8(x)** 1896 1897: Outputs the representation, in binary and hexadecimal, of **x** as a signed, 1898 two's-complement integer in **1** byte. Both outputs are split into bytes 1899 separated by spaces. 1900 1901 If **x** is not an integer or cannot fit into **1** byte, an error message 1902 is printed instead, but bc(1) is not reset (see the **RESET** section). 1903 1904 This is a **void** function (see the *Void Functions* subsection of the 1905 **FUNCTIONS** section). 1906 1907**uint16(x)** 1908 1909: Outputs the representation, in binary and hexadecimal, of **x** as an 1910 unsigned integer in **2** bytes. Both outputs are split into bytes separated 1911 by spaces. 1912 1913 If **x** is not an integer, is negative, or cannot fit into **2** bytes, an 1914 error message is printed instead, but bc(1) is not reset (see the **RESET** 1915 section). 1916 1917 This is a **void** function (see the *Void Functions* subsection of the 1918 **FUNCTIONS** section). 1919 1920**int16(x)** 1921 1922: Outputs the representation, in binary and hexadecimal, of **x** as a signed, 1923 two's-complement integer in **2** bytes. Both outputs are split into bytes 1924 separated by spaces. 1925 1926 If **x** is not an integer or cannot fit into **2** bytes, an error message 1927 is printed instead, but bc(1) is not reset (see the **RESET** section). 1928 1929 This is a **void** function (see the *Void Functions* subsection of the 1930 **FUNCTIONS** section). 1931 1932**uint32(x)** 1933 1934: Outputs the representation, in binary and hexadecimal, of **x** as an 1935 unsigned integer in **4** bytes. Both outputs are split into bytes separated 1936 by spaces. 1937 1938 If **x** is not an integer, is negative, or cannot fit into **4** bytes, an 1939 error message is printed instead, but bc(1) is not reset (see the **RESET** 1940 section). 1941 1942 This is a **void** function (see the *Void Functions* subsection of the 1943 **FUNCTIONS** section). 1944 1945**int32(x)** 1946 1947: Outputs the representation, in binary and hexadecimal, of **x** as a signed, 1948 two's-complement integer in **4** bytes. Both outputs are split into bytes 1949 separated by spaces. 1950 1951 If **x** is not an integer or cannot fit into **4** bytes, an error message 1952 is printed instead, but bc(1) is not reset (see the **RESET** section). 1953 1954 This is a **void** function (see the *Void Functions* subsection of the 1955 **FUNCTIONS** section). 1956 1957**uint64(x)** 1958 1959: Outputs the representation, in binary and hexadecimal, of **x** as an 1960 unsigned integer in **8** bytes. Both outputs are split into bytes separated 1961 by spaces. 1962 1963 If **x** is not an integer, is negative, or cannot fit into **8** bytes, an 1964 error message is printed instead, but bc(1) is not reset (see the **RESET** 1965 section). 1966 1967 This is a **void** function (see the *Void Functions* subsection of the 1968 **FUNCTIONS** section). 1969 1970**int64(x)** 1971 1972: Outputs the representation, in binary and hexadecimal, of **x** as a signed, 1973 two's-complement integer in **8** bytes. Both outputs are split into bytes 1974 separated by spaces. 1975 1976 If **x** is not an integer or cannot fit into **8** bytes, an error message 1977 is printed instead, but bc(1) is not reset (see the **RESET** section). 1978 1979 This is a **void** function (see the *Void Functions* subsection of the 1980 **FUNCTIONS** section). 1981 1982**hex_uint(x, n)** 1983 1984: Outputs the representation of the truncated absolute value of **x** as an 1985 unsigned integer in hexadecimal using **n** bytes. Not all of the value will 1986 be output if **n** is too small. 1987 1988 This is a **void** function (see the *Void Functions* subsection of the 1989 **FUNCTIONS** section). 1990 1991**binary_uint(x, n)** 1992 1993: Outputs the representation of the truncated absolute value of **x** as an 1994 unsigned integer in binary using **n** bytes. Not all of the value will be 1995 output if **n** is too small. 1996 1997 This is a **void** function (see the *Void Functions* subsection of the 1998 **FUNCTIONS** section). 1999 2000**output_uint(x, n)** 2001 2002: Outputs the representation of the truncated absolute value of **x** as an 2003 unsigned integer in the current **obase** (see the **SYNTAX** section) using 2004 **n** bytes. Not all of the value will be output if **n** is too small. 2005 2006 This is a **void** function (see the *Void Functions* subsection of the 2007 **FUNCTIONS** section). 2008 2009**output_byte(x, i)** 2010 2011: Outputs byte **i** of the truncated absolute value of **x**, where **0** is 2012 the least significant byte and **number_of_bytes - 1** is the most 2013 significant byte. 2014 2015 This is a **void** function (see the *Void Functions* subsection of the 2016 **FUNCTIONS** section). 2017 2018## Transcendental Functions 2019 2020All transcendental functions can return slightly inaccurate results, up to 1 ULP 2021(https://en.wikipedia.org/wiki/Unit_in_the_last_place). This is unavoidable, and 2022the article at https://people.eecs.berkeley.edu/~wkahan/LOG10HAF.TXT explains 2023why it is impossible and unnecessary to calculate exact results for the 2024transcendental functions. 2025 2026Because of the possible inaccuracy, I recommend that users call those functions 2027with the precision (**scale**) set to at least 1 higher than is necessary. If 2028exact results are *absolutely* required, users can double the precision 2029(**scale**) and then truncate. 2030 2031The transcendental functions in the standard math library are: 2032 2033* **s(x)** 2034* **c(x)** 2035* **a(x)** 2036* **l(x)** 2037* **e(x)** 2038* **j(x, n)** 2039 2040The transcendental functions in the extended math library are: 2041 2042* **l2(x)** 2043* **l10(x)** 2044* **log(x, b)** 2045* **pi(p)** 2046* **t(x)** 2047* **a2(y, x)** 2048* **sin(x)** 2049* **cos(x)** 2050* **tan(x)** 2051* **atan(x)** 2052* **atan2(y, x)** 2053* **r2d(x)** 2054* **d2r(x)** 2055 2056# RESET 2057 2058When bc(1) encounters an error or a signal that it has a non-default handler 2059for, it resets. This means that several things happen. 2060 2061First, any functions that are executing are stopped and popped off the stack. 2062The behavior is not unlike that of exceptions in programming languages. Then 2063the execution point is set so that any code waiting to execute (after all 2064functions returned) is skipped. 2065 2066Thus, when bc(1) resets, it skips any remaining code waiting to be executed. 2067Then, if it is interactive mode, and the error was not a fatal error (see the 2068**EXIT STATUS** section), it asks for more input; otherwise, it exits with the 2069appropriate return code. 2070 2071Note that this reset behavior is different from the GNU bc(1), which attempts to 2072start executing the statement right after the one that caused an error. 2073 2074# PERFORMANCE 2075 2076Most bc(1) implementations use **char** types to calculate the value of **1** 2077decimal digit at a time, but that can be slow. This bc(1) does something 2078different. 2079 2080It uses large integers to calculate more than **1** decimal digit at a time. If 2081built in a environment where **BC_LONG_BIT** (see the **LIMITS** section) is 2082**64**, then each integer has **9** decimal digits. If built in an environment 2083where **BC_LONG_BIT** is **32** then each integer has **4** decimal digits. This 2084value (the number of decimal digits per large integer) is called 2085**BC_BASE_DIGS**. 2086 2087The actual values of **BC_LONG_BIT** and **BC_BASE_DIGS** can be queried with 2088the **limits** statement. 2089 2090In addition, this bc(1) uses an even larger integer for overflow checking. This 2091integer type depends on the value of **BC_LONG_BIT**, but is always at least 2092twice as large as the integer type used to store digits. 2093 2094# LIMITS 2095 2096The following are the limits on bc(1): 2097 2098**BC_LONG_BIT** 2099 2100: The number of bits in the **long** type in the environment where bc(1) was 2101 built. This determines how many decimal digits can be stored in a single 2102 large integer (see the **PERFORMANCE** section). 2103 2104**BC_BASE_DIGS** 2105 2106: The number of decimal digits per large integer (see the **PERFORMANCE** 2107 section). Depends on **BC_LONG_BIT**. 2108 2109**BC_BASE_POW** 2110 2111: The max decimal number that each large integer can store (see 2112 **BC_BASE_DIGS**) plus **1**. Depends on **BC_BASE_DIGS**. 2113 2114**BC_OVERFLOW_MAX** 2115 2116: The max number that the overflow type (see the **PERFORMANCE** section) can 2117 hold. Depends on **BC_LONG_BIT**. 2118 2119**BC_BASE_MAX** 2120 2121: The maximum output base. Set at **BC_BASE_POW**. 2122 2123**BC_DIM_MAX** 2124 2125: The maximum size of arrays. Set at **SIZE_MAX-1**. 2126 2127**BC_SCALE_MAX** 2128 2129: The maximum **scale**. Set at **BC_OVERFLOW_MAX-1**. 2130 2131**BC_STRING_MAX** 2132 2133: The maximum length of strings. Set at **BC_OVERFLOW_MAX-1**. 2134 2135**BC_NAME_MAX** 2136 2137: The maximum length of identifiers. Set at **BC_OVERFLOW_MAX-1**. 2138 2139**BC_NUM_MAX** 2140 2141: The maximum length of a number (in decimal digits), which includes digits 2142 after the decimal point. Set at **BC_OVERFLOW_MAX-1**. 2143 2144**BC_RAND_MAX** 2145 2146: The maximum integer (inclusive) returned by the **rand()** operand. Set at 2147 **2\^BC_LONG_BIT-1**. 2148 2149Exponent 2150 2151: The maximum allowable exponent (positive or negative). Set at 2152 **BC_OVERFLOW_MAX**. 2153 2154Number of vars 2155 2156: The maximum number of vars/arrays. Set at **SIZE_MAX-1**. 2157 2158The actual values can be queried with the **limits** statement. 2159 2160These limits are meant to be effectively non-existent; the limits are so large 2161(at least on 64-bit machines) that there should not be any point at which they 2162become a problem. In fact, memory should be exhausted before these limits should 2163be hit. 2164 2165# ENVIRONMENT VARIABLES 2166 2167As **non-portable extensions**, bc(1) recognizes the following environment 2168variables: 2169 2170**POSIXLY_CORRECT** 2171 2172: If this variable exists (no matter the contents), bc(1) behaves as if 2173 the **-s** option was given. 2174 2175**BC_ENV_ARGS** 2176 2177: This is another way to give command-line arguments to bc(1). They should be 2178 in the same format as all other command-line arguments. These are always 2179 processed first, so any files given in **BC_ENV_ARGS** will be processed 2180 before arguments and files given on the command-line. This gives the user 2181 the ability to set up "standard" options and files to be used at every 2182 invocation. The most useful thing for such files to contain would be useful 2183 functions that the user might want every time bc(1) runs. 2184 2185 The code that parses **BC_ENV_ARGS** will correctly handle quoted arguments, 2186 but it does not understand escape sequences. For example, the string 2187 **"/home/gavin/some bc file.bc"** will be correctly parsed, but the string 2188 **"/home/gavin/some \"bc\" file.bc"** will include the backslashes. 2189 2190 The quote parsing will handle either kind of quotes, **'** or **"**. Thus, 2191 if you have a file with any number of single quotes in the name, you can use 2192 double quotes as the outside quotes, as in **"some 'bc' file.bc"**, and vice 2193 versa if you have a file with double quotes. However, handling a file with 2194 both kinds of quotes in **BC_ENV_ARGS** is not supported due to the 2195 complexity of the parsing, though such files are still supported on the 2196 command-line where the parsing is done by the shell. 2197 2198**BC_LINE_LENGTH** 2199 2200: If this environment variable exists and contains an integer that is greater 2201 than **1** and is less than **UINT16_MAX** (**2\^16-1**), bc(1) will output 2202 lines to that length, including the backslash (**\\**). The default line 2203 length is **70**. 2204 2205 The special value of **0** will disable line length checking and print 2206 numbers without regard to line length and without backslashes and newlines. 2207 2208**BC_BANNER** 2209 2210: If this environment variable exists and contains an integer, then a non-zero 2211 value activates the copyright banner when bc(1) is in interactive mode, 2212 while zero deactivates it. 2213 2214 If bc(1) is not in interactive mode (see the **INTERACTIVE MODE** section), 2215 then this environment variable has no effect because bc(1) does not print 2216 the banner when not in interactive mode. 2217 2218 This environment variable overrides the default, which can be queried with 2219 the **-h** or **-\-help** options. 2220 2221**BC_SIGINT_RESET** 2222 2223: If bc(1) is not in interactive mode (see the **INTERACTIVE MODE** section), 2224 then this environment variable has no effect because bc(1) exits on 2225 **SIGINT** when not in interactive mode. 2226 2227 However, when bc(1) is in interactive mode, then if this environment 2228 variable exists and contains an integer, a non-zero value makes bc(1) reset 2229 on **SIGINT**, rather than exit, and zero makes bc(1) exit. If this 2230 environment variable exists and is *not* an integer, then bc(1) will exit on 2231 **SIGINT**. 2232 2233 This environment variable overrides the default, which can be queried with 2234 the **-h** or **-\-help** options. 2235 2236**BC_TTY_MODE** 2237 2238: If TTY mode is *not* available (see the **TTY MODE** section), then this 2239 environment variable has no effect. 2240 2241 However, when TTY mode is available, then if this environment variable 2242 exists and contains an integer, then a non-zero value makes bc(1) use TTY 2243 mode, and zero makes bc(1) not use TTY mode. 2244 2245 This environment variable overrides the default, which can be queried with 2246 the **-h** or **-\-help** options. 2247 2248**BC_PROMPT** 2249 2250: If TTY mode is *not* available (see the **TTY MODE** section), then this 2251 environment variable has no effect. 2252 2253 However, when TTY mode is available, then if this environment variable 2254 exists and contains an integer, a non-zero value makes bc(1) use a prompt, 2255 and zero or a non-integer makes bc(1) not use a prompt. If this environment 2256 variable does not exist and **BC_TTY_MODE** does, then the value of the 2257 **BC_TTY_MODE** environment variable is used. 2258 2259 This environment variable and the **BC_TTY_MODE** environment variable 2260 override the default, which can be queried with the **-h** or **-\-help** 2261 options. 2262 2263**BC_EXPR_EXIT** 2264 2265: If any expressions or expression files are given on the command-line with 2266 **-e**, **-\-expression**, **-f**, or **-\-file**, then if this environment 2267 variable exists and contains an integer, a non-zero value makes bc(1) exit 2268 after executing the expressions and expression files, and a zero value makes 2269 bc(1) not exit. 2270 2271 This environment variable overrides the default, which can be queried with 2272 the **-h** or **-\-help** options. 2273 2274**BC_DIGIT_CLAMP** 2275 2276: When parsing numbers and if this environment variable exists and contains an 2277 integer, a non-zero value makes bc(1) clamp digits that are greater than or 2278 equal to the current **ibase** so that all such digits are considered equal 2279 to the **ibase** minus 1, and a zero value disables such clamping so that 2280 those digits are always equal to their value, which is multiplied by the 2281 power of the **ibase**. 2282 2283 This never applies to single-digit numbers, as per the standard (see the 2284 **STANDARDS** section). 2285 2286 This environment variable overrides the default, which can be queried with 2287 the **-h** or **-\-help** options. 2288 2289# EXIT STATUS 2290 2291bc(1) returns the following exit statuses: 2292 2293**0** 2294 2295: No error. 2296 2297**1** 2298 2299: A math error occurred. This follows standard practice of using **1** for 2300 expected errors, since math errors will happen in the process of normal 2301 execution. 2302 2303 Math errors include divide by **0**, taking the square root of a negative 2304 number, using a negative number as a bound for the pseudo-random number 2305 generator, attempting to convert a negative number to a hardware integer, 2306 overflow when converting a number to a hardware integer, overflow when 2307 calculating the size of a number, and attempting to use a non-integer where 2308 an integer is required. 2309 2310 Converting to a hardware integer happens for the second operand of the power 2311 (**\^**), places (**\@**), left shift (**\<\<**), and right shift (**\>\>**) 2312 operators and their corresponding assignment operators. 2313 2314**2** 2315 2316: A parse error occurred. 2317 2318 Parse errors include unexpected **EOF**, using an invalid character, failing 2319 to find the end of a string or comment, using a token where it is invalid, 2320 giving an invalid expression, giving an invalid print statement, giving an 2321 invalid function definition, attempting to assign to an expression that is 2322 not a named expression (see the *Named Expressions* subsection of the 2323 **SYNTAX** section), giving an invalid **auto** list, having a duplicate 2324 **auto**/function parameter, failing to find the end of a code block, 2325 attempting to return a value from a **void** function, attempting to use a 2326 variable as a reference, and using any extensions when the option **-s** or 2327 any equivalents were given. 2328 2329**3** 2330 2331: A runtime error occurred. 2332 2333 Runtime errors include assigning an invalid number to any global (**ibase**, 2334 **obase**, or **scale**), giving a bad expression to a **read()** call, 2335 calling **read()** inside of a **read()** call, type errors, passing the 2336 wrong number of arguments to functions, attempting to call an undefined 2337 function, and attempting to use a **void** function call as a value in an 2338 expression. 2339 2340**4** 2341 2342: A fatal error occurred. 2343 2344 Fatal errors include memory allocation errors, I/O errors, failing to open 2345 files, attempting to use files that do not have only ASCII characters (bc(1) 2346 only accepts ASCII characters), attempting to open a directory as a file, 2347 and giving invalid command-line options. 2348 2349The exit status **4** is special; when a fatal error occurs, bc(1) always exits 2350and returns **4**, no matter what mode bc(1) is in. 2351 2352The other statuses will only be returned when bc(1) is not in interactive mode 2353(see the **INTERACTIVE MODE** section), since bc(1) resets its state (see the 2354**RESET** section) and accepts more input when one of those errors occurs in 2355interactive mode. This is also the case when interactive mode is forced by the 2356**-i** flag or **-\-interactive** option. 2357 2358These exit statuses allow bc(1) to be used in shell scripting with error 2359checking, and its normal behavior can be forced by using the **-i** flag or 2360**-\-interactive** option. 2361 2362# INTERACTIVE MODE 2363 2364Per the standard (see the **STANDARDS** section), bc(1) has an interactive mode 2365and a non-interactive mode. Interactive mode is turned on automatically when 2366both **stdin** and **stdout** are hooked to a terminal, but the **-i** flag and 2367**-\-interactive** option can turn it on in other situations. 2368 2369In interactive mode, bc(1) attempts to recover from errors (see the **RESET** 2370section), and in normal execution, flushes **stdout** as soon as execution is 2371done for the current input. bc(1) may also reset on **SIGINT** instead of exit, 2372depending on the contents of, or default for, the **BC_SIGINT_RESET** 2373environment variable (see the **ENVIRONMENT VARIABLES** section). 2374 2375# TTY MODE 2376 2377If **stdin**, **stdout**, and **stderr** are all connected to a TTY, then "TTY 2378mode" is considered to be available, and thus, bc(1) can turn on TTY mode, 2379subject to some settings. 2380 2381If there is the environment variable **BC_TTY_MODE** in the environment (see the 2382**ENVIRONMENT VARIABLES** section), then if that environment variable contains a 2383non-zero integer, bc(1) will turn on TTY mode when **stdin**, **stdout**, and 2384**stderr** are all connected to a TTY. If the **BC_TTY_MODE** environment 2385variable exists but is *not* a non-zero integer, then bc(1) will not turn TTY 2386mode on. 2387 2388If the environment variable **BC_TTY_MODE** does *not* exist, the default 2389setting is used. The default setting can be queried with the **-h** or 2390**-\-help** options. 2391 2392TTY mode is different from interactive mode because interactive mode is required 2393in the bc(1) standard (see the **STANDARDS** section), and interactive mode 2394requires only **stdin** and **stdout** to be connected to a terminal. 2395 2396## Prompt 2397 2398If TTY mode is available, then a prompt can be enabled. Like TTY mode itself, it 2399can be turned on or off with an environment variable: **BC_PROMPT** (see the 2400**ENVIRONMENT VARIABLES** section). 2401 2402If the environment variable **BC_PROMPT** exists and is a non-zero integer, then 2403the prompt is turned on when **stdin**, **stdout**, and **stderr** are connected 2404to a TTY and the **-P** and **-\-no-prompt** options were not used. The read 2405prompt will be turned on under the same conditions, except that the **-R** and 2406**-\-no-read-prompt** options must also not be used. 2407 2408However, if **BC_PROMPT** does not exist, the prompt can be enabled or disabled 2409with the **BC_TTY_MODE** environment variable, the **-P** and **-\-no-prompt** 2410options, and the **-R** and **-\-no-read-prompt** options. See the **ENVIRONMENT 2411VARIABLES** and **OPTIONS** sections for more details. 2412 2413# SIGNAL HANDLING 2414 2415Sending a **SIGINT** will cause bc(1) to do one of two things. 2416 2417If bc(1) is not in interactive mode (see the **INTERACTIVE MODE** section), or 2418the **BC_SIGINT_RESET** environment variable (see the **ENVIRONMENT VARIABLES** 2419section), or its default, is either not an integer or it is zero, bc(1) will 2420exit. 2421 2422However, if bc(1) is in interactive mode, and the **BC_SIGINT_RESET** or its 2423default is an integer and non-zero, then bc(1) will stop executing the current 2424input and reset (see the **RESET** section) upon receiving a **SIGINT**. 2425 2426Note that "current input" can mean one of two things. If bc(1) is processing 2427input from **stdin** in interactive mode, it will ask for more input. If bc(1) 2428is processing input from a file in interactive mode, it will stop processing the 2429file and start processing the next file, if one exists, or ask for input from 2430**stdin** if no other file exists. 2431 2432This means that if a **SIGINT** is sent to bc(1) as it is executing a file, it 2433can seem as though bc(1) did not respond to the signal since it will immediately 2434start executing the next file. This is by design; most files that users execute 2435when interacting with bc(1) have function definitions, which are quick to parse. 2436If a file takes a long time to execute, there may be a bug in that file. The 2437rest of the files could still be executed without problem, allowing the user to 2438continue. 2439 2440**SIGTERM** and **SIGQUIT** cause bc(1) to clean up and exit, and it uses the 2441default handler for all other signals. 2442 2443# SEE ALSO 2444 2445dc(1) 2446 2447# STANDARDS 2448 2449bc(1) is compliant with the IEEE Std 1003.1-2017 (“POSIX.1-2017”) specification 2450at https://pubs.opengroup.org/onlinepubs/9699919799/utilities/bc.html . The 2451flags **-efghiqsvVw**, all long options, and the extensions noted above are 2452extensions to that specification. 2453 2454In addition, the behavior of the **quit** implements an interpretation of that 2455specification that is different from all known implementations. For more 2456information see the **Statements** subsection of the **SYNTAX** section. 2457 2458Note that the specification explicitly says that bc(1) only accepts numbers that 2459use a period (**.**) as a radix point, regardless of the value of 2460**LC_NUMERIC**. 2461 2462# BUGS 2463 2464Before version **6.1.0**, this bc(1) had incorrect behavior for the **quit** 2465statement. 2466 2467No other bugs are known. Report bugs at https://git.gavinhoward.com/gavin/bc . 2468 2469# AUTHORS 2470 2471Gavin D. Howard <gavin@gavinhoward.com> and contributors. 2472