bc [ lwsqv ] [longoptions] [ file … ]
Supports arbitrary precision numbers.
Executes files
on the command line, then reads from the standard input and processes interactively.
mathlib  Sets scale=20 loads math library.

warn  Give warnings for extensions to POSIX bc. 
standard  POSIX 
quiet  Do not print the welcome. 
version  Display version number, short copyright and quit. see warranty.bc 1.06 Copyright 19911994, 1997, 1998, 2000 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. 
Suggestion: In .profile
set up alias bc='/usr/bin/bc q ~/.bin/bc.ini' and
create ~/.bin/bc.ini
containing :scale=2
then echo 5/6bc
will output .83
length
: number of significant digits
scale
: number of digits after the dot. Default:0̸!1.23456
has a length of 6 and scale of 5. 1234.567
has a length of 7 and a scale of 3.
9
,A
F
. (NOT lowercase, which are variables).
ibase
. (i.e. A
= 10̸.)ibase
, are assigned the value of ibase
1 to each digit,ibase
=10̸, num=FF8CB
assigns 99899
to num.
a, f, x1, y, index23
, loop_counter
, x
[ ]
.
scale
defines how some operations use digits after the dot. Default 0̸. scale
, the numbers and the operation performed.scale
of the maximum scale of the expressions involved, unless specifically mentioned.1.234 in the asignment has a scale of 3 so result has scale of 3.scale=2 a=1.234 a 1.234
last
has the value of the last number output.
Some implementations also permit using dot (.
)
(extension)
history
size of readline history, 1 max, (not retained across sesssions.)
ibase
and obase
base for input and output. Default base 10, maximun ibase
16.obase=F+1
always sets obase
to 16 (i.e. hexadecimal)ibase=A
always sets ibase
to 10.ibase
is 16, ibase=10
_{16} keeps ibase
to 16 ! ibase
is 2, ibase=10
_{2} keeps ibase
to 2 !obase
is not synchronized with ibase
, Example: obase=2;binary=9;binary
displays 1001
!
For obase
s greater than 16, a multidigit, base 10 format is used.
ibase=F+1 obase=A FFFF 65535 obase=64 FFFF 06 55 35 ibase=A 99 01 35 1*64_{10} + 35_{10} 64*64 01 00 00 1*64*64_{10}
/*
and */
surround a comment, may start anywhere, appear as a single space in the input,
delimit other input items, can be multiline #
begins a comment which continues to the end of line.
 expr  negation of expr .

++var  incremented by one, the new value is the result of the expression. 
var  decremented by one, the new value is the result of the expression. 
var++  The result of the expression is the value of var , then var is incremented by one. 
var  The result of the expression is the value of var , then var is decremented by one. 
expr + expr  sum 
expr  expr  difference 
expr * expr  product 
expr / expr  divide. The scale of the result is scale !

expr1 % expr2  remainder computed by:

exprn ^ Iexprx  exprn raised to the integer Iexprx . If the exponent is negative: the scale of the result is scale . If the exponent is positive the scale of the result is the minimum of the scale of the first expression times the value of the exponent and the maximum of scale and the scale of the first expression. (example:. scale(a^b) = min(scale(a)*b, max( scale, scale(a))) .) exprn^0 returns 1

( expr )  alters precedence 
var = expr  assignment 
var op= expr example: sum += entry  equivalent to "var = var op expr " .var is evaluated only once. This can make a difference if var is an array.

Relational expressions may appear in an expression.
(POSIX bc requires that relational expressions are used only in if, while, and for statements and that only one relational test may be done in them.)
Relational operators  
result is 1 (true) if  
expr1 < expr2  expr1 is strictly less than expr2. 
expr1 <= expr2  expr1 is less than or equal to expr2. 
expr1 > expr2  expr1 is strictly greater than expr2. 
expr1 >= expr2  expr1 is greater than or equal to expr2. 
 expr1 is equal to expr2. 
 expr1 is not equal to expr2. 
Boolean operators (POSIX bc does NOT have boolean operations).  
!expr  1 if expr equals 0; 0 if expr is nonzero

expr && expr  both expr1 and expr2 are nonzero.

expr1  expr2  either expr1 or expr2 is nonzero.

Expression precedence (highest to lowest)
++   nonassociative 
Using relational and logical operators with assignment expressions evaluate differently than in many other languages.
Most programmers expect the result of "3 < 5" (the value 1 (true)) is assigned to 
^{†}  nonassociative  
^   
* / %  left associative  
+   left associative  
= += = …^{†}   
< <= > …^{†}  left associative ^{‡}  
!  nonassociative  
&&  left associative  
  left associative 
&  ^ &&  << >> &= = ^= &&= = <<= >>= ?:Are not available. Use easyOnLineConverter.com
appear as "name(parameters)".
read ( )  read a value from standard input . 
 number of significant digits . 
scale ( expression )  number of digits after the dot (same as special variable scale ).scale=5 1/2 .50000 scale(1/2) 5 scale(1/3) 5 scale(.5) 1 
sqrt ( expression )  square root. If the expression is negative, a run time error is generated.Runtime error (func=(main), adr=4): Square root of a negative number 
User defined functions provide a method of defining a computation that can be executed later which return a value to the caller.
A function definition :
define name ( [parameter[, …] ] ) { 
[ auto name [ , … ]] ; statement_list }
A function call:
name(parameters).
Parameters can be numbers or arrays. Numbers are call_by value (i.e. cannot be changed within the function).
Arrays are only call_by variable. Arrays are specified in the parameter definition by the notation name[]
.
In the function call, parameters are full expressions for number parameters. The same notation is
used for passing arrays as for defining array parameters. The named array is passed by variable to the function.
Variables are global (i.e. function B can access variables in the main as well as in function A) unless included in
auto
list.
Auto variables have their current values pushed onto a stack at the start of the function, initialized to zero
and used throughout the execution of the function.
At function exit, these variables are popped so that the original value (at the time of
the function call) of these variables are restored.
( The parameters are auto variables that are initialized to a value provided in the function call.)
Auto variables are subcall accessable, i.e. if function A calls function B, B may access function A's auto variables, unless
function B has declared them auto variables.
Constants in the function body will be converted using the value of ibase
at the time of the call.
Changes to ibase
will be ignored during the execution of the function except for read()
, which
will uses the current value of ibase
for conversion of numbers.
Function definitions are "dynamic" i.e. a function is undefined until a definition is encountered (aka no forward referencing).
That definition is used until another definition function for name
is encountered.
\
continutes a statment. expression 
 
"string"  string is output. No newline is appended.  
print list 
list is a list of strings and expressions separated by commas. No newline is appended. Expressions are evaluated, their value is printed and assigned to last . Strings may contain: \a (alert or bell), \b (backspace), \f (form feed), \n (newline),
\r (carriage return), \q (quotes, i.e. " ),\t (tab), and \\ (backslash).  
{ statement_list }  A compound statement, allows multiple statements to be grouped together.  
if ( expression ) statement1 [else statement2]
 
Evaluates expression and if expression is nonzero, statement1 is executed. if expression is 0, then statement2 is executed.
 
while ( expression ) statement  
execute statement while expression is nonzero. It evaluates expression before each execution of statement. Termination of the loop is caused by a zero expression value or the execution of a break
 
for ( [expression1] ; [expression2] ;
[expression3] ) statement
 
Controls repeated execution of statement. expression1 is evaluated before the loop. expression2 is evaluated before each execution of statement, if nonzero, statement is evaluated. If it is zero, the loop is terminated. After each execution of statement ,
expression3 is evaluated before the reevaluation of expression2. If expression1 or expression3 are missing, nothing is evaluated at the
point they would be evaluated.If expression2 is missing, it is the same as substituting the value 1 for expression2 .(POSIX bc requires all three expressions.)  
break  exits the most recent enclosing while or for .  
continue  causes the most recent enclosing for to start the next iteration.  
halt  causes bc to quit Note: if (0 == 1) halt will not cause bc to terminate because the halt is not executed.  
 Return the value of the expression from a function, default 0̸ .
 
PSEUDO STATEMENTS  
limits  display limits of the local version . an extension. BC_BASE_MAX = 2147483647 BC_DIM_MAX = 65535 BC_SCALE_MAX = 2147483647 BC_STRING_MAX = 2147483647 MAX Exponent = 9223372036854775807 Number of vars = 32767  
quit  
warranty  outputs version and a long nonwarranty notice. 
Due to the fact that auto variables and parameters are pushed onto a stack, bc supports recursive functions.
mathlib
, a math library is loaded and
the default scale
is set to 20. s (r)
sine of r, r is in radians. c (r)
cosine of r, r is in radians. a (x)
arctangent of x, arctangent returns radians. l (x)
natural logarithm of x. e (x)
exponential function of raising e to the value x. j (n,x)
bessel function of integer order n of x. $pi
using acrtan of 1. pi=$(echo "4*a(1)"  /usr/bin/bc l) # i.e. arcTan(1 radian) π/4 echo $pi 3.14159265358979323844
The exponential function used in the math library, written in POSIX bc.
scale = 20 /* Uses the fact that e^x = (e^(x/2))^2 When x is small enough, we use the series: e^x = 1 + x + x^2/2! + x^3/3! + ...
*/ define e(x) { auto a, d, e, f, i, m, v, z /* Check the sign of x. */ if (x<0) { m = 1 x = x } /* Precondition x. */ z = scale; scale = 4 + z + .44*x; while (x > 1) { f += 1; x /= 2; } /* Initialize the variables. */ v = 1+x a = x d = 1 for (i=2; 1; i++) { e = (a *= x) / (d *= i) if (e == 0) { if (f>0) while (f) v = v*v; scale = z if (m) return (1/v); return (v/1); } v += e } }
scale=2 print "\nCheck book program!\n" print " Remember, deposits are negative transactions.\n" print " Exit by a 0 transaction.\n\n" print "Initial balance? "; bal = read() bal /= 1 print "\n" while (1) { "current balance = "; bal "transaction? "; trans = read() if (trans == 0) break; bal = trans bal /= 1 } quitDefinition of the recursive factorial function.
define f (x) { if (x <= 1) return (1); return (f(x1) * x); } a=(1/3)^1 scale=4 a 3.0003 scale=5 a 3.00003
history
is the number of lines of
history retained. The default, 1 unlimited, 0 disables the history.
Differences & extensions
There exists GNU bc, man , brew install although it does not seem to have any(much) additional functionallity.
A single process which parses and runs a byte code translation of the program. c outputs the byte code, for debugging the parser and preparing the math library.  
LANG  not conform POSIX processing of the LANG environment variable and all environment
variables starting with LC_ . 
names  Traditional and POSIX bc have single letter names for functions,
variables and arrays. They have been extended to be multicharacter names that start with a letter and may contain letters,
numbers and the underscore character. 
Strings  Strings are not allowed to contain NUL characters. POSIX: all characters must be included in strings. 
last  POSIX bc does not have a last variable. Some implementations use the period (.) .

comparisons 
POSIX allows comparisons only in the if and while
statements, and the second expression of the for statement. Only one relational operation is allowed in each of those statements. 
if statement, else clause  POSIX bc does not have an else clause. 
for statement  POSIX bc requires all expressions to be present in the for statement. 
&&, , !  POSIX bc does not have logical operators. , read function, print or continue statement 
array parameters  POSIX bc does not (currently) support array parameters in full. The POSIX grammar allows for arrays in function definitions, but does not provide a method to specify an array as a parameter. Traditional implementations of bc have only call by value array parameters. 
=+, =, =*, =/, =%, =^ 
POSIX bc does not require these "old style" assignment operators
to be defined. This version may allow these "old style" assignments. Use the limits statement to see if the installed version
supports them. If it does support the "old style" assignment
operators, the statement "a = 1" will decrement a by 1 instead of setting a to the value 1. 
spaces in numbers  Not allowed. In some implementations, "x=1 3" assigns 13 to x. 
errors and execution 
The code will be executed when syntax and other errors are found in the program. If a syntax error is found in a function definition, error recovery tries to find the beginning of a statement and continue to parse the function. Once a syntax error is found in the function, the function will not be callable and becomes undefined. Syntax errors in the interactive execution code will invalidate the current execution block. The execution block is terminated by an end of line that appears after a complete sequence of statements. For example, a = 1 b = 2has two execution blocks and { a = 1 b = 2 }has one execution block. Any runtime error will terminate the execution of the current execution block. A runtime warning will not terminate the current execution block. 
limits
statment:
BC_BASE_MAX = 2147483647 0x7FFFFFF BC_DIM_MAX = 65535 BC_SCALE_MAX = 2147483647 BC_STRING_MAX = 2147483647 MAX Exponent = 9223372036854775807 Number of vars = 32767
BC_BASE_MAX  maximum output base is currently set at 999. The maximum input base is 16. 
BC_DIM_MAX  arbitrary limit of 65535 as distributed. 
BC_SCALE_MAX  number of digits after the dot is limited to INT_MAX digits.
The number of digits before the dot is limited to INT_MAX digits.

BC_STRING_MAX  limit on the number of characters in a string is INT_MAX characters. 
exponent  value of the exponent in the raise operation (^) is limited to LONG_MAX. 
multiply  multiply routine may yield incorrect results if a number has more than LONG_MAX / 90 total digits. For 32 bit longs, this number is 23,860,929 digits. 
code size  Each function and the "main" program are limited to 16384 bytes of compiled byte code each. BC_MAX_SEGS can be changed to have more than 16 segments of 1024 bytes. 
variable names  unique names for each of simple variables, arrays and functions. 
$POSIXLY_CORRECT  same as s

$BC_ENV_ARGS  Format is the same as the command line arguments, processed first, so any files listed in the environent arguments
are processed before any command line argument files. This
allows the user to set up "standard" options and files to be processed at every invocation. Files in the environment variables typically contain frequently used, custom function definitions. 
BC_LINE_LENGTH  Length of an output line for numbers. includes the backslash and new line characters for long numbers. 
/usr/local/lib/libmath.b.
may be /lib/libmath.b.
)