4.4BSD/usr/src/contrib/calc-1.26.4/help/builtin
Builtin functions
There is a large number of built-in functions. Many of the
functions work on several types of arguments, whereas some only
work for the correct types (e.g., numbers or strings). In the
following description, this is indicated by whether or not the
description refers to values or numbers. This display is generated
by the 'show builtins' command.
Name Args Description
abs 1-2 absolute value within accuracy b
acos 1-2 arccosine of a within accuracy b
acosh 1-2 hyperbolic arccosine of a within accuracy b
append 2 append value to end of list
appr 1-2 approximate a with simpler fraction to within b
arg 1-2 argument (the angle) of complex number
asin 1-2 arcsine of a within accuracy b
asinh 1-2 hyperbolic arcsine of a within accuracy b
atan 1-2 arctangent of a within accuracy b
atan2 2-3 angle to point (b,a) within accuracy c
atanh 1-2 hyperbolic arctangent of a within accuracy b
avg 1+ arithmetic mean of values
bround 1-2 round value a to b number of binary places
btrunc 1-2 truncate a to b number of binary places
ceil 1 smallest integer greater than or equal to number
cfappr 1-2 approximate a within accuracy b using
continued fractions
cfsim 1 simplify number using continued fractions
char 1 character corresponding to integer value
cmp 2 compare values returning -1, 0, or 1
comb 2 combinatorial number a!/b!(a-b)!
config 1-2 set or read configuration value
conj 1 complex conjugate of value
cos 1-2 cosine of value a within accuracy b
cosh 1-2 hyperbolic cosine of a within accuracy b
cp 2 Cross product of two vectors
delete 2 delete element from list a at position b
den 1 denominator of fraction
det 1 determinant of matrix
digit 2 digit at specified decimal place of number
digits 1 number of digits in number
dp 2 Dot product of two vectors
epsilon 0-1 set or read allowed error for real calculations
eval 1 Evaluate expression from string to value
exp 1-2 exponential of value a within accuracy b
fcnt 2 count of times one number divides another
fib 1 Fibonacci number F(n)
frem 2 number with all occurrences of factor removed
fact 1 factorial
fclose 1 close file
feof 1 whether EOF reached for file
ferror 1 whether error occurred for file
fflush 1 flush output to file
fgetc 1 read next char from file
fgetline 1 read next line from file
files 0-1 return opened file or max number of opened files
floor 1 greatest integer less than or equal to number
fopen 2 open file name a in mode b
fprintf 2+ print formatted output to opened file
frac 1 fractional part of value
gcd 1+ greatest common divisor
gcdrem 2 a divided repeatedly by gcd with b
highbit 1 high bit number in base 2 representation
hmean 1+ harmonic mean of values
hypot 2-3 hypotenuse of right triangle within accuracy c
ilog 2 integral log of one number with another
ilog10 1 integral log of a number base 10
ilog2 1 integral log of a number base 2
im 1 imaginary part of complex number
insert 3 insert value c into list a at position b
int 1 integer part of value
inverse 1 multiplicative inverse of value
iroot 2 integer b'th root of a
iseven 1 whether a value is an even integer
isfile 1 whether a value is a file
isint 1 whether a value is an integer
islist 1 whether a value is a list
ismat 1 whether a value is a matrix
ismult 2 whether a is a multiple of b
isnull 1 whether a value is the null value
isnum 1 whether a value is a number
isobj 1 whether a value is an object
isodd 1 whether a value is an odd integer
isqrt 1 integer part of square root
isreal 1 whether a value is a real number
isset 2 whether bit b of abs(a) (in base 2) is set
isstr 1 whether a value is a string
isrel 2 whether two numbers are relatively prime
issimple 1 whether value is a simple type
issq 1 whether or not number is a square
istype 2 whether the type of a is same as the type of b
jacobi 2 -1 => a is not quadratic residue mod b
1 => b is composite, or a is quad residue of b
lcm 1+ least common multiple
lcmfact 1 lcm of all integers up till number
lfactor 2 lowest prime factor of a in first b primes
list 0+ create list of specified values
ln 1-2 natural logarithm of value a within accuracy b
lowbit 1 low bit number in base 2 representation
ltol 1-2 leg-to-leg of unit right triangle (sqrt(1 - a^2))
matdim 1 number of dimensions of matrix
matfill 2-3 fill matrix with value b (value c on diagonal)
matmax 2 maximum index of matrix a dim b
matmin 2 minimum index of matrix a dim b
mattrans 1 transpose of matrix
max 1+ maximum value
meq 3 whether a and b are equal modulo c
min 1+ minimum value
minv 2 inverse of a modulo b
mmin 2 a mod b value with smallest abs value
mne 3 whether a and b are not equal modulo c
near 2-3 sign of (abs(a-b) - c)
norm 1 norm of a value (square of absolute value)
null 0 null value
num 1 numerator of fraction
ord 1 integer corresponding to character value
param 1 value of parameter n (or parameter count if n
is zero)
perm 2 permutation number a!/(a-b)!
pfact 1 product of primes up till number
pi 0-1 value of pi accurate to within epsilon
places 1 places after decimal point (-1 if infinite)
pmod 3 mod of a power (a ^ b (mod c))
polar 2-3 complex value of polar coordinate (a * exp(b*1i))
poly 2+ (a1,a2,...,an,x) = a1*x^n+a2*x^(n-1)+...+an
pop 1 pop value from front of list
power 2-3 value a raised to the power b within accuracy c
ptest 2 probabilistic primality test
printf 1+ print formatted output to stdout
prompt 1 prompt for input line using value a
push 2 push value onto front of list
quomod 4 set c and d to quotient and remainder of a
divided by b
rcin 2 convert normal number a to REDC number mod b
rcmul 3 multiply REDC numbers a and b mod c
rcout 2 convert REDC number a mod b to normal number
rcpow 3 raise REDC number a to power b mod c
rcsq 2 square REDC number a mod b
re 1 real part of complex number
remove 1 remove value from end of list
root 2-3 value a taken to the b'th root within accuracy c
round 1-2 round value a to b number of decimal places
rsearch 2-3 reverse search matrix or list for value b
starting at index c
runtime 0 user mode cpu time in seconds
scale 2 scale value up or down by a power of two
search 2-3 search matrix or list for value b starting
at index c
sgn 1 sign of value (-1, 0, 1)
sin 1-2 sine of value a within accuracy b
sinh 1-2 hyperbolic sine of a within accuracy b
size 1 total number of elements in value
sqrt 1-2 square root of value a within accuracy b
ssq 1+ sum of squares of values
str 1 simple value converted to string
strcat 1+ concatenate strings together
strlen 1 length of string
strprintf 1+ return formatted output as a string
substr 3 substring of a from position b for c chars
swap 2 swap values of variables a and b (can be dangerous)
tan 1-2 tangent of a within accuracy b
tanh 1-2 hyperbolic tangent of a within accuracy b
trunc 1-2 truncate a to b number of decimal places
xor 1+ logical xor
The config function sets or reads the value of a configuration
parameter. The first argument is a string which names the parameter
to be set or read. If only one argument is given, then the current
value of the named parameter is returned. If two arguments are given,
then the named parameter is set to the value of the second argument,
and the old value of the parameter is returned. Therefore you can
change a parameter and restore its old value later. The possible
parameters are explained in the next section.
The scale function multiplies or divides a number by a power of 2.
This is used for fractional calculations, unlike the << and >>
operators, which are only defined for integers. For example,
scale(6, -3) is 3/4.
The quomod function is used to obtain both the quotient and remainder
of a division in one operation. The first two arguments a and b are
the numbers to be divided. The last two arguments c and d are two
variables which will be assigned the quotient and remainder. For
nonnegative arguments, the results are equivalent to computing a//b
and a%b. If a is negative and the remainder is nonzero, then the
quotient will be one less than a//b. This makes the following three
properties always hold: The quotient c is always an integer. The
remainder d is always 0 <= d < b. The equation a = b * c + d always
holds. This function returns 0 if there is no remainder, and 1 if
there is a remainder. For examples, quomod(10, 3, x, y) sets x to 3,
y to 1, and returns the value 1, and quomod(-4, 3.14159, x, y) sets x
to -2, y to 2.28318, and returns the value 1.
The eval function accepts a string argument and evaluates the
expression represented by the string and returns its value.
The expression can include function calls and variable references.
For example, eval("fact(3) + 7") returns 13. When combined with
the prompt function, this allows the calculator to read values from
the user. For example, x=eval(prompt("Number: ")) sets x to the
value input by the user.
The digit and isset functions return individual digits of a number,
either in base 10 or in base 2, where the lowest digit of a number
is at digit position 0. For example, digit(5678, 3) is 5, and
isset(0b1000100, 2) is 1. Negative digit positions indicate places
to the right of the decimal or binary point, so that for example,
digit(3.456, -1) is 4.
The ptest function is a primality testing function. The first
argument is the suspected prime to be tested. The second argument
is an iteration count. The function returns 0 if the number is
definitely not prime, and 1 is the number is probably prime. The
chance of a number which is probably prime being actually composite
is less than 1/4 raised to the power of the iteration count. For
example, for a random number p, ptest(p, 10) incorrectly returns 1
less than once in every million numbers, and you will probably never
find a number where ptest(p, 20) gives the wrong answer.
The functions rcin, rcmul, rcout, rcpow, and rcsq are used to
perform modular arithmetic calculations for large odd numbers
faster than the usual methods. To do this, you first use the
rcin function to convert all input values into numbers which are
in a format called REDC format. Then you use rcmul, rcsq, and
rcpow to multiply such numbers together to produce results also
in REDC format. Finally, you use rcout to convert a number in
REDC format back to a normal number. The addition, subtraction,
negation, and equality comparison between REDC numbers are done
using the normal modular methods. For example, to calculate the
value 13 * 17 + 1 (mod 11), you could use:
p = 11;
t1 = rcin(13, p);
t2 = rcin(17, p);
t3 = rcin(1, p);
t4 = rcmul(t1, t2, p);
t5 = (t4 + t3) % p;
answer = rcout(t5, p);
The swap function exchanges the values of two variables without
performing copies. For example, after:
x = 17;
y = 19;
swap(x, y);
then x is 19 and y is 17. This function should not be used to
swap a value which is contained within another one. If this is
done, then some memory will be lost. For example, the following
should not be done:
mat x[5];
swap(x, x[0]);