AGA Toolkit '97

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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 builtin' 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 assoc 0 create new association array 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 base 0-1 get/set default output base 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 hash 1+ return non-negative hash value for one or more values 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 isassoc 1 whether a value is an association 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]); The hash function returns a relatively small non-negative integer for one or more input values. The hash values should not be used across runs of the calculator, since the algorithms used to generate the hash value may change with different versions of the calculator. The base function allows one to specify how numbers should be printer. The base function provides a numeric shorthand to the config("mode") interface. With no args, base() will return the current mode. With 1 arg, base(val) will set the mode according to the arg and return the previous mode. The following convention is used to declare modes: base config value string 2 "binary" binary fractions 8 "octal" octal fractions 10 "real" decimal floating point 16 "hex" hexadecimal fractions -10 "int" decimal integer 1/3 "frac" decimal fractions 1e20 "exp" decimal exponential For convenience, any non-integer value is assumed to mean "frac", and any integer >= 2^64 is assumed to mean "exp".