Here when g ( x ) = 0, the quotient is undefined.The quotient of division f and g : ( )( x ) =.For product f and g : ( fg )( x ) = f ( x )× g ( x ).For subtraction f and g : ( f – g )( x ) = f ( x ) – g ( x ).For sum f and g : ( f + g )( x ) = f ( x ) + g ( x ).These are the formulas implemented by the operations of the functions calculator. We need to determine the basic recognition of the basic functions we can implement in our operations. The basic formulas of combining functions: The solving functions calculator is best to find the solution of the algebraic functions, as it is simple to use. We can draw the graph of the function by finding x-intercept, y-intercept, slope value, and the curvature value. We can use the solving functions calculator to solve the functions. The functions are joined by the addition, subtraction,multiplication or division operation. In mathematics a function is defined as a relationship between the dependent and independent variable and defined algebraic. The operations on functions are essential to implement as you are calculating various arithmetic operations. The whole process of the combining of the functions can be easy if we have learned the basic formulas to combine the functions. We need to implement operations on functions and to combine the functions by the solving functions calculator. The execution times on battery power for composite numbers are a few seconds as long as the number does not have very big prime factors.Īn example: 999,999,999,999 executes in a few seconds while the smaller number 567,823,657,941 (=3^2*63,091,517,549) needs 40 seconds.Ī possible improvement to get rid of long execution times for composite numbers might to to further use PRM? to detect useless looping when the program tries to find non-existent factors of a big prime number.The function operations calculator helps us to implement the four basic like (addition, subtraction, multiplication, and division).When we are combining the functions by these operations, the domain and range of the new combined function can’t cross the domain of the shared elements. The changes reduces the program footprint from 463 byes to 269 bytes. The range can probably be further extended, but you might then hit some long execution times (See below). This also removes the need to save/recall the registers. Eliminated the use of register 00, so now all calculations are done in the stack.This also takes care of most of the initial checking that the number is valid. Added a call to PRM? so the program quickly detects a prime.In summary, I mainly made the following changes to FCTR: If the number is composite, it displays all prime factors for the number.If the number is a prime, it displays “Prime” in a few seconds.The program should run as-is on DM42, but with a few simple updates (see below) it can behave as follows when executed with a number in the X register: The program uses the 4-level stack, but switches to the big stack to create a List of MR-bases, so “Dynamic Stack Extension” must be enabled in SETUP.Ī useful companion to the PRM? function is Erik Ehrling’s HP42S factorisation program FCTR. The variables in stack are Result and D for LBL20 and Result and MR-base for LB元0. The rest of the program should be easy to understand. The two subroutines LBL20 (performs Miller-Rabin test for a MR-base) and LB元0 (calculates MR-base**D mod N with the fast Right-to-left binary method) might be somewhat hard to understand as they keep some variables in the stack instead of STO/RCLs. The program does not accept negative numbers and views the number 1 as neither prime nor composite in line with the common view among today’s mathematicians. The test range is up to 1E17 to enjoy fast execution time (a couple of seconds on battery power regardless of number size in the range) and no need for code to handle overflow conditions. It alters no user flags or registers including the Alpha and Stack registers. My program works like a built-in conditional function used in a program the next program line is skipped if test negative executed from the keyboard it reports the test result with Yes/No. The referenced Wikipedia article with the pseudo code fails to mention this. This bug appears because this deterministic Milller-Rabin test does not work when a MR-base mod N = 0. Using Boubker’s primality test program ( viewtopic.php?t=3073) as a base to explore the possibilities with the Free42 Extensions, I ended up with this program.īy the way, the thread briefly discusses a bug where the program, for instance, reports N=5 as NOT PRIME. I bought my HP42S in the summer 1994 and it is still in excellent condition and works fine.
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