calculator

This is a calculator that has some special functions. These function include Length of calculation is limited only by the hardware it is using. I have 3.5 terabytes of free space that I plan to use with this calculator. Addition, subtraction, multiplication and division can be limited by the length of a number depending on the system so the number can be stored on the hard drive. I know it can be slow but I have little other options in this particular situation. The final answer is written to a text file. This is so it doesn't have to be instantly displayed on the screen which can slow things down quite a bit. When the calculation is complete the program should displayed a calculation complete message. If the answer is over 100 mb's big it should be saved into multiple files. So for every 100 mb's there would be a part. An example would be 300 mb's 3 text documents part 1,2, and 3. If there are multiple answers such as prime numbers that have been generated they should be separated by a ";" I have some algorithms that I want used for the different operations. Addition: I wasn't able to find any algorithms that increase the speed of addition subtraction: Same as addition multiplication: There are 4 algorithms dependent on range. Their range is explained in better detail on wikipedia but to give you an idea they go from good for smaller calculations, good for bigger calculations then the previous,ect. The 4 algorithms are Karatsuba algorithm ? Toom-Cook multiplication ? Sch?nhage-Strassen algorithm ? F?rer's algorithm. The last functions are described below. ## Deliverables division:Here is an excerpt from wikipedia that I think explains things perfectly for division. "Methods designed for hardware implementation generally do not scale to integers with thousands or millions of decimal digits; these frequently occur, for example, in modular reductions in cryptography. For these large integers, more efficient division algorithms transform the problem to use a small number of multiplications, which can then be done using an asymptotically efficient multiplication algorithm such as Toom-Cook multiplication or the Sch?nhage-Strassen algorithm. Examples include reduction to multiplication by Newton's method as described above[5] as well as the slightly faster Barrett reduction algorithm.[6] Newton's method's is particularly efficient in scenarios where one must divide by the same divisor many times, since after the initial Newton inversion only one (truncated) multiplication is needed for each division." Using multiplication in the way that they described above with the algorithms we have for multiplication will be good for speed sake. powers:This is one of the best algorithms I have seen for powers and the best part is that it can help with factorial functions which I explain in more detail below. Here is the algorithm and make sure to read the users comments as well [login to view URL] square root:The work listed at this website is the best I have seen so far [login to view URL] factorials: This function can be difficult at times and there is many ways to tackle this algorithm but I want to use the method described at this page [login to view URL] By finding the factors of the factorial in combination with the powers algorithm we will be using we should be able to make a very powerful factorial function that is very fast. prime numbers This will be the most complex. It describes a variant of sunadrams sieve that I have made that should help find prime numbers given in a certain range. Here is how this should work. Enter a number. The program then tries to find the two odd square numbers that the number is in. My best suggestion for this is to use odd palindrome. For instance 11*11=121 101*101=10201 1001*1001= 1002001 Easy to predict and to scale from. Once the two squares have been found we get more complicated. If for instance we wanted to have a range between 121 which we will give for this example the variable of "T" and 169 which we will give in this example the variable "U" we know that the square root of the lower numbers is 11. We then take the number that the odd number would correlate with. To explain better imagine we are counting all the odd numbers except for 1 so 3,5,7,9,11,13 1,2,3,4,5, 6 A better way to say this is to run the square root through this algorithm lower square root (11 in our example) = x x-1=y y/2=z Now we have variable z=5 We now need to do two calculations using z and I will explain why after I show these calculations 6*z+3=A 4*z+2=B Ok these calculations are important for a few reasons. variable "A" in our example is equal to 33. Variable "B" in our example is equal to 22. Now we need to subtract "b" until T is equal to "A". The reason that we subtract until it is equal to "A" is because every difference is actually important. prevent us from getting too confused I will just list the differences without giving them variables. Just know that the numbers are important to the calculations and will become important later. so 121-22=99 99-22=77 77-22=55 55-22=33 Good now for each of these values we are going to add variable b until they are past variable "U". We need to keep all these values. However something important happens after we do this with variable T. We subtract 4 from b. So here listed out is what we do. We start with variable T. 121+22=143 143+22=165 165+22=187 Ok now we subtract 4 from b getting 18. Now we move on to 99 99+18=117 117+18=135 135+18=153 153+18=171 subtract 4 from 18 getting 14. move on to 77 77+14=91 91+14=105 105+14=119 119+14=133 133+14=147 147+14=161 161+14=175 subtract 4 from 14 getting 10. move on to 55 55+10=65 65+10=75 75+10=85 85+10=95 95+10=105 105+10=115 115+10=125 125+10=135 135+10=145 145+10=155 155+10=165 165+10=175 subtract 4 from 10 getting 6. 6 will always be the last value you ever have for this variable. move on to 33 33+6=39 39+6=45 45+6=51 51+6=57 57+6=63 63+6=69 69+6=75 75+6=81 81+6=87 87+6=93 93+6=99 99+6=105 105+6=111 111+6=117 117+6=123 123+6=129 129+6=135 135+6=141 141+6=147 147+6=153 153+6=159 159+6=165 165+6=171 Great now we take all the numbers that we have gathered which fall in the range of the T and U variables These numbers include 33's list 123 129 135 141 147 153 159 165 55's list 125 135 145 155 165 77's list 133 147 161 99's list 135 153 121's list 143 165 We can get rid of all duplicate numbers and combine all the lists. 121 123 125 129 133 135 141 143 145 147 153 155 159 161 165 169 Now the program will generate a list of all missing odd numbers that lie between the two squares 127 131 137 139 149 151 157 163 167 These numbers just listed are 100% guaranteed to be prime. The prime numbers should be saved in a text document and when they are done the screen should display how many prime numbers there were. This method isn't fast for small numbers but certain ranges for very large numbers it can do fairly well. While working on very large numbers this can obviously be computationally problematic however if you know the range of numbers we can shorten the values a bit. For instance if I wanted to work with numbers that had 100 digits in them but only 6 digits are being changed everytime we find a new number the program could store the numbers that will not be worked on for awhile on the harddrive until they need to be altered. I hope that makes sense. If you have any questions please feel free to let me know.