User:Thebigh/mysandbox: Difference between revisions
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Some FRACTRAN programs in case we ever have a category for it |
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An evil wizard has trapped you in the stairwell of his castle. Your only hope of escape is to run up all 100 steps to reach the top, and you can run one step per second. Unfortunately the wizard uses magic to lengthen the staircase by five steps per second. The new steps are inserted randomly between existing steps, so if you're lucky some of them might be beneath you and not ahead of you. |
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==A+B== |
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Can you escape, or are you doomed to run up an ever-lengthening staircase forever? |
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Input a number of the form 2^a 3^b |
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Write a program to simulate your escape attempt. How are you doing after ten minutes? For every second between 600 and 609 seconds inclusive print the number of steps behind you and the number still ahead of you. |
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2/3 |
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The output is 2^(a+b) |
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==Empty program== |
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If you escaped, run 10,000 tests and print the average time taken and the average final length of the staircase. |
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A list of no fractions does nothing, then immediately stops. |
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==header|FreeBASIC== |
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<lang fractran></lang> |
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==Integer Sequence== |
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Given the number 1 as input the following program will, as its (3n-2)th step, produce the number 2^n. |
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randomize timer |
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<lang fractran> 2/3, 9/2, 2/1</lang> |
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dim as uinteger steps_behind = 0, stairs_length = 100, seconds, j |
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dim as uinteger seconds_tot, steps_tot |
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print "Seconds", "steps behind", "steps ahead" |
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for trial as uinteger = 1 to 10000 'We'll have the runner try this 10000 times |
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steps_behind = 0 'runner starts at the bottom |
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seconds = 0 'reset time taken |
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stairs_length = 100 'Staircase has 100 steps |
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while steps_behind < stairs_length 'if the runner hasn't reached the top |
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steps_behind += 1 'go up one step |
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for j = 1 to 5 'The evil wizard conjures another five steps |
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if int(rnd*stairs_length) < steps_behind then steps_behind += 1 |
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'there's a chance that a new step will be behind you |
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stairs_length += 1 'but either way the staircase is one step longer |
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next j |
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seconds += 1 'that all took one second |
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if trial = 1 and seconds >599 and seconds < 610 then print seconds, steps_behind, stairs_length - steps_behind |
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'for the first attempt, see how the runner is doing after ten minutes |
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wend |
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seconds_tot += seconds 'if the runner escaped, track the time taken and the length of the stairs |
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steps_tot += stairs_length |
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next trial |
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==Logical operations== |
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print "Average time taken: ";seconds_tot/10000; " seconds." |
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It's not so hard to code up all sixteen possible two-input logic gates, so here they are. The input is 2^a 3^b where a,b are zero or one and the output is 5^1 for true and 5^0 for false. Gates that return true when all their inputs are false additionally require the flag 11 to be set as input (ie 2^a*3^b*11)- any FRACTRAN program with the number 1 as input either stops without doing anything or loops forever. |
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print "Average final staircase length: ";steps_tot/10000; " steps." |
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'if you noticed that last number is about 100*exp(5), that's no coincidence</lang> |
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<lang fractran> |
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{{out}}<pre> |
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5/6, 1/2, 1/3 AND gate |
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5/6, 5/2, 5/3 OR gate |
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1/22, 5/11 NOT gate (uses 11 as a halt flag, result of 2^a*11 is 5^not(a)) |
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1/6, 5/2, 5/3 XOR gate |
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1/66, 5/22, 5/33, 5/11 NAND gate (needs 11 flag) |
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603 2045 1070 |
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5/66, 1/22, 1/33, 5/11 NXOR gate (needs flag) |
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604 2048 1072 |
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1/66, 1/22, 1/33, 5/11 NOR gate (needs flag) |
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605 2053 1072 |
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606 2055 1075 |
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so much for all the commonly encountered ones, but there's still another eight to go. Most are obscure and of limited utility. |
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607 2060 1075 |
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608 2064 1076 |
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1/2, 1/3 ZERO gate, returns false regardless of its input |
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1/6, 5/2, 1/3 "A and not B", true only if A is true and B is false |
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Average time taken: 2921.9457 seconds. |
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5/2, 1/3 A , returns the state of A regardless of B |
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Average final staircase length: 14709.7285 steps. |
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1/6, 1/2, 5/3 "B and not A", true only if B is true and A is false |
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1/2, 5/3 B , returns the state of B regardless of A |
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1/66, 1/33, 5/11 "A or not B" (needs flag) |
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1/66, 1/22, 5/11 "B or not A" (needs flag) |
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5/66, 5/22, 5/33, 5/11 ONE gate, returns true regardless of its input, needs flag |
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NOT A and NOT B are omitted because the one-input NOT gate is already up there. |
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</lang> |
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==Sort three variables== |
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FRACTRAN's only data type is positive integers. Suppose (a,b,c) are the integers to be sorted. Give the following as input: |
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2^a 3^b 5^c |
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<lang fractran> |
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1001/30, 143/6, 143/10, 143/15, 13/2, 13/3, 13/5 |
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</lang> |
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Returns 7^A 11^B 13^C where (A,B,C) are (a,b,c) in ascending order. |
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Latest revision as of 11:27, 28 November 2021
Some FRACTRAN programs in case we ever have a category for it
A+B
Input a number of the form 2^a 3^b <lang fractran> 2/3 </lang> The output is 2^(a+b)
Empty program
A list of no fractions does nothing, then immediately stops. <lang fractran></lang>
Integer Sequence
Given the number 1 as input the following program will, as its (3n-2)th step, produce the number 2^n. <lang fractran> 2/3, 9/2, 2/1</lang>
Logical operations
It's not so hard to code up all sixteen possible two-input logic gates, so here they are. The input is 2^a 3^b where a,b are zero or one and the output is 5^1 for true and 5^0 for false. Gates that return true when all their inputs are false additionally require the flag 11 to be set as input (ie 2^a*3^b*11)- any FRACTRAN program with the number 1 as input either stops without doing anything or loops forever.
<lang fractran> 5/6, 1/2, 1/3 AND gate 5/6, 5/2, 5/3 OR gate 1/22, 5/11 NOT gate (uses 11 as a halt flag, result of 2^a*11 is 5^not(a)) 1/6, 5/2, 5/3 XOR gate 1/66, 5/22, 5/33, 5/11 NAND gate (needs 11 flag) 5/66, 1/22, 1/33, 5/11 NXOR gate (needs flag) 1/66, 1/22, 1/33, 5/11 NOR gate (needs flag)
so much for all the commonly encountered ones, but there's still another eight to go. Most are obscure and of limited utility.
1/2, 1/3 ZERO gate, returns false regardless of its input 1/6, 5/2, 1/3 "A and not B", true only if A is true and B is false 5/2, 1/3 A , returns the state of A regardless of B 1/6, 1/2, 5/3 "B and not A", true only if B is true and A is false 1/2, 5/3 B , returns the state of B regardless of A 1/66, 1/33, 5/11 "A or not B" (needs flag) 1/66, 1/22, 5/11 "B or not A" (needs flag) 5/66, 5/22, 5/33, 5/11 ONE gate, returns true regardless of its input, needs flag
NOT A and NOT B are omitted because the one-input NOT gate is already up there. </lang>
Sort three variables
FRACTRAN's only data type is positive integers. Suppose (a,b,c) are the integers to be sorted. Give the following as input: 2^a 3^b 5^c <lang fractran> 1001/30, 143/6, 143/10, 143/15, 13/2, 13/3, 13/5 </lang> Returns 7^A 11^B 13^C where (A,B,C) are (a,b,c) in ascending order.