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3
Task/Zeckendorf-arithmetic/00-META.yaml
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3
Task/Zeckendorf-arithmetic/00-META.yaml
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---
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from: http://rosettacode.org/wiki/Zeckendorf_arithmetic
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note: Arithmetic operations
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70
Task/Zeckendorf-arithmetic/00-TASK.txt
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70
Task/Zeckendorf-arithmetic/00-TASK.txt
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This task is a ''total immersion'' zeckendorf task; using decimal numbers will attract serious disapprobation.
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The task is to implement addition, subtraction, multiplication, and division using [[Zeckendorf number representation]]. [[Zeckendorf number representation#Using_a_C.2B.2B11_User_Defined_Literal|Optionally]] provide decrement, increment and comparitive operation functions.
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;Addition
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Like binary 1 + 1 = 10, note carry 1 left. There the similarity ends. 10 + 10 = 101, note carry 1 left and 1 right. 100 + 100 = 1001, note carry 1 left and 2 right, this is the general case.
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Occurrences of 11 must be changed to 100. Occurrences of 111 may be changed from the right by replacing 11 with 100, or from the left converting 111 to 100 + 100;
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;Subtraction
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10 - 1 = 1. The general rule is borrow 1 right carry 1 left. eg:
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<pre>
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abcde
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10100 -
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1000
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_____
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100 borrow 1 from a leaves 100
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+ 100 add the carry
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_____
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1001
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</pre>
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A larger example:
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<pre>
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abcdef
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100100 -
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1000
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______
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1*0100 borrow 1 from b
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+ 100 add the carry
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______
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1*1001
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Sadly we borrowed 1 from b which didn't have it to lend. So now b borrows from a:
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1001
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+ 1000 add the carry
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____
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10100
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</pre>
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;Multiplication
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Here you teach your computer its zeckendorf tables. eg. 101 * 1001:
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<pre>
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a = 1 * 101 = 101
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b = 10 * 101 = a + a = 10000
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c = 100 * 101 = b + a = 10101
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d = 1000 * 101 = c + b = 101010
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1001 = d + a therefore 101 * 1001 =
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101010
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+ 101
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______
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1000100
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</pre>
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;Division
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Lets try 1000101 divided by 101, so we can use the same table used for multiplication.
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<pre>
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1000101 -
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101010 subtract d (1000 * 101)
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_______
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1000 -
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101 b and c are too large to subtract, so subtract a
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____
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1 so 1000101 divided by 101 is d + a (1001) remainder 1
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</pre>
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[http://arxiv.org/pdf/1207.4497.pdf Efficient algorithms for Zeckendorf arithmetic] is interesting. The sections on addition and subtraction are particularly relevant for this task.
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143
Task/Zeckendorf-arithmetic/11l/zeckendorf-arithmetic.11l
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143
Task/Zeckendorf-arithmetic/11l/zeckendorf-arithmetic.11l
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@ -0,0 +1,143 @@
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T Zeckendorf
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Int dLen
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dVal = 0
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F (x = ‘0’)
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V q = 1
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V i = x.len - 1
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.dLen = i I/ 2
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L i >= 0
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.dVal = .dVal + (x[i].code - ‘0’.code) * q
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q = q * 2
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i = i - 1
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F a(n)
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V i = n
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L
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I .dLen < i
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.dLen = i
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V j = (.dVal >> (i * 2)) [&] 3
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I j == 0 | j == 1
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R
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I j == 2
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I (.dVal >> ((i + 1) * 2) [&] 1) != 1
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R
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.dVal = .dVal + (1 << (i * 2 + 1))
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R
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I j == 3
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V temp = 3 << (i * 2)
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temp = temp (+) -1
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.dVal = .dVal [&] temp
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.b((i + 1) * 2)
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i = i + 1
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F b(pos)
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I pos == 0
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.inc()
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R
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I (.dVal >> pos) [&] 1 == 0
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.dVal = .dVal + (1 << pos)
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.a(Int(pos / 2))
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I pos > 1
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.a(Int(pos / 2) - 1)
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E
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V temp = 1 << pos
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temp = temp (+) -1
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.dVal = .dVal [&] temp
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.b(pos + 1)
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.b(pos - (I pos > 1 {2} E 1))
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F c(pos)
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I (.dVal >> pos) [&] 1 == 1
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V temp = 1 << pos
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temp = temp (+) -1
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.dVal = .dVal [&] temp
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R
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.c(pos + 1)
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I pos > 0
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.b(pos - 1)
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E
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.inc()
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F inc() -> N
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.dVal = .dVal + 1
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.a(0)
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F +(rhs)
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V copy = (.)
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V rhs_dVal = rhs.dVal
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V limit = (rhs.dLen + 1) * 2
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L(gn) 0 .< limit
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I ((rhs_dVal >> gn) [&] 1) == 1
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copy.b(gn)
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R copy
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F -(rhs)
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V copy = (.)
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V rhs_dVal = rhs.dVal
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V limit = (rhs.dLen + 1) * 2
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L(gn) 0 .< limit
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I (rhs_dVal >> gn) [&] 1 == 1
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copy.c(gn)
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L (((copy.dVal >> ((copy.dLen * 2) [&] 31)) [&] 3) == 0) | (copy.dLen == 0)
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copy.dLen = copy.dLen - 1
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R copy
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F *(rhs)
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V na = copy(rhs)
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V nb = copy(rhs)
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V nr = Zeckendorf()
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V dVal = .dVal
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L(i) 0 .< (.dLen + 1) * 2
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I ((dVal >> i) [&] 1) > 0
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nr = nr + nb
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V nt = copy(nb)
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nb = nb + na
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na = copy(nt)
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R nr
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F String()
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V dig = [‘00’, ‘01’, ‘10’]
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V dig1 = [‘’, ‘1’, ‘10’]
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I .dVal == 0
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R ‘0’
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V idx = (.dVal >> ((.dLen * 2) [&] 31)) [&] 3
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String sb = dig1[idx]
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V i = .dLen - 1
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L i >= 0
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idx = (.dVal >> (i * 2)) [&] 3
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sb ‘’= dig[idx]
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i = i - 1
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R sb
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print(‘Addition:’)
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V g = Zeckendorf(‘10’)
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g = g + Zeckendorf(‘10’)
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print(g)
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g = g + Zeckendorf(‘10’)
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print(g)
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g = g + Zeckendorf(‘1001’)
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print(g)
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g = g + Zeckendorf(‘1000’)
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print(g)
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g = g + Zeckendorf(‘10101’)
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print(g)
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print()
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print(‘Subtraction:’)
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g = Zeckendorf(‘1000’)
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g = g - Zeckendorf(‘101’)
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print(g)
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g = Zeckendorf(‘10101010’)
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g = g - Zeckendorf(‘1010101’)
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print(g)
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print()
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print(‘Multiplication:’)
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g = Zeckendorf(‘1001’)
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g = g * Zeckendorf(‘101’)
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print(g)
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g = Zeckendorf(‘101010’)
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g = g + Zeckendorf(‘101’)
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print(g)
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72
Task/Zeckendorf-arithmetic/C++/zeckendorf-arithmetic-1.cpp
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72
Task/Zeckendorf-arithmetic/C++/zeckendorf-arithmetic-1.cpp
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@ -0,0 +1,72 @@
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// For a class N which implements Zeckendorf numbers:
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// I define an increment operation ++()
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// I define a comparison operation <=(other N)
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// I define an addition operation +=(other N)
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// I define a subtraction operation -=(other N)
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// Nigel Galloway October 28th., 2012
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#include <iostream>
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enum class zd {N00,N01,N10,N11};
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class N {
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private:
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int dVal = 0, dLen;
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void _a(int i) {
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for (;; i++) {
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if (dLen < i) dLen = i;
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switch ((zd)((dVal >> (i*2)) & 3)) {
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case zd::N00: case zd::N01: return;
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case zd::N10: if (((dVal >> ((i+1)*2)) & 1) != 1) return;
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dVal += (1 << (i*2+1)); return;
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case zd::N11: dVal &= ~(3 << (i*2)); _b((i+1)*2);
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}}}
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void _b(int pos) {
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if (pos == 0) {++*this; return;}
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if (((dVal >> pos) & 1) == 0) {
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dVal += 1 << pos;
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_a(pos/2);
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if (pos > 1) _a((pos/2)-1);
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} else {
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dVal &= ~(1 << pos);
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_b(pos + 1);
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_b(pos - ((pos > 1)? 2:1));
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}}
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void _c(int pos) {
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if (((dVal >> pos) & 1) == 1) {dVal &= ~(1 << pos); return;}
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_c(pos + 1);
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if (pos > 0) _b(pos - 1); else ++*this;
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return;
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}
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public:
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N(char const* x = "0") {
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int i = 0, q = 1;
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for (; x[i] > 0; i++);
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for (dLen = --i/2; i >= 0; i--) {dVal+=(x[i]-48)*q; q*=2;
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}}
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const N& operator++() {dVal += 1; _a(0); return *this;}
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const N& operator+=(const N& other) {
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for (int GN = 0; GN < (other.dLen + 1) * 2; GN++) if ((other.dVal >> GN) & 1 == 1) _b(GN);
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return *this;
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}
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const N& operator-=(const N& other) {
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for (int GN = 0; GN < (other.dLen + 1) * 2; GN++) if ((other.dVal >> GN) & 1 == 1) _c(GN);
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for (;((dVal >> dLen*2) & 3) == 0 or dLen == 0; dLen--);
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return *this;
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}
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const N& operator*=(const N& other) {
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N Na = other, Nb = other, Nt, Nr;
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for (int i = 0; i <= (dLen + 1) * 2; i++) {
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if (((dVal >> i) & 1) > 0) Nr += Nb;
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Nt = Nb; Nb += Na; Na = Nt;
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}
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return *this = Nr;
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}
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const bool operator<=(const N& other) const {return dVal <= other.dVal;}
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friend std::ostream& operator<<(std::ostream&, const N&);
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};
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N operator "" N(char const* x) {return N(x);}
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std::ostream &operator<<(std::ostream &os, const N &G) {
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const static std::string dig[] {"00","01","10"}, dig1[] {"","1","10"};
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if (G.dVal == 0) return os << "0";
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os << dig1[(G.dVal >> (G.dLen*2)) & 3];
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for (int i = G.dLen-1; i >= 0; i--) os << dig[(G.dVal >> (i*2)) & 3];
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return os;
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}
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15
Task/Zeckendorf-arithmetic/C++/zeckendorf-arithmetic-2.cpp
Normal file
15
Task/Zeckendorf-arithmetic/C++/zeckendorf-arithmetic-2.cpp
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@ -0,0 +1,15 @@
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int main(void) {
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N G;
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G = 10N;
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G += 10N;
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std::cout << G << std::endl;
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G += 10N;
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std::cout << G << std::endl;
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G += 1001N;
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std::cout << G << std::endl;
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G += 1000N;
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std::cout << G << std::endl;
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G += 10101N;
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std::cout << G << std::endl;
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return 0;
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}
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10
Task/Zeckendorf-arithmetic/C++/zeckendorf-arithmetic-3.cpp
Normal file
10
Task/Zeckendorf-arithmetic/C++/zeckendorf-arithmetic-3.cpp
Normal file
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@ -0,0 +1,10 @@
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int main(void) {
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N G;
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G = 1000N;
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G -= 101N;
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std::cout << G << std::endl;
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G = 10101010N;
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G -= 1010101N;
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std::cout << G << std::endl;
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return 0;
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}
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10
Task/Zeckendorf-arithmetic/C++/zeckendorf-arithmetic-4.cpp
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10
Task/Zeckendorf-arithmetic/C++/zeckendorf-arithmetic-4.cpp
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@ -0,0 +1,10 @@
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int main(void) {
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N G = 1001N;
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G *= 101N;
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std::cout << G << std::endl;
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G = 101010N;
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G += 101N;
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std::cout << G << std::endl;
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return 0;
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}
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189
Task/Zeckendorf-arithmetic/C-sharp/zeckendorf-arithmetic.cs
Normal file
189
Task/Zeckendorf-arithmetic/C-sharp/zeckendorf-arithmetic.cs
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@ -0,0 +1,189 @@
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using System;
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using System.Text;
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namespace ZeckendorfArithmetic {
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class Zeckendorf : IComparable<Zeckendorf> {
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private static readonly string[] dig = { "00", "01", "10" };
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private static readonly string[] dig1 = { "", "1", "10" };
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private int dVal = 0;
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private int dLen = 0;
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public Zeckendorf() : this("0") {
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// empty
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}
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public Zeckendorf(string x) {
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int q = 1;
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int i = x.Length - 1;
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dLen = i / 2;
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while (i >= 0) {
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dVal += (x[i] - '0') * q;
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q *= 2;
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i--;
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}
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}
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private void A(int n) {
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int i = n;
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while (true) {
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if (dLen < i) dLen = i;
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int j = (dVal >> (i * 2)) & 3;
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switch (j) {
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case 0:
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case 1:
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return;
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case 2:
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if (((dVal >> ((i + 1) * 2)) & 1) != 1) return;
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dVal += 1 << (i * 2 + 1);
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return;
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case 3:
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int temp = 3 << (i * 2);
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temp ^= -1;
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dVal = dVal & temp;
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B((i + 1) * 2);
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break;
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}
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i++;
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}
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}
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private void B(int pos) {
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if (pos == 0) {
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Inc();
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return;
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}
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if (((dVal >> pos) & 1) == 0) {
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dVal += 1 << pos;
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A(pos / 2);
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if (pos > 1) A(pos / 2 - 1);
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}
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else {
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int temp = 1 << pos;
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temp ^= -1;
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dVal = dVal & temp;
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B(pos + 1);
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B(pos - (pos > 1 ? 2 : 1));
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}
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}
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private void C(int pos) {
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if (((dVal >> pos) & 1) == 1) {
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int temp = 1 << pos;
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temp ^= -1;
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dVal = dVal & temp;
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return;
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}
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C(pos + 1);
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if (pos > 0) {
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B(pos - 1);
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}
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else {
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Inc();
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}
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}
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public Zeckendorf Inc() {
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dVal++;
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A(0);
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return this;
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}
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public Zeckendorf Copy() {
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Zeckendorf z = new Zeckendorf {
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dVal = dVal,
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dLen = dLen
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};
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return z;
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}
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public void PlusAssign(Zeckendorf other) {
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for (int gn = 0; gn < (other.dLen + 1) * 2; gn++) {
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if (((other.dVal >> gn) & 1) == 1) {
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B(gn);
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}
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}
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}
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public void MinusAssign(Zeckendorf other) {
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for (int gn = 0; gn < (other.dLen + 1) * 2; gn++) {
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||||
if (((other.dVal >> gn) & 1) == 1) {
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C(gn);
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||||
}
|
||||
}
|
||||
while ((((dVal >> dLen * 2) & 3) == 0) || (dLen == 0)) {
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dLen--;
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||||
}
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||||
}
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public void TimesAssign(Zeckendorf other) {
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Zeckendorf na = other.Copy();
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Zeckendorf nb = other.Copy();
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Zeckendorf nt;
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||||
Zeckendorf nr = new Zeckendorf();
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for (int i = 0; i < (dLen + 1) * 2; i++) {
|
||||
if (((dVal >> i) & 1) > 0) {
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nr.PlusAssign(nb);
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}
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nt = nb.Copy();
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nb.PlusAssign(na);
|
||||
na = nt.Copy();
|
||||
}
|
||||
dVal = nr.dVal;
|
||||
dLen = nr.dLen;
|
||||
}
|
||||
|
||||
public int CompareTo(Zeckendorf other) {
|
||||
return dVal.CompareTo(other.dVal);
|
||||
}
|
||||
|
||||
public override string ToString() {
|
||||
if (dVal == 0) {
|
||||
return "0";
|
||||
}
|
||||
|
||||
int idx = (dVal >> (dLen * 2)) & 3;
|
||||
StringBuilder sb = new StringBuilder(dig1[idx]);
|
||||
for (int i = dLen - 1; i >= 0; i--) {
|
||||
idx = (dVal >> (i * 2)) & 3;
|
||||
sb.Append(dig[idx]);
|
||||
}
|
||||
return sb.ToString();
|
||||
}
|
||||
}
|
||||
|
||||
class Program {
|
||||
static void Main(string[] args) {
|
||||
Console.WriteLine("Addition:");
|
||||
Zeckendorf g = new Zeckendorf("10");
|
||||
g.PlusAssign(new Zeckendorf("10"));
|
||||
Console.WriteLine(g);
|
||||
g.PlusAssign(new Zeckendorf("10"));
|
||||
Console.WriteLine(g);
|
||||
g.PlusAssign(new Zeckendorf("1001"));
|
||||
Console.WriteLine(g);
|
||||
g.PlusAssign(new Zeckendorf("1000"));
|
||||
Console.WriteLine(g);
|
||||
g.PlusAssign(new Zeckendorf("10101"));
|
||||
Console.WriteLine(g);
|
||||
Console.WriteLine();
|
||||
|
||||
Console.WriteLine("Subtraction:");
|
||||
g = new Zeckendorf("1000");
|
||||
g.MinusAssign(new Zeckendorf("101"));
|
||||
Console.WriteLine(g);
|
||||
g = new Zeckendorf("10101010");
|
||||
g.MinusAssign(new Zeckendorf("1010101"));
|
||||
Console.WriteLine(g);
|
||||
Console.WriteLine();
|
||||
|
||||
Console.WriteLine("Multiplication:");
|
||||
g = new Zeckendorf("1001");
|
||||
g.TimesAssign(new Zeckendorf("101"));
|
||||
Console.WriteLine(g);
|
||||
g = new Zeckendorf("101010");
|
||||
g.PlusAssign(new Zeckendorf("101"));
|
||||
Console.WriteLine(g);
|
||||
}
|
||||
}
|
||||
}
|
||||
189
Task/Zeckendorf-arithmetic/C/zeckendorf-arithmetic.c
Normal file
189
Task/Zeckendorf-arithmetic/C/zeckendorf-arithmetic.c
Normal file
|
|
@ -0,0 +1,189 @@
|
|||
#include <stdbool.h>
|
||||
#include <stdio.h>
|
||||
#include <string.h>
|
||||
|
||||
int inv(int a) {
|
||||
return a ^ -1;
|
||||
}
|
||||
|
||||
struct Zeckendorf {
|
||||
int dVal, dLen;
|
||||
};
|
||||
|
||||
void a(struct Zeckendorf *self, int n) {
|
||||
void b(struct Zeckendorf *, int); // forward declare
|
||||
|
||||
int i = n;
|
||||
while (true) {
|
||||
if (self->dLen < i) self->dLen = i;
|
||||
int j = (self->dVal >> (i * 2)) & 3;
|
||||
switch (j) {
|
||||
case 0:
|
||||
case 1:
|
||||
return;
|
||||
case 2:
|
||||
if (((self->dVal >> ((i + 1) * 2)) & 1) != 1) return;
|
||||
self->dVal += 1 << (i * 2 + 1);
|
||||
return;
|
||||
case 3:
|
||||
self->dVal = self->dVal & inv(3 << (i * 2));
|
||||
b(self, (i + 1) * 2);
|
||||
break;
|
||||
default:
|
||||
break;
|
||||
}
|
||||
i++;
|
||||
}
|
||||
}
|
||||
|
||||
void b(struct Zeckendorf *self, int pos) {
|
||||
void increment(struct Zeckendorf *); // forward declare
|
||||
|
||||
if (pos == 0) {
|
||||
increment(self);
|
||||
return;
|
||||
}
|
||||
if (((self->dVal >> pos) & 1) == 0) {
|
||||
self->dVal += 1 << pos;
|
||||
a(self, pos / 2);
|
||||
if (pos > 1) a(self, pos / 2 - 1);
|
||||
} else {
|
||||
self->dVal = self->dVal & inv(1 << pos);
|
||||
b(self, pos + 1);
|
||||
b(self, pos - (pos > 1 ? 2 : 1));
|
||||
}
|
||||
}
|
||||
|
||||
void c(struct Zeckendorf *self, int pos) {
|
||||
if (((self->dVal >> pos) & 1) == 1) {
|
||||
self->dVal = self->dVal & inv(1 << pos);
|
||||
return;
|
||||
}
|
||||
c(self, pos + 1);
|
||||
if (pos > 0) {
|
||||
b(self, pos - 1);
|
||||
} else {
|
||||
increment(self);
|
||||
}
|
||||
}
|
||||
|
||||
struct Zeckendorf makeZeckendorf(char *x) {
|
||||
struct Zeckendorf z = { 0, 0 };
|
||||
int i = strlen(x) - 1;
|
||||
int q = 1;
|
||||
|
||||
z.dLen = i / 2;
|
||||
while (i >= 0) {
|
||||
z.dVal += (x[i] - '0') * q;
|
||||
q *= 2;
|
||||
i--;
|
||||
}
|
||||
|
||||
return z;
|
||||
}
|
||||
|
||||
void increment(struct Zeckendorf *self) {
|
||||
self->dVal++;
|
||||
a(self, 0);
|
||||
}
|
||||
|
||||
void addAssign(struct Zeckendorf *self, struct Zeckendorf rhs) {
|
||||
int gn;
|
||||
for (gn = 0; gn < (rhs.dLen + 1) * 2; gn++) {
|
||||
if (((rhs.dVal >> gn) & 1) == 1) {
|
||||
b(self, gn);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void subAssign(struct Zeckendorf *self, struct Zeckendorf rhs) {
|
||||
int gn;
|
||||
for (gn = 0; gn < (rhs.dLen + 1) * 2; gn++) {
|
||||
if (((rhs.dVal >> gn) & 1) == 1) {
|
||||
c(self, gn);
|
||||
}
|
||||
}
|
||||
while ((((self->dVal >> self->dLen * 2) & 3) == 0) || (self->dLen == 0)) {
|
||||
self->dLen--;
|
||||
}
|
||||
}
|
||||
|
||||
void mulAssign(struct Zeckendorf *self, struct Zeckendorf rhs) {
|
||||
struct Zeckendorf na = rhs;
|
||||
struct Zeckendorf nb = rhs;
|
||||
struct Zeckendorf nr = makeZeckendorf("0");
|
||||
struct Zeckendorf nt;
|
||||
int i;
|
||||
|
||||
for (i = 0; i < (self->dLen + 1) * 2; i++) {
|
||||
if (((self->dVal >> i) & 1) > 0) addAssign(&nr, nb);
|
||||
nt = nb;
|
||||
addAssign(&nb, na);
|
||||
na = nt;
|
||||
}
|
||||
|
||||
*self = nr;
|
||||
}
|
||||
|
||||
void printZeckendorf(struct Zeckendorf z) {
|
||||
static const char *const dig[3] = { "00", "01", "10" };
|
||||
static const char *const dig1[3] = { "", "1", "10" };
|
||||
|
||||
if (z.dVal == 0) {
|
||||
printf("0");
|
||||
return;
|
||||
} else {
|
||||
int idx = (z.dVal >> (z.dLen * 2)) & 3;
|
||||
int i;
|
||||
|
||||
printf(dig1[idx]);
|
||||
for (i = z.dLen - 1; i >= 0; i--) {
|
||||
idx = (z.dVal >> (i * 2)) & 3;
|
||||
printf(dig[idx]);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
int main() {
|
||||
struct Zeckendorf g;
|
||||
|
||||
printf("Addition:\n");
|
||||
g = makeZeckendorf("10");
|
||||
addAssign(&g, makeZeckendorf("10"));
|
||||
printZeckendorf(g);
|
||||
printf("\n");
|
||||
addAssign(&g, makeZeckendorf("10"));
|
||||
printZeckendorf(g);
|
||||
printf("\n");
|
||||
addAssign(&g, makeZeckendorf("1001"));
|
||||
printZeckendorf(g);
|
||||
printf("\n");
|
||||
addAssign(&g, makeZeckendorf("1000"));
|
||||
printZeckendorf(g);
|
||||
printf("\n");
|
||||
addAssign(&g, makeZeckendorf("10101"));
|
||||
printZeckendorf(g);
|
||||
printf("\n\n");
|
||||
|
||||
printf("Subtraction:\n");
|
||||
g = makeZeckendorf("1000");
|
||||
subAssign(&g, makeZeckendorf("101"));
|
||||
printZeckendorf(g);
|
||||
printf("\n");
|
||||
g = makeZeckendorf("10101010");
|
||||
subAssign(&g, makeZeckendorf("1010101"));
|
||||
printZeckendorf(g);
|
||||
printf("\n\n");
|
||||
|
||||
printf("Multiplication:\n");
|
||||
g = makeZeckendorf("1001");
|
||||
mulAssign(&g, makeZeckendorf("101"));
|
||||
printZeckendorf(g);
|
||||
printf("\n");
|
||||
g = makeZeckendorf("101010");
|
||||
addAssign(&g, makeZeckendorf("101"));
|
||||
printZeckendorf(g);
|
||||
printf("\n");
|
||||
|
||||
return 0;
|
||||
}
|
||||
172
Task/Zeckendorf-arithmetic/D/zeckendorf-arithmetic.d
Normal file
172
Task/Zeckendorf-arithmetic/D/zeckendorf-arithmetic.d
Normal file
|
|
@ -0,0 +1,172 @@
|
|||
import std.stdio;
|
||||
|
||||
int inv(int a) {
|
||||
return a ^ -1;
|
||||
}
|
||||
|
||||
class Zeckendorf {
|
||||
private int dVal;
|
||||
private int dLen;
|
||||
|
||||
private void a(int n) {
|
||||
auto i = n;
|
||||
while (true) {
|
||||
if (dLen < i) dLen = i;
|
||||
auto j = (dVal >> (i * 2)) & 3;
|
||||
switch(j) {
|
||||
case 0:
|
||||
case 1:
|
||||
return;
|
||||
case 2:
|
||||
if (((dVal >> ((i + 1) * 2)) & 1) != 1) return;
|
||||
dVal += 1 << (i * 2 + 1);
|
||||
return;
|
||||
case 3:
|
||||
dVal = dVal & (3 << (i * 2)).inv();
|
||||
b((i + 1) * 2);
|
||||
break;
|
||||
default:
|
||||
assert(false);
|
||||
}
|
||||
i++;
|
||||
}
|
||||
}
|
||||
|
||||
private void b(int pos) {
|
||||
if (pos == 0) {
|
||||
this++;
|
||||
return;
|
||||
}
|
||||
if (((dVal >> pos) & 1) == 0) {
|
||||
dVal += 1 << pos;
|
||||
a(pos / 2);
|
||||
if (pos > 1) a(pos / 2 - 1);
|
||||
} else {
|
||||
dVal = dVal & (1 << pos).inv();
|
||||
b(pos + 1);
|
||||
b(pos - (pos > 1 ? 2 : 1));
|
||||
}
|
||||
}
|
||||
|
||||
private void c(int pos) {
|
||||
if (((dVal >> pos) & 1) == 1) {
|
||||
dVal = dVal & (1 << pos).inv();
|
||||
return;
|
||||
}
|
||||
c(pos + 1);
|
||||
if (pos > 0) {
|
||||
b(pos - 1);
|
||||
} else {
|
||||
++this;
|
||||
}
|
||||
}
|
||||
|
||||
this(string x = "0") {
|
||||
int q = 1;
|
||||
int i = x.length - 1;
|
||||
dLen = i / 2;
|
||||
while (i >= 0) {
|
||||
dVal += (x[i] - '0') * q;
|
||||
q *= 2;
|
||||
i--;
|
||||
}
|
||||
}
|
||||
|
||||
auto opUnary(string op : "++")() {
|
||||
dVal += 1;
|
||||
a(0);
|
||||
return this;
|
||||
}
|
||||
|
||||
void opOpAssign(string op : "+")(Zeckendorf rhs) {
|
||||
foreach (gn; 0..(rhs.dLen + 1) * 2) {
|
||||
if (((rhs.dVal >> gn) & 1) == 1) {
|
||||
b(gn);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void opOpAssign(string op : "-")(Zeckendorf rhs) {
|
||||
foreach (gn; 0..(rhs.dLen + 1) * 2) {
|
||||
if (((rhs.dVal >> gn) & 1) == 1) {
|
||||
c(gn);
|
||||
}
|
||||
}
|
||||
while ((((dVal >> dLen * 2) & 3) == 0) || (dLen == 0)) {
|
||||
dLen--;
|
||||
}
|
||||
}
|
||||
|
||||
void opOpAssign(string op : "*")(Zeckendorf rhs) {
|
||||
auto na = rhs.dup;
|
||||
auto nb = rhs.dup;
|
||||
Zeckendorf nt;
|
||||
auto nr = "0".Z;
|
||||
foreach (i; 0..(dLen + 1) * 2) {
|
||||
if (((dVal >> i) & 1) > 0) nr += nb;
|
||||
nt = nb.dup;
|
||||
nb += na;
|
||||
na = nt.dup;
|
||||
}
|
||||
dVal = nr.dVal;
|
||||
dLen = nr.dLen;
|
||||
}
|
||||
|
||||
void toString(scope void delegate(const(char)[]) sink) const {
|
||||
if (dVal == 0) {
|
||||
sink("0");
|
||||
return;
|
||||
}
|
||||
sink(dig1[(dVal >> (dLen * 2)) & 3]);
|
||||
foreach_reverse (i; 0..dLen) {
|
||||
sink(dig[(dVal >> (i * 2)) & 3]);
|
||||
}
|
||||
}
|
||||
|
||||
Zeckendorf dup() {
|
||||
auto z = "0".Z;
|
||||
z.dVal = dVal;
|
||||
z.dLen = dLen;
|
||||
return z;
|
||||
}
|
||||
|
||||
enum dig = ["00", "01", "10"];
|
||||
enum dig1 = ["", "1", "10"];
|
||||
}
|
||||
|
||||
auto Z(string val) {
|
||||
return new Zeckendorf(val);
|
||||
}
|
||||
|
||||
void main() {
|
||||
writeln("Addition:");
|
||||
auto g = "10".Z;
|
||||
g += "10".Z;
|
||||
writeln(g);
|
||||
g += "10".Z;
|
||||
writeln(g);
|
||||
g += "1001".Z;
|
||||
writeln(g);
|
||||
g += "1000".Z;
|
||||
writeln(g);
|
||||
g += "10101".Z;
|
||||
writeln(g);
|
||||
writeln();
|
||||
|
||||
writeln("Subtraction:");
|
||||
g = "1000".Z;
|
||||
g -= "101".Z;
|
||||
writeln(g);
|
||||
g = "10101010".Z;
|
||||
g -= "1010101".Z;
|
||||
writeln(g);
|
||||
writeln();
|
||||
|
||||
writeln("Multiplication:");
|
||||
g = "1001".Z;
|
||||
g *= "101".Z;
|
||||
writeln(g);
|
||||
g = "101010".Z;
|
||||
g += "101".Z;
|
||||
writeln(g);
|
||||
}
|
||||
249
Task/Zeckendorf-arithmetic/Elena/zeckendorf-arithmetic.elena
Normal file
249
Task/Zeckendorf-arithmetic/Elena/zeckendorf-arithmetic.elena
Normal file
|
|
@ -0,0 +1,249 @@
|
|||
import extensions;
|
||||
|
||||
const dig = new string[]{"00","01","10"};
|
||||
const dig1 = new string[]{"","1","10"};
|
||||
|
||||
sealed struct ZeckendorfNumber
|
||||
{
|
||||
int dVal;
|
||||
int dLen;
|
||||
|
||||
clone()
|
||||
= ZeckendorfNumber.newInternal(dVal,dLen);
|
||||
|
||||
cast n(string s)
|
||||
{
|
||||
int i := s.Length - 1;
|
||||
int q := 1;
|
||||
|
||||
dLen := i / 2;
|
||||
dVal := 0;
|
||||
|
||||
while (i >= 0)
|
||||
{
|
||||
dVal += ((intConvertor.convert(s[i]) - 48) * q);
|
||||
q *= 2;
|
||||
|
||||
i -= 1
|
||||
}
|
||||
}
|
||||
|
||||
internal readContent(ref int val, ref int len)
|
||||
{
|
||||
val := dVal;
|
||||
len := dLen;
|
||||
}
|
||||
|
||||
private a(int n)
|
||||
{
|
||||
int i := n;
|
||||
|
||||
while (true)
|
||||
{
|
||||
if (dLen < i)
|
||||
{
|
||||
dLen := i
|
||||
};
|
||||
|
||||
int v := (dVal $shr (i * 2)) && 3;
|
||||
v =>
|
||||
0 { ^ self }
|
||||
1 { ^ self }
|
||||
2 {
|
||||
ifnot ((dVal $shr ((i + 1) * 2)).allMask:1)
|
||||
{
|
||||
^ self
|
||||
};
|
||||
|
||||
dVal += (1 $shl (i*2 + 1));
|
||||
|
||||
^ self
|
||||
}
|
||||
3 {
|
||||
int tmp := 3 $shl (i * 2);
|
||||
tmp := tmp.xor(-1);
|
||||
dVal := dVal && tmp;
|
||||
|
||||
self.b((i+1)*2)
|
||||
};
|
||||
|
||||
i += 1
|
||||
}
|
||||
}
|
||||
|
||||
inc()
|
||||
{
|
||||
dVal += 1;
|
||||
self.a(0)
|
||||
}
|
||||
|
||||
private b(int pos)
|
||||
{
|
||||
if (pos == 0) { ^ self.inc() };
|
||||
|
||||
ifnot((dVal $shr pos).allMask:1)
|
||||
{
|
||||
dVal += (1 $shl pos);
|
||||
self.a(pos / 2);
|
||||
if (pos > 1) { self.a((pos / 2) - 1) }
|
||||
}
|
||||
else
|
||||
{
|
||||
dVal := dVal && (1 $shl pos).Inverted;
|
||||
self.b(pos + 1);
|
||||
int arg := pos - ((pos > 1) ? 2 : 1);
|
||||
self.b(/*pos - ((pos > 1) ? 2 : 1)*/arg)
|
||||
}
|
||||
}
|
||||
|
||||
private c(int pos)
|
||||
{
|
||||
if ((dVal $shr pos).allMask:1)
|
||||
{
|
||||
int tmp := 1 $shl pos;
|
||||
tmp := tmp.xor(-1);
|
||||
|
||||
dVal := dVal && tmp;
|
||||
|
||||
^ self
|
||||
};
|
||||
|
||||
self.c(pos + 1);
|
||||
|
||||
if (pos > 0)
|
||||
{
|
||||
self.b(pos - 1)
|
||||
}
|
||||
else
|
||||
{
|
||||
self.inc()
|
||||
}
|
||||
}
|
||||
|
||||
internal constructor sum(ZeckendorfNumber n, ZeckendorfNumber m)
|
||||
{
|
||||
int mVal := 0;
|
||||
int mLen := 0;
|
||||
|
||||
n.readContent(ref dVal, ref dLen);
|
||||
m.readContent(ref mVal, ref mLen);
|
||||
|
||||
for(int GN := 0, GN < (mLen + 1) * 2, GN += 1)
|
||||
{
|
||||
if ((mVal $shr GN).allMask:1)
|
||||
{
|
||||
self.b(GN)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
internal constructor difference(ZeckendorfNumber n, ZeckendorfNumber m)
|
||||
{
|
||||
int mVal := 0;
|
||||
int mLen := 0;
|
||||
|
||||
n.readContent(ref dVal, ref dLen);
|
||||
m.readContent(ref mVal, ref mLen);
|
||||
|
||||
for(int GN := 0, GN < (mLen + 1) * 2, GN += 1)
|
||||
{
|
||||
if ((mVal $shr GN).allMask:1)
|
||||
{
|
||||
self.c(GN)
|
||||
}
|
||||
};
|
||||
|
||||
while (((dVal $shr (dLen*2)) && 3) == 0 || dLen == 0)
|
||||
{
|
||||
dLen -= 1
|
||||
}
|
||||
}
|
||||
|
||||
internal constructor product(ZeckendorfNumber n, ZeckendorfNumber m)
|
||||
{
|
||||
n.readContent(ref dVal, ref dLen);
|
||||
|
||||
ZeckendorfNumber Na := m;
|
||||
ZeckendorfNumber Nb := m;
|
||||
ZeckendorfNumber Nr := 0n;
|
||||
ZeckendorfNumber Nt := 0n;
|
||||
|
||||
for(int i := 0, i < (dLen + 1) * 2, i += 1)
|
||||
{
|
||||
if (((dVal $shr i) && 1) > 0)
|
||||
{
|
||||
Nr += Nb
|
||||
};
|
||||
Nt := Nb;
|
||||
Nb += Na;
|
||||
Na := Nt
|
||||
};
|
||||
|
||||
Nr.readContent(ref dVal, ref dLen);
|
||||
}
|
||||
|
||||
internal constructor newInternal(int v, int l)
|
||||
{
|
||||
dVal := v;
|
||||
dLen := l
|
||||
}
|
||||
|
||||
string toPrintable()
|
||||
{
|
||||
if (dVal == 0)
|
||||
{ ^ "0" };
|
||||
|
||||
string s := dig1[(dVal $shr (dLen * 2)) && 3];
|
||||
int i := dLen - 1;
|
||||
while (i >= 0)
|
||||
{
|
||||
s := s + dig[(dVal $shr (i * 2)) && 3];
|
||||
|
||||
i-=1
|
||||
};
|
||||
|
||||
^ s
|
||||
}
|
||||
|
||||
add(ZeckendorfNumber n)
|
||||
= ZeckendorfNumber.sum(self, n);
|
||||
|
||||
subtract(ZeckendorfNumber n)
|
||||
= ZeckendorfNumber.difference(self, n);
|
||||
|
||||
multiply(ZeckendorfNumber n)
|
||||
= ZeckendorfNumber.product(self, n);
|
||||
}
|
||||
|
||||
public program()
|
||||
{
|
||||
console.printLine("Addition:");
|
||||
var n := 10n;
|
||||
|
||||
n += 10n;
|
||||
console.printLine(n);
|
||||
n += 10n;
|
||||
console.printLine(n);
|
||||
n += 1001n;
|
||||
console.printLine(n);
|
||||
n += 1000n;
|
||||
console.printLine(n);
|
||||
n += 10101n;
|
||||
console.printLine(n);
|
||||
|
||||
console.printLine("Subtraction:");
|
||||
n := 1000n;
|
||||
n -= 101n;
|
||||
console.printLine(n);
|
||||
n := 10101010n;
|
||||
n -= 1010101n;
|
||||
console.printLine(n);
|
||||
|
||||
console.printLine("Multiplication:");
|
||||
n := 1001n;
|
||||
n *= 101n;
|
||||
console.printLine(n);
|
||||
n := 101010n;
|
||||
n += 101n;
|
||||
console.printLine(n)
|
||||
}
|
||||
184
Task/Zeckendorf-arithmetic/Go/zeckendorf-arithmetic.go
Normal file
184
Task/Zeckendorf-arithmetic/Go/zeckendorf-arithmetic.go
Normal file
|
|
@ -0,0 +1,184 @@
|
|||
package main
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
"strings"
|
||||
)
|
||||
|
||||
var (
|
||||
dig = [3]string{"00", "01", "10"}
|
||||
dig1 = [3]string{"", "1", "10"}
|
||||
)
|
||||
|
||||
type Zeckendorf struct{ dVal, dLen int }
|
||||
|
||||
func NewZeck(x string) *Zeckendorf {
|
||||
z := new(Zeckendorf)
|
||||
if x == "" {
|
||||
x = "0"
|
||||
}
|
||||
q := 1
|
||||
i := len(x) - 1
|
||||
z.dLen = i / 2
|
||||
for ; i >= 0; i-- {
|
||||
z.dVal += int(x[i]-'0') * q
|
||||
q *= 2
|
||||
}
|
||||
return z
|
||||
}
|
||||
|
||||
func (z *Zeckendorf) a(i int) {
|
||||
for ; ; i++ {
|
||||
if z.dLen < i {
|
||||
z.dLen = i
|
||||
}
|
||||
j := (z.dVal >> uint(i*2)) & 3
|
||||
switch j {
|
||||
case 0, 1:
|
||||
return
|
||||
case 2:
|
||||
if ((z.dVal >> (uint(i+1) * 2)) & 1) != 1 {
|
||||
return
|
||||
}
|
||||
z.dVal += 1 << uint(i*2+1)
|
||||
return
|
||||
case 3:
|
||||
z.dVal &= ^(3 << uint(i*2))
|
||||
z.b((i + 1) * 2)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func (z *Zeckendorf) b(pos int) {
|
||||
if pos == 0 {
|
||||
z.Inc()
|
||||
return
|
||||
}
|
||||
if ((z.dVal >> uint(pos)) & 1) == 0 {
|
||||
z.dVal += 1 << uint(pos)
|
||||
z.a(pos / 2)
|
||||
if pos > 1 {
|
||||
z.a(pos/2 - 1)
|
||||
}
|
||||
} else {
|
||||
z.dVal &= ^(1 << uint(pos))
|
||||
z.b(pos + 1)
|
||||
temp := 1
|
||||
if pos > 1 {
|
||||
temp = 2
|
||||
}
|
||||
z.b(pos - temp)
|
||||
}
|
||||
}
|
||||
|
||||
func (z *Zeckendorf) c(pos int) {
|
||||
if ((z.dVal >> uint(pos)) & 1) == 1 {
|
||||
z.dVal &= ^(1 << uint(pos))
|
||||
return
|
||||
}
|
||||
z.c(pos + 1)
|
||||
if pos > 0 {
|
||||
z.b(pos - 1)
|
||||
} else {
|
||||
z.Inc()
|
||||
}
|
||||
}
|
||||
|
||||
func (z *Zeckendorf) Inc() {
|
||||
z.dVal++
|
||||
z.a(0)
|
||||
}
|
||||
|
||||
func (z1 *Zeckendorf) PlusAssign(z2 *Zeckendorf) {
|
||||
for gn := 0; gn < (z2.dLen+1)*2; gn++ {
|
||||
if ((z2.dVal >> uint(gn)) & 1) == 1 {
|
||||
z1.b(gn)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func (z1 *Zeckendorf) MinusAssign(z2 *Zeckendorf) {
|
||||
for gn := 0; gn < (z2.dLen+1)*2; gn++ {
|
||||
if ((z2.dVal >> uint(gn)) & 1) == 1 {
|
||||
z1.c(gn)
|
||||
}
|
||||
}
|
||||
|
||||
for z1.dLen > 0 && ((z1.dVal>>uint(z1.dLen*2))&3) == 0 {
|
||||
z1.dLen--
|
||||
}
|
||||
}
|
||||
|
||||
func (z1 *Zeckendorf) TimesAssign(z2 *Zeckendorf) {
|
||||
na := z2.Copy()
|
||||
nb := z2.Copy()
|
||||
nr := new(Zeckendorf)
|
||||
for i := 0; i <= (z1.dLen+1)*2; i++ {
|
||||
if ((z1.dVal >> uint(i)) & 1) > 0 {
|
||||
nr.PlusAssign(nb)
|
||||
}
|
||||
nt := nb.Copy()
|
||||
nb.PlusAssign(na)
|
||||
na = nt.Copy()
|
||||
}
|
||||
z1.dVal = nr.dVal
|
||||
z1.dLen = nr.dLen
|
||||
}
|
||||
|
||||
func (z *Zeckendorf) Copy() *Zeckendorf {
|
||||
return &Zeckendorf{z.dVal, z.dLen}
|
||||
}
|
||||
|
||||
func (z1 *Zeckendorf) Compare(z2 *Zeckendorf) int {
|
||||
switch {
|
||||
case z1.dVal < z2.dVal:
|
||||
return -1
|
||||
case z1.dVal > z2.dVal:
|
||||
return 1
|
||||
default:
|
||||
return 0
|
||||
}
|
||||
}
|
||||
|
||||
func (z *Zeckendorf) String() string {
|
||||
if z.dVal == 0 {
|
||||
return "0"
|
||||
}
|
||||
var sb strings.Builder
|
||||
sb.WriteString(dig1[(z.dVal>>uint(z.dLen*2))&3])
|
||||
for i := z.dLen - 1; i >= 0; i-- {
|
||||
sb.WriteString(dig[(z.dVal>>uint(i*2))&3])
|
||||
}
|
||||
return sb.String()
|
||||
}
|
||||
|
||||
func main() {
|
||||
fmt.Println("Addition:")
|
||||
g := NewZeck("10")
|
||||
g.PlusAssign(NewZeck("10"))
|
||||
fmt.Println(g)
|
||||
g.PlusAssign(NewZeck("10"))
|
||||
fmt.Println(g)
|
||||
g.PlusAssign(NewZeck("1001"))
|
||||
fmt.Println(g)
|
||||
g.PlusAssign(NewZeck("1000"))
|
||||
fmt.Println(g)
|
||||
g.PlusAssign(NewZeck("10101"))
|
||||
fmt.Println(g)
|
||||
|
||||
fmt.Println("\nSubtraction:")
|
||||
g = NewZeck("1000")
|
||||
g.MinusAssign(NewZeck("101"))
|
||||
fmt.Println(g)
|
||||
g = NewZeck("10101010")
|
||||
g.MinusAssign(NewZeck("1010101"))
|
||||
fmt.Println(g)
|
||||
|
||||
fmt.Println("\nMultiplication:")
|
||||
g = NewZeck("1001")
|
||||
g.TimesAssign(NewZeck("101"))
|
||||
fmt.Println(g)
|
||||
g = NewZeck("101010")
|
||||
g.PlusAssign(NewZeck("101"))
|
||||
fmt.Println(g)
|
||||
}
|
||||
186
Task/Zeckendorf-arithmetic/Haskell/zeckendorf-arithmetic.hs
Normal file
186
Task/Zeckendorf-arithmetic/Haskell/zeckendorf-arithmetic.hs
Normal file
|
|
@ -0,0 +1,186 @@
|
|||
{-# LANGUAGE LambdaCase #-}
|
||||
import Data.List (find, mapAccumL)
|
||||
import Control.Arrow (first, second)
|
||||
|
||||
-- Generalized Fibonacci series defined for any Num instance, and for Zeckendorf numbers as well.
|
||||
-- Used to build Zeckendorf tables.
|
||||
fibs :: Num a => a -> a -> [a]
|
||||
fibs a b = res
|
||||
where
|
||||
res = a : b : zipWith (+) res (tail res)
|
||||
|
||||
data Fib = Fib { sign :: Int, digits :: [Int]}
|
||||
|
||||
-- smart constructor
|
||||
mkFib s ds =
|
||||
case dropWhile (==0) ds of
|
||||
[] -> 0
|
||||
ds -> Fib s (reverse ds)
|
||||
|
||||
-- Textual representation
|
||||
instance Show Fib where
|
||||
show (Fib s ds) = sig s ++ foldMap show (reverse ds)
|
||||
where sig = \case { -1 -> "-"; s -> "" }
|
||||
|
||||
-- Equivalence relation
|
||||
instance Eq Fib where
|
||||
Fib sa a == Fib sb b = sa == sb && a == b
|
||||
|
||||
-- Order relation
|
||||
instance Ord Fib where
|
||||
a `compare` b =
|
||||
sign a `compare` sign b <>
|
||||
case find (/= 0) $ alignWith (-) (digits a) (digits b) of
|
||||
Nothing -> EQ
|
||||
Just 1 -> if sign a > 0 then GT else LT
|
||||
Just (-1) -> if sign a > 0 then LT else GT
|
||||
|
||||
-- Arithmetic
|
||||
instance Num Fib where
|
||||
negate (Fib s ds) = Fib (negate s) ds
|
||||
abs (Fib s ds) = Fib 1 ds
|
||||
signum (Fib s _) = fromIntegral s
|
||||
|
||||
fromInteger n =
|
||||
case compare n 0 of
|
||||
LT -> negate $ fromInteger (- n)
|
||||
EQ -> Fib 0 [0]
|
||||
GT -> Fib 1 . reverse . fst $ divModFib n 1
|
||||
|
||||
0 + a = a
|
||||
a + 0 = a
|
||||
a + b =
|
||||
case (sign a, sign b) of
|
||||
( 1, 1) -> res
|
||||
(-1, 1) -> b - (-a)
|
||||
( 1,-1) -> a - (-b)
|
||||
(-1,-1) -> - ((- a) + (- b))
|
||||
where
|
||||
res = mkFib 1 . process $ 0:0:c
|
||||
c = alignWith (+) (digits a) (digits b)
|
||||
-- use cellular automata
|
||||
process =
|
||||
runRight 3 r2 . runLeftR 3 r2 . runRightR 4 r1
|
||||
|
||||
0 - a = -a
|
||||
a - 0 = a
|
||||
a - b =
|
||||
case (sign a, sign b) of
|
||||
( 1, 1) -> res
|
||||
(-1, 1) -> - ((-a) + b)
|
||||
( 1,-1) -> a + (-b)
|
||||
(-1,-1) -> - ((-a) - (-b))
|
||||
where
|
||||
res = case find (/= 0) c of
|
||||
Just 1 -> mkFib 1 . process $ c
|
||||
Just (-1) -> - (b - a)
|
||||
Nothing -> 0
|
||||
c = alignWith (-) (digits a) (digits b)
|
||||
-- use cellular automata
|
||||
process =
|
||||
runRight 3 r2 . runLeftR 3 r2 . runRightR 4 r1 . runRight 3 r3
|
||||
|
||||
0 * a = 0
|
||||
a * 0 = 0
|
||||
1 * a = a
|
||||
a * 1 = a
|
||||
a * b =
|
||||
case (sign a, sign b) of
|
||||
(1, 1) -> res
|
||||
(-1, 1) -> - ((-a) * b)
|
||||
( 1,-1) -> - (a * (-b))
|
||||
(-1,-1) -> ((-a) * (-b))
|
||||
where
|
||||
-- use Zeckendorf table
|
||||
table = fibs a (a + a)
|
||||
res = sum $ onlyOnes $ zip (digits b) table
|
||||
onlyOnes = map snd . filter ((==1) . fst)
|
||||
|
||||
-- Enumeration
|
||||
instance Enum Fib where
|
||||
toEnum = fromInteger . fromIntegral
|
||||
fromEnum = fromIntegral . toInteger
|
||||
|
||||
instance Real Fib where
|
||||
toRational = fromInteger . toInteger
|
||||
|
||||
-- Integral division
|
||||
instance Integral Fib where
|
||||
toInteger (Fib s ds) = signum (fromIntegral s) * res
|
||||
where
|
||||
res = sum (zipWith (*) (fibs 1 2) (fromIntegral <$> ds))
|
||||
|
||||
quotRem 0 _ = (0, 0)
|
||||
quotRem a 0 = error "divide by zero"
|
||||
quotRem a b = case (sign a, sign b) of
|
||||
(1, 1) -> first (mkFib 1) $ divModFib a b
|
||||
(-1, 1) -> second negate . first negate $ quotRem (-a) b
|
||||
( 1,-1) -> first negate $ quotRem a (-b)
|
||||
(-1,-1) -> second negate $ quotRem (-a) (-b)
|
||||
|
||||
------------------------------------------------------------
|
||||
-- helper funtions
|
||||
|
||||
-- general division using Zeckendorf table
|
||||
divModFib :: (Ord a, Num c, Num a) => a -> a -> ([c], a)
|
||||
divModFib a b = (q, r)
|
||||
where
|
||||
(r, q) = mapAccumL f a $ reverse $ takeWhile (<= a) table
|
||||
table = fibs b (b+b)
|
||||
f n x = if n < x then (n, 0) else (n - x, 1)
|
||||
|
||||
-- application of rewriting rules
|
||||
-- runs window from left to right
|
||||
runRight n f = go
|
||||
where
|
||||
go [] = []
|
||||
go lst = let (w, r) = splitAt n lst
|
||||
(h: t) = f w
|
||||
in h : go (t ++ r)
|
||||
|
||||
-- runs window from left to right and reverses the result
|
||||
runRightR n f = go []
|
||||
where
|
||||
go res [] = res
|
||||
go res lst = let (w, r) = splitAt n lst
|
||||
(h: t) = f w
|
||||
in go (h : res) (t ++ r)
|
||||
|
||||
-- runs reversed window and reverses the result
|
||||
runLeftR n f = runRightR n (reverse . f . reverse)
|
||||
|
||||
-- rewriting rules from [C. Ahlbach et. all]
|
||||
r1 = \case [0,3,0] -> [1,1,1]
|
||||
[0,2,0] -> [1,0,1]
|
||||
[0,1,2] -> [1,0,1]
|
||||
[0,2,1] -> [1,1,0]
|
||||
[x,0,2] -> [x,1,0]
|
||||
[x,0,3] -> [x,1,1]
|
||||
[0,1,2,0] -> [1,0,1,0]
|
||||
[0,2,0,x] -> [1,0,0,x+1]
|
||||
[0,3,0,x] -> [1,1,0,x+1]
|
||||
[0,2,1,x] -> [1,1,0,x ]
|
||||
[0,1,2,x] -> [1,0,1,x ]
|
||||
l -> l
|
||||
|
||||
r2 = \case [0,1,1] -> [1,0,0]
|
||||
l -> l
|
||||
|
||||
r3 = \case [1,-1] -> [0,1]
|
||||
[2,-1] -> [1,1]
|
||||
[1, 0, 0] -> [0,1,1]
|
||||
[1,-1, 0] -> [0,0,1]
|
||||
[1,-1, 1] -> [0,0,2]
|
||||
[1, 0,-1] -> [0,1,0]
|
||||
[2, 0, 0] -> [1,1,1]
|
||||
[2,-1, 0] -> [1,0,1]
|
||||
[2,-1, 1] -> [1,0,2]
|
||||
[2, 0,-1] -> [1,1,0]
|
||||
l -> l
|
||||
|
||||
alignWith :: (Int -> Int -> a) -> [Int] -> [Int] -> [a]
|
||||
alignWith f a b = go [] a b
|
||||
where
|
||||
go res as [] = ((`f` 0) <$> reverse as) ++ res
|
||||
go res [] bs = ((0 `f`) <$> reverse bs) ++ res
|
||||
go res (a:as) (b:bs) = go (f a b : res) as bs
|
||||
15
Task/Zeckendorf-arithmetic/J/zeckendorf-arithmetic-1.j
Normal file
15
Task/Zeckendorf-arithmetic/J/zeckendorf-arithmetic-1.j
Normal file
|
|
@ -0,0 +1,15 @@
|
|||
zform=: {{ 10 |."1@(#.inv) y }} :. (10#.|."1) NB. use decimal numbers for representation
|
||||
zinc=: {{ carry ({.,2}.])carry 1,y }}
|
||||
zdec=: {{ (|.k$0 1),y }.~k=. 1+y i.1 }}
|
||||
zadd=: {{ x while. 1 e. y do. x=. zinc x [ y=. zdec y end. }}
|
||||
zsub=: {{ x while. 1 e. y do. x=. zdec x [ y=. zdec y end. }} NB. intended for unsigned arithmetic
|
||||
zmul=: {{ t=. 0 0 while. 1 e. y do. t=. t zadd x [ y=. zdec y end. }}
|
||||
zdiv=: {{ t=. 0 0 while. x zge y do. t=. zinc t [ x=. x zsub y end. }} NB. discards remainder
|
||||
carry=: {{
|
||||
s=. 0
|
||||
for_b. y do.
|
||||
if. (1+b) = s=. s-_1^b do. y=. (-.b) (b_index-0,b)} y end.
|
||||
end.
|
||||
if. 2=s do. y,1 else. y end.
|
||||
}}
|
||||
zge=: {{ cmp=. x -/@,: y while. (#cmp)*0={:cmp do. cmp=. }:cmp end. 0<:{:cmp }}
|
||||
18
Task/Zeckendorf-arithmetic/J/zeckendorf-arithmetic-2.j
Normal file
18
Task/Zeckendorf-arithmetic/J/zeckendorf-arithmetic-2.j
Normal file
|
|
@ -0,0 +1,18 @@
|
|||
1 zadd&.zform 1
|
||||
10
|
||||
10 zadd&.zform 10
|
||||
101
|
||||
10100 zadd&.zform 1010
|
||||
101000
|
||||
10100 zsub&.zform 1010
|
||||
101
|
||||
10100 zmul&.zform 100101
|
||||
10010010001
|
||||
10100 zdiv&.zform 1010
|
||||
1
|
||||
10100 zdiv&.zform 1000
|
||||
10
|
||||
100001000001 zdiv&.zform 100010
|
||||
100101
|
||||
100001000001 zdiv&.zform 100101
|
||||
100010
|
||||
186
Task/Zeckendorf-arithmetic/Java/zeckendorf-arithmetic.java
Normal file
186
Task/Zeckendorf-arithmetic/Java/zeckendorf-arithmetic.java
Normal file
|
|
@ -0,0 +1,186 @@
|
|||
import java.util.List;
|
||||
|
||||
public class Zeckendorf implements Comparable<Zeckendorf> {
|
||||
private static List<String> dig = List.of("00", "01", "10");
|
||||
private static List<String> dig1 = List.of("", "1", "10");
|
||||
|
||||
private String x;
|
||||
private int dVal = 0;
|
||||
private int dLen = 0;
|
||||
|
||||
public Zeckendorf() {
|
||||
this("0");
|
||||
}
|
||||
|
||||
public Zeckendorf(String x) {
|
||||
this.x = x;
|
||||
|
||||
int q = 1;
|
||||
int i = x.length() - 1;
|
||||
dLen = i / 2;
|
||||
while (i >= 0) {
|
||||
dVal += (x.charAt(i) - '0') * q;
|
||||
q *= 2;
|
||||
i--;
|
||||
}
|
||||
}
|
||||
|
||||
private void a(int n) {
|
||||
int i = n;
|
||||
while (true) {
|
||||
if (dLen < i) dLen = i;
|
||||
int j = (dVal >> (i * 2)) & 3;
|
||||
switch (j) {
|
||||
case 0:
|
||||
case 1:
|
||||
return;
|
||||
case 2:
|
||||
if (((dVal >> ((i + 1) * 2)) & 1) != 1) return;
|
||||
dVal += 1 << (i * 2 + 1);
|
||||
return;
|
||||
case 3:
|
||||
int temp = 3 << (i * 2);
|
||||
temp ^= -1;
|
||||
dVal = dVal & temp;
|
||||
b((i + 1) * 2);
|
||||
break;
|
||||
}
|
||||
i++;
|
||||
}
|
||||
}
|
||||
|
||||
private void b(int pos) {
|
||||
if (pos == 0) {
|
||||
Zeckendorf thiz = this;
|
||||
thiz.inc();
|
||||
return;
|
||||
}
|
||||
if (((dVal >> pos) & 1) == 0) {
|
||||
dVal += 1 << pos;
|
||||
a(pos / 2);
|
||||
if (pos > 1) a(pos / 2 - 1);
|
||||
} else {
|
||||
int temp = 1 << pos;
|
||||
temp ^= -1;
|
||||
dVal = dVal & temp;
|
||||
b(pos + 1);
|
||||
b(pos - (pos > 1 ? 2 : 1));
|
||||
}
|
||||
}
|
||||
|
||||
private void c(int pos) {
|
||||
if (((dVal >> pos) & 1) == 1) {
|
||||
int temp = 1 << pos;
|
||||
temp ^= -1;
|
||||
dVal = dVal & temp;
|
||||
return;
|
||||
}
|
||||
c(pos + 1);
|
||||
if (pos > 0) {
|
||||
b(pos - 1);
|
||||
} else {
|
||||
Zeckendorf thiz = this;
|
||||
thiz.inc();
|
||||
}
|
||||
}
|
||||
|
||||
public Zeckendorf inc() {
|
||||
dVal++;
|
||||
a(0);
|
||||
return this;
|
||||
}
|
||||
|
||||
public void plusAssign(Zeckendorf other) {
|
||||
for (int gn = 0; gn < (other.dLen + 1) * 2; gn++) {
|
||||
if (((other.dVal >> gn) & 1) == 1) {
|
||||
b(gn);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
public void minusAssign(Zeckendorf other) {
|
||||
for (int gn = 0; gn < (other.dLen + 1) * 2; gn++) {
|
||||
if (((other.dVal >> gn) & 1) == 1) {
|
||||
c(gn);
|
||||
}
|
||||
}
|
||||
while ((((dVal >> dLen * 2) & 3) == 0) || (dLen == 0)) {
|
||||
dLen--;
|
||||
}
|
||||
}
|
||||
|
||||
public void timesAssign(Zeckendorf other) {
|
||||
Zeckendorf na = other.copy();
|
||||
Zeckendorf nb = other.copy();
|
||||
Zeckendorf nt;
|
||||
Zeckendorf nr = new Zeckendorf();
|
||||
for (int i = 0; i < (dLen + 1) * 2; i++) {
|
||||
if (((dVal >> i) & 1) > 0) {
|
||||
nr.plusAssign(nb);
|
||||
}
|
||||
nt = nb.copy();
|
||||
nb.plusAssign(na);
|
||||
na = nt.copy();
|
||||
}
|
||||
dVal = nr.dVal;
|
||||
dLen = nr.dLen;
|
||||
}
|
||||
|
||||
private Zeckendorf copy() {
|
||||
Zeckendorf z = new Zeckendorf();
|
||||
z.dVal = dVal;
|
||||
z.dLen = dLen;
|
||||
return z;
|
||||
}
|
||||
|
||||
@Override
|
||||
public int compareTo(Zeckendorf other) {
|
||||
return ((Integer) dVal).compareTo(other.dVal);
|
||||
}
|
||||
|
||||
@Override
|
||||
public String toString() {
|
||||
if (dVal == 0) {
|
||||
return "0";
|
||||
}
|
||||
|
||||
int idx = (dVal >> (dLen * 2)) & 3;
|
||||
StringBuilder stringBuilder = new StringBuilder(dig1.get(idx));
|
||||
for (int i = dLen - 1; i >= 0; i--) {
|
||||
idx = (dVal >> (i * 2)) & 3;
|
||||
stringBuilder.append(dig.get(idx));
|
||||
}
|
||||
return stringBuilder.toString();
|
||||
}
|
||||
|
||||
public static void main(String[] args) {
|
||||
System.out.println("Addition:");
|
||||
Zeckendorf g = new Zeckendorf("10");
|
||||
g.plusAssign(new Zeckendorf("10"));
|
||||
System.out.println(g);
|
||||
g.plusAssign(new Zeckendorf("10"));
|
||||
System.out.println(g);
|
||||
g.plusAssign(new Zeckendorf("1001"));
|
||||
System.out.println(g);
|
||||
g.plusAssign(new Zeckendorf("1000"));
|
||||
System.out.println(g);
|
||||
g.plusAssign(new Zeckendorf("10101"));
|
||||
System.out.println(g);
|
||||
|
||||
System.out.println("\nSubtraction:");
|
||||
g = new Zeckendorf("1000");
|
||||
g.minusAssign(new Zeckendorf("101"));
|
||||
System.out.println(g);
|
||||
g = new Zeckendorf("10101010");
|
||||
g.minusAssign(new Zeckendorf("1010101"));
|
||||
System.out.println(g);
|
||||
|
||||
System.out.println("\nMultiplication:");
|
||||
g = new Zeckendorf("1001");
|
||||
g.timesAssign(new Zeckendorf("101"));
|
||||
System.out.println(g);
|
||||
g = new Zeckendorf("101010");
|
||||
g.plusAssign(new Zeckendorf("101"));
|
||||
System.out.println(g);
|
||||
}
|
||||
}
|
||||
172
Task/Zeckendorf-arithmetic/Julia/zeckendorf-arithmetic.julia
Normal file
172
Task/Zeckendorf-arithmetic/Julia/zeckendorf-arithmetic.julia
Normal file
|
|
@ -0,0 +1,172 @@
|
|||
import Base.*, Base.+, Base.-, Base./, Base.show, Base.!=, Base.==, Base.<=, Base.<, Base.>, Base.>=, Base.divrem
|
||||
|
||||
const z0 = "0"
|
||||
const z1 = "1"
|
||||
const flipordered = (z1 < z0)
|
||||
|
||||
mutable struct Z s::String end
|
||||
Z() = Z(z0)
|
||||
Z(z::Z) = Z(z.s)
|
||||
|
||||
pairlen(x::Z, y::Z) = max(length(x.s), length(y.s))
|
||||
tolen(x::Z, n::Int) = (s = x.s; while length(s) < n s = z0 * s end; s)
|
||||
|
||||
<(x::Z, y::Z) = (l = pairlen(x, y); flipordered ? tolen(x, l) > tolen(y, l) : tolen(x, l) < tolen(y, l))
|
||||
>(x::Z, y::Z) = (l = pairlen(x, y); flipordered ? tolen(x, l) < tolen(y, l) : tolen(x, l) > tolen(y, l))
|
||||
==(x::Z, y::Z) = (l = pairlen(x, y); tolen(x, l) == tolen(y, l))
|
||||
<=(x::Z, y::Z) = (l = pairlen(x, y); flipordered ? tolen(x, l) >= tolen(y, l) : tolen(x, l) <= tolen(y, l))
|
||||
>=(x::Z, y::Z) = (l = pairlen(x, y); flipordered ? tolen(x, l) <= tolen(y, l) : tolen(x, l) >= tolen(y, l))
|
||||
!=(x::Z, y::Z) = (l = pairlen(x, y); tolen(x, l) != tolen(y, l))
|
||||
|
||||
function tocanonical(z::Z)
|
||||
while occursin(z0 * z1 * z1, z.s)
|
||||
z.s = replace(z.s, z0 * z1 * z1 => z1 * z0 * z0)
|
||||
end
|
||||
len = length(z.s)
|
||||
if len > 1 && z.s[1:2] == z1 * z1
|
||||
z.s = z1 * z0 * z0 * ((len > 2) ? z.s[3:end] : "")
|
||||
end
|
||||
while (len = length(z.s)) > 1 && string(z.s[1]) == z0
|
||||
if len == 2
|
||||
if z.s == z0 * z0
|
||||
z.s = z0
|
||||
elseif z.s == z0 * z1
|
||||
z.s = z1
|
||||
end
|
||||
else
|
||||
z.s = z.s[2:end]
|
||||
end
|
||||
end
|
||||
z
|
||||
end
|
||||
|
||||
function inc(z)
|
||||
if z.s[end] == z0[1]
|
||||
z.s = z.s[1:end-1] * z1[1]
|
||||
elseif z.s[end] == z1[1]
|
||||
if length(z.s) > 1
|
||||
if z.s[end-1:end] == z0 * z1
|
||||
z.s = z.s[1:end-2] * z1 * z0
|
||||
end
|
||||
else
|
||||
z.s = z1 * z0
|
||||
end
|
||||
end
|
||||
tocanonical(z)
|
||||
end
|
||||
|
||||
function dec(z)
|
||||
if z.s[end] == z1[1]
|
||||
z.s = z.s[1:end-1] * z0
|
||||
else
|
||||
if (m = match(Regex(z1 * z0 * '+' * '$'), z.s)) != nothing
|
||||
len = length(m.match)
|
||||
if iseven(len)
|
||||
z.s = z.s[1:end-len] * (z0 * z1) ^ div(len, 2)
|
||||
else
|
||||
z.s = z.s[1:end-len] * (z0 * z1) ^ div(len, 2) * z0
|
||||
end
|
||||
end
|
||||
end
|
||||
tocanonical(z)
|
||||
z
|
||||
end
|
||||
|
||||
function +(x::Z, y::Z)
|
||||
a = Z(x.s)
|
||||
b = Z(y.s)
|
||||
while b.s != z0
|
||||
inc(a)
|
||||
dec(b)
|
||||
end
|
||||
a
|
||||
end
|
||||
|
||||
function -(x::Z, y::Z)
|
||||
a = Z(x.s)
|
||||
b = Z(y.s)
|
||||
while b.s != z0
|
||||
dec(a)
|
||||
dec(b)
|
||||
end
|
||||
a
|
||||
end
|
||||
|
||||
function *(x::Z, y::Z)
|
||||
if (x.s == z0) || (y.s == z0)
|
||||
return Z(z0)
|
||||
elseif x.s == z1
|
||||
return Z(y.s)
|
||||
elseif y.s == z1
|
||||
return Z(x.s)
|
||||
end
|
||||
a = Z(x.s)
|
||||
b = Z(z1)
|
||||
while b != y
|
||||
c = Z(z0)
|
||||
while c != x
|
||||
inc(a)
|
||||
inc(c)
|
||||
end
|
||||
inc(b)
|
||||
end
|
||||
a
|
||||
end
|
||||
|
||||
function divrem(x::Z, y::Z)
|
||||
if y.s == z0
|
||||
throw("Zeckendorf division by 0")
|
||||
elseif (y.s == z1) || (x.s == z0)
|
||||
return Z(x.s)
|
||||
end
|
||||
a = Z(x.s)
|
||||
b = Z(y.s)
|
||||
c = Z(z0)
|
||||
while a > b
|
||||
a = a - b
|
||||
inc(c)
|
||||
end
|
||||
tocanonical(c), tocanonical(a)
|
||||
end
|
||||
|
||||
function /(x::Z, y::Z)
|
||||
a, _ = divrem(x, y)
|
||||
a
|
||||
end
|
||||
|
||||
show(io::IO, z::Z) = show(io, parse(BigInt, tocanonical(z).s))
|
||||
|
||||
function zeckendorftest()
|
||||
a = Z("10")
|
||||
b = Z("1001")
|
||||
c = Z("1000")
|
||||
d = Z("10101")
|
||||
|
||||
println("Addition:")
|
||||
x = a
|
||||
println(x += a)
|
||||
println(x += a)
|
||||
println(x += b)
|
||||
println(x += c)
|
||||
println(x += d)
|
||||
|
||||
println("\nSubtraction:")
|
||||
x = Z("1000")
|
||||
println(x - Z("101"))
|
||||
x = Z("10101010")
|
||||
println(x - Z("1010101"))
|
||||
|
||||
println("\nMultiplication:")
|
||||
x = Z("1001")
|
||||
y = Z("101")
|
||||
println(x * y)
|
||||
println(Z("101010") * y)
|
||||
|
||||
println("\nDivision:")
|
||||
x = Z("1000101")
|
||||
y = Z("101")
|
||||
println(x / y)
|
||||
println(divrem(x, y))
|
||||
end
|
||||
|
||||
zeckendorftest()
|
||||
156
Task/Zeckendorf-arithmetic/Kotlin/zeckendorf-arithmetic.kotlin
Normal file
156
Task/Zeckendorf-arithmetic/Kotlin/zeckendorf-arithmetic.kotlin
Normal file
|
|
@ -0,0 +1,156 @@
|
|||
// version 1.1.51
|
||||
|
||||
class Zeckendorf(x: String = "0") : Comparable<Zeckendorf> {
|
||||
|
||||
var dVal = 0
|
||||
var dLen = 0
|
||||
|
||||
private fun a(n: Int) {
|
||||
var i = n
|
||||
while (true) {
|
||||
if (dLen < i) dLen = i
|
||||
val j = (dVal shr (i * 2)) and 3
|
||||
when (j) {
|
||||
0, 1 -> return
|
||||
|
||||
2 -> {
|
||||
if (((dVal shr ((i + 1) * 2)) and 1) != 1) return
|
||||
dVal += 1 shl (i * 2 + 1)
|
||||
return
|
||||
}
|
||||
|
||||
3 -> {
|
||||
dVal = dVal and (3 shl (i * 2)).inv()
|
||||
b((i + 1) * 2)
|
||||
}
|
||||
}
|
||||
i++
|
||||
}
|
||||
}
|
||||
|
||||
private fun b(pos: Int) {
|
||||
if (pos == 0) {
|
||||
var thiz = this
|
||||
++thiz
|
||||
return
|
||||
}
|
||||
if (((dVal shr pos) and 1) == 0) {
|
||||
dVal += 1 shl pos
|
||||
a(pos / 2)
|
||||
if (pos > 1) a(pos / 2 - 1)
|
||||
}
|
||||
else {
|
||||
dVal = dVal and (1 shl pos).inv()
|
||||
b(pos + 1)
|
||||
b(pos - (if (pos > 1) 2 else 1))
|
||||
}
|
||||
}
|
||||
|
||||
private fun c(pos: Int) {
|
||||
if (((dVal shr pos) and 1) == 1) {
|
||||
dVal = dVal and (1 shl pos).inv()
|
||||
return
|
||||
}
|
||||
c(pos + 1)
|
||||
if (pos > 0) b(pos - 1) else { var thiz = this; ++thiz }
|
||||
}
|
||||
|
||||
init {
|
||||
var q = 1
|
||||
var i = x.length - 1
|
||||
dLen = i / 2
|
||||
while (i >= 0) {
|
||||
dVal += (x[i] - '0').toInt() * q
|
||||
q *= 2
|
||||
i--
|
||||
}
|
||||
}
|
||||
|
||||
operator fun inc(): Zeckendorf {
|
||||
dVal += 1
|
||||
a(0)
|
||||
return this
|
||||
}
|
||||
|
||||
operator fun plusAssign(other: Zeckendorf) {
|
||||
for (gn in 0 until (other.dLen + 1) * 2) {
|
||||
if (((other.dVal shr gn) and 1) == 1) b(gn)
|
||||
}
|
||||
}
|
||||
|
||||
operator fun minusAssign(other: Zeckendorf) {
|
||||
for (gn in 0 until (other.dLen + 1) * 2) {
|
||||
if (((other.dVal shr gn) and 1) == 1) c(gn)
|
||||
}
|
||||
while ((((dVal shr dLen * 2) and 3) == 0) || (dLen == 0)) dLen--
|
||||
}
|
||||
|
||||
operator fun timesAssign(other: Zeckendorf) {
|
||||
var na = other.copy()
|
||||
var nb = other.copy()
|
||||
var nt: Zeckendorf
|
||||
var nr = "0".Z
|
||||
for (i in 0..(dLen + 1) * 2) {
|
||||
if (((dVal shr i) and 1) > 0) nr += nb
|
||||
nt = nb.copy()
|
||||
nb += na
|
||||
na = nt.copy()
|
||||
}
|
||||
dVal = nr.dVal
|
||||
dLen = nr.dLen
|
||||
}
|
||||
|
||||
override operator fun compareTo(other: Zeckendorf) = dVal.compareTo(other.dVal)
|
||||
|
||||
override fun toString(): String {
|
||||
if (dVal == 0) return "0"
|
||||
val sb = StringBuilder(dig1[(dVal shr (dLen * 2)) and 3])
|
||||
for (i in dLen - 1 downTo 0) {
|
||||
sb.append(dig[(dVal shr (i * 2)) and 3])
|
||||
}
|
||||
return sb.toString()
|
||||
}
|
||||
|
||||
fun copy(): Zeckendorf {
|
||||
val z = "0".Z
|
||||
z.dVal = dVal
|
||||
z.dLen = dLen
|
||||
return z
|
||||
}
|
||||
|
||||
companion object {
|
||||
val dig = listOf("00", "01", "10")
|
||||
val dig1 = listOf("", "1", "10")
|
||||
}
|
||||
}
|
||||
|
||||
val String.Z get() = Zeckendorf(this)
|
||||
|
||||
fun main(args: Array<String>) {
|
||||
println("Addition:")
|
||||
var g = "10".Z
|
||||
g += "10".Z
|
||||
println(g)
|
||||
g += "10".Z
|
||||
println(g)
|
||||
g += "1001".Z
|
||||
println(g)
|
||||
g += "1000".Z
|
||||
println(g)
|
||||
g += "10101".Z
|
||||
println(g)
|
||||
println("\nSubtraction:")
|
||||
g = "1000".Z
|
||||
g -= "101".Z
|
||||
println(g)
|
||||
g = "10101010".Z
|
||||
g -= "1010101".Z
|
||||
println(g)
|
||||
println("\nMultiplication:")
|
||||
g = "1001".Z
|
||||
g *= "101".Z
|
||||
println(g)
|
||||
g = "101010".Z
|
||||
g += "101".Z
|
||||
println(g)
|
||||
}
|
||||
142
Task/Zeckendorf-arithmetic/Nim/zeckendorf-arithmetic.nim
Normal file
142
Task/Zeckendorf-arithmetic/Nim/zeckendorf-arithmetic.nim
Normal file
|
|
@ -0,0 +1,142 @@
|
|||
type Zeckendorf = object
|
||||
dVal: Natural
|
||||
dLen: Natural
|
||||
|
||||
const
|
||||
Dig = ["00", "01", "10"]
|
||||
Dig1 = ["", "1", "10"]
|
||||
|
||||
# Forward references.
|
||||
func b(z: var Zeckendorf; pos: Natural)
|
||||
func inc(z: var Zeckendorf)
|
||||
|
||||
|
||||
func a(z: var Zeckendorf; n: Natural) =
|
||||
var i = n
|
||||
while true:
|
||||
|
||||
if z.dLen < i: z.dLen = i
|
||||
let j = z.dVal shr (i * 2) and 3
|
||||
|
||||
case j
|
||||
of 0, 1:
|
||||
return
|
||||
of 2:
|
||||
if (z.dVal shr ((i + 1) * 2) and 1) != 1: return
|
||||
z.dVal += 1 shl (i * 2 + 1)
|
||||
return
|
||||
of 3:
|
||||
z.dVal = z.dVal and not (3 shl (i * 2))
|
||||
z.b((i + 1) * 2)
|
||||
else:
|
||||
assert(false)
|
||||
|
||||
inc i
|
||||
|
||||
|
||||
func b(z: var Zeckendorf; pos: Natural) =
|
||||
if pos == 0:
|
||||
inc z
|
||||
return
|
||||
|
||||
if (z.dVal shr pos and 1) == 0:
|
||||
z.dVal += 1 shl pos
|
||||
z.a(pos div 2)
|
||||
if pos > 1: z.a(pos div 2 - 1)
|
||||
else:
|
||||
z.dVal = z.dVal and not(1 shl pos)
|
||||
z.b(pos + 1)
|
||||
z.b(pos - (if pos > 1: 2 else: 1))
|
||||
|
||||
|
||||
func c(z: var Zeckendorf; pos: Natural) =
|
||||
if (z.dVal shr pos and 1) == 1:
|
||||
z.dVal = z.dVal and not(1 shl pos)
|
||||
return
|
||||
|
||||
z.c(pos + 1)
|
||||
if pos > 0:
|
||||
z.b(pos - 1)
|
||||
else:
|
||||
inc z
|
||||
|
||||
|
||||
func initZeckendorf(s = "0"): Zeckendorf =
|
||||
var q = 1
|
||||
var i = s.high
|
||||
result.dLen = i div 2
|
||||
while i >= 0:
|
||||
result.dVal += (ord(s[i]) - ord('0')) * q
|
||||
q *= 2
|
||||
dec i
|
||||
|
||||
|
||||
func inc(z: var Zeckendorf) =
|
||||
inc z.dVal
|
||||
z.a(0)
|
||||
|
||||
|
||||
func `+=`(z1: var Zeckendorf; z2: Zeckendorf) =
|
||||
for gn in 0 .. (2 * z2.dLen + 1):
|
||||
if (z2.dVal shr gn and 1) == 1:
|
||||
z1.b(gn)
|
||||
|
||||
|
||||
func `-=`(z1: var Zeckendorf; z2: Zeckendorf) =
|
||||
for gn in 0 .. (2 * z2.dLen + 1):
|
||||
if (z2.dVal shr gn and 1) == 1:
|
||||
z1.c(gn)
|
||||
|
||||
while z1.dLen > 0 and (z1.dVal shr (z1.dLen * 2) and 3) == 0:
|
||||
dec z1.dLen
|
||||
|
||||
|
||||
func `*=`(z1: var Zeckendorf; z2: Zeckendorf) =
|
||||
var na, nb = z2
|
||||
var nr: Zeckendorf
|
||||
for i in 0 .. (z1.dLen + 1) * 2:
|
||||
if (z1.dVal shr i and 1) > 0: nr += nb
|
||||
let nt = nb
|
||||
nb += na
|
||||
na = nt
|
||||
z1 = nr
|
||||
|
||||
func`$`(z: var Zeckendorf): string =
|
||||
if z.dVal == 0: return "0"
|
||||
result.add Dig1[z.dVal shr (z.dLen * 2) and 3]
|
||||
for i in countdown(z.dLen - 1, 0):
|
||||
result.add Dig[z.dVal shr (i * 2) and 3]
|
||||
|
||||
when isMainModule:
|
||||
|
||||
var g: Zeckendorf
|
||||
|
||||
echo "Addition:"
|
||||
g = initZeckendorf("10")
|
||||
g += initZeckendorf("10")
|
||||
echo g
|
||||
g += initZeckendorf("10")
|
||||
echo g
|
||||
g += initZeckendorf("1001")
|
||||
echo g
|
||||
g += initZeckendorf("1000")
|
||||
echo g
|
||||
g += initZeckendorf("10101")
|
||||
echo g
|
||||
|
||||
|
||||
echo "\nSubtraction:"
|
||||
g = initZeckendorf("1000")
|
||||
g -= initZeckendorf("101")
|
||||
echo g
|
||||
g = initZeckendorf("10101010")
|
||||
g -= initZeckendorf("1010101")
|
||||
echo g
|
||||
|
||||
echo "\nMultiplication:"
|
||||
g = initZeckendorf("1001")
|
||||
g *= initZeckendorf("101")
|
||||
echo g
|
||||
g = initZeckendorf("101010")
|
||||
g += initZeckendorf("101")
|
||||
echo g
|
||||
98
Task/Zeckendorf-arithmetic/Perl/zeckendorf-arithmetic.pl
Normal file
98
Task/Zeckendorf-arithmetic/Perl/zeckendorf-arithmetic.pl
Normal file
|
|
@ -0,0 +1,98 @@
|
|||
use v5.36;
|
||||
|
||||
package Zeckendorf;
|
||||
use overload qw("" zstring + zadd - zsub ++ zinc -- zdec * zmul / zdiv ge zge);
|
||||
|
||||
sub new ($class, $value) {
|
||||
bless \$value, ref $class || $class;
|
||||
}
|
||||
|
||||
sub zinc ($self, $, $) {
|
||||
local $_ = $$self;
|
||||
s/0$/1/ or s/(?:^|0)1$/10/;
|
||||
1 while s/(?:^|0)11/100/;
|
||||
$$self = $self->new( s/^0+\B//r )
|
||||
}
|
||||
|
||||
sub zdec ($self, $, $) {
|
||||
local $_ = $$self;
|
||||
1 while s/100(?=0*$)/011/;
|
||||
s/1$/0/ || s/10$/01/;
|
||||
$$self = $self->new( s/^0+\B//r )
|
||||
}
|
||||
|
||||
sub zadd ($self, $other, $) {
|
||||
my ($x, $y) = map $self->new($$_), $self, $other;
|
||||
$x++, $y-- while $$y;
|
||||
$x
|
||||
}
|
||||
|
||||
sub zsub ($self, $other, $) {
|
||||
my ($x, $y) = map $self->new($$_), $self, $other;
|
||||
$x--, $y-- while $$y;
|
||||
$x
|
||||
}
|
||||
|
||||
sub zmul ($self, $other, $) {
|
||||
my ($x, $y) = map $self->new($$_), $self, $other;
|
||||
my $product = Zeckendorf->new(0);
|
||||
$product = $product + $x, $y-- while $y;
|
||||
$product
|
||||
}
|
||||
|
||||
sub zdiv ($self, $other, $) {
|
||||
my ($x, $y) = map $self->new($$_), $self, $other;
|
||||
my $quotient = Zeckendorf->new(0);
|
||||
$quotient++, $x = $x - $y while $x ge $y;
|
||||
$quotient
|
||||
}
|
||||
|
||||
sub zge ($self, $other, $) {
|
||||
my $l; $l = length $$other if length $other > ($l = length $$self);
|
||||
0 x ($l - length $$self) . $$self ge 0 x ($l - length $$other) . $$other;
|
||||
}
|
||||
|
||||
sub asdecimal ($self) {
|
||||
my($aa, $bb, $n) = (1, 1, 0);
|
||||
for ( reverse split '', $$self ) {
|
||||
$n += $bb * $_;
|
||||
($aa, $bb) = ($bb, $aa + $bb);
|
||||
}
|
||||
$n
|
||||
}
|
||||
|
||||
sub fromdecimal ($self, $value) {
|
||||
my $z = $self->new(0);
|
||||
$z++ for 1 .. $value;
|
||||
$z
|
||||
}
|
||||
|
||||
sub zstring { ${ shift() } }
|
||||
|
||||
package main;
|
||||
|
||||
for ( split /\n/, <<END ) # test cases
|
||||
1 + 1
|
||||
10 + 10
|
||||
10100 + 1010
|
||||
10100 - 1010
|
||||
10100 * 1010
|
||||
100010 * 100101
|
||||
10100 / 1010
|
||||
101000 / 1000
|
||||
100001000001 / 100010
|
||||
100001000001 / 100101
|
||||
END
|
||||
{
|
||||
my ($left, $op, $right) = split;
|
||||
my ($x, $y) = map Zeckendorf->new($_), $left, $right;
|
||||
my $answer =
|
||||
$op eq '+' ? $x + $y :
|
||||
$op eq '-' ? $x - $y :
|
||||
$op eq '*' ? $x * $y :
|
||||
$op eq '/' ? $x / $y :
|
||||
die "bad op <$op>";
|
||||
printf "%12s %s %-9s => %12s in Zeckendorf\n", $x, $op, $y, $answer;
|
||||
printf "%12d %s %-9d => %12d in decimal\n\n",
|
||||
$x->asdecimal, $op, $y->asdecimal, $answer->asdecimal;
|
||||
}
|
||||
276
Task/Zeckendorf-arithmetic/Phix/zeckendorf-arithmetic.phix
Normal file
276
Task/Zeckendorf-arithmetic/Phix/zeckendorf-arithmetic.phix
Normal file
|
|
@ -0,0 +1,276 @@
|
|||
(phixonline)-->
|
||||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
|
||||
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">fib</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">zeckendorf</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- Same as [[Zeckendorf_number_representation#Phix]]</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$]<</span><span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">fib</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">></span><span style="color: #000000;">2</span> <span style="color: #008080;">and</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">k</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">k</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #000000;">r</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">c</span>
|
||||
<span style="color: #000000;">n</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">*</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">r</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- Convert Zeckendorf number(s) to decimal</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">dec</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">bit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">z</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">dec</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[</span><span style="color: #000000;">bit</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">bit</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">bit</span><span style="color: #0000FF;">></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fib</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">fib</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">fib</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">dec</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">to_bits</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- Simplified copy of int_to_bits(), but in reverse order,
|
||||
-- and +ve only but (also only) as many bits as needed, and
|
||||
-- ensures there are *two* trailing 0 (most significant)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- sanity/avoid infinite loop</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">bits</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #000000;">bits</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- (since eg 101+101 -> 10000)</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">bits</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">to_bits2</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- Apply to_bits() to a and b, and pad to the same length</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sa</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">to_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span>
|
||||
<span style="color: #000000;">sb</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">to_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">diff</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">)-</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">diff</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">diff</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">sa</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">diff</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">else</span> <span style="color: #000000;">sb</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,+</span><span style="color: #000000;">diff</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">to_int</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">bits</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- Copy of bits_to_int(), but in reverse order (lsb last)</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">val</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">bits</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">val</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">p</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">p</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">p</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">val</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%b"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">ds</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">was</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">wth</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- helper for cleanup, validates replacements </span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">de</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ds</span><span style="color: #0000FF;">+</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">was</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ds</span><span style="color: #0000FF;">..</span><span style="color: #000000;">de</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">was</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">was</span><span style="color: #0000FF;">)!=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">wth</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">ds</span><span style="color: #0000FF;">..</span><span style="color: #000000;">de</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">wth</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">zcleanup</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- (shared by zadd and zsub)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000080;font-style:italic;">-- first stage, left to right, {020x -> 100x', 030x -> 110x', 021x->110x, 012x->101x}</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000080;font-style:italic;">-- first stage cleanup</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">3</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 030 -> 111</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 020 -> 101</span>
|
||||
<span style="color: #008080;">else</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 0120 -> 1010</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">3</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 03 -> 11</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 02 -> 10</span>
|
||||
<span style="color: #008080;">else</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rep</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- 012 -> 101</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000080;font-style:italic;">-- second stage, pass 1, right to left, 011 -> 100</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000080;font-style:italic;">-- second stage, pass 2, left to right, 011 -> 100</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]={</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">to_int</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">to_bits2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">zcleanup</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">)))</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">zinc</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">to_bits2</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">reverse</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sa</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sb</span><span style="color: #0000FF;">))</span>
|
||||
<span style="color: #000080;font-style:italic;">-- (/not/ combined with the first pass of the add routine!)</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s3</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s3</span><span style="color: #0000FF;">={</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #000080;font-style:italic;">-- copied from PicoLisp: {1,-1} -> {0,1} and {2,-1} -> {1,1}</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s2</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">s2</span><span style="color: #0000FF;">={</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">elsif</span> <span style="color: #000000;">s2</span><span style="color: #0000FF;">={</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">then</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- sanity check</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">zcleanup</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">zdec</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)}</span> <span style="color: #000080;font-style:italic;">-- (as per task desc)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">bits</span><span style="color: #0000FF;"><</span><span style="color: #000000;">b</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">[$],</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]))</span>
|
||||
<span style="color: #000000;">bits</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">2</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
|
||||
<span style="color: #000000;">bit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">b</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">and_bits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">[</span><span style="color: #000000;">bit</span><span style="color: #0000FF;">])</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">bit</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)}</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
|
||||
<span style="color: #008080;">while</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">[$]<</span><span style="color: #000000;">a</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #000000;">mult</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">[$],</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]))</span>
|
||||
<span style="color: #000000;">bits</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">2</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mult</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">mi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mult</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">mi</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">a</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mi</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #000000;">bits</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">bits</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">}</span> <span style="color: #000080;font-style:italic;">-- (a is the remainder)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
|
||||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">20</span> <span style="color: #008080;">do</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">zi</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zeckendorf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">atom</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zi</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d: %7b (%d)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zi</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
|
||||
<span style="color: #008080;">procedure</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">op</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">expected</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">string</span> <span style="color: #000000;">zres</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)?</span><span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">):</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span><span style="color: #008000;">" rem "</span><span style="color: #0000FF;">)),</span>
|
||||
<span style="color: #000000;">dres</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)?</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"%d rem %d"</span><span style="color: #0000FF;">),</span><span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)),</span>
|
||||
<span style="color: #000000;">aka</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"aka %d %s %d = %s"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span><span style="color: #000000;">op</span><span style="color: #0000FF;">,</span><span style="color: #000000;">decimal</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">),</span><span style="color: #000000;">dres</span><span style="color: #0000FF;">}),</span>
|
||||
<span style="color: #000000;">ok</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zres</span><span style="color: #0000FF;">=</span><span style="color: #000000;">expected</span><span style="color: #0000FF;">?</span><span style="color: #008000;">""</span><span style="color: #0000FF;">:</span><span style="color: #008000;">" *** ERROR ***!!"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s %s %s = %s, %s %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span><span style="color: #000000;">op</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zstr</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">),</span><span style="color: #000000;">zres</span><span style="color: #0000FF;">,</span><span style="color: #000000;">aka</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ok</span><span style="color: #0000FF;">})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
|
||||
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b0</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b0</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"0"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10000"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1001"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10100"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1000100"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1000101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1000101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1001 rem 1"</span><span style="color: #0000FF;">)</span>
|
||||
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1001"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10101"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"100101"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b10101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1010000"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10101010</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10101010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1000000"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1000100"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101010</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1000100"</span><span style="color: #0000FF;">)</span>
|
||||
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101000"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101000</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10100"</span><span style="color: #0000FF;">)</span>
|
||||
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100010</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100101</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"100001000001"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100001000001</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b100001000001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101010001 rem 0"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101000101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101000101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b101001</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101010000010101"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101010000010101</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b101010000010101</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1001010001001 rem 10"</span><span style="color: #0000FF;">)</span>
|
||||
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100010010100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100010010100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"100000000010101"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100010010100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100010010100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10010001000010"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10000</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1001000001</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10100010010100"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1010001010000001001</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100000000100000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b1010001010000001001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b100000000100000</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10001 rem 10100001010101"</span><span style="color: #0000FF;">)</span>
|
||||
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"+"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zadd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101000"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zsub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"101000001"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"1 rem 101"</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">integer</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zmul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0b10100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"/"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zdiv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0b1010</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"10100 rem 0"</span><span style="color: #0000FF;">)</span>
|
||||
<!--
|
||||
133
Task/Zeckendorf-arithmetic/PicoLisp/zeckendorf-arithmetic.l
Normal file
133
Task/Zeckendorf-arithmetic/PicoLisp/zeckendorf-arithmetic.l
Normal file
|
|
@ -0,0 +1,133 @@
|
|||
(seed (in "/dev/urandom" (rd 8)))
|
||||
|
||||
(de unpad (Lst)
|
||||
(while (=0 (car Lst))
|
||||
(pop 'Lst) )
|
||||
Lst )
|
||||
|
||||
(de numz (N)
|
||||
(let Fibs (1 1)
|
||||
(while (>= N (+ (car Fibs) (cadr Fibs)))
|
||||
(push 'Fibs (+ (car Fibs) (cadr Fibs))) )
|
||||
(make
|
||||
(for I (uniq Fibs)
|
||||
(if (> I N)
|
||||
(link 0)
|
||||
(link 1)
|
||||
(dec 'N I) ) ) ) ) )
|
||||
|
||||
(de znum (Lst)
|
||||
(let Fibs (1 1)
|
||||
(do (dec (length Lst))
|
||||
(push 'Fibs (+ (car Fibs) (cadr Fibs))) )
|
||||
(sum
|
||||
'((X Y) (unless (=0 X) Y))
|
||||
Lst
|
||||
(uniq Fibs) ) ) )
|
||||
|
||||
(de incz (Lst)
|
||||
(addz Lst (1)) )
|
||||
|
||||
(de decz (Lst)
|
||||
(subz Lst (1)) )
|
||||
|
||||
(de addz (Lst1 Lst2)
|
||||
(let Max (max (length Lst1) (length Lst2))
|
||||
(reorg
|
||||
(mapcar + (need Max Lst1 0) (need Max Lst2 0)) ) ) )
|
||||
|
||||
(de subz (Lst1 Lst2)
|
||||
(use (@A @B)
|
||||
(let
|
||||
(Max (max (length Lst1) (length Lst2))
|
||||
Lst (mapcar - (need Max Lst1 0) (need Max Lst2 0)) )
|
||||
(loop
|
||||
(while (match '(@A 1 0 0 @B) Lst)
|
||||
(setq Lst (append @A (0 1 1) @B)) )
|
||||
(while (match '(@A 1 -1 0 @B) Lst)
|
||||
(setq Lst (append @A (0 0 1) @B)) )
|
||||
(while (match '(@A 1 -1 1 @B) Lst)
|
||||
(setq Lst (append @A (0 0 2) @B)) )
|
||||
(while (match '(@A 1 0 -1 @B) Lst)
|
||||
(setq Lst (append @A (0 1 0) @B)) )
|
||||
(while (match '(@A 2 0 0 @B) Lst)
|
||||
(setq Lst (append @A (1 1 1) @B)) )
|
||||
(while (match '(@A 2 -1 0 @B) Lst)
|
||||
(setq Lst (append @A (1 0 1) @B)) )
|
||||
(while (match '(@A 2 -1 1 @B) Lst)
|
||||
(setq Lst (append @A (1 0 2) @B)) )
|
||||
(while (match '(@A 2 0 -1 @B) Lst)
|
||||
(setq Lst (append @A (1 1 0) @B)) )
|
||||
(while (match '(@A 1 -1) Lst)
|
||||
(setq Lst (append @A (0 1))) )
|
||||
(while (match '(@A 2 -1) Lst)
|
||||
(setq Lst (append @A (1 1))) )
|
||||
(NIL (match '(@A -1 @B) Lst)) )
|
||||
(reorg (unpad Lst)) ) ) )
|
||||
|
||||
(de mulz (Lst1 Lst2)
|
||||
(let (Sums (list Lst1) Mulz (0))
|
||||
(mapc
|
||||
'((X)
|
||||
(when (= 1 (car X))
|
||||
(setq Mulz (addz (cdr X) Mulz)) )
|
||||
Mulz )
|
||||
(mapcar
|
||||
'((X)
|
||||
(cons
|
||||
X
|
||||
(push 'Sums (addz (car Sums) (cadr Sums))) ) )
|
||||
(reverse Lst2) ) ) ) )
|
||||
|
||||
(de divz (Lst1 Lst2)
|
||||
(let Q 0
|
||||
(while (lez Lst2 Lst1)
|
||||
(setq Lst1 (subz Lst1 Lst2))
|
||||
(setq Q (incz Q)) )
|
||||
(list Q (or Lst1 (0))) ) )
|
||||
|
||||
(de reorg (Lst)
|
||||
(use (@A @B)
|
||||
(let Lst (reverse Lst)
|
||||
(loop
|
||||
(while (match '(@A 1 1 @B) Lst)
|
||||
(if @B
|
||||
(inc (nth @B 1))
|
||||
(setq @B (1)) )
|
||||
(setq Lst (append @A (0 0) @B) ) )
|
||||
(while (match '(@A 2 @B) Lst)
|
||||
(inc
|
||||
(if (cdr @A)
|
||||
(tail 2 @A)
|
||||
@A ) )
|
||||
(if @B
|
||||
(inc (nth @B 1))
|
||||
(setq @B (1)) )
|
||||
(setq Lst (append @A (0) @B)) )
|
||||
(NIL
|
||||
(or
|
||||
(match '(@A 1 1 @B) Lst)
|
||||
(match '(@A 2 @B) Lst) ) ) )
|
||||
(reverse Lst) ) ) )
|
||||
|
||||
(de lez (Lst1 Lst2)
|
||||
(let Max (max (length Lst1) (length Lst2))
|
||||
(<= (need Max Lst1 0) (need Max Lst2 0)) ) )
|
||||
|
||||
(let (X 0 Y 0)
|
||||
(do 1024
|
||||
(setq X (rand 1 1024))
|
||||
(setq Y (rand 1 1024))
|
||||
(test (numz (+ X Y)) (addz (numz X) (numz Y)))
|
||||
(test (numz (* X Y)) (mulz (numz X) (numz Y)))
|
||||
(test (numz (+ X 1)) (incz (numz X))) )
|
||||
|
||||
(do 1024
|
||||
(setq X (rand 129 1024))
|
||||
(setq Y (rand 1 128))
|
||||
(test (numz (- X Y)) (subz (numz X) (numz Y)))
|
||||
(test (numz (/ X Y)) (car (divz (numz X) (numz Y))))
|
||||
(test (numz (% X Y)) (cadr (divz (numz X) (numz Y))))
|
||||
(test (numz (- X 1)) (decz (numz X))) ) )
|
||||
|
||||
(bye)
|
||||
144
Task/Zeckendorf-arithmetic/Python/zeckendorf-arithmetic.py
Normal file
144
Task/Zeckendorf-arithmetic/Python/zeckendorf-arithmetic.py
Normal file
|
|
@ -0,0 +1,144 @@
|
|||
import copy
|
||||
|
||||
class Zeckendorf:
|
||||
def __init__(self, x='0'):
|
||||
q = 1
|
||||
i = len(x) - 1
|
||||
self.dLen = int(i / 2)
|
||||
self.dVal = 0
|
||||
while i >= 0:
|
||||
self.dVal = self.dVal + (ord(x[i]) - ord('0')) * q
|
||||
q = q * 2
|
||||
i = i -1
|
||||
|
||||
def a(self, n):
|
||||
i = n
|
||||
while True:
|
||||
if self.dLen < i:
|
||||
self.dLen = i
|
||||
j = (self.dVal >> (i * 2)) & 3
|
||||
if j == 0 or j == 1:
|
||||
return
|
||||
if j == 2:
|
||||
if (self.dVal >> ((i + 1) * 2) & 1) != 1:
|
||||
return
|
||||
self.dVal = self.dVal + (1 << (i * 2 + 1))
|
||||
return
|
||||
if j == 3:
|
||||
temp = 3 << (i * 2)
|
||||
temp = temp ^ -1
|
||||
self.dVal = self.dVal & temp
|
||||
self.b((i + 1) * 2)
|
||||
i = i + 1
|
||||
|
||||
def b(self, pos):
|
||||
if pos == 0:
|
||||
self.inc()
|
||||
return
|
||||
if (self.dVal >> pos) & 1 == 0:
|
||||
self.dVal = self.dVal + (1 << pos)
|
||||
self.a(int(pos / 2))
|
||||
if pos > 1:
|
||||
self.a(int(pos / 2) - 1)
|
||||
else:
|
||||
temp = 1 << pos
|
||||
temp = temp ^ -1
|
||||
self.dVal = self.dVal & temp
|
||||
self.b(pos + 1)
|
||||
self.b(pos - (2 if pos > 1 else 1))
|
||||
|
||||
def c(self, pos):
|
||||
if (self.dVal >> pos) & 1 == 1:
|
||||
temp = 1 << pos
|
||||
temp = temp ^ -1
|
||||
self.dVal = self.dVal & temp
|
||||
return
|
||||
self.c(pos + 1)
|
||||
if pos > 0:
|
||||
self.b(pos - 1)
|
||||
else:
|
||||
self.inc()
|
||||
|
||||
def inc(self):
|
||||
self.dVal = self.dVal + 1
|
||||
self.a(0)
|
||||
|
||||
def __add__(self, rhs):
|
||||
copy = self
|
||||
rhs_dVal = rhs.dVal
|
||||
limit = (rhs.dLen + 1) * 2
|
||||
for gn in range(0, limit):
|
||||
if ((rhs_dVal >> gn) & 1) == 1:
|
||||
copy.b(gn)
|
||||
return copy
|
||||
|
||||
def __sub__(self, rhs):
|
||||
copy = self
|
||||
rhs_dVal = rhs.dVal
|
||||
limit = (rhs.dLen + 1) * 2
|
||||
for gn in range(0, limit):
|
||||
if (rhs_dVal >> gn) & 1 == 1:
|
||||
copy.c(gn)
|
||||
while (((copy.dVal >> ((copy.dLen * 2) & 31)) & 3) == 0) or (copy.dLen == 0):
|
||||
copy.dLen = copy.dLen - 1
|
||||
return copy
|
||||
|
||||
def __mul__(self, rhs):
|
||||
na = copy.deepcopy(rhs)
|
||||
nb = copy.deepcopy(rhs)
|
||||
nr = Zeckendorf()
|
||||
dVal = self.dVal
|
||||
for i in range(0, (self.dLen + 1) * 2):
|
||||
if ((dVal >> i) & 1) > 0:
|
||||
nr = nr + nb
|
||||
nt = copy.deepcopy(nb)
|
||||
nb = nb + na
|
||||
na = copy.deepcopy(nt)
|
||||
return nr
|
||||
|
||||
def __str__(self):
|
||||
dig = ["00", "01", "10"]
|
||||
dig1 = ["", "1", "10"]
|
||||
|
||||
if self.dVal == 0:
|
||||
return '0'
|
||||
idx = (self.dVal >> ((self.dLen * 2) & 31)) & 3
|
||||
sb = dig1[idx]
|
||||
i = self.dLen - 1
|
||||
while i >= 0:
|
||||
idx = (self.dVal >> (i * 2)) & 3
|
||||
sb = sb + dig[idx]
|
||||
i = i - 1
|
||||
return sb
|
||||
|
||||
# main
|
||||
print "Addition:"
|
||||
g = Zeckendorf("10")
|
||||
g = g + Zeckendorf("10")
|
||||
print g
|
||||
g = g + Zeckendorf("10")
|
||||
print g
|
||||
g = g + Zeckendorf("1001")
|
||||
print g
|
||||
g = g + Zeckendorf("1000")
|
||||
print g
|
||||
g = g + Zeckendorf("10101")
|
||||
print g
|
||||
print
|
||||
|
||||
print "Subtraction:"
|
||||
g = Zeckendorf("1000")
|
||||
g = g - Zeckendorf("101")
|
||||
print g
|
||||
g = Zeckendorf("10101010")
|
||||
g = g - Zeckendorf("1010101")
|
||||
print g
|
||||
print
|
||||
|
||||
print "Multiplication:"
|
||||
g = Zeckendorf("1001")
|
||||
g = g * Zeckendorf("101")
|
||||
print g
|
||||
g = Zeckendorf("101010")
|
||||
g = g + Zeckendorf("101")
|
||||
print g
|
||||
|
|
@ -0,0 +1,178 @@
|
|||
[ nextword
|
||||
dup $ "" = if
|
||||
[ $ '"bin" needs to be followed by a string.'
|
||||
message put bail ]
|
||||
dup
|
||||
2 base put
|
||||
$->n
|
||||
base release
|
||||
not if
|
||||
[ drop
|
||||
$ " is not a binary number."
|
||||
join message put
|
||||
bail ]
|
||||
nip
|
||||
swap dip join ] builds bin ( [ $ --> [ $ )
|
||||
|
||||
[ ^ not ] is zeq ( z z --> b )
|
||||
|
||||
[ zeq not ] is zne ( z z --> b )
|
||||
|
||||
[ false unrot
|
||||
[ 2dup zne while
|
||||
rot drop
|
||||
dup 1 & unrot
|
||||
1 >> dip [ 1 >> ]
|
||||
again ]
|
||||
2drop ] is zlt ( z z --> b )
|
||||
|
||||
[ swap zlt ] is zgt ( z z --> b )
|
||||
|
||||
[ zlt not ] is zge ( z z --> b )
|
||||
|
||||
[ zgt not ] is zle ( z z --> b )
|
||||
|
||||
[ dup 1 << & 0 zeq ] is canonical ( z --> b )
|
||||
|
||||
[ [] swap
|
||||
[ dup 1 & rot join
|
||||
swap 1 >>
|
||||
dup not until ]
|
||||
drop ] is bits ( z --> [ )
|
||||
|
||||
[ dup canonical if done
|
||||
0 0 rot bits
|
||||
witheach
|
||||
[ |
|
||||
[ table
|
||||
[ 1 << 0 ]
|
||||
[ 1 << 1 | bin 10 ]
|
||||
[ 1 << 0 ]
|
||||
[ 1 >> 1 |
|
||||
bin 10 << 0 ] ]
|
||||
do ]
|
||||
drop again ] is canonise ( z --> z )
|
||||
|
||||
[ dup bin -100
|
||||
& swap bin 11 & ] is 2blit ( z --> z z )
|
||||
|
||||
[ 2blit bit | canonise ] is zinc ( z --> z )
|
||||
|
||||
[ dup 0 zeq if
|
||||
[ $ "Cannot zdec zero."
|
||||
fail ]
|
||||
1
|
||||
[ 2dup & if done
|
||||
1 << again ]
|
||||
tuck ^
|
||||
swap 1 <<
|
||||
[ bin 10 >>
|
||||
tuck | swap
|
||||
dup 0 zeq until ]
|
||||
drop ] is zdec ( z --> z )
|
||||
|
||||
forward is zadd ( z --> z )
|
||||
|
||||
[ dup 2blit
|
||||
[ table
|
||||
0 bin 10 bin 101 ]
|
||||
unrot bin 10 >>
|
||||
swap 1 <<
|
||||
rot | zadd ] is zdouble ( z --> z )
|
||||
|
||||
[ 2dup ^ canonise
|
||||
unrot &
|
||||
dup 0 zeq iff
|
||||
drop done
|
||||
zdouble again ] resolves zadd ( z z --> z )
|
||||
|
||||
[ tuck take zadd swap put ] is ztally ( z s --> )
|
||||
|
||||
[ 0 temp put
|
||||
dip dup
|
||||
[ dup while
|
||||
dup 1 & if
|
||||
[ over temp ztally ]
|
||||
dip [ tuck zadd ]
|
||||
1 >> again ]
|
||||
drop 2drop temp take ] is zmult ( z z --> z )
|
||||
|
||||
[ 2dup & ~ tuck & dip & ] is exorcise ( z z --> z z )
|
||||
|
||||
[ dup
|
||||
[ 0 ' [ 0 0 0 ] rot 1
|
||||
[ 2dup > while
|
||||
1 << again ]
|
||||
1 <<
|
||||
[ dup while
|
||||
2swap 2over & 0 !=
|
||||
dip
|
||||
[ dup
|
||||
' [ 1 0 0 ]
|
||||
= if
|
||||
[ drop
|
||||
' [ 0 1 1 ] ] ]
|
||||
join
|
||||
behead
|
||||
rot 1 << | swap
|
||||
2swap 1 >> again ]
|
||||
2drop
|
||||
witheach
|
||||
[ dip [ 1 << ] | ]
|
||||
dup bin 111 &
|
||||
bin 100 zeq if
|
||||
[ bin -1000 &
|
||||
bin 11 | ] ]
|
||||
2dup zeq iff drop done
|
||||
nip again ] is defrock ( z --> z )
|
||||
|
||||
[ 2dup zlt if swap
|
||||
dup 0 zeq iff drop done
|
||||
[ exorcise dup while
|
||||
dip defrock
|
||||
exorcise dup while
|
||||
dup dip zadd
|
||||
zdouble
|
||||
again ]
|
||||
drop canonise ] is zdiff ( z z --> z )
|
||||
|
||||
[ dup 0 zeq if
|
||||
[ $ "Z-division by zero."
|
||||
fail ]
|
||||
0 unrot swap
|
||||
temp put
|
||||
dup nested
|
||||
[ dup 0 peek
|
||||
tuck dip rot zadd
|
||||
temp share
|
||||
over zge while
|
||||
swap join
|
||||
again ]
|
||||
drop nip
|
||||
temp take
|
||||
swap witheach
|
||||
[ rot 1 << unrot
|
||||
2dup zge iff
|
||||
[ zdiff
|
||||
dip [ 1 | ] ]
|
||||
else drop ] ] is zdivmod ( z z --> z z )
|
||||
|
||||
[ zdivmod drop ] is zdiv ( z z --> z )
|
||||
|
||||
[ zdivmod nip ] is zmod ( z z --> z )
|
||||
|
||||
[ [ dup while
|
||||
tuck zmod again ]
|
||||
drop ] is zgcd ( z z --> z )
|
||||
|
||||
[ 2dup and iff
|
||||
[ 2dup zgcd
|
||||
zdiv zmult ]
|
||||
else and ] is zlcm ( z z --> z )
|
||||
|
||||
10 times
|
||||
[ 10 15 ** random
|
||||
10 15 ** random
|
||||
2dup lcm echo cr
|
||||
n->z dip n->z
|
||||
zlcm z->n echo cr cr ]
|
||||
195
Task/Zeckendorf-arithmetic/Racket/zeckendorf-arithmetic.rkt
Normal file
195
Task/Zeckendorf-arithmetic/Racket/zeckendorf-arithmetic.rkt
Normal file
|
|
@ -0,0 +1,195 @@
|
|||
#lang racket (require math)
|
||||
|
||||
(define sqrt5 (sqrt 5))
|
||||
(define phi (* 0.5 (+ 1 sqrt5)))
|
||||
|
||||
;; What is the nth fibonnaci number, shifted by 2 so that
|
||||
;; F(0) = 1, F(1) = 2, ...?
|
||||
;;
|
||||
(define (F n)
|
||||
(fibonacci (+ n 2)))
|
||||
|
||||
;; What is the largest n such that F(n) <= m?
|
||||
;;
|
||||
(define (F* m)
|
||||
(let ([n (- (inexact->exact (round (/ (log (* m sqrt5)) (log phi)))) 2)])
|
||||
(if (<= (F n) m) n (sub1 n))))
|
||||
|
||||
(define (zeck->natural z)
|
||||
(for/sum ([i (reverse z)]
|
||||
[j (in-naturals)])
|
||||
(* i (F j))))
|
||||
|
||||
(define (natural->zeck n)
|
||||
(if (zero? n)
|
||||
null
|
||||
(for/list ([i (in-range (F* n) -1 -1)])
|
||||
(let ([f (F i)])
|
||||
(cond [(>= n f) (set! n (- n f))
|
||||
1]
|
||||
[else 0])))))
|
||||
|
||||
; Extend list to the right to a length of len with repeated padding elements
|
||||
;
|
||||
(define (pad lst len [padding 0])
|
||||
(append lst (make-list (- len (length lst)) padding)))
|
||||
|
||||
; Strip padding elements from the left of the list
|
||||
;
|
||||
(define (unpad lst [padding 0])
|
||||
(cond [(null? lst) lst]
|
||||
[(equal? (first lst) padding) (unpad (rest lst) padding)]
|
||||
[else lst]))
|
||||
|
||||
;; Run a filter function across a window in a list from left to right
|
||||
;;
|
||||
(define (left->right width fn)
|
||||
(λ (lst)
|
||||
(let F ([a lst])
|
||||
(if (< (length a) width)
|
||||
a
|
||||
(let ([f (fn (take a width))])
|
||||
(cons (first f) (F (append (rest f) (drop a width)))))))))
|
||||
|
||||
;; Run a function fn across a window in a list from right to left
|
||||
;;
|
||||
(define (right->left width fn)
|
||||
(λ (lst)
|
||||
(let F ([a lst])
|
||||
(if (< (length a) width)
|
||||
a
|
||||
(let ([f (fn (take-right a width))])
|
||||
(append (F (append (drop-right a width) (drop-right f 1)))
|
||||
(list (last f))))))))
|
||||
|
||||
;; (a0 a1 a2 ... an) -> (a0 a1 a2 ... (fn ... an))
|
||||
;;
|
||||
(define (replace-tail width fn)
|
||||
(λ (lst)
|
||||
(append (drop-right lst width) (fn (take-right lst width)))))
|
||||
|
||||
(define (rule-a lst)
|
||||
(match lst
|
||||
[(list 0 2 0 x) (list 1 0 0 (add1 x))]
|
||||
[(list 0 3 0 x) (list 1 1 0 (add1 x))]
|
||||
[(list 0 2 1 x) (list 1 1 0 x)]
|
||||
[(list 0 1 2 x) (list 1 0 1 x)]
|
||||
[else lst]))
|
||||
|
||||
(define (rule-a-tail lst)
|
||||
(match lst
|
||||
[(list x 0 3 0) (list x 1 1 1)]
|
||||
[(list x 0 2 0) (list x 1 0 1)]
|
||||
[(list 0 1 2 0) (list 1 0 1 0)]
|
||||
[(list x y 0 3) (list x y 1 1)]
|
||||
[(list x y 0 2) (list x y 1 0)]
|
||||
[(list x 0 1 2) (list x 1 0 0)]
|
||||
[else lst]))
|
||||
|
||||
(define (rule-b lst)
|
||||
(match lst
|
||||
[(list 0 1 1) (list 1 0 0)]
|
||||
[else lst]))
|
||||
|
||||
(define (rule-c lst)
|
||||
(match lst
|
||||
[(list 1 0 0) (list 0 1 1)]
|
||||
[(list 1 -1 0) (list 0 0 1)]
|
||||
[(list 1 -1 1) (list 0 0 2)]
|
||||
[(list 1 0 -1) (list 0 1 0)]
|
||||
[(list 2 0 0) (list 1 1 1)]
|
||||
[(list 2 -1 0) (list 1 0 1)]
|
||||
[(list 2 -1 1) (list 1 0 2)]
|
||||
[(list 2 0 -1) (list 1 1 0)]
|
||||
[else lst]))
|
||||
|
||||
(define (zeck-combine op y z [f identity])
|
||||
(let* ([bits (max (add1 (length y)) (add1 (length z)) 4)]
|
||||
[f0 (λ (x) (pad (reverse x) bits))]
|
||||
[f1 (left->right 4 rule-a)]
|
||||
[f2 (replace-tail 4 rule-a-tail)]
|
||||
[f3 (right->left 3 rule-b)]
|
||||
[f4 (left->right 3 rule-b)])
|
||||
((compose1 unpad f4 f3 f2 f1 f reverse) (map op (f0 y) (f0 z)))))
|
||||
|
||||
(define (zeck+ y z)
|
||||
(zeck-combine + y z))
|
||||
|
||||
(define (zeck- y z)
|
||||
(when (zeck< y z) (error (format "~a" `(zeck-: cannot subtract since ,y < ,z))))
|
||||
(zeck-combine - y z (left->right 3 rule-c)))
|
||||
|
||||
(define (zeck* y z)
|
||||
(define (M ry Zn Zn_1 [acc null])
|
||||
(if (null? ry)
|
||||
acc
|
||||
(M (rest ry) (zeck+ Zn Zn_1) Zn
|
||||
(if (zero? (first ry)) acc (zeck+ acc Zn)))))
|
||||
(cond [(zeck< z y) (zeck* z y)]
|
||||
[(null? y) null] ; 0 * z -> 0
|
||||
[else (M (reverse y) z z)]))
|
||||
|
||||
(define (zeck-quotient/remainder y z)
|
||||
(define (M Zn acc)
|
||||
(if (zeck< y Zn)
|
||||
(drop-right acc 1)
|
||||
(M (zeck+ Zn (first acc)) (cons Zn acc))))
|
||||
(define (D x m [acc null])
|
||||
(if (null? m)
|
||||
(values (reverse acc) x)
|
||||
(let* ([v (first m)]
|
||||
[smaller (zeck< v x)]
|
||||
[bit (if smaller 1 0)]
|
||||
[x_ (if smaller (zeck- x v) x)])
|
||||
(D x_ (rest m) (cons bit acc)))))
|
||||
(D y (M z (list z))))
|
||||
|
||||
(define (zeck-quotient y z)
|
||||
(let-values ([(quotient _) (zeck-quotient/remainder y z)])
|
||||
quotient))
|
||||
|
||||
(define (zeck-remainder y z)
|
||||
(let-values ([(_ remainder) (zeck-quotient/remainder y z)])
|
||||
remainder))
|
||||
|
||||
(define (zeck-add1 z)
|
||||
(zeck+ z '(1)))
|
||||
|
||||
(define (zeck= y z)
|
||||
(equal? (unpad y) (unpad z)))
|
||||
|
||||
(define (zeck< y z)
|
||||
; Compare equal-length unpadded zecks
|
||||
(define (LT a b)
|
||||
(if (null? a)
|
||||
#f
|
||||
(let ([a0 (first a)] [b0 (first b)])
|
||||
(if (= a0 b0)
|
||||
(LT (rest a) (rest b))
|
||||
(= a0 0)))))
|
||||
|
||||
(let* ([a (unpad y)] [len-a (length a)]
|
||||
[b (unpad z)] [len-b (length b)])
|
||||
(cond [(< len-a len-b) #t]
|
||||
[(> len-a len-b) #f]
|
||||
[else (LT a b)])))
|
||||
|
||||
(define (zeck> y z)
|
||||
(not (or (zeck= y z) (zeck< y z))))
|
||||
|
||||
|
||||
;; Examples
|
||||
;;
|
||||
(define (example op-name op a b)
|
||||
(let* ([y (natural->zeck a)]
|
||||
[z (natural->zeck b)]
|
||||
[x (op y z)]
|
||||
[c (zeck->natural x)])
|
||||
(printf "~a ~a ~a = ~a ~a ~a = ~a = ~a\n"
|
||||
a op-name b y op-name z x c)))
|
||||
|
||||
(example '+ zeck+ 888 111)
|
||||
(example '- zeck- 888 111)
|
||||
(example '* zeck* 8 111)
|
||||
(example '/ zeck-quotient 9876 1000)
|
||||
(example '% zeck-remainder 9876 1000)
|
||||
99
Task/Zeckendorf-arithmetic/Raku/zeckendorf-arithmetic.raku
Normal file
99
Task/Zeckendorf-arithmetic/Raku/zeckendorf-arithmetic.raku
Normal file
|
|
@ -0,0 +1,99 @@
|
|||
my $z1 = '1'; # glyph to use for a '1'
|
||||
my $z0 = '0'; # glyph to use for a '0'
|
||||
|
||||
sub zorder($a) { ($z0 lt $z1) ?? $a !! $a.trans([$z0, $z1] => [$z1, $z0]) }
|
||||
|
||||
######## Zeckendorf comparison operators #########
|
||||
|
||||
# less than
|
||||
sub infix:<ltz>($a, $b) { $a.&zorder lt $b.&zorder }
|
||||
|
||||
# greater than
|
||||
sub infix:<gtz>($a, $b) { $a.&zorder gt $b.&zorder }
|
||||
|
||||
# equal
|
||||
sub infix:<eqz>($a, $b) { $a eq $b }
|
||||
|
||||
# not equal
|
||||
sub infix:<nez>($a, $b) { $a ne $b }
|
||||
|
||||
######## Operators for Zeckendorf arithmetic ########
|
||||
|
||||
# post increment
|
||||
sub postfix:<++z>($a is rw) {
|
||||
$a = ("$z0$z0"~$a).subst(/("$z0$z0")($z1+ %% $z0)?$/,
|
||||
-> $/ { "$z0$z1" ~ ($1 ?? $z0 x $1.chars !! '') });
|
||||
$a ~~ s/^$z0+//;
|
||||
$a
|
||||
}
|
||||
|
||||
# post decrement
|
||||
sub postfix:<--z>($a is rw) {
|
||||
$a.=subst(/$z1($z0*)$/,
|
||||
-> $/ {$z0 ~ "$z1$z0" x $0.chars div 2 ~ $z1 x $0.chars mod 2});
|
||||
$a ~~ s/^$z0+(.+)$/$0/;
|
||||
$a
|
||||
}
|
||||
|
||||
# addition
|
||||
sub infix:<+z>($a is copy, $b is copy) { $a++z; $a++z while $b--z nez $z0; $a }
|
||||
|
||||
# subtraction
|
||||
sub infix:<-z>($a is copy, $b is copy) { $a--z; $a--z while $b--z nez $z0; $a }
|
||||
|
||||
# multiplication
|
||||
sub infix:<×z>($a, $b) {
|
||||
return $z0 if $a eqz $z0 or $b eqz $z0;
|
||||
return $a if $b eqz $z1;
|
||||
return $b if $a eqz $z1;
|
||||
my $c = $a;
|
||||
my $d = $z1;
|
||||
repeat {
|
||||
my $e = $z0;
|
||||
repeat { $c++z; $e++z } until $e eqz $a;
|
||||
$d++z;
|
||||
} until $d eqz $b;
|
||||
$c
|
||||
}
|
||||
|
||||
# division (really more of a div mod)
|
||||
sub infix:</z>($a is copy, $b is copy) {
|
||||
fail "Divide by zero" if $b eqz $z0;
|
||||
return $a if $a eqz $z0 or $b eqz $z1;
|
||||
my $c = $z0;
|
||||
repeat {
|
||||
my $d = $b +z ($z1 ~ $z0);
|
||||
$c++z;
|
||||
$a++z;
|
||||
$a--z while $d--z nez $z0
|
||||
} until $a ltz $b;
|
||||
$c ~= " remainder $a" if $a nez $z0;
|
||||
$c
|
||||
}
|
||||
|
||||
###################### Testing ######################
|
||||
|
||||
# helper sub to translate constants into the particular glyphs you used
|
||||
sub z($a) { $a.trans([<1 0>] => [$z1, $z0]) }
|
||||
|
||||
say "Using the glyph '$z1' for 1 and '$z0' for 0\n";
|
||||
|
||||
my $fmt = "%-22s = %15s %s\n";
|
||||
|
||||
my $zeck = $z1;
|
||||
|
||||
printf( $fmt, "$zeck++z", $zeck++z, '# increment' ) for 1 .. 10;
|
||||
|
||||
printf $fmt, "$zeck +z {z('1010')}", $zeck +z= z('1010'), '# addition';
|
||||
|
||||
printf $fmt, "$zeck -z {z('100')}", $zeck -z= z('100'), '# subtraction';
|
||||
|
||||
printf $fmt, "$zeck ×z {z('100101')}", $zeck ×z= z('100101'), '# multiplication';
|
||||
|
||||
printf $fmt, "$zeck /z {z('100')}", $zeck /z= z('100'), '# division';
|
||||
|
||||
printf( $fmt, "$zeck--z", $zeck--z, '# decrement' ) for 1 .. 5;
|
||||
|
||||
printf $fmt, "$zeck ×z {z('101001')}", $zeck ×z= z('101001'), '# multiplication';
|
||||
|
||||
printf $fmt, "$zeck /z {z('100')}", $zeck /z= z('100'), '# division';
|
||||
331
Task/Zeckendorf-arithmetic/Scala/zeckendorf-arithmetic.scala
Normal file
331
Task/Zeckendorf-arithmetic/Scala/zeckendorf-arithmetic.scala
Normal file
|
|
@ -0,0 +1,331 @@
|
|||
import scala.collection.mutable.ListBuffer
|
||||
|
||||
object ZeckendorfArithmetic extends App {
|
||||
|
||||
|
||||
val elapsed: (=> Unit) => Long = f => {
|
||||
val s = System.currentTimeMillis
|
||||
|
||||
f
|
||||
|
||||
(System.currentTimeMillis - s) / 1000
|
||||
}
|
||||
val add: (Z, Z) => Z = (z1, z2) => z1 + z2
|
||||
val subtract: (Z, Z) => Z = (z1, z2) => z1 - z2
|
||||
val multiply: (Z, Z) => Z = (z1, z2) => z1 * z2
|
||||
val divide: (Z, Z) => Option[Z] = (z1, z2) => z1 / z2
|
||||
val modulo: (Z, Z) => Option[Z] = (z1, z2) => z1 % z2
|
||||
val ops = Map(("+", add), ("-", subtract), ("*", multiply), ("/", divide), ("%", modulo))
|
||||
val calcs = List(
|
||||
(Z("101"), "+", Z("10100"))
|
||||
, (Z("101"), "-", Z("10100"))
|
||||
, (Z("101"), "*", Z("10100"))
|
||||
, (Z("101"), "/", Z("10100"))
|
||||
, (Z("-1010101"), "+", Z("10100"))
|
||||
, (Z("-1010101"), "-", Z("10100"))
|
||||
, (Z("-1010101"), "*", Z("10100"))
|
||||
, (Z("-1010101"), "/", Z("10100"))
|
||||
, (Z("1000101010"), "+", Z("10101010"))
|
||||
, (Z("1000101010"), "-", Z("10101010"))
|
||||
, (Z("1000101010"), "*", Z("10101010"))
|
||||
, (Z("1000101010"), "/", Z("10101010"))
|
||||
, (Z("10100"), "+", Z("1010"))
|
||||
, (Z("100101"), "-", Z("100"))
|
||||
, (Z("1010101010101010101"), "+", Z("-1010101010101"))
|
||||
, (Z("1010101010101010101"), "-", Z("-1010101010101"))
|
||||
, (Z("1010101010101010101"), "*", Z("-1010101010101"))
|
||||
, (Z("1010101010101010101"), "/", Z("-1010101010101"))
|
||||
, (Z("1010101010101010101"), "%", Z("-1010101010101"))
|
||||
, (Z("1010101010101010101"), "+", Z("101010101010101"))
|
||||
, (Z("1010101010101010101"), "-", Z("101010101010101"))
|
||||
, (Z("1010101010101010101"), "*", Z("101010101010101"))
|
||||
, (Z("1010101010101010101"), "/", Z("101010101010101"))
|
||||
, (Z("1010101010101010101"), "%", Z("101010101010101"))
|
||||
, (Z("10101010101010101010"), "+", Z("1010101010101010"))
|
||||
, (Z("10101010101010101010"), "-", Z("1010101010101010"))
|
||||
, (Z("10101010101010101010"), "*", Z("1010101010101010"))
|
||||
, (Z("10101010101010101010"), "/", Z("1010101010101010"))
|
||||
, (Z("10101010101010101010"), "%", Z("1010101010101010"))
|
||||
, (Z("1010"), "%", Z("10"))
|
||||
, (Z("1010"), "%", Z("-10"))
|
||||
, (Z("-1010"), "%", Z("10"))
|
||||
, (Z("-1010"), "%", Z("-10"))
|
||||
, (Z("100"), "/", Z("0"))
|
||||
, (Z("100"), "%", Z("0"))
|
||||
)
|
||||
val iadd: (BigInt, BigInt) => BigInt = (a, b) => a + b
|
||||
val isub: (BigInt, BigInt) => BigInt = (a, b) => a - b
|
||||
|
||||
// just for result checking:
|
||||
|
||||
import Z._
|
||||
|
||||
val imul: (BigInt, BigInt) => BigInt = (a, b) => a * b
|
||||
val idiv: (BigInt, BigInt) => Option[BigInt] = (a, b) => if (b == 0) None else Some(a / b)
|
||||
val imod: (BigInt, BigInt) => Option[BigInt] = (a, b) => if (b == 0) None else Some(a % b)
|
||||
val iops = Map(("+", iadd), ("-", isub), ("*", imul), ("/", idiv), ("%", imod))
|
||||
|
||||
case class Z(var zs: String) {
|
||||
|
||||
import Z._
|
||||
|
||||
require((zs.toSet -- Set('-', '0', '1') == Set()) && (!zs.contains("11")))
|
||||
|
||||
//--- fa(summand1.z,summand2.z) --------------------------
|
||||
val fa: (BigInt, BigInt) => BigInt = (z1, z2) => {
|
||||
val v = z1.toString.toCharArray.map(_.asDigit).reverse.padTo(5, 0).zipAll(z2.toString.toCharArray.map(_.asDigit).reverse, 0, 0)
|
||||
val arr1 = (v.map(p => p._1 + p._2) :+ 0).reverse
|
||||
(0 to arr1.length - 4) foreach { i => //stage1
|
||||
val a = arr1.slice(i, i + 4).toList
|
||||
val b = a.foldRight("")("" + _ + _) dropRight 1
|
||||
val a1 = b match {
|
||||
case "020" => List(1, 0, 0, a(3) + 1)
|
||||
case "030" => List(1, 1, 0, a(3) + 1)
|
||||
case "021" => List(1, 1, 0, a(3))
|
||||
case "012" => List(1, 0, 1, a(3))
|
||||
case _ => a
|
||||
}
|
||||
0 to 3 foreach { j => arr1(j + i) = a1(j) }
|
||||
}
|
||||
val arr2 = arr1.foldRight("")("" + _ + _)
|
||||
.replace("0120", "1010").replace("030", "111").replace("003", "100").replace("020", "101")
|
||||
.replace("003", "100").replace("012", "101").replace("021", "110")
|
||||
.replace("02", "10").replace("03", "11")
|
||||
.reverse.toArray
|
||||
(0 to arr2.length - 3) foreach { i => //stage2, step1
|
||||
val a = arr2.slice(i, i + 3).toList
|
||||
val b = a.foldRight("")("" + _ + _)
|
||||
val a1 = b match {
|
||||
case "110" => List('0', '0', '1')
|
||||
case _ => a
|
||||
}
|
||||
0 to 2 foreach { j => arr2(j + i) = a1(j) }
|
||||
}
|
||||
val arr3 = arr2.foldRight("")("" + _ + _).concat("0").reverse.toArray
|
||||
(0 to arr3.length - 3) foreach { i => //stage2, step2
|
||||
val a = arr3.slice(i, i + 3).toList
|
||||
val b = a.foldRight("")("" + _ + _)
|
||||
val a1 = b match {
|
||||
case "011" => List('1', '0', '0')
|
||||
case _ => a
|
||||
}
|
||||
0 to 2 foreach { j => arr3(j + i) = a1(j) }
|
||||
}
|
||||
BigInt(arr3.foldRight("")("" + _ + _))
|
||||
}
|
||||
//--- fs(minuend.z,subtrahend.z) -------------------------
|
||||
val fs: (BigInt, BigInt) => BigInt = (min, sub) => {
|
||||
val zmvr = min.toString.toCharArray.map(_.asDigit).reverse
|
||||
val zsvr = sub.toString.toCharArray.map(_.asDigit).reverse.padTo(zmvr.length, 0)
|
||||
val v = zmvr.zipAll(zsvr, 0, 0).reverse
|
||||
val last = v.length - 1
|
||||
val zma = zmvr.reverse.toArray
|
||||
|
||||
val zsa = zsvr.reverse.toArray
|
||||
for (i <- (0 to last).reverse) {
|
||||
val e = zma(i) - zsa(i)
|
||||
if (e < 0) {
|
||||
zma(i - 1) = zma(i - 1) - 1
|
||||
zma(i) = 0
|
||||
val part = Z(((i to last).map(zma(_))).foldRight("")("" + _ + _))
|
||||
val carry = Z("1".padTo(last - i, "0").foldRight("")("" + _ + _))
|
||||
val sum = part + carry
|
||||
|
||||
val sums = sum.z.toString
|
||||
(1 to sum.size) foreach { j => zma(last - sum.size + j) = sums(j - 1).asDigit }
|
||||
if (zma(i - 1) < 0) {
|
||||
for (j <- (0 until i).reverse) {
|
||||
if (zma(j) < 0) {
|
||||
zma(j - 1) = zma(j - 1) - 1
|
||||
zma(j) = 0
|
||||
val part = Z(((j to last).map(zma(_))).foldRight("")("" + _ + _))
|
||||
val carry = Z("1".padTo(last - j, "0").foldRight("")("" + _ + _))
|
||||
val sum = part + carry
|
||||
|
||||
val sums = sum.z.toString
|
||||
(1 to sum.size) foreach { k => zma(last - sum.size + k) = sums(k - 1).asDigit }
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
else zma(i) = e
|
||||
zsa(i) = 0
|
||||
}
|
||||
BigInt(zma.foldRight("")("" + _ + _))
|
||||
}
|
||||
//--- fm(multiplicand.z,multplier.z) ---------------------
|
||||
val fm: (BigInt, BigInt) => BigInt = (mc, mp) => {
|
||||
val mct = mt(Z(mc.toString))
|
||||
val mpxi = mp.toString.reverse.toCharArray.map(_.asDigit).zipWithIndex.filter(_._1 != 0).map(_._2)
|
||||
mpxi.foldRight(Z("0"))((fi, sum) => sum + mct(fi)).z
|
||||
}
|
||||
//--- fd(dividend.z,divisor.z) ---------------------------
|
||||
val fd: (BigInt, BigInt) => BigInt = (dd, ds) => {
|
||||
val dst = dt(Z(dd.toString), Z(ds.toString)).reverse
|
||||
var diff = Z(dd.toString)
|
||||
val zd = ListBuffer[String]()
|
||||
0 until dst.length foreach { i =>
|
||||
if (dst(i) > diff) zd += "0" else {
|
||||
diff = diff - dst(i)
|
||||
|
||||
zd += "1"
|
||||
}
|
||||
}
|
||||
BigInt(zd.mkString)
|
||||
}
|
||||
val fasig: (Z, Z) => Int = (z1, z2) => if (z1.z.abs > z2.z.abs) z1.z.signum else z2.z.signum
|
||||
val fssig: (Z, Z) => Int = (z1, z2) =>
|
||||
if ((z1.z.abs > z2.z.abs && z1.z.signum > 0) || (z1.z.abs < z2.z.abs && z1.z.signum < 0)) 1 else -1
|
||||
var z: BigInt = BigInt(zs)
|
||||
|
||||
override def toString: String = "" + z + "Z(i:" + z2i(this) + ")"
|
||||
|
||||
def size: Int = z.abs.toString.length
|
||||
|
||||
def ++ : Z = {
|
||||
val za = this + Z("1")
|
||||
|
||||
this.zs = za.zs
|
||||
|
||||
this.z = za.z
|
||||
|
||||
this
|
||||
}
|
||||
|
||||
def +(that: Z): Z =
|
||||
if (this == Z("0")) that
|
||||
else if (that == Z("0")) this
|
||||
else if (this.z.signum == that.z.signum) Z((fa(this.z.abs.max(that.z.abs), this.z.abs.min(that.z.abs)) * this.z.signum).toString)
|
||||
else if (this.z.abs == that.z.abs) Z("0")
|
||||
else Z((fs(this.z.abs.max(that.z.abs), this.z.abs.min(that.z.abs)) * fasig(this, that)).toString)
|
||||
|
||||
def -- : Z = {
|
||||
val zs = this - Z("1")
|
||||
|
||||
this.zs = zs.zs
|
||||
|
||||
this.z = zs.z
|
||||
|
||||
this
|
||||
}
|
||||
|
||||
def -(that: Z): Z =
|
||||
if (this == Z("0")) Z((that.z * (-1)).toString)
|
||||
else if (that == Z("0")) this
|
||||
else if (this.z.signum != that.z.signum) Z((fa(this.z.abs.max(that.z.abs), this.z.abs.min(that.z.abs)) * this.z.signum).toString)
|
||||
else if (this.z.abs == that.z.abs) Z("0")
|
||||
else Z((fs(this.z.abs.max(that.z.abs), this.z.abs.min(that.z.abs)) * fssig(this, that)).toString)
|
||||
|
||||
def %(that: Z): Option[Z] =
|
||||
if (that == Z("0")) None
|
||||
else if (this == Z("0")) Some(Z("0"))
|
||||
else if (that == Z("1")) Some(Z("0"))
|
||||
else if (this.z.abs < that.z.abs) Some(this)
|
||||
else if (this.z == that.z) Some(Z("0"))
|
||||
else this / that match {
|
||||
case None => None
|
||||
|
||||
case Some(z) => Some(this - z * that)
|
||||
}
|
||||
|
||||
def *(that: Z): Z =
|
||||
if (this == Z("0") || that == Z("0")) Z("0")
|
||||
else if (this == Z("1")) that
|
||||
else if (that == Z("1")) this
|
||||
else Z((fm(this.z.abs.max(that.z.abs), this.z.abs.min(that.z.abs)) * this.z.signum * that.z.signum).toString)
|
||||
|
||||
def /(that: Z): Option[Z] =
|
||||
if (that == Z("0")) None
|
||||
else if (this == Z("0")) Some(Z("0"))
|
||||
else if (that == Z("1")) Some(Z("1"))
|
||||
else if (this.z.abs < that.z.abs) Some(Z("0"))
|
||||
else if (this.z == that.z) Some(Z("1"))
|
||||
else Some(Z((fd(this.z.abs.max(that.z.abs), this.z.abs.min(that.z.abs)) * this.z.signum * that.z.signum).toString))
|
||||
|
||||
def <(that: Z): Boolean = this.z < that.z
|
||||
|
||||
def <=(that: Z): Boolean = this.z <= that.z
|
||||
|
||||
def >(that: Z): Boolean = this.z > that.z
|
||||
|
||||
def >=(that: Z): Boolean = this.z >= that.z
|
||||
|
||||
}
|
||||
|
||||
object Z {
|
||||
// only for comfort and result checking:
|
||||
val fibs: LazyList[BigInt] = {
|
||||
def series(i: BigInt, j: BigInt): LazyList[BigInt] = i #:: series(j, i + j)
|
||||
|
||||
series(1, 0).tail.tail.tail
|
||||
}
|
||||
val z2i: Z => BigInt = z => z.z.abs.toString.toCharArray.map(_.asDigit).reverse.zipWithIndex.map { case (v, i) => v * fibs(i) }.foldRight(BigInt(0))(_ + _) * z.z.signum
|
||||
|
||||
var fmts: Map[Z, List[Z]] = Map(Z("0") -> List[Z](Z("0"))) //map of Fibonacci multiples table of divisors
|
||||
|
||||
// get division table (division weight vector)
|
||||
def dt(dd: Z, ds: Z): List[Z] = {
|
||||
val wv = new ListBuffer[Z]
|
||||
wv ++= mt(ds)
|
||||
var zs = ds.z.abs.toString
|
||||
val upper = dd.z.abs.toString
|
||||
while ((zs.length < upper.length)) {
|
||||
wv += (wv.toList.last + wv.toList.reverse.tail.head)
|
||||
|
||||
zs = "1" + zs
|
||||
}
|
||||
wv.toList
|
||||
}
|
||||
|
||||
// get multiply table from fmts
|
||||
def mt(z: Z): List[Z] = {
|
||||
fmts.getOrElse(z, Nil) match {
|
||||
case Nil =>
|
||||
val e = mwv(z)
|
||||
fmts = fmts + (z -> e)
|
||||
e
|
||||
case l => l
|
||||
}
|
||||
}
|
||||
|
||||
// multiply weight vector
|
||||
def mwv(z: Z): List[Z] = {
|
||||
val wv = new ListBuffer[Z]
|
||||
wv += z
|
||||
wv += (z + z)
|
||||
var zs = "11"
|
||||
val upper = z.z.abs.toString
|
||||
while ((zs.length < upper.length)) {
|
||||
wv += (wv.toList.last + wv.toList.reverse.tail.head)
|
||||
|
||||
zs = "1" + zs
|
||||
}
|
||||
wv.toList
|
||||
}
|
||||
}
|
||||
|
||||
println("elapsed time: " + elapsed {
|
||||
calcs foreach { case (op1, op, op2) => println("" + op1 + " " + op + " " + op2 + " = "
|
||||
+ {
|
||||
(ops(op)) (op1, op2) match {
|
||||
case None => None
|
||||
|
||||
case Some(z) => z
|
||||
|
||||
case z => z
|
||||
}
|
||||
}
|
||||
.ensuring { x =>
|
||||
(iops(op)) (z2i(op1), z2i(op2)) match {
|
||||
case None => None == x
|
||||
|
||||
case Some(i) => i == z2i(x.asInstanceOf[Z])
|
||||
|
||||
case i => i == z2i(x.asInstanceOf[Z])
|
||||
}
|
||||
})
|
||||
}
|
||||
} + " sec"
|
||||
)
|
||||
|
||||
}
|
||||
75
Task/Zeckendorf-arithmetic/Tcl/zeckendorf-arithmetic-1.tcl
Normal file
75
Task/Zeckendorf-arithmetic/Tcl/zeckendorf-arithmetic-1.tcl
Normal file
|
|
@ -0,0 +1,75 @@
|
|||
namespace eval zeckendorf {
|
||||
# Want to use alternate symbols? Change these
|
||||
variable zero "0"
|
||||
variable one "1"
|
||||
|
||||
# Base operations: increment and decrement
|
||||
proc zincr var {
|
||||
upvar 1 $var a
|
||||
namespace upvar [namespace current] zero 0 one 1
|
||||
if {![regsub "$0$" $a $1$0 a]} {append a $1}
|
||||
while {[regsub "$0$1$1" $a "$1$0$0" a]
|
||||
|| [regsub "^$1$1" $a "$1$0$0" a]} {}
|
||||
regsub ".$" $a "" a
|
||||
return $a
|
||||
}
|
||||
proc zdecr var {
|
||||
upvar 1 $var a
|
||||
namespace upvar [namespace current] zero 0 one 1
|
||||
regsub "^$0+(.+)$" [subst [regsub "${1}($0*)$" $a "$0\[
|
||||
string repeat {$1$0} \[regsub -all .. {\\1} {} x]]\[
|
||||
string repeat {$1} \[expr {\$x ne {}}]]"]
|
||||
] {\1} a
|
||||
return $a
|
||||
}
|
||||
|
||||
# Exported operations
|
||||
proc eq {a b} {
|
||||
expr {$a eq $b}
|
||||
}
|
||||
proc add {a b} {
|
||||
variable zero
|
||||
while {![eq $b $zero]} {
|
||||
zincr a
|
||||
zdecr b
|
||||
}
|
||||
return $a
|
||||
}
|
||||
proc sub {a b} {
|
||||
variable zero
|
||||
while {![eq $b $zero]} {
|
||||
zdecr a
|
||||
zdecr b
|
||||
}
|
||||
return $a
|
||||
}
|
||||
proc mul {a b} {
|
||||
variable zero
|
||||
variable one
|
||||
if {[eq $a $zero] || [eq $b $zero]} {return $zero}
|
||||
if {[eq $a $one]} {return $b}
|
||||
if {[eq $b $one]} {return $a}
|
||||
set c $a
|
||||
while {![eq [zdecr b] $zero]} {
|
||||
set c [add $c $a]
|
||||
}
|
||||
return $c
|
||||
}
|
||||
proc div {a b} {
|
||||
variable zero
|
||||
variable one
|
||||
if {[eq $b $zero]} {error "div zero"}
|
||||
if {[eq $a $zero] || [eq $b $one]} {return $a}
|
||||
set r $zero
|
||||
while {![eq $a $zero]} {
|
||||
if {![eq $a [add [set a [sub $a $b]] $b]]} break
|
||||
zincr r
|
||||
}
|
||||
return $r
|
||||
}
|
||||
# Note that there aren't any ordering operations in this version
|
||||
|
||||
# Assemble into a coherent API
|
||||
namespace export \[a-y\]*
|
||||
namespace ensemble create
|
||||
}
|
||||
|
|
@ -0,0 +1,5 @@
|
|||
puts [zeckendorf add "10100" "1010"]
|
||||
puts [zeckendorf sub "10100" "1010"]
|
||||
puts [zeckendorf mul "10100" "1010"]
|
||||
puts [zeckendorf div "10100" "1010"]
|
||||
puts [zeckendorf div [zeckendorf mul "10100" "1010"] "1010"]
|
||||
184
Task/Zeckendorf-arithmetic/V-(Vlang)/zeckendorf-arithmetic.v
Normal file
184
Task/Zeckendorf-arithmetic/V-(Vlang)/zeckendorf-arithmetic.v
Normal file
|
|
@ -0,0 +1,184 @@
|
|||
import strings
|
||||
const (
|
||||
dig = ["00", "01", "10"]
|
||||
dig1 = ["", "1", "10"]
|
||||
)
|
||||
|
||||
struct Zeckendorf {
|
||||
mut:
|
||||
d_val int
|
||||
d_len int
|
||||
}
|
||||
|
||||
fn new_zeck(xx string) Zeckendorf {
|
||||
mut z := Zeckendorf{}
|
||||
mut x := xx
|
||||
if x == "" {
|
||||
x = "0"
|
||||
}
|
||||
mut q := 1
|
||||
mut i := x.len - 1
|
||||
z.d_len = i / 2
|
||||
for ; i >= 0; i-- {
|
||||
z.d_val += int(x[i]-'0'[0]) * q
|
||||
q *= 2
|
||||
}
|
||||
return z
|
||||
}
|
||||
|
||||
fn (mut z Zeckendorf) a(ii int) {
|
||||
mut i:=ii
|
||||
for ; ; i++ {
|
||||
if z.d_len < i {
|
||||
z.d_len = i
|
||||
}
|
||||
j := (z.d_val >> u32(i*2)) & 3
|
||||
if j in [0, 1] {
|
||||
return
|
||||
} else if j==2 {
|
||||
if ((z.d_val >> (u32(i+1) * 2)) & 1) != 1 {
|
||||
return
|
||||
}
|
||||
z.d_val += 1 << u32(i*2+1)
|
||||
return
|
||||
} else {// 3
|
||||
z.d_val &= ~(3 << u32(i*2))
|
||||
z.b((i + 1) * 2)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fn (mut z Zeckendorf) b(p int) {
|
||||
mut pos := p
|
||||
if pos == 0 {
|
||||
z.inc()
|
||||
return
|
||||
}
|
||||
if ((z.d_val >> u32(pos)) & 1) == 0 {
|
||||
z.d_val += 1 << u32(pos)
|
||||
z.a(pos / 2)
|
||||
if pos > 1 {
|
||||
z.a(pos/2 - 1)
|
||||
}
|
||||
} else {
|
||||
z.d_val &= ~(1 << u32(pos))
|
||||
z.b(pos + 1)
|
||||
mut temp := 1
|
||||
if pos > 1 {
|
||||
temp = 2
|
||||
}
|
||||
z.b(pos - temp)
|
||||
}
|
||||
}
|
||||
|
||||
fn (mut z Zeckendorf) c(p int) {
|
||||
mut pos := p
|
||||
if ((z.d_val >> u32(pos)) & 1) == 1 {
|
||||
z.d_val &= ~(1 << u32(pos))
|
||||
return
|
||||
}
|
||||
z.c(pos + 1)
|
||||
if pos > 0 {
|
||||
z.b(pos - 1)
|
||||
} else {
|
||||
z.inc()
|
||||
}
|
||||
}
|
||||
|
||||
fn (mut z Zeckendorf) inc() {
|
||||
z.d_val++
|
||||
z.a(0)
|
||||
}
|
||||
|
||||
fn (mut z1 Zeckendorf) plus_assign(z2 Zeckendorf) {
|
||||
for gn := 0; gn < (z2.d_len+1)*2; gn++ {
|
||||
if ((z2.d_val >> u32(gn)) & 1) == 1 {
|
||||
z1.b(gn)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
fn (mut z1 Zeckendorf) minus_assign(z2 Zeckendorf) {
|
||||
for gn := 0; gn < (z2.d_len+1)*2; gn++ {
|
||||
if ((z2.d_val >> u32(gn)) & 1) == 1 {
|
||||
z1.c(gn)
|
||||
}
|
||||
}
|
||||
|
||||
for z1.d_len > 0 && ((z1.d_val>>u32(z1.d_len*2))&3) == 0 {
|
||||
z1.d_len--
|
||||
}
|
||||
}
|
||||
|
||||
fn (mut z1 Zeckendorf) times_assign(z2 Zeckendorf) {
|
||||
mut na := z2.copy()
|
||||
mut nb := z2.copy()
|
||||
mut nr := Zeckendorf{}
|
||||
for i := 0; i <= (z1.d_len+1)*2; i++ {
|
||||
if ((z1.d_val >> u32(i)) & 1) > 0 {
|
||||
nr.plus_assign(nb)
|
||||
}
|
||||
nt := nb.copy()
|
||||
nb.plus_assign(na)
|
||||
na = nt.copy()
|
||||
}
|
||||
z1.d_val = nr.d_val
|
||||
z1.d_len = nr.d_len
|
||||
}
|
||||
|
||||
fn (z Zeckendorf) copy() Zeckendorf {
|
||||
return Zeckendorf{z.d_val, z.d_len}
|
||||
}
|
||||
|
||||
fn (z1 Zeckendorf) compare(z2 Zeckendorf) int {
|
||||
if z1.d_val < z2.d_val {
|
||||
return -1
|
||||
} else if z1.d_val > z2.d_val {
|
||||
return 1
|
||||
} else {
|
||||
return 0
|
||||
}
|
||||
}
|
||||
|
||||
fn (z Zeckendorf) str() string {
|
||||
if z.d_val == 0 {
|
||||
return "0"
|
||||
}
|
||||
mut sb := strings.new_builder(128)
|
||||
sb.write_string(dig1[(z.d_val>>u32(z.d_len*2))&3])
|
||||
for i := z.d_len - 1; i >= 0; i-- {
|
||||
sb.write_string(dig[(z.d_val>>u32(i*2))&3])
|
||||
}
|
||||
return sb.str()
|
||||
}
|
||||
|
||||
fn main() {
|
||||
println("Addition:")
|
||||
mut g := new_zeck("10")
|
||||
g.plus_assign(new_zeck("10"))
|
||||
println(g)
|
||||
g.plus_assign(new_zeck("10"))
|
||||
println(g)
|
||||
g.plus_assign(new_zeck("1001"))
|
||||
println(g)
|
||||
g.plus_assign(new_zeck("1000"))
|
||||
println(g)
|
||||
g.plus_assign(new_zeck("10101"))
|
||||
println(g)
|
||||
|
||||
println("\nSubtraction:")
|
||||
g = new_zeck("1000")
|
||||
g.minus_assign(new_zeck("101"))
|
||||
println(g)
|
||||
g = new_zeck("10101010")
|
||||
g.minus_assign(new_zeck("1010101"))
|
||||
println(g)
|
||||
|
||||
println("\nMultiplication:")
|
||||
g = new_zeck("1001")
|
||||
g.times_assign(new_zeck("101"))
|
||||
println(g)
|
||||
g = new_zeck("101010")
|
||||
g.plus_assign(new_zeck("101"))
|
||||
println(g)
|
||||
}
|
||||
|
|
@ -0,0 +1,198 @@
|
|||
Imports System.Text
|
||||
|
||||
Module Module1
|
||||
|
||||
Class Zeckendorf
|
||||
Implements IComparable(Of Zeckendorf)
|
||||
|
||||
Private Shared ReadOnly dig As String() = {"00", "01", "10"}
|
||||
Private Shared ReadOnly dig1 As String() = {"", "1", "10"}
|
||||
|
||||
Private dVal As Integer = 0
|
||||
Private dLen As Integer = 0
|
||||
|
||||
Public Sub New(Optional x As String = "0")
|
||||
Dim q = 1
|
||||
Dim i = x.Length - 1
|
||||
dLen = i \ 2
|
||||
|
||||
Dim z = Asc("0")
|
||||
While i >= 0
|
||||
Dim a = Asc(x(i))
|
||||
dVal += (a - z) * q
|
||||
q *= 2
|
||||
i -= 1
|
||||
End While
|
||||
End Sub
|
||||
|
||||
Private Sub A(n As Integer)
|
||||
Dim i = n
|
||||
While True
|
||||
If dLen < i Then
|
||||
dLen = i
|
||||
End If
|
||||
Dim j = (dVal >> (i * 2)) And 3
|
||||
If j = 0 OrElse j = 1 Then
|
||||
Return
|
||||
ElseIf j = 2 Then
|
||||
If ((dVal >> ((i + 1) * 2)) And 1) <> 1 Then
|
||||
Return
|
||||
End If
|
||||
dVal += 1 << (i * 2 + 1)
|
||||
Return
|
||||
ElseIf j = 3 Then
|
||||
Dim temp = 3 << (i * 2)
|
||||
temp = temp Xor -1
|
||||
dVal = dVal And temp
|
||||
B((i + 1) * 2)
|
||||
End If
|
||||
i += 1
|
||||
End While
|
||||
End Sub
|
||||
|
||||
Private Sub B(pos As Integer)
|
||||
If pos = 0 Then
|
||||
Inc()
|
||||
Return
|
||||
End If
|
||||
If ((dVal >> pos) And 1) = 0 Then
|
||||
dVal += 1 << pos
|
||||
A(pos \ 2)
|
||||
If pos > 1 Then
|
||||
A(pos \ 2 - 1)
|
||||
End If
|
||||
Else
|
||||
Dim temp = 1 << pos
|
||||
temp = temp Xor -1
|
||||
dVal = dVal And temp
|
||||
B(pos + 1)
|
||||
B(pos - If(pos > 1, 2, 1))
|
||||
End If
|
||||
End Sub
|
||||
|
||||
Private Sub C(pos As Integer)
|
||||
If ((dVal >> pos) And 1) = 1 Then
|
||||
Dim temp = 1 << pos
|
||||
temp = temp Xor -1
|
||||
dVal = dVal And temp
|
||||
Return
|
||||
End If
|
||||
C(pos + 1)
|
||||
If pos > 0 Then
|
||||
B(pos - 1)
|
||||
Else
|
||||
Inc()
|
||||
End If
|
||||
End Sub
|
||||
|
||||
Public Function Inc() As Zeckendorf
|
||||
dVal += 1
|
||||
A(0)
|
||||
Return Me
|
||||
End Function
|
||||
|
||||
Public Function Copy() As Zeckendorf
|
||||
Dim z As New Zeckendorf With {
|
||||
.dVal = dVal,
|
||||
.dLen = dLen
|
||||
}
|
||||
Return z
|
||||
End Function
|
||||
|
||||
Public Sub PlusAssign(other As Zeckendorf)
|
||||
Dim gn = 0
|
||||
While gn < (other.dLen + 1) * 2
|
||||
If ((other.dVal >> gn) And 1) = 1 Then
|
||||
B(gn)
|
||||
End If
|
||||
gn += 1
|
||||
End While
|
||||
End Sub
|
||||
|
||||
Public Sub MinusAssign(other As Zeckendorf)
|
||||
Dim gn = 0
|
||||
While gn < (other.dLen + 1) * 2
|
||||
If ((other.dVal >> gn) And 1) = 1 Then
|
||||
C(gn)
|
||||
End If
|
||||
gn += 1
|
||||
End While
|
||||
While (((dVal >> dLen * 2) And 3) = 0) OrElse dLen = 0
|
||||
dLen -= 1
|
||||
End While
|
||||
End Sub
|
||||
|
||||
Public Sub TimesAssign(other As Zeckendorf)
|
||||
Dim na = other.Copy
|
||||
Dim nb = other.Copy
|
||||
Dim nt As Zeckendorf
|
||||
Dim nr As New Zeckendorf
|
||||
Dim i = 0
|
||||
While i < (dLen + 1) * 2
|
||||
If ((dVal >> i) And 1) > 0 Then
|
||||
nr.PlusAssign(nb)
|
||||
End If
|
||||
nt = nb.Copy
|
||||
nb.PlusAssign(na)
|
||||
na = nt.Copy
|
||||
i += 1
|
||||
End While
|
||||
dVal = nr.dVal
|
||||
dLen = nr.dLen
|
||||
End Sub
|
||||
|
||||
Public Function CompareTo(other As Zeckendorf) As Integer Implements IComparable(Of Zeckendorf).CompareTo
|
||||
Return dVal.CompareTo(other.dVal)
|
||||
End Function
|
||||
|
||||
Public Overrides Function ToString() As String
|
||||
If dVal = 0 Then
|
||||
Return "0"
|
||||
End If
|
||||
|
||||
Dim idx = (dVal >> (dLen * 2)) And 3
|
||||
Dim sb As New StringBuilder(dig1(idx))
|
||||
Dim i = dLen - 1
|
||||
While i >= 0
|
||||
idx = (dVal >> (i * 2)) And 3
|
||||
sb.Append(dig(idx))
|
||||
i -= 1
|
||||
End While
|
||||
Return sb.ToString
|
||||
End Function
|
||||
End Class
|
||||
|
||||
Sub Main()
|
||||
Console.WriteLine("Addition:")
|
||||
Dim g As New Zeckendorf("10")
|
||||
g.PlusAssign(New Zeckendorf("10"))
|
||||
Console.WriteLine(g)
|
||||
g.PlusAssign(New Zeckendorf("10"))
|
||||
Console.WriteLine(g)
|
||||
g.PlusAssign(New Zeckendorf("1001"))
|
||||
Console.WriteLine(g)
|
||||
g.PlusAssign(New Zeckendorf("1000"))
|
||||
Console.WriteLine(g)
|
||||
g.PlusAssign(New Zeckendorf("10101"))
|
||||
Console.WriteLine(g)
|
||||
Console.WriteLine()
|
||||
|
||||
Console.WriteLine("Subtraction:")
|
||||
g = New Zeckendorf("1000")
|
||||
g.MinusAssign(New Zeckendorf("101"))
|
||||
Console.WriteLine(g)
|
||||
g = New Zeckendorf("10101010")
|
||||
g.MinusAssign(New Zeckendorf("1010101"))
|
||||
Console.WriteLine(g)
|
||||
Console.WriteLine()
|
||||
|
||||
Console.WriteLine("Multiplication:")
|
||||
g = New Zeckendorf("1001")
|
||||
g.TimesAssign(New Zeckendorf("101"))
|
||||
Console.WriteLine(g)
|
||||
g = New Zeckendorf("101010")
|
||||
g.PlusAssign(New Zeckendorf("101"))
|
||||
Console.WriteLine(g)
|
||||
End Sub
|
||||
|
||||
End Module
|
||||
155
Task/Zeckendorf-arithmetic/Wren/zeckendorf-arithmetic.wren
Normal file
155
Task/Zeckendorf-arithmetic/Wren/zeckendorf-arithmetic.wren
Normal file
|
|
@ -0,0 +1,155 @@
|
|||
import "/trait" for Comparable
|
||||
|
||||
class Zeckendorf is Comparable {
|
||||
static dig { ["00", "01", "10"] }
|
||||
static dig1 { ["", "1", "10"] }
|
||||
|
||||
construct new(x) {
|
||||
var q = 1
|
||||
var i = x.count - 1
|
||||
_dLen = (i / 2).floor
|
||||
_dVal = 0
|
||||
while (i >= 0) {
|
||||
_dVal = _dVal + (x[i].bytes[0] - 48) * q
|
||||
q = q * 2
|
||||
i = i - 1
|
||||
}
|
||||
}
|
||||
|
||||
dLen { _dLen }
|
||||
dVal { _dVal }
|
||||
|
||||
dLen=(v) { _dLen = v }
|
||||
dVal=(v) { _dVal = v }
|
||||
|
||||
a(n) {
|
||||
var i = n
|
||||
while (true) {
|
||||
if (_dLen < i) _dLen = i
|
||||
var j = (_dVal >> (i * 2)) & 3
|
||||
if (j == 0 || j == 1) return
|
||||
if (j == 2) {
|
||||
if (((_dVal >> ((i + 1) * 2)) & 1) != 1) return
|
||||
_dVal = _dVal + (1 << (i * 2 + 1))
|
||||
return
|
||||
}
|
||||
if (j == 3) {
|
||||
_dVal = _dVal & ~(3 << (i * 2))
|
||||
b((i + 1) * 2)
|
||||
}
|
||||
i = i + 1
|
||||
}
|
||||
}
|
||||
|
||||
b(pos) {
|
||||
if (pos == 0) {
|
||||
var thiz = this
|
||||
thiz.inc
|
||||
return
|
||||
}
|
||||
if (((_dVal >> pos) & 1) == 0) {
|
||||
_dVal = _dVal + (1 << pos)
|
||||
a((pos / 2).floor)
|
||||
if (pos > 1) a((pos / 2).floor - 1)
|
||||
} else {
|
||||
_dVal = _dVal & ~(1 << pos)
|
||||
b(pos + 1)
|
||||
b(pos - ((pos > 1) ? 2 : 1))
|
||||
}
|
||||
}
|
||||
|
||||
c(pos) {
|
||||
if (((_dVal >> pos) & 1) == 1) {
|
||||
_dVal = _dVal & ~(1 << pos)
|
||||
return
|
||||
}
|
||||
c(pos + 1)
|
||||
if (pos > 0) {
|
||||
b(pos - 1)
|
||||
} else {
|
||||
var thiz = this
|
||||
thiz.inc
|
||||
}
|
||||
}
|
||||
|
||||
inc {
|
||||
_dVal = _dVal + 1
|
||||
a(0)
|
||||
return this
|
||||
}
|
||||
|
||||
plusAssign(other) {
|
||||
for (gn in 0...(other.dLen + 1) * 2) {
|
||||
if (((other.dVal >> gn) & 1) == 1) b(gn)
|
||||
}
|
||||
}
|
||||
|
||||
minusAssign(other) {
|
||||
for (gn in 0...(other.dLen + 1) * 2) {
|
||||
if (((other.dVal >> gn) & 1) == 1) c(gn)
|
||||
}
|
||||
while ((((_dVal >> _dLen * 2) & 3) == 0) || (_dLen == 0)) _dLen = _dLen - 1
|
||||
}
|
||||
|
||||
timesAssign(other) {
|
||||
var na = other.copy()
|
||||
var nb = other.copy()
|
||||
var nr = Zeckendorf.new("0")
|
||||
for (i in 0..(_dLen + 1) * 2) {
|
||||
if (((_dVal >> i) & 1) > 0) nr.plusAssign(nb)
|
||||
var nt = nb.copy()
|
||||
nb.plusAssign(na)
|
||||
na = nt.copy()
|
||||
}
|
||||
_dVal = nr.dVal
|
||||
_dLen = nr.dLen
|
||||
}
|
||||
|
||||
compare(other) { (_dVal - other.dVal).sign }
|
||||
|
||||
toString {
|
||||
if (_dVal == 0) return "0"
|
||||
var sb = Zeckendorf.dig1[(_dVal >> (_dLen * 2)) & 3]
|
||||
if (_dLen > 0) {
|
||||
for (i in _dLen - 1..0) {
|
||||
sb = sb + Zeckendorf.dig[(_dVal >> (i * 2)) & 3]
|
||||
}
|
||||
}
|
||||
return sb
|
||||
}
|
||||
|
||||
copy() {
|
||||
var z = Zeckendorf.new("0")
|
||||
z.dVal = _dVal
|
||||
z.dLen = _dLen
|
||||
return z
|
||||
}
|
||||
}
|
||||
|
||||
var Z = Zeckendorf // type alias
|
||||
System.print("Addition:")
|
||||
var g = Z.new("10")
|
||||
g.plusAssign(Z.new("10"))
|
||||
System.print(g)
|
||||
g.plusAssign(Z.new("10"))
|
||||
System.print(g)
|
||||
g.plusAssign(Z.new("1001"))
|
||||
System.print(g)
|
||||
g.plusAssign(Z.new("1000"))
|
||||
System.print(g)
|
||||
g.plusAssign(Z.new("10101"))
|
||||
System.print(g)
|
||||
System.print("\nSubtraction:")
|
||||
g = Z.new("1000")
|
||||
g.minusAssign(Z.new("101"))
|
||||
System.print(g)
|
||||
g = Z.new("10101010")
|
||||
g.minusAssign(Z.new("1010101"))
|
||||
System.print(g)
|
||||
System.print("\nMultiplication:")
|
||||
g = Z.new("1001")
|
||||
g.timesAssign(Z.new("101"))
|
||||
System.print(g)
|
||||
g = Z.new("101010")
|
||||
g.plusAssign(Z.new("101"))
|
||||
System.print(g)
|
||||
Loading…
Add table
Add a link
Reference in a new issue