Jacobi symbol: Difference between revisions
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(Adding Haskell version) |
Catskill549 (talk | contribs) |
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=={{header|AWK}}== |
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<lang AWK> |
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# syntax: GAWK -f JACOBI_SYMBOL.AWK |
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# converted from Go |
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BEGIN { |
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max_n = 29 |
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max_a = max_n + 1 |
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printf("n\\a") |
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for (i=1; i<=max_a; i++) { |
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printf("%3d",i) |
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underline = underline " --" |
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} |
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printf("\n---%s\n",underline) |
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for (n=1; n<=max_n; n+=2) { |
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printf("%3d",n) |
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for (a=1; a<=max_a; a++) { |
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printf("%3d",jacobi(a,n)) |
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} |
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printf("\n") |
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} |
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exit(0) |
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} |
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function jacobi(a,n, result,tmp) { |
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if (n%2 == 0) { |
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print("error: 'n' must be a positive odd integer") |
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exit |
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} |
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a %= n |
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result = 1 |
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while (a != 0) { |
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while (a%2 == 0) { |
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a /= 2 |
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if (n%8 == 3 || n%8 == 5) { |
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result = -result |
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} |
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} |
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tmp = a |
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a = n |
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n = tmp |
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if (a%4 == 3 && n%4 == 3) { |
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result = -result |
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} |
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a %= n |
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} |
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if (n == 1) { |
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return(result) |
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} |
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return(0) |
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} |
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</lang> |
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{{out}} |
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<pre> |
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n\a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 |
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--- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- |
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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
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3 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 |
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5 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 |
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7 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 |
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9 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 |
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11 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 |
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13 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 |
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15 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0 1 1 0 1 0 0 -1 1 0 0 -1 0 -1 -1 0 |
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17 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 |
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19 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1 -1 -1 1 1 1 1 -1 1 -1 1 |
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21 1 -1 0 1 1 0 0 -1 0 -1 -1 0 -1 0 0 1 1 0 -1 1 0 1 -1 0 1 1 0 0 -1 0 |
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23 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 0 1 1 1 1 -1 1 -1 |
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25 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 |
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27 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 |
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29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 1 0 1 |
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</pre> |
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=={{header|Factor}}== |
=={{header|Factor}}== |
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The <code>jacobi</code> word already exists in the <code>math.extras</code> vocabulary. See the implementation [https://docs.factorcode.org/content/word-jacobi%2Cmath.extras.html here]. |
The <code>jacobi</code> word already exists in the <code>math.extras</code> vocabulary. See the implementation [https://docs.factorcode.org/content/word-jacobi%2Cmath.extras.html here]. |
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