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Diffstat (limited to '')
-rw-r--r-- | security/nss/lib/freebl/mpi/doc/sqrt.txt | 50 |
1 files changed, 50 insertions, 0 deletions
diff --git a/security/nss/lib/freebl/mpi/doc/sqrt.txt b/security/nss/lib/freebl/mpi/doc/sqrt.txt new file mode 100644 index 0000000000..4529cbfc46 --- /dev/null +++ b/security/nss/lib/freebl/mpi/doc/sqrt.txt @@ -0,0 +1,50 @@ +Square Root + +A simple iterative algorithm is used to compute the greatest integer +less than or equal to the square root. Essentially, this is Newton's +linear approximation, computed by finding successive values of the +equation: + + x[k]^2 - V +x[k+1] = x[k] - ------------ + 2 x[k] + +...where V is the value for which the square root is being sought. In +essence, what is happening here is that we guess a value for the +square root, then figure out how far off we were by squaring our guess +and subtracting the target. Using this value, we compute a linear +approximation for the error, and adjust the "guess". We keep doing +this until the precision gets low enough that the above equation +yields a quotient of zero. At this point, our last guess is one +greater than the square root we're seeking. + +The initial guess is computed by dividing V by 4, which is a heuristic +I have found to be fairly good on average. This also has the +advantage of being very easy to compute efficiently, even for large +values. + +So, the resulting algorithm works as follows: + + x = V / 4 /* compute initial guess */ + + loop + t = (x * x) - V /* Compute absolute error */ + u = 2 * x /* Adjust by tangent slope */ + t = t / u + + /* Loop is done if error is zero */ + if(t == 0) + break + + /* Adjust guess by error term */ + x = x - t + end + + x = x - 1 + +The result of the computation is the value of x. + +------------------------------------------------------------------ + This Source Code Form is subject to the terms of the Mozilla Public + # License, v. 2.0. If a copy of the MPL was not distributed with this + # file, You can obtain one at http://mozilla.org/MPL/2.0/. |