A small kernel of code for playing with Galois fields of arbitrary characteristic
| 修订版 | 430a429881135d4234982e160ff76cc009132f13 (tree) |
|---|---|
| 时间 | 2021-03-15 14:52:04 |
| 作者 | Eric Hopper <hopper@omni...> |
| Commiter | Eric Hopper |
Merge in ratpi to grabbag.
grabbag.py (diff) ratpi.py| @@ -15,6 +15,7 @@ | ||
| 15 | 15 | bitpool >>= 1 |
| 16 | 16 | --bitpoolbits |
| 17 | 17 | |
| 18 | + | |
| 18 | 19 | def inewt(b, n): |
| 19 | 20 | newest = b >> (b.bit_length() - (b.bit_length() // n)) |
| 20 | 21 | est = 0 |
| @@ -26,6 +27,7 @@ | ||
| 26 | 27 | return min(est, newest) |
| 27 | 28 | return newest |
| 28 | 29 | |
| 30 | + | |
| 29 | 31 | def factors(n): |
| 30 | 32 | factors = [] |
| 31 | 33 | while n & 1 == 0: |
| @@ -43,8 +45,10 @@ | ||
| 43 | 45 | factors.append(n) |
| 44 | 46 | return factors |
| 45 | 47 | |
| 48 | + | |
| 46 | 49 | import math |
| 47 | 50 | |
| 51 | + | |
| 48 | 52 | def nth_root_big(b, n): |
| 49 | 53 | if b.bit_length() <= 1023: |
| 50 | 54 | return math.pow(b, 1/n) |
| @@ -58,3 +62,13 @@ | ||
| 58 | 62 | while (len(flist) > 0) and (runprod < chop_factor): |
| 59 | 63 | runprod *= flist.pop() |
| 60 | 64 | return math.pow(inewt(b, runprod), 1 / (n // runprod)) |
| 65 | + | |
| 66 | + | |
| 67 | +from fractions import Fraction as F | |
| 68 | + | |
| 69 | + | |
| 70 | +def ratpi(n): | |
| 71 | + """I have no better place to put this. This is a quickly converging series | |
| 72 | + for computing a rational approximation of pi. For when you want more | |
| 73 | + precision than math.pi will give you.""" | |
| 74 | + return sum(F(1/16**k)*(F(4,8*k+1) - F(2,8*k + 4) - F(1,8*k+5) - F(1, 8*k+6)) for k in range(0, n)) |
| @@ -1,8 +0,0 @@ | ||
| 1 | -from fractions import Fraction as F | |
| 2 | - | |
| 3 | -"""I have no better place to put this. This is a quickly converging series for | |
| 4 | -computing a rational approximation of pi. For when you want more precision | |
| 5 | -than math.pi will give you.""" | |
| 6 | - | |
| 7 | -def ratpi(n): | |
| 8 | - return sum(F(1/16**k)*(F(4,8*k+1) - F(2,8*k + 4) - F(1,8*k+5) - F(1, 8*k+6)) for k in range(0, n)) |
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