John Collins wrote: > Hi, > OS: XP > Py: 2.7.2 > > I am running some old scripts, not written by me, that produce > substantial calculated values data as decimals, 12 significant > figures. AFAIK, the keys calls are;
[On modern hardware] Python uses IEEE 754 double-precision <http://en.wikipedia.org/wiki/Double_precision> internally which gives 15 to 17 digits. But of course errors may accumulate. > def crosspoint(xa1,ya1,xa2,ya2,xb1,yb1,xb2,yb2): > "Give the intersection point of the (possibly extrapolated) lines\n"\ > "segments (xa1,ya1)-(xa2,ya2) and (xb1,yb1)-(xb2,yb2)." > dxa = xa2-xa1 > dya = ya2-ya1 > dxb = xb2-xb1 > dyb = yb2-yb1 > if dya * dxb == dxa * dyb: > return None > if dxa == 0: > return (xa1, (xa1 - xb1) * dyb / dxb + yb1) > if dxb == 0: > return (xb1, (xb1 - xa1) * dya / dxa + ya1) > if dya == 0: > return ((ya1 - yb1) * dxb / dyb + xb1, ya1) > if dyb == 0: > return ((yb1 - ya1) * dxa / dya + xa1, yb1) > > det = dya * dxb - dyb * dxa > xtop = dxb * dxa * (yb1-ya1) + dya * dxb * xa1 - dyb * dxa * xb1 > ytop = dya * dyb * (xa1-xb1) + dxb * dya * yb1 - dxa * dyb * ya1 > > return (xtop / det, ytop / det) > > > I am not sure what == means, Equality. >>> 1 == 0 False >>> 1 == 1 True Because of rounding errors this is a dangerous operation for floating point numbers: >>> print 1.0 == .1 + .1 + .1 + .1 + .1 + .1 + .1 + .1 + .1 + .1 False > nor if any 'special' maths functions are > called from crosspoint.py (to me, it appears not?), so, as I understand > it, the > > from math import > > line *is* the 'math engine' if you will, and is the source of the 12 > sig fig limit, yes? It is a toolbox rather than an engine. math is basically a wrapper around the C library, and these functions all use C's double and [most of the time] your hardware's floating point unit. > One other odd thing that occurs, is when the scripts are run, a weird, > small, non ASCII file called crosspoint.pyc is created? Is this the > interpreter 'compiling' crosspoint.py ( either before, during, or > after?) the 2nd script calls it? Yes, Python compiles the source to bytecode before it executes it, and for all modules except the main script this bytecode is cached in a .pyc file. > Sorry to bother, but if I can squeeze out *at least* 15 sig figs, (30 > or more would be better!) I'd be a happy camper! As you correctly observed crospoints() uses only +-*/ and ==, so you can feed it every type that supports these operations (this is called "duck typing"). For example: >>> from fractions import Fraction >>> from crosspoint import crosspoint >>> crosspoint(Fraction(0, 1), Fraction(1, 3), Fraction(1, 1), Fraction(1, 3), Fraction(5, 7), Fraction(0, 1), Fraction(5, 7), Fraction(1, 1)) (Fraction(5, 7), Fraction(1, 3)) >>> p = crosspoint(Fraction(0, 1), Fraction(1, 3), Fraction(1, 1), Fraction(1, 3), Fraction(5, 7), Fraction(0, 1), Fraction(5, 7), Fraction(1, 1)) >>> print "%s, %s" % p 5/7, 1/3 Yay, infinite precision ;) Of more practical relevance may be something like gmpy <http://code.google.com/p/gmpy/> _______________________________________________ Tutor maillist - Tutor@python.org To unsubscribe or change subscription options: http://mail.python.org/mailman/listinfo/tutor
