From: Kai Tietz <ktietz70@go...>  20110430 09:51:40

2011/4/30 Kai Tietz <ktietz70@...>: > 2011/4/30 Greg Chicares <gchicares@...>: >> On 20110429 19:55Z, K. Frank wrote: >>> >>> By the way, could someone confirm that mingw does use msvcrt for >>> sqrt and pow? >> >> http://cygwin.com/cgibin/cvsweb.cgi/src/winsup/mingw/mingwex/math/?cvsroot=src >> >> Looks to me like sqrt(double) calls into msvcrt. But pow() is a >> different story. Danny implemented it in libmingwex because of >> some qualityofimplementation problem with msvcrt; then people >> complained that the libmingwex version was slower, and I can't >> remember where it wound up, but it's all in the archives. >> >>> sqrt (x) and pow (x, 0.5) ought to give the same result (even if not required >>> to by IEEE754). >> >> If they should give exactly the same result always, then the >> first thing that needs to be fixed is any standard that allows >> them to differ. The language standards are so much looser than >> the numerical standard, even now, that I'd rather see C and C++ >> catch up to IEEE7541985 before asking them to go beyond. >> >>> Browsing some gcc lists, I did see some comments that suggest that >>> gcc (on linux) does try to transform pow (x, 0.5) to sqrt (x). This would >>> make sqrt and pow consistent (whether or not technically correct). >> >> Not so many years ago (perhaps when msvcrt was written), it was >> thought that correctlyrounded transcendental functions weren't >> feasible in practice, so library authors had a looser attitude >> toward exactness. If you have an ideal implementation of sqrt() >> but a pow() that's only approximate, should you specialcase >> the power of exactly 0.5? If you do, then pow() and sqrt() will >> be consistent, but then the powers >> x^(0.5*(1epsilon)) >> x^(0.5 ) >> x^(0.5*(1+epsilon)) >> might not be monotone. Some would call that a bad tradeoff. > > Well, I spent some efforts into log, exp, and pow implementation. Also > some other basemath functions I improved in mingww64's math library > in two terms. a) Make those functions behave as ISOC99 specification > tells in cornercases. and b) Improve accuracy in terms of gcc's > internal used gmp. As we noticed here result differences. > > The following example illustrates the issues pretty well: > > #include <stdio.h> > #include <math.h> > > double abc[3][2] = { { 2.2, 3.1 }, { 2.0, 3.0 }, { 4.0, 0.5 } }; > long double ab[3][2] = { { 2.2L, 3.1L }, { 2.0L, 3.0L }, { 4.0L, 0.5L } }; > int main() > { > double r[3]; > long double rl[3]; > int i; > for (i = 0; i < 3; i++) > __mingw_printf ("%.20F^%.20F = %.20F\n", abc[i][0], abc[i][1], > (r[i] = pow (abc[i][0], abc[i][1]))); > __mingw_printf ("%.20F %.20F %.20F\n", pow (2.2, 3.1), pow (2.0, > 3.0), pow (4.0, 0.5)); > r[0] = pow (2.2, 3.1); > r[1] = pow (2.0, 3.0); > r[2] = pow (4.0, 0.5); > __mingw_printf ("%.20F %.20F %.20F\n", r[0], r[1], r[2]); > > for (i = 0; i < 3; i++) > __mingw_printf ("%.20LF^%.20LF = %.20LF\n", ab[i][0], ab[i][1], > (rl[i] = powl (ab[i][0], ab[i][1]))); > __mingw_printf ("%.20LF %.20LF %.20LF\n", > powl (2.2L, 3.1L), powl (2.0L, 3.0L) , powl > (4.0L, 0.5L)); > rl[0] = powl (2.2L, 3.1L); > rl[1] = powl (2.0L, 3.0L); > rl[2] = powl (4.0L, 0.5L); > __mingw_printf ("%.20LF %.20LF %.20LF\n", rl[0], rl[1], rl[2]); > return 1; > } > > The interesting issue is here that gcc uses for constant > mathcalculations gmplibrary to get result. For more complex > variants, it uses crt's math. By this it is important for a gcc based > runtime to be in the IEEE 754 floating point compatible to gmp's > results. > > Btw new pow, log, and exp variant are slightly faster then variant in > msvcrt, but this is more or less just a sideeffect. > > I admit that this might be not that obvious to users, why results here > are different, but for a gcc based toolchain we need to play nice with > gcc's internal assumptions. > > Regards, > Kai > On closer look for long double, we can have rouding issues for long double precission. I see that powl (0.01L, 0.5L) we have a rounding difference to sqrtl (0.01L). Interestingly not for float or double types. So we we might need to specialcase in pow the case for y == 0.5 to solve this. Kai 