Date: Thu, 18 Sep 1997 16:18:06 +0000 (GMT) From: Terry Lambert <tlambert@primenet.com> To: kuku@gilberto.physik.RWTH-Aachen.DE (Christoph Kukulies) Cc: tlambert@primenet.com, kuku@gilberto.physik.RWTH-Aachen.DE, freebsd-hackers@freefall.FreeBSD.org Subject: Re: FPE problem Message-ID: <199709181618.JAA17494@usr03.primenet.com> In-Reply-To: <19970918163531.11717@gil.physik.rwth-aachen.de> from "Christoph Kukulies" at Sep 18, 97 04:35:31 pm
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> A little bit more info now: > > ret_val = -z__ * (spint_1.a1 * z__ * (spint_1.a2 * z__ * (spint_1.a3 * > z2 * (spint_1.a4 * z2 * (spint_1.a5 * z2 * (spint_1.a6 * z2 * > (spint_1.a7 * z2 * (spint_1.a8 * z2 * (spint_1.a9 * z2 * ( > spint_1.a10 * z2 + 1.) + 1.) + 1.) + 1.) + 1.) + 1.) + 1.) + > 1.) + 1.) + 1.) + spint_1.zeta2 + z__ * log(1. - *x); > > > (xxgdb) info float > u: status 0x82e1: exceptions: INVALID LOS FPSTACK; flags: 0010; top 0 > e: status 0x200: flags: 0010; top 0 > control 0x1272: compute to 53 bits; round NEAREST; mask: DENORM UNDERF LOS; > last instruction: opcode 0x1d0; pc 0x8:0xf01f9a96; operand 0x27:0x92844 [ ... ] > What is LOS ? Loss of significance? Uh, an acronym. 8-). I'd actually have to break out my Intel book to tell you for sure. It's something that means about that anyway. It could be "Loss Of Signal" knowing Intel... > When I'm seeing such a few steps before the exception occurs, does it mean > that an exception is pending? > ---------------------------vvv > status 0x3920: exceptions: LOS; flags: 0001; top 7 > control 0x1272: compute to 53 bits; round NEAREST; mask: DENORM UNDERF LOS; > last instruction: opcode 0x6d9; pc 0x1f:0x1b280; operand 0x27:0x1aca0 Floating point values are stored as sign, exponent, and mantisa. It means that given the exponent, the value that can be expressed by any given mantisa is domain limited. That is, it has the same range it's always had, but the effects are amplified to the degree that there is a loss of precision as a result. You can think of any given mantisa as a slow clockwise spiral from an exponenet of 1 out to the highest possible positive exponent, and a negative spiral from an exponent of 1 to 0. If you plot two adjacent mantisa'a in say a multiply operation, the arms of the spiral spread out the further out you get. The number space is basically quantized, with a decreasing radial density. Have you ever seen a circular log-decilog slide-rule with the top off? Another analogy might be a fixed number of sectors on all tracks on a hard drive. In the multiplicative and divisive underflow examples I gave in my previous mail, you were looking at the number of bits at which point the curve of the spiral became tangential to a bounding circle (in the counterclockwise direction). Binary numbers don't understand Zeno's paradox. ;-). When you are dealing with a small real number X, 1 > fabs(X) > 0, in an equation with associative properties, you should do the divides before you do the multiplies to keep the result "centered" in the highest precision area of the graph I described. Basically, you should dictate order of associativity. Since this is physics code, this should be easy; after all, you never do a physics problem where you don't have an expectation about the answer. If you did, you'd be a mathematician, not a physicist testing a model's ability to predict empirical data. 8-). For the original code, you can dictate order of associativity by putting parenthesis in the original FORTRAN code based on the quantities you expect to be multiplying or dividing. These should carry over to the post-translation C code. If it's any consolation, I was stumped for a good week the first time this happened to me. That's about 1.0e13 Proton-Proton pair production collisions on the very expensive hardware I was using. 8-(. Regards, Terry Lambert terry@lambert.org --- Any opinions in this posting are my own and not those of my present or previous employers.
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