In article <[email protected]>, Nelson H. F. Beebe <[email protected]> wrote:
> I run a large farm of physical and virtual machines that we use for > software testing. We have multiple versions of most of the major > operating systems, covering the major CPU families of the past 30 > years, including M68K. > In testing some numerical software on Debian 11 on M68k (emulated by > QEMU 4.2.1), I discovered that 80-bit subnormals are printed > incorrectly: they are exactly HALF their correct values. > A test program is provided below, and a snippet of its identical and > correct output on x86_64 and IA-64 (Itanium) physical hardware looks > like this around the transition from tiny normal numbers to subnormal > numbers: > k = -16380 x = 0x8.0000000000000000p-16383 = 1.344841257244837403e-4931 > = 0x0003_80000000_00000000 > k = -16381 x = 0x8.0000000000000000p-16384 = 6.724206286224187013e-4932 > = 0x0002_80000000_00000000 > k = -16382 x = 0x8.0000000000000000p-16385 = 3.362103143112093506e-4932 > = 0x0001_80000000_00000000 > ---------- begin subnormals ---------- > k = -16383 x = 0x4.0000000000000000p-16385 = 1.681051571556046753e-4932 > = 0x0000_40000000_00000000 > k = -16384 x = 0x2.0000000000000000p-16385 = 8.405257857780233766e-4933 > = 0x0000_20000000_00000000 > k = -16385 x = 0x1.0000000000000000p-16385 = 4.202628928890116883e-4933 > = 0x0000_10000000_00000000 > Here is the output from Debian 11 on M68k (identical with both gcc-9 > and gcc-10): > k = -16380 x = 0x8.0000000000000000p-16383 = 1.344841257244837403e-4931 > = 0x0003_80000000_00000000 > k = -16381 x = 0x8.0000000000000000p-16384 = 6.724206286224187013e-4932 > = 0x0002_80000000_00000000 > k = -16382 x = 0x8.0000000000000000p-16385 = 3.362103143112093506e-4932 > = 0x0001_80000000_00000000 > ---------- begin subnormals ---------- > k = -16383 x = 0x4.0000000000000000p-16386 = 8.405257857780233766e-4933 > = 0x0000_40000000_00000000 Here, the number has been divided by 4 instead of 2. The printf output is correct. This is a QEMU bug in the multiplication with subnormals. See the discussion in the MPFR mailing-list: https://sympa.inria.fr/sympa/arc/mpfr/2022-12/msg00036.html -- Vincent Lefèvre <[email protected]> - Web: <https://www.vinc17.net/> 100% accessible validated (X)HTML - Blog: <https://www.vinc17.net/blog/> Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)
