Everyone, say hello to a real floating point emulator!

The fpemul written for Linux by W. Metzenthen: ported to NetBSD and
then to FreeBSD, and now back to OpenBSD.

1 files changed, 278 insertions, 0 deletions

diff --git a/sys/gnu/arch/i386/fpemul/README b/sys/gnu/arch/i386/fpemul/README
new file mode 100644
index 00000000000..a477cbe0ff5
--- /dev/null
+++ b/sys/gnu/arch/i386/fpemul/README
@@ -0,0 +1,278 @@
+$OpenBSD: README,v 1.1 1996/08/27 10:32:39 downsj Exp $
+/*
+ *  wm-FPU-emu   an FPU emulator for 80386 and 80486SX microprocessors.
+ *
+ *
+ * Copyright (C) 1992,1993,1994
+ *                       W. Metzenthen, 22 Parker St, Ormond, Vic 3163,
+ *                       Australia.  E-mail   billm@vaxc.cc.monash.edu.au
+ * All rights reserved.
+ *
+ * This copyright notice covers the redistribution and use of the
+ * FPU emulator developed by W. Metzenthen. It covers only its use
+ * in the 386BSD, FreeBSD and NetBSD operating systems. Any other
+ * use is not permitted under this copyright.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must include information specifying
+ *    that source code for the emulator is freely available and include
+ *    either:
+ *      a) an offer to provide the source code for a nominal distribution
+ *         fee, or
+ *      b) list at least two alternative methods whereby the source
+ *         can be obtained, e.g. a publically accessible bulletin board
+ *         and an anonymous ftp site from which the software can be
+ *         downloaded.
+ * 3. All advertising materials specifically mentioning features or use of
+ *    this emulator must acknowledge that it was developed by W. Metzenthen.
+ * 4. The name of W. Metzenthen may not be used to endorse or promote
+ *    products derived from this software without specific prior written
+ *    permission.
+ *
+ * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES,
+ * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY
+ * AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL
+ * W. METZENTHEN BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ *
+ * The purpose of this copyright, based upon the Berkeley copyright, is to
+ * ensure that the covered software remains freely available to everyone.
+ *
+ * The software (with necessary differences) is also available, but under
+ * the terms of the GNU copyleft, for the Linux operating system and for
+ * the djgpp ms-dos extender.
+ *
+ * W. Metzenthen   June 1994.
+ *
+ */
+
+wm-FPU-emu is an FPU emulator for Linux. It is derived from wm-emu387
+which is my 80387 emulator for djgpp (gcc under msdos); wm-emu387 was
+in turn based upon emu387 which was written by DJ Delorie for djgpp.
+The interface to the Linux kernel is based upon the original Linux
+math emulator by Linus Torvalds.
+
+My target FPU for wm-FPU-emu is that described in the Intel486
+Programmer's Reference Manual (1992 edition). Numerous facets of the
+functioning of the FPU are not well covered in the Reference Manual;
+in the absence of clear details I have made guesses about the most
+reasonable behaviour. Recently, this situation has improved because
+I now have some access to the results produced by a real 80486 FPU.
+
+wm-FPU-emu does not implement all of the behaviour of the 80486 FPU. 
+See "Limitations" later in this file for a partial list of some
+differences.  I believe that the missing features are never used by
+normal C or FORTRAN programs. 
+
+
+Please report bugs, etc to me at:
+       apm233m@vaxc.cc.monash.edu.au
+
+
+--Bill Metzenthen
+  May 1993
+
+
+----------------------- Internals of wm-FPU-emu -----------------------
+
+Numeric algorithms:
+(1) Add, subtract, and multiply. Nothing remarkable in these.
+(2) Divide has been tuned to get reasonable performance. The algorithm
+    is not the obvious one which most people seem to use, but is designed
+    to take advantage of the characteristics of the 80386. I expect that
+    it has been invented many times before I discovered it, but I have not
+    seen it. It is based upon one of those ideas which one carries around
+    for years without ever bothering to check it out.
+(3) The sqrt function has been tuned to get good performance. It is based
+    upon Newton's classic method. Performance was improved by capitalizing
+    upon the properties of Newton's method, and the code is once again
+    structured taking account of the 80386 characteristics.
+(4) The trig, log, and exp functions are based in each case upon quasi-
+    "optimal" polynomial approximations. My definition of "optimal" was
+    based upon getting good accuracy with reasonable speed.
+
+The code of the emulator is complicated slightly by the need to
+account for a limited form of re-entrancy. Normally, the emulator will
+emulate each FPU instruction to completion without interruption.
+However, it may happen that when the emulator is accessing the user
+memory space, swapping may be needed. In this case the emulator may be
+temporarily suspended while disk i/o takes place. During this time
+another process may use the emulator, thereby changing some static
+variables (eg FPU_st0_ptr, etc). The code which accesses user memory
+is confined to five files:
+    fpu_entry.c
+    reg_ld_str.c
+    load_store.c
+    get_address.c
+    errors.c
+
+----------------------- Limitations of wm-FPU-emu -----------------------
+
+There are a number of differences between the current wm-FPU-emu
+(version beta 1.4) and the 80486 FPU (apart from bugs). Some of the
+more important differences are listed below:
+
+All internal computations are performed at 64 bit or higher precision
+and rounded etc as required by the PC bits of the FPU control word.
+Under the crt0 version for Linux current at March 1993, the FPU PC
+bits specify 53 bits precision.
+
+The precision flag (PE of the FPU status word) and the Roundup flag
+(C1 of the status word) are now partially implemented. Does anyone
+write code which uses these features?
+
+The functions which load/store the FPU state are partially implemented,
+but the implementation should be sufficient for handling FPU errors etc
+in 32 bit protected mode.
+
+The implementation of the exception mechanism is flawed for unmasked
+interrupts.
+
+Detection of certain conditions, such as denormal operands, is not yet
+complete.
+
+----------------------- Performance of wm-FPU-emu -----------------------
+
+Speed.
+-----
+
+The speed of floating point computation with the emulator will depend
+upon instruction mix. Relative performance is best for the instructions
+which require most computation. The simple instructions are adversely
+affected by the fpu instruction trap overhead.
+
+
+Timing: Some simple timing tests have been made on the emulator functions.
+The times include load/store instructions. All times are in microseconds
+measured on a 33MHz 386 with 64k cache. The Turbo C tests were under
+ms-dos, the next two columns are for emulators running with the djgpp
+ms-dos extender. The final column is for wm-FPU-emu in Linux 0.97,
+using libm4.0 (hard).
+
+function      Turbo C        djgpp 1.06        WM-emu387     wm-FPU-emu
+
+   +          60.5           154.8              76.5          139.4
+   -          61.1-65.5      157.3-160.8        76.2-79.5     142.9-144.7
+   *          71.0           190.8              79.6          146.6
+   /          61.2-75.0      261.4-266.9        75.3-91.6     142.2-158.1
+
+ sin()        310.8          4692.0            319.0          398.5
+ cos()        284.4          4855.2            308.0          388.7
+ tan()        495.0          8807.1            394.9          504.7
+ atan()       328.9          4866.4            601.1          419.5-491.9
+
+ sqrt()       128.7          crashed           145.2          227.0
+ log()        413.1-419.1    5103.4-5354.21    254.7-282.2    409.4-437.1
+ exp()        479.1          6619.2            469.1          850.8
+
+
+The performance under Linux is improved by the use of look-ahead code.
+The following results show the improvement which is obtained under
+Linux due to the look-ahead code. Also given are the times for the
+original Linux emulator with the 4.1 'soft' lib.
+
+ [ Linus' note: I changed look-ahead to be the default under linux, as
+   there was no reason not to use it after I had edited it to be
+   disabled during tracing ]
+
+            wm-FPU-emu w     original w
+            look-ahead       'soft' lib
+   +         106.4             190.2
+   -         108.6-111.6      192.4-216.2
+   *         113.4             193.1
+   /         108.8-124.4      700.1-706.2
+
+ sin()       390.5            2642.0
+ cos()       381.5            2767.4
+ tan()       496.5            3153.3
+ atan()      367.2-435.5     2439.4-3396.8
+
+ sqrt()      195.1            4732.5
+ log()       358.0-387.5     3359.2-3390.3
+ exp()       619.3            4046.4
+
+
+These figures are now somewhat out-of-date. The emulator has become
+progressively slower for most functions as more of the 80486 features
+have been implemented.
+
+
+----------------------- Accuracy of wm-FPU-emu -----------------------
+
+
+Accuracy: The following table gives the accuracy of the sqrt(), trig
+and log functions. Each function was tested at about 400 points. Ideal
+results would be 64 bits. The reduced accuracy of cos() and tan() for
+arguments greater than pi/4 can be thought of as being due to the
+precision of the argument x; e.g. an argument of pi/2-(1e-10) which is
+accurate to 64 bits can result in a relative accuracy in cos() of about
+64 + log2(cos(x)) = 31 bits. Results for the Turbo C emulator are given
+in the last column.
+
+
+Function      Tested x range            Worst result (bits)         Turbo C
+
+sqrt(x)       1 .. 2                    64.1                         63.2
+atan(x)       1e-10 .. 200              62.6                         62.8
+cos(x)        0 .. pi/2-(1e-10)         63.2 (x <= pi/4)             62.4
+                                        35.2 (x = pi/2-(1e-10))      31.9
+sin(x)        1e-10 .. pi/2             63.0                         62.8
+tan(x)        1e-10 .. pi/2-(1e-10)     62.4 (x <= pi/4)             62.1
+                                        35.2 (x = pi/2-(1e-10))      31.9
+exp(x)        0 .. 1                    63.1                         62.9
+log(x)        1+1e-6 .. 2               62.4                         62.1
+
+
+As of version 1.3 of the emulator, the accuracy of the basic
+arithmetic has been improved (by a small fraction of a bit). Care has
+been taken to ensure full accuracy of the rounding of the basic
+arithmetic functions (+,-,*,/,and fsqrt), and they all now produce
+results which are exact to the 64th bit (unless there are any bugs
+left). To ensure this, it was necessary to effectively get information
+of up to about 128 bits precision. The emulator now passes the
+"paranoia" tests (compiled with gcc 2.3.3) for 'float' variables (24
+bit precision numbers) when precision control is set to 24, 53 or 64
+bits, and for 'double' variables (53 bit precision numbers) when
+precision control is set to 53 bits (a properly performing FPU cannot
+pass the 'paranoia' tests for 'double' variables when precision
+control is set to 64 bits).
+
+------------------------- Contributors -------------------------------
+
+A number of people have contributed to the development of the
+emulator, often by just reporting bugs, sometimes with a suggested
+fix, and a few kind people have provided me with access in one way or
+another to an 80486 machine. Contributors include (to those people who
+I have forgotten, please excuse me):
+
+Linus Torvalds
+Tommy.Thorn@daimi.aau.dk
+Andrew.Tridgell@anu.edu.au
+Nick Holloway alfie@dcs.warwick.ac.uk
+Hermano Moura moura@dcs.gla.ac.uk
+Jon Jagger J.Jagger@scp.ac.uk
+Lennart Benschop
+Brian Gallew geek+@CMU.EDU
+Thomas Staniszewski ts3v+@andrew.cmu.edu
+Martin Howell mph@plasma.apana.org.au
+M Saggaf alsaggaf@athena.mit.edu
+Peter Barker PETER@socpsy.sci.fau.edu
+tom@vlsivie.tuwien.ac.at
+Dan Russel russed@rpi.edu
+Daniel Carosone danielce@ee.mu.oz.au
+cae@jpmorgan.com
+Hamish Coleman t933093@minyos.xx.rmit.oz.au
+
+...and numerous others who responded to my request for help with
+a real 80486.
+