Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc. This file is part of the GNU MP Library. The GNU MP Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. The GNU MP Library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with the GNU MP Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. X86 MPN SUBROUTINES This directory contains mpn functions for various 80x86 chips. CODE ORGANIZATION x86 i386, generic x86/i486 i486 x86/pentium Intel Pentium (P5, P54) x86/pentium/mmx Intel Pentium with MMX (P55) x86/p6 Intel Pentium Pro x86/p6/mmx Intel Pentium II, III x86/p6/p3mmx Intel Pentium III x86/k6 \ AMD K6 x86/k6/mmx / x86/k6/k62mmx AMD K6-2 x86/k7 \ AMD Athlon x86/k7/mmx / x86/pentium4 \ x86/pentium4/mmx | Intel Pentium 4 x86/pentium4/sse2 / The top-level x86 directory contains blended style code, meant to be reasonable on all x86s. STATUS The code is well-optimized for AMD and Intel chips, but there's nothing specific for Cyrix chips, nor for actual 80386 and 80486 chips. ASM FILES The x86 .asm files are BSD style assembler code, first put through m4 for macro processing. The generic mpn/asm-defs.m4 is used, together with mpn/x86/x86-defs.m4. See comments in those files. The code is meant for use with GNU "gas" or a system "as". There's no support for assemblers that demand Intel style code. STACK FRAME m4 macros are used to define the parameters passed on the stack, and these act like comments on what the stack frame looks like too. For example, mpn_mul_1() has the following. defframe(PARAM_MULTIPLIER, 16) defframe(PARAM_SIZE, 12) defframe(PARAM_SRC, 8) defframe(PARAM_DST, 4) PARAM_MULTIPLIER becomes `FRAME+16(%esp)', and the others similarly. The return address is at offset 0, but there's not normally any need to access that. FRAME is redefined as necessary through the code so it's the number of bytes pushed on the stack, and hence the offsets in the parameter macros stay correct. At the start of a routine FRAME should be zero. deflit(`FRAME',0) ... deflit(`FRAME',4) ... deflit(`FRAME',8) ... Helper macros FRAME_pushl(), FRAME_popl(), FRAME_addl_esp() and FRAME_subl_esp() exist to adjust FRAME for the effect of those instructions, and can be used instead of explicit definitions if preferred. defframe_pushl() is a combination FRAME_pushl() and defframe(). There's generally some slackness in redefining FRAME. If new values aren't going to get used then the redefinitions are omitted to keep from cluttering up the code. This happens for instance at the end of a routine, where there might be just four pops and then a ret, so FRAME isn't getting used. Local variables and saved registers can be similarly defined, with negative offsets representing stack space below the initial stack pointer. For example, defframe(SAVE_ESI, -4) defframe(SAVE_EDI, -8) defframe(VAR_COUNTER,-12) deflit(STACK_SPACE, 12) Here STACK_SPACE gets used in a "subl $STACK_SPACE, %esp" to allocate the space, and that instruction must be followed by a redefinition of FRAME (setting it equal to STACK_SPACE) to reflect the change in %esp. Definitions for pushed registers are only put in when they're going to be used. If registers are just saved and restored with pushes and pops then definitions aren't made. ASSEMBLER EXPRESSIONS Only addition and subtraction seem to be universally available, certainly that's all the Solaris 8 "as" seems to accept. If expressions are wanted then m4 eval() should be used. In particular note that a "/" anywhere in a line starts a comment in Solaris "as", and in some configurations of gas too. addl $32/2, %eax <-- wrong addl $eval(32/2), %eax <-- right Binutils gas/config/tc-i386.c has a choice between "/" being a comment anywhere in a line, or only at the start. FreeBSD patches 2.9.1 to select the latter, and from 2.9.5 it's the default for GNU/Linux too. ASSEMBLER COMMENTS Solaris "as" doesn't support "#" commenting, using /* */ instead. For that reason "C" commenting is used (see asm-defs.m4) and the intermediate ".s" files have no comments. Any comments before include(`../config.m4') must use m4 "dnl", since it's only after the include that "C" is available. By convention "dnl" is also used for comments about m4 macros. TEMPORARY LABELS Temporary numbered labels like "1:" used as "1f" or "1b" are available in "gas" and Solaris "as", but not in SCO "as". Normal L() labels should be used instead, possibly with a counter to make them unique, see jadcl0() in x86-defs.m4 for instance. A separate counter for each macro makes it possible to nest them, for instance movl_text_address() can be used within an ASSERT(). "1:" etc must be avoided in gcc __asm__ blocks too. "%=" for generating a unique number looks like a good alternative, but is that actually a documented feature? In any case this problem doesn't currently arise. ZERO DISPLACEMENTS In a couple of places addressing modes like 0(%ebx) with a byte-sized zero displacement are wanted, rather than (%ebx) with no displacement. These are either for computed jumps or to get desirable code alignment. Explicit .byte sequences are used to ensure the assembler doesn't turn 0(%ebx) into (%ebx). The Zdisp() macro in x86-defs.m4 is used for this. Current gas 2.9.5 or recent 2.9.1 leave 0(%ebx) as written, but old gas 1.92.3 changes it. In general changing would be the sort of "optimization" an assembler might perform, hence explicit ".byte"s are used where necessary. SHLD/SHRD INSTRUCTIONS The %cl count forms of double shift instructions like "shldl %cl,%eax,%ebx" must be written "shldl %eax,%ebx" for some assemblers. gas takes either, Solaris "as" doesn't allow %cl, gcc generates %cl for gas and NeXT (which is gas), and omits %cl elsewhere. For GMP an autoconf test GMP_ASM_X86_SHLDL_CL is used to determine whether %cl should be used, and the macros shldl, shrdl, shldw and shrdw in mpn/x86/x86-defs.m4 pass through or omit %cl as necessary. See the comments with those macros for usage. IMUL INSTRUCTION GCC config/i386/i386.md (cvs rev 1.187, 21 Oct 00) under *mulsi3_1 notes that the following two forms produce identical object code imul $12, %eax imul $12, %eax, %eax but that the former isn't accepted by some assemblers, in particular the SCO OSR5 COFF assembler. GMP follows GCC and uses only the latter form. (This applies only to immediate operands, the three operand form is only valid with an immediate.) DIRECTION FLAG The x86 calling conventions say that the direction flag should be clear at function entry and exit. (See iBCS2 and SVR4 ABI books, references below.) Although this has been so since the year dot, it's not absolutely clear whether it's universally respected. Since it's better to be safe than sorry, GMP follows glibc and does a "cld" if it depends on the direction flag being clear. This happens only in a few places. POSITION INDEPENDENT CODE Coding Style Defining the symbol PIC in m4 processing selects SVR4 / ELF style position independent code. This is necessary for shared libraries because they can be mapped into different processes at different virtual addresses. Actually, relocations are allowed but text pages with relocations aren't shared, defeating the purpose of a shared library. The GOT is used to access global data, and the PLT is used for functions. The use of the PLT adds a fixed cost to every function call, and the GOT adds a cost to any function accessing global variables. These are small but might be noticeable when working with small operands. Scope It's intended, as a matter of policy, that references within libmpir are resolved within libmpir. Certainly there's no need for an application to replace any internals, and we take the view that there's no value in an application subverting anything documented either. Resolving references within libmpir in theory means calls can be made with a plain PC-relative call instruction, which is faster and smaller than going through the PLT, and data references can be similarly PC-relative, saving a GOT entry and fetch from there. Unfortunately the normal linker behaviour doesn't allow us to do this. By default an R_386_PC32 PC-relative reference, either for a call or for data, is left in libmpir.so by the linker so that it can be resolved at runtime to a location in the application or another shared library. This means a text segment relocation which we don't want. -Bsymbolic Under the "-Bsymbolic" option, the linker resolves references to symbols within libmpir.so. This gives us the desired effect for R_386_PC32, ie. it's resolved at link time. It also resolves R_386_PLT32 calls directly to their target without creating a PLT entry (though if this is done to normal compiler-generated code it still leaves a setup of %ebx to _GLOBAL_OFFSET_TABLE_ which may then be unnecessary). Unfortunately -Bsymbolic does bad things to global variables defined in a shared library but accessed by non-PIC code from the mainline (or a static library). The problem is that the mainline needs a fixed data address to avoid text segment relocations, so space is allocated in its data segment and the value from the variable is copied from the shared library's data segment when the library is loaded. Under -Bsymbolic, however, references in the shared library are then resolved still to the shared library data area. Not surprisingly it bombs badly to have mainline code and library code accessing different locations for what should be one variable. Note that this -Bsymbolic effect for the shared library is not just for R_386_PC32 offsets which might have been cooked up in assembler, but is done also for the contents of GOT entries. -Bsymbolic simply applies a general rule that symbols are resolved first from the local module. Visibility Attributes GCC __attribute__ ((visibility ("protected"))), which is available in recent versions, eg. 3.3, is probably what we'd like to use. It makes gcc generate plain PC-relative calls to indicated functions, and directs the linker to resolve references to the given function within the link module. Unfortunately, as of debian binutils 2.13.90.0.16 at least, the resulting libmpir.so comes out with text segment relocations, references are not resolved at link time. If the gcc description is to be believed this is this not how it should work. If a symbol cannot be overridden by another module then surely references within that module can be resolved immediately (ie. at link time). Present In any case, all this means that we have no optimizations we can usefully make to function or variable usages, neither for assembler nor C code. Perhaps in the future the visibility attribute will work as we'd like. GLOBAL OFFSET TABLE The magic _GLOBAL_OFFSET_TABLE_ used by code establishing the address of the GOT sometimes requires an extra underscore prefix. SVR4 systems and NetBSD don't need a prefix, OpenBSD does need one. Note that NetBSD and OpenBSD are both a.out underscore systems, so the prefix for _GLOBAL_OFFSET_TABLE_ is not simply the same as the prefix for ordinary globals. In any case in the asm code we write _GLOBAL_OFFSET_TABLE_ and let a macro in x86-defs.m4 add an extra underscore if required (according to a configure test). Old gas 1.92.3 which comes with FreeBSD 2.2.8 gets a segmentation fault when asked to assemble the following, L1: addl $_GLOBAL_OFFSET_TABLE_+[.-L1], %ebx It seems that using the label in the same instruction it refers to is the problem, since a nop in between works. But the simplest workaround is to follow gcc and omit the +[.-L1] since it does nothing, addl $_GLOBAL_OFFSET_TABLE_, %ebx Current gas 2.10 generates incorrect object code when %eax is used in such a construction (with or without +[.-L1]), addl $_GLOBAL_OFFSET_TABLE_, %eax The R_386_GOTPC gets a displacement of 2 rather than the 1 appropriate for the 1 byte opcode of "addl $n,%eax". The best workaround is just to use any other register, since then it's a two byte opcode+mod/rm. GCC for example always uses %ebx (which is needed for calls through the PLT). A similar problem occurs in an leal (again with or without a +[.-L1]), leal _GLOBAL_OFFSET_TABLE_(%edi), %ebx This time the R_386_GOTPC gets a displacement of 0 rather than the 2 appropriate for the opcode and mod/rm, making this form unusable. SIMPLE LOOPS The overheads in setting up for an unrolled loop can mean that at small sizes a simple loop is faster. Making small sizes go fast is important, even if it adds a cycle or two to bigger sizes. To this end various routines choose between a simple loop and an unrolled loop according to operand size. The path to the simple loop, or to special case code for small sizes, is always as fast as possible. Adding a simple loop requires a conditional jump to choose between the simple and unrolled code. The size of a branch misprediction penalty affects whether a simple loop is worthwhile. The convention is for an m4 definition UNROLL_THRESHOLD to set the crossover point, with sizes < UNROLL_THRESHOLD using the simple loop, sizes >= UNROLL_THRESHOLD using the unrolled loop. If position independent code adds a couple of cycles to an unrolled loop setup, the threshold will vary with PIC or non-PIC. Something like the following is typical. deflit(UNROLL_THRESHOLD, ifdef(`PIC',10,8)) There's no automated way to determine the threshold. Setting it to a small value and then to a big value makes it possible to measure the simple and unrolled loops each over a range of sizes, from which the crossover point can be determined. Alternately, just adjust the threshold up or down until there's no more speedups. UNROLLED LOOP CODING The x86 addressing modes allow a byte displacement of -128 to +127, making it possible to access 256 bytes, which is 64 limbs, without adjusting pointer registers within the loop. Dword sized displacements can be used too, but they increase code size, and unrolling to 64 ought to be enough. When unrolling to the full 64 limbs/loop, the limb at the top of the loop will have a displacement of -128, so pointers have to have a corresponding +128 added before entering the loop. When unrolling to 32 limbs/loop displacements 0 to 127 can be used with 0 at the top of the loop and no adjustment needed to the pointers. Where 64 limbs/loop is supported, the +128 adjustment is done only when 64 limbs/loop is selected. Usually the gain in speed using 64 instead of 32 or 16 is small, so support for 64 limbs/loop is generally only for comparison. COMPUTED JUMPS When working from least significant limb to most significant limb (most routines) the computed jump and pointer calculations in preparation for an unrolled loop are as follows. S = operand size in limbs N = number of limbs per loop (UNROLL_COUNT) L = log2 of unrolling (UNROLL_LOG2) M = mask for unrolling (UNROLL_MASK) C = code bytes per limb in the loop B = bytes per limb (4 for x86) computed jump (-S & M) * C + entrypoint subtract from pointers (-S & M) * B initial loop counter (S-1) >> L displacements 0 to B*(N-1) The loop counter is decremented at the end of each loop, and the looping stops when the decrement takes the counter to -1. The displacements are for the addressing accessing each limb, eg. a load with "movl disp(%ebx), %eax". Usually the multiply by "C" can be handled without an imul, using instead an leal, or a shift and subtract. When working from most significant to least significant limb (eg. mpn_lshift and mpn_copyd), the calculations change as follows. add to pointers (-S & M) * B displacements 0 to -B*(N-1) OLD GAS 1.92.3 This version comes with FreeBSD 2.2.8 and has a couple of gremlins that affect GMP code. Firstly, an expression involving two forward references to labels comes out as zero. For example, addl $bar-foo, %eax foo: nop bar: This should lead to "addl $1, %eax", but it comes out as "addl $0, %eax". When only one forward reference is involved, it works correctly, as for example, foo: addl $bar-foo, %eax nop bar: Secondly, an expression involving two labels can't be used as the displacement for an leal. For example, foo: nop bar: leal bar-foo(%eax,%ebx,8), %ecx A slightly cryptic error is given, "Unimplemented segment type 0 in parse_operand". When only one label is used it's ok, and the label can be a forward reference too, as for example, leal foo(%eax,%ebx,8), %ecx nop foo: These problems only affect PIC computed jump calculations. The workarounds are just to do an leal without a displacement and then an addl, and to make sure the code is placed so that there's at most one forward reference in the addl. REFERENCES "Intel Architecture Software Developer's Manual", volumes 1, 2a, 2b, 3a, 3b, 2006, order numbers 253665 through 253669. Available on-line, ftp://download.intel.com/design/Pentium4/manuals/25366518.pdf ftp://download.intel.com/design/Pentium4/manuals/25366618.pdf ftp://download.intel.com/design/Pentium4/manuals/25366718.pdf ftp://download.intel.com/design/Pentium4/manuals/25366818.pdf ftp://download.intel.com/design/Pentium4/manuals/25366918.pdf "System V Application Binary Interface", Unix System Laboratories Inc, 1992, published by Prentice Hall, ISBN 0-13-880410-9. And the "Intel386 Processor Supplement", AT&T, 1991, ISBN 0-13-877689-X. These have details of calling conventions and ELF shared library PIC coding. Versions of both available on-line, http://www.sco.com/developer/devspecs "Intel386 Family Binary Compatibility Specification 2", Intel Corporation, published by McGraw-Hill, 1991, ISBN 0-07-031219-2. (Same as the above 386 ABI supplement.) ---------------- Local variables: mode: text fill-column: 76 End: