.explicit
.text
.ident "ia64.S, Version 2.1"
.ident "IA-64 ISA artwork by Andy Polyakov <appro@openssl.org>"
// Copyright 2001-2019 The OpenSSL Project Authors. All Rights Reserved.
//
// Licensed under the OpenSSL license (the "License"). You may not use
// this file except in compliance with the License. You can obtain a copy
// in the file LICENSE in the source distribution or at
// https://www.openssl.org/source/license.html
//
// ====================================================================
// Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
// project.
//
// Rights for redistribution and usage in source and binary forms are
// granted according to the OpenSSL license. Warranty of any kind is
// disclaimed.
// ====================================================================
//
// Version 2.x is Itanium2 re-tune. Few words about how Itanium2 is
// different from Itanium to this module viewpoint. Most notably, is it
// "wider" than Itanium? Can you experience loop scalability as
// discussed in commentary sections? Not really:-( Itanium2 has 6
// integer ALU ports, i.e. it's 2 ports wider, but it's not enough to
// spin twice as fast, as I need 8 IALU ports. Amount of floating point
// ports is the same, i.e. 2, while I need 4. In other words, to this
// module Itanium2 remains effectively as "wide" as Itanium. Yet it's
// essentially different in respect to this module, and a re-tune was
// required. Well, because some instruction latencies has changed. Most
// noticeably those intensively used:
//
// Itanium Itanium2
// ldf8 9 6 L2 hit
// ld8 2 1 L1 hit
// getf 2 5
// xma[->getf] 7[+1] 4[+0]
// add[->st8] 1[+1] 1[+0]
//
// What does it mean? You might ratiocinate that the original code
// should run just faster... Because sum of latencies is smaller...
// Wrong! Note that getf latency increased. This means that if a loop is
// scheduled for lower latency (as they were), then it will suffer from
// stall condition and the code will therefore turn anti-scalable, e.g.
// original bn_mul_words spun at 5*n or 2.5 times slower than expected
// on Itanium2! What to do? Reschedule loops for Itanium2? But then
// Itanium would exhibit anti-scalability. So I've chosen to reschedule
// for worst latency for every instruction aiming for best *all-round*
// performance.
// Q. How much faster does it get?
// A. Here is the output from 'openssl speed rsa dsa' for vanilla
// 0.9.6a compiled with gcc version 2.96 20000731 (Red Hat
// Linux 7.1 2.96-81):
//
// sign verify sign/s verify/s
// rsa 512 bits 0.0036s 0.0003s 275.3 2999.2
// rsa 1024 bits 0.0203s 0.0011s 49.3 894.1
// rsa 2048 bits 0.1331s 0.0040s 7.5 250.9
// rsa 4096 bits 0.9270s 0.0147s 1.1 68.1
// sign verify sign/s verify/s
// dsa 512 bits 0.0035s 0.0043s 288.3 234.8
// dsa 1024 bits 0.0111s 0.0135s 90.0 74.2
//
// And here is similar output but for this assembler
// implementation:-)
//
// sign verify sign/s verify/s
// rsa 512 bits 0.0021s 0.0001s 549.4 9638.5
// rsa 1024 bits 0.0055s 0.0002s 183.8 4481.1
// rsa 2048 bits 0.0244s 0.0006s 41.4 1726.3
// rsa 4096 bits 0.1295s 0.0018s 7.7 561.5
// sign verify sign/s verify/s
// dsa 512 bits 0.0012s 0.0013s 891.9 756.6
// dsa 1024 bits 0.0023s 0.0028s 440.4 376.2
//
// Yes, you may argue that it's not fair comparison as it's
// possible to craft the C implementation with BN_UMULT_HIGH
// inline assembler macro. But of course! Here is the output
// with the macro:
//
// sign verify sign/s verify/s
// rsa 512 bits 0.0020s 0.0002s 495.0 6561.0
// rsa 1024 bits 0.0086s 0.0004s 116.2 2235.7
// rsa 2048 bits 0.0519s 0.0015s 19.3 667.3
// rsa 4096 bits 0.3464s 0.0053s 2.9 187.7
// sign verify sign/s verify/s
// dsa 512 bits 0.0016s 0.0020s 613.1 510.5
// dsa 1024 bits 0.0045s 0.0054s 221.0 183.9
//
// My code is still way faster, huh:-) And I believe that even
// higher performance can be achieved. Note that as keys get
// longer, performance gain is larger. Why? According to the
// profiler there is another player in the field, namely
// BN_from_montgomery consuming larger and larger portion of CPU
// time as keysize decreases. I therefore consider putting effort
// to assembler implementation of the following routine:
//
// void bn_mul_add_mont (BN_ULONG *rp,BN_ULONG *np,int nl,BN_ULONG n0)
// {
// int i,j;
// BN_ULONG v;
//
// for (i=0; i<nl; i++)
// {
// v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
// nrp++;
// rp++;
// if (((nrp[-1]+=v)&BN_MASK2) < v)
// for (j=0; ((++nrp[j])&BN_MASK2) == 0; j++) ;
// }
// }
//
// It might as well be beneficial to implement even combaX
// variants, as it appears as it can literally unleash the
// performance (see comment section to bn_mul_comba8 below).
//
// And finally for your reference the output for 0.9.6a compiled
// with SGIcc version 0.01.0-12 (keep in mind that for the moment
// of this writing it's not possible to convince SGIcc to use
// BN_UMULT_HIGH inline assembler macro, yet the code is fast,
// i.e. for a compiler generated one:-):
//
// sign verify sign/s verify/s
// rsa 512 bits 0.0022s 0.0002s 452.7 5894.3
// rsa 1024 bits 0.0097s 0.0005s 102.7 2002.9
// rsa 2048 bits 0.0578s 0.0017s 17.3 600.2
// rsa 4096 bits 0.3838s 0.0061s 2.6 164.5
// sign verify sign/s verify/s
// dsa 512 bits 0.0018s 0.0022s 547.3 459.6
// dsa 1024 bits 0.0051s 0.0062s 196.6 161.3
//
// Oh! Benchmarks were performed on 733MHz Lion-class Itanium
// system running Redhat Linux 7.1 (very special thanks to Ray
// McCaffity of Williams Communications for providing an account).
//
// Q. What's the heck with 'rum 1<<5' at the end of every function?
// A. Well, by clearing the "upper FP registers written" bit of the
// User Mask I want to excuse the kernel from preserving upper
// (f32-f128) FP register bank over process context switch, thus
// minimizing bus bandwidth consumption during the switch (i.e.
// after PKI operation completes and the program is off doing
// something else like bulk symmetric encryption). Having said
// this, I also want to point out that it might be good idea
// to compile the whole toolkit (as well as majority of the
// programs for that matter) with -mfixed-range=f32-f127 command
// line option. No, it doesn't prevent the compiler from writing
// to upper bank, but at least discourages to do so. If you don't
// like the idea you have the option to compile the module with
// -Drum=nop.m in command line.
//
#if defined(_HPUX_SOURCE) && !defined(_LP64)
#define ADDP addp4
#else
#define ADDP add
#endif
#ifdef __VMS
.alias abort, "decc$abort"
#endif
#if 1
//
// bn_[add|sub]_words routines.
//
// Loops are spinning in 2*(n+5) ticks on Itanium (provided that the
// data reside in L1 cache, i.e. 2 ticks away). It's possible to
// compress the epilogue and get down to 2*n+6, but at the cost of
// scalability (the neat feature of this implementation is that it
// shall automagically spin in n+5 on "wider" IA-64 implementations:-)
// I consider that the epilogue is short enough as it is to trade tiny
// performance loss on Itanium for scalability.
//
// BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int num)
//
.global bn_add_words#
.proc bn_add_words#
.align 64
.skip 32 // makes the loop body aligned at 64-byte boundary
bn_add_words:
.prologue
.save ar.pfs,r2
{ .mii; alloc r2=ar.pfs,4,12,0,16
cmp4.le p6,p0=r35,r0 };;
{ .mfb; mov r8=r0 // return value
(p6) br.ret.spnt.many b0 };;
{ .mib; sub r10=r35,r0,1
.save ar.lc,r3
mov r3=ar.lc
brp.loop.imp .L_bn_add_words_ctop,.L_bn_add_words_cend-16
}
{ .mib; ADDP r14=0,r32 // rp
.save pr,r9
mov r9=pr };;
.body
{ .mii; ADDP r15=0,r33 // ap
mov ar.lc=r10
mov ar.ec=6 }
{ .mib; ADDP r16=0,r34 // bp
mov pr.rot=1<<16 };;
.L_bn_add_words_ctop:
{ .mii; (p16) ld8 r32=[r16],8 // b=*(bp++)
(p18) add r39=r37,r34
(p19) cmp.ltu.unc p56,p0=r40,r38 }
{ .mfb; (p0) nop.m 0x0
(p0) nop.f 0x0
(p0) nop.b 0x0 }
{ .mii; (p16) ld8 r35=[r15],8 // a=*(ap++)
(p58) cmp.eq.or p57,p0=-1,r41 // (p20)
(p58) add r41=1,r41 } // (p20)
{ .mfb; (p21) st8 [r14]=r42,8 // *(rp++)=r
(p0) nop.f 0x0
br.ctop.sptk .L_bn_add_words_ctop };;
.L_bn_add_words_cend:
{ .mii;
(p59) add r8=1,r8 // return value
mov pr=r9,0x1ffff
mov ar.lc=r3 }
{ .mbb; nop.b 0x0
br.ret.sptk.many b0 };;
.endp bn_add_words#
//
// BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int num)
//
.global bn_sub_words#
.proc bn_sub_words#
.align 64
.skip 32 // makes the loop body aligned at 64-byte boundary
bn_sub_words:
.prologue
.save ar.pfs,r2
{ .mii; alloc r2=ar.pfs,4,12,0,16
cmp4.le p6,p0=r35,r0 };;
{ .mfb; mov r8=r0 // return value
(p6) br.ret.spnt.many b0 };;
{ .mib; sub r10=r35,r0,1
.save ar.lc,r3
mov r3=ar.lc
brp.loop.imp .L_bn_sub_words_ctop,.L_bn_sub_words_cend-16
}
{ .mib; ADDP r14=0,r32 // rp
.save pr,r9
mov r9=pr };;
.body
{ .mii; ADDP r15=0,r33 // ap
mov ar.lc=r10
mov ar.ec=6 }
{ .mib; ADDP r16=0,r34 // bp
mov pr.rot=1<<16 };;
.L_bn_sub_words_ctop:
{ .mii; (p16) ld8 r32=[r16],8 // b=*(bp++)
(p18) sub r39=r37,r34
(p19) cmp.gtu.unc p56,p0=r40,r38 }
{ .mfb; (p0) nop.m 0x0
(p0) nop.f 0x0
(p0) nop.b 0x0 }
{ .mii; (p16) ld8 r35=[r15],8 // a=*(ap++)
(p58) cmp.eq.or p57,p0=0,r41 // (p20)
(p58) add r41=-1,r41 } // (p20)
{ .mbb; (p21) st8 [r14]=r42,8 // *(rp++)=r
(p0) nop.b 0x0
br.ctop.sptk .L_bn_sub_words_ctop };;
.L_bn_sub_words_cend:
{ .mii;
(p59) add r8=1,r8 // return value
mov pr=r9,0x1ffff
mov ar.lc=r3 }
{ .mbb; nop.b 0x0
br.ret.sptk.many b0 };;
.endp bn_sub_words#
#endif
#if 0
#define XMA_TEMPTATION
#endif
#if 1
//
// BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w)
//
.global bn_mul_words#
.proc bn_mul_words#
.align 64
.skip 32 // makes the loop body aligned at 64-byte boundary
bn_mul_words:
.prologue
.save ar.pfs,r2
#ifdef XMA_TEMPTATION
{ .mfi; alloc r2=ar.pfs,4,0,0,0 };;
#else
{ .mfi; alloc r2=ar.pfs,4,12,0,16 };;
#endif
{ .mib; mov r8=r0 // return value
cmp4.le p6,p0=r34,r0
(p6) br.ret.spnt.many b0 };;
{ .mii; sub r10=r34,r0,1
.save ar.lc,r3
mov r3=ar.lc
.save pr,r9
mov r9=pr };;
.body
{ .mib; setf.sig f8=r35 // w
mov pr.rot=0x800001<<16
// ------^----- serves as (p50) at first (p27)
brp.loop.imp .L_bn_mul_words_ctop,.L_bn_mul_words_cend-16
}
#ifndef XMA_TEMPTATION
{ .mmi; ADDP r14=0,r32 // rp
ADDP r15=0,r33 // ap
mov ar.lc=r10 }
{ .mmi; mov r40=0 // serves as r35 at first (p27)
mov ar.ec=13 };;
// This loop spins in 2*(n+12) ticks. It's scheduled for data in Itanium
// L2 cache (i.e. 9 ticks away) as floating point load/store instructions
// bypass L1 cache and L2 latency is actually best-case scenario for
// ldf8. The loop is not scalable and shall run in 2*(n+12) even on
// "wider" IA-64 implementations. It's a trade-off here. n+24 loop
// would give us ~5% in *overall* performance improvement on "wider"
// IA-64, but would hurt Itanium for about same because of longer
// epilogue. As it's a matter of few percents in either case I've
// chosen to trade the scalability for development time (you can see
// this very instruction sequence in bn_mul_add_words loop which in
// turn is scalable).
.L_bn_mul_words_ctop:
{ .mfi; (p25) getf.sig r36=f52 // low
(p21) xmpy.lu f48=f37,f8
(p28) cmp.ltu p54,p50=r41,r39 }
{ .mfi; (p16) ldf8 f32=[r15],8
(p21) xmpy.hu f40=f37,f8
(p0) nop.i 0x0 };;
{ .mii; (p25) getf.sig r32=f44 // high
.pred.rel "mutex",p50,p54
(p50) add r40=r38,r35 // (p27)
(p54) add r40=r38,r35,1 } // (p27)
{ .mfb; (p28) st8 [r14]=r41,8
(p0) nop.f 0x0
br.ctop.sptk .L_bn_mul_words_ctop };;
.L_bn_mul_words_cend:
{ .mii; nop.m 0x0
.pred.rel "mutex",p51,p55
(p51) add r8=r36,r0
(p55) add r8=r36,r0,1 }
{ .mfb; nop.m 0x0
nop.f 0x0
nop.b 0x0 }
#else // XMA_TEMPTATION
setf.sig f37=r0 // serves as carry at (p18) tick
mov ar.lc=r10
mov ar.ec=5;;
// Most of you examining this code very likely wonder why in the name
// of Intel the following loop is commented out? Indeed, it looks so
// neat that you find it hard to believe that it's something wrong
// with it, right? The catch is that every iteration depends on the
// result from previous one and the latter isn't available instantly.
// The loop therefore spins at the latency of xma minus 1, or in other
// words at 6*(n+4) ticks:-( Compare to the "production" loop above
// that runs in 2*(n+11) where the low latency problem is worked around
// by moving the dependency to one-tick latent integer ALU. Note that
// "distance" between ldf8 and xma is not latency of ldf8, but the
// *difference* between xma and ldf8 latencies.
.L_bn_mul_words_ctop:
{ .mfi; (p16) ldf8 f32=[r33],8
(p18) xma.hu f38=f34,f8,f39 }
{ .mfb; (p20) stf8 [r32]=f37,8
(p18) xma.lu f35=f34,f8,f39
br.ctop.sptk .L_bn_mul_words_ctop };;
.L_bn_mul_words_cend:
getf.sig r8=f41 // the return value
#endif // XMA_TEMPTATION
{ .mii; nop.m 0x0
mov pr=r9,0x1ffff
mov ar.lc=r3 }
{ .mfb; rum 1<<5 // clear um.mfh
nop.f 0x0
br.ret.sptk.many b0 };;
.endp bn_mul_words#
#endif
#if 1
//
// BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w)
//
.global bn_mul_add_words#
.proc bn_mul_add_words#
.align 64
.skip 48 // makes the loop body aligned at 64-byte boundary
bn_mul_add_words:
.prologue
.save ar.pfs,r2
{ .mmi; alloc r2=ar.pfs,4,4,0,8
cmp4.le p6,p0=r34,r0
.save ar.lc,r3
mov r3=ar.lc };;
{ .mib; mov r8=r0 // return value
sub r10=r34,r0,1
(p6) br.ret.spnt.many b0 };;
{ .mib; setf.sig f8=r35 // w
.save pr,r9
mov r9=pr
brp.loop.imp .L_bn_mul_add_words_ctop,.L_bn_mul_add_words_cend-16
}
.body
{ .mmi; ADDP r14=0,r32 // rp
ADDP r15=0,r33 // ap
mov ar.lc=r10 }
{ .mii; ADDP r16=0,r32 // rp copy
mov pr.rot=0x2001<<16
// ------^----- serves as (p40) at first (p27)
mov ar.ec=11 };;
// This loop spins in 3*(n+10) ticks on Itanium and in 2*(n+10) on
// Itanium 2. Yes, unlike previous versions it scales:-) Previous
// version was performing *all* additions in IALU and was starving
// for those even on Itanium 2. In this version one addition is
// moved to FPU and is folded with multiplication. This is at cost
// of propagating the result from previous call to this subroutine
// to L2 cache... In other words negligible even for shorter keys.
// *Overall* performance improvement [over previous version] varies
// from 11 to 22 percent depending on key length.
.L_bn_mul_add_words_ctop:
.pred.rel "mutex",p40,p42
{ .mfi; (p23) getf.sig r36=f45 // low
(p20) xma.lu f42=f36,f8,f50 // low
(p40) add r39=r39,r35 } // (p27)
{ .mfi; (p16) ldf8 f32=[r15],8 // *(ap++)
(p20) xma.hu f36=f36,f8,f50 // high
(p42) add r39=r39,r35,1 };; // (p27)
{ .mmi; (p24) getf.sig r32=f40 // high
(p16) ldf8 f46=[r16],8 // *(rp1++)
(p40) cmp.ltu p41,p39=r39,r35 } // (p27)
{ .mib; (p26) st8 [r14]=r39,8 // *(rp2++)
(p42) cmp.leu p41,p39=r39,r35 // (p27)
br.ctop.sptk .L_bn_mul_add_words_ctop};;
.L_bn_mul_add_words_cend:
{ .mmi; .pred.rel "mutex",p40,p42
(p40) add r8=r35,r0
(p42) add r8=r35,r0,1
mov pr=r9,0x1ffff }
{ .mib; rum 1<<5 // clear um.mfh
mov ar.lc=r3
br.ret.sptk.many b0 };;
.endp bn_mul_add_words#
#endif
#if 1
//
// void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num)
//
.global bn_sqr_words#
.proc bn_sqr_words#
.align 64
.skip 32 // makes the loop body aligned at 64-byte boundary
bn_sqr_words:
.prologue
.save ar.pfs,r2
{ .mii; alloc r2=ar.pfs,3,0,0,0
sxt4 r34=r34 };;
{ .mii; cmp.le p6,p0=r34,r0
mov r8=r0 } // return value
{ .mfb; ADDP r32=0,r32
nop.f 0x0
(p6) br.ret.spnt.many b0 };;
{ .mii; sub r10=r34,r0,1
.save ar.lc,r3
mov r3=ar.lc
.save pr,r9
mov r9=pr };;
.body
{ .mib; ADDP r33=0,r33
mov pr.rot=1<<16
brp.loop.imp .L_bn_sqr_words_ctop,.L_bn_sqr_words_cend-16
}
{ .mii; add r34=8,r32
mov ar.lc=r10
mov ar.ec=18 };;
// 2*(n+17) on Itanium, (n+17) on "wider" IA-64 implementations. It's
// possible to compress the epilogue (I'm getting tired to write this
// comment over and over) and get down to 2*n+16 at the cost of
// scalability. The decision will very likely be reconsidered after the
// benchmark program is profiled. I.e. if performance gain on Itanium
// will appear larger than loss on "wider" IA-64, then the loop should
// be explicitly split and the epilogue compressed.
.L_bn_sqr_words_ctop:
{ .mfi; (p16) ldf8 f32=[r33],8
(p25) xmpy.lu f42=f41,f41
(p0) nop.i 0x0 }
{ .mib; (p33) stf8 [r32]=f50,16
(p0) nop.i 0x0
(p0) nop.b 0x0 }
{ .mfi; (p0) nop.m 0x0
(p25) xmpy.hu f52=f41,f41
(p0) nop.i 0x0 }
{ .mib; (p33) stf8 [r34]=f60,16
(p0) nop.i 0x0
br.ctop.sptk .L_bn_sqr_words_ctop };;
.L_bn_sqr_words_cend:
{ .mii; nop.m 0x0
mov pr=r9,0x1ffff
mov ar.lc=r3 }
{ .mfb; rum 1<<5 // clear um.mfh
nop.f 0x0
br.ret.sptk.many b0 };;
.endp bn_sqr_words#
#endif
#if 1
// Apparently we win nothing by implementing special bn_sqr_comba8.
// Yes, it is possible to reduce the number of multiplications by
// almost factor of two, but then the amount of additions would
// increase by factor of two (as we would have to perform those
// otherwise performed by xma ourselves). Normally we would trade
// anyway as multiplications are way more expensive, but not this
// time... Multiplication kernel is fully pipelined and as we drain
// one 128-bit multiplication result per clock cycle multiplications
// are effectively as inexpensive as additions. Special implementation
// might become of interest for "wider" IA-64 implementation as you'll
// be able to get through the multiplication phase faster (there won't
// be any stall issues as discussed in the commentary section below and
// you therefore will be able to employ all 4 FP units)... But these
// Itanium days it's simply too hard to justify the effort so I just
// drop down to bn_mul_comba8 code:-)
//
// void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a)
//
.global bn_sqr_comba8#
.proc bn_sqr_comba8#
.align 64
bn_sqr_comba8:
.prologue
.save ar.pfs,r2
#if defined(_HPUX_SOURCE) && !defined(_LP64)
{ .mii; alloc r2=ar.pfs,2,1,0,0
addp4 r33=0,r33
addp4 r32=0,r32 };;
{ .mii;
#else
{ .mii; alloc r2=ar.pfs,2,1,0,0
#endif
mov r34=r33
add r14=8,r33 };;
.body
{ .mii; add r17=8,r34
add r15=16,r33
add r18=16,r34 }
{ .mfb; add r16=24,r33
br .L_cheat_entry_point8 };;
.endp bn_sqr_comba8#
#endif
#if 1
// I've estimated this routine to run in ~120 ticks, but in reality
// (i.e. according to ar.itc) it takes ~160 ticks. Are those extra
// cycles consumed for instructions fetch? Or did I misinterpret some
// clause in Itanium ยต-architecture manual? Comments are welcomed and
// highly appreciated.
//
// On Itanium 2 it takes ~190 ticks. This is because of stalls on
// result from getf.sig. I do nothing about it at this point for
// reasons depicted below.
//
// However! It should be noted that even 160 ticks is darn good result
// as it's over 10 (yes, ten, spelled as t-e-n) times faster than the
// C version (compiled with gcc with inline assembler). I really
// kicked compiler's butt here, didn't I? Yeah! This brings us to the
// following statement. It's damn shame that this routine isn't called
// very often nowadays! According to the profiler most CPU time is
// consumed by bn_mul_add_words called from BN_from_montgomery. In
// order to estimate what we're missing, I've compared the performance
// of this routine against "traditional" implementation, i.e. against
// following routine:
//
// void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
// { r[ 8]=bn_mul_words( &(r[0]),a,8,b[0]);
// r[ 9]=bn_mul_add_words(&(r[1]),a,8,b[1]);
// r[10]=bn_mul_add_words(&(r[2]),a,8,b[2]);
// r[11]=bn_mul_add_words(&(r[3]),a,8,b[3]);
// r[12]=bn_mul_add_words(&(r[4]),a,8,b[4]);
// r[13]=bn_mul_add_words(&(r[5]),a,8,b[5]);
// r[14]=bn_mul_add_words(&(r[6]),a,8,b[6]);
// r[15]=bn_mul_add_words(&(r[7]),a,8,b[7]);
// }
//
// The one below is over 8 times faster than the one above:-( Even
// more reasons to "combafy" bn_mul_add_mont...
//
// And yes, this routine really made me wish there were an optimizing
// assembler! It also feels like it deserves a dedication.
//
// To my wife for being there and to my kids...
//
// void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
//
#define carry1 r14
#define carry2 r15
#define carry3 r34
.global bn_mul_comba8#
.proc bn_mul_comba8#
.align 64
bn_mul_comba8:
.prologue
.save ar.pfs,r2
#if defined(_HPUX_SOURCE) && !defined(_LP64)
{ .mii; alloc r2=ar.pfs,3,0,0,0
addp4 r33=0,r33
addp4 r34=0,r34 };;
{ .mii; addp4 r32=0,r32
#else
{ .mii; alloc r2=ar.pfs,3,0,0,0
#endif
add r14=8,r33
add r17=8,r34 }
.body
{ .mii; add r15=16,r33
add r18=16,r34
add r16=24,r33 }
.L_cheat_entry_point8:
{ .mmi; add r19=24,r34
ldf8 f32=[r33],32 };;
{ .mmi; ldf8 f120=[r34],32
ldf8 f121=[r17],32 }
{ .mmi; ldf8 f122=[r18],32
ldf8 f123=[r19],32 };;
{ .mmi; ldf8 f124=[r34]
ldf8 f125=[r17] }
{ .mmi; ldf8 f126=[r18]
ldf8 f127=[r19] }
{ .mmi; ldf8 f33=[r14],32
ldf8 f34=[r15],32 }
{ .mmi; ldf8 f35=[r16],32;;
ldf8 f36=[r33] }
{ .mmi; ldf8 f37=[r14]
ldf8 f38=[r15] }
{ .mfi; ldf8 f39=[r16]
// -------\ Entering multiplier's heaven /-------
// ------------\ /------------
// -----------------\ /-----------------
// ----------------------\/----------------------
xma.hu f41=f32,f120,f0 }
{ .mfi; xma.lu f40=f32,f120,f0 };; // (*)
{ .mfi; xma.hu f51=f32,f121,f0 }
{ .mfi; xma.lu f50=f32,f121,f0 };;
{ .mfi; xma.hu f61=f32,f122,f0 }
{ .mfi; xma.lu f60=f32,f122,f0 };;
{ .mfi; xma.hu f71=f32,f123,f0 }
{ .mfi; xma.lu f70=f32,f123,f0 };;
{ .mfi; xma.hu f81=f32,f124,f0 }
{ .mfi; xma.lu f80=f32,f124,f0 };;
{ .mfi; xma.hu f91=f32,f125,f0 }
{ .mfi; xma.lu f90=f32,f125,f0 };;
{ .mfi; xma.hu f101=f32,f126,f0 }
{ .mfi; xma.lu f100=f32,f126,f0 };;
{ .mfi; xma.hu f111=f32,f127,f0 }
{ .mfi; xma.lu f110=f32,f127,f0 };;//
// (*) You can argue that splitting at every second bundle would
// prevent "wider" IA-64 implementations from achieving the peak
// performance. Well, not really... The catch is that if you
// intend to keep 4 FP units busy by splitting at every fourth
// bundle and thus perform these 16 multiplications in 4 ticks,
// the first bundle *below* would stall because the result from
// the first xma bundle *above* won't be available for another 3
// ticks (if not more, being an optimist, I assume that "wider"
// implementation will have same latency:-). This stall will hold
// you back and the performance would be as if every second bundle
// were split *anyway*...
{ .mfi; getf.sig r16=f40
xma.hu f42=f33,f120,f41
add r33=8,r32 }
{ .mfi; xma.lu f41=f33,f120,f41 };;
{ .mfi; getf.sig r24=f50
xma.hu f52=f33,f121,f51 }
{ .mfi; xma.lu f51=f33,f121,f51 };;
{ .mfi; st8 [r32]=r16,16
xma.hu f62=f33,f122,f61 }
{ .mfi; xma.lu f61=f33,f122,f61 };;
{ .mfi; xma.hu f72=f33,f123,f71 }
{ .mfi; xma.lu f71=f33,f123,f71 };;
{ .mfi; xma.hu f82=f33,f124,f81 }
{ .mfi; xma.lu f81=f33,f124,f81 };;
{ .mfi; xma.hu f92=f33,f125,f91 }
{ .mfi; xma.lu f91=f33,f125,f91 };;
{ .mfi; xma.hu f102=f33,f126,f101 }
{ .mfi; xma.lu f101=f33,f126,f101 };;
{ .mfi; xma.hu f112=f33,f127,f111 }
{ .mfi; xma.lu f111=f33,f127,f111 };;//
//-------------------------------------------------//
{ .mfi; getf.sig r25=f41
xma.hu f43=f34,f120,f42 }
{ .mfi; xma.lu f42=f34,f120,f42 };;
{ .mfi; getf.sig r16=f60
xma.hu f53=f34,f121,f52 }
{ .mfi; xma.lu f52=f34,f121,f52 };;
{ .mfi; getf.sig r17=f51
xma.hu f63=f34,f122,f62
add r25=r25,r24 }
{ .mfi; xma.lu f62=f34,f122,f62
mov carry1=0 };;
{ .mfi; cmp.ltu p6,p0=r25,r24
xma.hu f73=f34,f123,f72 }
{ .mfi; xma.lu f72=f34,f123,f72 };;
{ .mfi; st8 [r33]=r25,16
xma.hu f83=f34,f124,f82
(p6) add carry1=1,carry1 }
{ .mfi; xma.lu f82=f34,f124,f82 };;
{ .mfi; xma.hu f93=f34,f125,f92 }
{ .mfi; xma.lu f92=f34,f125,f92 };;
{ .mfi; xma.hu f103=f34,f126,f102 }
{ .mfi; xma.lu f102=f34,f126,f102 };;
{ .mfi; xma.hu f113=f34,f127,f112 }
{ .mfi; xma.lu f112=f34,f127,f112 };;//
//-------------------------------------------------//
{ .mfi; getf.sig r18=f42
xma.hu f44=f35,f120,f43
add r17=r17,r16 }
{ .mfi; xma.lu f43=f35,f120,f43 };;
{ .mfi; getf.sig r24=f70
xma.hu f54=f35,f121,f53 }
{ .mfi; mov carry2=0
xma.lu f53=f35,f121,f53 };;
{ .mfi; getf.sig r25=f61
xma.hu f64=f35,f122,f63
cmp.ltu p7,p0=r17,r16 }
{ .mfi; add r18=r18,r17
xma.lu f63=f35,f122,f63 };;
{ .mfi; getf.sig r26=f52
xma.hu f74=f35,f123,f73
(p7) add carry2=1,carry2 }
{ .mfi; cmp.ltu p7,p0=r18,r17
xma.lu f73=f35,f123,f73
add r18=r18,carry1 };;
{ .mfi;
xma.hu f84=f35,f124,f83
(p7) add carry2=1,carry2 }
{ .mfi; cmp.ltu p7,p0=r18,carry1
xma.lu f83=f35,f124,f83 };;
{ .mfi; st8 [r32]=r18,16
xma.hu f94=f35,f125,f93
(p7) add carry2=1,carry2 }
{ .mfi; xma.lu f93=f35,f125,f93 };;
{ .mfi; xma.hu f104=f35,f126,f103 }
{ .mfi; xma.lu f103=f35,f126,f103 };;
{ .mfi; xma.hu f114=f35,f127,f113 }
{ .mfi; mov carry1=0
xma.lu f113=f35,f127,f113
add r25=r25,r24 };;//
//-------------------------------------------------//
{ .mfi; getf.sig r27=f43
xma.hu f45=f36,f120,f44
cmp.ltu p6,p0=r25,r24 }
{ .mfi; xma.lu f44=f36,f120,f44
add r26=r26,r25 };;
{ .mfi; getf.sig r16=f80
xma.hu f55=f36,f121,f54
(p6) add carry1=1,carry1 }
{ .mfi; xma.lu f54=f36,f121,f54 };;
{ .mfi; getf.sig r17=f71
xma.hu f65=f36,f122,f64
cmp.ltu p6,p0=r26,r25 }
{ .mfi; xma.lu f64=f36,f122,f64
add r27=r27,r26 };;
{ .mfi; getf.sig r18=f62
xma.hu f75=f36,f123,f74
(p6) add carry1=1,carry1 }
{ .mfi; cmp.ltu p6,p0=r27,r26
xma.lu f74=f36,f123,f74
add r27=r27,carry2 };;
{ .mfi; getf.sig r19=f53
xma.hu f85=f36,f124,f84
(p6) add carry1=1,carry1 }
{ .mfi; xma.lu f84=f36,f124,f84
cmp.ltu p6,p0=r27,carry2 };;
{ .mfi; st8 [r33]=r27,16
xma.hu f95=f36,f125,f94
(p6) add carry1=1,carry1 }
{ .mfi; xma.lu f94=f36,f125,f94 };;
{ .mfi; xma.hu f105=f36,f126,f104 }
{ .mfi; mov carry2=0
xma.lu f104=f36,f126,f104
add r17=r17,r16 };;
{ .mfi; xma.hu f115=f36,f127,f114
cmp.ltu p7,p0=r17,r16 }
{ .mfi; xma.lu f114=f36,f127,f114
add r18=r18,r17 };;//
//-------------------------------------------------//
{ .mfi; getf.sig r20=f44
xma.hu f46=f37,f120,f45
(p7) add carry2=1,carry2 }
{ .mfi; cmp.ltu p7,p0=r18,r17
xma.lu f45=f37,f120,f45
add r19=r19,r18 };;
{ .mfi; getf.sig r24=f90
xma.hu f56=f37,f121,f55 }
{ .mfi; xma.lu f55=f37,f121,f55 };;
{ .mfi; getf.sig r25=f81
xma.hu f66=f37,f122,f65
(p7) add carry2=1,carry2 }
{ .mfi; cmp.ltu p7,p0=r19,r18
xma.lu f65=f37,f122,f65
add r20=r20,r19 };;
{ .mfi; getf.sig r26=f72
xma.hu f76=f37,f123,f75
(p7) add carry2=1,carry2 }
{ .mfi; cmp.ltu p7,p0=r20,r19
xma.lu f75=f37,f123,f75
add r20=r20,carry1 };;
{ .mfi; getf.sig r27=f63
xma.hu f86=f37,f124,f85
(p7) add carry2=1,carry2 }
{ .mfi; xma.lu f85=f37,f124,f85
cmp.ltu p7,p0=r20,carry1 };;
{ .mfi; getf.sig r28=f54
xma.hu f96=f37,f125,f95
(p7) add carry2=1,carry2 }
{ .mfi; st8 [r32]=r20,16
xma.lu f95=f37,f125,f95 };;
{ .mfi; xma.hu f106=f37,f126,f105 }
{ .mfi; mov carry1=0
xma.lu f105=f37,f126,f105
add r25=r25,r24 };;
{ .mfi; xma.hu f116=f37,f127,f115
cmp.ltu p6,p0=r25,r24 }
{ .mfi; xma.lu f115=f37,f127,f115
add r26=r26,r25 };;//
//-------------------------------------------------//
{ .mfi; getf.sig r29=f45
xma.hu f47=f38,f120,f46
(p6) add carry1=1,carry1 }
{ .mfi; cmp.ltu p6,p0=r26,r25
xma.lu f46=f38,f120,f46
add r27=r27,r26 };;
{ .mfi; getf.sig r16=f100
xma.hu f57=f38,f121,f56
(p6) add carry1=1,carry1 }
{ .mfi; cmp.ltu p6,p0=r27,r26
xma.lu f56=f38,f121,f56
add r28=r28,r27 };;
{ .mfi; getf.sig r17=f91
xma.hu f67=f38,f122,f66
(p6) add carry1=1,carry1 }
{ .mfi; cmp.ltu p6,p0=r28,r27
xma.lu f66=f38,f122,f66
add r29=r29,r28 };;
{ .mfi; getf.sig r18=f82
xma.hu f77=f38,f123,f76
(p6) add carry1=1,carry1 }
{ .mfi; cmp.ltu p6,p0=r29,r28
xma.lu f76=f38,f123,f76
add r29=r29,carry2 };;
{ .mfi; getf.sig r19=f73
xma.hu f87=f38,f124,f86
(p6) add carry1=1,carry1 }
{ .mfi; xma.lu f86=f38,f124,f86
cmp.ltu p6,p0=r29,carry2 };;
{ .mfi; getf.sig r20=f64
xma.hu f97=f38,f125,f96
(p6) add carry1=1,carry1 }
{ .mfi; st8 [r33]=r29,16
xma.lu f96=f38,f125,f96 };;
{ .mfi; getf.sig r21=f55
xma.hu f107=f38,f126,f106 }
{ .mfi; mov carry2=0
xma.lu f106=f38,f126,f106
add r17=r17,r16 };;
{ .mfi; xma.hu f117=f38,f127,f116
cmp.ltu p7,p0=r17,r16 }
{ .mfi; xma.lu f116=f38,f127,f116
add r18=r18,r17 };;//
//-------------------------------------------------//
{ .mfi; getf.sig r22=f46
xma.hu f48=f39,f120,f47
(p7) add carry2=1,carry2 }
{ .mfi; cmp.ltu p7,p0=r18,r17
xma.lu f47=f39,f120,f47
add r19=r19,r18 };;
{ .mfi; getf.sig r24=f110
xma.hu f58=f39,f121,f57
(p7) add carry2=1,carry2 }
{ .mfi; cmp.ltu p7,p0=r19,r18
xma.lu f57=f39,f121,f57
add r20=r20,r19 };;
{ .mfi; getf.sig r25=f101
xma.hu f68=f39,f122,f67
(p7) add carry2=1,carry2 }
{ .mfi; cmp.ltu p7,p0=r20,r19
xma.lu f67=f39,f122,f67
add r21=r21,r20 };;
{ .mfi; getf.sig r26=f92
xma.hu f78=f39,f123,f77
(p7) add carry2=1,carry2 }
{ .mfi; cmp.ltu p7,p0=r21,r20
xma.lu f77=f39,f123,f77
add r22=r22,r21 };;
{ .mfi; getf.sig r27=f83
xma.hu f88=f39,f124,f87
(p7) add carry2=1,carry2 }
{ .mfi; cmp.ltu p7,p0=r22,r21
xma.lu f87=f39,f124,f87
add r22=r22,carry1 };;
{ .mfi; getf.sig r28=f74
xma.hu f98=f39,f125,f97
(p7) add carry2=1,carry2 }
{ .mfi; xma.lu f97=f39,f125,f97
cmp.ltu p7,p0=r22,carry1 };;
{ .mfi; getf.sig r29=f65
xma.hu f108=f39,f126,f107
(p7) add carry2=1,carry2 }
{ .mfi; st8 [r32]=r22,16
xma.lu f107=f39,f126,f107 };;
{ .mfi; getf.sig r30=f56
xma.hu f118=f39,f127,f117 }
{ .mfi; xma.lu f117=f39,f127,f117 };;//
//-------------------------------------------------//
// Leaving multiplier's heaven... Quite a ride, huh?
{ .mii; getf.sig r31=f47
add r25=r25,r24
mov carry1=0 };;
{ .mii; getf.sig r16=f111
cmp.ltu p6,p0=r25,r24
add r26=r26,r25 };;
{ .mfb; getf.sig r17=f102 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r26,r25
add r27=r27,r26 };;
{ .mfb; nop.m 0x0 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r27,r26
add r28=r28,r27 };;
{ .mii; getf.sig r18=f93
add r17=r17,r16
mov carry3=0 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r28,r27
add r29=r29,r28 };;
{ .mii; getf.sig r19=f84
cmp.ltu p7,p0=r17,r16 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r29,r28
add r30=r30,r29 };;
{ .mii; getf.sig r20=f75
add r18=r18,r17 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r30,r29
add r31=r31,r30 };;
{ .mfb; getf.sig r21=f66 }
{ .mii; (p7) add carry3=1,carry3
cmp.ltu p7,p0=r18,r17
add r19=r19,r18 }
{ .mfb; nop.m 0x0 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r31,r30
add r31=r31,carry2 };;
{ .mfb; getf.sig r22=f57 }
{ .mii; (p7) add carry3=1,carry3
cmp.ltu p7,p0=r19,r18
add r20=r20,r19 }
{ .mfb; nop.m 0x0 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r31,carry2 };;
{ .mfb; getf.sig r23=f48 }
{ .mii; (p7) add carry3=1,carry3
cmp.ltu p7,p0=r20,r19
add r21=r21,r20 }
{ .mii;
(p6) add carry1=1,carry1 }
{ .mfb; st8 [r33]=r31,16 };;
{ .mfb; getf.sig r24=f112 }
{ .mii; (p7) add carry3=1,carry3
cmp.ltu p7,p0=r21,r20
add r22=r22,r21 };;
{ .mfb; getf.sig r25=f103 }
{ .mii; (p7) add carry3=1,carry3
cmp.ltu p7,p0=r22,r21
add r23=r23,r22 };;
{ .mfb; getf.sig r26=f94 }
{ .mii; (p7) add carry3=1,carry3
cmp.ltu p7,p0=r23,r22
add r23=r23,carry1 };;
{ .mfb; getf.sig r27=f85 }
{ .mii; (p7) add carry3=1,carry3
cmp.ltu p7,p8=r23,carry1};;
{ .mii; getf.sig r28=f76
add r25=r25,r24
mov carry1=0 }
{ .mii; st8 [r32]=r23,16
(p7) add carry2=1,carry3
(p8) add carry2=0,carry3 };;
{ .mfb; nop.m 0x0 }
{ .mii; getf.sig r29=f67
cmp.ltu p6,p0=r25,r24
add r26=r26,r25 };;
{ .mfb; getf.sig r30=f58 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r26,r25
add r27=r27,r26 };;
{ .mfb; getf.sig r16=f113 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r27,r26
add r28=r28,r27 };;
{ .mfb; getf.sig r17=f104 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r28,r27
add r29=r29,r28 };;
{ .mfb; getf.sig r18=f95 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r29,r28
add r30=r30,r29 };;
{ .mii; getf.sig r19=f86
add r17=r17,r16
mov carry3=0 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r30,r29
add r30=r30,carry2 };;
{ .mii; getf.sig r20=f77
cmp.ltu p7,p0=r17,r16
add r18=r18,r17 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r30,carry2 };;
{ .mfb; getf.sig r21=f68 }
{ .mii; st8 [r33]=r30,16
(p6) add carry1=1,carry1 };;
{ .mfb; getf.sig r24=f114 }
{ .mii; (p7) add carry3=1,carry3
cmp.ltu p7,p0=r18,r17
add r19=r19,r18 };;
{ .mfb; getf.sig r25=f105 }
{ .mii; (p7) add carry3=1,carry3
cmp.ltu p7,p0=r19,r18
add r20=r20,r19 };;
{ .mfb; getf.sig r26=f96 }
{ .mii; (p7) add carry3=1,carry3
cmp.ltu p7,p0=r20,r19
add r21=r21,r20 };;
{ .mfb; getf.sig r27=f87 }
{ .mii; (p7) add carry3=1,carry3
cmp.ltu p7,p0=r21,r20
add r21=r21,carry1 };;
{ .mib; getf.sig r28=f78
add r25=r25,r24 }
{ .mib; (p7) add carry3=1,carry3
cmp.ltu p7,p8=r21,carry1};;
{ .mii; st8 [r32]=r21,16
(p7) add carry2=1,carry3
(p8) add carry2=0,carry3 }
{ .mii; mov carry1=0
cmp.ltu p6,p0=r25,r24
add r26=r26,r25 };;
{ .mfb; getf.sig r16=f115 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r26,r25
add r27=r27,r26 };;
{ .mfb; getf.sig r17=f106 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r27,r26
add r28=r28,r27 };;
{ .mfb; getf.sig r18=f97 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r28,r27
add r28=r28,carry2 };;
{ .mib; getf.sig r19=f88
add r17=r17,r16 }
{ .mib;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r28,carry2 };;
{ .mii; st8 [r33]=r28,16
(p6) add carry1=1,carry1 }
{ .mii; mov carry2=0
cmp.ltu p7,p0=r17,r16
add r18=r18,r17 };;
{ .mfb; getf.sig r24=f116 }
{ .mii; (p7) add carry2=1,carry2
cmp.ltu p7,p0=r18,r17
add r19=r19,r18 };;
{ .mfb; getf.sig r25=f107 }
{ .mii; (p7) add carry2=1,carry2
cmp.ltu p7,p0=r19,r18
add r19=r19,carry1 };;
{ .mfb; getf.sig r26=f98 }
{ .mii; (p7) add carry2=1,carry2
cmp.ltu p7,p0=r19,carry1};;
{ .mii; st8 [r32]=r19,16
(p7) add carry2=1,carry2 }
{ .mfb; add r25=r25,r24 };;
{ .mfb; getf.sig r16=f117 }
{ .mii; mov carry1=0
cmp.ltu p6,p0=r25,r24
add r26=r26,r25 };;
{ .mfb; getf.sig r17=f108 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r26,r25
add r26=r26,carry2 };;
{ .mfb; nop.m 0x0 }
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r26,carry2 };;
{ .mii; st8 [r33]=r26,16
(p6) add carry1=1,carry1 }
{ .mfb; add r17=r17,r16 };;
{ .mfb; getf.sig r24=f118 }
{ .mii; mov carry2=0
cmp.ltu p7,p0=r17,r16
add r17=r17,carry1 };;
{ .mii; (p7) add carry2=1,carry2
cmp.ltu p7,p0=r17,carry1};;
{ .mii; st8 [r32]=r17
(p7) add carry2=1,carry2 };;
{ .mfb; add r24=r24,carry2 };;
{ .mib; st8 [r33]=r24 }
{ .mib; rum 1<<5 // clear um.mfh
br.ret.sptk.many b0 };;
.endp bn_mul_comba8#
#undef carry3
#undef carry2
#undef carry1
#endif
#if 1
// It's possible to make it faster (see comment to bn_sqr_comba8), but
// I reckon it doesn't worth the effort. Basically because the routine
// (actually both of them) practically never called... So I just play
// same trick as with bn_sqr_comba8.
//
// void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a)
//
.global bn_sqr_comba4#
.proc bn_sqr_comba4#
.align 64
bn_sqr_comba4:
.prologue
.save ar.pfs,r2
#if defined(_HPUX_SOURCE) && !defined(_LP64)
{ .mii; alloc r2=ar.pfs,2,1,0,0
addp4 r32=0,r32
addp4 r33=0,r33 };;
{ .mii;
#else
{ .mii; alloc r2=ar.pfs,2,1,0,0
#endif
mov r34=r33
add r14=8,r33 };;
.body
{ .mii; add r17=8,r34
add r15=16,r33
add r18=16,r34 }
{ .mfb; add r16=24,r33
br .L_cheat_entry_point4 };;
.endp bn_sqr_comba4#
#endif
#if 1
// Runs in ~115 cycles and ~4.5 times faster than C. Well, whatever...
//
// void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
//
#define carry1 r14
#define carry2 r15
.global bn_mul_comba4#
.proc bn_mul_comba4#
.align 64
bn_mul_comba4:
.prologue
.save ar.pfs,r2
#if defined(_HPUX_SOURCE) && !defined(_LP64)
{ .mii; alloc r2=ar.pfs,3,0,0,0
addp4 r33=0,r33
addp4 r34=0,r34 };;
{ .mii; addp4 r32=0,r32
#else
{ .mii; alloc r2=ar.pfs,3,0,0,0
#endif
add r14=8,r33
add r17=8,r34 }
.body
{ .mii; add r15=16,r33
add r18=16,r34
add r16=24,r33 };;
.L_cheat_entry_point4:
{ .mmi; add r19=24,r34
ldf8 f32=[r33] }
{ .mmi; ldf8 f120=[r34]
ldf8 f121=[r17] };;
{ .mmi; ldf8 f122=[r18]
ldf8 f123=[r19] }
{ .mmi; ldf8 f33=[r14]
ldf8 f34=[r15] }
{ .mfi; ldf8 f35=[r16]
xma.hu f41=f32,f120,f0 }
{ .mfi; xma.lu f40=f32,f120,f0 };;
{ .mfi; xma.hu f51=f32,f121,f0 }
{ .mfi; xma.lu f50=f32,f121,f0 };;
{ .mfi; xma.hu f61=f32,f122,f0 }
{ .mfi; xma.lu f60=f32,f122,f0 };;
{ .mfi; xma.hu f71=f32,f123,f0 }
{ .mfi; xma.lu f70=f32,f123,f0 };;//
// Major stall takes place here, and 3 more places below. Result from
// first xma is not available for another 3 ticks.
{ .mfi; getf.sig r16=f40
xma.hu f42=f33,f120,f41
add r33=8,r32 }
{ .mfi; xma.lu f41=f33,f120,f41 };;
{ .mfi; getf.sig r24=f50
xma.hu f52=f33,f121,f51 }
{ .mfi; xma.lu f51=f33,f121,f51 };;
{ .mfi; st8 [r32]=r16,16
xma.hu f62=f33,f122,f61 }
{ .mfi; xma.lu f61=f33,f122,f61 };;
{ .mfi; xma.hu f72=f33,f123,f71 }
{ .mfi; xma.lu f71=f33,f123,f71 };;//
//-------------------------------------------------//
{ .mfi; getf.sig r25=f41
xma.hu f43=f34,f120,f42 }
{ .mfi; xma.lu f42=f34,f120,f42 };;
{ .mfi; getf.sig r16=f60
xma.hu f53=f34,f121,f52 }
{ .mfi; xma.lu f52=f34,f121,f52 };;
{ .mfi; getf.sig r17=f51
xma.hu f63=f34,f122,f62
add r25=r25,r24 }
{ .mfi; mov carry1=0
xma.lu f62=f34,f122,f62 };;
{ .mfi; st8 [r33]=r25,16
xma.hu f73=f34,f123,f72
cmp.ltu p6,p0=r25,r24 }
{ .mfi; xma.lu f72=f34,f123,f72 };;//
//-------------------------------------------------//
{ .mfi; getf.sig r18=f42
xma.hu f44=f35,f120,f43
(p6) add carry1=1,carry1 }
{ .mfi; add r17=r17,r16
xma.lu f43=f35,f120,f43
mov carry2=0 };;
{ .mfi; getf.sig r24=f70
xma.hu f54=f35,f121,f53
cmp.ltu p7,p0=r17,r16 }
{ .mfi; xma.lu f53=f35,f121,f53 };;
{ .mfi; getf.sig r25=f61
xma.hu f64=f35,f122,f63
add r18=r18,r17 }
{ .mfi; xma.lu f63=f35,f122,f63
(p7) add carry2=1,carry2 };;
{ .mfi; getf.sig r26=f52
xma.hu f74=f35,f123,f73
cmp.ltu p7,p0=r18,r17 }
{ .mfi; xma.lu f73=f35,f123,f73
add r18=r18,carry1 };;
//-------------------------------------------------//
{ .mii; st8 [r32]=r18,16
(p7) add carry2=1,carry2
cmp.ltu p7,p0=r18,carry1 };;
{ .mfi; getf.sig r27=f43 // last major stall
(p7) add carry2=1,carry2 };;
{ .mii; getf.sig r16=f71
add r25=r25,r24
mov carry1=0 };;
{ .mii; getf.sig r17=f62
cmp.ltu p6,p0=r25,r24
add r26=r26,r25 };;
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r26,r25
add r27=r27,r26 };;
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r27,r26
add r27=r27,carry2 };;
{ .mii; getf.sig r18=f53
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r27,carry2 };;
{ .mfi; st8 [r33]=r27,16
(p6) add carry1=1,carry1 }
{ .mii; getf.sig r19=f44
add r17=r17,r16
mov carry2=0 };;
{ .mii; getf.sig r24=f72
cmp.ltu p7,p0=r17,r16
add r18=r18,r17 };;
{ .mii; (p7) add carry2=1,carry2
cmp.ltu p7,p0=r18,r17
add r19=r19,r18 };;
{ .mii; (p7) add carry2=1,carry2
cmp.ltu p7,p0=r19,r18
add r19=r19,carry1 };;
{ .mii; getf.sig r25=f63
(p7) add carry2=1,carry2
cmp.ltu p7,p0=r19,carry1};;
{ .mii; st8 [r32]=r19,16
(p7) add carry2=1,carry2 }
{ .mii; getf.sig r26=f54
add r25=r25,r24
mov carry1=0 };;
{ .mii; getf.sig r16=f73
cmp.ltu p6,p0=r25,r24
add r26=r26,r25 };;
{ .mii;
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r26,r25
add r26=r26,carry2 };;
{ .mii; getf.sig r17=f64
(p6) add carry1=1,carry1
cmp.ltu p6,p0=r26,carry2 };;
{ .mii; st8 [r33]=r26,16
(p6) add carry1=1,carry1 }
{ .mii; getf.sig r24=f74
add r17=r17,r16
mov carry2=0 };;
{ .mii; cmp.ltu p7,p0=r17,r16
add r17=r17,carry1 };;
{ .mii; (p7) add carry2=1,carry2
cmp.ltu p7,p0=r17,carry1};;
{ .mii; st8 [r32]=r17,16
(p7) add carry2=1,carry2 };;
{ .mii; add r24=r24,carry2 };;
{ .mii; st8 [r33]=r24 }
{ .mib; rum 1<<5 // clear um.mfh
br.ret.sptk.many b0 };;
.endp bn_mul_comba4#
#undef carry2
#undef carry1
#endif
#if 1
//
// BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
//
// In the nutshell it's a port of my MIPS III/IV implementation.
//
#define AT r14
#define H r16
#define HH r20
#define L r17
#define D r18
#define DH r22
#define I r21
#if 0
// Some preprocessors (most notably HP-UX) appear to be allergic to
// macros enclosed to parenthesis [as these three were].
#define cont p16
#define break p0 // p20
#define equ p24
#else
cont=p16
break=p0
equ=p24
#endif
.global abort#
.global bn_div_words#
.proc bn_div_words#
.align 64
bn_div_words:
.prologue
.save ar.pfs,r2
{ .mii; alloc r2=ar.pfs,3,5,0,8
.save b0,r3
mov r3=b0
.save pr,r10
mov r10=pr };;
{ .mmb; cmp.eq p6,p0=r34,r0
mov r8=-1
(p6) br.ret.spnt.many b0 };;
.body
{ .mii; mov H=r32 // save h
mov ar.ec=0 // don't rotate at exit
mov pr.rot=0 }
{ .mii; mov L=r33 // save l
mov r25=r0 // needed if abort is called on VMS
mov r36=r0 };;
.L_divw_shift: // -vv- note signed comparison
{ .mfi; (p0) cmp.lt p16,p0=r0,r34 // d
(p0) shladd r33=r34,1,r0 }
{ .mfb; (p0) add r35=1,r36
(p0) nop.f 0x0
(p16) br.wtop.dpnt .L_divw_shift };;
{ .mii; mov D=r34
shr.u DH=r34,32
sub r35=64,r36 };;
{ .mii; setf.sig f7=DH
shr.u AT=H,r35
mov I=r36 };;
{ .mib; cmp.ne p6,p0=r0,AT
shl H=H,r36
(p6) br.call.spnt.clr b0=abort };; // overflow, die...
{ .mfi; fcvt.xuf.s1 f7=f7
shr.u AT=L,r35 };;
{ .mii; shl L=L,r36
or H=H,AT };;
{ .mii; nop.m 0x0
cmp.leu p6,p0=D,H;;
(p6) sub H=H,D }
{ .mlx; setf.sig f14=D
movl AT=0xffffffff };;
///////////////////////////////////////////////////////////
{ .mii; setf.sig f6=H
shr.u HH=H,32;;
cmp.eq p6,p7=HH,DH };;
{ .mfb;
(p6) setf.sig f8=AT
(p7) fcvt.xuf.s1 f6=f6
(p7) br.call.sptk b6=.L_udiv64_32_b6 };;
{ .mfi; getf.sig r33=f8 // q
xmpy.lu f9=f8,f14 }
{ .mfi; xmpy.hu f10=f8,f14
shrp H=H,L,32 };;
{ .mmi; getf.sig r35=f9 // tl
getf.sig r31=f10 };; // th
.L_divw_1st_iter:
{ .mii; (p0) add r32=-1,r33
(p0) cmp.eq equ,cont=HH,r31 };;
{ .mii; (p0) cmp.ltu p8,p0=r35,D
(p0) sub r34=r35,D
(equ) cmp.leu break,cont=r35,H };;
{ .mib; (cont) cmp.leu cont,break=HH,r31
(p8) add r31=-1,r31
(cont) br.wtop.spnt .L_divw_1st_iter };;
///////////////////////////////////////////////////////////
{ .mii; sub H=H,r35
shl r8=r33,32
shl L=L,32 };;
///////////////////////////////////////////////////////////
{ .mii; setf.sig f6=H
shr.u HH=H,32;;
cmp.eq p6,p7=HH,DH };;
{ .mfb;
(p6) setf.sig f8=AT
(p7) fcvt.xuf.s1 f6=f6
(p7) br.call.sptk b6=.L_udiv64_32_b6 };;
{ .mfi; getf.sig r33=f8 // q
xmpy.lu f9=f8,f14 }
{ .mfi; xmpy.hu f10=f8,f14
shrp H=H,L,32 };;
{ .mmi; getf.sig r35=f9 // tl
getf.sig r31=f10 };; // th
.L_divw_2nd_iter:
{ .mii; (p0) add r32=-1,r33
(p0) cmp.eq equ,cont=HH,r31 };;
{ .mii; (p0) cmp.ltu p8,p0=r35,D
(p0) sub r34=r35,D
(equ) cmp.leu break,cont=r35,H };;
{ .mib; (cont) cmp.leu cont,break=HH,r31
(p8) add r31=-1,r31
(cont) br.wtop.spnt .L_divw_2nd_iter };;
///////////////////////////////////////////////////////////
{ .mii; sub H=H,r35
or r8=r8,r33
mov ar.pfs=r2 };;
{ .mii; shr.u r9=H,I // remainder if anybody wants it
mov pr=r10,0x1ffff }
{ .mfb; br.ret.sptk.many b0 };;
// Unsigned 64 by 32 (well, by 64 for the moment) bit integer division
// procedure.
//
// inputs: f6 = (double)a, f7 = (double)b
// output: f8 = (int)(a/b)
// clobbered: f8,f9,f10,f11,pred
pred=p15
// This snippet is based on text found in the "Divide, Square
// Root and Remainder" section at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
// Yes, I admit that the referred code was used as template,
// but after I realized that there hardly is any other instruction
// sequence which would perform this operation. I mean I figure that
// any independent attempt to implement high-performance division
// will result in code virtually identical to the Intel code. It
// should be noted though that below division kernel is 1 cycle
// faster than Intel one (note commented splits:-), not to mention
// original prologue (rather lack of one) and epilogue.
.align 32
.skip 16
.L_udiv64_32_b6:
frcpa.s1 f8,pred=f6,f7;; // [0] y0 = 1 / b
(pred) fnma.s1 f9=f7,f8,f1 // [5] e0 = 1 - b * y0
(pred) fmpy.s1 f10=f6,f8;; // [5] q0 = a * y0
(pred) fmpy.s1 f11=f9,f9 // [10] e1 = e0 * e0
(pred) fma.s1 f10=f9,f10,f10;; // [10] q1 = q0 + e0 * q0
(pred) fma.s1 f8=f9,f8,f8 //;; // [15] y1 = y0 + e0 * y0
(pred) fma.s1 f9=f11,f10,f10;; // [15] q2 = q1 + e1 * q1
(pred) fma.s1 f8=f11,f8,f8 //;; // [20] y2 = y1 + e1 * y1
(pred) fnma.s1 f10=f7,f9,f6;; // [20] r2 = a - b * q2
(pred) fma.s1 f8=f10,f8,f9;; // [25] q3 = q2 + r2 * y2
fcvt.fxu.trunc.s1 f8=f8 // [30] q = trunc(q3)
br.ret.sptk.many b6;;
.endp bn_div_words#
#endif