| .explicit |
| .text |
| .ident "ia64.S, Version 2.1" |
| .ident "IA-64 ISA artwork by Andy Polyakov <appro@fy.chalmers.se>" |
| |
| // |
| // ==================================================================== |
| // Written by Andy Polyakov <appro@fy.chalmers.se> 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 Itanum2 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 intruction 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 opration 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 |
| |
| #if 1 |
| // |
| // bn_[add|sub]_words routines. |
| // |
| // Loops are spinning in 2*(n+5) ticks on Itanuim (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 interger 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 propogating 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 perfomance gain on Itanium |
| // will appear larger than loss on "wider" IA-64, then the loop should |
| // be explicitely 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 µ-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 muliplier'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 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 |
| // One can argue that this snippet is copyrighted to Intel |
| // Corporation, as it's essentially identical to one of those |
| // found in "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 |
