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1.explicit
2.text
3.ident "ia64.S, Version 2.0"
4.ident "IA-64 ISA artwork by Andy Polyakov <appro@fy.chalmers.se>"
5
6//
7// ====================================================================
8// Written by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL
9// project.
10//
11// Rights for redistribution and usage in source and binary forms are
12// granted according to the OpenSSL license. Warranty of any kind is
13// disclaimed.
14// ====================================================================
15//
16// Version 2.x is Itanium2 re-tune. Few words about how Itanum2 is
17// different from Itanium to this module viewpoint. Most notably, is it
18// "wider" than Itanium? Can you experience loop scalability as
19// discussed in commentary sections? Not really:-( Itanium2 has 6
20// integer ALU ports, i.e. it's 2 ports wider, but it's not enough to
21// spin twice as fast, as I need 8 IALU ports. Amount of floating point
22// ports is the same, i.e. 2, while I need 4. In other words, to this
23// module Itanium2 remains effectively as "wide" as Itanium. Yet it's
24// essentially different in respect to this module, and a re-tune was
25// required. Well, because some intruction latencies has changed. Most
26// noticeably those intensively used:
27//
28// Itanium Itanium2
29// ldf8 9 6 L2 hit
30// ld8 2 1 L1 hit
31// getf 2 5
32// xma[->getf] 7[+1] 4[+0]
33// add[->st8] 1[+1] 1[+0]
34//
35// What does it mean? You might ratiocinate that the original code
36// should run just faster... Because sum of latencies is smaller...
37// Wrong! Note that getf latency increased. This means that if a loop is
38// scheduled for lower latency (and they are), then it will suffer from
39// stall condition and the code will therefore turn anti-scalable, e.g.
40// original bn_mul_words spun at 5*n or 2.5 times slower than expected
41// on Itanium2! What to do? Reschedule loops for Itanium2? But then
42// Itanium would exhibit anti-scalability. So I've chosen to reschedule
43// for worst latency for every instruction aiming for best *all-round*
44// performance.
45
46// Q. How much faster does it get?
47// A. Here is the output from 'openssl speed rsa dsa' for vanilla
48// 0.9.6a compiled with gcc version 2.96 20000731 (Red Hat
49// Linux 7.1 2.96-81):
50//
51// sign verify sign/s verify/s
52// rsa 512 bits 0.0036s 0.0003s 275.3 2999.2
53// rsa 1024 bits 0.0203s 0.0011s 49.3 894.1
54// rsa 2048 bits 0.1331s 0.0040s 7.5 250.9
55// rsa 4096 bits 0.9270s 0.0147s 1.1 68.1
56// sign verify sign/s verify/s
57// dsa 512 bits 0.0035s 0.0043s 288.3 234.8
58// dsa 1024 bits 0.0111s 0.0135s 90.0 74.2
59//
60// And here is similar output but for this assembler
61// implementation:-)
62//
63// sign verify sign/s verify/s
64// rsa 512 bits 0.0021s 0.0001s 549.4 9638.5
65// rsa 1024 bits 0.0055s 0.0002s 183.8 4481.1
66// rsa 2048 bits 0.0244s 0.0006s 41.4 1726.3
67// rsa 4096 bits 0.1295s 0.0018s 7.7 561.5
68// sign verify sign/s verify/s
69// dsa 512 bits 0.0012s 0.0013s 891.9 756.6
70// dsa 1024 bits 0.0023s 0.0028s 440.4 376.2
71//
72// Yes, you may argue that it's not fair comparison as it's
73// possible to craft the C implementation with BN_UMULT_HIGH
74// inline assembler macro. But of course! Here is the output
75// with the macro:
76//
77// sign verify sign/s verify/s
78// rsa 512 bits 0.0020s 0.0002s 495.0 6561.0
79// rsa 1024 bits 0.0086s 0.0004s 116.2 2235.7
80// rsa 2048 bits 0.0519s 0.0015s 19.3 667.3
81// rsa 4096 bits 0.3464s 0.0053s 2.9 187.7
82// sign verify sign/s verify/s
83// dsa 512 bits 0.0016s 0.0020s 613.1 510.5
84// dsa 1024 bits 0.0045s 0.0054s 221.0 183.9
85//
86// My code is still way faster, huh:-) And I believe that even
87// higher performance can be achieved. Note that as keys get
88// longer, performance gain is larger. Why? According to the
89// profiler there is another player in the field, namely
90// BN_from_montgomery consuming larger and larger portion of CPU
91// time as keysize decreases. I therefore consider putting effort
92// to assembler implementation of the following routine:
93//
94// void bn_mul_add_mont (BN_ULONG *rp,BN_ULONG *np,int nl,BN_ULONG n0)
95// {
96// int i,j;
97// BN_ULONG v;
98//
99// for (i=0; i<nl; i++)
100// {
101// v=bn_mul_add_words(rp,np,nl,(rp[0]*n0)&BN_MASK2);
102// nrp++;
103// rp++;
104// if (((nrp[-1]+=v)&BN_MASK2) < v)
105// for (j=0; ((++nrp[j])&BN_MASK2) == 0; j++) ;
106// }
107// }
108//
109// It might as well be beneficial to implement even combaX
110// variants, as it appears as it can literally unleash the
111// performance (see comment section to bn_mul_comba8 below).
112//
113// And finally for your reference the output for 0.9.6a compiled
114// with SGIcc version 0.01.0-12 (keep in mind that for the moment
115// of this writing it's not possible to convince SGIcc to use
116// BN_UMULT_HIGH inline assembler macro, yet the code is fast,
117// i.e. for a compiler generated one:-):
118//
119// sign verify sign/s verify/s
120// rsa 512 bits 0.0022s 0.0002s 452.7 5894.3
121// rsa 1024 bits 0.0097s 0.0005s 102.7 2002.9
122// rsa 2048 bits 0.0578s 0.0017s 17.3 600.2
123// rsa 4096 bits 0.3838s 0.0061s 2.6 164.5
124// sign verify sign/s verify/s
125// dsa 512 bits 0.0018s 0.0022s 547.3 459.6
126// dsa 1024 bits 0.0051s 0.0062s 196.6 161.3
127//
128// Oh! Benchmarks were performed on 733MHz Lion-class Itanium
129// system running Redhat Linux 7.1 (very special thanks to Ray
130// McCaffity of Williams Communications for providing an account).
131//
132// Q. What's the heck with 'rum 1<<5' at the end of every function?
133// A. Well, by clearing the "upper FP registers written" bit of the
134// User Mask I want to excuse the kernel from preserving upper
135// (f32-f128) FP register bank over process context switch, thus
136// minimizing bus bandwidth consumption during the switch (i.e.
137// after PKI opration completes and the program is off doing
138// something else like bulk symmetric encryption). Having said
139// this, I also want to point out that it might be good idea
140// to compile the whole toolkit (as well as majority of the
141// programs for that matter) with -mfixed-range=f32-f127 command
142// line option. No, it doesn't prevent the compiler from writing
143// to upper bank, but at least discourages to do so. If you don't
144// like the idea you have the option to compile the module with
145// -Drum=nop.m in command line.
146//
147
148#if 1
149//
150// bn_[add|sub]_words routines.
151//
152// Loops are spinning in 2*(n+5) ticks on Itanuim (provided that the
153// data reside in L1 cache, i.e. 2 ticks away). It's possible to
154// compress the epilogue and get down to 2*n+6, but at the cost of
155// scalability (the neat feature of this implementation is that it
156// shall automagically spin in n+5 on "wider" IA-64 implementations:-)
157// I consider that the epilogue is short enough as it is to trade tiny
158// performance loss on Itanium for scalability.
159//
160// BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int num)
161//
162.global bn_add_words#
163.proc bn_add_words#
164.align 64
165.skip 32 // makes the loop body aligned at 64-byte boundary
166bn_add_words:
167 .prologue
168 .fframe 0
169 .save ar.pfs,r2
170{ .mii; alloc r2=ar.pfs,4,12,0,16
171 cmp4.le p6,p0=r35,r0 };;
172{ .mfb; mov r8=r0 // return value
173(p6) br.ret.spnt.many b0 };;
174
175 .save ar.lc,r3
176{ .mib; sub r10=r35,r0,1
177 mov r3=ar.lc
178 brp.loop.imp .L_bn_add_words_ctop,.L_bn_add_words_cend-16
179 }
180 .body
181{ .mib;
182#if defined(_HPUX_SOURCE) && defined(_ILP32)
183 addp4 r14=0,r32 // rp
184#else
185 mov r14=r32 // rp
186#endif
187 mov r9=pr };;
188{ .mii;
189#if defined(_HPUX_SOURCE) && defined(_ILP32)
190 addp4 r15=0,r33 // ap
191#else
192 mov r15=r33 // ap
193#endif
194 mov ar.lc=r10
195 mov ar.ec=6 }
196{ .mib;
197#if defined(_HPUX_SOURCE) && defined(_ILP32)
198 addp4 r16=0,r34 // bp
199#else
200 mov r16=r34 // bp
201#endif
202 mov pr.rot=1<<16 };;
203
204.L_bn_add_words_ctop:
205{ .mii; (p16) ld8 r32=[r16],8 // b=*(bp++)
206 (p18) add r39=r37,r34
207 (p19) cmp.ltu.unc p56,p0=r40,r38 }
208{ .mfb; (p0) nop.m 0x0
209 (p0) nop.f 0x0
210 (p0) nop.b 0x0 }
211{ .mii; (p16) ld8 r35=[r15],8 // a=*(ap++)
212 (p58) cmp.eq.or p57,p0=-1,r41 // (p20)
213 (p58) add r41=1,r41 } // (p20)
214{ .mfb; (p21) st8 [r14]=r42,8 // *(rp++)=r
215 (p0) nop.f 0x0
216 br.ctop.sptk .L_bn_add_words_ctop };;
217.L_bn_add_words_cend:
218
219{ .mii;
220(p59) add r8=1,r8 // return value
221 mov pr=r9,0x1ffff
222 mov ar.lc=r3 }
223{ .mbb; nop.b 0x0
224 br.ret.sptk.many b0 };;
225.endp bn_add_words#
226
227//
228// BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int num)
229//
230.global bn_sub_words#
231.proc bn_sub_words#
232.align 64
233.skip 32 // makes the loop body aligned at 64-byte boundary
234bn_sub_words:
235 .prologue
236 .fframe 0
237 .save ar.pfs,r2
238{ .mii; alloc r2=ar.pfs,4,12,0,16
239 cmp4.le p6,p0=r35,r0 };;
240{ .mfb; mov r8=r0 // return value
241(p6) br.ret.spnt.many b0 };;
242
243 .save ar.lc,r3
244{ .mib; sub r10=r35,r0,1
245 mov r3=ar.lc
246 brp.loop.imp .L_bn_sub_words_ctop,.L_bn_sub_words_cend-16
247 }
248 .body
249{ .mib;
250#if defined(_HPUX_SOURCE) && defined(_ILP32)
251 addp4 r14=0,r32 // rp
252#else
253 mov r14=r32 // rp
254#endif
255 mov r9=pr };;
256{ .mii;
257#if defined(_HPUX_SOURCE) && defined(_ILP32)
258 addp4 r15=0,r33 // ap
259#else
260 mov r15=r33 // ap
261#endif
262 mov ar.lc=r10
263 mov ar.ec=6 }
264{ .mib;
265#if defined(_HPUX_SOURCE) && defined(_ILP32)
266 addp4 r16=0,r34 // bp
267#else
268 mov r16=r34 // bp
269#endif
270 mov pr.rot=1<<16 };;
271
272.L_bn_sub_words_ctop:
273{ .mii; (p16) ld8 r32=[r16],8 // b=*(bp++)
274 (p18) sub r39=r37,r34
275 (p19) cmp.gtu.unc p56,p0=r40,r38 }
276{ .mfb; (p0) nop.m 0x0
277 (p0) nop.f 0x0
278 (p0) nop.b 0x0 }
279{ .mii; (p16) ld8 r35=[r15],8 // a=*(ap++)
280 (p58) cmp.eq.or p57,p0=0,r41 // (p20)
281 (p58) add r41=-1,r41 } // (p20)
282{ .mbb; (p21) st8 [r14]=r42,8 // *(rp++)=r
283 (p0) nop.b 0x0
284 br.ctop.sptk .L_bn_sub_words_ctop };;
285.L_bn_sub_words_cend:
286
287{ .mii;
288(p59) add r8=1,r8 // return value
289 mov pr=r9,0x1ffff
290 mov ar.lc=r3 }
291{ .mbb; nop.b 0x0
292 br.ret.sptk.many b0 };;
293.endp bn_sub_words#
294#endif
295
296#if 0
297#define XMA_TEMPTATION
298#endif
299
300#if 1
301//
302// BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w)
303//
304.global bn_mul_words#
305.proc bn_mul_words#
306.align 64
307.skip 32 // makes the loop body aligned at 64-byte boundary
308bn_mul_words:
309 .prologue
310 .fframe 0
311 .save ar.pfs,r2
312#ifdef XMA_TEMPTATION
313{ .mfi; alloc r2=ar.pfs,4,0,0,0 };;
314#else
315{ .mfi; alloc r2=ar.pfs,4,12,0,16 };;
316#endif
317{ .mib; mov r8=r0 // return value
318 cmp4.le p6,p0=r34,r0
319(p6) br.ret.spnt.many b0 };;
320
321 .save ar.lc,r3
322{ .mii; sub r10=r34,r0,1
323 mov r3=ar.lc
324 mov r9=pr };;
325
326 .body
327{ .mib; setf.sig f8=r35 // w
328 mov pr.rot=0x800001<<16
329 // ------^----- serves as (p50) at first (p27)
330 brp.loop.imp .L_bn_mul_words_ctop,.L_bn_mul_words_cend-16
331 }
332
333#ifndef XMA_TEMPTATION
334
335{ .mii;
336#if defined(_HPUX_SOURCE) && defined(_ILP32)
337 addp4 r14=0,r32 // rp
338 addp4 r15=0,r33 // ap
339#else
340 mov r14=r32 // rp
341 mov r15=r33 // ap
342#endif
343 mov ar.lc=r10 }
344{ .mii; mov r40=0 // serves as r35 at first (p27)
345 mov ar.ec=13 };;
346
347// This loop spins in 2*(n+12) ticks. It's scheduled for data in Itanium
348// L2 cache (i.e. 9 ticks away) as floating point load/store instructions
349// bypass L1 cache and L2 latency is actually best-case scenario for
350// ldf8. The loop is not scalable and shall run in 2*(n+12) even on
351// "wider" IA-64 implementations. It's a trade-off here. n+24 loop
352// would give us ~5% in *overall* performance improvement on "wider"
353// IA-64, but would hurt Itanium for about same because of longer
354// epilogue. As it's a matter of few percents in either case I've
355// chosen to trade the scalability for development time (you can see
356// this very instruction sequence in bn_mul_add_words loop which in
357// turn is scalable).
358.L_bn_mul_words_ctop:
359{ .mfi; (p25) getf.sig r36=f52 // low
360 (p21) xmpy.lu f48=f37,f8
361 (p28) cmp.ltu p54,p50=r41,r39 }
362{ .mfi; (p16) ldf8 f32=[r15],8
363 (p21) xmpy.hu f40=f37,f8
364 (p0) nop.i 0x0 };;
365{ .mii; (p25) getf.sig r32=f44 // high
366 .pred.rel "mutex",p50,p54
367 (p50) add r40=r38,r35 // (p27)
368 (p54) add r40=r38,r35,1 } // (p27)
369{ .mfb; (p28) st8 [r14]=r41,8
370 (p0) nop.f 0x0
371 br.ctop.sptk .L_bn_mul_words_ctop };;
372.L_bn_mul_words_cend:
373
374{ .mii; nop.m 0x0
375.pred.rel "mutex",p51,p55
376(p51) add r8=r36,r0
377(p55) add r8=r36,r0,1 }
378{ .mfb; nop.m 0x0
379 nop.f 0x0
380 nop.b 0x0 }
381
382#else // XMA_TEMPTATION
383
384 setf.sig f37=r0 // serves as carry at (p18) tick
385 mov ar.lc=r10
386 mov ar.ec=5;;
387
388// Most of you examining this code very likely wonder why in the name
389// of Intel the following loop is commented out? Indeed, it looks so
390// neat that you find it hard to believe that it's something wrong
391// with it, right? The catch is that every iteration depends on the
392// result from previous one and the latter isn't available instantly.
393// The loop therefore spins at the latency of xma minus 1, or in other
394// words at 6*(n+4) ticks:-( Compare to the "production" loop above
395// that runs in 2*(n+11) where the low latency problem is worked around
396// by moving the dependency to one-tick latent interger ALU. Note that
397// "distance" between ldf8 and xma is not latency of ldf8, but the
398// *difference* between xma and ldf8 latencies.
399.L_bn_mul_words_ctop:
400{ .mfi; (p16) ldf8 f32=[r33],8
401 (p18) xma.hu f38=f34,f8,f39 }
402{ .mfb; (p20) stf8 [r32]=f37,8
403 (p18) xma.lu f35=f34,f8,f39
404 br.ctop.sptk .L_bn_mul_words_ctop };;
405.L_bn_mul_words_cend:
406
407 getf.sig r8=f41 // the return value
408
409#endif // XMA_TEMPTATION
410
411{ .mii; nop.m 0x0
412 mov pr=r9,0x1ffff
413 mov ar.lc=r3 }
414{ .mfb; rum 1<<5 // clear um.mfh
415 nop.f 0x0
416 br.ret.sptk.many b0 };;
417.endp bn_mul_words#
418#endif
419
420#if 1
421//
422// BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w)
423//
424.global bn_mul_add_words#
425.proc bn_mul_add_words#
426.align 64
427//.skip 0 // makes the loop split at 64-byte boundary
428bn_mul_add_words:
429 .prologue
430 .fframe 0
431 .save ar.pfs,r2
432{ .mii; alloc r2=ar.pfs,4,12,0,16
433 cmp4.le p6,p0=r34,r0 };;
434{ .mfb; mov r8=r0 // return value
435(p6) br.ret.spnt.many b0 };;
436
437 .save ar.lc,r3
438{ .mii; sub r10=r34,r0,1
439 mov r3=ar.lc
440 mov r9=pr };;
441
442 .body
443{ .mib; setf.sig f8=r35 // w
444 mov pr.rot=0x800001<<16
445 // ------^----- serves as (p50) at first (p27)
446 brp.loop.imp .L_bn_mul_add_words_ctop,.L_bn_mul_add_words_cend-16
447 }
448{ .mii;
449#if defined(_HPUX_SOURCE) && defined(_ILP32)
450 addp4 r14=0,r32 // rp
451 addp4 r15=0,r33 // ap
452#else
453 mov r14=r32 // rp
454 mov r15=r33 // ap
455#endif
456 mov ar.lc=r10 }
457{ .mii; mov r40=0 // serves as r35 at first (p27)
458#if defined(_HPUX_SOURCE) && defined(_ILP32)
459 addp4 r18=0,r32 // rp copy
460#else
461 mov r18=r32 // rp copy
462#endif
463 mov ar.ec=15 };;
464
465// This loop spins in 3*(n+14) ticks on Itanium and should spin in
466// 2*(n+14) on "wider" IA-64 implementations (to be verified with new
467// µ-architecture manuals as they become available). As usual it's
468// possible to compress the epilogue, down to 10 in this case, at the
469// cost of scalability. Compressed (and therefore non-scalable) loop
470// running at 3*(n+11) would buy you ~10% on Itanium but take ~35%
471// from "wider" IA-64 so let it be scalable! Special attention was
472// paid for having the loop body split at 64-byte boundary. ld8 is
473// scheduled for L1 cache as the data is more than likely there.
474// Indeed, bn_mul_words has put it there a moment ago:-)
475.L_bn_mul_add_words_ctop:
476{ .mfi; (p25) getf.sig r36=f52 // low
477 (p21) xmpy.lu f48=f37,f8
478 (p28) cmp.ltu p54,p50=r41,r39 }
479{ .mfi; (p16) ldf8 f32=[r15],8
480 (p21) xmpy.hu f40=f37,f8
481 (p28) add r45=r45,r41 };;
482{ .mii; (p25) getf.sig r32=f44 // high
483 .pred.rel "mutex",p50,p54
484 (p50) add r40=r38,r35 // (p27)
485 (p54) add r40=r38,r35,1 } // (p27)
486{ .mfb; (p28) cmp.ltu.unc p60,p0=r45,r41
487 (p0) nop.f 0x0
488 (p0) nop.b 0x0 }
489{ .mii; (p27) ld8 r44=[r18],8
490 (p62) cmp.eq.or p61,p0=-1,r46
491 (p62) add r46=1,r46 }
492{ .mfb; (p30) st8 [r14]=r47,8
493 (p0) nop.f 0x0
494 br.ctop.sptk .L_bn_mul_add_words_ctop};;
495.L_bn_mul_add_words_cend:
496
497{ .mii; nop.m 0x0
498.pred.rel "mutex",p53,p57
499(p53) add r8=r38,r0
500(p57) add r8=r38,r0,1 }
501{ .mfb; nop.m 0x0
502 nop.f 0x0
503 nop.b 0x0 };;
504{ .mii;
505(p63) add r8=1,r8
506 mov pr=r9,0x1ffff
507 mov ar.lc=r3 }
508{ .mfb; rum 1<<5 // clear um.mfh
509 nop.f 0x0
510 br.ret.sptk.many b0 };;
511.endp bn_mul_add_words#
512#endif
513
514#if 1
515//
516// void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num)
517//
518.global bn_sqr_words#
519.proc bn_sqr_words#
520.align 64
521.skip 32 // makes the loop body aligned at 64-byte boundary
522bn_sqr_words:
523 .prologue
524 .fframe 0
525 .save ar.pfs,r2
526{ .mii; alloc r2=ar.pfs,3,0,0,0
527 sxt4 r34=r34 };;
528{ .mii; cmp.le p6,p0=r34,r0
529 mov r8=r0 } // return value
530{ .mfb; nop.f 0x0
531(p6) br.ret.spnt.many b0 };;
532
533 .save ar.lc,r3
534{ .mii; sub r10=r34,r0,1
535 mov r3=ar.lc
536 mov r9=pr };;
537
538 .body
539#if defined(_HPUX_SOURCE) && defined(_ILP32)
540{ .mii; addp4 r32=0,r32
541 addp4 r33=0,r33 };;
542#endif
543{ .mib;
544 mov pr.rot=1<<16
545 brp.loop.imp .L_bn_sqr_words_ctop,.L_bn_sqr_words_cend-16
546 }
547{ .mii; add r34=8,r32
548 mov ar.lc=r10
549 mov ar.ec=18 };;
550
551// 2*(n+17) on Itanium, (n+17) on "wider" IA-64 implementations. It's
552// possible to compress the epilogue (I'm getting tired to write this
553// comment over and over) and get down to 2*n+16 at the cost of
554// scalability. The decision will very likely be reconsidered after the
555// benchmark program is profiled. I.e. if perfomance gain on Itanium
556// will appear larger than loss on "wider" IA-64, then the loop should
557// be explicitely split and the epilogue compressed.
558.L_bn_sqr_words_ctop:
559{ .mfi; (p16) ldf8 f32=[r33],8
560 (p25) xmpy.lu f42=f41,f41
561 (p0) nop.i 0x0 }
562{ .mib; (p33) stf8 [r32]=f50,16
563 (p0) nop.i 0x0
564 (p0) nop.b 0x0 }
565{ .mfi; (p0) nop.m 0x0
566 (p25) xmpy.hu f52=f41,f41
567 (p0) nop.i 0x0 }
568{ .mib; (p33) stf8 [r34]=f60,16
569 (p0) nop.i 0x0
570 br.ctop.sptk .L_bn_sqr_words_ctop };;
571.L_bn_sqr_words_cend:
572
573{ .mii; nop.m 0x0
574 mov pr=r9,0x1ffff
575 mov ar.lc=r3 }
576{ .mfb; rum 1<<5 // clear um.mfh
577 nop.f 0x0
578 br.ret.sptk.many b0 };;
579.endp bn_sqr_words#
580#endif
581
582#if 1
583// Apparently we win nothing by implementing special bn_sqr_comba8.
584// Yes, it is possible to reduce the number of multiplications by
585// almost factor of two, but then the amount of additions would
586// increase by factor of two (as we would have to perform those
587// otherwise performed by xma ourselves). Normally we would trade
588// anyway as multiplications are way more expensive, but not this
589// time... Multiplication kernel is fully pipelined and as we drain
590// one 128-bit multiplication result per clock cycle multiplications
591// are effectively as inexpensive as additions. Special implementation
592// might become of interest for "wider" IA-64 implementation as you'll
593// be able to get through the multiplication phase faster (there won't
594// be any stall issues as discussed in the commentary section below and
595// you therefore will be able to employ all 4 FP units)... But these
596// Itanium days it's simply too hard to justify the effort so I just
597// drop down to bn_mul_comba8 code:-)
598//
599// void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a)
600//
601.global bn_sqr_comba8#
602.proc bn_sqr_comba8#
603.align 64
604bn_sqr_comba8:
605 .prologue
606 .fframe 0
607 .save ar.pfs,r2
608#if defined(_HPUX_SOURCE) && defined(_ILP32)
609{ .mii; alloc r2=ar.pfs,2,1,0,0
610 addp4 r33=0,r33
611 addp4 r32=0,r32 };;
612{ .mii;
613#else
614{ .mii; alloc r2=ar.pfs,2,1,0,0
615#endif
616 mov r34=r33
617 add r14=8,r33 };;
618 .body
619{ .mii; add r17=8,r34
620 add r15=16,r33
621 add r18=16,r34 }
622{ .mfb; add r16=24,r33
623 br .L_cheat_entry_point8 };;
624.endp bn_sqr_comba8#
625#endif
626
627#if 1
628// I've estimated this routine to run in ~120 ticks, but in reality
629// (i.e. according to ar.itc) it takes ~160 ticks. Are those extra
630// cycles consumed for instructions fetch? Or did I misinterpret some
631// clause in Itanium µ-architecture manual? Comments are welcomed and
632// highly appreciated.
633//
634// However! It should be noted that even 160 ticks is darn good result
635// as it's over 10 (yes, ten, spelled as t-e-n) times faster than the
636// C version (compiled with gcc with inline assembler). I really
637// kicked compiler's butt here, didn't I? Yeah! This brings us to the
638// following statement. It's damn shame that this routine isn't called
639// very often nowadays! According to the profiler most CPU time is
640// consumed by bn_mul_add_words called from BN_from_montgomery. In
641// order to estimate what we're missing, I've compared the performance
642// of this routine against "traditional" implementation, i.e. against
643// following routine:
644//
645// void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
646// { r[ 8]=bn_mul_words( &(r[0]),a,8,b[0]);
647// r[ 9]=bn_mul_add_words(&(r[1]),a,8,b[1]);
648// r[10]=bn_mul_add_words(&(r[2]),a,8,b[2]);
649// r[11]=bn_mul_add_words(&(r[3]),a,8,b[3]);
650// r[12]=bn_mul_add_words(&(r[4]),a,8,b[4]);
651// r[13]=bn_mul_add_words(&(r[5]),a,8,b[5]);
652// r[14]=bn_mul_add_words(&(r[6]),a,8,b[6]);
653// r[15]=bn_mul_add_words(&(r[7]),a,8,b[7]);
654// }
655//
656// The one below is over 8 times faster than the one above:-( Even
657// more reasons to "combafy" bn_mul_add_mont...
658//
659// And yes, this routine really made me wish there were an optimizing
660// assembler! It also feels like it deserves a dedication.
661//
662// To my wife for being there and to my kids...
663//
664// void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
665//
666#define carry1 r14
667#define carry2 r15
668#define carry3 r34
669.global bn_mul_comba8#
670.proc bn_mul_comba8#
671.align 64
672bn_mul_comba8:
673 .prologue
674 .fframe 0
675 .save ar.pfs,r2
676#if defined(_HPUX_SOURCE) && defined(_ILP32)
677{ .mii; alloc r2=ar.pfs,3,0,0,0
678 addp4 r33=0,r33
679 addp4 r34=0,r34 };;
680{ .mii; addp4 r32=0,r32
681#else
682{ .mii; alloc r2=ar.pfs,3,0,0,0
683#endif
684 add r14=8,r33
685 add r17=8,r34 }
686 .body
687{ .mii; add r15=16,r33
688 add r18=16,r34
689 add r16=24,r33 }
690.L_cheat_entry_point8:
691{ .mmi; add r19=24,r34
692
693 ldf8 f32=[r33],32 };;
694
695{ .mmi; ldf8 f120=[r34],32
696 ldf8 f121=[r17],32 }
697{ .mmi; ldf8 f122=[r18],32
698 ldf8 f123=[r19],32 };;
699{ .mmi; ldf8 f124=[r34]
700 ldf8 f125=[r17] }
701{ .mmi; ldf8 f126=[r18]
702 ldf8 f127=[r19] }
703
704{ .mmi; ldf8 f33=[r14],32
705 ldf8 f34=[r15],32 }
706{ .mmi; ldf8 f35=[r16],32;;
707 ldf8 f36=[r33] }
708{ .mmi; ldf8 f37=[r14]
709 ldf8 f38=[r15] }
710{ .mfi; ldf8 f39=[r16]
711// -------\ Entering multiplier's heaven /-------
712// ------------\ /------------
713// -----------------\ /-----------------
714// ----------------------\/----------------------
715 xma.hu f41=f32,f120,f0 }
716{ .mfi; xma.lu f40=f32,f120,f0 };; // (*)
717{ .mfi; xma.hu f51=f32,f121,f0 }
718{ .mfi; xma.lu f50=f32,f121,f0 };;
719{ .mfi; xma.hu f61=f32,f122,f0 }
720{ .mfi; xma.lu f60=f32,f122,f0 };;
721{ .mfi; xma.hu f71=f32,f123,f0 }
722{ .mfi; xma.lu f70=f32,f123,f0 };;
723{ .mfi; xma.hu f81=f32,f124,f0 }
724{ .mfi; xma.lu f80=f32,f124,f0 };;
725{ .mfi; xma.hu f91=f32,f125,f0 }
726{ .mfi; xma.lu f90=f32,f125,f0 };;
727{ .mfi; xma.hu f101=f32,f126,f0 }
728{ .mfi; xma.lu f100=f32,f126,f0 };;
729{ .mfi; xma.hu f111=f32,f127,f0 }
730{ .mfi; xma.lu f110=f32,f127,f0 };;//
731// (*) You can argue that splitting at every second bundle would
732// prevent "wider" IA-64 implementations from achieving the peak
733// performance. Well, not really... The catch is that if you
734// intend to keep 4 FP units busy by splitting at every fourth
735// bundle and thus perform these 16 multiplications in 4 ticks,
736// the first bundle *below* would stall because the result from
737// the first xma bundle *above* won't be available for another 3
738// ticks (if not more, being an optimist, I assume that "wider"
739// implementation will have same latency:-). This stall will hold
740// you back and the performance would be as if every second bundle
741// were split *anyway*...
742{ .mfi; getf.sig r16=f40
743 xma.hu f42=f33,f120,f41
744 add r33=8,r32 }
745{ .mfi; xma.lu f41=f33,f120,f41 };;
746{ .mfi; getf.sig r24=f50
747 xma.hu f52=f33,f121,f51 }
748{ .mfi; xma.lu f51=f33,f121,f51 };;
749{ .mfi; st8 [r32]=r16,16
750 xma.hu f62=f33,f122,f61 }
751{ .mfi; xma.lu f61=f33,f122,f61 };;
752{ .mfi; xma.hu f72=f33,f123,f71 }
753{ .mfi; xma.lu f71=f33,f123,f71 };;
754{ .mfi; xma.hu f82=f33,f124,f81 }
755{ .mfi; xma.lu f81=f33,f124,f81 };;
756{ .mfi; xma.hu f92=f33,f125,f91 }
757{ .mfi; xma.lu f91=f33,f125,f91 };;
758{ .mfi; xma.hu f102=f33,f126,f101 }
759{ .mfi; xma.lu f101=f33,f126,f101 };;
760{ .mfi; xma.hu f112=f33,f127,f111 }
761{ .mfi; xma.lu f111=f33,f127,f111 };;//
762//-------------------------------------------------//
763{ .mfi; getf.sig r25=f41
764 xma.hu f43=f34,f120,f42 }
765{ .mfi; xma.lu f42=f34,f120,f42 };;
766{ .mfi; getf.sig r16=f60
767 xma.hu f53=f34,f121,f52 }
768{ .mfi; xma.lu f52=f34,f121,f52 };;
769{ .mfi; getf.sig r17=f51
770 xma.hu f63=f34,f122,f62
771 add r25=r25,r24 }
772{ .mfi; xma.lu f62=f34,f122,f62
773 mov carry1=0 };;
774{ .mfi; cmp.ltu p6,p0=r25,r24
775 xma.hu f73=f34,f123,f72 }
776{ .mfi; xma.lu f72=f34,f123,f72 };;
777{ .mfi; st8 [r33]=r25,16
778 xma.hu f83=f34,f124,f82
779(p6) add carry1=1,carry1 }
780{ .mfi; xma.lu f82=f34,f124,f82 };;
781{ .mfi; xma.hu f93=f34,f125,f92 }
782{ .mfi; xma.lu f92=f34,f125,f92 };;
783{ .mfi; xma.hu f103=f34,f126,f102 }
784{ .mfi; xma.lu f102=f34,f126,f102 };;
785{ .mfi; xma.hu f113=f34,f127,f112 }
786{ .mfi; xma.lu f112=f34,f127,f112 };;//
787//-------------------------------------------------//
788{ .mfi; getf.sig r18=f42
789 xma.hu f44=f35,f120,f43
790 add r17=r17,r16 }
791{ .mfi; xma.lu f43=f35,f120,f43 };;
792{ .mfi; getf.sig r24=f70
793 xma.hu f54=f35,f121,f53 }
794{ .mfi; mov carry2=0
795 xma.lu f53=f35,f121,f53 };;
796{ .mfi; getf.sig r25=f61
797 xma.hu f64=f35,f122,f63
798 cmp.ltu p7,p0=r17,r16 }
799{ .mfi; add r18=r18,r17
800 xma.lu f63=f35,f122,f63 };;
801{ .mfi; getf.sig r26=f52
802 xma.hu f74=f35,f123,f73
803(p7) add carry2=1,carry2 }
804{ .mfi; cmp.ltu p7,p0=r18,r17
805 xma.lu f73=f35,f123,f73
806 add r18=r18,carry1 };;
807{ .mfi;
808 xma.hu f84=f35,f124,f83
809(p7) add carry2=1,carry2 }
810{ .mfi; cmp.ltu p7,p0=r18,carry1
811 xma.lu f83=f35,f124,f83 };;
812{ .mfi; st8 [r32]=r18,16
813 xma.hu f94=f35,f125,f93
814(p7) add carry2=1,carry2 }
815{ .mfi; xma.lu f93=f35,f125,f93 };;
816{ .mfi; xma.hu f104=f35,f126,f103 }
817{ .mfi; xma.lu f103=f35,f126,f103 };;
818{ .mfi; xma.hu f114=f35,f127,f113 }
819{ .mfi; mov carry1=0
820 xma.lu f113=f35,f127,f113
821 add r25=r25,r24 };;//
822//-------------------------------------------------//
823{ .mfi; getf.sig r27=f43
824 xma.hu f45=f36,f120,f44
825 cmp.ltu p6,p0=r25,r24 }
826{ .mfi; xma.lu f44=f36,f120,f44
827 add r26=r26,r25 };;
828{ .mfi; getf.sig r16=f80
829 xma.hu f55=f36,f121,f54
830(p6) add carry1=1,carry1 }
831{ .mfi; xma.lu f54=f36,f121,f54 };;
832{ .mfi; getf.sig r17=f71
833 xma.hu f65=f36,f122,f64
834 cmp.ltu p6,p0=r26,r25 }
835{ .mfi; xma.lu f64=f36,f122,f64
836 add r27=r27,r26 };;
837{ .mfi; getf.sig r18=f62
838 xma.hu f75=f36,f123,f74
839(p6) add carry1=1,carry1 }
840{ .mfi; cmp.ltu p6,p0=r27,r26
841 xma.lu f74=f36,f123,f74
842 add r27=r27,carry2 };;
843{ .mfi; getf.sig r19=f53
844 xma.hu f85=f36,f124,f84
845(p6) add carry1=1,carry1 }
846{ .mfi; xma.lu f84=f36,f124,f84
847 cmp.ltu p6,p0=r27,carry2 };;
848{ .mfi; st8 [r33]=r27,16
849 xma.hu f95=f36,f125,f94
850(p6) add carry1=1,carry1 }
851{ .mfi; xma.lu f94=f36,f125,f94 };;
852{ .mfi; xma.hu f105=f36,f126,f104 }
853{ .mfi; mov carry2=0
854 xma.lu f104=f36,f126,f104
855 add r17=r17,r16 };;
856{ .mfi; xma.hu f115=f36,f127,f114
857 cmp.ltu p7,p0=r17,r16 }
858{ .mfi; xma.lu f114=f36,f127,f114
859 add r18=r18,r17 };;//
860//-------------------------------------------------//
861{ .mfi; getf.sig r20=f44
862 xma.hu f46=f37,f120,f45
863(p7) add carry2=1,carry2 }
864{ .mfi; cmp.ltu p7,p0=r18,r17
865 xma.lu f45=f37,f120,f45
866 add r19=r19,r18 };;
867{ .mfi; getf.sig r24=f90
868 xma.hu f56=f37,f121,f55 }
869{ .mfi; xma.lu f55=f37,f121,f55 };;
870{ .mfi; getf.sig r25=f81
871 xma.hu f66=f37,f122,f65
872(p7) add carry2=1,carry2 }
873{ .mfi; cmp.ltu p7,p0=r19,r18
874 xma.lu f65=f37,f122,f65
875 add r20=r20,r19 };;
876{ .mfi; getf.sig r26=f72
877 xma.hu f76=f37,f123,f75
878(p7) add carry2=1,carry2 }
879{ .mfi; cmp.ltu p7,p0=r20,r19
880 xma.lu f75=f37,f123,f75
881 add r20=r20,carry1 };;
882{ .mfi; getf.sig r27=f63
883 xma.hu f86=f37,f124,f85
884(p7) add carry2=1,carry2 }
885{ .mfi; xma.lu f85=f37,f124,f85
886 cmp.ltu p7,p0=r20,carry1 };;
887{ .mfi; getf.sig r28=f54
888 xma.hu f96=f37,f125,f95
889(p7) add carry2=1,carry2 }
890{ .mfi; st8 [r32]=r20,16
891 xma.lu f95=f37,f125,f95 };;
892{ .mfi; xma.hu f106=f37,f126,f105 }
893{ .mfi; mov carry1=0
894 xma.lu f105=f37,f126,f105
895 add r25=r25,r24 };;
896{ .mfi; xma.hu f116=f37,f127,f115
897 cmp.ltu p6,p0=r25,r24 }
898{ .mfi; xma.lu f115=f37,f127,f115
899 add r26=r26,r25 };;//
900//-------------------------------------------------//
901{ .mfi; getf.sig r29=f45
902 xma.hu f47=f38,f120,f46
903(p6) add carry1=1,carry1 }
904{ .mfi; cmp.ltu p6,p0=r26,r25
905 xma.lu f46=f38,f120,f46
906 add r27=r27,r26 };;
907{ .mfi; getf.sig r16=f100
908 xma.hu f57=f38,f121,f56
909(p6) add carry1=1,carry1 }
910{ .mfi; cmp.ltu p6,p0=r27,r26
911 xma.lu f56=f38,f121,f56
912 add r28=r28,r27 };;
913{ .mfi; getf.sig r17=f91
914 xma.hu f67=f38,f122,f66
915(p6) add carry1=1,carry1 }
916{ .mfi; cmp.ltu p6,p0=r28,r27
917 xma.lu f66=f38,f122,f66
918 add r29=r29,r28 };;
919{ .mfi; getf.sig r18=f82
920 xma.hu f77=f38,f123,f76
921(p6) add carry1=1,carry1 }
922{ .mfi; cmp.ltu p6,p0=r29,r28
923 xma.lu f76=f38,f123,f76
924 add r29=r29,carry2 };;
925{ .mfi; getf.sig r19=f73
926 xma.hu f87=f38,f124,f86
927(p6) add carry1=1,carry1 }
928{ .mfi; xma.lu f86=f38,f124,f86
929 cmp.ltu p6,p0=r29,carry2 };;
930{ .mfi; getf.sig r20=f64
931 xma.hu f97=f38,f125,f96
932(p6) add carry1=1,carry1 }
933{ .mfi; st8 [r33]=r29,16
934 xma.lu f96=f38,f125,f96 };;
935{ .mfi; getf.sig r21=f55
936 xma.hu f107=f38,f126,f106 }
937{ .mfi; mov carry2=0
938 xma.lu f106=f38,f126,f106
939 add r17=r17,r16 };;
940{ .mfi; xma.hu f117=f38,f127,f116
941 cmp.ltu p7,p0=r17,r16 }
942{ .mfi; xma.lu f116=f38,f127,f116
943 add r18=r18,r17 };;//
944//-------------------------------------------------//
945{ .mfi; getf.sig r22=f46
946 xma.hu f48=f39,f120,f47
947(p7) add carry2=1,carry2 }
948{ .mfi; cmp.ltu p7,p0=r18,r17
949 xma.lu f47=f39,f120,f47
950 add r19=r19,r18 };;
951{ .mfi; getf.sig r24=f110
952 xma.hu f58=f39,f121,f57
953(p7) add carry2=1,carry2 }
954{ .mfi; cmp.ltu p7,p0=r19,r18
955 xma.lu f57=f39,f121,f57
956 add r20=r20,r19 };;
957{ .mfi; getf.sig r25=f101
958 xma.hu f68=f39,f122,f67
959(p7) add carry2=1,carry2 }
960{ .mfi; cmp.ltu p7,p0=r20,r19
961 xma.lu f67=f39,f122,f67
962 add r21=r21,r20 };;
963{ .mfi; getf.sig r26=f92
964 xma.hu f78=f39,f123,f77
965(p7) add carry2=1,carry2 }
966{ .mfi; cmp.ltu p7,p0=r21,r20
967 xma.lu f77=f39,f123,f77
968 add r22=r22,r21 };;
969{ .mfi; getf.sig r27=f83
970 xma.hu f88=f39,f124,f87
971(p7) add carry2=1,carry2 }
972{ .mfi; cmp.ltu p7,p0=r22,r21
973 xma.lu f87=f39,f124,f87
974 add r22=r22,carry1 };;
975{ .mfi; getf.sig r28=f74
976 xma.hu f98=f39,f125,f97
977(p7) add carry2=1,carry2 }
978{ .mfi; xma.lu f97=f39,f125,f97
979 cmp.ltu p7,p0=r22,carry1 };;
980{ .mfi; getf.sig r29=f65
981 xma.hu f108=f39,f126,f107
982(p7) add carry2=1,carry2 }
983{ .mfi; st8 [r32]=r22,16
984 xma.lu f107=f39,f126,f107 };;
985{ .mfi; getf.sig r30=f56
986 xma.hu f118=f39,f127,f117 }
987{ .mfi; xma.lu f117=f39,f127,f117 };;//
988//-------------------------------------------------//
989// Leaving muliplier's heaven... Quite a ride, huh?
990
991{ .mii; getf.sig r31=f47
992 add r25=r25,r24
993 mov carry1=0 };;
994{ .mii; getf.sig r16=f111
995 cmp.ltu p6,p0=r25,r24
996 add r26=r26,r25 };;
997{ .mfb; getf.sig r17=f102 }
998{ .mii;
999(p6) add carry1=1,carry1
1000 cmp.ltu p6,p0=r26,r25
1001 add r27=r27,r26 };;
1002{ .mfb; nop.m 0x0 }
1003{ .mii;
1004(p6) add carry1=1,carry1
1005 cmp.ltu p6,p0=r27,r26
1006 add r28=r28,r27 };;
1007{ .mii; getf.sig r18=f93
1008 add r17=r17,r16
1009 mov carry3=0 }
1010{ .mii;
1011(p6) add carry1=1,carry1
1012 cmp.ltu p6,p0=r28,r27
1013 add r29=r29,r28 };;
1014{ .mii; getf.sig r19=f84
1015 cmp.ltu p7,p0=r17,r16 }
1016{ .mii;
1017(p6) add carry1=1,carry1
1018 cmp.ltu p6,p0=r29,r28
1019 add r30=r30,r29 };;
1020{ .mii; getf.sig r20=f75
1021 add r18=r18,r17 }
1022{ .mii;
1023(p6) add carry1=1,carry1
1024 cmp.ltu p6,p0=r30,r29
1025 add r31=r31,r30 };;
1026{ .mfb; getf.sig r21=f66 }
1027{ .mii; (p7) add carry3=1,carry3
1028 cmp.ltu p7,p0=r18,r17
1029 add r19=r19,r18 }
1030{ .mfb; nop.m 0x0 }
1031{ .mii;
1032(p6) add carry1=1,carry1
1033 cmp.ltu p6,p0=r31,r30
1034 add r31=r31,carry2 };;
1035{ .mfb; getf.sig r22=f57 }
1036{ .mii; (p7) add carry3=1,carry3
1037 cmp.ltu p7,p0=r19,r18
1038 add r20=r20,r19 }
1039{ .mfb; nop.m 0x0 }
1040{ .mii;
1041(p6) add carry1=1,carry1
1042 cmp.ltu p6,p0=r31,carry2 };;
1043{ .mfb; getf.sig r23=f48 }
1044{ .mii; (p7) add carry3=1,carry3
1045 cmp.ltu p7,p0=r20,r19
1046 add r21=r21,r20 }
1047{ .mii;
1048(p6) add carry1=1,carry1 }
1049{ .mfb; st8 [r33]=r31,16 };;
1050
1051{ .mfb; getf.sig r24=f112 }
1052{ .mii; (p7) add carry3=1,carry3
1053 cmp.ltu p7,p0=r21,r20
1054 add r22=r22,r21 };;
1055{ .mfb; getf.sig r25=f103 }
1056{ .mii; (p7) add carry3=1,carry3
1057 cmp.ltu p7,p0=r22,r21
1058 add r23=r23,r22 };;
1059{ .mfb; getf.sig r26=f94 }
1060{ .mii; (p7) add carry3=1,carry3
1061 cmp.ltu p7,p0=r23,r22
1062 add r23=r23,carry1 };;
1063{ .mfb; getf.sig r27=f85 }
1064{ .mii; (p7) add carry3=1,carry3
1065 cmp.ltu p7,p8=r23,carry1};;
1066{ .mii; getf.sig r28=f76
1067 add r25=r25,r24
1068 mov carry1=0 }
1069{ .mii; st8 [r32]=r23,16
1070 (p7) add carry2=1,carry3
1071 (p8) add carry2=0,carry3 };;
1072
1073{ .mfb; nop.m 0x0 }
1074{ .mii; getf.sig r29=f67
1075 cmp.ltu p6,p0=r25,r24
1076 add r26=r26,r25 };;
1077{ .mfb; getf.sig r30=f58 }
1078{ .mii;
1079(p6) add carry1=1,carry1
1080 cmp.ltu p6,p0=r26,r25
1081 add r27=r27,r26 };;
1082{ .mfb; getf.sig r16=f113 }
1083{ .mii;
1084(p6) add carry1=1,carry1
1085 cmp.ltu p6,p0=r27,r26
1086 add r28=r28,r27 };;
1087{ .mfb; getf.sig r17=f104 }
1088{ .mii;
1089(p6) add carry1=1,carry1
1090 cmp.ltu p6,p0=r28,r27
1091 add r29=r29,r28 };;
1092{ .mfb; getf.sig r18=f95 }
1093{ .mii;
1094(p6) add carry1=1,carry1
1095 cmp.ltu p6,p0=r29,r28
1096 add r30=r30,r29 };;
1097{ .mii; getf.sig r19=f86
1098 add r17=r17,r16
1099 mov carry3=0 }
1100{ .mii;
1101(p6) add carry1=1,carry1
1102 cmp.ltu p6,p0=r30,r29
1103 add r30=r30,carry2 };;
1104{ .mii; getf.sig r20=f77
1105 cmp.ltu p7,p0=r17,r16
1106 add r18=r18,r17 }
1107{ .mii;
1108(p6) add carry1=1,carry1
1109 cmp.ltu p6,p0=r30,carry2 };;
1110{ .mfb; getf.sig r21=f68 }
1111{ .mii; st8 [r33]=r30,16
1112(p6) add carry1=1,carry1 };;
1113
1114{ .mfb; getf.sig r24=f114 }
1115{ .mii; (p7) add carry3=1,carry3
1116 cmp.ltu p7,p0=r18,r17
1117 add r19=r19,r18 };;
1118{ .mfb; getf.sig r25=f105 }
1119{ .mii; (p7) add carry3=1,carry3
1120 cmp.ltu p7,p0=r19,r18
1121 add r20=r20,r19 };;
1122{ .mfb; getf.sig r26=f96 }
1123{ .mii; (p7) add carry3=1,carry3
1124 cmp.ltu p7,p0=r20,r19
1125 add r21=r21,r20 };;
1126{ .mfb; getf.sig r27=f87 }
1127{ .mii; (p7) add carry3=1,carry3
1128 cmp.ltu p7,p0=r21,r20
1129 add r21=r21,carry1 };;
1130{ .mib; getf.sig r28=f78
1131 add r25=r25,r24 }
1132{ .mib; (p7) add carry3=1,carry3
1133 cmp.ltu p7,p8=r21,carry1};;
1134{ .mii; st8 [r32]=r21,16
1135 (p7) add carry2=1,carry3
1136 (p8) add carry2=0,carry3 }
1137
1138{ .mii; mov carry1=0
1139 cmp.ltu p6,p0=r25,r24
1140 add r26=r26,r25 };;
1141{ .mfb; getf.sig r16=f115 }
1142{ .mii;
1143(p6) add carry1=1,carry1
1144 cmp.ltu p6,p0=r26,r25
1145 add r27=r27,r26 };;
1146{ .mfb; getf.sig r17=f106 }
1147{ .mii;
1148(p6) add carry1=1,carry1
1149 cmp.ltu p6,p0=r27,r26
1150 add r28=r28,r27 };;
1151{ .mfb; getf.sig r18=f97 }
1152{ .mii;
1153(p6) add carry1=1,carry1
1154 cmp.ltu p6,p0=r28,r27
1155 add r28=r28,carry2 };;
1156{ .mib; getf.sig r19=f88
1157 add r17=r17,r16 }
1158{ .mib;
1159(p6) add carry1=1,carry1
1160 cmp.ltu p6,p0=r28,carry2 };;
1161{ .mii; st8 [r33]=r28,16
1162(p6) add carry1=1,carry1 }
1163
1164{ .mii; mov carry2=0
1165 cmp.ltu p7,p0=r17,r16
1166 add r18=r18,r17 };;
1167{ .mfb; getf.sig r24=f116 }
1168{ .mii; (p7) add carry2=1,carry2
1169 cmp.ltu p7,p0=r18,r17
1170 add r19=r19,r18 };;
1171{ .mfb; getf.sig r25=f107 }
1172{ .mii; (p7) add carry2=1,carry2
1173 cmp.ltu p7,p0=r19,r18
1174 add r19=r19,carry1 };;
1175{ .mfb; getf.sig r26=f98 }
1176{ .mii; (p7) add carry2=1,carry2
1177 cmp.ltu p7,p0=r19,carry1};;
1178{ .mii; st8 [r32]=r19,16
1179 (p7) add carry2=1,carry2 }
1180
1181{ .mfb; add r25=r25,r24 };;
1182
1183{ .mfb; getf.sig r16=f117 }
1184{ .mii; mov carry1=0
1185 cmp.ltu p6,p0=r25,r24
1186 add r26=r26,r25 };;
1187{ .mfb; getf.sig r17=f108 }
1188{ .mii;
1189(p6) add carry1=1,carry1
1190 cmp.ltu p6,p0=r26,r25
1191 add r26=r26,carry2 };;
1192{ .mfb; nop.m 0x0 }
1193{ .mii;
1194(p6) add carry1=1,carry1
1195 cmp.ltu p6,p0=r26,carry2 };;
1196{ .mii; st8 [r33]=r26,16
1197(p6) add carry1=1,carry1 }
1198
1199{ .mfb; add r17=r17,r16 };;
1200{ .mfb; getf.sig r24=f118 }
1201{ .mii; mov carry2=0
1202 cmp.ltu p7,p0=r17,r16
1203 add r17=r17,carry1 };;
1204{ .mii; (p7) add carry2=1,carry2
1205 cmp.ltu p7,p0=r17,carry1};;
1206{ .mii; st8 [r32]=r17
1207 (p7) add carry2=1,carry2 };;
1208{ .mfb; add r24=r24,carry2 };;
1209{ .mib; st8 [r33]=r24 }
1210
1211{ .mib; rum 1<<5 // clear um.mfh
1212 br.ret.sptk.many b0 };;
1213.endp bn_mul_comba8#
1214#undef carry3
1215#undef carry2
1216#undef carry1
1217#endif
1218
1219#if 1
1220// It's possible to make it faster (see comment to bn_sqr_comba8), but
1221// I reckon it doesn't worth the effort. Basically because the routine
1222// (actually both of them) practically never called... So I just play
1223// same trick as with bn_sqr_comba8.
1224//
1225// void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a)
1226//
1227.global bn_sqr_comba4#
1228.proc bn_sqr_comba4#
1229.align 64
1230bn_sqr_comba4:
1231 .prologue
1232 .fframe 0
1233 .save ar.pfs,r2
1234#if defined(_HPUX_SOURCE) && defined(_ILP32)
1235{ .mii; alloc r2=ar.pfs,2,1,0,0
1236 addp4 r32=0,r32
1237 addp4 r33=0,r33 };;
1238{ .mii;
1239#else
1240{ .mii; alloc r2=ar.pfs,2,1,0,0
1241#endif
1242 mov r34=r33
1243 add r14=8,r33 };;
1244 .body
1245{ .mii; add r17=8,r34
1246 add r15=16,r33
1247 add r18=16,r34 }
1248{ .mfb; add r16=24,r33
1249 br .L_cheat_entry_point4 };;
1250.endp bn_sqr_comba4#
1251#endif
1252
1253#if 1
1254// Runs in ~115 cycles and ~4.5 times faster than C. Well, whatever...
1255//
1256// void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
1257//
1258#define carry1 r14
1259#define carry2 r15
1260.global bn_mul_comba4#
1261.proc bn_mul_comba4#
1262.align 64
1263bn_mul_comba4:
1264 .prologue
1265 .fframe 0
1266 .save ar.pfs,r2
1267#if defined(_HPUX_SOURCE) && defined(_ILP32)
1268{ .mii; alloc r2=ar.pfs,3,0,0,0
1269 addp4 r33=0,r33
1270 addp4 r34=0,r34 };;
1271{ .mii; addp4 r32=0,r32
1272#else
1273{ .mii; alloc r2=ar.pfs,3,0,0,0
1274#endif
1275 add r14=8,r33
1276 add r17=8,r34 }
1277 .body
1278{ .mii; add r15=16,r33
1279 add r18=16,r34
1280 add r16=24,r33 };;
1281.L_cheat_entry_point4:
1282{ .mmi; add r19=24,r34
1283
1284 ldf8 f32=[r33] }
1285
1286{ .mmi; ldf8 f120=[r34]
1287 ldf8 f121=[r17] };;
1288{ .mmi; ldf8 f122=[r18]
1289 ldf8 f123=[r19] }
1290
1291{ .mmi; ldf8 f33=[r14]
1292 ldf8 f34=[r15] }
1293{ .mfi; ldf8 f35=[r16]
1294
1295 xma.hu f41=f32,f120,f0 }
1296{ .mfi; xma.lu f40=f32,f120,f0 };;
1297{ .mfi; xma.hu f51=f32,f121,f0 }
1298{ .mfi; xma.lu f50=f32,f121,f0 };;
1299{ .mfi; xma.hu f61=f32,f122,f0 }
1300{ .mfi; xma.lu f60=f32,f122,f0 };;
1301{ .mfi; xma.hu f71=f32,f123,f0 }
1302{ .mfi; xma.lu f70=f32,f123,f0 };;//
1303// Major stall takes place here, and 3 more places below. Result from
1304// first xma is not available for another 3 ticks.
1305{ .mfi; getf.sig r16=f40
1306 xma.hu f42=f33,f120,f41
1307 add r33=8,r32 }
1308{ .mfi; xma.lu f41=f33,f120,f41 };;
1309{ .mfi; getf.sig r24=f50
1310 xma.hu f52=f33,f121,f51 }
1311{ .mfi; xma.lu f51=f33,f121,f51 };;
1312{ .mfi; st8 [r32]=r16,16
1313 xma.hu f62=f33,f122,f61 }
1314{ .mfi; xma.lu f61=f33,f122,f61 };;
1315{ .mfi; xma.hu f72=f33,f123,f71 }
1316{ .mfi; xma.lu f71=f33,f123,f71 };;//
1317//-------------------------------------------------//
1318{ .mfi; getf.sig r25=f41
1319 xma.hu f43=f34,f120,f42 }
1320{ .mfi; xma.lu f42=f34,f120,f42 };;
1321{ .mfi; getf.sig r16=f60
1322 xma.hu f53=f34,f121,f52 }
1323{ .mfi; xma.lu f52=f34,f121,f52 };;
1324{ .mfi; getf.sig r17=f51
1325 xma.hu f63=f34,f122,f62
1326 add r25=r25,r24 }
1327{ .mfi; mov carry1=0
1328 xma.lu f62=f34,f122,f62 };;
1329{ .mfi; st8 [r33]=r25,16
1330 xma.hu f73=f34,f123,f72
1331 cmp.ltu p6,p0=r25,r24 }
1332{ .mfi; xma.lu f72=f34,f123,f72 };;//
1333//-------------------------------------------------//
1334{ .mfi; getf.sig r18=f42
1335 xma.hu f44=f35,f120,f43
1336(p6) add carry1=1,carry1 }
1337{ .mfi; add r17=r17,r16
1338 xma.lu f43=f35,f120,f43
1339 mov carry2=0 };;
1340{ .mfi; getf.sig r24=f70
1341 xma.hu f54=f35,f121,f53
1342 cmp.ltu p7,p0=r17,r16 }
1343{ .mfi; xma.lu f53=f35,f121,f53 };;
1344{ .mfi; getf.sig r25=f61
1345 xma.hu f64=f35,f122,f63
1346 add r18=r18,r17 }
1347{ .mfi; xma.lu f63=f35,f122,f63
1348(p7) add carry2=1,carry2 };;
1349{ .mfi; getf.sig r26=f52
1350 xma.hu f74=f35,f123,f73
1351 cmp.ltu p7,p0=r18,r17 }
1352{ .mfi; xma.lu f73=f35,f123,f73
1353 add r18=r18,carry1 };;
1354//-------------------------------------------------//
1355{ .mii; st8 [r32]=r18,16
1356(p7) add carry2=1,carry2
1357 cmp.ltu p7,p0=r18,carry1 };;
1358
1359{ .mfi; getf.sig r27=f43 // last major stall
1360(p7) add carry2=1,carry2 };;
1361{ .mii; getf.sig r16=f71
1362 add r25=r25,r24
1363 mov carry1=0 };;
1364{ .mii; getf.sig r17=f62
1365 cmp.ltu p6,p0=r25,r24
1366 add r26=r26,r25 };;
1367{ .mii;
1368(p6) add carry1=1,carry1
1369 cmp.ltu p6,p0=r26,r25
1370 add r27=r27,r26 };;
1371{ .mii;
1372(p6) add carry1=1,carry1
1373 cmp.ltu p6,p0=r27,r26
1374 add r27=r27,carry2 };;
1375{ .mii; getf.sig r18=f53
1376(p6) add carry1=1,carry1
1377 cmp.ltu p6,p0=r27,carry2 };;
1378{ .mfi; st8 [r33]=r27,16
1379(p6) add carry1=1,carry1 }
1380
1381{ .mii; getf.sig r19=f44
1382 add r17=r17,r16
1383 mov carry2=0 };;
1384{ .mii; getf.sig r24=f72
1385 cmp.ltu p7,p0=r17,r16
1386 add r18=r18,r17 };;
1387{ .mii; (p7) add carry2=1,carry2
1388 cmp.ltu p7,p0=r18,r17
1389 add r19=r19,r18 };;
1390{ .mii; (p7) add carry2=1,carry2
1391 cmp.ltu p7,p0=r19,r18
1392 add r19=r19,carry1 };;
1393{ .mii; getf.sig r25=f63
1394 (p7) add carry2=1,carry2
1395 cmp.ltu p7,p0=r19,carry1};;
1396{ .mii; st8 [r32]=r19,16
1397 (p7) add carry2=1,carry2 }
1398
1399{ .mii; getf.sig r26=f54
1400 add r25=r25,r24
1401 mov carry1=0 };;
1402{ .mii; getf.sig r16=f73
1403 cmp.ltu p6,p0=r25,r24
1404 add r26=r26,r25 };;
1405{ .mii;
1406(p6) add carry1=1,carry1
1407 cmp.ltu p6,p0=r26,r25
1408 add r26=r26,carry2 };;
1409{ .mii; getf.sig r17=f64
1410(p6) add carry1=1,carry1
1411 cmp.ltu p6,p0=r26,carry2 };;
1412{ .mii; st8 [r33]=r26,16
1413(p6) add carry1=1,carry1 }
1414
1415{ .mii; getf.sig r24=f74
1416 add r17=r17,r16
1417 mov carry2=0 };;
1418{ .mii; cmp.ltu p7,p0=r17,r16
1419 add r17=r17,carry1 };;
1420
1421{ .mii; (p7) add carry2=1,carry2
1422 cmp.ltu p7,p0=r17,carry1};;
1423{ .mii; st8 [r32]=r17,16
1424 (p7) add carry2=1,carry2 };;
1425
1426{ .mii; add r24=r24,carry2 };;
1427{ .mii; st8 [r33]=r24 }
1428
1429{ .mib; rum 1<<5 // clear um.mfh
1430 br.ret.sptk.many b0 };;
1431.endp bn_mul_comba4#
1432#undef carry2
1433#undef carry1
1434#endif
1435
1436#if 1
1437//
1438// BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
1439//
1440// In the nutshell it's a port of my MIPS III/IV implementation.
1441//
1442#define AT r14
1443#define H r16
1444#define HH r20
1445#define L r17
1446#define D r18
1447#define DH r22
1448#define I r21
1449
1450#if 0
1451// Some preprocessors (most notably HP-UX) apper to be allergic to
1452// macros enclosed to parenthesis as these three will be.
1453#define cont p16
1454#define break p0 // p20
1455#define equ p24
1456#else
1457cont=p16
1458break=p0
1459equ=p24
1460#endif
1461
1462.global abort#
1463.global bn_div_words#
1464.proc bn_div_words#
1465.align 64
1466bn_div_words:
1467 .prologue
1468 .fframe 0
1469 .save ar.pfs,r2
1470 .save b0,r3
1471{ .mii; alloc r2=ar.pfs,3,5,0,8
1472 mov r3=b0
1473 mov r10=pr };;
1474{ .mmb; cmp.eq p6,p0=r34,r0
1475 mov r8=-1
1476(p6) br.ret.spnt.many b0 };;
1477
1478 .body
1479{ .mii; mov H=r32 // save h
1480 mov ar.ec=0 // don't rotate at exit
1481 mov pr.rot=0 }
1482{ .mii; mov L=r33 // save l
1483 mov r36=r0 };;
1484
1485.L_divw_shift: // -vv- note signed comparison
1486{ .mfi; (p0) cmp.lt p16,p0=r0,r34 // d
1487 (p0) shladd r33=r34,1,r0 }
1488{ .mfb; (p0) add r35=1,r36
1489 (p0) nop.f 0x0
1490(p16) br.wtop.dpnt .L_divw_shift };;
1491
1492{ .mii; mov D=r34
1493 shr.u DH=r34,32
1494 sub r35=64,r36 };;
1495{ .mii; setf.sig f7=DH
1496 shr.u AT=H,r35
1497 mov I=r36 };;
1498{ .mib; cmp.ne p6,p0=r0,AT
1499 shl H=H,r36
1500(p6) br.call.spnt.clr b0=abort };; // overflow, die...
1501
1502{ .mfi; fcvt.xuf.s1 f7=f7
1503 shr.u AT=L,r35 };;
1504{ .mii; shl L=L,r36
1505 or H=H,AT };;
1506
1507{ .mii; nop.m 0x0
1508 cmp.leu p6,p0=D,H;;
1509(p6) sub H=H,D }
1510
1511{ .mlx; setf.sig f14=D
1512 movl AT=0xffffffff };;
1513///////////////////////////////////////////////////////////
1514{ .mii; setf.sig f6=H
1515 shr.u HH=H,32;;
1516 cmp.eq p6,p7=HH,DH };;
1517{ .mfb;
1518(p6) setf.sig f8=AT
1519(p7) fcvt.xuf.s1 f6=f6
1520(p7) br.call.sptk b6=.L_udiv64_32_b6 };;
1521
1522{ .mfi; getf.sig r33=f8 // q
1523 xmpy.lu f9=f8,f14 }
1524{ .mfi; xmpy.hu f10=f8,f14
1525 shrp H=H,L,32 };;
1526
1527{ .mmi; getf.sig r35=f9 // tl
1528 getf.sig r31=f10 };; // th
1529
1530.L_divw_1st_iter:
1531{ .mii; (p0) add r32=-1,r33
1532 (p0) cmp.eq equ,cont=HH,r31 };;
1533{ .mii; (p0) cmp.ltu p8,p0=r35,D
1534 (p0) sub r34=r35,D
1535 (equ) cmp.leu break,cont=r35,H };;
1536{ .mib; (cont) cmp.leu cont,break=HH,r31
1537 (p8) add r31=-1,r31
1538(cont) br.wtop.spnt .L_divw_1st_iter };;
1539///////////////////////////////////////////////////////////
1540{ .mii; sub H=H,r35
1541 shl r8=r33,32
1542 shl L=L,32 };;
1543///////////////////////////////////////////////////////////
1544{ .mii; setf.sig f6=H
1545 shr.u HH=H,32;;
1546 cmp.eq p6,p7=HH,DH };;
1547{ .mfb;
1548(p6) setf.sig f8=AT
1549(p7) fcvt.xuf.s1 f6=f6
1550(p7) br.call.sptk b6=.L_udiv64_32_b6 };;
1551
1552{ .mfi; getf.sig r33=f8 // q
1553 xmpy.lu f9=f8,f14 }
1554{ .mfi; xmpy.hu f10=f8,f14
1555 shrp H=H,L,32 };;
1556
1557{ .mmi; getf.sig r35=f9 // tl
1558 getf.sig r31=f10 };; // th
1559
1560.L_divw_2nd_iter:
1561{ .mii; (p0) add r32=-1,r33
1562 (p0) cmp.eq equ,cont=HH,r31 };;
1563{ .mii; (p0) cmp.ltu p8,p0=r35,D
1564 (p0) sub r34=r35,D
1565 (equ) cmp.leu break,cont=r35,H };;
1566{ .mib; (cont) cmp.leu cont,break=HH,r31
1567 (p8) add r31=-1,r31
1568(cont) br.wtop.spnt .L_divw_2nd_iter };;
1569///////////////////////////////////////////////////////////
1570{ .mii; sub H=H,r35
1571 or r8=r8,r33
1572 mov ar.pfs=r2 };;
1573{ .mii; shr.u r9=H,I // remainder if anybody wants it
1574 mov pr=r10,0x1ffff }
1575{ .mfb; br.ret.sptk.many b0 };;
1576
1577// Unsigned 64 by 32 (well, by 64 for the moment) bit integer division
1578// procedure.
1579//
1580// inputs: f6 = (double)a, f7 = (double)b
1581// output: f8 = (int)(a/b)
1582// clobbered: f8,f9,f10,f11,pred
1583pred=p15
1584// This procedure is essentially Intel code and therefore is
1585// copyrighted to Intel Corporation (I suppose...). It's sligtly
1586// modified for specific needs.
1587.align 32
1588.skip 16
1589.L_udiv64_32_b6:
1590 frcpa.s1 f8,pred=f6,f7;; // [0] y0 = 1 / b
1591
1592(pred) fnma.s1 f9=f7,f8,f1 // [5] e0 = 1 - b * y0
1593(pred) fmpy.s1 f10=f6,f8;; // [5] q0 = a * y0
1594(pred) fmpy.s1 f11=f9,f9 // [10] e1 = e0 * e0
1595(pred) fma.s1 f10=f9,f10,f10;; // [10] q1 = q0 + e0 * q0
1596(pred) fma.s1 f8=f9,f8,f8 //;; // [15] y1 = y0 + e0 * y0
1597(pred) fma.s1 f9=f11,f10,f10;; // [15] q2 = q1 + e1 * q1
1598(pred) fma.s1 f8=f11,f8,f8 //;; // [20] y2 = y1 + e1 * y1
1599(pred) fnma.s1 f10=f7,f9,f6;; // [20] r2 = a - b * q2
1600(pred) fma.s1 f8=f10,f8,f9;; // [25] q3 = q2 + r2 * y2
1601
1602 fcvt.fxu.trunc.s1 f8=f8 // [30] q = trunc(q3)
1603 br.ret.sptk.many b6;;
1604.endp bn_div_words#
1605#endif