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1.explicit
2.text
3.ident "ia64.S, Version 2.1"
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 (as they were), 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 defined(_HPUX_SOURCE) && !defined(_LP64)
149#define ADDP addp4
150#else
151#define ADDP add
152#endif
153
154#if 1
155//
156// bn_[add|sub]_words routines.
157//
158// Loops are spinning in 2*(n+5) ticks on Itanuim (provided that the
159// data reside in L1 cache, i.e. 2 ticks away). It's possible to
160// compress the epilogue and get down to 2*n+6, but at the cost of
161// scalability (the neat feature of this implementation is that it
162// shall automagically spin in n+5 on "wider" IA-64 implementations:-)
163// I consider that the epilogue is short enough as it is to trade tiny
164// performance loss on Itanium for scalability.
165//
166// BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int num)
167//
168.global bn_add_words#
169.proc bn_add_words#
170.align 64
171.skip 32 // makes the loop body aligned at 64-byte boundary
172bn_add_words:
173 .prologue
174 .fframe 0
175 .save ar.pfs,r2
176{ .mii; alloc r2=ar.pfs,4,12,0,16
177 cmp4.le p6,p0=r35,r0 };;
178{ .mfb; mov r8=r0 // return value
179(p6) br.ret.spnt.many b0 };;
180
181 .save ar.lc,r3
182{ .mib; sub r10=r35,r0,1
183 mov r3=ar.lc
184 brp.loop.imp .L_bn_add_words_ctop,.L_bn_add_words_cend-16
185 }
186 .body
187{ .mib; ADDP r14=0,r32 // rp
188 mov r9=pr };;
189{ .mii; ADDP r15=0,r33 // ap
190 mov ar.lc=r10
191 mov ar.ec=6 }
192{ .mib; ADDP r16=0,r34 // bp
193 mov pr.rot=1<<16 };;
194
195.L_bn_add_words_ctop:
196{ .mii; (p16) ld8 r32=[r16],8 // b=*(bp++)
197 (p18) add r39=r37,r34
198 (p19) cmp.ltu.unc p56,p0=r40,r38 }
199{ .mfb; (p0) nop.m 0x0
200 (p0) nop.f 0x0
201 (p0) nop.b 0x0 }
202{ .mii; (p16) ld8 r35=[r15],8 // a=*(ap++)
203 (p58) cmp.eq.or p57,p0=-1,r41 // (p20)
204 (p58) add r41=1,r41 } // (p20)
205{ .mfb; (p21) st8 [r14]=r42,8 // *(rp++)=r
206 (p0) nop.f 0x0
207 br.ctop.sptk .L_bn_add_words_ctop };;
208.L_bn_add_words_cend:
209
210{ .mii;
211(p59) add r8=1,r8 // return value
212 mov pr=r9,0x1ffff
213 mov ar.lc=r3 }
214{ .mbb; nop.b 0x0
215 br.ret.sptk.many b0 };;
216.endp bn_add_words#
217
218//
219// BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp,int num)
220//
221.global bn_sub_words#
222.proc bn_sub_words#
223.align 64
224.skip 32 // makes the loop body aligned at 64-byte boundary
225bn_sub_words:
226 .prologue
227 .fframe 0
228 .save ar.pfs,r2
229{ .mii; alloc r2=ar.pfs,4,12,0,16
230 cmp4.le p6,p0=r35,r0 };;
231{ .mfb; mov r8=r0 // return value
232(p6) br.ret.spnt.many b0 };;
233
234 .save ar.lc,r3
235{ .mib; sub r10=r35,r0,1
236 mov r3=ar.lc
237 brp.loop.imp .L_bn_sub_words_ctop,.L_bn_sub_words_cend-16
238 }
239 .body
240{ .mib; ADDP r14=0,r32 // rp
241 mov r9=pr };;
242{ .mii; ADDP r15=0,r33 // ap
243 mov ar.lc=r10
244 mov ar.ec=6 }
245{ .mib; ADDP r16=0,r34 // bp
246 mov pr.rot=1<<16 };;
247
248.L_bn_sub_words_ctop:
249{ .mii; (p16) ld8 r32=[r16],8 // b=*(bp++)
250 (p18) sub r39=r37,r34
251 (p19) cmp.gtu.unc p56,p0=r40,r38 }
252{ .mfb; (p0) nop.m 0x0
253 (p0) nop.f 0x0
254 (p0) nop.b 0x0 }
255{ .mii; (p16) ld8 r35=[r15],8 // a=*(ap++)
256 (p58) cmp.eq.or p57,p0=0,r41 // (p20)
257 (p58) add r41=-1,r41 } // (p20)
258{ .mbb; (p21) st8 [r14]=r42,8 // *(rp++)=r
259 (p0) nop.b 0x0
260 br.ctop.sptk .L_bn_sub_words_ctop };;
261.L_bn_sub_words_cend:
262
263{ .mii;
264(p59) add r8=1,r8 // return value
265 mov pr=r9,0x1ffff
266 mov ar.lc=r3 }
267{ .mbb; nop.b 0x0
268 br.ret.sptk.many b0 };;
269.endp bn_sub_words#
270#endif
271
272#if 0
273#define XMA_TEMPTATION
274#endif
275
276#if 1
277//
278// BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w)
279//
280.global bn_mul_words#
281.proc bn_mul_words#
282.align 64
283.skip 32 // makes the loop body aligned at 64-byte boundary
284bn_mul_words:
285 .prologue
286 .fframe 0
287 .save ar.pfs,r2
288#ifdef XMA_TEMPTATION
289{ .mfi; alloc r2=ar.pfs,4,0,0,0 };;
290#else
291{ .mfi; alloc r2=ar.pfs,4,12,0,16 };;
292#endif
293{ .mib; mov r8=r0 // return value
294 cmp4.le p6,p0=r34,r0
295(p6) br.ret.spnt.many b0 };;
296
297 .save ar.lc,r3
298{ .mii; sub r10=r34,r0,1
299 mov r3=ar.lc
300 mov r9=pr };;
301
302 .body
303{ .mib; setf.sig f8=r35 // w
304 mov pr.rot=0x800001<<16
305 // ------^----- serves as (p50) at first (p27)
306 brp.loop.imp .L_bn_mul_words_ctop,.L_bn_mul_words_cend-16
307 }
308
309#ifndef XMA_TEMPTATION
310
311{ .mmi; ADDP r14=0,r32 // rp
312 ADDP r15=0,r33 // ap
313 mov ar.lc=r10 }
314{ .mmi; mov r40=0 // serves as r35 at first (p27)
315 mov ar.ec=13 };;
316
317// This loop spins in 2*(n+12) ticks. It's scheduled for data in Itanium
318// L2 cache (i.e. 9 ticks away) as floating point load/store instructions
319// bypass L1 cache and L2 latency is actually best-case scenario for
320// ldf8. The loop is not scalable and shall run in 2*(n+12) even on
321// "wider" IA-64 implementations. It's a trade-off here. n+24 loop
322// would give us ~5% in *overall* performance improvement on "wider"
323// IA-64, but would hurt Itanium for about same because of longer
324// epilogue. As it's a matter of few percents in either case I've
325// chosen to trade the scalability for development time (you can see
326// this very instruction sequence in bn_mul_add_words loop which in
327// turn is scalable).
328.L_bn_mul_words_ctop:
329{ .mfi; (p25) getf.sig r36=f52 // low
330 (p21) xmpy.lu f48=f37,f8
331 (p28) cmp.ltu p54,p50=r41,r39 }
332{ .mfi; (p16) ldf8 f32=[r15],8
333 (p21) xmpy.hu f40=f37,f8
334 (p0) nop.i 0x0 };;
335{ .mii; (p25) getf.sig r32=f44 // high
336 .pred.rel "mutex",p50,p54
337 (p50) add r40=r38,r35 // (p27)
338 (p54) add r40=r38,r35,1 } // (p27)
339{ .mfb; (p28) st8 [r14]=r41,8
340 (p0) nop.f 0x0
341 br.ctop.sptk .L_bn_mul_words_ctop };;
342.L_bn_mul_words_cend:
343
344{ .mii; nop.m 0x0
345.pred.rel "mutex",p51,p55
346(p51) add r8=r36,r0
347(p55) add r8=r36,r0,1 }
348{ .mfb; nop.m 0x0
349 nop.f 0x0
350 nop.b 0x0 }
351
352#else // XMA_TEMPTATION
353
354 setf.sig f37=r0 // serves as carry at (p18) tick
355 mov ar.lc=r10
356 mov ar.ec=5;;
357
358// Most of you examining this code very likely wonder why in the name
359// of Intel the following loop is commented out? Indeed, it looks so
360// neat that you find it hard to believe that it's something wrong
361// with it, right? The catch is that every iteration depends on the
362// result from previous one and the latter isn't available instantly.
363// The loop therefore spins at the latency of xma minus 1, or in other
364// words at 6*(n+4) ticks:-( Compare to the "production" loop above
365// that runs in 2*(n+11) where the low latency problem is worked around
366// by moving the dependency to one-tick latent interger ALU. Note that
367// "distance" between ldf8 and xma is not latency of ldf8, but the
368// *difference* between xma and ldf8 latencies.
369.L_bn_mul_words_ctop:
370{ .mfi; (p16) ldf8 f32=[r33],8
371 (p18) xma.hu f38=f34,f8,f39 }
372{ .mfb; (p20) stf8 [r32]=f37,8
373 (p18) xma.lu f35=f34,f8,f39
374 br.ctop.sptk .L_bn_mul_words_ctop };;
375.L_bn_mul_words_cend:
376
377 getf.sig r8=f41 // the return value
378
379#endif // XMA_TEMPTATION
380
381{ .mii; nop.m 0x0
382 mov pr=r9,0x1ffff
383 mov ar.lc=r3 }
384{ .mfb; rum 1<<5 // clear um.mfh
385 nop.f 0x0
386 br.ret.sptk.many b0 };;
387.endp bn_mul_words#
388#endif
389
390#if 1
391//
392// BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w)
393//
394.global bn_mul_add_words#
395.proc bn_mul_add_words#
396.align 64
397.skip 48 // makes the loop body aligned at 64-byte boundary
398bn_mul_add_words:
399 .prologue
400 .fframe 0
401 .save ar.pfs,r2
402 .save ar.lc,r3
403 .save pr,r9
404{ .mmi; alloc r2=ar.pfs,4,4,0,8
405 cmp4.le p6,p0=r34,r0
406 mov r3=ar.lc };;
407{ .mib; mov r8=r0 // return value
408 sub r10=r34,r0,1
409(p6) br.ret.spnt.many b0 };;
410
411 .body
412{ .mib; setf.sig f8=r35 // w
413 mov r9=pr
414 brp.loop.imp .L_bn_mul_add_words_ctop,.L_bn_mul_add_words_cend-16
415 }
416{ .mmi; ADDP r14=0,r32 // rp
417 ADDP r15=0,r33 // ap
418 mov ar.lc=r10 }
419{ .mii; ADDP r16=0,r32 // rp copy
420 mov pr.rot=0x2001<<16
421 // ------^----- serves as (p40) at first (p27)
422 mov ar.ec=11 };;
423
424// This loop spins in 3*(n+10) ticks on Itanium and in 2*(n+10) on
425// Itanium 2. Yes, unlike previous versions it scales:-) Previous
426// version was peforming *all* additions in IALU and was starving
427// for those even on Itanium 2. In this version one addition is
428// moved to FPU and is folded with multiplication. This is at cost
429// of propogating the result from previous call to this subroutine
430// to L2 cache... In other words negligible even for shorter keys.
431// *Overall* performance improvement [over previous version] varies
432// from 11 to 22 percent depending on key length.
433.L_bn_mul_add_words_ctop:
434.pred.rel "mutex",p40,p42
435{ .mfi; (p23) getf.sig r36=f45 // low
436 (p20) xma.lu f42=f36,f8,f50 // low
437 (p40) add r39=r39,r35 } // (p27)
438{ .mfi; (p16) ldf8 f32=[r15],8 // *(ap++)
439 (p20) xma.hu f36=f36,f8,f50 // high
440 (p42) add r39=r39,r35,1 };; // (p27)
441{ .mmi; (p24) getf.sig r32=f40 // high
442 (p16) ldf8 f46=[r16],8 // *(rp1++)
443 (p40) cmp.ltu p41,p39=r39,r35 } // (p27)
444{ .mib; (p26) st8 [r14]=r39,8 // *(rp2++)
445 (p42) cmp.leu p41,p39=r39,r35 // (p27)
446 br.ctop.sptk .L_bn_mul_add_words_ctop};;
447.L_bn_mul_add_words_cend:
448
449{ .mmi; .pred.rel "mutex",p40,p42
450(p40) add r8=r35,r0
451(p42) add r8=r35,r0,1
452 mov pr=r9,0x1ffff }
453{ .mib; rum 1<<5 // clear um.mfh
454 mov ar.lc=r3
455 br.ret.sptk.many b0 };;
456.endp bn_mul_add_words#
457#endif
458
459#if 1
460//
461// void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num)
462//
463.global bn_sqr_words#
464.proc bn_sqr_words#
465.align 64
466.skip 32 // makes the loop body aligned at 64-byte boundary
467bn_sqr_words:
468 .prologue
469 .fframe 0
470 .save ar.pfs,r2
471{ .mii; alloc r2=ar.pfs,3,0,0,0
472 sxt4 r34=r34 };;
473{ .mii; cmp.le p6,p0=r34,r0
474 mov r8=r0 } // return value
475{ .mfb; ADDP r32=0,r32
476 nop.f 0x0
477(p6) br.ret.spnt.many b0 };;
478
479 .save ar.lc,r3
480{ .mii; sub r10=r34,r0,1
481 mov r3=ar.lc
482 mov r9=pr };;
483
484 .body
485{ .mib; ADDP r33=0,r33
486 mov pr.rot=1<<16
487 brp.loop.imp .L_bn_sqr_words_ctop,.L_bn_sqr_words_cend-16
488 }
489{ .mii; add r34=8,r32
490 mov ar.lc=r10
491 mov ar.ec=18 };;
492
493// 2*(n+17) on Itanium, (n+17) on "wider" IA-64 implementations. It's
494// possible to compress the epilogue (I'm getting tired to write this
495// comment over and over) and get down to 2*n+16 at the cost of
496// scalability. The decision will very likely be reconsidered after the
497// benchmark program is profiled. I.e. if perfomance gain on Itanium
498// will appear larger than loss on "wider" IA-64, then the loop should
499// be explicitely split and the epilogue compressed.
500.L_bn_sqr_words_ctop:
501{ .mfi; (p16) ldf8 f32=[r33],8
502 (p25) xmpy.lu f42=f41,f41
503 (p0) nop.i 0x0 }
504{ .mib; (p33) stf8 [r32]=f50,16
505 (p0) nop.i 0x0
506 (p0) nop.b 0x0 }
507{ .mfi; (p0) nop.m 0x0
508 (p25) xmpy.hu f52=f41,f41
509 (p0) nop.i 0x0 }
510{ .mib; (p33) stf8 [r34]=f60,16
511 (p0) nop.i 0x0
512 br.ctop.sptk .L_bn_sqr_words_ctop };;
513.L_bn_sqr_words_cend:
514
515{ .mii; nop.m 0x0
516 mov pr=r9,0x1ffff
517 mov ar.lc=r3 }
518{ .mfb; rum 1<<5 // clear um.mfh
519 nop.f 0x0
520 br.ret.sptk.many b0 };;
521.endp bn_sqr_words#
522#endif
523
524#if 1
525// Apparently we win nothing by implementing special bn_sqr_comba8.
526// Yes, it is possible to reduce the number of multiplications by
527// almost factor of two, but then the amount of additions would
528// increase by factor of two (as we would have to perform those
529// otherwise performed by xma ourselves). Normally we would trade
530// anyway as multiplications are way more expensive, but not this
531// time... Multiplication kernel is fully pipelined and as we drain
532// one 128-bit multiplication result per clock cycle multiplications
533// are effectively as inexpensive as additions. Special implementation
534// might become of interest for "wider" IA-64 implementation as you'll
535// be able to get through the multiplication phase faster (there won't
536// be any stall issues as discussed in the commentary section below and
537// you therefore will be able to employ all 4 FP units)... But these
538// Itanium days it's simply too hard to justify the effort so I just
539// drop down to bn_mul_comba8 code:-)
540//
541// void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a)
542//
543.global bn_sqr_comba8#
544.proc bn_sqr_comba8#
545.align 64
546bn_sqr_comba8:
547 .prologue
548 .fframe 0
549 .save ar.pfs,r2
550#if defined(_HPUX_SOURCE) && !defined(_LP64)
551{ .mii; alloc r2=ar.pfs,2,1,0,0
552 addp4 r33=0,r33
553 addp4 r32=0,r32 };;
554{ .mii;
555#else
556{ .mii; alloc r2=ar.pfs,2,1,0,0
557#endif
558 mov r34=r33
559 add r14=8,r33 };;
560 .body
561{ .mii; add r17=8,r34
562 add r15=16,r33
563 add r18=16,r34 }
564{ .mfb; add r16=24,r33
565 br .L_cheat_entry_point8 };;
566.endp bn_sqr_comba8#
567#endif
568
569#if 1
570// I've estimated this routine to run in ~120 ticks, but in reality
571// (i.e. according to ar.itc) it takes ~160 ticks. Are those extra
572// cycles consumed for instructions fetch? Or did I misinterpret some
573// clause in Itanium µ-architecture manual? Comments are welcomed and
574// highly appreciated.
575//
576// On Itanium 2 it takes ~190 ticks. This is because of stalls on
577// result from getf.sig. I do nothing about it at this point for
578// reasons depicted below.
579//
580// However! It should be noted that even 160 ticks is darn good result
581// as it's over 10 (yes, ten, spelled as t-e-n) times faster than the
582// C version (compiled with gcc with inline assembler). I really
583// kicked compiler's butt here, didn't I? Yeah! This brings us to the
584// following statement. It's damn shame that this routine isn't called
585// very often nowadays! According to the profiler most CPU time is
586// consumed by bn_mul_add_words called from BN_from_montgomery. In
587// order to estimate what we're missing, I've compared the performance
588// of this routine against "traditional" implementation, i.e. against
589// following routine:
590//
591// void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
592// { r[ 8]=bn_mul_words( &(r[0]),a,8,b[0]);
593// r[ 9]=bn_mul_add_words(&(r[1]),a,8,b[1]);
594// r[10]=bn_mul_add_words(&(r[2]),a,8,b[2]);
595// r[11]=bn_mul_add_words(&(r[3]),a,8,b[3]);
596// r[12]=bn_mul_add_words(&(r[4]),a,8,b[4]);
597// r[13]=bn_mul_add_words(&(r[5]),a,8,b[5]);
598// r[14]=bn_mul_add_words(&(r[6]),a,8,b[6]);
599// r[15]=bn_mul_add_words(&(r[7]),a,8,b[7]);
600// }
601//
602// The one below is over 8 times faster than the one above:-( Even
603// more reasons to "combafy" bn_mul_add_mont...
604//
605// And yes, this routine really made me wish there were an optimizing
606// assembler! It also feels like it deserves a dedication.
607//
608// To my wife for being there and to my kids...
609//
610// void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
611//
612#define carry1 r14
613#define carry2 r15
614#define carry3 r34
615.global bn_mul_comba8#
616.proc bn_mul_comba8#
617.align 64
618bn_mul_comba8:
619 .prologue
620 .fframe 0
621 .save ar.pfs,r2
622#if defined(_HPUX_SOURCE) && !defined(_LP64)
623{ .mii; alloc r2=ar.pfs,3,0,0,0
624 addp4 r33=0,r33
625 addp4 r34=0,r34 };;
626{ .mii; addp4 r32=0,r32
627#else
628{ .mii; alloc r2=ar.pfs,3,0,0,0
629#endif
630 add r14=8,r33
631 add r17=8,r34 }
632 .body
633{ .mii; add r15=16,r33
634 add r18=16,r34
635 add r16=24,r33 }
636.L_cheat_entry_point8:
637{ .mmi; add r19=24,r34
638
639 ldf8 f32=[r33],32 };;
640
641{ .mmi; ldf8 f120=[r34],32
642 ldf8 f121=[r17],32 }
643{ .mmi; ldf8 f122=[r18],32
644 ldf8 f123=[r19],32 };;
645{ .mmi; ldf8 f124=[r34]
646 ldf8 f125=[r17] }
647{ .mmi; ldf8 f126=[r18]
648 ldf8 f127=[r19] }
649
650{ .mmi; ldf8 f33=[r14],32
651 ldf8 f34=[r15],32 }
652{ .mmi; ldf8 f35=[r16],32;;
653 ldf8 f36=[r33] }
654{ .mmi; ldf8 f37=[r14]
655 ldf8 f38=[r15] }
656{ .mfi; ldf8 f39=[r16]
657// -------\ Entering multiplier's heaven /-------
658// ------------\ /------------
659// -----------------\ /-----------------
660// ----------------------\/----------------------
661 xma.hu f41=f32,f120,f0 }
662{ .mfi; xma.lu f40=f32,f120,f0 };; // (*)
663{ .mfi; xma.hu f51=f32,f121,f0 }
664{ .mfi; xma.lu f50=f32,f121,f0 };;
665{ .mfi; xma.hu f61=f32,f122,f0 }
666{ .mfi; xma.lu f60=f32,f122,f0 };;
667{ .mfi; xma.hu f71=f32,f123,f0 }
668{ .mfi; xma.lu f70=f32,f123,f0 };;
669{ .mfi; xma.hu f81=f32,f124,f0 }
670{ .mfi; xma.lu f80=f32,f124,f0 };;
671{ .mfi; xma.hu f91=f32,f125,f0 }
672{ .mfi; xma.lu f90=f32,f125,f0 };;
673{ .mfi; xma.hu f101=f32,f126,f0 }
674{ .mfi; xma.lu f100=f32,f126,f0 };;
675{ .mfi; xma.hu f111=f32,f127,f0 }
676{ .mfi; xma.lu f110=f32,f127,f0 };;//
677// (*) You can argue that splitting at every second bundle would
678// prevent "wider" IA-64 implementations from achieving the peak
679// performance. Well, not really... The catch is that if you
680// intend to keep 4 FP units busy by splitting at every fourth
681// bundle and thus perform these 16 multiplications in 4 ticks,
682// the first bundle *below* would stall because the result from
683// the first xma bundle *above* won't be available for another 3
684// ticks (if not more, being an optimist, I assume that "wider"
685// implementation will have same latency:-). This stall will hold
686// you back and the performance would be as if every second bundle
687// were split *anyway*...
688{ .mfi; getf.sig r16=f40
689 xma.hu f42=f33,f120,f41
690 add r33=8,r32 }
691{ .mfi; xma.lu f41=f33,f120,f41 };;
692{ .mfi; getf.sig r24=f50
693 xma.hu f52=f33,f121,f51 }
694{ .mfi; xma.lu f51=f33,f121,f51 };;
695{ .mfi; st8 [r32]=r16,16
696 xma.hu f62=f33,f122,f61 }
697{ .mfi; xma.lu f61=f33,f122,f61 };;
698{ .mfi; xma.hu f72=f33,f123,f71 }
699{ .mfi; xma.lu f71=f33,f123,f71 };;
700{ .mfi; xma.hu f82=f33,f124,f81 }
701{ .mfi; xma.lu f81=f33,f124,f81 };;
702{ .mfi; xma.hu f92=f33,f125,f91 }
703{ .mfi; xma.lu f91=f33,f125,f91 };;
704{ .mfi; xma.hu f102=f33,f126,f101 }
705{ .mfi; xma.lu f101=f33,f126,f101 };;
706{ .mfi; xma.hu f112=f33,f127,f111 }
707{ .mfi; xma.lu f111=f33,f127,f111 };;//
708//-------------------------------------------------//
709{ .mfi; getf.sig r25=f41
710 xma.hu f43=f34,f120,f42 }
711{ .mfi; xma.lu f42=f34,f120,f42 };;
712{ .mfi; getf.sig r16=f60
713 xma.hu f53=f34,f121,f52 }
714{ .mfi; xma.lu f52=f34,f121,f52 };;
715{ .mfi; getf.sig r17=f51
716 xma.hu f63=f34,f122,f62
717 add r25=r25,r24 }
718{ .mfi; xma.lu f62=f34,f122,f62
719 mov carry1=0 };;
720{ .mfi; cmp.ltu p6,p0=r25,r24
721 xma.hu f73=f34,f123,f72 }
722{ .mfi; xma.lu f72=f34,f123,f72 };;
723{ .mfi; st8 [r33]=r25,16
724 xma.hu f83=f34,f124,f82
725(p6) add carry1=1,carry1 }
726{ .mfi; xma.lu f82=f34,f124,f82 };;
727{ .mfi; xma.hu f93=f34,f125,f92 }
728{ .mfi; xma.lu f92=f34,f125,f92 };;
729{ .mfi; xma.hu f103=f34,f126,f102 }
730{ .mfi; xma.lu f102=f34,f126,f102 };;
731{ .mfi; xma.hu f113=f34,f127,f112 }
732{ .mfi; xma.lu f112=f34,f127,f112 };;//
733//-------------------------------------------------//
734{ .mfi; getf.sig r18=f42
735 xma.hu f44=f35,f120,f43
736 add r17=r17,r16 }
737{ .mfi; xma.lu f43=f35,f120,f43 };;
738{ .mfi; getf.sig r24=f70
739 xma.hu f54=f35,f121,f53 }
740{ .mfi; mov carry2=0
741 xma.lu f53=f35,f121,f53 };;
742{ .mfi; getf.sig r25=f61
743 xma.hu f64=f35,f122,f63
744 cmp.ltu p7,p0=r17,r16 }
745{ .mfi; add r18=r18,r17
746 xma.lu f63=f35,f122,f63 };;
747{ .mfi; getf.sig r26=f52
748 xma.hu f74=f35,f123,f73
749(p7) add carry2=1,carry2 }
750{ .mfi; cmp.ltu p7,p0=r18,r17
751 xma.lu f73=f35,f123,f73
752 add r18=r18,carry1 };;
753{ .mfi;
754 xma.hu f84=f35,f124,f83
755(p7) add carry2=1,carry2 }
756{ .mfi; cmp.ltu p7,p0=r18,carry1
757 xma.lu f83=f35,f124,f83 };;
758{ .mfi; st8 [r32]=r18,16
759 xma.hu f94=f35,f125,f93
760(p7) add carry2=1,carry2 }
761{ .mfi; xma.lu f93=f35,f125,f93 };;
762{ .mfi; xma.hu f104=f35,f126,f103 }
763{ .mfi; xma.lu f103=f35,f126,f103 };;
764{ .mfi; xma.hu f114=f35,f127,f113 }
765{ .mfi; mov carry1=0
766 xma.lu f113=f35,f127,f113
767 add r25=r25,r24 };;//
768//-------------------------------------------------//
769{ .mfi; getf.sig r27=f43
770 xma.hu f45=f36,f120,f44
771 cmp.ltu p6,p0=r25,r24 }
772{ .mfi; xma.lu f44=f36,f120,f44
773 add r26=r26,r25 };;
774{ .mfi; getf.sig r16=f80
775 xma.hu f55=f36,f121,f54
776(p6) add carry1=1,carry1 }
777{ .mfi; xma.lu f54=f36,f121,f54 };;
778{ .mfi; getf.sig r17=f71
779 xma.hu f65=f36,f122,f64
780 cmp.ltu p6,p0=r26,r25 }
781{ .mfi; xma.lu f64=f36,f122,f64
782 add r27=r27,r26 };;
783{ .mfi; getf.sig r18=f62
784 xma.hu f75=f36,f123,f74
785(p6) add carry1=1,carry1 }
786{ .mfi; cmp.ltu p6,p0=r27,r26
787 xma.lu f74=f36,f123,f74
788 add r27=r27,carry2 };;
789{ .mfi; getf.sig r19=f53
790 xma.hu f85=f36,f124,f84
791(p6) add carry1=1,carry1 }
792{ .mfi; xma.lu f84=f36,f124,f84
793 cmp.ltu p6,p0=r27,carry2 };;
794{ .mfi; st8 [r33]=r27,16
795 xma.hu f95=f36,f125,f94
796(p6) add carry1=1,carry1 }
797{ .mfi; xma.lu f94=f36,f125,f94 };;
798{ .mfi; xma.hu f105=f36,f126,f104 }
799{ .mfi; mov carry2=0
800 xma.lu f104=f36,f126,f104
801 add r17=r17,r16 };;
802{ .mfi; xma.hu f115=f36,f127,f114
803 cmp.ltu p7,p0=r17,r16 }
804{ .mfi; xma.lu f114=f36,f127,f114
805 add r18=r18,r17 };;//
806//-------------------------------------------------//
807{ .mfi; getf.sig r20=f44
808 xma.hu f46=f37,f120,f45
809(p7) add carry2=1,carry2 }
810{ .mfi; cmp.ltu p7,p0=r18,r17
811 xma.lu f45=f37,f120,f45
812 add r19=r19,r18 };;
813{ .mfi; getf.sig r24=f90
814 xma.hu f56=f37,f121,f55 }
815{ .mfi; xma.lu f55=f37,f121,f55 };;
816{ .mfi; getf.sig r25=f81
817 xma.hu f66=f37,f122,f65
818(p7) add carry2=1,carry2 }
819{ .mfi; cmp.ltu p7,p0=r19,r18
820 xma.lu f65=f37,f122,f65
821 add r20=r20,r19 };;
822{ .mfi; getf.sig r26=f72
823 xma.hu f76=f37,f123,f75
824(p7) add carry2=1,carry2 }
825{ .mfi; cmp.ltu p7,p0=r20,r19
826 xma.lu f75=f37,f123,f75
827 add r20=r20,carry1 };;
828{ .mfi; getf.sig r27=f63
829 xma.hu f86=f37,f124,f85
830(p7) add carry2=1,carry2 }
831{ .mfi; xma.lu f85=f37,f124,f85
832 cmp.ltu p7,p0=r20,carry1 };;
833{ .mfi; getf.sig r28=f54
834 xma.hu f96=f37,f125,f95
835(p7) add carry2=1,carry2 }
836{ .mfi; st8 [r32]=r20,16
837 xma.lu f95=f37,f125,f95 };;
838{ .mfi; xma.hu f106=f37,f126,f105 }
839{ .mfi; mov carry1=0
840 xma.lu f105=f37,f126,f105
841 add r25=r25,r24 };;
842{ .mfi; xma.hu f116=f37,f127,f115
843 cmp.ltu p6,p0=r25,r24 }
844{ .mfi; xma.lu f115=f37,f127,f115
845 add r26=r26,r25 };;//
846//-------------------------------------------------//
847{ .mfi; getf.sig r29=f45
848 xma.hu f47=f38,f120,f46
849(p6) add carry1=1,carry1 }
850{ .mfi; cmp.ltu p6,p0=r26,r25
851 xma.lu f46=f38,f120,f46
852 add r27=r27,r26 };;
853{ .mfi; getf.sig r16=f100
854 xma.hu f57=f38,f121,f56
855(p6) add carry1=1,carry1 }
856{ .mfi; cmp.ltu p6,p0=r27,r26
857 xma.lu f56=f38,f121,f56
858 add r28=r28,r27 };;
859{ .mfi; getf.sig r17=f91
860 xma.hu f67=f38,f122,f66
861(p6) add carry1=1,carry1 }
862{ .mfi; cmp.ltu p6,p0=r28,r27
863 xma.lu f66=f38,f122,f66
864 add r29=r29,r28 };;
865{ .mfi; getf.sig r18=f82
866 xma.hu f77=f38,f123,f76
867(p6) add carry1=1,carry1 }
868{ .mfi; cmp.ltu p6,p0=r29,r28
869 xma.lu f76=f38,f123,f76
870 add r29=r29,carry2 };;
871{ .mfi; getf.sig r19=f73
872 xma.hu f87=f38,f124,f86
873(p6) add carry1=1,carry1 }
874{ .mfi; xma.lu f86=f38,f124,f86
875 cmp.ltu p6,p0=r29,carry2 };;
876{ .mfi; getf.sig r20=f64
877 xma.hu f97=f38,f125,f96
878(p6) add carry1=1,carry1 }
879{ .mfi; st8 [r33]=r29,16
880 xma.lu f96=f38,f125,f96 };;
881{ .mfi; getf.sig r21=f55
882 xma.hu f107=f38,f126,f106 }
883{ .mfi; mov carry2=0
884 xma.lu f106=f38,f126,f106
885 add r17=r17,r16 };;
886{ .mfi; xma.hu f117=f38,f127,f116
887 cmp.ltu p7,p0=r17,r16 }
888{ .mfi; xma.lu f116=f38,f127,f116
889 add r18=r18,r17 };;//
890//-------------------------------------------------//
891{ .mfi; getf.sig r22=f46
892 xma.hu f48=f39,f120,f47
893(p7) add carry2=1,carry2 }
894{ .mfi; cmp.ltu p7,p0=r18,r17
895 xma.lu f47=f39,f120,f47
896 add r19=r19,r18 };;
897{ .mfi; getf.sig r24=f110
898 xma.hu f58=f39,f121,f57
899(p7) add carry2=1,carry2 }
900{ .mfi; cmp.ltu p7,p0=r19,r18
901 xma.lu f57=f39,f121,f57
902 add r20=r20,r19 };;
903{ .mfi; getf.sig r25=f101
904 xma.hu f68=f39,f122,f67
905(p7) add carry2=1,carry2 }
906{ .mfi; cmp.ltu p7,p0=r20,r19
907 xma.lu f67=f39,f122,f67
908 add r21=r21,r20 };;
909{ .mfi; getf.sig r26=f92
910 xma.hu f78=f39,f123,f77
911(p7) add carry2=1,carry2 }
912{ .mfi; cmp.ltu p7,p0=r21,r20
913 xma.lu f77=f39,f123,f77
914 add r22=r22,r21 };;
915{ .mfi; getf.sig r27=f83
916 xma.hu f88=f39,f124,f87
917(p7) add carry2=1,carry2 }
918{ .mfi; cmp.ltu p7,p0=r22,r21
919 xma.lu f87=f39,f124,f87
920 add r22=r22,carry1 };;
921{ .mfi; getf.sig r28=f74
922 xma.hu f98=f39,f125,f97
923(p7) add carry2=1,carry2 }
924{ .mfi; xma.lu f97=f39,f125,f97
925 cmp.ltu p7,p0=r22,carry1 };;
926{ .mfi; getf.sig r29=f65
927 xma.hu f108=f39,f126,f107
928(p7) add carry2=1,carry2 }
929{ .mfi; st8 [r32]=r22,16
930 xma.lu f107=f39,f126,f107 };;
931{ .mfi; getf.sig r30=f56
932 xma.hu f118=f39,f127,f117 }
933{ .mfi; xma.lu f117=f39,f127,f117 };;//
934//-------------------------------------------------//
935// Leaving muliplier's heaven... Quite a ride, huh?
936
937{ .mii; getf.sig r31=f47
938 add r25=r25,r24
939 mov carry1=0 };;
940{ .mii; getf.sig r16=f111
941 cmp.ltu p6,p0=r25,r24
942 add r26=r26,r25 };;
943{ .mfb; getf.sig r17=f102 }
944{ .mii;
945(p6) add carry1=1,carry1
946 cmp.ltu p6,p0=r26,r25
947 add r27=r27,r26 };;
948{ .mfb; nop.m 0x0 }
949{ .mii;
950(p6) add carry1=1,carry1
951 cmp.ltu p6,p0=r27,r26
952 add r28=r28,r27 };;
953{ .mii; getf.sig r18=f93
954 add r17=r17,r16
955 mov carry3=0 }
956{ .mii;
957(p6) add carry1=1,carry1
958 cmp.ltu p6,p0=r28,r27
959 add r29=r29,r28 };;
960{ .mii; getf.sig r19=f84
961 cmp.ltu p7,p0=r17,r16 }
962{ .mii;
963(p6) add carry1=1,carry1
964 cmp.ltu p6,p0=r29,r28
965 add r30=r30,r29 };;
966{ .mii; getf.sig r20=f75
967 add r18=r18,r17 }
968{ .mii;
969(p6) add carry1=1,carry1
970 cmp.ltu p6,p0=r30,r29
971 add r31=r31,r30 };;
972{ .mfb; getf.sig r21=f66 }
973{ .mii; (p7) add carry3=1,carry3
974 cmp.ltu p7,p0=r18,r17
975 add r19=r19,r18 }
976{ .mfb; nop.m 0x0 }
977{ .mii;
978(p6) add carry1=1,carry1
979 cmp.ltu p6,p0=r31,r30
980 add r31=r31,carry2 };;
981{ .mfb; getf.sig r22=f57 }
982{ .mii; (p7) add carry3=1,carry3
983 cmp.ltu p7,p0=r19,r18
984 add r20=r20,r19 }
985{ .mfb; nop.m 0x0 }
986{ .mii;
987(p6) add carry1=1,carry1
988 cmp.ltu p6,p0=r31,carry2 };;
989{ .mfb; getf.sig r23=f48 }
990{ .mii; (p7) add carry3=1,carry3
991 cmp.ltu p7,p0=r20,r19
992 add r21=r21,r20 }
993{ .mii;
994(p6) add carry1=1,carry1 }
995{ .mfb; st8 [r33]=r31,16 };;
996
997{ .mfb; getf.sig r24=f112 }
998{ .mii; (p7) add carry3=1,carry3
999 cmp.ltu p7,p0=r21,r20
1000 add r22=r22,r21 };;
1001{ .mfb; getf.sig r25=f103 }
1002{ .mii; (p7) add carry3=1,carry3
1003 cmp.ltu p7,p0=r22,r21
1004 add r23=r23,r22 };;
1005{ .mfb; getf.sig r26=f94 }
1006{ .mii; (p7) add carry3=1,carry3
1007 cmp.ltu p7,p0=r23,r22
1008 add r23=r23,carry1 };;
1009{ .mfb; getf.sig r27=f85 }
1010{ .mii; (p7) add carry3=1,carry3
1011 cmp.ltu p7,p8=r23,carry1};;
1012{ .mii; getf.sig r28=f76
1013 add r25=r25,r24
1014 mov carry1=0 }
1015{ .mii; st8 [r32]=r23,16
1016 (p7) add carry2=1,carry3
1017 (p8) add carry2=0,carry3 };;
1018
1019{ .mfb; nop.m 0x0 }
1020{ .mii; getf.sig r29=f67
1021 cmp.ltu p6,p0=r25,r24
1022 add r26=r26,r25 };;
1023{ .mfb; getf.sig r30=f58 }
1024{ .mii;
1025(p6) add carry1=1,carry1
1026 cmp.ltu p6,p0=r26,r25
1027 add r27=r27,r26 };;
1028{ .mfb; getf.sig r16=f113 }
1029{ .mii;
1030(p6) add carry1=1,carry1
1031 cmp.ltu p6,p0=r27,r26
1032 add r28=r28,r27 };;
1033{ .mfb; getf.sig r17=f104 }
1034{ .mii;
1035(p6) add carry1=1,carry1
1036 cmp.ltu p6,p0=r28,r27
1037 add r29=r29,r28 };;
1038{ .mfb; getf.sig r18=f95 }
1039{ .mii;
1040(p6) add carry1=1,carry1
1041 cmp.ltu p6,p0=r29,r28
1042 add r30=r30,r29 };;
1043{ .mii; getf.sig r19=f86
1044 add r17=r17,r16
1045 mov carry3=0 }
1046{ .mii;
1047(p6) add carry1=1,carry1
1048 cmp.ltu p6,p0=r30,r29
1049 add r30=r30,carry2 };;
1050{ .mii; getf.sig r20=f77
1051 cmp.ltu p7,p0=r17,r16
1052 add r18=r18,r17 }
1053{ .mii;
1054(p6) add carry1=1,carry1
1055 cmp.ltu p6,p0=r30,carry2 };;
1056{ .mfb; getf.sig r21=f68 }
1057{ .mii; st8 [r33]=r30,16
1058(p6) add carry1=1,carry1 };;
1059
1060{ .mfb; getf.sig r24=f114 }
1061{ .mii; (p7) add carry3=1,carry3
1062 cmp.ltu p7,p0=r18,r17
1063 add r19=r19,r18 };;
1064{ .mfb; getf.sig r25=f105 }
1065{ .mii; (p7) add carry3=1,carry3
1066 cmp.ltu p7,p0=r19,r18
1067 add r20=r20,r19 };;
1068{ .mfb; getf.sig r26=f96 }
1069{ .mii; (p7) add carry3=1,carry3
1070 cmp.ltu p7,p0=r20,r19
1071 add r21=r21,r20 };;
1072{ .mfb; getf.sig r27=f87 }
1073{ .mii; (p7) add carry3=1,carry3
1074 cmp.ltu p7,p0=r21,r20
1075 add r21=r21,carry1 };;
1076{ .mib; getf.sig r28=f78
1077 add r25=r25,r24 }
1078{ .mib; (p7) add carry3=1,carry3
1079 cmp.ltu p7,p8=r21,carry1};;
1080{ .mii; st8 [r32]=r21,16
1081 (p7) add carry2=1,carry3
1082 (p8) add carry2=0,carry3 }
1083
1084{ .mii; mov carry1=0
1085 cmp.ltu p6,p0=r25,r24
1086 add r26=r26,r25 };;
1087{ .mfb; getf.sig r16=f115 }
1088{ .mii;
1089(p6) add carry1=1,carry1
1090 cmp.ltu p6,p0=r26,r25
1091 add r27=r27,r26 };;
1092{ .mfb; getf.sig r17=f106 }
1093{ .mii;
1094(p6) add carry1=1,carry1
1095 cmp.ltu p6,p0=r27,r26
1096 add r28=r28,r27 };;
1097{ .mfb; getf.sig r18=f97 }
1098{ .mii;
1099(p6) add carry1=1,carry1
1100 cmp.ltu p6,p0=r28,r27
1101 add r28=r28,carry2 };;
1102{ .mib; getf.sig r19=f88
1103 add r17=r17,r16 }
1104{ .mib;
1105(p6) add carry1=1,carry1
1106 cmp.ltu p6,p0=r28,carry2 };;
1107{ .mii; st8 [r33]=r28,16
1108(p6) add carry1=1,carry1 }
1109
1110{ .mii; mov carry2=0
1111 cmp.ltu p7,p0=r17,r16
1112 add r18=r18,r17 };;
1113{ .mfb; getf.sig r24=f116 }
1114{ .mii; (p7) add carry2=1,carry2
1115 cmp.ltu p7,p0=r18,r17
1116 add r19=r19,r18 };;
1117{ .mfb; getf.sig r25=f107 }
1118{ .mii; (p7) add carry2=1,carry2
1119 cmp.ltu p7,p0=r19,r18
1120 add r19=r19,carry1 };;
1121{ .mfb; getf.sig r26=f98 }
1122{ .mii; (p7) add carry2=1,carry2
1123 cmp.ltu p7,p0=r19,carry1};;
1124{ .mii; st8 [r32]=r19,16
1125 (p7) add carry2=1,carry2 }
1126
1127{ .mfb; add r25=r25,r24 };;
1128
1129{ .mfb; getf.sig r16=f117 }
1130{ .mii; mov carry1=0
1131 cmp.ltu p6,p0=r25,r24
1132 add r26=r26,r25 };;
1133{ .mfb; getf.sig r17=f108 }
1134{ .mii;
1135(p6) add carry1=1,carry1
1136 cmp.ltu p6,p0=r26,r25
1137 add r26=r26,carry2 };;
1138{ .mfb; nop.m 0x0 }
1139{ .mii;
1140(p6) add carry1=1,carry1
1141 cmp.ltu p6,p0=r26,carry2 };;
1142{ .mii; st8 [r33]=r26,16
1143(p6) add carry1=1,carry1 }
1144
1145{ .mfb; add r17=r17,r16 };;
1146{ .mfb; getf.sig r24=f118 }
1147{ .mii; mov carry2=0
1148 cmp.ltu p7,p0=r17,r16
1149 add r17=r17,carry1 };;
1150{ .mii; (p7) add carry2=1,carry2
1151 cmp.ltu p7,p0=r17,carry1};;
1152{ .mii; st8 [r32]=r17
1153 (p7) add carry2=1,carry2 };;
1154{ .mfb; add r24=r24,carry2 };;
1155{ .mib; st8 [r33]=r24 }
1156
1157{ .mib; rum 1<<5 // clear um.mfh
1158 br.ret.sptk.many b0 };;
1159.endp bn_mul_comba8#
1160#undef carry3
1161#undef carry2
1162#undef carry1
1163#endif
1164
1165#if 1
1166// It's possible to make it faster (see comment to bn_sqr_comba8), but
1167// I reckon it doesn't worth the effort. Basically because the routine
1168// (actually both of them) practically never called... So I just play
1169// same trick as with bn_sqr_comba8.
1170//
1171// void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a)
1172//
1173.global bn_sqr_comba4#
1174.proc bn_sqr_comba4#
1175.align 64
1176bn_sqr_comba4:
1177 .prologue
1178 .fframe 0
1179 .save ar.pfs,r2
1180#if defined(_HPUX_SOURCE) && !defined(_LP64)
1181{ .mii; alloc r2=ar.pfs,2,1,0,0
1182 addp4 r32=0,r32
1183 addp4 r33=0,r33 };;
1184{ .mii;
1185#else
1186{ .mii; alloc r2=ar.pfs,2,1,0,0
1187#endif
1188 mov r34=r33
1189 add r14=8,r33 };;
1190 .body
1191{ .mii; add r17=8,r34
1192 add r15=16,r33
1193 add r18=16,r34 }
1194{ .mfb; add r16=24,r33
1195 br .L_cheat_entry_point4 };;
1196.endp bn_sqr_comba4#
1197#endif
1198
1199#if 1
1200// Runs in ~115 cycles and ~4.5 times faster than C. Well, whatever...
1201//
1202// void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
1203//
1204#define carry1 r14
1205#define carry2 r15
1206.global bn_mul_comba4#
1207.proc bn_mul_comba4#
1208.align 64
1209bn_mul_comba4:
1210 .prologue
1211 .fframe 0
1212 .save ar.pfs,r2
1213#if defined(_HPUX_SOURCE) && !defined(_LP64)
1214{ .mii; alloc r2=ar.pfs,3,0,0,0
1215 addp4 r33=0,r33
1216 addp4 r34=0,r34 };;
1217{ .mii; addp4 r32=0,r32
1218#else
1219{ .mii; alloc r2=ar.pfs,3,0,0,0
1220#endif
1221 add r14=8,r33
1222 add r17=8,r34 }
1223 .body
1224{ .mii; add r15=16,r33
1225 add r18=16,r34
1226 add r16=24,r33 };;
1227.L_cheat_entry_point4:
1228{ .mmi; add r19=24,r34
1229
1230 ldf8 f32=[r33] }
1231
1232{ .mmi; ldf8 f120=[r34]
1233 ldf8 f121=[r17] };;
1234{ .mmi; ldf8 f122=[r18]
1235 ldf8 f123=[r19] }
1236
1237{ .mmi; ldf8 f33=[r14]
1238 ldf8 f34=[r15] }
1239{ .mfi; ldf8 f35=[r16]
1240
1241 xma.hu f41=f32,f120,f0 }
1242{ .mfi; xma.lu f40=f32,f120,f0 };;
1243{ .mfi; xma.hu f51=f32,f121,f0 }
1244{ .mfi; xma.lu f50=f32,f121,f0 };;
1245{ .mfi; xma.hu f61=f32,f122,f0 }
1246{ .mfi; xma.lu f60=f32,f122,f0 };;
1247{ .mfi; xma.hu f71=f32,f123,f0 }
1248{ .mfi; xma.lu f70=f32,f123,f0 };;//
1249// Major stall takes place here, and 3 more places below. Result from
1250// first xma is not available for another 3 ticks.
1251{ .mfi; getf.sig r16=f40
1252 xma.hu f42=f33,f120,f41
1253 add r33=8,r32 }
1254{ .mfi; xma.lu f41=f33,f120,f41 };;
1255{ .mfi; getf.sig r24=f50
1256 xma.hu f52=f33,f121,f51 }
1257{ .mfi; xma.lu f51=f33,f121,f51 };;
1258{ .mfi; st8 [r32]=r16,16
1259 xma.hu f62=f33,f122,f61 }
1260{ .mfi; xma.lu f61=f33,f122,f61 };;
1261{ .mfi; xma.hu f72=f33,f123,f71 }
1262{ .mfi; xma.lu f71=f33,f123,f71 };;//
1263//-------------------------------------------------//
1264{ .mfi; getf.sig r25=f41
1265 xma.hu f43=f34,f120,f42 }
1266{ .mfi; xma.lu f42=f34,f120,f42 };;
1267{ .mfi; getf.sig r16=f60
1268 xma.hu f53=f34,f121,f52 }
1269{ .mfi; xma.lu f52=f34,f121,f52 };;
1270{ .mfi; getf.sig r17=f51
1271 xma.hu f63=f34,f122,f62
1272 add r25=r25,r24 }
1273{ .mfi; mov carry1=0
1274 xma.lu f62=f34,f122,f62 };;
1275{ .mfi; st8 [r33]=r25,16
1276 xma.hu f73=f34,f123,f72
1277 cmp.ltu p6,p0=r25,r24 }
1278{ .mfi; xma.lu f72=f34,f123,f72 };;//
1279//-------------------------------------------------//
1280{ .mfi; getf.sig r18=f42
1281 xma.hu f44=f35,f120,f43
1282(p6) add carry1=1,carry1 }
1283{ .mfi; add r17=r17,r16
1284 xma.lu f43=f35,f120,f43
1285 mov carry2=0 };;
1286{ .mfi; getf.sig r24=f70
1287 xma.hu f54=f35,f121,f53
1288 cmp.ltu p7,p0=r17,r16 }
1289{ .mfi; xma.lu f53=f35,f121,f53 };;
1290{ .mfi; getf.sig r25=f61
1291 xma.hu f64=f35,f122,f63
1292 add r18=r18,r17 }
1293{ .mfi; xma.lu f63=f35,f122,f63
1294(p7) add carry2=1,carry2 };;
1295{ .mfi; getf.sig r26=f52
1296 xma.hu f74=f35,f123,f73
1297 cmp.ltu p7,p0=r18,r17 }
1298{ .mfi; xma.lu f73=f35,f123,f73
1299 add r18=r18,carry1 };;
1300//-------------------------------------------------//
1301{ .mii; st8 [r32]=r18,16
1302(p7) add carry2=1,carry2
1303 cmp.ltu p7,p0=r18,carry1 };;
1304
1305{ .mfi; getf.sig r27=f43 // last major stall
1306(p7) add carry2=1,carry2 };;
1307{ .mii; getf.sig r16=f71
1308 add r25=r25,r24
1309 mov carry1=0 };;
1310{ .mii; getf.sig r17=f62
1311 cmp.ltu p6,p0=r25,r24
1312 add r26=r26,r25 };;
1313{ .mii;
1314(p6) add carry1=1,carry1
1315 cmp.ltu p6,p0=r26,r25
1316 add r27=r27,r26 };;
1317{ .mii;
1318(p6) add carry1=1,carry1
1319 cmp.ltu p6,p0=r27,r26
1320 add r27=r27,carry2 };;
1321{ .mii; getf.sig r18=f53
1322(p6) add carry1=1,carry1
1323 cmp.ltu p6,p0=r27,carry2 };;
1324{ .mfi; st8 [r33]=r27,16
1325(p6) add carry1=1,carry1 }
1326
1327{ .mii; getf.sig r19=f44
1328 add r17=r17,r16
1329 mov carry2=0 };;
1330{ .mii; getf.sig r24=f72
1331 cmp.ltu p7,p0=r17,r16
1332 add r18=r18,r17 };;
1333{ .mii; (p7) add carry2=1,carry2
1334 cmp.ltu p7,p0=r18,r17
1335 add r19=r19,r18 };;
1336{ .mii; (p7) add carry2=1,carry2
1337 cmp.ltu p7,p0=r19,r18
1338 add r19=r19,carry1 };;
1339{ .mii; getf.sig r25=f63
1340 (p7) add carry2=1,carry2
1341 cmp.ltu p7,p0=r19,carry1};;
1342{ .mii; st8 [r32]=r19,16
1343 (p7) add carry2=1,carry2 }
1344
1345{ .mii; getf.sig r26=f54
1346 add r25=r25,r24
1347 mov carry1=0 };;
1348{ .mii; getf.sig r16=f73
1349 cmp.ltu p6,p0=r25,r24
1350 add r26=r26,r25 };;
1351{ .mii;
1352(p6) add carry1=1,carry1
1353 cmp.ltu p6,p0=r26,r25
1354 add r26=r26,carry2 };;
1355{ .mii; getf.sig r17=f64
1356(p6) add carry1=1,carry1
1357 cmp.ltu p6,p0=r26,carry2 };;
1358{ .mii; st8 [r33]=r26,16
1359(p6) add carry1=1,carry1 }
1360
1361{ .mii; getf.sig r24=f74
1362 add r17=r17,r16
1363 mov carry2=0 };;
1364{ .mii; cmp.ltu p7,p0=r17,r16
1365 add r17=r17,carry1 };;
1366
1367{ .mii; (p7) add carry2=1,carry2
1368 cmp.ltu p7,p0=r17,carry1};;
1369{ .mii; st8 [r32]=r17,16
1370 (p7) add carry2=1,carry2 };;
1371
1372{ .mii; add r24=r24,carry2 };;
1373{ .mii; st8 [r33]=r24 }
1374
1375{ .mib; rum 1<<5 // clear um.mfh
1376 br.ret.sptk.many b0 };;
1377.endp bn_mul_comba4#
1378#undef carry2
1379#undef carry1
1380#endif
1381
1382#if 1
1383//
1384// BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
1385//
1386// In the nutshell it's a port of my MIPS III/IV implementation.
1387//
1388#define AT r14
1389#define H r16
1390#define HH r20
1391#define L r17
1392#define D r18
1393#define DH r22
1394#define I r21
1395
1396#if 0
1397// Some preprocessors (most notably HP-UX) appear to be allergic to
1398// macros enclosed to parenthesis [as these three were].
1399#define cont p16
1400#define break p0 // p20
1401#define equ p24
1402#else
1403cont=p16
1404break=p0
1405equ=p24
1406#endif
1407
1408.global abort#
1409.global bn_div_words#
1410.proc bn_div_words#
1411.align 64
1412bn_div_words:
1413 .prologue
1414 .fframe 0
1415 .save ar.pfs,r2
1416 .save b0,r3
1417{ .mii; alloc r2=ar.pfs,3,5,0,8
1418 mov r3=b0
1419 mov r10=pr };;
1420{ .mmb; cmp.eq p6,p0=r34,r0
1421 mov r8=-1
1422(p6) br.ret.spnt.many b0 };;
1423
1424 .body
1425{ .mii; mov H=r32 // save h
1426 mov ar.ec=0 // don't rotate at exit
1427 mov pr.rot=0 }
1428{ .mii; mov L=r33 // save l
1429 mov r36=r0 };;
1430
1431.L_divw_shift: // -vv- note signed comparison
1432{ .mfi; (p0) cmp.lt p16,p0=r0,r34 // d
1433 (p0) shladd r33=r34,1,r0 }
1434{ .mfb; (p0) add r35=1,r36
1435 (p0) nop.f 0x0
1436(p16) br.wtop.dpnt .L_divw_shift };;
1437
1438{ .mii; mov D=r34
1439 shr.u DH=r34,32
1440 sub r35=64,r36 };;
1441{ .mii; setf.sig f7=DH
1442 shr.u AT=H,r35
1443 mov I=r36 };;
1444{ .mib; cmp.ne p6,p0=r0,AT
1445 shl H=H,r36
1446(p6) br.call.spnt.clr b0=abort };; // overflow, die...
1447
1448{ .mfi; fcvt.xuf.s1 f7=f7
1449 shr.u AT=L,r35 };;
1450{ .mii; shl L=L,r36
1451 or H=H,AT };;
1452
1453{ .mii; nop.m 0x0
1454 cmp.leu p6,p0=D,H;;
1455(p6) sub H=H,D }
1456
1457{ .mlx; setf.sig f14=D
1458 movl AT=0xffffffff };;
1459///////////////////////////////////////////////////////////
1460{ .mii; setf.sig f6=H
1461 shr.u HH=H,32;;
1462 cmp.eq p6,p7=HH,DH };;
1463{ .mfb;
1464(p6) setf.sig f8=AT
1465(p7) fcvt.xuf.s1 f6=f6
1466(p7) br.call.sptk b6=.L_udiv64_32_b6 };;
1467
1468{ .mfi; getf.sig r33=f8 // q
1469 xmpy.lu f9=f8,f14 }
1470{ .mfi; xmpy.hu f10=f8,f14
1471 shrp H=H,L,32 };;
1472
1473{ .mmi; getf.sig r35=f9 // tl
1474 getf.sig r31=f10 };; // th
1475
1476.L_divw_1st_iter:
1477{ .mii; (p0) add r32=-1,r33
1478 (p0) cmp.eq equ,cont=HH,r31 };;
1479{ .mii; (p0) cmp.ltu p8,p0=r35,D
1480 (p0) sub r34=r35,D
1481 (equ) cmp.leu break,cont=r35,H };;
1482{ .mib; (cont) cmp.leu cont,break=HH,r31
1483 (p8) add r31=-1,r31
1484(cont) br.wtop.spnt .L_divw_1st_iter };;
1485///////////////////////////////////////////////////////////
1486{ .mii; sub H=H,r35
1487 shl r8=r33,32
1488 shl L=L,32 };;
1489///////////////////////////////////////////////////////////
1490{ .mii; setf.sig f6=H
1491 shr.u HH=H,32;;
1492 cmp.eq p6,p7=HH,DH };;
1493{ .mfb;
1494(p6) setf.sig f8=AT
1495(p7) fcvt.xuf.s1 f6=f6
1496(p7) br.call.sptk b6=.L_udiv64_32_b6 };;
1497
1498{ .mfi; getf.sig r33=f8 // q
1499 xmpy.lu f9=f8,f14 }
1500{ .mfi; xmpy.hu f10=f8,f14
1501 shrp H=H,L,32 };;
1502
1503{ .mmi; getf.sig r35=f9 // tl
1504 getf.sig r31=f10 };; // th
1505
1506.L_divw_2nd_iter:
1507{ .mii; (p0) add r32=-1,r33
1508 (p0) cmp.eq equ,cont=HH,r31 };;
1509{ .mii; (p0) cmp.ltu p8,p0=r35,D
1510 (p0) sub r34=r35,D
1511 (equ) cmp.leu break,cont=r35,H };;
1512{ .mib; (cont) cmp.leu cont,break=HH,r31
1513 (p8) add r31=-1,r31
1514(cont) br.wtop.spnt .L_divw_2nd_iter };;
1515///////////////////////////////////////////////////////////
1516{ .mii; sub H=H,r35
1517 or r8=r8,r33
1518 mov ar.pfs=r2 };;
1519{ .mii; shr.u r9=H,I // remainder if anybody wants it
1520 mov pr=r10,0x1ffff }
1521{ .mfb; br.ret.sptk.many b0 };;
1522
1523// Unsigned 64 by 32 (well, by 64 for the moment) bit integer division
1524// procedure.
1525//
1526// inputs: f6 = (double)a, f7 = (double)b
1527// output: f8 = (int)(a/b)
1528// clobbered: f8,f9,f10,f11,pred
1529pred=p15
1530// One can argue that this snippet is copyrighted to Intel
1531// Corporation, as it's essentially identical to one of those
1532// found in "Divide, Square Root and Remainder" section at
1533// http://www.intel.com/software/products/opensource/libraries/num.htm.
1534// Yes, I admit that the referred code was used as template,
1535// but after I realized that there hardly is any other instruction
1536// sequence which would perform this operation. I mean I figure that
1537// any independent attempt to implement high-performance division
1538// will result in code virtually identical to the Intel code. It
1539// should be noted though that below division kernel is 1 cycle
1540// faster than Intel one (note commented splits:-), not to mention
1541// original prologue (rather lack of one) and epilogue.
1542.align 32
1543.skip 16
1544.L_udiv64_32_b6:
1545 frcpa.s1 f8,pred=f6,f7;; // [0] y0 = 1 / b
1546
1547(pred) fnma.s1 f9=f7,f8,f1 // [5] e0 = 1 - b * y0
1548(pred) fmpy.s1 f10=f6,f8;; // [5] q0 = a * y0
1549(pred) fmpy.s1 f11=f9,f9 // [10] e1 = e0 * e0
1550(pred) fma.s1 f10=f9,f10,f10;; // [10] q1 = q0 + e0 * q0
1551(pred) fma.s1 f8=f9,f8,f8 //;; // [15] y1 = y0 + e0 * y0
1552(pred) fma.s1 f9=f11,f10,f10;; // [15] q2 = q1 + e1 * q1
1553(pred) fma.s1 f8=f11,f8,f8 //;; // [20] y2 = y1 + e1 * y1
1554(pred) fnma.s1 f10=f7,f9,f6;; // [20] r2 = a - b * q2
1555(pred) fma.s1 f8=f10,f8,f9;; // [25] q3 = q2 + r2 * y2
1556
1557 fcvt.fxu.trunc.s1 f8=f8 // [30] q = trunc(q3)
1558 br.ret.sptk.many b6;;
1559.endp bn_div_words#
1560#endif