Index: gcc/gmp/mpn/ia64/mode1o.asm |
diff --git a/gcc/gmp/mpn/ia64/mode1o.asm b/gcc/gmp/mpn/ia64/mode1o.asm |
deleted file mode 100644 |
index 6b3626ebe6e80a1b780269323066c78ccf65868f..0000000000000000000000000000000000000000 |
--- a/gcc/gmp/mpn/ia64/mode1o.asm |
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@@ -1,329 +0,0 @@ |
-dnl Itanium-2 mpn_modexact_1c_odd -- mpn by 1 exact remainder. |
- |
-dnl Copyright 2003, 2004, 2005 Free Software Foundation, Inc. |
-dnl |
-dnl This file is part of the GNU MP Library. |
-dnl |
-dnl The GNU MP Library is free software; you can redistribute it and/or |
-dnl modify it under the terms of the GNU Lesser General Public License as |
-dnl published by the Free Software Foundation; either version 3 of the |
-dnl License, or (at your option) any later version. |
-dnl |
-dnl The GNU MP Library is distributed in the hope that it will be useful, |
-dnl but WITHOUT ANY WARRANTY; without even the implied warranty of |
-dnl MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
-dnl Lesser General Public License for more details. |
-dnl |
-dnl You should have received a copy of the GNU Lesser General Public License |
-dnl along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. |
- |
-include(`../config.m4') |
- |
- |
-C cycles/limb |
-C Itanium: 15 |
-C Itanium 2: 8 |
- |
- |
-dnl Usage: ABI32(`code') |
-dnl |
-dnl Emit the given code only under HAVE_ABI_32. |
-dnl |
-define(ABI32, |
-m4_assert_onearg() |
-`ifdef(`HAVE_ABI_32',`$1')') |
- |
- |
-C mp_limb_t mpn_modexact_1c_odd (mp_srcptr src, mp_size_t size, |
-C mp_limb_t divisor, mp_limb_t carry); |
-C |
-C The modexact algorithm is usually conceived as a dependent chain |
-C |
-C l = src[i] - c |
-C q = low(l * inverse) |
-C c = high(q*divisor) + (src[i]<c) |
-C |
-C but we can work the src[i]-c into an xma by calculating si=src[i]*inverse |
-C separately (off the dependent chain) and using |
-C |
-C q = low(c * inverse + si) |
-C c = high(q*divisor + c) |
-C |
-C This means the dependent chain is simply xma.l followed by xma.hu, for a |
-C total 8 cycles/limb on itanium-2. |
-C |
-C The reason xma.hu works for the new c is that the low of q*divisor is |
-C src[i]-c (being the whole purpose of the q generated, and it can be |
-C verified algebraically). If there was an underflow from src[i]-c, then |
-C there will be an overflow from (src-c)+c, thereby adding 1 to the new c |
-C the same as the borrow bit (src[i]<c) gives in the first style shown. |
-C |
-C Incidentally, fcmp is not an option for treating src[i]-c, since it |
-C apparently traps to the kernel for unnormalized operands like those used |
-C and generated by ldf8 and xma. On one GNU/Linux system it took about 1200 |
-C cycles. |
-C |
-C |
-C First Limb: |
-C |
-C The first limb uses q = (src[0]-c) * inverse shown in the first style. |
-C This lets us get the first q as soon as the inverse is ready, without |
-C going through si=s*inverse. Basically at the start we have c and can use |
-C it while waiting for the inverse, whereas for the second and subsequent |
-C limbs it's the other way around, ie. we have the inverse and are waiting |
-C for c. |
-C |
-C At .Lentry the first two instructions in the loop have been done already. |
-C The load of f11=src[1] at the start (predicated on size>=2), and the |
-C calculation of q by the initial different scheme. |
-C |
-C |
-C Entry Sequence: |
-C |
-C In the entry sequence, the critical path is the calculation of the |
-C inverse, so this is begun first and optimized. Apart from that, ar.lc is |
-C established nice and early so the br.cloop's should predict perfectly. |
-C And the load for the low limbs src[0] and src[1] can be initiated long |
-C ahead of where they're needed. |
-C |
-C |
-C Inverse Calculation: |
-C |
-C The initial 8-bit inverse is calculated using a table lookup. If it hits |
-C L1 (which is likely if we're called several times) then it should take a |
-C total 4 cycles, otherwise hopefully L2 for 9 cycles. This is considered |
-C the best approach, on balance. It could be done bitwise, but that would |
-C probably be about 14 cycles (2 per bit beyond the first couple). Or it |
-C could be taken from 4 bits to 8 with xmpy doubling as used beyond 8 bits, |
-C but that would be about 11 cycles. |
-C |
-C The table is not the same as binvert_limb_table, instead it's 256 bytes, |
-C designed to be indexed by the low byte of the divisor. The divisor is |
-C always odd, so the relevant data is every second byte in the table. The |
-C padding lets us use zxt1 instead of extr.u, the latter would cost an extra |
-C cycle because it must go down I0, and we're using the first I0 slot to get |
-C ip. The extra 128 bytes of padding should be insignificant compared to |
-C typical ia64 code bloat. |
-C |
-C Having the table in .text allows us to use IP-relative addressing, |
-C avoiding a fetch from ltoff. .rodata is apparently not suitable for use |
-C IP-relative, it gets a linker relocation overflow on GNU/Linux. |
-C |
-C |
-C Load Scheduling: |
-C |
-C In the main loop, the data loads are scheduled for an L2 hit, which means |
-C 6 cycles for the data ready to use. In fact we end up 7 cycles ahead. In |
-C any case that scheduling is achieved simply by doing the load (and xmpy.l |
-C for "si") in the immediately preceding iteration. |
-C |
-C The main loop requires size >= 2, and we handle size==1 by an initial |
-C br.cloop to enter the loop only if size>1. Since ar.lc is established |
-C early, this should predict perfectly. |
-C |
-C |
-C Not done: |
-C |
-C Consideration was given to using a plain "(src[0]-c) % divisor" for |
-C size==1, but cycle counting suggests about 50 for the sort of approach |
-C taken by gcc __umodsi3, versus about 47 for the modexact. (Both assuming |
-C L1 hits for their respective fetching.) |
-C |
-C Consideration was given to a test for high<divisor and replacing the last |
-C loop iteration with instead c-=src[size-1] followed by c+=d if underflow. |
-C Branching on high<divisor wouldn't be good since a mispredict would cost |
-C more than the loop iteration saved, and the condition is of course data |
-C dependent. So the theory would be to shorten the loop count if |
-C high<divisor, and predicate extra operations at the end. That would mean |
-C a gain of 6 when high<divisor, or a cost of 2 if not. |
-C |
-C Whether such a tradeoff is a win on average depends on assumptions about |
-C how many bits in the high and the divisor. If both are uniformly |
-C distributed then high<divisor about 50% of the time. But smallish |
-C divisors (less chance of high<divisor) might be more likely from |
-C applications (mpz_divisible_ui, mpz_gcd_ui, etc). Though biggish divisors |
-C would be normal internally from say mpn/generic/perfsqr.c. On balance, |
-C for the moment, it's felt the gain is not really enough to be worth the |
-C trouble. |
-C |
-C |
-C Enhancement: |
-C |
-C Process two source limbs per iteration using a two-limb inverse and a |
-C sequence like |
-C |
-C ql = low (c * il + sil) quotient low limb |
-C qlc = high(c * il + sil) |
-C qh1 = low (c * ih + sih) quotient high, partial |
-C |
-C cl = high (ql * d + c) carry out of low |
-C qh = low (qlc * 1 + qh1) quotient high limb |
-C |
-C new c = high (qh * d + cl) carry out of high |
-C |
-C This would be 13 cycles/iteration, giving 6.5 cycles/limb. The two limb |
-C s*inverse as sih:sil = sh:sl * ih:il would be calculated off the dependent |
-C chain with 4 multiplies. The bigger inverse would take extra time to |
-C calculate, but a one limb iteration to handle an odd size could be done as |
-C soon as 64-bits of inverse were ready. |
-C |
-C Perhaps this could even extend to a 3 limb inverse, which might promise 17 |
-C or 18 cycles for 3 limbs, giving 5.66 or 6.0 cycles/limb. |
-C |
- |
-ASM_START() |
- .explicit |
- |
- .text |
- .align 32 |
-.Ltable: |
-data1 0,0x01, 0,0xAB, 0,0xCD, 0,0xB7, 0,0x39, 0,0xA3, 0,0xC5, 0,0xEF |
-data1 0,0xF1, 0,0x1B, 0,0x3D, 0,0xA7, 0,0x29, 0,0x13, 0,0x35, 0,0xDF |
-data1 0,0xE1, 0,0x8B, 0,0xAD, 0,0x97, 0,0x19, 0,0x83, 0,0xA5, 0,0xCF |
-data1 0,0xD1, 0,0xFB, 0,0x1D, 0,0x87, 0,0x09, 0,0xF3, 0,0x15, 0,0xBF |
-data1 0,0xC1, 0,0x6B, 0,0x8D, 0,0x77, 0,0xF9, 0,0x63, 0,0x85, 0,0xAF |
-data1 0,0xB1, 0,0xDB, 0,0xFD, 0,0x67, 0,0xE9, 0,0xD3, 0,0xF5, 0,0x9F |
-data1 0,0xA1, 0,0x4B, 0,0x6D, 0,0x57, 0,0xD9, 0,0x43, 0,0x65, 0,0x8F |
-data1 0,0x91, 0,0xBB, 0,0xDD, 0,0x47, 0,0xC9, 0,0xB3, 0,0xD5, 0,0x7F |
-data1 0,0x81, 0,0x2B, 0,0x4D, 0,0x37, 0,0xB9, 0,0x23, 0,0x45, 0,0x6F |
-data1 0,0x71, 0,0x9B, 0,0xBD, 0,0x27, 0,0xA9, 0,0x93, 0,0xB5, 0,0x5F |
-data1 0,0x61, 0,0x0B, 0,0x2D, 0,0x17, 0,0x99, 0,0x03, 0,0x25, 0,0x4F |
-data1 0,0x51, 0,0x7B, 0,0x9D, 0,0x07, 0,0x89, 0,0x73, 0,0x95, 0,0x3F |
-data1 0,0x41, 0,0xEB, 0,0x0D, 0,0xF7, 0,0x79, 0,0xE3, 0,0x05, 0,0x2F |
-data1 0,0x31, 0,0x5B, 0,0x7D, 0,0xE7, 0,0x69, 0,0x53, 0,0x75, 0,0x1F |
-data1 0,0x21, 0,0xCB, 0,0xED, 0,0xD7, 0,0x59, 0,0xC3, 0,0xE5, 0,0x0F |
-data1 0,0x11, 0,0x3B, 0,0x5D, 0,0xC7, 0,0x49, 0,0x33, 0,0x55, 0,0xFF |
- |
- |
-PROLOGUE(mpn_modexact_1c_odd) |
- |
- C r32 src |
- C r33 size |
- C r34 divisor |
- C r35 carry |
- |
- .prologue |
-.Lhere: |
-{ .mmi; add r33 = -1, r33 C M0 size-1 |
- mov r14 = 2 C M1 2 |
- mov r15 = ip C I0 .Lhere |
-}{.mmi; setf.sig f6 = r34 C M2 divisor |
- setf.sig f9 = r35 C M3 carry |
- zxt1 r3 = r34 C I1 divisor low byte |
-} ;; |
- |
-{ .mmi; add r3 = .Ltable-.Lhere, r3 C M0 table offset ip and index |
- sub r16 = 0, r34 C M1 -divisor |
- .save ar.lc, r2 |
- mov r2 = ar.lc C I0 |
-}{.mmi; .body |
- setf.sig f13 = r14 C M2 2 in significand |
- mov r17 = -1 C M3 -1 |
-ABI32(` zxt4 r33 = r33') C I1 size extend |
-} ;; |
- |
-{ .mmi; add r3 = r3, r15 C M0 table entry address |
-ABI32(` addp4 r32 = 0, r32') C M1 src extend |
- mov ar.lc = r33 C I0 size-1 loop count |
-}{.mmi; setf.sig f12 = r16 C M2 -divisor |
- setf.sig f8 = r17 C M3 -1 |
-} ;; |
- |
-{ .mmi; ld1 r3 = [r3] C M0 inverse, 8 bits |
- ldf8 f10 = [r32], 8 C M1 src[0] |
- cmp.ne p6,p0 = 0, r33 C I0 test size!=1 |
-} ;; |
- |
- C Wait for table load. |
- C Hope for an L1 hit of 1 cycles to ALU, but could be more. |
- setf.sig f7 = r3 C M2 inverse, 8 bits |
-(p6) ldf8 f11 = [r32], 8 C M1 src[1], if size!=1 |
- ;; |
- |
- C 5 cycles |
- |
- C f6 divisor |
- C f7 inverse, being calculated |
- C f8 -1, will be -inverse |
- C f9 carry |
- C f10 src[0] |
- C f11 src[1] |
- C f12 -divisor |
- C f13 2 |
- C f14 scratch |
- |
- xmpy.l f14 = f13, f7 C 2*i |
- xmpy.l f7 = f7, f7 C i*i |
- ;; |
- xma.l f7 = f7, f12, f14 C i*i*-d + 2*i, inverse 16 bits |
- ;; |
- |
- xmpy.l f14 = f13, f7 C 2*i |
- xmpy.l f7 = f7, f7 C i*i |
- ;; |
- xma.l f7 = f7, f12, f14 C i*i*-d + 2*i, inverse 32 bits |
- ;; |
- |
- xmpy.l f14 = f13, f7 C 2*i |
- xmpy.l f7 = f7, f7 C i*i |
- ;; |
- |
- xma.l f7 = f7, f12, f14 C i*i*-d + 2*i, inverse 64 bits |
- xma.l f10 = f9, f8, f10 C sc = c * -1 + src[0] |
- ;; |
-ASSERT(p6, ` |
- xmpy.l f15 = f6, f7 ;; C divisor*inverse |
- getf.sig r31 = f15 ;; |
- cmp.eq p6,p0 = 1, r31 C should == 1 |
-') |
- |
- xmpy.l f10 = f10, f7 C q = sc * inverse |
- xmpy.l f8 = f7, f8 C -inverse = inverse * -1 |
- br.cloop.sptk.few.clr .Lentry C main loop, if size > 1 |
- ;; |
- |
- C size==1, finish up now |
- xma.hu f9 = f10, f6, f9 C c = high(q * divisor + c) |
- mov ar.lc = r2 C I0 |
- ;; |
- getf.sig r8 = f9 C M2 return c |
- br.ret.sptk.many b0 |
- |
- |
- |
-.Ltop: |
- C r2 saved ar.lc |
- C f6 divisor |
- C f7 inverse |
- C f8 -inverse |
- C f9 carry |
- C f10 src[i] * inverse |
- C f11 scratch src[i+1] |
- |
- add r16 = 160, r32 |
- ldf8 f11 = [r32], 8 C src[i+1] |
- ;; |
- C 2 cycles |
- |
- lfetch [r16] |
- xma.l f10 = f9, f8, f10 C q = c * -inverse + si |
- ;; |
- C 3 cycles |
- |
-.Lentry: |
- xma.hu f9 = f10, f6, f9 C c = high(q * divisor + c) |
- xmpy.l f10 = f11, f7 C si = src[i] * inverse |
- br.cloop.sptk.few.clr .Ltop |
- ;; |
- |
- |
- |
- xma.l f10 = f9, f8, f10 C q = c * -inverse + si |
- mov ar.lc = r2 C I0 |
- ;; |
- xma.hu f9 = f10, f6, f9 C c = high(q * divisor + c) |
- ;; |
- getf.sig r8 = f9 C M2 return c |
- br.ret.sptk.many b0 |
- |
-EPILOGUE() |