--- /dev/null
+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()
projects / msp430-gcc.git / blobdiff