dnl X86-64 mpn_sqr_basecase optimised for Intel Nehalem/Westmere. dnl It also seems good for Conroe/Wolfdale. dnl Contributed to the GNU project by Torbjörn Granlund. dnl Copyright 2008, 2011-2013 Free Software Foundation, Inc. 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 modify dnl it under the terms of either: dnl dnl * the GNU Lesser General Public License as published by the Free dnl Software Foundation; either version 3 of the License, or (at your dnl option) any later version. dnl dnl or dnl dnl * the GNU General Public License as published by the Free Software dnl Foundation; either version 2 of the License, or (at your option) any dnl later version. dnl dnl or both in parallel, as here. dnl dnl The GNU MP Library is distributed in the hope that it will be useful, but dnl WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY dnl or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License dnl for more details. dnl dnl You should have received copies of the GNU General Public License and the dnl GNU Lesser General Public License along with the GNU MP Library. If not, dnl see https://www.gnu.org/licenses/. include(`../config.m4') C cycles/limb mul_2 addmul_2 sqr_diag_addlsh1 C AMD K8,K9 C AMD K10 C AMD bull C AMD pile C AMD steam C AMD bobcat C AMD jaguar C Intel P4 C Intel core 4.9 4.18-4.25 3.87 C Intel NHM 3.8 4.06-4.2 3.5 C Intel SBR C Intel IBR C Intel HWL C Intel BWL C Intel atom C VIA nano C The inner loops of this code are the result of running a code generation and C optimisation tool suite written by David Harvey and Torbjörn Granlund. C Code structure: C C C m_2(0m4) m_2(2m4) m_2(1m4) m_2(3m4) C | | | | C | | | | C | | | | C \|/ \|/ \|/ \|/ C ____________ ____________ C / \ / \ C \|/ \ \|/ \ C am_2(3m4) am_2(1m4) am_2(0m4) am_2(2m4) C \ /|\ \ /|\ C \____________/ \____________/ C \ / C \ / C \ / C tail(0m2) tail(1m2) C \ / C \ / C sqr_diag_addlsh1 C TODO C * Tune. None done so far. C * Currently 2761 bytes, making it smaller would be nice. C * Consider using a jumptab-based entry sequence. One might even use a mask- C less sequence, if the table is large enough to support tuneup's needs. C The code would be, using non-PIC code, C lea tab(%rip),%rax; jmp *(n,%rax) C or, C lea tab(%rip),%rax; lea (%rip),%rbx; add (n,%rax),%rbx; jmp *%rbx C using PIC code. The table entries would be Ln1,Ln2,Ln3,Lm0,Lm1,Lm2,Lm3,.. C with the last four entries repeated a safe number of times. C * Consider expanding feed-in code in order to avoid zeroing registers. C * Zero consistently with xor. C * Check if using "lea (reg),reg" should be done in more places; we have some C explicit "mov %rax,reg" now. C * Try zeroing with xor in m2 loops. C * Try re-rolling the m2 loops to avoid the current 9 insn code duplication C between loop header and wind-down code. C * Consider adc reg,reg instead of adc $0,reg in m2 loops. This save a byte. C When playing with pointers, set this to $2 to fall back to conservative C indexing in wind-down code. define(`I',`$1') C Define this to $1 to use late loop index variable as zero, $2 to use an C explicit $0. define(`Z',`$1') define(`rp', `%rdi') define(`up', `%rsi') define(`n_param', `%rdx') define(`n', `%r8') define(`v0', `%r10') define(`v1', `%r11') define(`w0', `%rbx') define(`w1', `%rcx') define(`w2', `%rbp') define(`w3', `%r9') define(`i', `%r13') define(`X0', `%r12') define(`X1', `%r14') C rax rbx rcx rdx rdi rsi rbp r8 r9 r10 r11 r12 r13 r14 r15 ABI_SUPPORT(DOS64) ABI_SUPPORT(STD64) define(`ALIGNx', `ALIGN(16)') define(`N', 85) ifdef(`N',,`define(`N',0)') define(`MOV', `ifelse(eval(N & $3),0,`mov $1, $2',`lea ($1), $2')') ASM_START() TEXT ALIGN(32) PROLOGUE(mpn_sqr_basecase) FUNC_ENTRY(3) cmp $4, n_param jl L(small) push %rbx push %rbp push %r12 push %r13 push %r14 mov (up), v0 mov 8(up), %rax mov %rax, v1 mov $1, R32(n) sub n_param, n C n = -n_param+1 push n lea (up,n_param,8), up lea (rp,n_param,8), rp mul v0 test $1, R8(n) jnz L(bx1) L(bx0): test $2, R8(n) mov %rax, (rp,n,8) jnz L(b10) L(b00): lea (n), i C n = 5, 9, ... mov %rdx, w1 C FIXME: Use lea? xor R32(w2), R32(w2) jmp L(m2e0) L(b10): lea 2(n), i C n = 7, 11, ... mov 8(up,n,8), %rax mov %rdx, w3 C FIXME: Use lea? xor R32(w0), R32(w0) xor R32(w1), R32(w1) jmp L(m2e2) L(bx1): test $2, R8(n) mov %rax, (rp,n,8) jz L(b11) L(b01): lea 1(n), i C n = 6, 10, ... mov %rdx, w0 C FIXME: Use lea? xor R32(w1), R32(w1) jmp L(m2e1) L(b11): lea -1(n), i C n = 4, 8, 12, ... mov %rdx, w2 C FIXME: Use lea? xor R32(w3), R32(w3) jmp L(m2e3) ALIGNx L(m2top1): mul v0 add %rax, w3 mov -8(up,i,8), %rax mov w3, -8(rp,i,8) adc %rdx, w0 adc $0, R32(w1) mul v1 add %rax, w0 adc %rdx, w1 L(m2e1):mov $0, R32(w2) mov (up,i,8), %rax mul v0 add %rax, w0 mov w0, (rp,i,8) adc %rdx, w1 mov (up,i,8), %rax adc $0, R32(w2) mul v1 add %rax, w1 adc %rdx, w2 mov 8(up,i,8), %rax mul v0 mov $0, R32(w3) add %rax, w1 adc %rdx, w2 adc $0, R32(w3) mov 8(up,i,8), %rax mul v1 add %rax, w2 mov w1, 8(rp,i,8) adc %rdx, w3 mov $0, R32(w0) mov 16(up,i,8), %rax mul v0 add %rax, w2 mov 16(up,i,8), %rax adc %rdx, w3 adc $0, R32(w0) mul v1 mov $0, R32(w1) add %rax, w3 mov 24(up,i,8), %rax mov w2, 16(rp,i,8) adc %rdx, w0 add $4, i js L(m2top1) mul v0 add %rax, w3 mov I(-8(up),-8(up,i,8)), %rax mov w3, I(-8(rp),-8(rp,i,8)) adc %rdx, w0 adc R32(w1), R32(w1) mul v1 add w0, %rax adc w1, %rdx mov %rax, I((rp),(rp,i,8)) mov %rdx, I(8(rp),8(rp,i,8)) lea 16(rp), rp add $2, n C decrease |n| jmp L(am2o3) ALIGNx L(m2top3): mul v0 add %rax, w3 mov -8(up,i,8), %rax mov w3, -8(rp,i,8) adc %rdx, w0 adc $0, R32(w1) mul v1 add %rax, w0 adc %rdx, w1 mov $0, R32(w2) mov (up,i,8), %rax mul v0 add %rax, w0 mov w0, (rp,i,8) adc %rdx, w1 mov (up,i,8), %rax adc $0, R32(w2) mul v1 add %rax, w1 adc %rdx, w2 mov 8(up,i,8), %rax mul v0 mov $0, R32(w3) add %rax, w1 adc %rdx, w2 adc $0, R32(w3) mov 8(up,i,8), %rax mul v1 add %rax, w2 mov w1, 8(rp,i,8) adc %rdx, w3 L(m2e3):mov $0, R32(w0) mov 16(up,i,8), %rax mul v0 add %rax, w2 mov 16(up,i,8), %rax adc %rdx, w3 adc $0, R32(w0) mul v1 mov $0, R32(w1) add %rax, w3 mov 24(up,i,8), %rax mov w2, 16(rp,i,8) adc %rdx, w0 add $4, i js L(m2top3) mul v0 add %rax, w3 mov I(-8(up),-8(up,i,8)), %rax mov w3, I(-8(rp),-8(rp,i,8)) adc %rdx, w0 adc R32(w1), R32(w1) mul v1 add w0, %rax adc w1, %rdx mov %rax, I((rp),(rp,i,8)) mov %rdx, I(8(rp),8(rp,i,8)) lea 16(rp), rp add $2, n C decrease |n| cmp $-1, n jz L(cor1) C jumps iff entry n = 4 L(am2o1): mov -8(up,n,8), v0 mov (up,n,8), %rax mov %rax, v1 lea 1(n), i mul v0 mov %rax, X1 MOV( %rdx, X0, 128) mov (rp,n,8), w1 xor R32(w2), R32(w2) mov 8(up,n,8), %rax xor R32(w3), R32(w3) jmp L(lo1) ALIGNx L(am2top1): mul v1 add w0, w1 adc %rax, w2 mov (up,i,8), %rax MOV( %rdx, w3, 1) adc $0, w3 L(lo1): mul v0 add w1, X1 mov X1, -8(rp,i,8) adc %rax, X0 MOV( %rdx, X1, 2) adc $0, X1 mov (up,i,8), %rax mul v1 MOV( %rdx, w0, 4) mov (rp,i,8), w1 add w1, w2 adc %rax, w3 adc $0, w0 mov 8(up,i,8), %rax mul v0 add w2, X0 adc %rax, X1 mov X0, (rp,i,8) MOV( %rdx, X0, 8) adc $0, X0 mov 8(up,i,8), %rax mov 8(rp,i,8), w2 mul v1 add w2, w3 adc %rax, w0 MOV( %rdx, w1, 16) adc $0, w1 mov 16(up,i,8), %rax mul v0 add w3, X1 mov X1, 8(rp,i,8) adc %rax, X0 MOV( %rdx, X1, 32) mov 16(rp,i,8), w3 adc $0, X1 mov 16(up,i,8), %rax mul v1 add w3, w0 MOV( %rdx, w2, 64) adc %rax, w1 mov 24(up,i,8), %rax adc $0, w2 mul v0 add w0, X0 mov X0, 16(rp,i,8) MOV( %rdx, X0, 128) adc %rax, X1 mov 24(up,i,8), %rax mov 24(rp,i,8), w0 adc $0, X0 add $4, i jnc L(am2top1) mul v1 add w0, w1 adc w2, %rax adc Z(i,$0), %rdx add w1, X1 adc Z(i,$0), X0 mov X1, I(-8(rp),-8(rp,i,8)) add X0, %rax mov %rax, I((rp),(rp,i,8)) adc Z(i,$0), %rdx mov %rdx, I(8(rp),8(rp,i,8)) lea 16(rp), rp add $2, n L(am2o3): mov -8(up,n,8), v0 mov (up,n,8), %rax mov %rax, v1 lea -1(n), i mul v0 mov %rax, X1 MOV( %rdx, X0, 8) mov (rp,n,8), w3 xor R32(w0), R32(w0) xor R32(w1), R32(w1) mov 8(up,n,8), %rax jmp L(lo3) ALIGNx L(am2top3): mul v1 add w0, w1 adc %rax, w2 mov (up,i,8), %rax MOV( %rdx, w3, 1) adc $0, w3 mul v0 add w1, X1 mov X1, -8(rp,i,8) adc %rax, X0 MOV( %rdx, X1, 2) adc $0, X1 mov (up,i,8), %rax mul v1 MOV( %rdx, w0, 4) mov (rp,i,8), w1 add w1, w2 adc %rax, w3 adc $0, w0 mov 8(up,i,8), %rax mul v0 add w2, X0 adc %rax, X1 mov X0, (rp,i,8) MOV( %rdx, X0, 8) adc $0, X0 mov 8(up,i,8), %rax mov 8(rp,i,8), w2 mul v1 add w2, w3 adc %rax, w0 MOV( %rdx, w1, 16) adc $0, w1 mov 16(up,i,8), %rax L(lo3): mul v0 add w3, X1 mov X1, 8(rp,i,8) adc %rax, X0 MOV( %rdx, X1, 32) mov 16(rp,i,8), w3 adc $0, X1 mov 16(up,i,8), %rax mul v1 add w3, w0 MOV( %rdx, w2, 64) adc %rax, w1 mov 24(up,i,8), %rax adc $0, w2 mul v0 add w0, X0 mov X0, 16(rp,i,8) MOV( %rdx, X0, 128) adc %rax, X1 mov 24(up,i,8), %rax mov 24(rp,i,8), w0 adc $0, X0 add $4, i jnc L(am2top3) mul v1 add w0, w1 adc w2, %rax adc Z(i,$0), %rdx add w1, X1 adc Z(i,$0), X0 mov X1, I(-8(rp),-8(rp,i,8)) add X0, %rax mov %rax, I((rp),(rp,i,8)) adc Z(i,$0), %rdx mov %rdx, I(8(rp),8(rp,i,8)) lea 16(rp), rp add $2, n cmp $-1, n jnz L(am2o1) L(cor1):pop n mov %rdx, w3 mov -16(up), v0 mov -8(up), %rax mul v0 add w3, %rax adc $0, %rdx mov %rax, -8(rp) mov %rdx, (rp) jmp L(sqr_diag_addlsh1) ALIGNx L(m2top2): L(m2e2):mul v0 add %rax, w3 mov -8(up,i,8), %rax mov w3, -8(rp,i,8) adc %rdx, w0 adc $0, R32(w1) mul v1 add %rax, w0 adc %rdx, w1 mov $0, R32(w2) mov (up,i,8), %rax mul v0 add %rax, w0 mov w0, (rp,i,8) adc %rdx, w1 mov (up,i,8), %rax adc $0, R32(w2) mul v1 add %rax, w1 adc %rdx, w2 mov 8(up,i,8), %rax mul v0 mov $0, R32(w3) add %rax, w1 adc %rdx, w2 adc $0, R32(w3) mov 8(up,i,8), %rax mul v1 add %rax, w2 mov w1, 8(rp,i,8) adc %rdx, w3 mov $0, R32(w0) mov 16(up,i,8), %rax mul v0 add %rax, w2 mov 16(up,i,8), %rax adc %rdx, w3 adc $0, R32(w0) mul v1 mov $0, R32(w1) add %rax, w3 mov 24(up,i,8), %rax mov w2, 16(rp,i,8) adc %rdx, w0 add $4, i js L(m2top2) mul v0 add %rax, w3 mov I(-8(up),-8(up,i,8)), %rax mov w3, I(-8(rp),-8(rp,i,8)) adc %rdx, w0 adc R32(w1), R32(w1) mul v1 add w0, %rax adc w1, %rdx mov %rax, I((rp),(rp,i,8)) mov %rdx, I(8(rp),8(rp,i,8)) lea 16(rp), rp add $2, n C decrease |n| jmp L(am2o0) ALIGNx L(m2top0): mul v0 add %rax, w3 mov -8(up,i,8), %rax mov w3, -8(rp,i,8) adc %rdx, w0 adc $0, R32(w1) mul v1 add %rax, w0 adc %rdx, w1 mov $0, R32(w2) mov (up,i,8), %rax mul v0 add %rax, w0 mov w0, (rp,i,8) adc %rdx, w1 mov (up,i,8), %rax adc $0, R32(w2) mul v1 add %rax, w1 adc %rdx, w2 L(m2e0):mov 8(up,i,8), %rax mul v0 mov $0, R32(w3) add %rax, w1 adc %rdx, w2 adc $0, R32(w3) mov 8(up,i,8), %rax mul v1 add %rax, w2 mov w1, 8(rp,i,8) adc %rdx, w3 mov $0, R32(w0) mov 16(up,i,8), %rax mul v0 add %rax, w2 mov 16(up,i,8), %rax adc %rdx, w3 adc $0, R32(w0) mul v1 mov $0, R32(w1) add %rax, w3 mov 24(up,i,8), %rax mov w2, 16(rp,i,8) adc %rdx, w0 add $4, i js L(m2top0) mul v0 add %rax, w3 mov I(-8(up),-8(up,i,8)), %rax mov w3, I(-8(rp),-8(rp,i,8)) adc %rdx, w0 adc R32(w1), R32(w1) mul v1 add w0, %rax adc w1, %rdx mov %rax, I((rp),(rp,i,8)) mov %rdx, I(8(rp),8(rp,i,8)) lea 16(rp), rp add $2, n C decrease |n| cmp $-2, n jz L(cor2) C jumps iff entry n = 5 L(am2o2): mov -8(up,n,8), v0 mov (up,n,8), %rax mov %rax, v1 lea -2(n), i mul v0 mov %rax, X0 MOV( %rdx, X1, 32) mov (rp,n,8), w0 xor R32(w1), R32(w1) xor R32(w2), R32(w2) mov 8(up,n,8), %rax jmp L(lo2) ALIGNx L(am2top2): mul v1 add w0, w1 adc %rax, w2 mov (up,i,8), %rax MOV( %rdx, w3, 1) adc $0, w3 mul v0 add w1, X1 mov X1, -8(rp,i,8) adc %rax, X0 MOV( %rdx, X1, 2) adc $0, X1 mov (up,i,8), %rax mul v1 MOV( %rdx, w0, 4) mov (rp,i,8), w1 add w1, w2 adc %rax, w3 adc $0, w0 mov 8(up,i,8), %rax mul v0 add w2, X0 adc %rax, X1 mov X0, (rp,i,8) MOV( %rdx, X0, 8) adc $0, X0 mov 8(up,i,8), %rax mov 8(rp,i,8), w2 mul v1 add w2, w3 adc %rax, w0 MOV( %rdx, w1, 16) adc $0, w1 mov 16(up,i,8), %rax mul v0 add w3, X1 mov X1, 8(rp,i,8) adc %rax, X0 MOV( %rdx, X1, 32) mov 16(rp,i,8), w3 adc $0, X1 mov 16(up,i,8), %rax mul v1 add w3, w0 MOV( %rdx, w2, 64) adc %rax, w1 mov 24(up,i,8), %rax adc $0, w2 L(lo2): mul v0 add w0, X0 mov X0, 16(rp,i,8) MOV( %rdx, X0, 128) adc %rax, X1 mov 24(up,i,8), %rax mov 24(rp,i,8), w0 adc $0, X0 add $4, i jnc L(am2top2) mul v1 add w0, w1 adc w2, %rax adc Z(i,$0), %rdx add w1, X1 adc Z(i,$0), X0 mov X1, I(-8(rp),-8(rp,i,8)) add X0, %rax mov %rax, I((rp),(rp,i,8)) adc Z(i,$0), %rdx mov %rdx, I(8(rp),8(rp,i,8)) lea 16(rp), rp add $2, n L(am2o0): mov -8(up,n,8), v0 mov (up,n,8), %rax mov %rax, v1 lea 0(n), i mul v0 mov %rax, X0 MOV( %rdx, X1, 2) xor R32(w0), R32(w0) mov (rp,n,8), w2 xor R32(w3), R32(w3) jmp L(lo0) ALIGNx L(am2top0): mul v1 add w0, w1 adc %rax, w2 mov (up,i,8), %rax MOV( %rdx, w3, 1) adc $0, w3 mul v0 add w1, X1 mov X1, -8(rp,i,8) adc %rax, X0 MOV( %rdx, X1, 2) adc $0, X1 mov (up,i,8), %rax mul v1 MOV( %rdx, w0, 4) mov (rp,i,8), w1 add w1, w2 adc %rax, w3 adc $0, w0 L(lo0): mov 8(up,i,8), %rax mul v0 add w2, X0 adc %rax, X1 mov X0, (rp,i,8) MOV( %rdx, X0, 8) adc $0, X0 mov 8(up,i,8), %rax mov 8(rp,i,8), w2 mul v1 add w2, w3 adc %rax, w0 MOV( %rdx, w1, 16) adc $0, w1 mov 16(up,i,8), %rax mul v0 add w3, X1 mov X1, 8(rp,i,8) adc %rax, X0 MOV( %rdx, X1, 32) mov 16(rp,i,8), w3 adc $0, X1 mov 16(up,i,8), %rax mul v1 add w3, w0 MOV( %rdx, w2, 64) adc %rax, w1 mov 24(up,i,8), %rax adc $0, w2 mul v0 add w0, X0 mov X0, 16(rp,i,8) MOV( %rdx, X0, 128) adc %rax, X1 mov 24(up,i,8), %rax mov 24(rp,i,8), w0 adc $0, X0 add $4, i jnc L(am2top0) mul v1 add w0, w1 adc w2, %rax adc Z(i,$0), %rdx add w1, X1 adc Z(i,$0), X0 mov X1, I(-8(rp),-8(rp,i,8)) add X0, %rax mov %rax, I((rp),(rp,i,8)) adc Z(i,$0), %rdx mov %rdx, I(8(rp),8(rp,i,8)) lea 16(rp), rp add $2, n cmp $-2, n jnz L(am2o2) L(cor2):pop n mov -24(up), v0 mov %rax, w2 mov %rdx, w0 mov -16(up), %rax mov %rax, v1 mul v0 mov %rax, X0 MOV( %rdx, X1, 32) mov -8(up), %rax mul v0 add w2, X0 mov X0, -16(rp) MOV( %rdx, X0, 128) adc %rax, X1 mov -8(up), %rax adc $0, X0 mul v1 add w0, X1 adc $0, X0 mov X1, -8(rp) add X0, %rax mov %rax, (rp) adc $0, %rdx mov %rdx, 8(rp) lea 8(rp), rp L(sqr_diag_addlsh1): mov -8(up,n,8), %rax shl n xor R32(%rbx), R32(%rbx) mul %rax mov 8(rp,n,8), %r11 lea (%rdx), %r10 mov 16(rp,n,8), %r9 add %r11, %r11 jmp L(dm) ALIGNx L(dtop):mul %rax add %r11, %r10 mov 8(rp,n,8), %r11 mov %r10, -8(rp,n,8) adc %r9, %rax lea (%rdx,%rbx), %r10 mov 16(rp,n,8), %r9 adc %r11, %r11 L(dm): mov %rax, (rp,n,8) mov (up,n,4), %rax adc %r9, %r9 setc R8(%rbx) add $2, n js L(dtop) mul %rax add %r11, %r10 mov %r10, -8(rp) adc %r9, %rax lea (%rdx,%rbx), %r10 mov %rax, (rp) adc $0, %r10 mov %r10, 8(rp) pop %r14 pop %r13 pop %r12 pop %rbp pop %rbx FUNC_EXIT() ret ALIGN(16) L(small): mov (up), %rax cmp $2, n_param jae L(gt1) L(n1): mul %rax mov %rax, (rp) mov %rdx, 8(rp) FUNC_EXIT() ret L(gt1): jne L(gt2) L(n2): mov %rax, %r8 mul %rax mov 8(up), %r11 mov %rax, (rp) mov %r11, %rax mov %rdx, %r9 mul %rax mov %rax, %r10 mov %r11, %rax mov %rdx, %r11 mul %r8 xor %r8, %r8 add %rax, %r9 adc %rdx, %r10 adc %r8, %r11 add %rax, %r9 mov %r9, 8(rp) adc %rdx, %r10 mov %r10, 16(rp) adc %r8, %r11 mov %r11, 24(rp) FUNC_EXIT() ret L(gt2): L(n3): mov %rax, %r10 mul %rax mov 8(up), %r11 mov %rax, (rp) mov %r11, %rax mov %rdx, 8(rp) mul %rax mov 16(up), %rcx mov %rax, 16(rp) mov %rcx, %rax mov %rdx, 24(rp) mul %rax mov %rax, 32(rp) mov %rdx, 40(rp) mov %r11, %rax mul %r10 mov %rax, %r8 mov %rcx, %rax mov %rdx, %r9 mul %r10 xor %r10, %r10 add %rax, %r9 mov %r11, %rax mov %r10, %r11 adc %rdx, %r10 mul %rcx add %rax, %r10 adc %r11, %rdx add %r8, %r8 adc %r9, %r9 adc %r10, %r10 adc %rdx, %rdx adc %r11, %r11 add %r8, 8(rp) adc %r9, 16(rp) adc %r10, 24(rp) adc %rdx, 32(rp) adc %r11, 40(rp) FUNC_EXIT() ret EPILOGUE() CF_PROT