diff options
Diffstat (limited to 'REORG.TODO/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S')
| -rw-r--r-- | REORG.TODO/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S | 432 |
1 files changed, 432 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S b/REORG.TODO/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S new file mode 100644 index 0000000000..ad7c215ff0 --- /dev/null +++ b/REORG.TODO/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S @@ -0,0 +1,432 @@ +/* Function pow vectorized with SSE4. + Copyright (C) 2014-2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <sysdep.h> +#include "svml_d_pow_data.h" + + .text +ENTRY (_ZGVbN2vv_pow_sse4) +/* + ALGORITHM DESCRIPTION: + + 1) Calculating log2|x| + Here we use the following formula. + Let |x|=2^k1*X1, where k1 is integer, 1<=X1<2. + Let C ~= 1/ln(2), + Rcp1 ~= 1/X1, X2=Rcp1*X1, + Rcp2 ~= 1/X2, X3=Rcp2*X2, + Rcp3 ~= 1/X3, Rcp3C ~= C/X3. + Then + log2|x| = k1 + log2(1/Rcp1) + log2(1/Rcp2) + log2(C/Rcp3C) + + log2(X1*Rcp1*Rcp2*Rcp3C/C), + where X1*Rcp1*Rcp2*Rcp3C = C*(1+q), q is very small. + + The values of Rcp1, log2(1/Rcp1), Rcp2, log2(1/Rcp2), + Rcp3C, log2(C/Rcp3C) are taken from tables. + Values of Rcp1, Rcp2, Rcp3C are such that RcpC=Rcp1*Rcp2*Rcp3C + is exactly represented in target precision. + + log2(X1*Rcp1*Rcp2*Rcp3C/C) = log2(1+q) = ln(1+q)/ln2 = + = 1/(ln2)*q - 1/(2ln2)*q^2 + 1/(3ln2)*q^3 - ... = + = 1/(C*ln2)*cq - 1/(2*C^2*ln2)*cq^2 + 1/(3*C^3*ln2)*cq^3 - ... = + = (1 + a1)*cq + a2*cq^2 + a3*cq^3 + ..., + where cq = X1*Rcp1*Rcp2*Rcp3C-C, + a1=1/(C*ln(2))-1 is small, + a2=1/(2*C^2*ln2), + a3=1/(3*C^3*ln2), + ... + We get 3 parts of log2 result: HH+HL+HLL ~= log2|x|. + + 2) Calculation of y*(HH+HL+HLL). + Split y into YHi+YLo. + Get high PH and medium PL parts of y*log2|x|. + Get low PLL part of y*log2|x|. + Now we have PH+PL+PLL ~= y*log2|x|. + + 3) Calculation of 2^(PH+PL+PLL). + Mathematical idea of computing 2^(PH+PL+PLL) is the following. + Let's represent PH+PL+PLL in the form N + j/2^expK + Z, + where expK=7 in this implementation, N and j are integers, + 0<=j<=2^expK-1, |Z|<2^(-expK-1). + Hence 2^(PH+PL+PLL) ~= 2^N * 2^(j/2^expK) * 2^Z, + where 2^(j/2^expK) is stored in a table, and + 2^Z ~= 1 + B1*Z + B2*Z^2 ... + B5*Z^5. + + We compute 2^(PH+PL+PLL) as follows. + Break PH into PHH + PHL, where PHH = N + j/2^expK. + Z = PHL + PL + PLL + Exp2Poly = B1*Z + B2*Z^2 ... + B5*Z^5 + Get 2^(j/2^expK) from table in the form THI+TLO. + Now we have 2^(PH+PL+PLL) ~= 2^N * (THI + TLO) * (1 + Exp2Poly). + + Get significand of 2^(PH+PL+PLL) in the form ResHi+ResLo: + ResHi := THI + ResLo := THI * Exp2Poly + TLO + + Get exponent ERes of the result: + Res := ResHi + ResLo: + Result := ex(Res) + N. */ + + pushq %rbp + cfi_adjust_cfa_offset (8) + cfi_rel_offset (%rbp, 0) + movq %rsp, %rbp + cfi_def_cfa_register (%rbp) + andq $-64, %rsp + subq $256, %rsp + movq __svml_dpow_data@GOTPCREL(%rip), %rdx + movups %xmm14, 80(%rsp) + movups %xmm9, 176(%rsp) + movaps %xmm1, %xmm9 + pshufd $221, %xmm0, %xmm1 + movq _iIndexMask(%rdx), %xmm14 + movq _iIndexAdd(%rdx), %xmm6 + +/* i = (((Hi(x) & 0x000ffe00) + 0x00000200) >> 10); -> i = (b1..b11 + 1) / 2 */ + pand %xmm1, %xmm14 + paddd %xmm6, %xmm14 + psrld $10, %xmm14 + movups %xmm13, 96(%rsp) + +/* Index for reciprocal table */ + movdqa %xmm14, %xmm13 + pslld $3, %xmm13 + +/* Index for log2 table */ + pslld $4, %xmm14 + movd %xmm13, %eax + movups %xmm10, 160(%rsp) + movups _iMantissaMask(%rdx), %xmm10 + movslq %eax, %rax + +/* x1 = x; Hi(x1) = (Hi(x1)&0x000fffff)|0x3ff00000 */ + andps %xmm0, %xmm10 + pextrd $1, %xmm13, %ecx + movslq %ecx, %rcx + movups %xmm0, (%rsp) + movdqa %xmm1, %xmm0 + +/* k = Hi(x); k = k - 0x3fe7fe00; k = k >> 20 */ + movq _i3fe7fe00(%rdx), %xmm6 + psubd %xmm6, %xmm0 + movups _iHighMask(%rdx), %xmm6 + psrad $20, %xmm0 + movups %xmm15, 48(%rsp) + movups %xmm12, 112(%rsp) + orps _dbOne(%rdx), %xmm10 + movsd 11712(%rdx,%rax), %xmm12 + movd %xmm14, %r8d + movq _i2p20_2p19(%rdx), %xmm15 + movhpd 11712(%rdx,%rcx), %xmm12 + paddd %xmm15, %xmm0 + pextrd $1, %xmm14, %r9d + +/* x1Hi=x1; Lo(x1Hi)&=0xf8000000; x1Lo = x1-x1Hi */ + movaps %xmm6, %xmm14 + andps %xmm10, %xmm14 + movaps %xmm10, %xmm15 + subpd %xmm14, %xmm15 + +/* r1 = x1*rcp1 */ + mulpd %xmm12, %xmm10 + +/* E = -r1+__fence(x1Hi*rcp1) */ + mulpd %xmm12, %xmm14 + +/* E=E+x1Lo*rcp1 */ + mulpd %xmm15, %xmm12 + subpd %xmm10, %xmm14 + pshufd $80, %xmm0, %xmm0 + movslq %r8d, %r8 + andps _iffffffff00000000(%rdx), %xmm0 + subpd _db2p20_2p19(%rdx), %xmm0 + addpd %xmm12, %xmm14 + movslq %r9d, %r9 + +/* T_Rh_Eh = T_Rh + E */ + movaps %xmm14, %xmm15 + movups %xmm8, 208(%rsp) + movups 19968(%rdx,%r8), %xmm8 + movups %xmm11, 144(%rsp) + movaps %xmm8, %xmm11 + +/* cq = c+r1 */ + movups _LHN(%rdx), %xmm13 + movhpd 19968(%rdx,%r9), %xmm11 + addpd %xmm10, %xmm13 + +/* T = k + L1hi */ + addpd %xmm0, %xmm11 + +/* T_Rh = T + cq */ + movaps %xmm13, %xmm12 + addpd %xmm11, %xmm12 + addpd %xmm12, %xmm15 + +/* Rl = T-T_Rh; -> -Rh */ + subpd %xmm12, %xmm11 + +/* HLL = T_Rh - T_Rh_Eh; -> -Eh */ + subpd %xmm15, %xmm12 + +/* Rl=Rl+cq; */ + addpd %xmm13, %xmm11 + +/* cq = cq + E */ + addpd %xmm14, %xmm13 + +/* HLL+=E; -> El */ + addpd %xmm14, %xmm12 + +/* HLL+=Rl */ + addpd %xmm12, %xmm11 + unpckhpd 19968(%rdx,%r9), %xmm8 + +/* T_Rh_Eh_HLLhi = T_Rh_Eh + HLL */ + movaps %xmm15, %xmm14 + +/* HLL+=L1lo; */ + addpd %xmm11, %xmm8 + movups _clv_2(%rdx), %xmm11 + +/* HH = T_Rh_Eh_HLLhi; Lo(HH)&=0xf8000000 */ + movaps %xmm6, %xmm12 + +/* HLL = HLL + (((((((a7)*cq+a6)*cq+a5)*cq+a4)*cq+a3)*cq+a2)*cq+a1)*cq */ + mulpd %xmm13, %xmm11 + addpd _clv_3(%rdx), %xmm11 + mulpd %xmm13, %xmm11 + addpd _clv_4(%rdx), %xmm11 + mulpd %xmm13, %xmm11 + addpd _clv_5(%rdx), %xmm11 + mulpd %xmm13, %xmm11 + addpd _clv_6(%rdx), %xmm11 + mulpd %xmm13, %xmm11 + addpd _clv_7(%rdx), %xmm11 + mulpd %xmm11, %xmm13 + addpd %xmm13, %xmm8 + addpd %xmm8, %xmm14 + +/* + 2^(y*(HH+HL+HLL)) starts here: + yH = y; Lo(yH)&=0xf8000000 + */ + andps %xmm9, %xmm6 + +/* yL = y-yH; */ + movaps %xmm9, %xmm11 + subpd %xmm6, %xmm11 + andps %xmm14, %xmm12 + +/* HLLhi = T_Rh_Eh_HLLhi - T_Rh_Eh */ + movaps %xmm14, %xmm10 + +/* HL = T_Rh_Eh_HLLhi-HH; */ + subpd %xmm12, %xmm14 + subpd %xmm15, %xmm10 + movq _HIDELTA(%rdx), %xmm2 + +/* pH = yH*HH; */ + movaps %xmm6, %xmm13 + movq _LORANGE(%rdx), %xmm3 + paddd %xmm2, %xmm1 + pcmpgtd %xmm1, %xmm3 + +/* pL=yL*HL+yH*HL; pL+=yL*HH; */ + movaps %xmm11, %xmm1 + mulpd %xmm14, %xmm1 + mulpd %xmm14, %xmm6 + mulpd %xmm12, %xmm13 + mulpd %xmm11, %xmm12 + addpd %xmm6, %xmm1 + +/* HLL = HLL - HLLhi */ + subpd %xmm10, %xmm8 + addpd %xmm12, %xmm1 + +/* pLL = y*HLL */ + mulpd %xmm9, %xmm8 + movups _db2p45_2p44(%rdx), %xmm11 + +/* pHH = pH + *(double*)&db2p45_2p44 */ + movaps %xmm11, %xmm12 + addpd %xmm13, %xmm12 + +/* t=pL+pLL; t+=pHL */ + addpd %xmm8, %xmm1 + movq _ABSMASK(%rdx), %xmm5 + pshufd $221, %xmm9, %xmm4 + pand %xmm5, %xmm4 + movq _INF(%rdx), %xmm7 + movdqa %xmm4, %xmm2 + pcmpgtd %xmm7, %xmm2 + pcmpeqd %xmm7, %xmm4 + pshufd $136, %xmm12, %xmm7 + por %xmm4, %xmm2 + +/* pHH = pHH - *(double*)&db2p45_2p44 */ + subpd %xmm11, %xmm12 + pshufd $221, %xmm13, %xmm10 + por %xmm2, %xmm3 + +/* pHL = pH - pHH; */ + subpd %xmm12, %xmm13 + pand %xmm5, %xmm10 + movq _DOMAINRANGE(%rdx), %xmm5 + movdqa %xmm10, %xmm4 + addpd %xmm1, %xmm13 + pcmpgtd %xmm5, %xmm4 + pcmpeqd %xmm5, %xmm10 + por %xmm10, %xmm4 + movq _jIndexMask(%rdx), %xmm6 + por %xmm4, %xmm3 + movmskps %xmm3, %eax + +/* j = Lo(pHH)&0x0000007f */ + pand %xmm7, %xmm6 + movq _iOne(%rdx), %xmm3 + +/* _n = Lo(pHH); + _n = _n & 0xffffff80; + _n = _n >> 7; + Hi(_2n) = (0x3ff+_n)<<20; Lo(_2n) = 0; -> 2^n + */ + pslld $13, %xmm7 + paddd %xmm3, %xmm7 + pslld $4, %xmm6 + movups _cev_1(%rdx), %xmm3 + movaps %xmm13, %xmm4 + mulpd %xmm13, %xmm3 + +/* T1 = ((double*)exp2_tbl)[ 2*j ] */ + movd %xmm6, %r10d + pshufd $80, %xmm7, %xmm0 + andps _ifff0000000000000(%rdx), %xmm0 + addpd _cev_2(%rdx), %xmm3 + mulpd %xmm13, %xmm3 + addpd _cev_3(%rdx), %xmm3 + mulpd %xmm13, %xmm3 + movslq %r10d, %r10 + andl $3, %eax + pextrd $1, %xmm6, %r11d + movslq %r11d, %r11 + addpd _cev_4(%rdx), %xmm3 + movsd 36416(%rdx,%r10), %xmm2 + movhpd 36416(%rdx,%r11), %xmm2 + mulpd %xmm2, %xmm0 + mulpd %xmm3, %xmm13 + mulpd %xmm0, %xmm4 + addpd _cev_5(%rdx), %xmm13 + mulpd %xmm4, %xmm13 + addpd %xmm13, %xmm0 + jne .LBL_1_3 + +.LBL_1_2: + cfi_remember_state + movups 208(%rsp), %xmm8 + movups 176(%rsp), %xmm9 + movups 160(%rsp), %xmm10 + movups 144(%rsp), %xmm11 + movups 112(%rsp), %xmm12 + movups 96(%rsp), %xmm13 + movups 80(%rsp), %xmm14 + movups 48(%rsp), %xmm15 + movq %rbp, %rsp + cfi_def_cfa_register (%rsp) + popq %rbp + cfi_adjust_cfa_offset (-8) + cfi_restore (%rbp) + ret + +.LBL_1_3: + cfi_restore_state + movups (%rsp), %xmm1 + movups %xmm1, 64(%rsp) + movups %xmm9, 128(%rsp) + movups %xmm0, 192(%rsp) + je .LBL_1_2 + + xorb %cl, %cl + xorl %edx, %edx + movq %rsi, 8(%rsp) + movq %rdi, (%rsp) + movq %r12, 40(%rsp) + cfi_offset_rel_rsp (12, 40) + movb %cl, %r12b + movq %r13, 32(%rsp) + cfi_offset_rel_rsp (13, 32) + movl %eax, %r13d + movq %r14, 24(%rsp) + cfi_offset_rel_rsp (14, 24) + movl %edx, %r14d + movq %r15, 16(%rsp) + cfi_offset_rel_rsp (15, 16) + cfi_remember_state + +.LBL_1_6: + btl %r14d, %r13d + jc .LBL_1_12 + +.LBL_1_7: + lea 1(%r14), %esi + btl %esi, %r13d + jc .LBL_1_10 + +.LBL_1_8: + incb %r12b + addl $2, %r14d + cmpb $16, %r12b + jb .LBL_1_6 + + movq 8(%rsp), %rsi + movq (%rsp), %rdi + movq 40(%rsp), %r12 + cfi_restore (%r12) + movq 32(%rsp), %r13 + cfi_restore (%r13) + movq 24(%rsp), %r14 + cfi_restore (%r14) + movq 16(%rsp), %r15 + cfi_restore (%r15) + movups 192(%rsp), %xmm0 + jmp .LBL_1_2 + +.LBL_1_10: + cfi_restore_state + movzbl %r12b, %r15d + shlq $4, %r15 + movsd 72(%rsp,%r15), %xmm0 + movsd 136(%rsp,%r15), %xmm1 + + call JUMPTARGET(__pow_finite) + + movsd %xmm0, 200(%rsp,%r15) + jmp .LBL_1_8 + +.LBL_1_12: + movzbl %r12b, %r15d + shlq $4, %r15 + movsd 64(%rsp,%r15), %xmm0 + movsd 128(%rsp,%r15), %xmm1 + + call JUMPTARGET(__pow_finite) + + movsd %xmm0, 192(%rsp,%r15) + jmp .LBL_1_7 + +END (_ZGVbN2vv_pow_sse4) |