| /* Function pow vectorized with SSE4. |
| Copyright (C) 2014-2018 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) |
