/* 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)