/* Function powf vectorized with AVX2.
Copyright (C) 2014-2016 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
. */
#include
#include "svml_s_powf_data.h"
.text
ENTRY(_ZGVdN8vv_powf_avx2)
/*
ALGORITHM DESCRIPTION:
We are using the next identity : pow(x,y) = 2^(y * log2(x)).
1) log2(x) calculation
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),
...
Log2 result is split by three parts: HH+HL+HLL
2) Calculation of y*log2(x)
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^(y*log2(x))
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 $448, %rsp
lea __VPACK_ODD_ind.6357.0.1(%rip), %rcx
vmovups %ymm14, 320(%rsp)
/* hi bits */
lea __VPACK_ODD_ind.6358.0.1(%rip), %rax
vmovups %ymm12, 256(%rsp)
vmovups %ymm9, 96(%rsp)
vmovups %ymm13, 224(%rsp)
vmovups %ymm15, 352(%rsp)
vmovups %ymm11, 384(%rsp)
vmovups %ymm10, 288(%rsp)
vmovups (%rcx), %ymm10
vmovups %ymm8, 160(%rsp)
vmovdqa %ymm1, %ymm9
movq __svml_spow_data@GOTPCREL(%rip), %rdx
vextractf128 $1, %ymm0, %xmm7
vcvtps2pd %xmm0, %ymm14
vcvtps2pd %xmm7, %ymm12
vpsubd _NMINNORM(%rdx), %ymm0, %ymm7
/* preserve mantissa, set input exponent to 2^(-10) */
vandpd _ExpMask(%rdx), %ymm14, %ymm3
vandpd _ExpMask(%rdx), %ymm12, %ymm13
/* exponent bits selection */
vpsrlq $20, %ymm12, %ymm12
vpsrlq $20, %ymm14, %ymm14
vextractf128 $1, %ymm9, %xmm2
vcvtps2pd %xmm9, %ymm1
vpand _ABSMASK(%rdx), %ymm9, %ymm8
vcvtps2pd %xmm2, %ymm6
vorpd _Two10(%rdx), %ymm3, %ymm2
vorpd _Two10(%rdx), %ymm13, %ymm3
/* reciprocal approximation good to at least 11 bits */
vcvtpd2ps %ymm2, %xmm5
vcvtpd2ps %ymm3, %xmm15
vrcpps %xmm5, %xmm4
vrcpps %xmm15, %xmm11
vcvtps2pd %xmm4, %ymm13
vcvtps2pd %xmm11, %ymm4
vpermps %ymm12, %ymm10, %ymm11
/* round reciprocal to nearest integer, will have 1+9 mantissa bits */
vroundpd $0, %ymm13, %ymm12
vpermps %ymm14, %ymm10, %ymm5
vroundpd $0, %ymm4, %ymm14
vmovupd _One(%rdx), %ymm4
/* table lookup */
vpsrlq $40, %ymm12, %ymm10
vfmsub213pd %ymm4, %ymm12, %ymm2
vfmsub213pd %ymm4, %ymm14, %ymm3
vcmpgt_oqpd _Threshold(%rdx), %ymm12, %ymm12
vxorpd %ymm4, %ymm4, %ymm4
vandpd _Bias(%rdx), %ymm12, %ymm12
/* biased exponent in DP format */
vcvtdq2pd %xmm11, %ymm13
vpcmpeqd %ymm11, %ymm11, %ymm11
vgatherqpd %ymm11, _Log2Rcp_lookup(%rdx,%ymm10), %ymm4
vpsrlq $40, %ymm14, %ymm10
vcmpgt_oqpd _Threshold(%rdx), %ymm14, %ymm14
vpcmpeqd %ymm11, %ymm11, %ymm11
vandpd _Bias(%rdx), %ymm14, %ymm14
vcvtdq2pd %xmm5, %ymm15
vxorpd %ymm5, %ymm5, %ymm5
vgatherqpd %ymm11, _Log2Rcp_lookup(%rdx,%ymm10), %ymm5
vorpd _Bias1(%rdx), %ymm12, %ymm11
vorpd _Bias1(%rdx), %ymm14, %ymm10
vsubpd %ymm11, %ymm15, %ymm11
vsubpd %ymm10, %ymm13, %ymm14
vmovupd _poly_coeff_4(%rdx), %ymm15
vmovupd _poly_coeff_3(%rdx), %ymm13
vmulpd %ymm3, %ymm3, %ymm10
vfmadd213pd %ymm15, %ymm3, %ymm13
vmovdqa %ymm15, %ymm12
vfmadd231pd _poly_coeff_3(%rdx), %ymm2, %ymm12
vmulpd %ymm2, %ymm2, %ymm15
/* reconstruction */
vfmadd213pd %ymm3, %ymm10, %ymm13
vfmadd213pd %ymm2, %ymm15, %ymm12
vaddpd %ymm5, %ymm13, %ymm13
vaddpd %ymm4, %ymm12, %ymm2
vfmadd231pd _L2(%rdx), %ymm14, %ymm13
vfmadd132pd _L2(%rdx), %ymm2, %ymm11
vmulpd %ymm6, %ymm13, %ymm2
vmulpd %ymm1, %ymm11, %ymm10
vmulpd __dbInvLn2(%rdx), %ymm2, %ymm6
vmulpd __dbInvLn2(%rdx), %ymm10, %ymm15
/* to round down; if dR is an integer we will get R = 1, which is ok */
vsubpd __dbHALF(%rdx), %ymm6, %ymm3
vsubpd __dbHALF(%rdx), %ymm15, %ymm1
vaddpd __dbShifter(%rdx), %ymm3, %ymm13
vaddpd __dbShifter(%rdx), %ymm1, %ymm14
vsubpd __dbShifter(%rdx), %ymm13, %ymm12
vmovups (%rax), %ymm1
vsubpd __dbShifter(%rdx), %ymm14, %ymm11
/* [0..1) */
vsubpd %ymm12, %ymm6, %ymm6
vpermps %ymm10, %ymm1, %ymm3
vpermps %ymm2, %ymm1, %ymm10
vpcmpgtd _NMAXVAL(%rdx), %ymm7, %ymm4
vpcmpgtd _INF(%rdx), %ymm8, %ymm1
vpcmpeqd _NMAXVAL(%rdx), %ymm7, %ymm7
vpcmpeqd _INF(%rdx), %ymm8, %ymm8
vpor %ymm7, %ymm4, %ymm2
vpor %ymm8, %ymm1, %ymm1
vsubpd %ymm11, %ymm15, %ymm7
vinsertf128 $1, %xmm10, %ymm3, %ymm10
vpor %ymm1, %ymm2, %ymm3
/* iAbsX = iAbsX&iAbsMask */
vandps __iAbsMask(%rdx), %ymm10, %ymm10
/* iRangeMask = (iAbsX>iDomainRange) */
vpcmpgtd __iDomainRange(%rdx), %ymm10, %ymm4
vpor %ymm4, %ymm3, %ymm5
vmulpd __dbC1(%rdx), %ymm7, %ymm4
vmovmskps %ymm5, %ecx
vmulpd __dbC1(%rdx), %ymm6, %ymm5
/* low K bits */
vandps __lbLOWKBITS(%rdx), %ymm14, %ymm6
/* dpP= _dbT+lJ*T_ITEM_GRAN */
vxorpd %ymm7, %ymm7, %ymm7
vpcmpeqd %ymm1, %ymm1, %ymm1
vandps __lbLOWKBITS(%rdx), %ymm13, %ymm2
vxorpd %ymm10, %ymm10, %ymm10
vpcmpeqd %ymm3, %ymm3, %ymm3
vgatherqpd %ymm1, 13952(%rdx,%ymm6,8), %ymm7
vgatherqpd %ymm3, 13952(%rdx,%ymm2,8), %ymm10
vpsrlq $11, %ymm14, %ymm14
vpsrlq $11, %ymm13, %ymm13
vfmadd213pd %ymm7, %ymm4, %ymm7
vfmadd213pd %ymm10, %ymm5, %ymm10
/* NB : including +/- sign for the exponent!! */
vpsllq $52, %ymm14, %ymm8
vpsllq $52, %ymm13, %ymm11
vpaddq %ymm8, %ymm7, %ymm12
vpaddq %ymm11, %ymm10, %ymm1
vcvtpd2ps %ymm12, %xmm15
vcvtpd2ps %ymm1, %xmm2
vinsertf128 $1, %xmm2, %ymm15, %ymm1
testl %ecx, %ecx
jne .LBL_1_3
.LBL_1_2:
cfi_remember_state
vmovups 160(%rsp), %ymm8
vmovups 96(%rsp), %ymm9
vmovups 288(%rsp), %ymm10
vmovups 384(%rsp), %ymm11
vmovups 256(%rsp), %ymm12
vmovups 224(%rsp), %ymm13
vmovups 320(%rsp), %ymm14
vmovups 352(%rsp), %ymm15
vmovdqa %ymm1, %ymm0
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
vmovups %ymm0, 64(%rsp)
vmovups %ymm9, 128(%rsp)
vmovups %ymm1, 192(%rsp)
je .LBL_1_2
xorb %dl, %dl
xorl %eax, %eax
movq %rsi, 8(%rsp)
movq %rdi, (%rsp)
movq %r12, 40(%rsp)
cfi_offset_rel_rsp (12, 40)
movb %dl, %r12b
movq %r13, 32(%rsp)
cfi_offset_rel_rsp (13, 32)
movl %ecx, %r13d
movq %r14, 24(%rsp)
cfi_offset_rel_rsp (14, 24)
movl %eax, %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)
vmovups 192(%rsp), %ymm1
jmp .LBL_1_2
.LBL_1_10:
cfi_restore_state
movzbl %r12b, %r15d
vmovss 68(%rsp,%r15,8), %xmm0
vmovss 132(%rsp,%r15,8), %xmm1
vzeroupper
call powf@PLT
vmovss %xmm0, 196(%rsp,%r15,8)
jmp .LBL_1_8
.LBL_1_12:
movzbl %r12b, %r15d
vmovss 64(%rsp,%r15,8), %xmm0
vmovss 128(%rsp,%r15,8), %xmm1
vzeroupper
call powf@PLT
vmovss %xmm0, 192(%rsp,%r15,8)
jmp .LBL_1_7
END(_ZGVdN8vv_powf_avx2)
.section .rodata, "a"
__VPACK_ODD_ind.6357.0.1:
.long 1
.long 3
.long 5
.long 7
.long 0
.long 0
.long 0
.long 0
.space 32, 0x00
__VPACK_ODD_ind.6358.0.1:
.long 1
.long 3
.long 5
.long 7
.long 0
.long 0
.long 0
.long 0