/* Function powf vectorized with SSE4.
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 (_ZGVbN4vv_powf_sse4)
/*
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 $256, %rsp
movaps %xmm0, %xmm3
movhlps %xmm0, %xmm3
movaps %xmm1, %xmm5
movups %xmm8, 112(%rsp)
movaps %xmm5, %xmm2
cvtps2pd %xmm3, %xmm8
cvtps2pd %xmm5, %xmm7
movups %xmm9, 96(%rsp)
movaps %xmm0, %xmm4
cvtps2pd %xmm0, %xmm9
movq __svml_spow_data@GOTPCREL(%rip), %rdx
movups %xmm10, 176(%rsp)
movups %xmm13, 48(%rsp)
movups _ExpMask(%rdx), %xmm6
/* preserve mantissa, set input exponent to 2^(-10) */
movaps %xmm6, %xmm10
andps %xmm8, %xmm6
andps %xmm9, %xmm10
/* exponent bits selection */
psrlq $20, %xmm9
orps _Two10(%rdx), %xmm6
psrlq $20, %xmm8
orps _Two10(%rdx), %xmm10
/* reciprocal approximation good to at least 11 bits */
cvtpd2ps %xmm6, %xmm13
cvtpd2ps %xmm10, %xmm1
movlhps %xmm13, %xmm13
movhlps %xmm5, %xmm2
movlhps %xmm1, %xmm1
movups %xmm12, 208(%rsp)
rcpps %xmm13, %xmm12
movups %xmm11, 80(%rsp)
cvtps2pd %xmm2, %xmm11
rcpps %xmm1, %xmm2
movups %xmm14, 144(%rsp)
cvtps2pd %xmm12, %xmm14
movups %xmm15, 160(%rsp)
cvtps2pd %xmm2, %xmm15
shufps $221, %xmm8, %xmm9
/* round reciprocal to nearest integer, will have 1+9 mantissa bits */
roundpd $0, %xmm14, %xmm14
/* biased exponent in DP format */
pshufd $238, %xmm9, %xmm8
roundpd $0, %xmm15, %xmm15
cvtdq2pd %xmm8, %xmm1
mulpd %xmm15, %xmm10
mulpd %xmm14, %xmm6
cvtdq2pd %xmm9, %xmm2
subpd _One(%rdx), %xmm10
subpd _One(%rdx), %xmm6
/* table lookup */
movaps %xmm14, %xmm8
movaps %xmm15, %xmm9
psrlq $40, %xmm8
psrlq $40, %xmm9
movd %xmm8, %r8d
movd %xmm9, %eax
psubd _NMINNORM(%rdx), %xmm4
movdqu _ABSMASK(%rdx), %xmm3
pextrd $2, %xmm8, %r9d
pand %xmm5, %xmm3
movups _Threshold(%rdx), %xmm8
pextrd $2, %xmm9, %ecx
movaps %xmm8, %xmm9
cmpltpd %xmm15, %xmm9
cmpltpd %xmm14, %xmm8
andps _Bias(%rdx), %xmm9
movaps %xmm10, %xmm14
andps _Bias(%rdx), %xmm8
movaps %xmm6, %xmm15
orps _Bias1(%rdx), %xmm9
orps _Bias1(%rdx), %xmm8
subpd %xmm9, %xmm2
subpd %xmm8, %xmm1
mulpd %xmm10, %xmm14
mulpd %xmm6, %xmm15
mulpd _L2(%rdx), %xmm2
mulpd _L2(%rdx), %xmm1
movups _poly_coeff_3(%rdx), %xmm9
movaps %xmm9, %xmm8
mulpd %xmm10, %xmm8
mulpd %xmm6, %xmm9
addpd _poly_coeff_4(%rdx), %xmm8
addpd _poly_coeff_4(%rdx), %xmm9
mulpd %xmm14, %xmm8
mulpd %xmm15, %xmm9
/* reconstruction */
addpd %xmm8, %xmm10
addpd %xmm9, %xmm6
movslq %eax, %rax
movslq %r8d, %r8
movslq %ecx, %rcx
movslq %r9d, %r9
movsd _Log2Rcp_lookup(%rdx,%rax), %xmm13
movsd _Log2Rcp_lookup(%rdx,%r8), %xmm12
movhpd _Log2Rcp_lookup(%rdx,%rcx), %xmm13
movhpd _Log2Rcp_lookup(%rdx,%r9), %xmm12
addpd %xmm10, %xmm13
addpd %xmm6, %xmm12
addpd %xmm13, %xmm2
addpd %xmm12, %xmm1
mulpd %xmm7, %xmm2
mulpd %xmm11, %xmm1
movups __dbInvLn2(%rdx), %xmm11
movdqa %xmm4, %xmm12
movaps %xmm11, %xmm10
mulpd %xmm2, %xmm10
mulpd %xmm1, %xmm11
/* to round down; if dR is an integer we will get R = 1, which is ok */
movaps %xmm10, %xmm8
movaps %xmm11, %xmm9
subpd __dbHALF(%rdx), %xmm8
subpd __dbHALF(%rdx), %xmm9
addpd __dbShifter(%rdx), %xmm8
addpd __dbShifter(%rdx), %xmm9
movaps %xmm8, %xmm6
movaps %xmm9, %xmm7
subpd __dbShifter(%rdx), %xmm6
subpd __dbShifter(%rdx), %xmm7
/* [0..1) */
subpd %xmm6, %xmm10
subpd %xmm7, %xmm11
mulpd __dbC1(%rdx), %xmm10
mulpd __dbC1(%rdx), %xmm11
/* hi bits */
shufps $221, %xmm1, %xmm2
movdqu _NMAXVAL(%rdx), %xmm1
pcmpgtd %xmm1, %xmm12
pcmpeqd %xmm1, %xmm4
por %xmm4, %xmm12
movdqa %xmm3, %xmm1
movdqu _INF(%rdx), %xmm4
pcmpgtd %xmm4, %xmm1
pcmpeqd %xmm4, %xmm3
/* iAbsX = iAbsX&iAbsMask */
pand __iAbsMask(%rdx), %xmm2
por %xmm3, %xmm1
/* iRangeMask = (iAbsX>iDomainRange) */
pcmpgtd __iDomainRange(%rdx), %xmm2
por %xmm1, %xmm12
movups __lbLOWKBITS(%rdx), %xmm3
por %xmm2, %xmm12
/* low K bits */
movaps %xmm3, %xmm2
andps %xmm9, %xmm3
andps %xmm8, %xmm2
psrlq $11, %xmm8
/* dpP= _dbT+lJ*T_ITEM_GRAN */
movd %xmm2, %r10d
psrlq $11, %xmm9
movd %xmm3, %ecx
/* NB : including +/- sign for the exponent!! */
psllq $52, %xmm8
psllq $52, %xmm9
pextrw $4, %xmm2, %r11d
pextrw $4, %xmm3, %r8d
movmskps %xmm12, %eax
shll $3, %r10d
shll $3, %ecx
shll $3, %r11d
shll $3, %r8d
movq 13952(%rdx,%r10), %xmm6
movq 13952(%rdx,%rcx), %xmm7
movhpd 13952(%rdx,%r11), %xmm6
movhpd 13952(%rdx,%r8), %xmm7
mulpd %xmm6, %xmm10
mulpd %xmm7, %xmm11
addpd %xmm10, %xmm6
addpd %xmm11, %xmm7
paddq %xmm8, %xmm6
paddq %xmm9, %xmm7
cvtpd2ps %xmm6, %xmm1
cvtpd2ps %xmm7, %xmm4
movlhps %xmm4, %xmm1
testl %eax, %eax
jne .LBL_1_3
.LBL_1_2:
cfi_remember_state
movups 112(%rsp), %xmm8
movaps %xmm1, %xmm0
movups 96(%rsp), %xmm9
movups 176(%rsp), %xmm10
movups 80(%rsp), %xmm11
movups 208(%rsp), %xmm12
movups 48(%rsp), %xmm13
movups 144(%rsp), %xmm14
movups 160(%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 %xmm0, 64(%rsp)
movups %xmm5, 128(%rsp)
movups %xmm1, 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), %xmm1
jmp .LBL_1_2
.LBL_1_10:
cfi_restore_state
movzbl %r12b, %r15d
movss 68(%rsp,%r15,8), %xmm0
movss 132(%rsp,%r15,8), %xmm1
call powf@PLT
movss %xmm0, 196(%rsp,%r15,8)
jmp .LBL_1_8
.LBL_1_12:
movzbl %r12b, %r15d
movss 64(%rsp,%r15,8), %xmm0
movss 128(%rsp,%r15,8), %xmm1
call powf@PLT
movss %xmm0, 192(%rsp,%r15,8)
jmp .LBL_1_7
END (_ZGVbN4vv_powf_sse4)