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-rw-r--r--sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S432
1 files changed, 432 insertions, 0 deletions
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S
new file mode 100644
index 0000000000..9f6ec29ac5
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_pow2_core_sse4.S
@@ -0,0 +1,432 @@
+/* Function pow vectorized with SSE4.
+ Copyright (C) 2014-2015 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 pow@PLT
+
+ 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 pow@PLT
+
+ movsd %xmm0, 192(%rsp,%r15)
+ jmp .LBL_1_7
+
+END (_ZGVbN2vv_pow_sse4)
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-23 10:23:12 +0000