x86-64: Add vector acosh/acoshf implementation to libmvec

Implement vectorized acosh/acoshf containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI.  It also contains
accuracy and ABI tests for vector acosh/acoshf with regenerated ulps.

Reviewed-by: H.J. Lu <hjl.tools@gmail.com>

1 files changed, 480 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_acosh8_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_d_acosh8_core_avx512.S
new file mode 100644
index 0000000..3199ef7
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_acosh8_core_avx512.S
@@ -0,0 +1,480 @@
+/* Function acosh vectorized with AVX-512.
+   Copyright (C) 2021 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
+   https://www.gnu.org/licenses/.  */
+
+/*
+ * ALGORITHM DESCRIPTION:
+ *
+ *   Compute acosh(x) as log(x + sqrt(x*x - 1))
+ *   using RSQRT instructions for starting the
+ *   square root approximation, and small table lookups for log
+ *   that map to AVX-512 permute instructions
+ *
+ *   Special cases:
+ *
+ *   acosh(NaN)  = quiet NaN, and raise invalid exception
+ *   acosh(-INF) = NaN
+ *   acosh(+INF) = +INF
+ *   acosh(x)    = NaN if x < 1
+ *   acosh(1)    = +0
+ *
+ */
+
+/* Offsets for data table __svml_dacosh_data_internal_avx512
+ */
+#define Log_tbl_H                     	0
+#define Log_tbl_L                     	128
+#define One                           	256
+#define SmallThreshold                	320
+#define Threshold                     	384
+#define LargeThreshold                	448
+#define ca2                           	512
+#define ca1                           	576
+#define c4s                           	640
+#define c3s                           	704
+#define c2s                           	768
+#define c1s                           	832
+#define AddB5                         	896
+#define RcpBitMask                    	960
+#define OneEighth                     	1024
+#define Four                          	1088
+#define poly_coeff9                   	1152
+#define poly_coeff8                   	1216
+#define poly_coeff7                   	1280
+#define poly_coeff6                   	1344
+#define poly_coeff5                   	1408
+#define poly_coeff4                   	1472
+#define poly_coeff3                   	1536
+#define poly_coeff2                   	1600
+#define poly_coeff1                   	1664
+#define L2H                           	1728
+#define L2L                           	1792
+
+#include <sysdep.h>
+
+        .text
+	.section .text.evex512,"ax",@progbits
+ENTRY(_ZGVeN8v_acosh_skx)
+        pushq     %rbp
+        cfi_def_cfa_offset(16)
+        movq      %rsp, %rbp
+        cfi_def_cfa(6, 16)
+        cfi_offset(6, -16)
+        andq      $-64, %rsp
+        subq      $192, %rsp
+        vmovups   One+__svml_dacosh_data_internal_avx512(%rip), %zmm5
+
+/* polynomial computation for small inputs */
+        vmovups   ca2+__svml_dacosh_data_internal_avx512(%rip), %zmm13
+        vmovups   ca1+__svml_dacosh_data_internal_avx512(%rip), %zmm14
+
+/*
+ * sqrt(1+x^2) ~ Sh + Sl + Sh*Eh*poly_s
+ * poly_s = c1+c2*Eh+c3*Eh^2
+ */
+        vmovups   c4s+__svml_dacosh_data_internal_avx512(%rip), %zmm1
+        vmovups   c2s+__svml_dacosh_data_internal_avx512(%rip), %zmm2
+        vmovups   c1s+__svml_dacosh_data_internal_avx512(%rip), %zmm6
+
+/* very large inputs ? */
+        vmovups   Threshold+__svml_dacosh_data_internal_avx512(%rip), %zmm15
+
+/* out of range inputs? */
+        vmovups   LargeThreshold+__svml_dacosh_data_internal_avx512(%rip), %zmm3
+
+/* not a very small input ? */
+        vmovups   SmallThreshold+__svml_dacosh_data_internal_avx512(%rip), %zmm10
+        vmovaps   %zmm0, %zmm12
+
+/* x^2 - 1 */
+        vmovaps   %zmm5, %zmm11
+        vfmsub231pd {rn-sae}, %zmm12, %zmm12, %zmm11
+        vcmppd    $21, {sae}, %zmm15, %zmm12, %k2
+        vcmppd    $22, {sae}, %zmm3, %zmm12, %k0
+        vcmppd    $18, {sae}, %zmm5, %zmm12, %k1
+        vrsqrt14pd %zmm11, %zmm4
+        vcmppd    $21, {sae}, %zmm10, %zmm11, %k3
+        vfmadd231pd {rn-sae}, %zmm11, %zmm13, %zmm14
+        vmovups   c3s+__svml_dacosh_data_internal_avx512(%rip), %zmm13
+
+/* Sh ~sqrt(-1+x^2) */
+        vmulpd    {rn-sae}, %zmm4, %zmm11, %zmm9
+        vmulpd    {rn-sae}, %zmm11, %zmm14, %zmm8
+
+/* Sh+x */
+        vaddpd    {rn-sae}, %zmm12, %zmm9, %zmm15
+
+/* Shh */
+        vsubpd    {rn-sae}, %zmm12, %zmm15, %zmm14
+
+/* (Yh*R0)_low */
+        vmovaps   %zmm11, %zmm0
+        korw      %k0, %k1, %k0
+
+/* rel. error term: Eh=1-Sh*R0 */
+        vmovaps   %zmm5, %zmm7
+        vfmsub213pd {rn-sae}, %zmm9, %zmm4, %zmm0
+        vfnmadd231pd {rn-sae}, %zmm9, %zmm4, %zmm7
+
+/* rel. error term: Eh=(1-Sh*R0)-Sl*R0 */
+        vfnmadd231pd {rn-sae}, %zmm0, %zmm4, %zmm7
+
+/* Shl */
+        vsubpd    {rn-sae}, %zmm14, %zmm9, %zmm4
+        vmovups   poly_coeff7+__svml_dacosh_data_internal_avx512(%rip), %zmm14
+        vfmadd231pd {rn-sae}, %zmm7, %zmm1, %zmm13
+        vfmadd213pd {rn-sae}, %zmm2, %zmm7, %zmm13
+        vfmadd213pd {rn-sae}, %zmm6, %zmm7, %zmm13
+
+/* Sh*Eh */
+        vmulpd    {rn-sae}, %zmm7, %zmm9, %zmm7
+
+/* Sl + Sh*Eh*poly_s */
+        vfmadd213pd {rn-sae}, %zmm0, %zmm13, %zmm7
+
+/* polynomials */
+        vmovups   poly_coeff9+__svml_dacosh_data_internal_avx512(%rip), %zmm13
+
+/* polynomial computation for small inputs */
+        vaddpd    {rn-sae}, %zmm7, %zmm9, %zmm0
+
+/* Xin0+Sl+Sh*Eh*poly_s ~ x+sqrt(1+x^2) */
+        vaddpd    {rn-sae}, %zmm7, %zmm15, %zmm6
+        vfmadd231pd {rn-sae}, %zmm0, %zmm8, %zmm0
+
+/* fixup for very large inputs */
+        vmovups   OneEighth+__svml_dacosh_data_internal_avx512(%rip), %zmm8
+
+/* Sl_high */
+        vsubpd    {rn-sae}, %zmm15, %zmm6, %zmm9
+        vmovups   poly_coeff6+__svml_dacosh_data_internal_avx512(%rip), %zmm15
+        vmulpd    {rn-sae}, %zmm8, %zmm12, %zmm6{%k2}
+
+/* Sl_l */
+        vsubpd    {rn-sae}, %zmm9, %zmm7, %zmm3
+        vrcp14pd  %zmm6, %zmm1
+
+/* Xin_low */
+        vaddpd    {rn-sae}, %zmm4, %zmm3, %zmm7
+
+/* Table lookups */
+        vmovups   __svml_dacosh_data_internal_avx512(%rip), %zmm3
+
+/* round reciprocal to 1+4b mantissas */
+        vpaddq    AddB5+__svml_dacosh_data_internal_avx512(%rip), %zmm1, %zmm2
+
+/* fixup for very large inputs */
+        vxorpd    %zmm7, %zmm7, %zmm7{%k2}
+        vmovups   poly_coeff8+__svml_dacosh_data_internal_avx512(%rip), %zmm1
+        vandpd    RcpBitMask+__svml_dacosh_data_internal_avx512(%rip), %zmm2, %zmm8
+        vmovups   Log_tbl_L+__svml_dacosh_data_internal_avx512(%rip), %zmm2
+
+/* Prepare table index */
+        vpsrlq    $48, %zmm8, %zmm9
+
+/* reduced argument for log(): (Rcp*Xin-1)+Rcp*Xin_low */
+        vfmsub231pd {rn-sae}, %zmm8, %zmm6, %zmm5
+
+/* exponents */
+        vgetexppd {sae}, %zmm8, %zmm4
+        vmovups   Four+__svml_dacosh_data_internal_avx512(%rip), %zmm6
+        vpermt2pd Log_tbl_H+64+__svml_dacosh_data_internal_avx512(%rip), %zmm9, %zmm3
+        vpermt2pd Log_tbl_L+64+__svml_dacosh_data_internal_avx512(%rip), %zmm9, %zmm2
+        vsubpd    {rn-sae}, %zmm6, %zmm4, %zmm4{%k2}
+        vfmadd231pd {rn-sae}, %zmm8, %zmm7, %zmm5
+        vmovups   poly_coeff5+__svml_dacosh_data_internal_avx512(%rip), %zmm6
+        vmovups   poly_coeff4+__svml_dacosh_data_internal_avx512(%rip), %zmm7
+
+/* -K*L2H + Th */
+        vmovups   L2H+__svml_dacosh_data_internal_avx512(%rip), %zmm8
+
+/* -K*L2L + Tl */
+        vmovups   L2L+__svml_dacosh_data_internal_avx512(%rip), %zmm9
+        vfmadd231pd {rn-sae}, %zmm5, %zmm13, %zmm1
+        vmovups   poly_coeff2+__svml_dacosh_data_internal_avx512(%rip), %zmm13
+        vfnmadd231pd {rn-sae}, %zmm4, %zmm8, %zmm3
+        vfnmadd213pd {rn-sae}, %zmm2, %zmm9, %zmm4
+        vfmadd213pd {rn-sae}, %zmm14, %zmm5, %zmm1
+        vmovups   poly_coeff3+__svml_dacosh_data_internal_avx512(%rip), %zmm2
+        vmovups   poly_coeff1+__svml_dacosh_data_internal_avx512(%rip), %zmm14
+        vfmadd213pd {rn-sae}, %zmm15, %zmm5, %zmm1
+
+/* R^2 */
+        vmulpd    {rn-sae}, %zmm5, %zmm5, %zmm15
+        vfmadd213pd {rn-sae}, %zmm6, %zmm5, %zmm1
+        vfmadd213pd {rn-sae}, %zmm7, %zmm5, %zmm1
+        vfmadd213pd {rn-sae}, %zmm2, %zmm5, %zmm1
+        vfmadd213pd {rn-sae}, %zmm13, %zmm5, %zmm1
+        vfmadd213pd {rn-sae}, %zmm14, %zmm5, %zmm1
+
+/* Tl + R^2*Poly */
+        vfmadd213pd {rn-sae}, %zmm4, %zmm15, %zmm1
+
+/* R+Tl + R^2*Poly */
+        vaddpd    {rn-sae}, %zmm5, %zmm1, %zmm5
+        vaddpd    {rn-sae}, %zmm5, %zmm3, %zmm0{%k3}
+
+/* Go to special inputs processing branch */
+        jne       L(SPECIAL_VALUES_BRANCH)
+                                # LOE rbx r12 r13 r14 r15 k0 zmm0 zmm12
+
+/* Restore registers
+ * and exit the function
+ */
+
+L(EXIT):
+        movq      %rbp, %rsp
+        popq      %rbp
+        cfi_def_cfa(7, 8)
+        cfi_restore(6)
+        ret
+        cfi_def_cfa(6, 16)
+        cfi_offset(6, -16)
+
+/* Branch to process
+ * special inputs
+ */
+
+L(SPECIAL_VALUES_BRANCH):
+        vmovups   %zmm12, 64(%rsp)
+        vmovups   %zmm0, 128(%rsp)
+                                # LOE rbx r12 r13 r14 r15 k0 zmm0
+
+        xorl      %eax, %eax
+                                # LOE rbx r12 r13 r14 r15 eax k0
+
+        vzeroupper
+        movq      %r12, 16(%rsp)
+        /*  DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
+        movl      %eax, %r12d
+        movq      %r13, 8(%rsp)
+        /*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
+        kmovd     %k0, %r13d
+        movq      %r14, (%rsp)
+        /*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
+                                # LOE rbx r15 r12d r13d
+
+/* Range mask
+ * bits check
+ */
+
+L(RANGEMASK_CHECK):
+        btl       %r12d, %r13d
+
+/* Call scalar math function */
+        jc        L(SCALAR_MATH_CALL)
+                                # LOE rbx r15 r12d r13d
+
+/* Special inputs
+ * processing loop
+ */
+
+L(SPECIAL_VALUES_LOOP):
+        incl      %r12d
+        cmpl      $8, %r12d
+
+/* Check bits in range mask */
+        jl        L(RANGEMASK_CHECK)
+                                # LOE rbx r15 r12d r13d
+
+        movq      16(%rsp), %r12
+        cfi_restore(12)
+        movq      8(%rsp), %r13
+        cfi_restore(13)
+        movq      (%rsp), %r14
+        cfi_restore(14)
+        vmovups   128(%rsp), %zmm0
+
+/* Go to exit */
+        jmp       L(EXIT)
+        /*  DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -176; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
+        /*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -184; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
+        /*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -192; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
+                                # LOE rbx r12 r13 r14 r15 zmm0
+
+/* Scalar math fucntion call
+ * to process special input
+ */
+
+L(SCALAR_MATH_CALL):
+        movl      %r12d, %r14d
+        movsd     64(%rsp,%r14,8), %xmm0
+        call      acosh@PLT
+                                # LOE rbx r14 r15 r12d r13d xmm0
+
+        movsd     %xmm0, 128(%rsp,%r14,8)
+
+/* Process special inputs in loop */
+        jmp       L(SPECIAL_VALUES_LOOP)
+                                # LOE rbx r15 r12d r13d
+END(_ZGVeN8v_acosh_skx)
+
+        .section .rodata, "a"
+        .align 64
+
+#ifdef __svml_dacosh_data_internal_avx512_typedef
+typedef unsigned int VUINT32;
+typedef struct {
+        __declspec(align(64)) VUINT32 Log_tbl_H[16][2];
+        __declspec(align(64)) VUINT32 Log_tbl_L[16][2];
+        __declspec(align(64)) VUINT32 One[8][2];
+        __declspec(align(64)) VUINT32 SmallThreshold[8][2];
+        __declspec(align(64)) VUINT32 Threshold[8][2];
+        __declspec(align(64)) VUINT32 LargeThreshold[8][2];
+        __declspec(align(64)) VUINT32 ca2[8][2];
+        __declspec(align(64)) VUINT32 ca1[8][2];
+        __declspec(align(64)) VUINT32 c4s[8][2];
+        __declspec(align(64)) VUINT32 c3s[8][2];
+        __declspec(align(64)) VUINT32 c2s[8][2];
+        __declspec(align(64)) VUINT32 c1s[8][2];
+        __declspec(align(64)) VUINT32 AddB5[8][2];
+        __declspec(align(64)) VUINT32 RcpBitMask[8][2];
+        __declspec(align(64)) VUINT32 OneEighth[8][2];
+        __declspec(align(64)) VUINT32 Four[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff9[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff8[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff7[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff6[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff5[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff4[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff3[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff2[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff1[8][2];
+        __declspec(align(64)) VUINT32 L2H[8][2];
+        __declspec(align(64)) VUINT32 L2L[8][2];
+    } __svml_dacosh_data_internal_avx512;
+#endif
+__svml_dacosh_data_internal_avx512:
+        /*== Log_tbl_H ==*/
+        .quad 0x0000000000000000
+        .quad 0xbfaf0a30c0120000
+        .quad 0xbfbe27076e2b0000
+        .quad 0xbfc5ff3070a78000
+        .quad 0xbfcc8ff7c79a8000
+        .quad 0xbfd1675cababc000
+        .quad 0xbfd4618bc21c4000
+        .quad 0xbfd739d7f6bbc000
+        .quad 0xbfd9f323ecbf8000
+        .quad 0xbfdc8ff7c79a8000
+        .quad 0xbfdf128f5faf0000
+        .quad 0xbfe0be72e4252000
+        .quad 0xbfe1e85f5e704000
+        .quad 0xbfe307d7334f2000
+        .quad 0xbfe41d8fe8468000
+        .quad 0xbfe52a2d265bc000
+        /*== Log_tbl_L ==*/
+        .align 64
+        .quad 0x0000000000000000
+        .quad 0x3d53ab33d066d1d2
+        .quad 0x3d2a342c2af0003c
+        .quad 0xbd43d3c873e20a07
+        .quad 0xbd4a21ac25d81ef3
+        .quad 0x3d59f1fc63382a8f
+        .quad 0xbd5ec27d0b7b37b3
+        .quad 0xbd50069ce24c53fb
+        .quad 0xbd584bf2b68d766f
+        .quad 0xbd5a21ac25d81ef3
+        .quad 0xbd3bb2cd720ec44c
+        .quad 0xbd55056d312f7668
+        .quad 0xbd1a07bd8b34be7c
+        .quad 0x3d5e83c094debc15
+        .quad 0x3d5aa33736867a17
+        .quad 0xbd46abb9df22bc57
+        /*== One ==*/
+        .align 64
+        .quad 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000, 0x3ff0000000000000
+        /*== SmallThreshold ==*/
+        .align 64
+        .quad 0x3ef0000000000000, 0x3ef0000000000000, 0x3ef0000000000000, 0x3ef0000000000000, 0x3ef0000000000000, 0x3ef0000000000000, 0x3ef0000000000000, 0x3ef0000000000000
+        /*== Threshold ==*/
+        .align 64
+        .quad 0x5fe0000000000000, 0x5fe0000000000000, 0x5fe0000000000000, 0x5fe0000000000000, 0x5fe0000000000000, 0x5fe0000000000000, 0x5fe0000000000000, 0x5fe0000000000000
+        /*== LargeThreshold ==*/
+        .align 64
+        .quad 0x7fefffffffffffff, 0x7fefffffffffffff, 0x7fefffffffffffff, 0x7fefffffffffffff, 0x7fefffffffffffff, 0x7fefffffffffffff, 0x7fefffffffffffff, 0x7fefffffffffffff
+        /*== ca2 ==*/
+        .align 64
+        .quad 0x3fb333220eaf02e7, 0x3fb333220eaf02e7, 0x3fb333220eaf02e7, 0x3fb333220eaf02e7, 0x3fb333220eaf02e7, 0x3fb333220eaf02e7, 0x3fb333220eaf02e7, 0x3fb333220eaf02e7
+        /*== ca1 ==*/
+        .align 64
+        .quad 0xbfc5555555521e7e, 0xbfc5555555521e7e, 0xbfc5555555521e7e, 0xbfc5555555521e7e, 0xbfc5555555521e7e, 0xbfc5555555521e7e, 0xbfc5555555521e7e, 0xbfc5555555521e7e
+        /*== c4s ==*/
+        .align 64
+        .quad 0x3fd1800001943612, 0x3fd1800001943612, 0x3fd1800001943612, 0x3fd1800001943612, 0x3fd1800001943612, 0x3fd1800001943612, 0x3fd1800001943612, 0x3fd1800001943612
+        /*== c3s ==*/
+        .align 64
+        .quad 0x3fd40000013b0000, 0x3fd40000013b0000, 0x3fd40000013b0000, 0x3fd40000013b0000, 0x3fd40000013b0000, 0x3fd40000013b0000, 0x3fd40000013b0000, 0x3fd40000013b0000
+        /*== c2s ==*/
+        .align 64
+        .quad 0x3fd8000000000000, 0x3fd8000000000000, 0x3fd8000000000000, 0x3fd8000000000000, 0x3fd8000000000000, 0x3fd8000000000000, 0x3fd8000000000000, 0x3fd8000000000000
+        /*== c1s ==*/
+        .align 64
+        .quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000
+        /*== AddB5 ==*/
+        .align 64
+        .quad 0x0000800000000000, 0x0000800000000000, 0x0000800000000000, 0x0000800000000000, 0x0000800000000000, 0x0000800000000000, 0x0000800000000000, 0x0000800000000000
+        /*== RcpBitMask ==*/
+        .align 64
+        .quad 0xffff000000000000, 0xffff000000000000, 0xffff000000000000, 0xffff000000000000, 0xffff000000000000, 0xffff000000000000, 0xffff000000000000, 0xffff000000000000
+        /*==OneEighth ==*/
+        .align 64
+        .quad 0x3fc0000000000000, 0x3fc0000000000000, 0x3fc0000000000000, 0x3fc0000000000000, 0x3fc0000000000000, 0x3fc0000000000000, 0x3fc0000000000000, 0x3fc0000000000000
+        /*== Four ==*/
+        .align 64
+        .quad 0x4010000000000000, 0x4010000000000000, 0x4010000000000000, 0x4010000000000000, 0x4010000000000000, 0x4010000000000000, 0x4010000000000000, 0x4010000000000000
+        /*== poly_coeff9 ==*/
+        .align 64
+        .quad 0xbfb9a9b040214368, 0xbfb9a9b040214368, 0xbfb9a9b040214368, 0xbfb9a9b040214368, 0xbfb9a9b040214368, 0xbfb9a9b040214368, 0xbfb9a9b040214368, 0xbfb9a9b040214368
+        /*== poly_coeff8 ==*/
+        .align 64
+        .quad 0x3fbc80666e249778, 0x3fbc80666e249778, 0x3fbc80666e249778, 0x3fbc80666e249778, 0x3fbc80666e249778, 0x3fbc80666e249778, 0x3fbc80666e249778, 0x3fbc80666e249778
+        /*== poly_coeff7 ==*/
+        .align 64
+        .quad 0xbfbffffb8a054bc9, 0xbfbffffb8a054bc9, 0xbfbffffb8a054bc9, 0xbfbffffb8a054bc9, 0xbfbffffb8a054bc9, 0xbfbffffb8a054bc9, 0xbfbffffb8a054bc9, 0xbfbffffb8a054bc9
+        /*== poly_coeff6 ==*/
+        .align 64
+        .quad 0x3fc24922f71256f1, 0x3fc24922f71256f1, 0x3fc24922f71256f1, 0x3fc24922f71256f1, 0x3fc24922f71256f1, 0x3fc24922f71256f1, 0x3fc24922f71256f1, 0x3fc24922f71256f1
+        /*== poly_coeff5 ==*/
+        .align 64
+        .quad 0xbfc55555559ba736, 0xbfc55555559ba736, 0xbfc55555559ba736, 0xbfc55555559ba736, 0xbfc55555559ba736, 0xbfc55555559ba736, 0xbfc55555559ba736, 0xbfc55555559ba736
+        /*== poly_coeff4 ==*/
+        .align 64
+        .quad 0x3fc9999999be77af, 0x3fc9999999be77af, 0x3fc9999999be77af, 0x3fc9999999be77af, 0x3fc9999999be77af, 0x3fc9999999be77af, 0x3fc9999999be77af, 0x3fc9999999be77af
+        /*== poly_coeff3 ==*/
+        .align 64
+        .quad 0xbfcffffffffffc65, 0xbfcffffffffffc65, 0xbfcffffffffffc65, 0xbfcffffffffffc65, 0xbfcffffffffffc65, 0xbfcffffffffffc65, 0xbfcffffffffffc65, 0xbfcffffffffffc65
+        /*== poly_coeff2 ==*/
+        .align 64
+        .quad 0x3fd55555555554c1, 0x3fd55555555554c1, 0x3fd55555555554c1, 0x3fd55555555554c1, 0x3fd55555555554c1, 0x3fd55555555554c1, 0x3fd55555555554c1, 0x3fd55555555554c1
+        /*== poly_coeff1 ==*/
+        .align 64
+        .quad 0xbfe0000000000000, 0xbfe0000000000000, 0xbfe0000000000000, 0xbfe0000000000000, 0xbfe0000000000000, 0xbfe0000000000000, 0xbfe0000000000000, 0xbfe0000000000000
+        /*== L2H = log(2)_high ==*/
+        .align 64
+        .quad 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000, 0x3fe62E42FEFA0000
+        /*== L2L = log(2)_low ==*/
+        .align 64
+        .quad 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000, 0x3d7cf79abc9e0000
+        .align 64
+        .type	__svml_dacosh_data_internal_avx512,@object
+        .size	__svml_dacosh_data_internal_avx512,.-__svml_dacosh_data_internal_avx512