x86-64: Add vector exp10/exp10f implementation to libmvec

Implement vectorized exp10/exp10f containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI.  It also contains
accuracy and ABI tests for vector exp10/exp10f with regenerated ulps.

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

1 files changed, 429 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_exp104_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_d_exp104_core_avx2.S
new file mode 100644
index 0000000000..1a53f43c9e
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_exp104_core_avx2.S
@@ -0,0 +1,429 @@
+/* Function exp10 vectorized with AVX2.
+   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:
+ *
+ *   exp10(x)  = 2^x/log10(2) = 2^n * (1 + T[j]) * (1 + P(y))
+ *   where
+ *        x = m*log10(2)/K + y,  y in [-log10(2)/K..log10(2)/K]
+ *        m = n*K + j,           m,n,j - signed integer, j in [-K/2..K/2]
+ *
+ *        values of 2^j/K are tabulated
+ *
+ *        P(y) is a minimax polynomial approximation of exp10(x)-1
+ *        on small interval [-log10(2)/K..log10(2)/K]
+ *
+ *  Special cases:
+ *
+ *   exp10(NaN)  = NaN
+ *   exp10(+INF) = +INF
+ *   exp10(-INF) = 0
+ *   exp10(x)    = 1 for subnormals
+ *   For IEEE double
+ *     if x >  3.39782712893383973096e+02 then exp10(x) overflow
+ *     if x < -3.45133219101941108420e+02 then exp10(x) underflow
+ *
+ */
+
+/* Offsets for data table __svml_dexp10_data_internal
+ */
+#define _dbT                          	0
+#define _dbLg2_10                     	1024
+#define _dbShifter                    	1056
+#define _dbInvLg2_10hi                	1088
+#define _dbInvLg2_10lo                	1120
+#define _dPC1                         	1152
+#define _dPC2                         	1184
+#define _dPC3                         	1216
+#define _dPC4                         	1248
+#define _dPC5                         	1280
+#define _lExpMask                     	1312
+#define _iIndexMask                   	1344
+#define _iAbsMask                     	1376
+#define _iDomainRange                 	1408
+
+#include <sysdep.h>
+
+        .text
+	.section .text.avx2,"ax",@progbits
+ENTRY(_ZGVdN4v_exp10_avx2)
+        pushq     %rbp
+        cfi_def_cfa_offset(16)
+        movq      %rsp, %rbp
+        cfi_def_cfa(6, 16)
+        cfi_offset(6, -16)
+        andq      $-32, %rsp
+        subq      $96, %rsp
+        lea       __svml_dexp10_data_internal(%rip), %r8
+        vmovapd   %ymm0, %ymm2
+        vmovupd   _dbShifter+__svml_dexp10_data_internal(%rip), %ymm3
+
+/*  Load arument  */
+        vmovupd   _dbLg2_10+__svml_dexp10_data_internal(%rip), %ymm0
+        vfmadd213pd %ymm3, %ymm2, %ymm0
+        vsubpd    %ymm3, %ymm0, %ymm1
+
+/*  R  */
+        vmovupd   _dbInvLg2_10hi+__svml_dexp10_data_internal(%rip), %ymm3
+        vfnmadd213pd %ymm2, %ymm1, %ymm3
+
+/* Check for overflow\underflow  */
+        vextractf128 $1, %ymm2, %xmm4
+        vfnmadd132pd _dbInvLg2_10lo+__svml_dexp10_data_internal(%rip), %ymm3, %ymm1
+        vshufps   $221, %xmm4, %xmm2, %xmm5
+        vandps    _iAbsMask+__svml_dexp10_data_internal(%rip), %xmm5, %xmm6
+        vpcmpgtd  _iDomainRange+__svml_dexp10_data_internal(%rip), %xmm6, %xmm7
+
+/*
+ *  Polynomial
+ * poly(dN) = a1*dR+...+a5*dR^5
+ */
+        vmovupd   _dPC5+__svml_dexp10_data_internal(%rip), %ymm4
+        vmovmskps %xmm7, %eax
+        vfmadd213pd _dPC4+__svml_dexp10_data_internal(%rip), %ymm1, %ymm4
+        vfmadd213pd _dPC3+__svml_dexp10_data_internal(%rip), %ymm1, %ymm4
+        vfmadd213pd _dPC2+__svml_dexp10_data_internal(%rip), %ymm1, %ymm4
+
+/* a1+...+a5*dR^4 ! */
+        vfmadd213pd _dPC1+__svml_dexp10_data_internal(%rip), %ymm1, %ymm4
+
+/* a1*dR+...+a5*dR^5 */
+        vmulpd    %ymm4, %ymm1, %ymm1
+
+/*  Index and lookup  */
+        vextractf128 $1, %ymm0, %xmm8
+        vshufps   $136, %xmm8, %xmm0, %xmm9
+        vandps    _iIndexMask+__svml_dexp10_data_internal(%rip), %xmm9, %xmm10
+
+/* iIndex*=sizeof(D); */
+        vpslld    $3, %xmm10, %xmm13
+        vmovd     %xmm13, %edx
+
+/*  2^N  */
+        vpsllq    $45, %ymm0, %ymm0
+        vpextrd   $2, %xmm13, %esi
+        movslq    %edx, %rdx
+        vpextrd   $1, %xmm13, %ecx
+        movslq    %esi, %rsi
+        vpextrd   $3, %xmm13, %edi
+        movslq    %ecx, %rcx
+        movslq    %edi, %rdi
+        vmovsd    (%r8,%rdx), %xmm11
+        vmovsd    (%r8,%rsi), %xmm14
+        vmovhpd   (%r8,%rcx), %xmm11, %xmm12
+        vmovhpd   (%r8,%rdi), %xmm14, %xmm15
+
+/* lM==EXP(2^N) */
+        vpand     _lExpMask+__svml_dexp10_data_internal(%rip), %ymm0, %ymm6
+        vinsertf128 $1, %xmm15, %ymm12, %ymm5
+
+/* Tj*poly */
+        vfmadd213pd %ymm5, %ymm5, %ymm1
+
+/* quick 2^N */
+        vpaddq    %ymm6, %ymm1, %ymm0
+
+/*  Finish   */
+        testl     %eax, %eax
+
+/* Go to special inputs processing branch */
+        jne       L(SPECIAL_VALUES_BRANCH)
+                                # LOE rbx r12 r13 r14 r15 eax ymm0 ymm2
+
+/* 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):
+        vmovupd   %ymm2, 32(%rsp)
+        vmovupd   %ymm0, 64(%rsp)
+                                # LOE rbx r12 r13 r14 r15 eax ymm0
+
+        xorl      %edx, %edx
+                                # LOE rbx r12 r13 r14 r15 eax edx
+
+        vzeroupper
+        movq      %r12, 16(%rsp)
+        /*  DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
+        movl      %edx, %r12d
+        movq      %r13, 8(%rsp)
+        /*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
+        movl      %eax, %r13d
+        movq      %r14, (%rsp)
+        /*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 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      $4, %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)
+        vmovupd   64(%rsp), %ymm0
+
+/* Go to exit */
+        jmp       L(EXIT)
+        /*  DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
+        /*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
+        /*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
+                                # LOE rbx r12 r13 r14 r15 ymm0
+
+/* Scalar math fucntion call
+ * to process special input
+ */
+
+L(SCALAR_MATH_CALL):
+        movl      %r12d, %r14d
+        movsd     32(%rsp,%r14,8), %xmm0
+        call      exp10@PLT
+                                # LOE rbx r14 r15 r12d r13d xmm0
+
+        movsd     %xmm0, 64(%rsp,%r14,8)
+
+/* Process special inputs in loop */
+        jmp       L(SPECIAL_VALUES_LOOP)
+                                # LOE rbx r15 r12d r13d
+END(_ZGVdN4v_exp10_avx2)
+
+        .section .rodata, "a"
+        .align 32
+
+#ifdef __svml_dexp10_data_internal_typedef
+typedef unsigned int VUINT32;
+typedef struct
+{
+        __declspec(align(32)) VUINT32 _dbT[(1<<7)][2];
+        __declspec(align(32)) VUINT32 _dbLg2_10[4][2];
+        __declspec(align(32)) VUINT32 _dbShifter[4][2];
+        __declspec(align(32)) VUINT32 _dbInvLg2_10hi[4][2];
+        __declspec(align(32)) VUINT32 _dbInvLg2_10lo[4][2];
+        __declspec(align(32)) VUINT32 _dPC1[4][2];
+        __declspec(align(32)) VUINT32 _dPC2[4][2];
+        __declspec(align(32)) VUINT32 _dPC3[4][2];
+        __declspec(align(32)) VUINT32 _dPC4[4][2];
+        __declspec(align(32)) VUINT32 _dPC5[4][2];
+        __declspec(align(32)) VUINT32 _lExpMask[4][2];
+        __declspec(align(32)) VUINT32 _iIndexMask[8][1];
+        __declspec(align(32)) VUINT32 _iAbsMask[8][1];
+        __declspec(align(32)) VUINT32 _iDomainRange[8][1];
+} __svml_dexp10_data_internal;
+#endif
+__svml_dexp10_data_internal:
+        /*== _dbT ==*/
+        .quad 0x3ff0000000000000    /*2^( 0 /128)*/
+        .quad 0x3ff0163da9fb3335    /*2^( 1 /128)*/
+        .quad 0x3ff02c9a3e778061    /*2^( 2 /128)*/
+        .quad 0x3ff04315e86e7f85    /*2^( 3 /128)*/
+        .quad 0x3ff059b0d3158574    /*2^( 4 /128)*/
+        .quad 0x3ff0706b29ddf6de    /*2^( 5 /128)*/
+        .quad 0x3ff0874518759bc8    /*2^( 6 /128)*/
+        .quad 0x3ff09e3ecac6f383    /*2^( 7 /128)*/
+        .quad 0x3ff0b5586cf9890f    /*2^( 8 /128)*/
+        .quad 0x3ff0cc922b7247f7    /*2^( 9 /128)*/
+        .quad 0x3ff0e3ec32d3d1a2    /*2^( 10 /128)*/
+        .quad 0x3ff0fb66affed31b    /*2^( 11 /128)*/
+        .quad 0x3ff11301d0125b51    /*2^( 12 /128)*/
+        .quad 0x3ff12abdc06c31cc    /*2^( 13 /128)*/
+        .quad 0x3ff1429aaea92de0    /*2^( 14 /128)*/
+        .quad 0x3ff15a98c8a58e51    /*2^( 15 /128)*/
+        .quad 0x3ff172b83c7d517b    /*2^( 16 /128)*/
+        .quad 0x3ff18af9388c8dea    /*2^( 17 /128)*/
+        .quad 0x3ff1a35beb6fcb75    /*2^( 18 /128)*/
+        .quad 0x3ff1bbe084045cd4    /*2^( 19 /128)*/
+        .quad 0x3ff1d4873168b9aa    /*2^( 20 /128)*/
+        .quad 0x3ff1ed5022fcd91d    /*2^( 21 /128)*/
+        .quad 0x3ff2063b88628cd6    /*2^( 22 /128)*/
+        .quad 0x3ff21f49917ddc96    /*2^( 23 /128)*/
+        .quad 0x3ff2387a6e756238    /*2^( 24 /128)*/
+        .quad 0x3ff251ce4fb2a63f    /*2^( 25 /128)*/
+        .quad 0x3ff26b4565e27cdd    /*2^( 26 /128)*/
+        .quad 0x3ff284dfe1f56381    /*2^( 27 /128)*/
+        .quad 0x3ff29e9df51fdee1    /*2^( 28 /128)*/
+        .quad 0x3ff2b87fd0dad990    /*2^( 29 /128)*/
+        .quad 0x3ff2d285a6e4030b    /*2^( 30 /128)*/
+        .quad 0x3ff2ecafa93e2f56    /*2^( 31 /128)*/
+        .quad 0x3ff306fe0a31b715    /*2^( 32 /128)*/
+        .quad 0x3ff32170fc4cd831    /*2^( 33 /128)*/
+        .quad 0x3ff33c08b26416ff    /*2^( 34 /128)*/
+        .quad 0x3ff356c55f929ff1    /*2^( 35 /128)*/
+        .quad 0x3ff371a7373aa9cb    /*2^( 36 /128)*/
+        .quad 0x3ff38cae6d05d866    /*2^( 37 /128)*/
+        .quad 0x3ff3a7db34e59ff7    /*2^( 38 /128)*/
+        .quad 0x3ff3c32dc313a8e5    /*2^( 39 /128)*/
+        .quad 0x3ff3dea64c123422    /*2^( 40 /128)*/
+        .quad 0x3ff3fa4504ac801c    /*2^( 41 /128)*/
+        .quad 0x3ff4160a21f72e2a    /*2^( 42 /128)*/
+        .quad 0x3ff431f5d950a897    /*2^( 43 /128)*/
+        .quad 0x3ff44e086061892d    /*2^( 44 /128)*/
+        .quad 0x3ff46a41ed1d0057    /*2^( 45 /128)*/
+        .quad 0x3ff486a2b5c13cd0    /*2^( 46 /128)*/
+        .quad 0x3ff4a32af0d7d3de    /*2^( 47 /128)*/
+        .quad 0x3ff4bfdad5362a27    /*2^( 48 /128)*/
+        .quad 0x3ff4dcb299fddd0d    /*2^( 49 /128)*/
+        .quad 0x3ff4f9b2769d2ca7    /*2^( 50 /128)*/
+        .quad 0x3ff516daa2cf6642    /*2^( 51 /128)*/
+        .quad 0x3ff5342b569d4f82    /*2^( 52 /128)*/
+        .quad 0x3ff551a4ca5d920f    /*2^( 53 /128)*/
+        .quad 0x3ff56f4736b527da    /*2^( 54 /128)*/
+        .quad 0x3ff58d12d497c7fd    /*2^( 55 /128)*/
+        .quad 0x3ff5ab07dd485429    /*2^( 56 /128)*/
+        .quad 0x3ff5c9268a5946b7    /*2^( 57 /128)*/
+        .quad 0x3ff5e76f15ad2148    /*2^( 58 /128)*/
+        .quad 0x3ff605e1b976dc09    /*2^( 59 /128)*/
+        .quad 0x3ff6247eb03a5585    /*2^( 60 /128)*/
+        .quad 0x3ff6434634ccc320    /*2^( 61 /128)*/
+        .quad 0x3ff6623882552225    /*2^( 62 /128)*/
+        .quad 0x3ff68155d44ca973    /*2^( 63 /128)*/
+        .quad 0x3ff6a09e667f3bcd    /*2^( 64 /128)*/
+        .quad 0x3ff6c012750bdabf    /*2^( 65 /128)*/
+        .quad 0x3ff6dfb23c651a2f    /*2^( 66 /128)*/
+        .quad 0x3ff6ff7df9519484    /*2^( 67 /128)*/
+        .quad 0x3ff71f75e8ec5f74    /*2^( 68 /128)*/
+        .quad 0x3ff73f9a48a58174    /*2^( 69 /128)*/
+        .quad 0x3ff75feb564267c9    /*2^( 70 /128)*/
+        .quad 0x3ff780694fde5d3f    /*2^( 71 /128)*/
+        .quad 0x3ff7a11473eb0187    /*2^( 72 /128)*/
+        .quad 0x3ff7c1ed0130c132    /*2^( 73 /128)*/
+        .quad 0x3ff7e2f336cf4e62    /*2^( 74 /128)*/
+        .quad 0x3ff80427543e1a12    /*2^( 75 /128)*/
+        .quad 0x3ff82589994cce13    /*2^( 76 /128)*/
+        .quad 0x3ff8471a4623c7ad    /*2^( 77 /128)*/
+        .quad 0x3ff868d99b4492ed    /*2^( 78 /128)*/
+        .quad 0x3ff88ac7d98a6699    /*2^( 79 /128)*/
+        .quad 0x3ff8ace5422aa0db    /*2^( 80 /128)*/
+        .quad 0x3ff8cf3216b5448c    /*2^( 81 /128)*/
+        .quad 0x3ff8f1ae99157736    /*2^( 82 /128)*/
+        .quad 0x3ff9145b0b91ffc6    /*2^( 83 /128)*/
+        .quad 0x3ff93737b0cdc5e5    /*2^( 84 /128)*/
+        .quad 0x3ff95a44cbc8520f    /*2^( 85 /128)*/
+        .quad 0x3ff97d829fde4e50    /*2^( 86 /128)*/
+        .quad 0x3ff9a0f170ca07ba    /*2^( 87 /128)*/
+        .quad 0x3ff9c49182a3f090    /*2^( 88 /128)*/
+        .quad 0x3ff9e86319e32323    /*2^( 89 /128)*/
+        .quad 0x3ffa0c667b5de565    /*2^( 90 /128)*/
+        .quad 0x3ffa309bec4a2d33    /*2^( 91 /128)*/
+        .quad 0x3ffa5503b23e255d    /*2^( 92 /128)*/
+        .quad 0x3ffa799e1330b358    /*2^( 93 /128)*/
+        .quad 0x3ffa9e6b5579fdbf    /*2^( 94 /128)*/
+        .quad 0x3ffac36bbfd3f37a    /*2^( 95 /128)*/
+        .quad 0x3ffae89f995ad3ad    /*2^( 96 /128)*/
+        .quad 0x3ffb0e07298db666    /*2^( 97 /128)*/
+        .quad 0x3ffb33a2b84f15fb    /*2^( 98 /128)*/
+        .quad 0x3ffb59728de5593a    /*2^( 99 /128)*/
+        .quad 0x3ffb7f76f2fb5e47    /*2^( 100 /128)*/
+        .quad 0x3ffba5b030a1064a    /*2^( 101 /128)*/
+        .quad 0x3ffbcc1e904bc1d2    /*2^( 102 /128)*/
+        .quad 0x3ffbf2c25bd71e09    /*2^( 103 /128)*/
+        .quad 0x3ffc199bdd85529c    /*2^( 104 /128)*/
+        .quad 0x3ffc40ab5fffd07a    /*2^( 105 /128)*/
+        .quad 0x3ffc67f12e57d14b    /*2^( 106 /128)*/
+        .quad 0x3ffc8f6d9406e7b5    /*2^( 107 /128)*/
+        .quad 0x3ffcb720dcef9069    /*2^( 108 /128)*/
+        .quad 0x3ffcdf0b555dc3fa    /*2^( 109 /128)*/
+        .quad 0x3ffd072d4a07897c    /*2^( 110 /128)*/
+        .quad 0x3ffd2f87080d89f2    /*2^( 111 /128)*/
+        .quad 0x3ffd5818dcfba487    /*2^( 112 /128)*/
+        .quad 0x3ffd80e316c98398    /*2^( 113 /128)*/
+        .quad 0x3ffda9e603db3285    /*2^( 114 /128)*/
+        .quad 0x3ffdd321f301b460    /*2^( 115 /128)*/
+        .quad 0x3ffdfc97337b9b5f    /*2^( 116 /128)*/
+        .quad 0x3ffe264614f5a129    /*2^( 117 /128)*/
+        .quad 0x3ffe502ee78b3ff6    /*2^( 118 /128)*/
+        .quad 0x3ffe7a51fbc74c83    /*2^( 119 /128)*/
+        .quad 0x3ffea4afa2a490da    /*2^( 120 /128)*/
+        .quad 0x3ffecf482d8e67f1    /*2^( 121 /128)*/
+        .quad 0x3ffefa1bee615a27    /*2^( 122 /128)*/
+        .quad 0x3fff252b376bba97    /*2^( 123 /128)*/
+        .quad 0x3fff50765b6e4540    /*2^( 124 /128)*/
+        .quad 0x3fff7bfdad9cbe14    /*2^( 125 /128)*/
+        .quad 0x3fffa7c1819e90d8    /*2^( 126 /128)*/
+        .quad 0x3fffd3c22b8f71f1     /*2^( 127 /128)*/
+        .align 32
+        .quad 0x407a934f0979a371, 0x407a934f0979a371, 0x407a934f0979a371, 0x407a934f0979a371  /* _dbLg2_10*2^K */
+        .align 32
+        .quad 0x4338800000000000, 0x4338800000000000, 0x4338800000000000, 0x4338800000000000  /* _dbShifter */
+        .align 32
+        .quad 0x3f63441350a00000, 0x3f63441350a00000, 0x3f63441350a00000, 0x3f63441350a00000  /* _dbInvLg2_10hi/2^K 53-11-K bits*/
+        .align 32
+        .quad 0xbd10c0219dc1da99, 0xbd10c0219dc1da99, 0xbd10c0219dc1da99, 0xbd10c0219dc1da99  /* _dbInvLg2_10lo/2^K */
+        //PC0 = 1.0
+        .align 32
+        .quad 0x40026bb1bbb55516, 0x40026bb1bbb55516, 0x40026bb1bbb55516, 0x40026bb1bbb55516  /* _dPC1 */
+        .align 32
+        .quad 0x40053524c73ce8e3, 0x40053524c73ce8e3, 0x40053524c73ce8e3, 0x40053524c73ce8e3  /* _dPC2 */
+        .align 32
+        .quad 0x4000470591ccea8b, 0x4000470591ccea8b, 0x4000470591ccea8b, 0x4000470591ccea8b  /* _dPC3 */
+        .align 32
+        .quad 0x3ff2bd767584db59, 0x3ff2bd767584db59, 0x3ff2bd767584db59, 0x3ff2bd767584db59  /* _dPC4 */
+        .align 32
+        .quad 0x3fe144c03efafb54, 0x3fe144c03efafb54, 0x3fe144c03efafb54, 0x3fe144c03efafb54  /* _dPC5 */
+        .align 32
+        .quad 0xfff0000000000000, 0xfff0000000000000, 0xfff0000000000000, 0xfff0000000000000  /* _lExpMask */
+        .align 32
+        .long 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f, 0x0000007f          /* _iIndexMask =(2^K-1)*/
+        //common
+        .align 32
+        .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff          /* _iAbsMask */
+        .align 32
+        .long 0x40733a70, 0x40733a70, 0x40733a70, 0x40733a70, 0x40733a70, 0x40733a70, 0x40733a70, 0x40733a70 /* _iDomainRange */
+        .align 32
+        .type	__svml_dexp10_data_internal,@object
+        .size	__svml_dexp10_data_internal,.-__svml_dexp10_data_internal