x86-64: Add vector sinh/sinhf implementation to libmvec

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

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

1 files changed, 461 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_sinh8_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_d_sinh8_core_avx512.S
new file mode 100644
index 0000000000..d057d6c7eb
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_sinh8_core_avx512.S
@@ -0,0 +1,461 @@
+/* Function sinh 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 sinh(x) as (exp(x)-exp(-x))/2,
+ *   where exp is calculated as
+ *   exp(M*ln2 + ln2*(j/2^k) + r) = 2^M * 2^(j/2^k) * exp(r)
+ *
+ *   Special cases:
+ *
+ *   sinh(NaN) = quiet NaN, and raise invalid exception
+ *   sinh(INF) = that INF
+ *   sinh(x)   = x for subnormals
+ *   sinh(x) overflows for big x and returns MAXLOG+log(2)
+ *
+ */
+
+/* Offsets for data table __svml_dsinh_data_internal
+ */
+#define _dbInvLn2                     	0
+#define _dbLn2hi                      	64
+#define _dbLn2lo                      	128
+#define _dSign                        	192
+#define _dbT                          	256
+#define _dbShifter                    	2304
+#define _iDomainRange                 	2368
+#define _dPC2                         	2432
+#define _dPC3                         	2496
+#define _dPC4                         	2560
+#define _dPC5                         	2624
+#define _lIndexMask                   	2688
+
+#include <sysdep.h>
+
+        .text
+	.section .text.evex512,"ax",@progbits
+ENTRY(_ZGVeN8v_sinh_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
+        lea       _dbT+8+__svml_dsinh_data_internal(%rip), %rax
+        vmovaps   %zmm0, %zmm8
+
+/*  Abs argument  */
+        vandpd    _dSign+__svml_dsinh_data_internal(%rip), %zmm8, %zmm7
+        vmovups   _dbShifter+__svml_dsinh_data_internal(%rip), %zmm13
+
+/*
+ *  Load argument
+ * dM = x*2^K/log(2) + RShifter
+ */
+        vmovups   _dbInvLn2+__svml_dsinh_data_internal(%rip), %zmm12
+        vmovups   _dbLn2hi+__svml_dsinh_data_internal(%rip), %zmm14
+        vmovups   _dPC5+__svml_dsinh_data_internal(%rip), %zmm6
+
+/* VLOAD_CONST( D, dPC[0],         TAB._dPC1 ); */
+        vmovups   _dPC4+__svml_dsinh_data_internal(%rip), %zmm4
+        vxorpd    %zmm8, %zmm7, %zmm5
+        kxnorw    %k0, %k0, %k1
+        kxnorw    %k0, %k0, %k2
+        vfmadd213pd {rn-sae}, %zmm13, %zmm5, %zmm12
+
+/*
+ * Check for overflow\underflow
+ *
+ */
+        vpsrlq    $32, %zmm5, %zmm9
+
+/*
+ *  R
+ * dN = dM - RShifter
+ */
+        vsubpd    {rn-sae}, %zmm13, %zmm12, %zmm2
+        vpmovqd   %zmm9, %ymm10
+        vmovups   _dbLn2lo+__svml_dsinh_data_internal(%rip), %zmm9
+
+/* dR = dX - dN*Log2_hi/2^K */
+        vfnmadd231pd {rn-sae}, %zmm14, %zmm2, %zmm5
+
+/*
+ * sinh(r) = r*((a1=1)+r^2*(a3+r^2*a5)) = r + r*(r^2*(a3+r^2*a5)) ....
+ * dSinh_r = (a3+r^2*a5)
+ */
+        vmovups   _dPC3+__svml_dsinh_data_internal(%rip), %zmm14
+
+/* dR = (dX - dN*Log2_hi/2^K) - dN*Log2_lo/2^K */
+        vfnmadd231pd {rn-sae}, %zmm9, %zmm2, %zmm5
+        vpcmpgtd  _iDomainRange+__svml_dsinh_data_internal(%rip), %ymm10, %ymm11
+        vmovmskps %ymm11, %edx
+
+/* dR2 = dR^2 */
+        vmulpd    {rn-sae}, %zmm5, %zmm5, %zmm2
+        vfmadd231pd {rn-sae}, %zmm2, %zmm6, %zmm14
+
+/*
+ *  Index and lookup
+ * j
+ */
+        vpandq    _lIndexMask+__svml_dsinh_data_internal(%rip), %zmm12, %zmm15
+        vpsllq    $4, %zmm15, %zmm1
+        vpmovqd   %zmm1, %ymm0
+        vpxord    %zmm11, %zmm11, %zmm11
+        vpxord    %zmm10, %zmm10, %zmm10
+        vgatherdpd (%rax,%ymm0), %zmm11{%k1}
+        vgatherdpd -8(%rax,%ymm0), %zmm10{%k2}
+
+/* split j and N */
+        vpxorq    %zmm15, %zmm12, %zmm3
+
+/*
+ *  G1,G2,G3: dTdif,dTn * 2^N,2^(-N)
+ * lM now is an EXP(2^N)
+ */
+        vpsllq    $45, %zmm3, %zmm3
+        vpaddq    %zmm3, %zmm10, %zmm1
+
+/*  */
+        vpaddq    %zmm3, %zmm11, %zmm12
+
+/*  */
+        vpsubq    %zmm3, %zmm11, %zmm13
+
+/* dSinh_r = r^2*(a3+r^2*a5) */
+        vmulpd    {rn-sae}, %zmm2, %zmm14, %zmm3
+
+/* dG2 = dTn*2^N - dTn*2^-N */
+        vsubpd    {rn-sae}, %zmm13, %zmm12, %zmm15
+
+/* dG3 = dTn*2^N + dTn*2^-N */
+        vaddpd    {rn-sae}, %zmm13, %zmm12, %zmm0
+
+/* dSinh_r = r + r*(r^2*(a3+r^2*a5)) */
+        vfmadd213pd {rn-sae}, %zmm5, %zmm5, %zmm3
+
+/*
+ * poly(r) = (dG2+dG1)+dG3*sinh(dR)+dG1*sinh(dR)+(dG1+dG2)*dR2*(a2 +a4*dR2)
+ * dOut = (a2 +a4*dR2)
+ */
+        vmovups   _dPC2+__svml_dsinh_data_internal(%rip), %zmm5
+
+/* dG1 += dG3 */
+        vaddpd    {rn-sae}, %zmm0, %zmm1, %zmm6
+        vfmadd231pd {rn-sae}, %zmm2, %zmm4, %zmm5
+
+/* dOut = dR2*(a2 +a4*dR2) */
+        vmulpd    {rn-sae}, %zmm2, %zmm5, %zmm4
+
+/* dG2 += dG1 */
+        vaddpd    {rn-sae}, %zmm15, %zmm1, %zmm2
+
+/* dOut = dG2*dR2*(a2 +a4*dR2) */
+        vmulpd    {rn-sae}, %zmm2, %zmm4, %zmm4
+
+/* dOut = dG1*sinh(dR)+dG2*dR2*(a2 +a4*dR2) */
+        vfmadd213pd {rn-sae}, %zmm4, %zmm6, %zmm3
+
+/* dOut = dG2 + dG1*sinh(dR)+dG2*dR2*(a2 +a4*dR2) */
+        vaddpd    {rn-sae}, %zmm2, %zmm3, %zmm0
+
+/*  Ret H  */
+        vorpd     %zmm0, %zmm7, %zmm0
+        testl     %edx, %edx
+
+/* Go to special inputs processing branch */
+        jne       L(SPECIAL_VALUES_BRANCH)
+                                # LOE rbx r12 r13 r14 r15 edx zmm0 zmm8
+
+/* 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   %zmm8, 64(%rsp)
+        vmovups   %zmm0, 128(%rsp)
+                                # LOE rbx r12 r13 r14 r15 edx zmm0
+
+        xorl      %eax, %eax
+                                # 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: -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
+        movl      %edx, %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      sinh@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_sinh_skx)
+
+        .section .rodata, "a"
+        .align 64
+
+#ifdef __svml_dsinh_data_internal_typedef
+typedef unsigned int VUINT32;
+typedef struct
+{
+        __declspec(align(64)) VUINT32 _dbInvLn2[8][2];
+        __declspec(align(64)) VUINT32 _dbLn2hi[8][2];
+        __declspec(align(64)) VUINT32 _dbLn2lo[8][2];
+        __declspec(align(64)) VUINT32 _dSign[8][2];                //0x8000000000000000
+        __declspec(align(64)) VUINT32 _dbT[(1<<7)][2][2]; //precalc poly coeff
+        __declspec(align(64)) VUINT32 _dbShifter[8][2];
+        __declspec(align(64)) VUINT32 _iDomainRange[16][1];
+        __declspec(align(64)) VUINT32 _dPC2[8][2];
+        __declspec(align(64)) VUINT32 _dPC3[8][2];
+        __declspec(align(64)) VUINT32 _dPC4[8][2];
+        __declspec(align(64)) VUINT32 _dPC5[8][2];
+        __declspec(align(64)) VUINT32 _lIndexMask[8][2];
+} __svml_dsinh_data_internal;
+#endif
+__svml_dsinh_data_internal:
+        .quad 0x3FF71547652B82FE, 0x3FF71547652B82FE, 0x3FF71547652B82FE, 0x3FF71547652B82FE, 0x3FF71547652B82FE, 0x3FF71547652B82FE, 0x3FF71547652B82FE, 0x3FF71547652B82FE /* _dbInvLn2 = 1/log(2) */
+        .align 64
+        .quad 0x3FE62E42FEFA0000, 0x3FE62E42FEFA0000, 0x3FE62E42FEFA0000, 0x3FE62E42FEFA0000, 0x3FE62E42FEFA0000, 0x3FE62E42FEFA0000, 0x3FE62E42FEFA0000, 0x3FE62E42FEFA0000 /* _dbLn2hi  = log(2) hi*/
+        .align 64
+        .quad 0x3D7CF79ABC9E3B3A, 0x3D7CF79ABC9E3B3A, 0x3D7CF79ABC9E3B3A, 0x3D7CF79ABC9E3B3A, 0x3D7CF79ABC9E3B3A, 0x3D7CF79ABC9E3B3A, 0x3D7CF79ABC9E3B3A, 0x3D7CF79ABC9E3B3A /* _dbLn2lo  = log(2) lo*/
+        .align 64
+        .quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000 /* _dSign */
+        //_dbT
+        .align 64
+        .quad 0x0000000000000000, 0x3FE0000000000000  //2^( 0 /128-1) - 2^(- 0 /128-1), 2^(- 0 /128-1)
+        .quad 0x3F762E4A19BD1E74, 0x3FDFD3C22B8F71F1  //2^( 1 /128-1) - 2^(- 1 /128-1), 2^(- 1 /128-1)
+        .quad 0x3F862E5F6A0DFD36, 0x3FDFA7C1819E90D8  //2^( 2 /128-1) - 2^(- 2 /128-1), 2^(- 2 /128-1)
+        .quad 0x3F90A2E234040F5F, 0x3FDF7BFDAD9CBE14  //2^( 3 /128-1) - 2^(- 3 /128-1), 2^(- 3 /128-1)
+        .quad 0x3F962EB4ABCC5A81, 0x3FDF50765B6E4540  //2^( 4 /128-1) - 2^(- 4 /128-1), 2^(- 4 /128-1)
+        .quad 0x3F9BBAB1C5033244, 0x3FDF252B376BBA97  //2^( 5 /128-1) - 2^(- 5 /128-1), 2^(- 5 /128-1)
+        .quad 0x3FA0A372144EEB45, 0x3FDEFA1BEE615A27  //2^( 6 /128-1) - 2^(- 6 /128-1), 2^(- 6 /128-1)
+        .quad 0x3FA369AB3FFBF8B0, 0x3FDECF482D8E67F1  //2^( 7 /128-1) - 2^(- 7 /128-1), 2^(- 7 /128-1)
+        .quad 0x3FA63009BA740A2A, 0x3FDEA4AFA2A490DA  //2^( 8 /128-1) - 2^(- 8 /128-1), 2^(- 8 /128-1)
+        .quad 0x3FA8F692D8EA1B5A, 0x3FDE7A51FBC74C83  //2^( 9 /128-1) - 2^(- 9 /128-1), 2^(- 9 /128-1)
+        .quad 0x3FABBD4BF0E31A6F, 0x3FDE502EE78B3FF6  //2^( 10 /128-1) - 2^(- 10 /128-1), 2^(- 10 /128-1)
+        .quad 0x3FAE843A5840286A, 0x3FDE264614F5A129  //2^( 11 /128-1) - 2^(- 11 /128-1), 2^(- 11 /128-1)
+        .quad 0x3FB0A5B1B2A46D0A, 0x3FDDFC97337B9B5F  //2^( 12 /128-1) - 2^(- 12 /128-1), 2^(- 12 /128-1)
+        .quad 0x3FB20966375ABCDF, 0x3FDDD321F301B460  //2^( 13 /128-1) - 2^(- 13 /128-1), 2^(- 13 /128-1)
+        .quad 0x3FB36D3D65DCA4E8, 0x3FDDA9E603DB3285  //2^( 14 /128-1) - 2^(- 14 /128-1), 2^(- 14 /128-1)
+        .quad 0x3FB4D139EA06642A, 0x3FDD80E316C98398  //2^( 15 /128-1) - 2^(- 15 /128-1), 2^(- 15 /128-1)
+        .quad 0x3FB6355E6FFBF9BA, 0x3FDD5818DCFBA487  //2^( 16 /128-1) - 2^(- 16 /128-1), 2^(- 16 /128-1)
+        .quad 0x3FB799ADA42E4788, 0x3FDD2F87080D89F2  //2^( 17 /128-1) - 2^(- 17 /128-1), 2^(- 17 /128-1)
+        .quad 0x3FB8FE2A336035BC, 0x3FDD072D4A07897C  //2^( 18 /128-1) - 2^(- 18 /128-1), 2^(- 18 /128-1)
+        .quad 0x3FBA62D6CAABD6B6, 0x3FDCDF0B555DC3FA  //2^( 19 /128-1) - 2^(- 19 /128-1), 2^(- 19 /128-1)
+        .quad 0x3FBBC7B617878BAF, 0x3FDCB720DCEF9069  //2^( 20 /128-1) - 2^(- 20 /128-1), 2^(- 20 /128-1)
+        .quad 0x3FBD2CCAC7CB2A11, 0x3FDC8F6D9406E7B5  //2^( 21 /128-1) - 2^(- 21 /128-1), 2^(- 21 /128-1)
+        .quad 0x3FBE921789B52185, 0x3FDC67F12E57D14B  //2^( 22 /128-1) - 2^(- 22 /128-1), 2^(- 22 /128-1)
+        .quad 0x3FBFF79F0BEFA2C7, 0x3FDC40AB5FFFD07A  //2^( 23 /128-1) - 2^(- 23 /128-1), 2^(- 23 /128-1)
+        .quad 0x3FC0AEB1FECAE3A9, 0x3FDC199BDD85529C  //2^( 24 /128-1) - 2^(- 24 /128-1), 2^(- 24 /128-1)
+        .quad 0x3FC161B4871C5CEC, 0x3FDBF2C25BD71E09  //2^( 25 /128-1) - 2^(- 25 /128-1), 2^(- 25 /128-1)
+        .quad 0x3FC214D876F26FD0, 0x3FDBCC1E904BC1D2  //2^( 26 /128-1) - 2^(- 26 /128-1), 2^(- 26 /128-1)
+        .quad 0x3FC2C81F2693816F, 0x3FDBA5B030A1064A  //2^( 27 /128-1) - 2^(- 27 /128-1), 2^(- 27 /128-1)
+        .quad 0x3FC37B89EE88BEF7, 0x3FDB7F76F2FB5E47  //2^( 28 /128-1) - 2^(- 28 /128-1), 2^(- 28 /128-1)
+        .quad 0x3FC42F1A27A0B3CD, 0x3FDB59728DE5593A  //2^( 29 /128-1) - 2^(- 29 /128-1), 2^(- 29 /128-1)
+        .quad 0x3FC4E2D12AF1E037, 0x3FDB33A2B84F15FB  //2^( 30 /128-1) - 2^(- 30 /128-1), 2^(- 30 /128-1)
+        .quad 0x3FC596B051DD508D, 0x3FDB0E07298DB666  //2^( 31 /128-1) - 2^(- 31 /128-1), 2^(- 31 /128-1)
+        .quad 0x3FC64AB8F61134FA, 0x3FDAE89F995AD3AD  //2^( 32 /128-1) - 2^(- 32 /128-1), 2^(- 32 /128-1)
+        .quad 0x3FC6FEEC718B79D1, 0x3FDAC36BBFD3F37A  //2^( 33 /128-1) - 2^(- 33 /128-1), 2^(- 33 /128-1)
+        .quad 0x3FC7B34C1E9C607F, 0x3FDA9E6B5579FDBF  //2^( 34 /128-1) - 2^(- 34 /128-1), 2^(- 34 /128-1)
+        .quad 0x3FC867D957E91912, 0x3FDA799E1330B358  //2^( 35 /128-1) - 2^(- 35 /128-1), 2^(- 35 /128-1)
+        .quad 0x3FC91C95786E5C72, 0x3FDA5503B23E255D  //2^( 36 /128-1) - 2^(- 36 /128-1), 2^(- 36 /128-1)
+        .quad 0x3FC9D181DB83072F, 0x3FDA309BEC4A2D33  //2^( 37 /128-1) - 2^(- 37 /128-1), 2^(- 37 /128-1)
+        .quad 0x3FCA869FDCDAB512, 0x3FDA0C667B5DE565  //2^( 38 /128-1) - 2^(- 38 /128-1), 2^(- 38 /128-1)
+        .quad 0x3FCB3BF0D8885D4C, 0x3FD9E86319E32323  //2^( 39 /128-1) - 2^(- 39 /128-1), 2^(- 39 /128-1)
+        .quad 0x3FCBF1762B00EF69, 0x3FD9C49182A3F090  //2^( 40 /128-1) - 2^(- 40 /128-1), 2^(- 40 /128-1)
+        .quad 0x3FCCA731311DF0FB, 0x3FD9A0F170CA07BA  //2^( 41 /128-1) - 2^(- 41 /128-1), 2^(- 41 /128-1)
+        .quad 0x3FCD5D2348201C09, 0x3FD97D829FDE4E50  //2^( 42 /128-1) - 2^(- 42 /128-1), 2^(- 42 /128-1)
+        .quad 0x3FCE134DCDB1FE3E, 0x3FD95A44CBC8520F  //2^( 43 /128-1) - 2^(- 43 /128-1), 2^(- 43 /128-1)
+        .quad 0x3FCEC9B21FEA98EA, 0x3FD93737B0CDC5E5  //2^( 44 /128-1) - 2^(- 44 /128-1), 2^(- 44 /128-1)
+        .quad 0x3FCF80519D5001D3, 0x3FD9145B0B91FFC6  //2^( 45 /128-1) - 2^(- 45 /128-1), 2^(- 45 /128-1)
+        .quad 0x3FD01B96D26D026A, 0x3FD8F1AE99157736  //2^( 46 /128-1) - 2^(- 46 /128-1), 2^(- 46 /128-1)
+        .quad 0x3FD07723CAFA6331, 0x3FD8CF3216B5448C  //2^( 47 /128-1) - 2^(- 47 /128-1), 2^(- 47 /128-1)
+        .quad 0x3FD0D2D06841B373, 0x3FD8ACE5422AA0DB  //2^( 48 /128-1) - 2^(- 48 /128-1), 2^(- 48 /128-1)
+        .quad 0x3FD12E9D5A715381, 0x3FD88AC7D98A6699  //2^( 49 /128-1) - 2^(- 49 /128-1), 2^(- 49 /128-1)
+        .quad 0x3FD18A8B51F5C661, 0x3FD868D99B4492ED  //2^( 50 /128-1) - 2^(- 50 /128-1), 2^(- 50 /128-1)
+        .quad 0x3FD1E69AFF7B04D7, 0x3FD8471A4623C7AD  //2^( 51 /128-1) - 2^(- 51 /128-1), 2^(- 51 /128-1)
+        .quad 0x3FD242CD13EDD0F1, 0x3FD82589994CCE13  //2^( 52 /128-1) - 2^(- 52 /128-1), 2^(- 52 /128-1)
+        .quad 0x3FD29F22407D0A0C, 0x3FD80427543E1A12  //2^( 53 /128-1) - 2^(- 53 /128-1), 2^(- 53 /128-1)
+        .quad 0x3FD2FB9B369B0153, 0x3FD7E2F336CF4E62  //2^( 54 /128-1) - 2^(- 54 /128-1), 2^(- 54 /128-1)
+        .quad 0x3FD35838A7FECEC8, 0x3FD7C1ED0130C132  //2^( 55 /128-1) - 2^(- 55 /128-1), 2^(- 55 /128-1)
+        .quad 0x3FD3B4FB46A5A6CC, 0x3FD7A11473EB0187  //2^( 56 /128-1) - 2^(- 56 /128-1), 2^(- 56 /128-1)
+        .quad 0x3FD411E3C4D4302F, 0x3FD780694FDE5D3F  //2^( 57 /128-1) - 2^(- 57 /128-1), 2^(- 57 /128-1)
+        .quad 0x3FD46EF2D517DAC8, 0x3FD75FEB564267C9  //2^( 58 /128-1) - 2^(- 58 /128-1), 2^(- 58 /128-1)
+        .quad 0x3FD4CC292A48369E, 0x3FD73F9A48A58174  //2^( 59 /128-1) - 2^(- 59 /128-1), 2^(- 59 /128-1)
+        .quad 0x3FD5298777884B96, 0x3FD71F75E8EC5F74  //2^( 60 /128-1) - 2^(- 60 /128-1), 2^(- 60 /128-1)
+        .quad 0x3FD5870E7047F1BC, 0x3FD6FF7DF9519484  //2^( 61 /128-1) - 2^(- 61 /128-1), 2^(- 61 /128-1)
+        .quad 0x3FD5E4BEC8452A1A, 0x3FD6DFB23C651A2F  //2^( 62 /128-1) - 2^(- 62 /128-1), 2^(- 62 /128-1)
+        .quad 0x3FD64299338D7827, 0x3FD6C012750BDABF  //2^( 63 /128-1) - 2^(- 63 /128-1), 2^(- 63 /128-1)
+        .quad 0x3FD6A09E667F3BCD, 0x3FD6A09E667F3BCD  //2^( 64 /128-1) - 2^(- 64 /128-1), 2^(- 64 /128-1)
+        .quad 0x3FD6FECF15CB0C0B, 0x3FD68155D44CA973  //2^( 65 /128-1) - 2^(- 65 /128-1), 2^(- 65 /128-1)
+        .quad 0x3FD75D2BF6751239, 0x3FD6623882552225  //2^( 66 /128-1) - 2^(- 66 /128-1), 2^(- 66 /128-1)
+        .quad 0x3FD7BBB5BDD665E8, 0x3FD6434634CCC320  //2^( 67 /128-1) - 2^(- 67 /128-1), 2^(- 67 /128-1)
+        .quad 0x3FD81A6D219E6963, 0x3FD6247EB03A5585  //2^( 68 /128-1) - 2^(- 68 /128-1), 2^(- 68 /128-1)
+        .quad 0x3FD87952D7D426DF, 0x3FD605E1B976DC09  //2^( 69 /128-1) - 2^(- 69 /128-1), 2^(- 69 /128-1)
+        .quad 0x3FD8D86796D7AE49, 0x3FD5E76F15AD2148  //2^( 70 /128-1) - 2^(- 70 /128-1), 2^(- 70 /128-1)
+        .quad 0x3FD937AC156373C8, 0x3FD5C9268A5946B7  //2^( 71 /128-1) - 2^(- 71 /128-1), 2^(- 71 /128-1)
+        .quad 0x3FD997210A8DAEE4, 0x3FD5AB07DD485429  //2^( 72 /128-1) - 2^(- 72 /128-1), 2^(- 72 /128-1)
+        .quad 0x3FD9F6C72DC9BA68, 0x3FD58D12D497C7FD  //2^( 73 /128-1) - 2^(- 73 /128-1), 2^(- 73 /128-1)
+        .quad 0x3FDA569F36E974EA, 0x3FD56F4736B527DA  //2^( 74 /128-1) - 2^(- 74 /128-1), 2^(- 74 /128-1)
+        .quad 0x3FDAB6A9DE1EA215, 0x3FD551A4CA5D920F  //2^( 75 /128-1) - 2^(- 75 /128-1), 2^(- 75 /128-1)
+        .quad 0x3FDB16E7DBFC4CA3, 0x3FD5342B569D4F82  //2^( 76 /128-1) - 2^(- 76 /128-1), 2^(- 76 /128-1)
+        .quad 0x3FDB7759E9782918, 0x3FD516DAA2CF6642  //2^( 77 /128-1) - 2^(- 77 /128-1), 2^(- 77 /128-1)
+        .quad 0x3FDBD800BFEBF932, 0x3FD4F9B2769D2CA7  //2^( 78 /128-1) - 2^(- 78 /128-1), 2^(- 78 /128-1)
+        .quad 0x3FDC38DD1916F025, 0x3FD4DCB299FDDD0D  //2^( 79 /128-1) - 2^(- 79 /128-1), 2^(- 79 /128-1)
+        .quad 0x3FDC99EFAF1F1790, 0x3FD4BFDAD5362A27  //2^( 80 /128-1) - 2^(- 80 /128-1), 2^(- 80 /128-1)
+        .quad 0x3FDCFB393C92B539, 0x3FD4A32AF0D7D3DE  //2^( 81 /128-1) - 2^(- 81 /128-1), 2^(- 81 /128-1)
+        .quad 0x3FDD5CBA7C69B19C, 0x3FD486A2B5C13CD0  //2^( 82 /128-1) - 2^(- 82 /128-1), 2^(- 82 /128-1)
+        .quad 0x3FDDBE742A06FF34, 0x3FD46A41ED1D0057  //2^( 83 /128-1) - 2^(- 83 /128-1), 2^(- 83 /128-1)
+        .quad 0x3FDE2067013A029D, 0x3FD44E086061892D  //2^( 84 /128-1) - 2^(- 84 /128-1), 2^(- 84 /128-1)
+        .quad 0x3FDE8293BE3FFB87, 0x3FD431F5D950A897  //2^( 85 /128-1) - 2^(- 85 /128-1), 2^(- 85 /128-1)
+        .quad 0x3FDEE4FB1DC56E75, 0x3FD4160A21F72E2A  //2^( 86 /128-1) - 2^(- 86 /128-1), 2^(- 86 /128-1)
+        .quad 0x3FDF479DDCE78F58, 0x3FD3FA4504AC801C  //2^( 87 /128-1) - 2^(- 87 /128-1), 2^(- 87 /128-1)
+        .quad 0x3FDFAA7CB935ACFE, 0x3FD3DEA64C123422  //2^( 88 /128-1) - 2^(- 88 /128-1), 2^(- 88 /128-1)
+        .quad 0x3FE006CC38594EB1, 0x3FD3C32DC313A8E5  //2^( 89 /128-1) - 2^(- 89 /128-1), 2^(- 89 /128-1)
+        .quad 0x3FE03878E0EB1569, 0x3FD3A7DB34E59FF7  //2^( 90 /128-1) - 2^(- 90 /128-1), 2^(- 90 /128-1)
+        .quad 0x3FE06A44B5C74101, 0x3FD38CAE6D05D866  //2^( 91 /128-1) - 2^(- 91 /128-1), 2^(- 91 /128-1)
+        .quad 0x3FE09C3016A0D077, 0x3FD371A7373AA9CB  //2^( 92 /128-1) - 2^(- 92 /128-1), 2^(- 92 /128-1)
+        .quad 0x3FE0CE3B63676360, 0x3FD356C55F929FF1  //2^( 93 /128-1) - 2^(- 93 /128-1), 2^(- 93 /128-1)
+        .quad 0x3FE10066FC47F240, 0x3FD33C08B26416FF  //2^( 94 /128-1) - 2^(- 94 /128-1), 2^(- 94 /128-1)
+        .quad 0x3FE132B341AD8761, 0x3FD32170FC4CD831  //2^( 95 /128-1) - 2^(- 95 /128-1), 2^(- 95 /128-1)
+        .quad 0x3FE165209441F823, 0x3FD306FE0A31B715  //2^( 96 /128-1) - 2^(- 96 /128-1), 2^(- 96 /128-1)
+        .quad 0x3FE197AF54EE9EBB, 0x3FD2ECAFA93E2F56  //2^( 97 /128-1) - 2^(- 97 /128-1), 2^(- 97 /128-1)
+        .quad 0x3FE1CA5FE4DD1475, 0x3FD2D285A6E4030B  //2^( 98 /128-1) - 2^(- 98 /128-1), 2^(- 98 /128-1)
+        .quad 0x3FE1FD32A577EC72, 0x3FD2B87FD0DAD990  //2^( 99 /128-1) - 2^(- 99 /128-1), 2^(- 99 /128-1)
+        .quad 0x3FE23027F86B6ED6, 0x3FD29E9DF51FDEE1  //2^( 100 /128-1) - 2^(- 100 /128-1), 2^(- 100 /128-1)
+        .quad 0x3FE263403FA65489, 0x3FD284DFE1F56381  //2^( 101 /128-1) - 2^(- 101 /128-1), 2^(- 101 /128-1)
+        .quad 0x3FE2967BDD5A8364, 0x3FD26B4565E27CDD  //2^( 102 /128-1) - 2^(- 102 /128-1), 2^(- 102 /128-1)
+        .quad 0x3FE2C9DB33FDCAE9, 0x3FD251CE4FB2A63F  //2^( 103 /128-1) - 2^(- 103 /128-1), 2^(- 103 /128-1)
+        .quad 0x3FE2FD5EA64AA180, 0x3FD2387A6E756238  //2^( 104 /128-1) - 2^(- 104 /128-1), 2^(- 104 /128-1)
+        .quad 0x3FE331069740E22F, 0x3FD21F49917DDC96  //2^( 105 /128-1) - 2^(- 105 /128-1), 2^(- 105 /128-1)
+        .quad 0x3FE364D36A268AE0, 0x3FD2063B88628CD6  //2^( 106 /128-1) - 2^(- 106 /128-1), 2^(- 106 /128-1)
+        .quad 0x3FE398C582887B27, 0x3FD1ED5022FCD91D  //2^( 107 /128-1) - 2^(- 107 /128-1), 2^(- 107 /128-1)
+        .quad 0x3FE3CCDD443B3394, 0x3FD1D4873168B9AA  //2^( 108 /128-1) - 2^(- 108 /128-1), 2^(- 108 /128-1)
+        .quad 0x3FE4011B135B9590, 0x3FD1BBE084045CD4  //2^( 109 /128-1) - 2^(- 109 /128-1), 2^(- 109 /128-1)
+        .quad 0x3FE4357F544FA3C1, 0x3FD1A35BEB6FCB75  //2^( 110 /128-1) - 2^(- 110 /128-1), 2^(- 110 /128-1)
+        .quad 0x3FE46A0A6BC742FD, 0x3FD18AF9388C8DEA  //2^( 111 /128-1) - 2^(- 111 /128-1), 2^(- 111 /128-1)
+        .quad 0x3FE49EBCBEBCFBCA, 0x3FD172B83C7D517B  //2^( 112 /128-1) - 2^(- 112 /128-1), 2^(- 112 /128-1)
+        .quad 0x3FE4D396B276BC6F, 0x3FD15A98C8A58E51  //2^( 113 /128-1) - 2^(- 113 /128-1), 2^(- 113 /128-1)
+        .quad 0x3FE50898AC869B96, 0x3FD1429AAEA92DE0  //2^( 114 /128-1) - 2^(- 114 /128-1), 2^(- 114 /128-1)
+        .quad 0x3FE53DC312CB9B7A, 0x3FD12ABDC06C31CC  //2^( 115 /128-1) - 2^(- 115 /128-1), 2^(- 115 /128-1)
+        .quad 0x3FE573164B726DB6, 0x3FD11301D0125B51  //2^( 116 /128-1) - 2^(- 116 /128-1), 2^(- 116 /128-1)
+        .quad 0x3FE5A892BCF6379B, 0x3FD0FB66AFFED31B  //2^( 117 /128-1) - 2^(- 117 /128-1), 2^(- 117 /128-1)
+        .quad 0x3FE5DE38CE215725, 0x3FD0E3EC32D3D1A2  //2^( 118 /128-1) - 2^(- 118 /128-1), 2^(- 118 /128-1)
+        .quad 0x3FE61408E60E2888, 0x3FD0CC922B7247F7  //2^( 119 /128-1) - 2^(- 119 /128-1), 2^(- 119 /128-1)
+        .quad 0x3FE64A036C27CC52, 0x3FD0B5586CF9890F  //2^( 120 /128-1) - 2^(- 120 /128-1), 2^(- 120 /128-1)
+        .quad 0x3FE68028C82AEE2F, 0x3FD09E3ECAC6F383  //2^( 121 /128-1) - 2^(- 121 /128-1), 2^(- 121 /128-1)
+        .quad 0x3FE6B67962268C43, 0x3FD0874518759BC8  //2^( 122 /128-1) - 2^(- 122 /128-1), 2^(- 122 /128-1)
+        .quad 0x3FE6ECF5A27CBF28, 0x3FD0706B29DDF6DE  //2^( 123 /128-1) - 2^(- 123 /128-1), 2^(- 123 /128-1)
+        .quad 0x3FE7239DF1E38286, 0x3FD059B0D3158574  //2^( 124 /128-1) - 2^(- 124 /128-1), 2^(- 124 /128-1)
+        .quad 0x3FE75A72B9657E51, 0x3FD04315E86E7F85  //2^( 125 /128-1) - 2^(- 125 /128-1), 2^(- 125 /128-1)
+        .quad 0x3FE791746262D0A8, 0x3FD02C9A3E778061  //2^( 126 /128-1) - 2^(- 126 /128-1), 2^(- 126 /128-1)
+        .quad 0x3FE7C8A35691D856, 0x3FD0163DA9FB3335 //2^( 127 /128-1) - 2^(- 127 /128-1), 2^(- 127 /128-1)
+        .align 64
+        .quad 0x42C8000000000000, 0x42C8000000000000, 0x42C8000000000000, 0x42C8000000000000, 0x42C8000000000000, 0x42C8000000000000, 0x42C8000000000000, 0x42C8000000000000 /* _dbShifter = 1.5 * 2^(52-k)*/
+        .align 64
+        .long 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99, 0x40861d99         /* _iDomainRange 0x40861d9ac12a3e85 =(1021*2^K-0.5)*log(2)/2^K -needed for quick exp*/
+        .align 64
+        .quad 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD, 0x3FDFFFFFFFFFFDBD /* _dPC2 */
+        .align 64
+        .quad 0x3FC55555555554AD, 0x3FC55555555554AD, 0x3FC55555555554AD, 0x3FC55555555554AD, 0x3FC55555555554AD, 0x3FC55555555554AD, 0x3FC55555555554AD, 0x3FC55555555554AD /* _dPC3 */
+        .align 64
+        .quad 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299, 0x3FA55555CF16D299 /* _dPC4 */
+        .align 64
+        .quad 0x3F8111115712F425, 0x3F8111115712F425, 0x3F8111115712F425, 0x3F8111115712F425, 0x3F8111115712F425, 0x3F8111115712F425, 0x3F8111115712F425, 0x3F8111115712F425 /* _dPC5 */
+        .align 64
+        .quad 0x000000000000007f, 0x000000000000007f, 0x000000000000007f, 0x000000000000007f, 0x000000000000007f, 0x000000000000007f, 0x000000000000007f, 0x000000000000007f /* _lIndexMask */
+        .align 64
+        .type	__svml_dsinh_data_internal,@object
+        .size	__svml_dsinh_data_internal,.-__svml_dsinh_data_internal