x86-64: Add vector tanh/tanhf implementation to libmvec

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

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

1 files changed, 472 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_tanh8_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_d_tanh8_core_avx512.S
new file mode 100644
index 0000000000..01fc22ba6f
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_tanh8_core_avx512.S
@@ -0,0 +1,472 @@
+/* Function tanh 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:
+ *
+ *   NOTE: Since the hyperbolic tangent function is odd
+ *         (tanh(x) = -tanh(-x)), below algorithm deals with the absolute
+ *         value of the argument |x|: tanh(x) = sign(x) * tanh(|x|)
+ *
+ *   We use a table lookup method to compute tanh(|x|).
+ *   The basic idea is to split the input range into a number of subintervals
+ *   and to approximate tanh(.) with a polynomial on each of them.
+ *
+ *   IEEE SPECIAL CONDITIONS:
+ *   x = [+,-]0, r = [+,-]0
+ *   x = +Inf,   r = +1
+ *   x = -Inf,   r = -1
+ *   x = QNaN,   r = QNaN
+ *   x = SNaN,   r = QNaN
+ *
+ *
+ *   ALGORITHM DETAILS
+ *   We handle special values in a callout function, aside from main path
+ *   computations. "Special" for this algorithm are:
+ *   INF, NAN, |x| > HUGE_THRESHOLD
+ *
+ *
+ *   Main path computations are organized as follows:
+ *   Actually we split the interval [0, SATURATION_THRESHOLD)
+ *   into a number of subintervals.  On each subinterval we approximate tanh(.)
+ *   with a minimax polynomial of pre-defined degree. Polynomial coefficients
+ *   are computed beforehand and stored in table. We also use
+ *
+ *       y := |x| + B,
+ *
+ *   here B depends on subinterval and is used to make argument
+ *   closer to zero.
+ *   We also add large fake interval [SATURATION_THRESHOLD, HUGE_THRESHOLD],
+ *   where 1.0 + 0.0*y + 0.0*y^2 ... coefficients are stored - just to
+ *   preserve main path computation logic but return 1.0 for all arguments.
+ *
+ *   Hence reconstruction looks as follows:
+ *   we extract proper polynomial and range reduction coefficients
+ *        (Pj and B), corresponding to subinterval, to which |x| belongs,
+ *        and return
+ *
+ *       r := sign(x) * (P0 + P1 * y + ... + Pn * y^n)
+ *
+ *   NOTE: we use multiprecision technique to multiply and sum the first
+ *         K terms of the polynomial. So Pj, j = 0..K are stored in
+ *         table each as a pair of target precision numbers (Pj and PLj) to
+ *         achieve wider than target precision.
+ *
+ *
+ */
+
+/* Offsets for data table __svml_dtanh_data_internal
+ */
+#define _dC                           	0
+#define _dP0                          	128
+#define _dP1                          	256
+#define _dP2                          	384
+#define _dP3                          	512
+#define _dP4                          	640
+#define _dP5                          	768
+#define _dP6                          	896
+#define _dP7                          	1024
+#define _dP8                          	1152
+#define _dP9                          	1280
+#define _dP10                         	1408
+#define _dP11                         	1536
+#define _dP12                         	1664
+#define _dP13                         	1792
+#define _dP14                         	1920
+#define _dP15                         	2048
+#define _dP16                         	2176
+#define _dP17                         	2304
+#define _iExpMantMask_UISA            	2432
+#define _iMinIdxOfsMask_UISA          	2496
+#define _iMaxIdxMask_UISA             	2560
+#define _dbSignMask                   	2624
+#define _dbAbsMask                    	2688
+#define _iExpMantMask                 	2752
+#define _iExpMask                     	2816
+#define _iMinIdxOfsMask               	2880
+#define _iMaxIdxMask                  	2944
+
+#include <sysdep.h>
+
+        .text
+	.section .text.evex512,"ax",@progbits
+ENTRY(_ZGVeN8v_tanh_skx)
+        pushq     %rbp
+        cfi_def_cfa_offset(16)
+        movq      %rsp, %rbp
+        cfi_def_cfa(6, 16)
+        cfi_offset(6, -16)
+        andq      $-64, %rsp
+        subq      $320, %rsp
+        vpsrlq    $32, %zmm0, %zmm4
+        vmovups   %zmm0, (%rsp)
+        vmovups   __svml_dtanh_data_internal(%rip), %zmm14
+        vmovups   _dP0+__svml_dtanh_data_internal(%rip), %zmm15
+        vpmovqd   %zmm4, %ymm5
+
+/*  Constant loading  */
+        vandpd    _dbAbsMask+__svml_dtanh_data_internal(%rip), %zmm0, %zmm13
+        vandpd    _dbSignMask+__svml_dtanh_data_internal(%rip), %zmm0, %zmm3
+
+/* Here huge arguments, INF and NaNs are filtered out to callout. */
+        vpand     _iExpMantMask_UISA+__svml_dtanh_data_internal(%rip), %ymm5, %ymm7
+        vmovups   _dP2+__svml_dtanh_data_internal(%rip), %zmm0
+        vmovups   _dP16+__svml_dtanh_data_internal(%rip), %zmm4
+        vmovups   _dP15+__svml_dtanh_data_internal(%rip), %zmm5
+        vmovups   %zmm3, 64(%rsp)
+        vmovups   _dP3+__svml_dtanh_data_internal(%rip), %zmm3
+        vpsubd    _iMinIdxOfsMask_UISA+__svml_dtanh_data_internal(%rip), %ymm7, %ymm8
+
+/* if VMIN, VMAX is defined for I type */
+        vxorps    %ymm9, %ymm9, %ymm9
+        vpmaxsd   %ymm9, %ymm8, %ymm10
+        vpminsd   _iMaxIdxMask_UISA+__svml_dtanh_data_internal(%rip), %ymm10, %ymm11
+        vpsrld    $19, %ymm11, %ymm12
+        vmovups   _dP12+__svml_dtanh_data_internal(%rip), %zmm8
+        vmovups   _dP11+__svml_dtanh_data_internal(%rip), %zmm9
+        vmovups   _dP10+__svml_dtanh_data_internal(%rip), %zmm10
+        vmovups   _dP9+__svml_dtanh_data_internal(%rip), %zmm11
+        vpmovzxdq %ymm12, %zmm2
+        vmovups   _dP8+__svml_dtanh_data_internal(%rip), %zmm12
+        vpermt2pd _dP2+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm0
+        vpermt2pd _dC+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm14
+        vpermt2pd _dP16+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm4
+        vpermt2pd _dP15+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm5
+        vsubpd    {rn-sae}, %zmm14, %zmm13, %zmm1
+        vpermt2pd _dP12+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm8
+        vpermt2pd _dP11+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm9
+        vpermt2pd _dP10+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm10
+        vpermt2pd _dP9+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm11
+        vpermt2pd _dP8+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm12
+        vpermt2pd _dP3+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm3
+        vpermt2pd _dP0+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm15
+        vmovups   %zmm0, 192(%rsp)
+        vmovups   _dP17+__svml_dtanh_data_internal(%rip), %zmm0
+        vmovups   _dP7+__svml_dtanh_data_internal(%rip), %zmm13
+        vmovups   _dP6+__svml_dtanh_data_internal(%rip), %zmm14
+        vmovups   %zmm3, 256(%rsp)
+        vmovups   _dP5+__svml_dtanh_data_internal(%rip), %zmm3
+        vmovups   %zmm15, 128(%rsp)
+        vmovups   _dP4+__svml_dtanh_data_internal(%rip), %zmm15
+        vpermt2pd _dP17+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm0
+        vpermt2pd _dP7+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm13
+        vpermt2pd _dP6+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm14
+        vpermt2pd _dP5+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm3
+        vpermt2pd _dP4+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm15
+        vfmadd213pd {rn-sae}, %zmm4, %zmm1, %zmm0
+        vpcmpgtd  _iExpMask+__svml_dtanh_data_internal(%rip), %ymm7, %ymm6
+        vmovmskps %ymm6, %edx
+        vmovups   _dP14+__svml_dtanh_data_internal(%rip), %zmm6
+        vfmadd213pd {rn-sae}, %zmm5, %zmm1, %zmm0
+        vmovups   _dP13+__svml_dtanh_data_internal(%rip), %zmm7
+        vpermt2pd _dP14+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm6
+        vpermt2pd _dP13+64+__svml_dtanh_data_internal(%rip), %zmm2, %zmm7
+        vfmadd213pd {rn-sae}, %zmm6, %zmm1, %zmm0
+        vmovups   256(%rsp), %zmm2
+        vfmadd213pd {rn-sae}, %zmm7, %zmm1, %zmm0
+        vfmadd213pd {rn-sae}, %zmm8, %zmm1, %zmm0
+        vfmadd213pd {rn-sae}, %zmm9, %zmm1, %zmm0
+        vfmadd213pd {rn-sae}, %zmm10, %zmm1, %zmm0
+        vfmadd213pd {rn-sae}, %zmm11, %zmm1, %zmm0
+        vfmadd213pd {rn-sae}, %zmm12, %zmm1, %zmm0
+        vfmadd213pd {rn-sae}, %zmm13, %zmm1, %zmm0
+        vfmadd213pd {rn-sae}, %zmm14, %zmm1, %zmm0
+        vfmadd213pd {rn-sae}, %zmm3, %zmm1, %zmm0
+        vmovups   128(%rsp), %zmm3
+        vfmadd213pd {rn-sae}, %zmm15, %zmm1, %zmm0
+        vfmadd213pd {rn-sae}, %zmm2, %zmm1, %zmm0
+        vmovups   192(%rsp), %zmm2
+        vfmadd213pd {rn-sae}, %zmm2, %zmm1, %zmm0
+        vfmadd213pd {rn-sae}, %zmm3, %zmm1, %zmm0
+        vorpd     64(%rsp), %zmm0, %zmm0
+        testl     %edx, %edx
+
+/* Go to special inputs processing branch */
+        jne       L(SPECIAL_VALUES_BRANCH)
+                                # LOE rbx r12 r13 r14 r15 edx zmm0
+
+/* 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   (%rsp), %zmm1
+        vmovups   %zmm0, 128(%rsp)
+        vmovups   %zmm1, 64(%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: -304; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xd0, 0xfe, 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: -312; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xc8, 0xfe, 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: -320; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xc0, 0xfe, 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: -304; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xd0, 0xfe, 0xff, 0xff, 0x22
+        /*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -312; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xc8, 0xfe, 0xff, 0xff, 0x22
+        /*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -64; DW_OP_and; DW_OP_const4s: -320; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xc0, 0xfe, 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      tanh@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_tanh_skx)
+
+        .section .rodata, "a"
+        .align 64
+
+#ifdef __svml_dtanh_data_internal_typedef
+typedef unsigned int VUINT32;
+typedef struct
+{
+        __declspec(align(64)) VUINT32 _dC[16][2];
+        __declspec(align(64)) VUINT32 _dP0[16][2];
+        __declspec(align(64)) VUINT32 _dP1[16][2];
+        __declspec(align(64)) VUINT32 _dP2[16][2];
+        __declspec(align(64)) VUINT32 _dP3[16][2];
+        __declspec(align(64)) VUINT32 _dP4[16][2];
+        __declspec(align(64)) VUINT32 _dP5[16][2];
+        __declspec(align(64)) VUINT32 _dP6[16][2];
+        __declspec(align(64)) VUINT32 _dP7[16][2];
+        __declspec(align(64)) VUINT32 _dP8[16][2];
+        __declspec(align(64)) VUINT32 _dP9[16][2];
+        __declspec(align(64)) VUINT32 _dP10[16][2];
+        __declspec(align(64)) VUINT32 _dP11[16][2];
+        __declspec(align(64)) VUINT32 _dP12[16][2];
+        __declspec(align(64)) VUINT32 _dP13[16][2];
+        __declspec(align(64)) VUINT32 _dP14[16][2];
+        __declspec(align(64)) VUINT32 _dP15[16][2];
+        __declspec(align(64)) VUINT32 _dP16[16][2];
+        __declspec(align(64)) VUINT32 _dP17[16][2];
+        __declspec(align(64)) VUINT32 _iExpMantMask_UISA[16][1];
+        __declspec(align(64)) VUINT32 _iMinIdxOfsMask_UISA[16][1];
+        __declspec(align(64)) VUINT32 _iMaxIdxMask_UISA[16][1];
+        __declspec(align(64)) VUINT32 _dbSignMask[8][2];
+        __declspec(align(64)) VUINT32 _dbAbsMask[8][2];
+        __declspec(align(64)) VUINT32 _iExpMantMask[16][1];
+        __declspec(align(64)) VUINT32 _iExpMask[16][1];
+        __declspec(align(64)) VUINT32 _iMinIdxOfsMask[16][1];
+        __declspec(align(64)) VUINT32 _iMaxIdxMask[16][1];
+} __svml_dtanh_data_internal;
+#endif
+__svml_dtanh_data_internal:
+        /*== _dC ==*/
+        .quad 0x0000000000000000, 0x3fcc000000000000, 0x3fd4000000000000, 0x3fdc000000000000
+        .quad 0x3fe4000000000000, 0x3fec000000000000, 0x3ff4000000000000, 0x3ffc000000000000
+        .quad 0x4004000000000000, 0x400c000000000000, 0x4014000000000000, 0x401c000000000000
+        .quad 0x4024000000000000, 0x402c000000000000, 0x4034000000000000, 0x0000000000000000
+        /*== p0 ==*/
+        .align 64
+        .quad 0x0000000000000000, 0x3fcb8fd0416a7c92, 0x3fd35f98a0ea650e, 0x3fda5729ee488037
+        .quad 0x3fe1bf47eabb8f95, 0x3fe686650b8c2015, 0x3feb2523bb6b2dee, 0x3fee1fbf97e33527
+        .quad 0x3fef9258260a71c2, 0x3feff112c63a9077, 0x3fefff419668df11, 0x3feffffc832750f2
+        .quad 0x3feffffffdc96f35, 0x3fefffffffffcf58, 0x3ff0000000000000, 0x3ff0000000000000
+        /*== p1 ==*/
+        .align 64
+        .quad 0x0000000000000000, 0x3c65e23ebcd3bcbe, 0xbc4c600bac3adf00, 0x3c6c44091785d040
+        .quad 0x3c8221d7a6e3674b, 0x3c69f89d2cf6b85c, 0x3c73b3e9ec0b8f1c, 0xbc7f8d4b0428aada
+        .quad 0xbc7c52d880cf43c0, 0x3c7dd36e37096480, 0x3c7b4f6380c442ca, 0xbc729755de470096
+        .quad 0x3c84cf852845efbd, 0x3c6fc4fb440a5378, 0xbc63981083b55870, 0x0000000000000000
+        /*== p2 ==*/
+        .align 64
+        .quad 0x3ff0000000000000, 0x3fee842ca3f08532, 0x3fed11574af58f1b, 0x3fea945b9c24e4f9
+        .quad 0x3fe6284c3374f815, 0x3fe02500a09f8d6e, 0x3fd1f25131e3a8c0, 0x3fbd22ca1c24a139
+        .quad 0x3f9b3afe1fba5c76, 0x3f6dd37d19b22b21, 0x3f27ccec13a9ef96, 0x3ecbe6c3f33250ae
+        .quad 0x3e41b4865394f75f, 0x3d8853f01bda5f28, 0x3c73953c0197ef58, 0x0000000000000000
+        /*== p3 ==*/
+        .align 64
+        .quad 0xbbf0b3ea3fdfaa19, 0xbfca48aaeb53bc21, 0xbfd19921f4329916, 0xbfd5e0f09bef8011
+        .quad 0xbfd893b59c35c882, 0xbfd6ba7cb7576538, 0xbfce7291743d7555, 0xbfbb6d85a01efb80
+        .quad 0xbf9addae58c7141a, 0xbf6dc59376c7aa19, 0xbf27cc5e74677410, 0xbecbe6c0e8b4cc87
+        .quad 0xbe41b486526b0565, 0xbd8853f01bef63a4, 0xbc73955be519be31, 0x0000000000000000
+        /*== p4 ==*/
+        .align 64
+        .quad 0xbfd5555555555555, 0xbfd183afc292ba11, 0xbfcc1a4b039c9bfa, 0xbfc16e1e6d8d0be6
+        .quad 0xbf92426c751e48a2, 0x3fb4f152b2bad124, 0x3fbbba40cbef72be, 0x3fb01ba038be6a3d
+        .quad 0x3f916df44871efc8, 0x3f63c6869dfc8870, 0x3f1fb9aef915d828, 0x3ec299d1e27c6e11
+        .quad 0x3e379b5ddcca334c, 0x3d8037f57bc62c9a, 0x3c6a2d4b50a2cff7, 0x0000000000000000
+        /*== p5 ==*/
+        .align 64
+        .quad 0xbce6863ee44ed636, 0x3fc04dcd0476c75e, 0x3fc43d3449a80f08, 0x3fc5c26f3699b7e7
+        .quad 0x3fc1a686f6ab2533, 0x3faf203c316ce730, 0xbf89c7a02788557c, 0xbf98157e26e0d541
+        .quad 0xbf807b55c1c7d278, 0xbf53a18d5843190f, 0xbf0fb6bbc89b1a5b, 0xbeb299c9c684a963
+        .quad 0xbe279b5dd4fb3d01, 0xbd7037f57ae72aa6, 0xbc5a2ca2bba78e86, 0x0000000000000000
+        /*== p6 ==*/
+        .align 64
+        .quad 0x3fc1111111112ab5, 0x3fb5c19efdfc08ad, 0x3fa74c98dc34fbac, 0xbf790d6a8eff0a77
+        .quad 0xbfac3c021789a786, 0xbfae2196b7326859, 0xbf93a7a011ff8c2a, 0x3f6e4709c7e8430e
+        .quad 0x3f67682afa611151, 0x3f3ef2ee77717cbf, 0x3ef95a4482f180b7, 0x3e9dc2c27da3b603
+        .quad 0x3e12e2afd9f7433e, 0x3d59f320348679ba, 0x3c44b61d9bbcc940, 0x0000000000000000
+        /*== p7 ==*/
+        .align 64
+        .quad 0xbda1ea19ddddb3b4, 0xbfb0b8df995ce4df, 0xbfb2955cf41e8164, 0xbfaf9d05c309f7c6
+        .quad 0xbf987d27ccff4291, 0x3f8b2ca62572b098, 0x3f8f1cf6c7f5b00a, 0x3f60379811e43dd5
+        .quad 0xbf4793826f78537e, 0xbf2405695e36240f, 0xbee0e08de39ce756, 0xbe83d709ba5f714e
+        .quad 0xbdf92e3fc5ee63e0, 0xbd414cc030f2110e, 0xbc2ba022e8d82a87, 0x0000000000000000
+        /*== p8 ==*/
+        .align 64
+        .quad 0xbfaba1ba1990520b, 0xbf96e37bba52f6fc, 0x3ecff7df18455399, 0x3f97362834d33a4e
+        .quad 0x3f9e7f8380184b45, 0x3f869543e7c420d4, 0xbf7326bd4914222a, 0xbf5fc15b0a9d98fa
+        .quad 0x3f14cffcfa69fbb6, 0x3f057e48e5b79d10, 0x3ec33b66d7d77264, 0x3e66ac4e578b9b10
+        .quad 0x3ddcc74b8d3d5c42, 0x3d23c589137f92b4, 0x3c107f8e2c8707a1, 0x0000000000000000
+        /*== p9 ==*/
+        .align 64
+        .quad 0xbe351ca7f096011f, 0x3f9eaaf3320c3851, 0x3f9cf823fe761fc1, 0x3f9022271754ff1f
+        .quad 0xbf731fe77c9c60af, 0xbf84a6046865ec7d, 0xbf4ca3f1f2b9192b, 0x3f4c77dee0afd227
+        .quad 0x3f04055bce68597a, 0xbee2bf0cb4a71647, 0xbea31eaafe73efd5, 0xbe46abb02c4368ed
+        .quad 0xbdbcc749ca8079dd, 0xbd03c5883836b9d2, 0xbbf07a5416264aec, 0x0000000000000000
+        /*== p10 ==*/
+        .align 64
+        .quad 0x3f9664f94e6ac14e, 0xbf94d3343bae39dd, 0xbf7bc748e60df843, 0xbf8c89372b43ba85
+        .quad 0xbf8129a092de747a, 0x3f60c85b4d538746, 0x3f5be9392199ec18, 0xbf2a0c68a4489f10
+        .quad 0xbf00462601dc2faa, 0x3eb7b6a219dea9f4, 0x3e80cbcc8d4c5c8a, 0x3e2425bb231a5e29
+        .quad 0x3d9992a4beac8662, 0x3ce191ba5ed3fb67, 0x3bc892450bad44c4, 0x0000000000000000
+        /*== p11 ==*/
+        .align 64
+        .quad 0xbea8c4c1fd7852fe, 0xbfccce16b1046f13, 0xbf81a16f224bb7b6, 0xbf62cbf00406bc09
+        .quad 0x3f75b29bb02cf69b, 0x3f607df0f9f90c17, 0xbf4b852a6e0758d5, 0xbf0078c63d1b8445
+        .quad 0x3eec12eadd55be7a, 0xbe6fa600f593181b, 0xbe5a3c935dce3f7d, 0xbe001c6d95e3ae96
+        .quad 0xbd74755a00ea1fd3, 0xbcbc1c6c063bb7ac, 0xbba3be9a4460fe00, 0x0000000000000000
+        /*== p12 ==*/
+        .align 64
+        .quad 0xbf822404577aa9dd, 0x403d8b07f7a82aa3, 0xbf9f44ab92fbab0a, 0x3fb2eac604473d6a
+        .quad 0x3f45f87d903aaac8, 0xbf5e104671036300, 0x3f19bc98ddf0f340, 0x3f0d4304bc9246e8
+        .quad 0xbed13c415f7b9d41, 0xbe722b8d9720cdb0, 0x3e322666d739bec0, 0x3dd76a553d7e7918
+        .quad 0x3d4de0fa59416a39, 0x3c948716cf3681b4, 0x3b873f9f2d2fda99, 0x0000000000000000
+        /*== p13 ==*/
+        .align 64
+        .quad 0xbefdd99a221ed573, 0x4070593a3735bab4, 0xbfccab654e44835e, 0x3fd13ed80037dbac
+        .quad 0xbf6045b9076cc487, 0x3f2085ee7e8ac170, 0x3f23524622610430, 0xbeff12a6626911b4
+        .quad 0x3eab9008bca408af, 0x3e634df71865f620, 0xbe05bb1bcf83ca73, 0xbdaf2ac143fb6762
+        .quad 0xbd23eae52a3dbf57, 0xbc6b5e3e9ca0955e, 0xbb5eca68e2c1ba2e, 0x0000000000000000
+        /*== p14 ==*/
+        .align 64
+        .quad 0x3f6e3be689423841, 0xc0d263511f5baac1, 0x40169f73b15ebe5c, 0xc025c1dd41cd6cb5
+        .quad 0xbf58fd89fe05e0d1, 0x3f73f7af01d5af7a, 0xbf1e40bdead17e6b, 0x3ee224cd6c4513e5
+        .quad 0xbe24b645e68eeaa3, 0xbe4abfebfb72bc83, 0x3dd51c38f8695ed3, 0x3d8313ac38c6832b
+        .quad 0x3cf7787935626685, 0x3c401ffc49c6bc29, 0xbabf0b21acfa52ab, 0x0000000000000000
+        /*== p15 ==*/
+        .align 64
+        .quad 0xbf2a1306713a4f3a, 0xc1045e509116b066, 0x4041fab9250984ce, 0xc0458d090ec3de95
+        .quad 0xbf74949d60113d63, 0x3f7c9fd6200d0ade, 0x3f02cd40e0ad0a9f, 0xbe858ab8e019f311
+        .quad 0xbe792fa6323b7cf8, 0x3e2df04d67876402, 0xbd95c72be95e4d2c, 0xbd55a89c30203106
+        .quad 0xbccad6b3bb9eff65, 0xbc12705ccd3dd884, 0xba8e0a4c47ae75f5, 0x0000000000000000
+        /*== p16 ==*/
+        .align 64
+        .quad 0xbf55d7e76dc56871, 0x41528c38809c90c7, 0xc076d57fb5190b02, 0x4085f09f888f8ada
+        .quad 0x3fa246332a2fcba5, 0xbfb29d851a896fcd, 0x3ed9065ae369b212, 0xbeb8e1ba4c98a030
+        .quad 0x3e6ffd0766ad4016, 0xbe0c63c29f505f5b, 0xbd7fab216b9e0e49, 0x3d2826b62056aa27
+        .quad 0x3ca313e31762f523, 0x3bea37aa21895319, 0x3ae5c7f1fd871496, 0x0000000000000000
+        /*== p17 ==*/
+        .align 64
+        .quad 0x3f35e67ab76a26e7, 0x41848ee0627d8206, 0xc0a216d618b489ec, 0x40a5b89107c8af4f
+        .quad 0x3fb69d8374520eda, 0xbfbded519f981716, 0xbef02d288b5b3371, 0x3eb290981209c1a6
+        .quad 0xbe567e924bf5ff6e, 0x3de3f7f7de6b0eb6, 0x3d69ed18bae3ebbc, 0xbcf7534c4f3dfa71
+        .quad 0xbc730b73f1eaff20, 0xbbba2cff8135d462, 0xbab5a71b5f7d9035, 0x0000000000000000
+        .align 64
+        .long 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000           /* _iExpMantMask_UISA     */
+        .align 64
+        .long 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000, 0x3fc00000           /* _iMinIdxOfsMask_UISA   */
+        .align 64
+        .long 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000, 0x00780000           /* _iMaxIdxMask_UISA      */
+        .align 64
+        .quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000   /* _dbSignMask       */
+        .align 64
+        .quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff   /* _dbAbsMask        */
+        .align 64
+        .long 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000, 0x7ffe0000           /* _iExpMantMask     */
+        .align 64
+        .long 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000           /* _iExpMask         */
+        .align 64
+        .long 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000, 0x3fbe0000           /* _iMinIdxOfsMask   */
+        .align 64
+        .long 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000, 0x00760000           /* _iMaxIdxMask      */
+        .align 64
+        .type	__svml_dtanh_data_internal,@object
+        .size	__svml_dtanh_data_internal,.-__svml_dtanh_data_internal