x86-64: Add vector atan2/atan2f implementation to libmvec

Implement vectorized atan2/atan2f containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI.  It also contains
accuracy and ABI tests for vector atan2/atan2f with regenerated ulps.

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

1 files changed, 475 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_atan28_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_d_atan28_core_avx512.S
new file mode 100644
index 0000000000..6d18f5f757
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_atan28_core_avx512.S
@@ -0,0 +1,475 @@
+/* Function atan2 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:
+ *      For    0.0    <= x <=  7.0/16.0: atan(x) = atan(0.0) + atan(s), where s=(x-0.0)/(1.0+0.0*x)
+ *      For  7.0/16.0 <= x <= 11.0/16.0: atan(x) = atan(0.5) + atan(s), where s=(x-0.5)/(1.0+0.5*x)
+ *      For 11.0/16.0 <= x <= 19.0/16.0: atan(x) = atan(1.0) + atan(s), where s=(x-1.0)/(1.0+1.0*x)
+ *      For 19.0/16.0 <= x <= 39.0/16.0: atan(x) = atan(1.5) + atan(s), where s=(x-1.5)/(1.0+1.5*x)
+ *      For 39.0/16.0 <= x <=    inf   : atan(x) = atan(inf) + atan(s), where s=-1.0/x
+ *      Where atan(s) ~= s+s^3*Poly11(s^2) on interval |s|<7.0/0.16.
+ *
+ *
+ */
+
+/* Offsets for data table __svml_datan2_data_internal
+ */
+#define dPI                           	0
+#define dPIO2                         	64
+#define dA19                          	128
+#define dA18                          	192
+#define dA17                          	256
+#define dA16                          	320
+#define dA15                          	384
+#define dA14                          	448
+#define dA13                          	512
+#define dA12                          	576
+#define dA11                          	640
+#define dA10                          	704
+#define dA09                          	768
+#define dA08                          	832
+#define dA07                          	896
+#define dA06                          	960
+#define dA05                          	1024
+#define dA04                          	1088
+#define dA03                          	1152
+#define dA02                          	1216
+#define dA01                          	1280
+#define dA00                          	1344
+#define dSIGN_MASK                    	1408
+#define iCHK_WORK_SUB                 	1472
+#define iCHK_WORK_CMP                 	1536
+#define dABS_MASK                     	1600
+#define dZERO                         	1664
+
+#include <sysdep.h>
+
+        .text
+	.section .text.evex512,"ax",@progbits
+ENTRY(_ZGVeN8vv_atan2_skx)
+        pushq     %rbp
+        cfi_def_cfa_offset(16)
+        movq      %rsp, %rbp
+        cfi_def_cfa(6, 16)
+        cfi_offset(6, -16)
+        andq      $-64, %rsp
+        subq      $256, %rsp
+        xorl      %edx, %edx
+
+/*
+ * #define NO_VECTOR_ZERO_ATAN2_ARGS
+ *  Declarations
+ * Variables
+ * Constants
+ *  The end of declarations
+ *  Implementation
+ * Get r0~=1/B
+ * Cannot be replaced by VQRCP(D, dR0, dB);
+ * Argument Absolute values
+ */
+        vmovups   dABS_MASK+__svml_datan2_data_internal(%rip), %zmm4
+
+/* Argument signs */
+        vmovups   dSIGN_MASK+__svml_datan2_data_internal(%rip), %zmm6
+
+/*
+ * 1) If y<x then a= y, b=x, PIO2=0
+ * 2) If y>x then a=-x, b=y, PIO2=Pi/2
+ */
+        vmovups   dPIO2+__svml_datan2_data_internal(%rip), %zmm3
+        vandpd    %zmm4, %zmm0, %zmm11
+        vmovaps   %zmm1, %zmm7
+        vandpd    %zmm4, %zmm7, %zmm2
+        vandpd    %zmm6, %zmm7, %zmm5
+        vandpd    %zmm6, %zmm0, %zmm4
+        vorpd     %zmm6, %zmm2, %zmm12
+        vcmppd    $17, {sae}, %zmm2, %zmm11, %k1
+        vmovdqu   iCHK_WORK_CMP+__svml_datan2_data_internal(%rip), %ymm6
+        vmovups   %zmm11, 64(%rsp)
+
+/* Check if y and x are on main path. */
+        vpsrlq    $32, %zmm2, %zmm9
+        vblendmpd %zmm11, %zmm12, %zmm13{%k1}
+        vblendmpd %zmm2, %zmm11, %zmm15{%k1}
+        vpsrlq    $32, %zmm11, %zmm8
+        vmovdqu   iCHK_WORK_SUB+__svml_datan2_data_internal(%rip), %ymm12
+        vdivpd    {rn-sae}, %zmm15, %zmm13, %zmm1
+        vmovups   %zmm15, (%rsp)
+        vpmovqd   %zmm9, %ymm14
+        vpmovqd   %zmm8, %ymm10
+        vxorpd    %zmm3, %zmm3, %zmm3{%k1}
+        vpsubd    %ymm12, %ymm14, %ymm13
+        vpsubd    %ymm12, %ymm10, %ymm9
+
+/* Polynomial. */
+        vmulpd    {rn-sae}, %zmm1, %zmm1, %zmm12
+        vpcmpgtd  %ymm6, %ymm13, %ymm15
+        vpcmpeqd  %ymm6, %ymm13, %ymm11
+        vmulpd    {rn-sae}, %zmm12, %zmm12, %zmm13
+        vpor      %ymm11, %ymm15, %ymm8
+        vmovups   dA19+__svml_datan2_data_internal(%rip), %zmm11
+        vmovups   dA15+__svml_datan2_data_internal(%rip), %zmm15
+        vpcmpgtd  %ymm6, %ymm9, %ymm14
+        vpcmpeqd  %ymm6, %ymm9, %ymm6
+        vpor      %ymm6, %ymm14, %ymm10
+        vmulpd    {rn-sae}, %zmm13, %zmm13, %zmm14
+        vmovups   dA18+__svml_datan2_data_internal(%rip), %zmm9
+        vpor      %ymm10, %ymm8, %ymm6
+        vmovups   dA17+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd231pd {rn-sae}, %zmm14, %zmm11, %zmm15
+        vmovups   dA14+__svml_datan2_data_internal(%rip), %zmm11
+        vmovups   dA12+__svml_datan2_data_internal(%rip), %zmm8
+        vfmadd231pd {rn-sae}, %zmm14, %zmm9, %zmm11
+        vmovups   dA13+__svml_datan2_data_internal(%rip), %zmm9
+        vfmadd231pd {rn-sae}, %zmm14, %zmm10, %zmm9
+        vmovups   dA16+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd231pd {rn-sae}, %zmm14, %zmm10, %zmm8
+        vmovups   dA11+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd213pd {rn-sae}, %zmm10, %zmm14, %zmm15
+        vmovups   dA10+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd213pd {rn-sae}, %zmm10, %zmm14, %zmm11
+        vmovups   dA09+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd213pd {rn-sae}, %zmm10, %zmm14, %zmm9
+        vmovups   dA08+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd213pd {rn-sae}, %zmm10, %zmm14, %zmm8
+        vmovups   dA07+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd213pd {rn-sae}, %zmm10, %zmm14, %zmm15
+        vmovups   dA06+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd213pd {rn-sae}, %zmm10, %zmm14, %zmm11
+        vmovups   dA05+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd213pd {rn-sae}, %zmm10, %zmm14, %zmm9
+        vmovups   dA04+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd213pd {rn-sae}, %zmm10, %zmm14, %zmm8
+        vmovups   dA03+__svml_datan2_data_internal(%rip), %zmm10
+
+/* A00=1.0, account for it later  VQFMA(D, dP4, dP4, dR8, dA00); */
+        vmulpd    {rn-sae}, %zmm14, %zmm8, %zmm8
+        vfmadd213pd {rn-sae}, %zmm10, %zmm14, %zmm15
+        vmovups   dA02+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd213pd {rn-sae}, %zmm10, %zmm14, %zmm11
+        vmovups   dA01+__svml_datan2_data_internal(%rip), %zmm10
+        vfmadd213pd {rn-sae}, %zmm11, %zmm12, %zmm15
+        vfmadd213pd {rn-sae}, %zmm10, %zmm14, %zmm9
+        vfmadd213pd {rn-sae}, %zmm8, %zmm12, %zmm9
+        vmovups   __svml_datan2_data_internal(%rip), %zmm8
+        vfmadd213pd {rn-sae}, %zmm9, %zmm13, %zmm15
+
+/*
+ * Reconstruction.
+ * dP=(R+R*dP) + dPIO2
+ */
+        vfmadd213pd {rn-sae}, %zmm1, %zmm1, %zmm15
+        vaddpd    {rn-sae}, %zmm3, %zmm15, %zmm1
+        vorpd     %zmm5, %zmm1, %zmm9
+
+/* if x<0, dPI = Pi, else dPI =0 */
+        vmovups   dZERO+__svml_datan2_data_internal(%rip), %zmm1
+        vcmppd    $18, {sae}, %zmm1, %zmm7, %k2
+        vaddpd    {rn-sae}, %zmm8, %zmm9, %zmm9{%k2}
+        vmovmskps %ymm6, %eax
+        vorpd     %zmm4, %zmm9, %zmm11
+
+/*  Special branch for fast (vector) processing of zero arguments  */
+        vmovups   64(%rsp), %zmm9
+        testl     %eax, %eax
+
+/* Go to auxilary branch */
+        jne       L(AUX_BRANCH)
+                                # LOE rbx r12 r13 r14 r15 edx ymm6 zmm0 zmm2 zmm3 zmm4 zmm5 zmm7 zmm9 zmm11
+
+/* Return from auxilary branch
+ * for out of main path inputs
+ */
+
+L(AUX_BRANCH_RETURN):
+/*
+ *  Special branch for fast (vector) processing of zero arguments
+ *  The end of implementation
+ */
+        testl     %edx, %edx
+
+/* Go to special inputs processing branch */
+        jne       L(SPECIAL_VALUES_BRANCH)
+                                # LOE rbx r12 r13 r14 r15 edx zmm0 zmm7 zmm11
+
+/* Restore registers
+ * and exit the function
+ */
+
+L(EXIT):
+        vmovaps   %zmm11, %zmm0
+        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   %zmm0, 64(%rsp)
+        vmovups   %zmm7, 128(%rsp)
+        vmovups   %zmm11, 192(%rsp)
+                                # LOE rbx r12 r13 r14 r15 edx zmm11
+
+        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: -240; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x10, 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: -248; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x08, 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: -256; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x00, 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   192(%rsp), %zmm11
+
+/* 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: -240; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x10, 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: -248; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x08, 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: -256; DW_OP_plus)  */
+        .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x00, 0xff, 0xff, 0xff, 0x22
+                                # LOE rbx r12 r13 r14 r15 zmm11
+
+/* Scalar math fucntion call
+ * to process special input
+ */
+
+L(SCALAR_MATH_CALL):
+        movl      %r12d, %r14d
+        movsd     64(%rsp,%r14,8), %xmm0
+        movsd     128(%rsp,%r14,8), %xmm1
+        call      atan2@PLT
+                                # LOE rbx r14 r15 r12d r13d xmm0
+
+        movsd     %xmm0, 192(%rsp,%r14,8)
+
+/* Process special inputs in loop */
+        jmp       L(SPECIAL_VALUES_LOOP)
+        cfi_restore(12)
+        cfi_restore(13)
+        cfi_restore(14)
+                                # LOE rbx r15 r12d r13d
+
+/* Auxilary branch
+ * for out of main path inputs
+ */
+
+L(AUX_BRANCH):
+/* Check if at least on of Y or Y is zero: iAXAYZERO */
+        vmovups   dZERO+__svml_datan2_data_internal(%rip), %zmm8
+
+/* Check if both X & Y are not NaNs:  iXYnotNAN */
+        vcmppd    $3, {sae}, %zmm7, %zmm7, %k1
+        vcmppd    $3, {sae}, %zmm0, %zmm0, %k2
+        vcmppd    $4, {sae}, %zmm8, %zmm2, %k3
+        vcmppd    $4, {sae}, %zmm8, %zmm9, %k4
+
+/* Res = sign(Y)*(X<0)?(PIO2+PI):PIO2 */
+        vpcmpgtq  %zmm7, %zmm8, %k6
+        vpternlogd $0xff, %zmm1, %zmm1, %zmm10
+        vmovaps   %zmm10, %zmm15
+        vmovaps   %zmm10, %zmm12
+        vmovaps   %zmm10, %zmm13
+        vpandnq   %zmm2, %zmm2, %zmm15{%k3}
+        vmovaps   %zmm10, %zmm2
+        vpandnq   %zmm7, %zmm7, %zmm12{%k1}
+        vpandnq   %zmm0, %zmm0, %zmm13{%k2}
+        vpandnq   %zmm9, %zmm9, %zmm2{%k4}
+        vandpd    %zmm13, %zmm12, %zmm14
+        vorpd     %zmm2, %zmm15, %zmm9
+        vpsrlq    $32, %zmm14, %zmm1
+        vpsrlq    $32, %zmm9, %zmm2
+        vpmovqd   %zmm1, %ymm1
+        vpmovqd   %zmm2, %ymm9
+
+/* Check if at least on of Y or Y is zero and not NaN: iAXAYZEROnotNAN */
+        vpand     %ymm1, %ymm9, %ymm2
+
+/*
+ *  Path for zero arguments (at least one of both)
+ * Check if both args are zeros (den. is zero)
+ */
+        vmovups   (%rsp), %zmm1
+
+/* Exclude from previous callout mask zero (and not NaN) arguments */
+        vpandn    %ymm6, %ymm2, %ymm6
+        vcmppd    $4, {sae}, %zmm8, %zmm1, %k5
+
+/* Go to callout */
+        vmovmskps %ymm6, %edx
+        vpandnq   %zmm1, %zmm1, %zmm10{%k5}
+
+/* Set sPIO2 to zero if den. is zero */
+        vpandnq   %zmm3, %zmm10, %zmm3
+        vpandq    %zmm10, %zmm8, %zmm1
+        vporq     %zmm1, %zmm3, %zmm3
+        vorpd     %zmm5, %zmm3, %zmm1
+        vmovups   __svml_datan2_data_internal(%rip), %zmm5
+        vaddpd    {rn-sae}, %zmm5, %zmm1, %zmm1{%k6}
+        vorpd     %zmm4, %zmm1, %zmm1
+
+/* Merge results from main and spec path */
+        vpmovzxdq %ymm2, %zmm4
+        vpsllq    $32, %zmm4, %zmm2
+        vpord     %zmm2, %zmm4, %zmm3
+        vpandnq   %zmm11, %zmm3, %zmm11
+        vpandq    %zmm3, %zmm1, %zmm1
+        vporq     %zmm1, %zmm11, %zmm11
+
+/* Return to main vector processing path */
+        jmp       L(AUX_BRANCH_RETURN)
+                                # LOE rbx r12 r13 r14 r15 edx zmm0 zmm7 zmm11
+END(_ZGVeN8vv_atan2_skx)
+
+        .section .rodata, "a"
+        .align 64
+
+#ifdef __svml_datan2_data_internal_typedef
+typedef unsigned int VUINT32;
+typedef struct {
+        __declspec(align(64)) VUINT32 dPI[8][2];
+        __declspec(align(64)) VUINT32 dPIO2[8][2];
+        __declspec(align(64)) VUINT32 dA19[8][2];
+        __declspec(align(64)) VUINT32 dA18[8][2];
+        __declspec(align(64)) VUINT32 dA17[8][2];
+        __declspec(align(64)) VUINT32 dA16[8][2];
+        __declspec(align(64)) VUINT32 dA15[8][2];
+        __declspec(align(64)) VUINT32 dA14[8][2];
+        __declspec(align(64)) VUINT32 dA13[8][2];
+        __declspec(align(64)) VUINT32 dA12[8][2];
+        __declspec(align(64)) VUINT32 dA11[8][2];
+        __declspec(align(64)) VUINT32 dA10[8][2];
+        __declspec(align(64)) VUINT32 dA09[8][2];
+        __declspec(align(64)) VUINT32 dA08[8][2];
+        __declspec(align(64)) VUINT32 dA07[8][2];
+        __declspec(align(64)) VUINT32 dA06[8][2];
+        __declspec(align(64)) VUINT32 dA05[8][2];
+        __declspec(align(64)) VUINT32 dA04[8][2];
+        __declspec(align(64)) VUINT32 dA03[8][2];
+        __declspec(align(64)) VUINT32 dA02[8][2];
+        __declspec(align(64)) VUINT32 dA01[8][2];
+        __declspec(align(64)) VUINT32 dA00[8][2];
+        __declspec(align(64)) VUINT32 dSIGN_MASK[8][2];
+        __declspec(align(64)) VUINT32 iCHK_WORK_SUB[16][1];
+        __declspec(align(64)) VUINT32 iCHK_WORK_CMP[16][1];
+        __declspec(align(64)) VUINT32 dABS_MASK[8][2];
+        __declspec(align(64)) VUINT32 dZERO[8][2];
+} __svml_datan2_data_internal;
+#endif
+__svml_datan2_data_internal:
+        .quad 0x400921FB54442D18, 0x400921FB54442D18, 0x400921FB54442D18, 0x400921FB54442D18, 0x400921FB54442D18, 0x400921FB54442D18, 0x400921FB54442D18, 0x400921FB54442D18 //dPI
+        .align 64
+        .quad 0x3FF921FB54442D18, 0x3FF921FB54442D18, 0x3FF921FB54442D18, 0x3FF921FB54442D18, 0x3FF921FB54442D18, 0x3FF921FB54442D18, 0x3FF921FB54442D18, 0x3FF921FB54442D18 //dPIO2
+        .align 64
+        .quad 0xBEF4FDB537ABC7A3, 0xBEF4FDB537ABC7A3, 0xBEF4FDB537ABC7A3, 0xBEF4FDB537ABC7A3, 0xBEF4FDB537ABC7A3, 0xBEF4FDB537ABC7A3, 0xBEF4FDB537ABC7A3, 0xBEF4FDB537ABC7A3 // dA19
+        .align 64
+        .quad 0x3F2CED0A36665209, 0x3F2CED0A36665209, 0x3F2CED0A36665209, 0x3F2CED0A36665209, 0x3F2CED0A36665209, 0x3F2CED0A36665209, 0x3F2CED0A36665209, 0x3F2CED0A36665209 // dA18
+        .align 64
+        .quad 0xBF52E67C93954C23, 0xBF52E67C93954C23, 0xBF52E67C93954C23, 0xBF52E67C93954C23, 0xBF52E67C93954C23, 0xBF52E67C93954C23, 0xBF52E67C93954C23, 0xBF52E67C93954C23 // dA17
+        .align 64
+        .quad 0x3F6F5A1DAE82AFB3, 0x3F6F5A1DAE82AFB3, 0x3F6F5A1DAE82AFB3, 0x3F6F5A1DAE82AFB3, 0x3F6F5A1DAE82AFB3, 0x3F6F5A1DAE82AFB3, 0x3F6F5A1DAE82AFB3, 0x3F6F5A1DAE82AFB3 // dA16
+        .align 64
+        .quad 0xBF82B2EC618E4BAD, 0xBF82B2EC618E4BAD, 0xBF82B2EC618E4BAD, 0xBF82B2EC618E4BAD, 0xBF82B2EC618E4BAD, 0xBF82B2EC618E4BAD, 0xBF82B2EC618E4BAD, 0xBF82B2EC618E4BAD // dA15
+        .align 64
+        .quad 0x3F914F4C661116A5, 0x3F914F4C661116A5, 0x3F914F4C661116A5, 0x3F914F4C661116A5, 0x3F914F4C661116A5, 0x3F914F4C661116A5, 0x3F914F4C661116A5, 0x3F914F4C661116A5 // dA14
+        .align 64
+        .quad 0xBF9A5E83B081F69C, 0xBF9A5E83B081F69C, 0xBF9A5E83B081F69C, 0xBF9A5E83B081F69C, 0xBF9A5E83B081F69C, 0xBF9A5E83B081F69C, 0xBF9A5E83B081F69C, 0xBF9A5E83B081F69C // dA13
+        .align 64
+        .quad 0x3FA169980CB6AD4F, 0x3FA169980CB6AD4F, 0x3FA169980CB6AD4F, 0x3FA169980CB6AD4F, 0x3FA169980CB6AD4F, 0x3FA169980CB6AD4F, 0x3FA169980CB6AD4F, 0x3FA169980CB6AD4F // dA12
+        .align 64
+        .quad 0xBFA4EFA2E563C1BC, 0xBFA4EFA2E563C1BC, 0xBFA4EFA2E563C1BC, 0xBFA4EFA2E563C1BC, 0xBFA4EFA2E563C1BC, 0xBFA4EFA2E563C1BC, 0xBFA4EFA2E563C1BC, 0xBFA4EFA2E563C1BC // dA11
+        .align 64
+        .quad 0x3FA7EC0FBC50683B, 0x3FA7EC0FBC50683B, 0x3FA7EC0FBC50683B, 0x3FA7EC0FBC50683B, 0x3FA7EC0FBC50683B, 0x3FA7EC0FBC50683B, 0x3FA7EC0FBC50683B, 0x3FA7EC0FBC50683B // dA10
+        .align 64
+        .quad 0xBFAAD261EAA09954, 0xBFAAD261EAA09954, 0xBFAAD261EAA09954, 0xBFAAD261EAA09954, 0xBFAAD261EAA09954, 0xBFAAD261EAA09954, 0xBFAAD261EAA09954, 0xBFAAD261EAA09954 // dA09
+        .align 64
+        .quad 0x3FAE1749BD612DCF, 0x3FAE1749BD612DCF, 0x3FAE1749BD612DCF, 0x3FAE1749BD612DCF, 0x3FAE1749BD612DCF, 0x3FAE1749BD612DCF, 0x3FAE1749BD612DCF, 0x3FAE1749BD612DCF // dA08
+        .align 64
+        .quad 0xBFB11084009435E0, 0xBFB11084009435E0, 0xBFB11084009435E0, 0xBFB11084009435E0, 0xBFB11084009435E0, 0xBFB11084009435E0, 0xBFB11084009435E0, 0xBFB11084009435E0 // dA07
+        .align 64
+        .quad 0x3FB3B12A49295651, 0x3FB3B12A49295651, 0x3FB3B12A49295651, 0x3FB3B12A49295651, 0x3FB3B12A49295651, 0x3FB3B12A49295651, 0x3FB3B12A49295651, 0x3FB3B12A49295651 // dA06
+        .align 64
+        .quad 0xBFB745D009BADA94, 0xBFB745D009BADA94, 0xBFB745D009BADA94, 0xBFB745D009BADA94, 0xBFB745D009BADA94, 0xBFB745D009BADA94, 0xBFB745D009BADA94, 0xBFB745D009BADA94 // dA05
+        .align 64
+        .quad 0x3FBC71C707F7D5B5, 0x3FBC71C707F7D5B5, 0x3FBC71C707F7D5B5, 0x3FBC71C707F7D5B5, 0x3FBC71C707F7D5B5, 0x3FBC71C707F7D5B5, 0x3FBC71C707F7D5B5, 0x3FBC71C707F7D5B5 // dA04
+        .align 64
+        .quad 0xBFC2492491EE55C7, 0xBFC2492491EE55C7, 0xBFC2492491EE55C7, 0xBFC2492491EE55C7, 0xBFC2492491EE55C7, 0xBFC2492491EE55C7, 0xBFC2492491EE55C7, 0xBFC2492491EE55C7 // dA03
+        .align 64
+        .quad 0x3FC999999997EE34, 0x3FC999999997EE34, 0x3FC999999997EE34, 0x3FC999999997EE34, 0x3FC999999997EE34, 0x3FC999999997EE34, 0x3FC999999997EE34, 0x3FC999999997EE34 // dA02
+        .align 64
+        .quad 0xBFD55555555553C5, 0xBFD55555555553C5, 0xBFD55555555553C5, 0xBFD55555555553C5, 0xBFD55555555553C5, 0xBFD55555555553C5, 0xBFD55555555553C5, 0xBFD55555555553C5 // dA01
+        .align 64
+        .quad 0x3FF0000000000000, 0x3FF0000000000000, 0x3FF0000000000000, 0x3FF0000000000000, 0x3FF0000000000000, 0x3FF0000000000000, 0x3FF0000000000000, 0x3FF0000000000000 // dA00
+        .align 64
+        .quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000 //dSIGN_MASK
+        .align 64
+        .long 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000, 0x80300000 //iCHK_WORK_SUB
+        .align 64
+        .long 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000, 0xfdd00000 //iCHK_WORK_CMP
+        .align 64
+        .quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff //dABS_MASK
+        .align 64
+        .quad 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000 //dZERO
+        .align 64
+        .type	__svml_datan2_data_internal,@object
+        .size	__svml_datan2_data_internal,.-__svml_datan2_data_internal