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, 399 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_atan2f16_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_s_atan2f16_core_avx512.S
new file mode 100644
index 0000000000..f3477cc8e6
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atan2f16_core_avx512.S
@@ -0,0 +1,399 @@
+/* Function atan2f 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_satan2_data_internal
+ */
+#define sZERO                         	0
+#define sONE                          	64
+#define sSIGN_MASK                    	128
+#define sABS_MASK                     	192
+#define sPIO2                         	256
+#define sPI                           	320
+#define sPC8                          	384
+#define sPC7                          	448
+#define sPC6                          	512
+#define sPC5                          	576
+#define sPC4                          	640
+#define sPC3                          	704
+#define sPC2                          	768
+#define sPC1                          	832
+#define sPC0                          	896
+#define iCHK_WORK_SUB                 	960
+#define iCHK_WORK_CMP                 	1024
+
+#include <sysdep.h>
+
+        .text
+	.section .text.exex512,"ax",@progbits
+ENTRY(_ZGVeN16vv_atan2f_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
+ * Arguments signs
+ */
+        vmovups   sABS_MASK+__svml_satan2_data_internal(%rip), %zmm6
+        vmovups   sONE+__svml_satan2_data_internal(%rip), %zmm3
+
+/* Testing on working interval. */
+        vmovups   iCHK_WORK_SUB+__svml_satan2_data_internal(%rip), %zmm9
+        vmovups   iCHK_WORK_CMP+__svml_satan2_data_internal(%rip), %zmm14
+
+/*
+ * 1) If y<x then a= y, b=x, PIO2=0
+ * 2) If y>x then a=-x, b=y, PIO2=Pi/2
+ */
+        vmovups   sPIO2+__svml_satan2_data_internal(%rip), %zmm4
+        vpternlogd $255, %zmm13, %zmm13, %zmm13
+        vmovaps   %zmm1, %zmm8
+        vandps    %zmm6, %zmm8, %zmm2
+        vandps    %zmm6, %zmm0, %zmm1
+        vorps     sSIGN_MASK+__svml_satan2_data_internal(%rip), %zmm2, %zmm5
+        vpsubd    %zmm9, %zmm2, %zmm10
+        vpsubd    %zmm9, %zmm1, %zmm12
+        vxorps    %zmm2, %zmm8, %zmm7
+        vxorps    %zmm1, %zmm0, %zmm6
+        vcmpps    $17, {sae}, %zmm2, %zmm1, %k1
+        vpcmpgtd  %zmm10, %zmm14, %k2
+        vpcmpgtd  %zmm12, %zmm14, %k3
+        vmovups   sPC6+__svml_satan2_data_internal(%rip), %zmm14
+        vblendmps %zmm1, %zmm5, %zmm11{%k1}
+        vblendmps %zmm2, %zmm1, %zmm5{%k1}
+        vxorps    %zmm4, %zmm4, %zmm4{%k1}
+
+/*
+ * Division a/b.
+ * Enabled when FMA is available and
+ * performance is better with NR iteration
+ */
+        vrcp14ps  %zmm5, %zmm15
+        vfnmadd231ps {rn-sae}, %zmm5, %zmm15, %zmm3
+        vfmadd213ps {rn-sae}, %zmm15, %zmm3, %zmm15
+        vmulps    {rn-sae}, %zmm15, %zmm11, %zmm3
+        vfnmadd231ps {rn-sae}, %zmm5, %zmm3, %zmm11
+        vfmadd213ps {rn-sae}, %zmm3, %zmm11, %zmm15
+        vmovups   sPC8+__svml_satan2_data_internal(%rip), %zmm11
+        vpternlogd $255, %zmm3, %zmm3, %zmm3
+
+/* Polynomial. */
+        vmulps    {rn-sae}, %zmm15, %zmm15, %zmm9
+        vpandnd   %zmm10, %zmm10, %zmm13{%k2}
+        vmulps    {rn-sae}, %zmm9, %zmm9, %zmm10
+        vfmadd231ps {rn-sae}, %zmm10, %zmm11, %zmm14
+        vmovups   sPC5+__svml_satan2_data_internal(%rip), %zmm11
+        vpandnd   %zmm12, %zmm12, %zmm3{%k3}
+        vpord     %zmm3, %zmm13, %zmm3
+        vmovups   sPC4+__svml_satan2_data_internal(%rip), %zmm13
+        vmovups   sPC7+__svml_satan2_data_internal(%rip), %zmm12
+        vptestmd  %zmm3, %zmm3, %k0
+        vfmadd213ps {rn-sae}, %zmm13, %zmm10, %zmm14
+        vfmadd231ps {rn-sae}, %zmm10, %zmm12, %zmm11
+        vmovups   sPC3+__svml_satan2_data_internal(%rip), %zmm12
+        vmovups   sPC2+__svml_satan2_data_internal(%rip), %zmm13
+
+/*  Special branch for fast (vector) processing of zero arguments  */
+        kortestw  %k0, %k0
+        vfmadd213ps {rn-sae}, %zmm12, %zmm10, %zmm11
+        vmovups   sPC1+__svml_satan2_data_internal(%rip), %zmm12
+        vfmadd213ps {rn-sae}, %zmm13, %zmm10, %zmm14
+        vmovups   sPC0+__svml_satan2_data_internal(%rip), %zmm13
+        vfmadd213ps {rn-sae}, %zmm12, %zmm10, %zmm11
+        vfmadd213ps {rn-sae}, %zmm13, %zmm10, %zmm14
+        vfmadd213ps {rn-sae}, %zmm14, %zmm9, %zmm11
+
+/* Reconstruction. */
+        vfmadd213ps {rn-sae}, %zmm4, %zmm15, %zmm11
+
+/* if x<0, sPI = Pi, else sPI =0 */
+        vmovups   __svml_satan2_data_internal(%rip), %zmm15
+        vorps     %zmm7, %zmm11, %zmm9
+        vcmpps    $18, {sae}, %zmm15, %zmm8, %k4
+        vmovups   sPI+__svml_satan2_data_internal(%rip), %zmm11
+        vaddps    {rn-sae}, %zmm11, %zmm9, %zmm9{%k4}
+        vorps     %zmm6, %zmm9, %zmm10
+
+/* Go to auxilary branch */
+        jne       L(AUX_BRANCH)
+                                # LOE rbx r12 r13 r14 r15 edx zmm0 zmm1 zmm2 zmm3 zmm4 zmm5 zmm6 zmm7 zmm8 zmm10 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 zmm8 zmm10
+
+/* Restore registers
+ * and exit the function
+ */
+
+L(EXIT):
+        vmovaps   %zmm10, %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   %zmm8, 128(%rsp)
+        vmovups   %zmm10, 192(%rsp)
+                                # LOE rbx r12 r13 r14 r15 edx zmm10
+
+        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      $16, %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), %zmm10
+
+/* 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 zmm10
+
+/* Scalar math fucntion call
+ * to process special input
+ */
+
+L(SCALAR_MATH_CALL):
+        movl      %r12d, %r14d
+        movss     64(%rsp,%r14,4), %xmm0
+        movss     128(%rsp,%r14,4), %xmm1
+        call      atan2f@PLT
+                                # LOE rbx r14 r15 r12d r13d xmm0
+
+        movss     %xmm0, 192(%rsp,%r14,4)
+
+/* 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   __svml_satan2_data_internal(%rip), %zmm9
+
+/* Check if both X & Y are not NaNs:  iXYnotNAN */
+        vcmpps    $3, {sae}, %zmm8, %zmm8, %k1
+        vcmpps    $3, {sae}, %zmm0, %zmm0, %k2
+        vpcmpd    $4, %zmm9, %zmm2, %k3
+        vpcmpd    $4, %zmm9, %zmm1, %k4
+
+/*
+ *  Path for zero arguments (at least one of both)
+ * Check if both args are zeros (den. is zero)
+ */
+        vcmpps    $4, {sae}, %zmm9, %zmm5, %k5
+
+/* Res = sign(Y)*(X<0)?(PIO2+PI):PIO2 */
+        vpcmpgtd  %zmm8, %zmm9, %k6
+        vpternlogd $255, %zmm14, %zmm14, %zmm14
+        vpternlogd $255, %zmm12, %zmm12, %zmm12
+        vpternlogd $255, %zmm13, %zmm13, %zmm13
+        vpandnd   %zmm2, %zmm2, %zmm14{%k3}
+        vpternlogd $255, %zmm2, %zmm2, %zmm2
+        vpandnd   %zmm1, %zmm1, %zmm2{%k4}
+        vpord     %zmm2, %zmm14, %zmm15
+        vpternlogd $255, %zmm2, %zmm2, %zmm2
+        vpandnd   %zmm5, %zmm5, %zmm2{%k5}
+
+/* Set sPIO2 to zero if den. is zero */
+        vpandnd   %zmm4, %zmm2, %zmm4
+        vpandd    %zmm2, %zmm9, %zmm5
+        vpord     %zmm5, %zmm4, %zmm2
+        vorps     %zmm7, %zmm2, %zmm7
+        vaddps    {rn-sae}, %zmm11, %zmm7, %zmm7{%k6}
+        vorps     %zmm6, %zmm7, %zmm6
+        vpandnd   %zmm8, %zmm8, %zmm12{%k1}
+        vpandnd   %zmm0, %zmm0, %zmm13{%k2}
+        vandps    %zmm13, %zmm12, %zmm12
+
+/* Check if at least on of Y or Y is zero and not NaN: iAXAYZEROnotNAN */
+        vpandd    %zmm12, %zmm15, %zmm1
+
+/* Exclude from previous callout mask zero (and not NaN) arguments */
+        vpandnd   %zmm3, %zmm1, %zmm3
+
+/* Go to callout */
+        vptestmd  %zmm3, %zmm3, %k0
+        kmovw     %k0, %edx
+
+/* Merge results from main and spec path */
+        vpandnd   %zmm10, %zmm1, %zmm10
+        vpandd    %zmm1, %zmm6, %zmm11
+        vpord     %zmm11, %zmm10, %zmm10
+
+/* Return to main vector processing path */
+        jmp       L(AUX_BRANCH_RETURN)
+                                # LOE rbx r12 r13 r14 r15 edx zmm0 zmm8 zmm10
+END(_ZGVeN16vv_atan2f_skx)
+
+        .section .rodata, "a"
+        .align 64
+
+#ifdef __svml_satan2_data_internal_typedef
+typedef unsigned int VUINT32;
+typedef struct {
+        __declspec(align(64)) VUINT32 sZERO[16][1];
+        __declspec(align(64)) VUINT32 sONE[16][1];
+        __declspec(align(64)) VUINT32 sSIGN_MASK[16][1];
+        __declspec(align(64)) VUINT32 sABS_MASK[16][1];
+        __declspec(align(64)) VUINT32 sPIO2[16][1];
+        __declspec(align(64)) VUINT32 sPI[16][1];
+        __declspec(align(64)) VUINT32 sPC8[16][1];
+        __declspec(align(64)) VUINT32 sPC7[16][1];
+        __declspec(align(64)) VUINT32 sPC6[16][1];
+        __declspec(align(64)) VUINT32 sPC5[16][1];
+        __declspec(align(64)) VUINT32 sPC4[16][1];
+        __declspec(align(64)) VUINT32 sPC3[16][1];
+        __declspec(align(64)) VUINT32 sPC2[16][1];
+        __declspec(align(64)) VUINT32 sPC1[16][1];
+        __declspec(align(64)) VUINT32 sPC0[16][1];
+        __declspec(align(64)) VUINT32 iCHK_WORK_SUB[16][1];
+        __declspec(align(64)) VUINT32 iCHK_WORK_CMP[16][1];
+} __svml_satan2_data_internal;
+#endif
+__svml_satan2_data_internal:
+        .long 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000 // sZERO
+        .align 64
+        .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 // sONE
+        .align 64
+        .long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000 // sSIGN_MASK
+        .align 64
+        .long 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF // sABS_MASK
+        .align 64
+        .long 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB // sPIO2
+        .align 64
+        .long 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB, 0x40490FDB // sPI
+        .align 64
+        .long 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0 // sA08
+        .align 64
+        .long 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631 // sA07
+        .align 64
+        .long 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384 // sA06
+        .align 64
+        .long 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629 // sA05
+        .align 64
+        .long 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474 // sA04
+        .align 64
+        .long 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8 // sA03
+        .align 64
+        .long 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F // sA02
+        .align 64
+        .long 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49 // sA01
+        .align 64
+        .long 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000, 0x3F800000 // sA00
+        .align 64
+        .long 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000, 0x81000000 //iCHK_WORK_SUB
+        .align 64
+        .long 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000, 0xFC000000 //iCHK_WORK_CMP
+        .align 64
+        .type	__svml_satan2_data_internal,@object
+        .size	__svml_satan2_data_internal,.-__svml_satan2_data_internal