x86-64: Add vector atan/atanf implementation to libmvec

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

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

1 files changed, 148 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_atanf8_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_s_atanf8_core_avx2.S
new file mode 100644
index 0000000000..e333f979c4
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_atanf8_core_avx2.S
@@ -0,0 +1,148 @@
+/* Function atanf vectorized with AVX2.
+   Copyright (C) 2021 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   https://www.gnu.org/licenses/.  */
+
+/*
+ * ALGORITHM DESCRIPTION:
+ *
+ *      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_satan_data_internal
+ */
+#define _sSIGN_MASK                   	0
+#define _sABS_MASK                    	32
+#define _sONE                         	64
+#define _sPIO2                        	96
+#define _sPC8                         	128
+#define _sPC7                         	160
+#define _sPC6                         	192
+#define _sPC5                         	224
+#define _sPC4                         	256
+#define _sPC3                         	288
+#define _sPC2                         	320
+#define _sPC1                         	352
+#define _sPC0                         	384
+
+#include <sysdep.h>
+
+        .text
+	.section .text.avx2,"ax",@progbits
+ENTRY(_ZGVdN8v_atanf_avx2)
+/*
+ * 1) If x>1,      then r=-1/x, PIO2=Pi/2
+ * 2) If -1<=x<=1, then r=x,    PIO2=0
+ * 3) If x<-1,     then r=-1/x, PIO2=-Pi/2
+ */
+        vmovups   _sONE+__svml_satan_data_internal(%rip), %ymm2
+        vmovups   __svml_satan_data_internal(%rip), %ymm7
+        vmovups   _sPC7+__svml_satan_data_internal(%rip), %ymm13
+
+/*
+ * To use minps\maxps operations for argument reduction
+ * uncomment _AT_USEMINMAX_ definition
+ *  Declarations
+ * Variables
+ * Constants
+ */
+        vandps    _sABS_MASK+__svml_satan_data_internal(%rip), %ymm0, %ymm3
+        vmaxps    %ymm3, %ymm2, %ymm5
+        vminps    %ymm3, %ymm2, %ymm4
+        vcmple_oqps %ymm2, %ymm3, %ymm6
+        vdivps    %ymm5, %ymm4, %ymm11
+        vandps    %ymm7, %ymm0, %ymm9
+        vandnps   %ymm7, %ymm6, %ymm8
+        vxorps    %ymm9, %ymm8, %ymm10
+        vxorps    %ymm11, %ymm10, %ymm15
+
+/* Polynomial. */
+        vmulps    %ymm15, %ymm15, %ymm14
+        vmovups   _sPC8+__svml_satan_data_internal(%rip), %ymm0
+        vmulps    %ymm14, %ymm14, %ymm12
+        vfmadd213ps _sPC6+__svml_satan_data_internal(%rip), %ymm12, %ymm0
+        vfmadd213ps _sPC5+__svml_satan_data_internal(%rip), %ymm12, %ymm13
+        vfmadd213ps _sPC4+__svml_satan_data_internal(%rip), %ymm12, %ymm0
+        vfmadd213ps _sPC3+__svml_satan_data_internal(%rip), %ymm12, %ymm13
+        vfmadd213ps _sPC2+__svml_satan_data_internal(%rip), %ymm12, %ymm0
+        vfmadd213ps _sPC1+__svml_satan_data_internal(%rip), %ymm12, %ymm13
+        vfmadd213ps %ymm13, %ymm14, %ymm0
+        vfmadd213ps _sPC0+__svml_satan_data_internal(%rip), %ymm14, %ymm0
+        vandnps   _sPIO2+__svml_satan_data_internal(%rip), %ymm6, %ymm1
+        vxorps    %ymm9, %ymm1, %ymm1
+
+/* Reconstruction. */
+        vfmadd213ps %ymm1, %ymm15, %ymm0
+        ret
+
+END(_ZGVdN8v_atanf_avx2)
+
+        .section .rodata, "a"
+        .align 32
+
+#ifdef __svml_satan_data_internal_typedef
+typedef unsigned int VUINT32;
+typedef struct {
+        __declspec(align(32)) VUINT32 _sSIGN_MASK[8][1];
+        __declspec(align(32)) VUINT32 _sABS_MASK[8][1];
+        __declspec(align(32)) VUINT32 _sONE[8][1];
+        __declspec(align(32)) VUINT32 _sPIO2[8][1];
+        __declspec(align(32)) VUINT32 _sPC8[8][1];
+        __declspec(align(32)) VUINT32 _sPC7[8][1];
+        __declspec(align(32)) VUINT32 _sPC6[8][1];
+        __declspec(align(32)) VUINT32 _sPC5[8][1];
+        __declspec(align(32)) VUINT32 _sPC4[8][1];
+        __declspec(align(32)) VUINT32 _sPC3[8][1];
+        __declspec(align(32)) VUINT32 _sPC2[8][1];
+        __declspec(align(32)) VUINT32 _sPC1[8][1];
+        __declspec(align(32)) VUINT32 _sPC0[8][1];
+} __svml_satan_data_internal;
+#endif
+__svml_satan_data_internal:
+        .long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000 //_sSIGN_MASK
+        .align 32
+        .long 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF //_sABS_MASK
+        .align 32
+        .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 //_sONE
+        .align 32
+        .long 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB, 0x3FC90FDB //_sPIO2
+        .align 32
+        .long 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0, 0x3B322CC0 //_sPC8
+        .align 32
+        .long 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631, 0xBC7F2631 //_sPC7
+        .align 32
+        .long 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384, 0x3D2BC384 //_sPC6
+        .align 32
+        .long 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629, 0xBD987629 //_sPC5
+        .align 32
+        .long 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474, 0x3DD96474 //_sPC4
+        .align 32
+        .long 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8, 0xBE1161F8 //_sPC3
+        .align 32
+        .long 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F, 0x3E4CB79F //_sPC2
+        .align 32
+        .long 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49, 0xBEAAAA49 //_sPC1
+        .align 32
+        .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000 //_sPC0
+        .align 32
+        .type	__svml_satan_data_internal,@object
+        .size	__svml_satan_data_internal,.-__svml_satan_data_internal