x86-64: Add vector acos/acosf implementation to libmvec

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

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

1 files changed, 307 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_acos8_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_d_acos8_core_avx512.S
new file mode 100644
index 0000000000..521ff739c5
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_acos8_core_avx512.S
@@ -0,0 +1,307 @@
+/* Function acos 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:
+ *
+ *      SelMask = (|x| >= 0.5) ? 1 : 0;
+ *      R = SelMask ? sqrt(0.5 - 0.5*|x|) : |x|
+ *      acos(|x|) = SelMask ? 2*Poly(R) : (Pi/2 - Poly(R))
+ *      acos(x) = sign(x) ? (Pi - acos(|x|)) : acos(|x|)
+ *
+ */
+
+/* Offsets for data table __svml_dacos_data_internal
+ */
+#define SgnBit                        	0
+#define OneHalf                       	64
+#define SmallNorm                     	128
+#define MOne                          	192
+#define Two                           	256
+#define sqrt_coeff_1                  	320
+#define sqrt_coeff_2                  	384
+#define sqrt_coeff_3                  	448
+#define sqrt_coeff_4                  	512
+#define poly_coeff_1                  	576
+#define poly_coeff_2                  	640
+#define poly_coeff_3                  	704
+#define poly_coeff_4                  	768
+#define poly_coeff_5                  	832
+#define poly_coeff_6                  	896
+#define poly_coeff_7                  	960
+#define poly_coeff_8                  	1024
+#define poly_coeff_9                  	1088
+#define poly_coeff_10                 	1152
+#define poly_coeff_11                 	1216
+#define poly_coeff_12                 	1280
+#define PiH                           	1344
+#define Pi2H                          	1408
+
+#include <sysdep.h>
+
+        .text
+	.section .text.evex512,"ax",@progbits
+ENTRY(_ZGVeN8v_acos_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
+        vmovups   __svml_dacos_data_internal(%rip), %zmm7
+        vmovups   OneHalf+__svml_dacos_data_internal(%rip), %zmm8
+
+/* S ~ 2*sqrt(Y) */
+        vmovups   SmallNorm+__svml_dacos_data_internal(%rip), %zmm11
+        vmovups   Two+__svml_dacos_data_internal(%rip), %zmm14
+        vmovups   sqrt_coeff_1+__svml_dacos_data_internal(%rip), %zmm15
+        vmovups   sqrt_coeff_2+__svml_dacos_data_internal(%rip), %zmm2
+        vmovups   sqrt_coeff_3+__svml_dacos_data_internal(%rip), %zmm1
+        vmovups   MOne+__svml_dacos_data_internal(%rip), %zmm10
+        vmovaps   %zmm0, %zmm6
+
+/* x = -|arg| */
+        vorpd     %zmm6, %zmm7, %zmm5
+        vandpd    %zmm6, %zmm7, %zmm4
+
+/* Y = 0.5 + 0.5*(-x) */
+        vfmadd231pd {rn-sae}, %zmm5, %zmm8, %zmm8
+
+/* x^2 */
+        vmulpd    {rn-sae}, %zmm5, %zmm5, %zmm9
+        vrsqrt14pd %zmm8, %zmm12
+        vcmppd    $17, {sae}, %zmm11, %zmm8, %k1
+        vcmppd    $17, {sae}, %zmm10, %zmm5, %k0
+        vmovups   poly_coeff_5+__svml_dacos_data_internal(%rip), %zmm10
+        vmovups   poly_coeff_7+__svml_dacos_data_internal(%rip), %zmm11
+        vminpd    {sae}, %zmm8, %zmm9, %zmm3
+        vmovups   poly_coeff_3+__svml_dacos_data_internal(%rip), %zmm9
+        vxorpd    %zmm12, %zmm12, %zmm12{%k1}
+        vaddpd    {rn-sae}, %zmm8, %zmm8, %zmm0
+        vcmppd    $21, {sae}, %zmm8, %zmm3, %k4
+
+/* X<X^2 iff X<0 */
+        vcmppd    $17, {sae}, %zmm3, %zmm6, %k2
+        vmulpd    {rn-sae}, %zmm12, %zmm12, %zmm13
+        vmulpd    {rn-sae}, %zmm12, %zmm0, %zmm7
+        vmovups   poly_coeff_4+__svml_dacos_data_internal(%rip), %zmm12
+
+/* polynomial */
+        vmovups   poly_coeff_1+__svml_dacos_data_internal(%rip), %zmm8
+        vfmsub213pd {rn-sae}, %zmm14, %zmm13, %zmm0
+        vmovups   sqrt_coeff_4+__svml_dacos_data_internal(%rip), %zmm13
+        vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm12
+        vmovups   poly_coeff_11+__svml_dacos_data_internal(%rip), %zmm9
+        vfmadd231pd {rn-sae}, %zmm0, %zmm15, %zmm2
+        vmovups   poly_coeff_9+__svml_dacos_data_internal(%rip), %zmm15
+        vmulpd    {rn-sae}, %zmm0, %zmm7, %zmm14
+        vfmadd213pd {rn-sae}, %zmm1, %zmm0, %zmm2
+        vmovups   poly_coeff_2+__svml_dacos_data_internal(%rip), %zmm1
+        kmovw     %k0, %edx
+        vfmadd213pd {rn-sae}, %zmm13, %zmm0, %zmm2
+        vfmadd231pd {rn-sae}, %zmm3, %zmm8, %zmm1
+        vmovups   poly_coeff_10+__svml_dacos_data_internal(%rip), %zmm8
+        vmulpd    {rn-sae}, %zmm3, %zmm3, %zmm0
+        vfnmadd213pd {rn-sae}, %zmm7, %zmm14, %zmm2
+        vmovups   poly_coeff_6+__svml_dacos_data_internal(%rip), %zmm7
+        vfmadd231pd {rn-sae}, %zmm3, %zmm15, %zmm8
+        vfmadd213pd {rn-sae}, %zmm12, %zmm0, %zmm1
+        vblendmpd %zmm2, %zmm5, %zmm2{%k4}
+        vfmadd231pd {rn-sae}, %zmm3, %zmm10, %zmm7
+        vmovups   poly_coeff_8+__svml_dacos_data_internal(%rip), %zmm10
+        vfmadd231pd {rn-sae}, %zmm3, %zmm11, %zmm10
+        vmovups   poly_coeff_12+__svml_dacos_data_internal(%rip), %zmm11
+        kandw     %k4, %k2, %k3
+        vfmadd213pd {rn-sae}, %zmm10, %zmm0, %zmm7
+        vfmadd231pd {rn-sae}, %zmm3, %zmm9, %zmm11
+        vmulpd    {rn-sae}, %zmm0, %zmm0, %zmm10
+        vfmadd213pd {rn-sae}, %zmm7, %zmm10, %zmm1
+        vfmadd213pd {rn-sae}, %zmm8, %zmm0, %zmm1
+        vfmadd213pd {rn-sae}, %zmm11, %zmm0, %zmm1
+        vmovups   Pi2H+__svml_dacos_data_internal(%rip), %zmm0
+        vmulpd    {rn-sae}, %zmm3, %zmm1, %zmm1
+        vxorpd    %zmm4, %zmm2, %zmm3
+        vxorpd    %zmm0, %zmm0, %zmm0{%k4}
+        vfmadd213pd {rn-sae}, %zmm3, %zmm3, %zmm1
+        vorpd     PiH+__svml_dacos_data_internal(%rip), %zmm0, %zmm0{%k3}
+        vaddpd    {rn-sae}, %zmm1, %zmm0, %zmm0
+        testl     %edx, %edx
+
+/* Go to special inputs processing branch */
+        jne       L(SPECIAL_VALUES_BRANCH)
+                                # LOE rbx r12 r13 r14 r15 edx zmm0 zmm6
+
+/* 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   %zmm6, 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      acos@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_acos_skx)
+
+        .section .rodata, "a"
+        .align 64
+
+#ifdef __svml_dacos_data_internal_typedef
+typedef unsigned int VUINT32;
+typedef struct {
+        __declspec(align(64)) VUINT32 SgnBit[8][2];
+        __declspec(align(64)) VUINT32 OneHalf[8][2];
+        __declspec(align(64)) VUINT32 SmallNorm[8][2];
+        __declspec(align(64)) VUINT32 MOne[8][2];
+        __declspec(align(64)) VUINT32 Two[8][2];
+        __declspec(align(64)) VUINT32 sqrt_coeff[4][8][2];
+        __declspec(align(64)) VUINT32 poly_coeff[12][8][2];
+        __declspec(align(64)) VUINT32 PiH[8][2];
+        __declspec(align(64)) VUINT32 Pi2H[8][2];
+} __svml_dacos_data_internal;
+#endif
+__svml_dacos_data_internal:
+        /*== SgnBit ==*/
+        .quad 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000, 0x8000000000000000
+        /*== OneHalf ==*/
+        .align 64
+        .quad 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000, 0x3fe0000000000000
+        /*== SmallNorm ==*/
+        .align 64
+        .quad 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000, 0x3000000000000000
+        /*== MOne ==*/
+        .align 64
+        .quad 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000, 0xbff0000000000000
+        /*== Two ==*/
+        .align 64
+        .quad 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000, 0x4000000000000000
+        /*== sqrt_coeff[4] ==*/
+        .align 64
+        .quad 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3, 0xbf918000993B24C3 /* sqrt_coeff4 */
+        .quad 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D, 0x3fa400006F70D42D /* sqrt_coeff3 */
+        .quad 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97, 0xbfb7FFFFFFFFFE97 /* sqrt_coeff2 */
+        .quad 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D, 0x3fcFFFFFFFFFFF9D /* sqrt_coeff1 */
+        /*== poly_coeff[12] ==*/
+        .align 64
+        .quad 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909, 0x3fa07520C70EB909 /* poly_coeff12 */
+        .quad 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED, 0xbf90FB17F7DBB0ED /* poly_coeff11 */
+        .quad 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE, 0x3f943F44BFBC3BAE /* poly_coeff10 */
+        .quad 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5, 0x3f7A583395D45ED5 /* poly_coeff9 */
+        .quad 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6, 0x3f88F8DC2AFCCAD6 /* poly_coeff8 */
+        .quad 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57, 0x3f8C6DBBCB88BD57 /* poly_coeff7 */
+        .quad 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E, 0x3f91C6DCF538AD2E /* poly_coeff6 */
+        .quad 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd, 0x3f96E89CEBDEFadd /* poly_coeff5 */
+        .quad 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE, 0x3f9F1C72E13AD8BE /* poly_coeff4 */
+        .quad 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8, 0x3fa6DB6DB3B445F8 /* poly_coeff3 */
+        .quad 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE, 0x3fb333333337E0DE /* poly_coeff2 */
+        .quad 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C, 0x3fc555555555529C /* poly_coeff1 */
+        /*== PiH ==*/
+        .align 64
+        .quad 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18, 0x400921fb54442d18
+        /*== Pi2H ==*/
+        .align 64
+        .quad 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18, 0x3ff921fb54442d18
+        .align 64
+        .type	__svml_dacos_data_internal,@object
+        .size	__svml_dacos_data_internal,.-__svml_dacos_data_internal