x86-64: Add vector exp2/exp2f implementation to libmvec

Implement vectorized exp2/exp2f containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI.  It also contains
accuracy and ABI tests for vector exp2/exp2f with regenerated ulps.

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

1 files changed, 301 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_exp28_core_avx512.S b/sysdeps/x86_64/fpu/multiarch/svml_d_exp28_core_avx512.S
new file mode 100644
index 0000000000..90f21695f0
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_exp28_core_avx512.S
@@ -0,0 +1,301 @@
+/* Function exp2 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:
+ *
+ *     Double precision mantissa represented as: 1.b1b2b3 ... b52
+ *     Constant for double precision: S = 2^48 x 1.5
+ *
+ *     2^X = 2^Xo  x  2^{X-Xo}
+ *     2^X = 2^K  x  2^fo  x  2^{X-Xo}
+ *     2^X = 2^K  x  2^fo  x  2^r
+ *
+ *     2^K  --> Manual scaling
+ *     2^fo --> Table lookup
+ *     r    --> 1 + poly    (r = X - Xo)
+ *
+ *     Xo = K  +  fo
+ *     Xo = K  +  0.x1x2x3x4
+ *
+ *     r = X - Xo
+ *       = Vreduce(X, imm)
+ *       = X - VRndScale(X, imm),    where Xo = VRndScale(X, imm)
+ *
+ *     Rnd(S + X) = S + Xo,    where S is selected as S = 2^19 x 1.5
+ *         S + X = S + floor(X) + 0.x1x2x3x4
+ *     Rnd(S + X) = Rnd(2^48 x 1.5 + X)
+ *     (Note: 2^exp x 1.b1b2b3 ... b52,  2^{exp-52} = 2^-4 for exp=48)
+ *
+ *     exp2(x) =  2^K  x  2^fo  x (1 + poly(r)),   where 2^r = 1 + poly(r)
+ *
+ *     Scale back:
+ *     dest = src1 x 2^floor(src2)
+ *
+ *
+ */
+
+/* Offsets for data table __svml_dexp2_data_internal_avx512
+ */
+#define Frac_PowerD0                  	0
+#define poly_coeff1                   	128
+#define poly_coeff2                   	192
+#define poly_coeff3                   	256
+#define poly_coeff4                   	320
+#define poly_coeff5                   	384
+#define poly_coeff6                   	448
+#define add_const                     	512
+#define AbsMask                       	576
+#define Threshold                     	640
+#define _lIndexMask                   	704
+
+#include <sysdep.h>
+
+        .text
+	.section .text.evex512,"ax",@progbits
+ENTRY(_ZGVeN8v_exp2_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   poly_coeff5+__svml_dexp2_data_internal_avx512(%rip), %zmm14
+        vmovups   poly_coeff6+__svml_dexp2_data_internal_avx512(%rip), %zmm6
+
+/*
+ * Reduced argument
+ * where VREDUCE is available
+ */
+        vreducepd $65, {sae}, %zmm0, %zmm10
+        vmovups   poly_coeff4+__svml_dexp2_data_internal_avx512(%rip), %zmm7
+        vmovups   add_const+__svml_dexp2_data_internal_avx512(%rip), %zmm3
+        vmovups   poly_coeff3+__svml_dexp2_data_internal_avx512(%rip), %zmm8
+        vmovups   __svml_dexp2_data_internal_avx512(%rip), %zmm13
+
+/* c6*r   + c5 */
+        vfmadd231pd {rn-sae}, %zmm10, %zmm6, %zmm14
+        vmovups   poly_coeff2+__svml_dexp2_data_internal_avx512(%rip), %zmm9
+        vmovups   Threshold+__svml_dexp2_data_internal_avx512(%rip), %zmm2
+
+/*
+ *
+ *  HA
+ * Variables and constants
+ * Load constants and vector(s)
+ */
+        vmovups   poly_coeff1+__svml_dexp2_data_internal_avx512(%rip), %zmm11
+
+/* c6*r^2 + c5*r + c4 */
+        vfmadd213pd {rn-sae}, %zmm7, %zmm10, %zmm14
+
+/*
+ * Integer form of K+0.b1b2b3b4 in lower bits - call K_plus_f0
+ * Mantisssa of normalized double precision FP: 1.b1b2...b52
+ */
+        vaddpd    {rd-sae}, %zmm3, %zmm0, %zmm4
+        vandpd    AbsMask+__svml_dexp2_data_internal_avx512(%rip), %zmm0, %zmm1
+
+/* c6*r^3 + c5*r^2 + c4*r + c3 */
+        vfmadd213pd {rn-sae}, %zmm8, %zmm10, %zmm14
+        vcmppd    $29, {sae}, %zmm2, %zmm1, %k0
+
+/* c6*r^4 + c5*r^3 + c4*r^2 + c3*r + c2 */
+        vfmadd213pd {rn-sae}, %zmm9, %zmm10, %zmm14
+        kmovw     %k0, %edx
+
+/* c6*r^5 + c5*r^4 + c4*r^3 + c3*r^2 + c2*r + c1 */
+        vfmadd213pd {rn-sae}, %zmm11, %zmm10, %zmm14
+
+/* Table value: 2^(0.b1b2b3b4) */
+        vpandq    _lIndexMask+__svml_dexp2_data_internal_avx512(%rip), %zmm4, %zmm5
+        vpermt2pd Frac_PowerD0+64+__svml_dexp2_data_internal_avx512(%rip), %zmm5, %zmm13
+
+/* T*r */
+        vmulpd    {rn-sae}, %zmm10, %zmm13, %zmm12
+
+/* T + (T*r*(c6*r^5 + c5*r^4 + c4*r^3 + c3*r^2 + c2*r + c1)) */
+        vfmadd213pd {rn-sae}, %zmm13, %zmm12, %zmm14
+
+/* Scaling placed at the end to avoid accuracy loss when T*r*scale underflows */
+        vscalefpd {rn-sae}, %zmm0, %zmm14, %zmm1
+        testl     %edx, %edx
+
+/* Go to special inputs processing branch */
+        jne       L(SPECIAL_VALUES_BRANCH)
+                                # LOE rbx r12 r13 r14 r15 edx zmm0 zmm1
+
+/* Restore registers
+ * and exit the function
+ */
+
+L(EXIT):
+        vmovaps   %zmm1, %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   %zmm1, 128(%rsp)
+                                # LOE rbx r12 r13 r14 r15 edx zmm1
+
+        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), %zmm1
+
+/* 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 zmm1
+
+/* Scalar math fucntion call
+ * to process special input
+ */
+
+L(SCALAR_MATH_CALL):
+        movl      %r12d, %r14d
+        movsd     64(%rsp,%r14,8), %xmm0
+        call      exp2@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_exp2_skx)
+
+        .section .rodata, "a"
+        .align 64
+
+#ifdef __svml_dexp2_data_internal_avx512_typedef
+typedef unsigned int VUINT32;
+typedef struct {
+        __declspec(align(64)) VUINT32 Frac_PowerD0[16][2];
+        __declspec(align(64)) VUINT32 poly_coeff1[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff2[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff3[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff4[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff5[8][2];
+        __declspec(align(64)) VUINT32 poly_coeff6[8][2];
+        __declspec(align(64)) VUINT32 add_const[8][2];
+        __declspec(align(64)) VUINT32 AbsMask[8][2];
+        __declspec(align(64)) VUINT32 Threshold[8][2];
+        __declspec(align(64)) VUINT32 _lIndexMask[8][2];
+} __svml_dexp2_data_internal_avx512;
+#endif
+__svml_dexp2_data_internal_avx512:
+        /*== Frac_PowerD0 ==*/
+        .quad 0x3FF0000000000000
+        .quad 0x3FF0B5586CF9890F
+        .quad 0x3FF172B83C7D517B
+        .quad 0x3FF2387A6E756238
+        .quad 0x3FF306FE0A31B715
+        .quad 0x3FF3DEA64C123422
+        .quad 0x3FF4BFDAD5362A27
+        .quad 0x3FF5AB07DD485429
+        .quad 0x3FF6A09E667F3BCD
+        .quad 0x3FF7A11473EB0187
+        .quad 0x3FF8ACE5422AA0DB
+        .quad 0x3FF9C49182A3F090
+        .quad 0x3FFAE89F995AD3AD
+        .quad 0x3FFC199BDD85529C
+        .quad 0x3FFD5818DCFBA487
+        .quad 0x3FFEA4AFA2A490DA
+        .align 64
+        .quad 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B, 0x3FE62E42FEFA398B  /*== poly_coeff1 ==*/
+        .align 64
+        .quad 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A, 0x3FCEBFBDFF84555A  /*== poly_coeff2 ==*/
+        .align 64
+        .quad 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9, 0x3FAC6B08D4AD86B9  /*== poly_coeff3 ==*/
+        .align 64
+        .quad 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252, 0x3F83B2AD1B172252  /*== poly_coeff4 ==*/
+        .align 64
+        .quad 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19, 0x3F55D7472713CD19  /*== poly_coeff5 ==*/
+        .align 64
+        .quad 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B, 0x3F24A1D7F526371B  /*== poly_coeff6 ==*/
+        .align 64
+        .quad 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000, 0x42F8000000000000  /* add_const     */
+        .align 64
+        .quad 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff, 0x7fffffffffffffff  /* AbsMask       */
+        .align 64
+        .quad 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000, 0x408fefff00000000  /* Threshold     */
+        .align 64
+        .quad 0x000000000000000F, 0x000000000000000F, 0x000000000000000F, 0x000000000000000F, 0x000000000000000F, 0x000000000000000F, 0x000000000000000F, 0x000000000000000F  /* _lIndexMask   */
+        .align 64
+        .type	__svml_dexp2_data_internal_avx512,@object
+        .size	__svml_dexp2_data_internal_avx512,.-__svml_dexp2_data_internal_avx512