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, 325 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_exp22_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_d_exp22_core_sse4.S
new file mode 100644
index 0000000000..7388c242f6
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_exp22_core_sse4.S
@@ -0,0 +1,325 @@
+/* Function exp2 vectorized with SSE4.
+   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:
+ *
+ *   exp2(x)  = 2^n * T[j] * (1 + P(y))
+ *   where
+ *        x = m*(1/K) + y,    y in [-1/K..1/K]
+ *        m = n*K + j,           m,n,j - signed integer, j in [-K/2..K/2]
+ *
+ *        values of 2^j/K are tabulated
+ *
+ *        P(y) is a minimax polynomial approximation of exp2(x)-1
+ *        on small interval [-1/K..1/K]
+ *
+ *  Special cases:
+ *
+ *   exp2(NaN)  = NaN
+ *   exp2(+INF) = +INF
+ *   exp2(-INF) = 0
+ *   exp2(x)    = 1 for subnormals
+ *   For IEEE double
+ *     if x >= 1024.0 then exp2(x) overflows
+ *     if x < -1076.0 then exp2(x) underflows
+ *
+ */
+
+/* Offsets for data table __svml_dexp2_data_internal
+ */
+#define _dbT                          	0
+#define _dbShifter                    	1024
+#define _dPC1                         	1040
+#define _dPC2                         	1056
+#define _dPC3                         	1072
+#define _dPC4                         	1088
+#define _lIndexMask                   	1104
+#define _iAbsMask                     	1120
+#define _iDomainRange                 	1136
+
+#include <sysdep.h>
+
+        .text
+	.section .text.sse4,"ax",@progbits
+ENTRY(_ZGVbN2v_exp2_sse4)
+        subq      $72, %rsp
+        cfi_def_cfa_offset(80)
+
+/*  R  */
+        movaps    %xmm0, %xmm7
+        movups    _dbShifter+__svml_dexp2_data_internal(%rip), %xmm1
+
+/* out, basePtr, iIndex, iBaseOfs, iSize, iGran, iOfs */
+        lea       __svml_dexp2_data_internal(%rip), %rsi
+
+/*  Load arument  */
+        movaps    %xmm1, %xmm10
+        addpd     %xmm0, %xmm10
+        movaps    %xmm10, %xmm6
+        subpd     %xmm1, %xmm6
+        subpd     %xmm6, %xmm7
+
+/*
+ *  Polynomial
+ * poly(dN) = a1*dR+...+a4*dR^4
+ */
+        movups    _dPC4+__svml_dexp2_data_internal(%rip), %xmm8
+        mulpd     %xmm7, %xmm8
+        addpd     _dPC3+__svml_dexp2_data_internal(%rip), %xmm8
+        mulpd     %xmm7, %xmm8
+        addpd     _dPC2+__svml_dexp2_data_internal(%rip), %xmm8
+        movdqu    _lIndexMask+__svml_dexp2_data_internal(%rip), %xmm9
+
+/*  Index and lookup  */
+        movdqa    %xmm9, %xmm5
+        pandn     %xmm10, %xmm9
+        pand      %xmm10, %xmm5
+
+/*  2^N  */
+        psllq     $45, %xmm9
+        movd      %xmm5, %eax
+        movq      _iAbsMask+__svml_dexp2_data_internal(%rip), %xmm2
+
+/* Check for overflow\underflow  */
+        pshufd    $221, %xmm0, %xmm4
+        pextrw    $4, %xmm5, %ecx
+
+/* a1+...+a4*dR^3 ! */
+        mulpd     %xmm7, %xmm8
+        shll      $3, %eax
+        pand      %xmm2, %xmm4
+        shll      $3, %ecx
+        movq      (%rsi,%rax), %xmm1
+        movhpd    (%rsi,%rcx), %xmm1
+
+/* dR=dR*dT */
+        mulpd     %xmm1, %xmm7
+        addpd     _dPC1+__svml_dexp2_data_internal(%rip), %xmm8
+
+/*
+ *  Reconstruction
+ * exp2 = {2^N later}*(Tj+Tj*poly)
+ * dN = dT+dT*dR*(a1+...+a4*dR^3)
+ */
+        mulpd     %xmm7, %xmm8
+        addpd     %xmm8, %xmm1
+        movq      _iDomainRange+__svml_dexp2_data_internal(%rip), %xmm3
+        pcmpgtd   %xmm3, %xmm4
+        movmskps  %xmm4, %edx
+
+/* quick 2^N */
+        paddq     %xmm9, %xmm1
+        andl      $3, %edx
+
+/*  Finish   */
+
+/* Go to special inputs processing branch */
+        jne       L(SPECIAL_VALUES_BRANCH)
+                                # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm1
+
+/* Restore registers
+ * and exit the function
+ */
+
+L(EXIT):
+        movaps    %xmm1, %xmm0
+        addq      $72, %rsp
+        cfi_def_cfa_offset(8)
+        ret
+        cfi_def_cfa_offset(80)
+
+/* Branch to process
+ * special inputs
+ */
+
+L(SPECIAL_VALUES_BRANCH):
+        movups    %xmm0, 32(%rsp)
+        movups    %xmm1, 48(%rsp)
+                                # LOE rbx rbp r12 r13 r14 r15 edx xmm1
+
+        xorl      %eax, %eax
+        movq      %r12, 16(%rsp)
+        cfi_offset(12, -64)
+        movl      %eax, %r12d
+        movq      %r13, 8(%rsp)
+        cfi_offset(13, -72)
+        movl      %edx, %r13d
+        movq      %r14, (%rsp)
+        cfi_offset(14, -80)
+                                # LOE rbx rbp r15 r12d r13d
+
+/* Range mask
+ * bits check
+ */
+
+L(RANGEMASK_CHECK):
+        btl       %r12d, %r13d
+
+/* Call scalar math function */
+        jc        L(SCALAR_MATH_CALL)
+                                # LOE rbx rbp r15 r12d r13d
+
+/* Special inputs
+ * processing loop
+ */
+
+L(SPECIAL_VALUES_LOOP):
+        incl      %r12d
+        cmpl      $2, %r12d
+
+/* Check bits in range mask */
+        jl        L(RANGEMASK_CHECK)
+                                # LOE rbx rbp r15 r12d r13d
+
+        movq      16(%rsp), %r12
+        cfi_restore(12)
+        movq      8(%rsp), %r13
+        cfi_restore(13)
+        movq      (%rsp), %r14
+        cfi_restore(14)
+        movups    48(%rsp), %xmm1
+
+/* Go to exit */
+        jmp       L(EXIT)
+        cfi_offset(12, -64)
+        cfi_offset(13, -72)
+        cfi_offset(14, -80)
+                                # LOE rbx rbp r12 r13 r14 r15 xmm1
+
+/* Scalar math fucntion call
+ * to process special input
+ */
+
+L(SCALAR_MATH_CALL):
+        movl      %r12d, %r14d
+        movsd     32(%rsp,%r14,8), %xmm0
+        call      exp2@PLT
+                                # LOE rbx rbp r14 r15 r12d r13d xmm0
+
+        movsd     %xmm0, 48(%rsp,%r14,8)
+
+/* Process special inputs in loop */
+        jmp       L(SPECIAL_VALUES_LOOP)
+                                # LOE rbx rbp r15 r12d r13d
+END(_ZGVbN2v_exp2_sse4)
+
+        .section .rodata, "a"
+        .align 16
+
+#ifdef __svml_dexp2_data_internal_typedef
+typedef unsigned int VUINT32;
+typedef struct
+{
+        __declspec(align(16)) VUINT32 _dbT[(1<<7)][2];
+        __declspec(align(16)) VUINT32 _dbShifter[2][2];
+        __declspec(align(16)) VUINT32 _dPC1[2][2];
+        __declspec(align(16)) VUINT32 _dPC2[2][2];
+        __declspec(align(16)) VUINT32 _dPC3[2][2];
+        __declspec(align(16)) VUINT32 _dPC4[2][2];
+        __declspec(align(16)) VUINT32 _lIndexMask[2][2];
+        __declspec(align(16)) VUINT32 _iAbsMask[4][1];
+        __declspec(align(16)) VUINT32 _iDomainRange[4][1];
+} __svml_dexp2_data_internal;
+#endif
+__svml_dexp2_data_internal:
+        /*== _dbT ==*/
+        .quad 0x3ff0000000000000, 0x3ff0163da9fb3335   /*2^( 0 /128),2^( 1 /128)*/
+        .quad 0x3ff02c9a3e778061, 0x3ff04315e86e7f85   /*2^( 2 /128),2^( 3 /128)*/
+        .quad 0x3ff059b0d3158574, 0x3ff0706b29ddf6de   /*2^( 4 /128),2^( 5 /128)*/
+        .quad 0x3ff0874518759bc8, 0x3ff09e3ecac6f383   /*2^( 6 /128),2^( 7 /128)*/
+        .quad 0x3ff0b5586cf9890f, 0x3ff0cc922b7247f7   /*2^( 8 /128),2^( 9 /128)*/
+        .quad 0x3ff0e3ec32d3d1a2, 0x3ff0fb66affed31b   /*2^( 10 /128),2^( 11 /128)*/
+        .quad 0x3ff11301d0125b51, 0x3ff12abdc06c31cc   /*2^( 12 /128),2^( 13 /128)*/
+        .quad 0x3ff1429aaea92de0, 0x3ff15a98c8a58e51   /*2^( 14 /128),2^( 15 /128)*/
+        .quad 0x3ff172b83c7d517b, 0x3ff18af9388c8dea   /*2^( 16 /128),2^( 17 /128)*/
+        .quad 0x3ff1a35beb6fcb75, 0x3ff1bbe084045cd4   /*2^( 18 /128),2^( 19 /128)*/
+        .quad 0x3ff1d4873168b9aa, 0x3ff1ed5022fcd91d   /*2^( 20 /128),2^( 21 /128)*/
+        .quad 0x3ff2063b88628cd6, 0x3ff21f49917ddc96   /*2^( 22 /128),2^( 23 /128)*/
+        .quad 0x3ff2387a6e756238, 0x3ff251ce4fb2a63f   /*2^( 24 /128),2^( 25 /128)*/
+        .quad 0x3ff26b4565e27cdd, 0x3ff284dfe1f56381   /*2^( 26 /128),2^( 27 /128)*/
+        .quad 0x3ff29e9df51fdee1, 0x3ff2b87fd0dad990   /*2^( 28 /128),2^( 29 /128)*/
+        .quad 0x3ff2d285a6e4030b, 0x3ff2ecafa93e2f56   /*2^( 30 /128),2^( 31 /128)*/
+        .quad 0x3ff306fe0a31b715, 0x3ff32170fc4cd831   /*2^( 32 /128),2^( 33 /128)*/
+        .quad 0x3ff33c08b26416ff, 0x3ff356c55f929ff1   /*2^( 34 /128),2^( 35 /128)*/
+        .quad 0x3ff371a7373aa9cb, 0x3ff38cae6d05d866   /*2^( 36 /128),2^( 37 /128)*/
+        .quad 0x3ff3a7db34e59ff7, 0x3ff3c32dc313a8e5   /*2^( 38 /128),2^( 39 /128)*/
+        .quad 0x3ff3dea64c123422, 0x3ff3fa4504ac801c   /*2^( 40 /128),2^( 41 /128)*/
+        .quad 0x3ff4160a21f72e2a, 0x3ff431f5d950a897   /*2^( 42 /128),2^( 43 /128)*/
+        .quad 0x3ff44e086061892d, 0x3ff46a41ed1d0057   /*2^( 44 /128),2^( 45 /128)*/
+        .quad 0x3ff486a2b5c13cd0, 0x3ff4a32af0d7d3de   /*2^( 46 /128),2^( 47 /128)*/
+        .quad 0x3ff4bfdad5362a27, 0x3ff4dcb299fddd0d   /*2^( 48 /128),2^( 49 /128)*/
+        .quad 0x3ff4f9b2769d2ca7, 0x3ff516daa2cf6642   /*2^( 50 /128),2^( 51 /128)*/
+        .quad 0x3ff5342b569d4f82, 0x3ff551a4ca5d920f   /*2^( 52 /128),2^( 53 /128)*/
+        .quad 0x3ff56f4736b527da, 0x3ff58d12d497c7fd   /*2^( 54 /128),2^( 55 /128)*/
+        .quad 0x3ff5ab07dd485429, 0x3ff5c9268a5946b7   /*2^( 56 /128),2^( 57 /128)*/
+        .quad 0x3ff5e76f15ad2148, 0x3ff605e1b976dc09   /*2^( 58 /128),2^( 59 /128)*/
+        .quad 0x3ff6247eb03a5585, 0x3ff6434634ccc320   /*2^( 60 /128),2^( 61 /128)*/
+        .quad 0x3ff6623882552225, 0x3ff68155d44ca973   /*2^( 62 /128),2^( 63 /128)*/
+        .quad 0x3ff6a09e667f3bcd, 0x3ff6c012750bdabf   /*2^( 64 /128),2^( 65 /128)*/
+        .quad 0x3ff6dfb23c651a2f, 0x3ff6ff7df9519484   /*2^( 66 /128),2^( 67 /128)*/
+        .quad 0x3ff71f75e8ec5f74, 0x3ff73f9a48a58174   /*2^( 68 /128),2^( 69 /128)*/
+        .quad 0x3ff75feb564267c9, 0x3ff780694fde5d3f   /*2^( 70 /128),2^( 71 /128)*/
+        .quad 0x3ff7a11473eb0187, 0x3ff7c1ed0130c132   /*2^( 72 /128),2^( 73 /128)*/
+        .quad 0x3ff7e2f336cf4e62, 0x3ff80427543e1a12   /*2^( 74 /128),2^( 75 /128)*/
+        .quad 0x3ff82589994cce13, 0x3ff8471a4623c7ad   /*2^( 76 /128),2^( 77 /128)*/
+        .quad 0x3ff868d99b4492ed, 0x3ff88ac7d98a6699   /*2^( 78 /128),2^( 79 /128)*/
+        .quad 0x3ff8ace5422aa0db, 0x3ff8cf3216b5448c   /*2^( 80 /128),2^( 81 /128)*/
+        .quad 0x3ff8f1ae99157736, 0x3ff9145b0b91ffc6   /*2^( 82 /128),2^( 83 /128)*/
+        .quad 0x3ff93737b0cdc5e5, 0x3ff95a44cbc8520f   /*2^( 84 /128),2^( 85 /128)*/
+        .quad 0x3ff97d829fde4e50, 0x3ff9a0f170ca07ba   /*2^( 86 /128),2^( 87 /128)*/
+        .quad 0x3ff9c49182a3f090, 0x3ff9e86319e32323   /*2^( 88 /128),2^( 89 /128)*/
+        .quad 0x3ffa0c667b5de565, 0x3ffa309bec4a2d33   /*2^( 90 /128),2^( 91 /128)*/
+        .quad 0x3ffa5503b23e255d, 0x3ffa799e1330b358   /*2^( 92 /128),2^( 93 /128)*/
+        .quad 0x3ffa9e6b5579fdbf, 0x3ffac36bbfd3f37a   /*2^( 94 /128),2^( 95 /128)*/
+        .quad 0x3ffae89f995ad3ad, 0x3ffb0e07298db666   /*2^( 96 /128),2^( 97 /128)*/
+        .quad 0x3ffb33a2b84f15fb, 0x3ffb59728de5593a   /*2^( 98 /128),2^( 99 /128)*/
+        .quad 0x3ffb7f76f2fb5e47, 0x3ffba5b030a1064a   /*2^( 100 /128),2^( 101 /128)*/
+        .quad 0x3ffbcc1e904bc1d2, 0x3ffbf2c25bd71e09   /*2^( 102 /128),2^( 103 /128)*/
+        .quad 0x3ffc199bdd85529c, 0x3ffc40ab5fffd07a   /*2^( 104 /128),2^( 105 /128)*/
+        .quad 0x3ffc67f12e57d14b, 0x3ffc8f6d9406e7b5   /*2^( 106 /128),2^( 107 /128)*/
+        .quad 0x3ffcb720dcef9069, 0x3ffcdf0b555dc3fa   /*2^( 108 /128),2^( 109 /128)*/
+        .quad 0x3ffd072d4a07897c, 0x3ffd2f87080d89f2   /*2^( 110 /128),2^( 111 /128)*/
+        .quad 0x3ffd5818dcfba487, 0x3ffd80e316c98398   /*2^( 112 /128),2^( 113 /128)*/
+        .quad 0x3ffda9e603db3285, 0x3ffdd321f301b460   /*2^( 114 /128),2^( 115 /128)*/
+        .quad 0x3ffdfc97337b9b5f, 0x3ffe264614f5a129   /*2^( 116 /128),2^( 117 /128)*/
+        .quad 0x3ffe502ee78b3ff6, 0x3ffe7a51fbc74c83   /*2^( 118 /128),2^( 119 /128)*/
+        .quad 0x3ffea4afa2a490da, 0x3ffecf482d8e67f1   /*2^( 120 /128),2^( 121 /128)*/
+        .quad 0x3ffefa1bee615a27, 0x3fff252b376bba97   /*2^( 122 /128),2^( 123 /128)*/
+        .quad 0x3fff50765b6e4540, 0x3fff7bfdad9cbe14   /*2^( 124 /128),2^( 125 /128)*/
+        .quad 0x3fffa7c1819e90d8, 0x3fffd3c22b8f71f1 /*2^( 126 /128),2^( 127 /128)*/
+        .align 16
+        .quad 0x42c8000000000000, 0x42c8000000000000  /* _dbShifter - 0x433-7=0x42c shifted right on K!*/
+        //log2(relerr) = -53.547756365162
+        .align 16
+        .quad 0x3fe62e42fefa3685, 0x3fe62e42fefa3685 /* _dPC1 */
+        .align 16
+        .quad 0x3fcebfbdff82ca48, 0x3fcebfbdff82ca48 /* _dPC2 */
+        .align 16
+        .quad 0x3fac6b09b180f045, 0x3fac6b09b180f045 /* _dPC3 */
+        .align 16
+        .quad 0x3f83b2ab5bb1268f, 0x3f83b2ab5bb1268f /* _dPC4 */
+        .align 16
+        .quad 0x000000000000007f, 0x000000000000007f          /* _lIndexMask =(2^K-1)*/
+        .align 16
+        .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff          /* _iAbsMask */
+        .align 16
+        .long 0x408fefff, 0x408fefff, 0x408fefff, 0x408fefff /* _iDomainRange */
+        .align 16
+        .type	__svml_dexp2_data_internal,@object
+        .size	__svml_dexp2_data_internal,.-__svml_dexp2_data_internal