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|
/* Function tanhf vectorized with AVX-512.
Copyright (C) 2021-2022 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:
*
* NOTE: Since the hyperbolic tangent function is odd
* (tanh(x) = -tanh(-x)), below algorithm deals with the absolute
* value of the argument |x|: tanh(x) = sign(x) * tanh(|x|)
*
* We use a table lookup method to compute tanh(|x|).
* The basic idea is to split the input range into a number of subintervals
* and to approximate tanh(.) with a polynomial on each of them.
*
* IEEE SPECIAL CONDITIONS:
* x = [+,-]0, r = [+,-]0
* x = +Inf, r = +1
* x = -Inf, r = -1
* x = QNaN, r = QNaN
* x = SNaN, r = QNaN
*
*
* ALGORITHM DETAILS
* We handle special values in a callout function, aside from main path
* computations. "Special" for this algorithm are:
* INF, NAN, |x| > HUGE_THRESHOLD
*
*
* Main path computations are organized as follows:
* Actually we split the interval [0, SATURATION_THRESHOLD)
* into a number of subintervals. On each subinterval we approximate tanh(.)
* with a minimax polynomial of pre-defined degree. Polynomial coefficients
* are computed beforehand and stored in table. We also use
*
* y := |x| + B,
*
* here B depends on subinterval and is used to make argument
* closer to zero.
* We also add large fake interval [SATURATION_THRESHOLD, HUGE_THRESHOLD],
* where 1.0 + 0.0*y + 0.0*y^2 ... coefficients are stored - just to
* preserve main path computation logic but return 1.0 for all arguments.
*
* Hence reconstruction looks as follows:
* we extract proper polynomial and range reduction coefficients
* (Pj and B), corresponding to subinterval, to which |x| belongs,
* and return
*
* r := sign(x) * (P0 + P1 * y + ... + Pn * y^n)
*
* NOTE: we use multiprecision technique to multiply and sum the first
* K terms of the polynomial. So Pj, j = 0..K are stored in
* table each as a pair of target precision numbers (Pj and PLj) to
* achieve wider than target precision.
*
*
*/
/* Offsets for data table __svml_stanh_data_internal
*/
#define _sC 0
#define _sP0 128
#define _sP2 256
#define _sP3 384
#define _sP4 512
#define _sP5 640
#define _sP6 768
#define _sP7 896
#define _iExpMantMask_UISA 1024
#define _iMinIdxOfsMask_UISA 1088
#define _iMaxIdxMask_UISA 1152
#define _sSignMask 1216
#define _sAbsMask 1280
#define _iExpMantMask 1344
#define _iExpMask 1408
#define _iMinIdxOfsMask 1472
#define _iMaxIdxMask 1536
#include <sysdep.h>
.text
.section .text.exex512,"ax",@progbits
ENTRY(_ZGVeN16v_tanhf_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
vmovaps %zmm0, %zmm1
vmovups __svml_stanh_data_internal(%rip), %zmm9
vmovups _sP6+__svml_stanh_data_internal(%rip), %zmm11
vmovups _sP5+__svml_stanh_data_internal(%rip), %zmm12
vmovups _sP4+__svml_stanh_data_internal(%rip), %zmm13
vmovups _sP3+__svml_stanh_data_internal(%rip), %zmm14
vmovups _sP2+__svml_stanh_data_internal(%rip), %zmm15
vpternlogd $255, %zmm2, %zmm2, %zmm2
vandps _sAbsMask+__svml_stanh_data_internal(%rip), %zmm1, %zmm8
vandps _sSignMask+__svml_stanh_data_internal(%rip), %zmm1, %zmm0
/* Here huge arguments, INF and NaNs are filtered out to callout. */
vpandd _iExpMantMask_UISA+__svml_stanh_data_internal(%rip), %zmm1, %zmm3
vpsubd _iMinIdxOfsMask_UISA+__svml_stanh_data_internal(%rip), %zmm3, %zmm4
vpcmpd $2, _iExpMask+__svml_stanh_data_internal(%rip), %zmm3, %k1
/*
* small table specific variables *
* Constant loading
*/
vpxord %zmm5, %zmm5, %zmm5
/* if VMIN, VMAX is defined for I type */
vpmaxsd %zmm5, %zmm4, %zmm6
vpminsd _iMaxIdxMask_UISA+__svml_stanh_data_internal(%rip), %zmm6, %zmm7
vpsrld $21, %zmm7, %zmm10
vmovups _sP7+__svml_stanh_data_internal(%rip), %zmm4
vpermt2ps _sC+64+__svml_stanh_data_internal(%rip), %zmm10, %zmm9
vpermt2ps _sP6+64+__svml_stanh_data_internal(%rip), %zmm10, %zmm11
vpermt2ps _sP7+64+__svml_stanh_data_internal(%rip), %zmm10, %zmm4
vpermt2ps _sP5+64+__svml_stanh_data_internal(%rip), %zmm10, %zmm12
vpermt2ps _sP4+64+__svml_stanh_data_internal(%rip), %zmm10, %zmm13
vpermt2ps _sP3+64+__svml_stanh_data_internal(%rip), %zmm10, %zmm14
vpermt2ps _sP2+64+__svml_stanh_data_internal(%rip), %zmm10, %zmm15
vpandnd %zmm3, %zmm3, %zmm2{%k1}
vptestmd %zmm2, %zmm2, %k0
vmovups _sP0+__svml_stanh_data_internal(%rip), %zmm3
vsubps {rn-sae}, %zmm9, %zmm8, %zmm2
kmovw %k0, %edx
vfmadd213ps {rn-sae}, %zmm11, %zmm2, %zmm4
vpermt2ps _sP0+64+__svml_stanh_data_internal(%rip), %zmm10, %zmm3
vfmadd213ps {rn-sae}, %zmm12, %zmm2, %zmm4
vfmadd213ps {rn-sae}, %zmm13, %zmm2, %zmm4
vfmadd213ps {rn-sae}, %zmm14, %zmm2, %zmm4
vfmadd213ps {rn-sae}, %zmm15, %zmm2, %zmm4
vfmadd213ps {rn-sae}, %zmm3, %zmm2, %zmm4
vorps %zmm0, %zmm4, %zmm0
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):
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 %zmm1, 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 $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 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
movss 64(%rsp,%r14,4), %xmm0
call tanhf@PLT
# LOE rbx r14 r15 r12d r13d xmm0
movss %xmm0, 128(%rsp,%r14,4)
/* Process special inputs in loop */
jmp L(SPECIAL_VALUES_LOOP)
# LOE rbx r15 r12d r13d
END(_ZGVeN16v_tanhf_skx)
.section .rodata, "a"
.align 64
#ifdef __svml_stanh_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct
{
__declspec(align(64)) VUINT32 _sC[32][1];
__declspec(align(64)) VUINT32 _sP0[32][1];
__declspec(align(64)) VUINT32 _sP2[32][1];
__declspec(align(64)) VUINT32 _sP3[32][1];
__declspec(align(64)) VUINT32 _sP4[32][1];
__declspec(align(64)) VUINT32 _sP5[32][1];
__declspec(align(64)) VUINT32 _sP6[32][1];
__declspec(align(64)) VUINT32 _sP7[32][1];
__declspec(align(64)) VUINT32 _iExpMantMask_UISA[16][1];
__declspec(align(64)) VUINT32 _iMinIdxOfsMask_UISA[16][1];
__declspec(align(64)) VUINT32 _iMaxIdxMask_UISA[16][1];
__declspec(align(64)) VUINT32 _sSignMask[16][1];
__declspec(align(64)) VUINT32 _sAbsMask[16][1];
__declspec(align(64)) VUINT32 _iExpMantMask[16][1];
__declspec(align(64)) VUINT32 _iExpMask[16][1];
__declspec(align(64)) VUINT32 _iMinIdxOfsMask[16][1];
__declspec(align(64)) VUINT32 _iMaxIdxMask[16][1];
} __svml_stanh_data_internal;
#endif
__svml_stanh_data_internal:
/*== _sC ==*/
.long 0x00000000, 0x3d700000, 0x3d900000, 0x3db00000
.long 0x3dd00000, 0x3df00000, 0x3e100000, 0x3e300000
.long 0x3e500000, 0x3e700000, 0x3e900000, 0x3eb00000
.long 0x3ed00000, 0x3ef00000, 0x3f100000, 0x3f300000
.long 0x3f500000, 0x3f700000, 0x3f900000, 0x3fb00000
.long 0x3fd00000, 0x3ff00000, 0x40100000, 0x40300000
.long 0x40500000, 0x40700000, 0x40900000, 0x40b00000
.long 0x40d00000, 0x40f00000, 0x41100000, 0x00000000
/*== p0 ==*/
.align 64
.long 0x00000000, 0x3d6fb9c9, 0x3d8fc35f, 0x3daf9169
.long 0x3dcf49ab, 0x3deee849, 0x3e0f0ee8, 0x3e2e4984
.long 0x3e4d2f8e, 0x3e6bb32e, 0x3e8c51cd, 0x3ea96163
.long 0x3ec543f1, 0x3edfd735, 0x3f028438, 0x3f18abf0
.long 0x3f2bc480, 0x3f3bec1c, 0x3f4f2e5b, 0x3f613c53
.long 0x3f6ce37d, 0x3f743c4f, 0x3f7a5feb, 0x3f7dea85
.long 0x3f7f3b3d, 0x3f7fb78c, 0x3f7fefd4, 0x3f7ffdd0
.long 0x3f7fffb4, 0x3f7ffff6, 0x3f7fffff, 0x3f800000
/*== p2 ==*/
.align 64
.long 0x3f800000, 0x3f7f1f84, 0x3f7ebd11, 0x3f7e1e5f
.long 0x3f7d609f, 0x3f7c842d, 0x3f7b00e5, 0x3f789580
.long 0x3f75b8ad, 0x3f726fd9, 0x3f6cc59b, 0x3f63fb92
.long 0x3f59ff97, 0x3f4f11d7, 0x3f3d7573, 0x3f24f360
.long 0x3f0cbfe7, 0x3eec1a69, 0x3eb0a801, 0x3e6753a2
.long 0x3e132f1a, 0x3db7e7d3, 0x3d320845, 0x3c84d3d4
.long 0x3bc477b7, 0x3b10d3da, 0x3a01601e, 0x388c1a3b
.long 0x3717b0da, 0x35a43bce, 0x338306c6, 0x00000000
/*== p3 ==*/
.align 64
.long 0xb0343c7b, 0xbd6ee69d, 0xbd8f0da7, 0xbdae477d
.long 0xbdcd2a1f, 0xbdeba80d, 0xbe0c443b, 0xbe293cf3
.long 0xbe44f282, 0xbe5f3651, 0xbe81c7c0, 0xbe96d7ca
.long 0xbea7fb8e, 0xbeb50e9e, 0xbec12efe, 0xbec4be92
.long 0xbebce070, 0xbead510e, 0xbe8ef7d6, 0xbe4b8704
.long 0xbe083237, 0xbdaf7449, 0xbd2e1ec4, 0xbc83bf06
.long 0xbbc3e0b5, 0xbb10aadc, 0xba0157db, 0xb88c18f2
.long 0xb717b096, 0xb5a43bae, 0xb383012c, 0x00000000
/*== p4 ==*/
.align 64
.long 0xbeaaaaa5, 0xbeab0612, 0xbea7f01f, 0xbea4e120
.long 0xbea387b7, 0xbea15962, 0xbe9d57f7, 0xbe976b5a
.long 0xbe90230d, 0xbe880dff, 0xbe7479b3, 0xbe4c3d88
.long 0xbe212482, 0xbdeb8cba, 0xbd5e78ad, 0x3c6b5e6e
.long 0x3d839143, 0x3dc21ee1, 0x3de347af, 0x3dcbec96
.long 0x3d99ef2d, 0x3d542ea1, 0x3cdde701, 0x3c2cca67
.long 0x3b81cb27, 0x3ac073a1, 0x39ac3032, 0x383a94d9
.long 0x36ca081d, 0x355abd4c, 0x332b3cb6, 0x00000000
/*== p5 ==*/
.align 64
.long 0xb76dd6b9, 0xbe1c276d, 0x3c1dcf2f, 0x3dc1a78d
.long 0x3d96f985, 0x3da2b61b, 0x3dc13397, 0x3dd2f670
.long 0x3df48a0a, 0x3e06c5a8, 0x3e1a3aba, 0x3e27c405
.long 0x3e2e78d0, 0x3e2c3e44, 0x3e1d3097, 0x3df4a8f4
.long 0x3da38508, 0x3d31416a, 0x3b562657, 0xbcaeeac9
.long 0xbcce9419, 0xbcaaeac4, 0xbc49e7d0, 0xbba71ddd
.long 0xbb003b0e, 0xba3f9a05, 0xb92c08a7, 0xb7ba9232
.long 0xb64a0b0f, 0xb4dac169, 0xb2ab78ac, 0x00000000
/*== p6 ==*/
.align 64
.long 0x3e0910e9, 0x43761143, 0x4165ecdc, 0xc190f756
.long 0xc08c097d, 0xc02ba813, 0xbf7f6bda, 0x3f2b1dc0
.long 0x3ece105d, 0x3f426a94, 0xbadb0dc4, 0x3da43b17
.long 0xbd51ab88, 0xbcaea23d, 0xbd3b6d8d, 0xbd6caaad
.long 0xbd795bed, 0xbd5fddda, 0xbd038f3b, 0xbc1cad63
.long 0x3abb4766, 0x3b95f10b, 0x3b825873, 0x3afaea66
.long 0x3a49f878, 0x39996bf3, 0x388f3e6c, 0x371bb0e3
.long 0x35a8a5e6, 0x34369b17, 0x322487b0, 0x00000000
/*== p7 ==*/
.align 64
.long 0xbc0e2f66, 0x460bda12, 0x43d638ef, 0xc3e11c3e
.long 0xc2baa4e9, 0xc249da2d, 0xc1859b82, 0x40dd5b57
.long 0x40494640, 0x40c730a8, 0xbf0f160e, 0x3e30e76f
.long 0xbea81387, 0xbdb26a1c, 0xbd351e57, 0xbb4c01a0
.long 0x3c1d7bfb, 0x3c722cd1, 0x3c973f1c, 0x3c33a31b
.long 0x3b862ef4, 0x3a27b3d0, 0xba3b5907, 0xba0efc22
.long 0xb97f9f0f, 0xb8c8af50, 0xb7bdddfb, 0xb64f2950
.long 0xb4e085b1, 0xb3731dfa, 0xb15a1f04, 0x00000000
.align 64
.long 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000, 0x7fe00000 /* _iExpMantMask_UISA */
.align 64
.long 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000, 0x3d400000 /* _iMinIdxOfsMask_UISA */
.align 64
.long 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000, 0x03e00000 /* _iMaxIdxMask_UISA */
.align 64
.long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000 /* _sSignMask */
.align 64
.long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff /* _sAbsMask */
.align 64
.long 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000, 0x7ff80000 /* _iExpMantMask */
.align 64
.long 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000, 0x7f000000 /* _iExpMask */
.align 64
.long 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000, 0x3cf80000 /* _iMinIdxOfsMask */
.align 64
.long 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000, 0x04280000 /* _iMaxIdxMask */
.align 64
.type __svml_stanh_data_internal,@object
.size __svml_stanh_data_internal,.-__svml_stanh_data_internal
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