/* Function asinhf vectorized with AVX2.
   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:
 *
 *   Compute asinh(x) as log(x + sqrt(x*x + 1))
 *
 *   Special cases:
 *
 *   asinh(NaN) = quiet NaN, and raise invalid exception
 *   asinh(INF) = that INF
 *   asinh(0)   = that 0
 *
 */

/* Offsets for data table __svml_sasinh_data_internal
 */
#define SgnMask                       	0
#define sOne                          	32
#define sPoly                         	64
#define iBrkValue                     	320
#define iOffExpoMask                  	352
#define sBigThreshold                 	384
#define sC2                           	416
#define sC3                           	448
#define sHalf                         	480
#define sLargestFinite                	512
#define sLittleThreshold              	544
#define sSign                         	576
#define sThirtyOne                    	608
#define sTopMask8                     	640
#define XScale                        	672
#define sLn2                          	704

#include <sysdep.h>

        .text
	.section .text.avx2,"ax",@progbits
ENTRY(_ZGVdN8v_asinhf_avx2)
        pushq     %rbp
        cfi_def_cfa_offset(16)
        movq      %rsp, %rbp
        cfi_def_cfa(6, 16)
        cfi_offset(6, -16)
        andq      $-32, %rsp
        subq      $96, %rsp
        vmovaps   %ymm0, %ymm9

/* Load the constant 1 and a sign mask */
        vmovups   sOne+__svml_sasinh_data_internal(%rip), %ymm8

/* No need to split X when FMA is available in hardware. */
        vmulps    %ymm9, %ymm9, %ymm5
        vmovups   sTopMask8+__svml_sasinh_data_internal(%rip), %ymm1

/*
 * Finally, express Y + W = X^2 + 1 accurately where Y has <= 8 bits.
 * If |X| <= 1 then |XHi| <= 1 and so |X2Hi| <= 1, so we can treat 1
 * as the dominant component in the compensated summation. Otherwise,
 * if |X| >= 1, then since X2Hi only has 22 significant bits, the basic
 * addition will be exact anyway until we get to |X| >= 2^24. But by
 * that time the log function is well-conditioned enough that the
 * rounding error doesn't matter. Hence we can treat 1 as dominant even
 * if it literally isn't.
 */
        vaddps    %ymm5, %ymm8, %ymm13
        vandps    %ymm1, %ymm13, %ymm2
        vmovaps   %ymm9, %ymm4
        vsubps    %ymm13, %ymm8, %ymm11
        vsubps    %ymm2, %ymm13, %ymm15

/*
 * Compute R = 1/sqrt(Y + W) * (1 + d)
 * Force R to <= 8 significant bits.
 * This means that R * Y and R^2 * Y are exactly representable.
 */
        vrsqrtps  %ymm2, %ymm0
        vfmsub213ps %ymm5, %ymm9, %ymm4
        vaddps    %ymm11, %ymm5, %ymm12

/*
 * Get the absolute value of the input, since we will exploit antisymmetry
 * and mostly assume X >= 0 in the core computation
 */
        vandps    SgnMask+__svml_sasinh_data_internal(%rip), %ymm9, %ymm6

/*
 * Check whether the input is finite, by checking |X| <= MaxFloat
 * Otherwise set the rangemask so that the callout will get used.
 * Note that this will also use the callout for NaNs since not(NaN <= MaxFloat)
 */
        vcmpnle_uqps sLargestFinite+__svml_sasinh_data_internal(%rip), %ymm6, %ymm10
        vaddps    %ymm12, %ymm4, %ymm14

/*
 * Unfortunately, we can still be in trouble if |X| <= 2^-5, since
 * the absolute error 2^-(7+24)-ish in sqrt(1 + X^2) gets scaled up
 * by 1/X and comes close to our threshold. Hence if |X| <= 2^-4,
 * perform an alternative computation
 * sqrt(1 + X^2) - 1 = X^2/2 - X^4/8 + X^6/16
 * X2 = X^2
 */
        vaddps    %ymm4, %ymm5, %ymm4

/*
 * The following computation can go wrong for very large X, basically
 * because X^2 overflows. But for large X we have
 * asinh(X) / log(2 X) - 1 =~= 1/(4 * X^2), so for X >= 2^30
 * we can just later stick X back into the log and tweak up the exponent.
 * Actually we scale X by 2^-30 and tweak the exponent up by 31,
 * to stay in the safe range for the later log computation.
 * Compute a flag now telling us when do do this.
 */
        vcmplt_oqps sBigThreshold+__svml_sasinh_data_internal(%rip), %ymm6, %ymm7
        vaddps    %ymm15, %ymm14, %ymm3

/*
 * Now       1 / (1 + d)
 * = 1 / (1 + (sqrt(1 - e) - 1))
 * = 1 / sqrt(1 - e)
 * = 1 + 1/2 * e + 3/8 * e^2 + 5/16 * e^3 + 35/128 * e^4 + ...
 * So compute the first three nonconstant terms of that, so that
 * we have a relative correction (1 + Corr) to apply to S etc.
 * C1 = 1/2
 * C2 = 3/8
 * C3 = 5/16
 */
        vmovups   sC3+__svml_sasinh_data_internal(%rip), %ymm12
        vmovmskps %ymm10, %edx
        vandps    %ymm1, %ymm0, %ymm10

/*
 * Compute S = (Y/sqrt(Y + W)) * (1 + d)
 * and T = (W/sqrt(Y + W)) * (1 + d)
 * so that S + T = sqrt(Y + W) * (1 + d)
 * S is exact, and the rounding error in T is OK.
 */
        vmulps    %ymm10, %ymm2, %ymm15
        vmulps    %ymm3, %ymm10, %ymm14
        vmovups   sHalf+__svml_sasinh_data_internal(%rip), %ymm3
        vsubps    %ymm8, %ymm15, %ymm0

/*
 * Obtain sqrt(1 + X^2) - 1 in two pieces
 * sqrt(1 + X^2) - 1
 * = sqrt(Y + W) - 1
 * = (S + T) * (1 + Corr) - 1
 * = [S - 1] + [T + (S + T) * Corr]
 * We need a compensated summation for the last part. We treat S - 1
 * as the larger part; it certainly is until about X < 2^-4, and in that
 * case, the error is affordable since X dominates over sqrt(1 + X^2) - 1
 * Final sum is dTmp5 (hi) + dTmp7 (lo)
 */
        vaddps    %ymm14, %ymm15, %ymm13

/*
 * Compute e = -(2 * d + d^2)
 * The first FMR is exact, and the rounding error in the other is acceptable
 * since d and e are ~ 2^-8
 */
        vmovaps   %ymm8, %ymm11
        vfnmadd231ps %ymm15, %ymm10, %ymm11
        vfnmadd231ps %ymm14, %ymm10, %ymm11
        vfmadd213ps sC2+__svml_sasinh_data_internal(%rip), %ymm11, %ymm12
        vfmadd213ps %ymm3, %ymm11, %ymm12
        vmulps    %ymm12, %ymm11, %ymm1

/* Now multiplex the two possible computations */
        vcmple_oqps sLittleThreshold+__svml_sasinh_data_internal(%rip), %ymm6, %ymm11
        vfmadd213ps %ymm14, %ymm13, %ymm1
        vaddps    %ymm0, %ymm1, %ymm2
        vsubps    %ymm2, %ymm0, %ymm10

/* sX2over2 = X^2/2 */
        vmulps    %ymm4, %ymm3, %ymm0
        vaddps    %ymm10, %ymm1, %ymm1

/* sX4over4 = X^4/4 */
        vmulps    %ymm0, %ymm0, %ymm5

/* sX46 = -X^4/4 + X^6/8 */
        vfmsub231ps %ymm0, %ymm5, %ymm5

/* sX46over2 = -X^4/8 + x^6/16 */
        vmulps    %ymm5, %ymm3, %ymm3
        vaddps    %ymm3, %ymm0, %ymm5
        vblendvps %ymm11, %ymm5, %ymm2, %ymm2
        vsubps    %ymm5, %ymm0, %ymm4

/*
 * Now do another compensated sum to add |X| + [sqrt(1 + X^2) - 1].
 * It's always safe to assume |X| is larger.
 * This is the final 2-part argument to the log1p function
 */
        vaddps    %ymm2, %ymm6, %ymm14

/*
 * Now resume the main code.
 * reduction: compute r,n
 */
        vmovups   iBrkValue+__svml_sasinh_data_internal(%rip), %ymm5
        vaddps    %ymm4, %ymm3, %ymm10

/*
 * Now we feed into the log1p code, using H in place of _VARG1 and
 * also adding L into Xl.
 * compute 1+x as high, low parts
 */
        vmaxps    %ymm14, %ymm8, %ymm15
        vminps    %ymm14, %ymm8, %ymm0
        vblendvps %ymm11, %ymm10, %ymm1, %ymm12
        vsubps    %ymm14, %ymm6, %ymm1
        vaddps    %ymm0, %ymm15, %ymm3

/* Now multiplex to the case X = 2^-30 * input, Xl = sL = 0 in the "big" case. */
        vmulps    XScale+__svml_sasinh_data_internal(%rip), %ymm6, %ymm6
        vaddps    %ymm1, %ymm2, %ymm13
        vsubps    %ymm3, %ymm15, %ymm15
        vaddps    %ymm13, %ymm12, %ymm1
        vaddps    %ymm15, %ymm0, %ymm2
        vblendvps %ymm7, %ymm3, %ymm6, %ymm0
        vaddps    %ymm2, %ymm1, %ymm4
        vpsubd    %ymm5, %ymm0, %ymm1
        vpsrad    $23, %ymm1, %ymm6
        vpand     iOffExpoMask+__svml_sasinh_data_internal(%rip), %ymm1, %ymm2
        vmovups   sPoly+224+__svml_sasinh_data_internal(%rip), %ymm1
        vpslld    $23, %ymm6, %ymm10
        vpaddd    %ymm5, %ymm2, %ymm13
        vcvtdq2ps %ymm6, %ymm0
        vpsubd    %ymm10, %ymm8, %ymm12

/* polynomial evaluation */
        vsubps    %ymm8, %ymm13, %ymm8

/* Add 31 to the exponent in the "large" case to get log(2 * input) */
        vaddps    sThirtyOne+__svml_sasinh_data_internal(%rip), %ymm0, %ymm3
        vandps    %ymm7, %ymm4, %ymm11
        vmulps    %ymm12, %ymm11, %ymm14
        vblendvps %ymm7, %ymm0, %ymm3, %ymm0
        vaddps    %ymm8, %ymm14, %ymm2
        vfmadd213ps sPoly+192+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
        vfmadd213ps sPoly+160+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
        vfmadd213ps sPoly+128+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
        vfmadd213ps sPoly+96+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
        vfmadd213ps sPoly+64+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
        vfmadd213ps sPoly+32+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
        vfmadd213ps sPoly+__svml_sasinh_data_internal(%rip), %ymm2, %ymm1
        vmulps    %ymm1, %ymm2, %ymm4
        vfmadd213ps %ymm2, %ymm2, %ymm4

/* final reconstruction */
        vfmadd132ps sLn2+__svml_sasinh_data_internal(%rip), %ymm4, %ymm0

/* Finally, reincorporate the original sign. */
        vandps    sSign+__svml_sasinh_data_internal(%rip), %ymm9, %ymm7
        vxorps    %ymm0, %ymm7, %ymm0
        testl     %edx, %edx

/* Go to special inputs processing branch */
        jne       L(SPECIAL_VALUES_BRANCH)
                                # LOE rbx r12 r13 r14 r15 edx ymm0 ymm9

/* 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   %ymm9, 32(%rsp)
        vmovups   %ymm0, 64(%rsp)
                                # LOE rbx r12 r13 r14 r15 edx ymm0

        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: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus)  */
        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 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: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus)  */
        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
        movl      %edx, %r13d
        movq      %r14, (%rsp)
        /*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus)  */
        .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 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   64(%rsp), %ymm0

/* Go to exit */
        jmp       L(EXIT)
        /*  DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -80; DW_OP_plus)  */
        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
        /*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -88; DW_OP_plus)  */
        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa8, 0xff, 0xff, 0xff, 0x22
        /*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -96; DW_OP_plus)  */
        .cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
                                # LOE rbx r12 r13 r14 r15 ymm0

/* Scalar math fucntion call
 * to process special input
 */

L(SCALAR_MATH_CALL):
        movl      %r12d, %r14d
        movss     32(%rsp,%r14,4), %xmm0
        call      asinhf@PLT
                                # LOE rbx r14 r15 r12d r13d xmm0

        movss     %xmm0, 64(%rsp,%r14,4)

/* Process special inputs in loop */
        jmp       L(SPECIAL_VALUES_LOOP)
                                # LOE rbx r15 r12d r13d
END(_ZGVdN8v_asinhf_avx2)

        .section .rodata, "a"
        .align 32

#ifdef __svml_sasinh_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
        __declspec(align(32)) VUINT32 SgnMask[8][1];
        __declspec(align(32)) VUINT32 sOne[8][1];
        __declspec(align(32)) VUINT32 sPoly[8][8][1];
        __declspec(align(32)) VUINT32 iBrkValue[8][1];
        __declspec(align(32)) VUINT32 iOffExpoMask[8][1];
        __declspec(align(32)) VUINT32 sBigThreshold[8][1];
        __declspec(align(32)) VUINT32 sC2[8][1];
        __declspec(align(32)) VUINT32 sC3[8][1];
        __declspec(align(32)) VUINT32 sHalf[8][1];
        __declspec(align(32)) VUINT32 sLargestFinite[8][1];
        __declspec(align(32)) VUINT32 sLittleThreshold[8][1];
        __declspec(align(32)) VUINT32 sSign[8][1];
        __declspec(align(32)) VUINT32 sThirtyOne[8][1];
        __declspec(align(32)) VUINT32 sTopMask8[8][1];
        __declspec(align(32)) VUINT32 XScale[8][1];
        __declspec(align(32)) VUINT32 sLn2[8][1];
} __svml_sasinh_data_internal;
#endif
__svml_sasinh_data_internal:
        /*== SgnMask ==*/
        .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
        /*== sOne = SP 1.0 ==*/
        .align 32
        .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
        /*== sPoly[] = SP polynomial ==*/
        .align 32
        .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
        .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /*  3.3333265781402587890625000e-01 P1 */
        .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
        .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /*  2.0007920265197753906250000e-01 P3 */
        .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
        .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /*  1.4042308926582336425781250e-01 P5 */
        .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
        .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /*  1.3820238411426544189453125e-01 P7 */
        /*== iBrkValue = SP 2/3 ==*/
        .align 32
        .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
        /*== iOffExpoMask = SP significand mask ==*/
        .align 32
        .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
        /*== sBigThreshold ==*/
        .align 32
        .long 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000
        /*== sC2 ==*/
        .align 32
        .long 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000
        /*== sC3 ==*/
        .align 32
        .long 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000
        /*== sHalf ==*/
        .align 32
        .long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
        /*== sLargestFinite ==*/
        .align 32
        .long 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF
        /*== sLittleThreshold ==*/
        .align 32
        .long 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000
        /*== sSign ==*/
        .align 32
        .long 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000, 0x80000000
        /*== sThirtyOne ==*/
        .align 32
        .long 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000
        /*== sTopMask8 ==*/
        .align 32
        .long 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000
        /*== XScale ==*/
        .align 32
        .long 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000, 0x30800000
        /*== sLn2 = SP ln(2) ==*/
        .align 32
        .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
        .align 32
        .type	__svml_sasinh_data_internal,@object
        .size	__svml_sasinh_data_internal,.-__svml_sasinh_data_internal
