path: root/sysdeps/x86_64/fpu/multiarch/svml_s_asinhf4_core_sse4.S

/* Function asinhf 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:
 *
 *   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                          	16
#define sPoly                         	32
#define iBrkValue                     	160
#define iOffExpoMask                  	176
#define sBigThreshold                 	192
#define sC2                           	208
#define sC3                           	224
#define sHalf                         	240
#define sLargestFinite                	256
#define sLittleThreshold              	272
#define sSign                         	288
#define sThirtyOne                    	304
#define sTopMask11                    	320
#define sTopMask8                     	336
#define XScale                        	352
#define sLn2                          	368

#include <sysdep.h>

        .text
	.section .text.sse4,"ax",@progbits
ENTRY(_ZGVbN4v_asinhf_sse4)
        subq      $72, %rsp
        cfi_def_cfa_offset(80)
        movaps    %xmm0, %xmm8

/*
 * Split X into high and low parts, XHi (<= 11 bits) and XLo (<= 13 bits)
 * We could use either X or |X| here, but it doesn't seem to matter
 */
        movups    sTopMask11+__svml_sasinh_data_internal(%rip), %xmm10
        movaps    %xmm8, %xmm2
        andps     %xmm8, %xmm10

/*
 * Compute X^2 = (XHi + XLo)^2 = XHi^2 + XLo * (X + XHi)
 * The two parts are shifted off by around 11 bits. So even though
 * the low bit will not in general be exact, it's near enough
 */
        movaps    %xmm10, %xmm3
        subps     %xmm10, %xmm2
        mulps     %xmm10, %xmm3
        addps     %xmm8, %xmm10

/* Load the constant 1 and a sign mask */
        movups    sOne+__svml_sasinh_data_internal(%rip), %xmm7

/*
 * 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.
 */
        movaps    %xmm7, %xmm11
        movaps    %xmm7, %xmm4
        movups    sTopMask8+__svml_sasinh_data_internal(%rip), %xmm12
        addps     %xmm3, %xmm11
        mulps     %xmm10, %xmm2
        subps     %xmm11, %xmm4
        movaps    %xmm12, %xmm0
        addps     %xmm3, %xmm4

/*
 * 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
 */
        addps     %xmm2, %xmm3
        addps     %xmm2, %xmm4
        andps     %xmm11, %xmm0

/*
 * 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.
 */
        rsqrtps   %xmm0, %xmm14
        subps     %xmm0, %xmm11
        andps     %xmm12, %xmm14
        addps     %xmm11, %xmm4

/*
 * 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.
 */
        mulps     %xmm14, %xmm0
        mulps     %xmm14, %xmm4

/*
 * Get the absolute value of the input, since we will exploit antisymmetry
 * and mostly assume X >= 0 in the core computation
 */
        movups    SgnMask+__svml_sasinh_data_internal(%rip), %xmm6

/*
 * 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
 */
        movaps    %xmm14, %xmm13
        andps     %xmm8, %xmm6

/*
 * 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)
 */
        movaps    %xmm0, %xmm1

/*
 * 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)
 */
        movaps    %xmm6, %xmm9

/*
 * 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.
 */
        movaps    %xmm6, %xmm5
        cmpnleps  sLargestFinite+__svml_sasinh_data_internal(%rip), %xmm9
        cmpltps   sBigThreshold+__svml_sasinh_data_internal(%rip), %xmm5
        mulps     %xmm0, %xmm13
        addps     %xmm4, %xmm1
        subps     %xmm7, %xmm0
        mulps     %xmm4, %xmm14
        movmskps  %xmm9, %edx
        movaps    %xmm7, %xmm9

/*
 * 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
 */
        movups    sC3+__svml_sasinh_data_internal(%rip), %xmm15
        subps     %xmm13, %xmm9
        movups    sHalf+__svml_sasinh_data_internal(%rip), %xmm10
        subps     %xmm14, %xmm9

/* sX2over2 = X^2/2 */
        mulps     %xmm10, %xmm3
        mulps     %xmm9, %xmm15

/* sX46 = -X^4/4 + X^6/8 */
        movaps    %xmm3, %xmm2
        movaps    %xmm3, %xmm12

/*
 * 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
 */
        movaps    %xmm6, %xmm14
        addps     sC2+__svml_sasinh_data_internal(%rip), %xmm15
        mulps     %xmm9, %xmm15
        addps     %xmm10, %xmm15
        mulps     %xmm15, %xmm9
        mulps     %xmm1, %xmm9

/* Now multiplex to the case X = 2^-30 * input, Xl = sL = 0 in the "big" case. */
        movups    XScale+__svml_sasinh_data_internal(%rip), %xmm15
        addps     %xmm9, %xmm4
        movaps    %xmm4, %xmm11
        addps     %xmm0, %xmm11
        subps     %xmm11, %xmm0
        addps     %xmm0, %xmm4

/* sX4over4 = X^4/4 */
        movaps    %xmm3, %xmm0
        mulps     %xmm3, %xmm0
        mulps     %xmm0, %xmm2
        subps     %xmm0, %xmm2

/*
 * 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
 */
        movaps    %xmm7, %xmm0

/* sX46over2 = -X^4/8 + x^6/16 */
        mulps     %xmm2, %xmm10
        movaps    %xmm7, %xmm2
        addps     %xmm10, %xmm12
        subps     %xmm12, %xmm3
        addps     %xmm3, %xmm10

/* Now multiplex the two possible computations */
        movaps    %xmm6, %xmm3
        cmpleps   sLittleThreshold+__svml_sasinh_data_internal(%rip), %xmm3
        movaps    %xmm3, %xmm13
        andps     %xmm3, %xmm12
        andnps    %xmm11, %xmm13
        movaps    %xmm3, %xmm1
        orps      %xmm12, %xmm13
        andnps    %xmm4, %xmm1
        andps     %xmm3, %xmm10
        movaps    %xmm6, %xmm4
        orps      %xmm10, %xmm1
        addps     %xmm13, %xmm14
        mulps     %xmm15, %xmm6
        maxps     %xmm14, %xmm0
        minps     %xmm14, %xmm2
        subps     %xmm14, %xmm4
        movaps    %xmm0, %xmm3
        addps     %xmm4, %xmm13
        addps     %xmm2, %xmm3
        addps     %xmm13, %xmm1
        subps     %xmm3, %xmm0
        movaps    %xmm5, %xmm4
        andps     %xmm5, %xmm3
        andnps    %xmm6, %xmm4
        addps     %xmm0, %xmm2

/*
 * Now resume the main code.
 * reduction: compute r,n
 */
        movdqu    iBrkValue+__svml_sasinh_data_internal(%rip), %xmm6
        orps      %xmm3, %xmm4
        psubd     %xmm6, %xmm4
        movaps    %xmm7, %xmm0
        addps     %xmm2, %xmm1
        movdqu    iOffExpoMask+__svml_sasinh_data_internal(%rip), %xmm2
        pand      %xmm4, %xmm2
        psrad     $23, %xmm4
        cvtdq2ps  %xmm4, %xmm3
        pslld     $23, %xmm4
        andps     %xmm5, %xmm1
        paddd     %xmm6, %xmm2
        psubd     %xmm4, %xmm0
        mulps     %xmm0, %xmm1

/* polynomial evaluation */
        subps     %xmm7, %xmm2
        movups    sPoly+112+__svml_sasinh_data_internal(%rip), %xmm7
        addps     %xmm2, %xmm1
        mulps     %xmm1, %xmm7
        movaps    %xmm5, %xmm2

/* Add 31 to the exponent in the "large" case to get log(2 * input) */
        movups    sThirtyOne+__svml_sasinh_data_internal(%rip), %xmm0
        addps     sPoly+96+__svml_sasinh_data_internal(%rip), %xmm7
        addps     %xmm3, %xmm0
        mulps     %xmm1, %xmm7
        andnps    %xmm0, %xmm2
        andps     %xmm5, %xmm3
        orps      %xmm3, %xmm2
        addps     sPoly+80+__svml_sasinh_data_internal(%rip), %xmm7

/* final reconstruction */
        mulps     sLn2+__svml_sasinh_data_internal(%rip), %xmm2
        mulps     %xmm1, %xmm7

/* Finally, reincorporate the original sign. */
        movups    sSign+__svml_sasinh_data_internal(%rip), %xmm0
        andps     %xmm8, %xmm0
        addps     sPoly+64+__svml_sasinh_data_internal(%rip), %xmm7
        mulps     %xmm1, %xmm7
        addps     sPoly+48+__svml_sasinh_data_internal(%rip), %xmm7
        mulps     %xmm1, %xmm7
        addps     sPoly+32+__svml_sasinh_data_internal(%rip), %xmm7
        mulps     %xmm1, %xmm7
        addps     sPoly+16+__svml_sasinh_data_internal(%rip), %xmm7
        mulps     %xmm1, %xmm7
        addps     sPoly+__svml_sasinh_data_internal(%rip), %xmm7
        mulps     %xmm1, %xmm7
        mulps     %xmm1, %xmm7
        addps     %xmm7, %xmm1
        addps     %xmm2, %xmm1
        pxor      %xmm1, %xmm0
        testl     %edx, %edx

/* Go to special inputs processing branch */
        jne       L(SPECIAL_VALUES_BRANCH)
                                # LOE rbx rbp r12 r13 r14 r15 edx xmm0 xmm8

/* Restore registers
 * and exit the function
 */

L(EXIT):
        addq      $72, %rsp
        cfi_def_cfa_offset(8)
        ret
        cfi_def_cfa_offset(80)

/* Branch to process
 * special inputs
 */

L(SPECIAL_VALUES_BRANCH):
        movups    %xmm8, 32(%rsp)
        movups    %xmm0, 48(%rsp)
                                # LOE rbx rbp r12 r13 r14 r15 edx

        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      $4, %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), %xmm0

/* 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 xmm0

/* 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 rbp r14 r15 r12d r13d xmm0

        movss     %xmm0, 48(%rsp,%r14,4)

/* Process special inputs in loop */
        jmp       L(SPECIAL_VALUES_LOOP)
                                # LOE rbx rbp r15 r12d r13d
END(_ZGVbN4v_asinhf_sse4)

        .section .rodata, "a"
        .align 16

#ifdef __svml_sasinh_data_internal_typedef
typedef unsigned int VUINT32;
typedef struct {
        __declspec(align(16)) VUINT32 SgnMask[4][1];
        __declspec(align(16)) VUINT32 sOne[4][1];
        __declspec(align(16)) VUINT32 sPoly[8][4][1];
        __declspec(align(16)) VUINT32 iBrkValue[4][1];
        __declspec(align(16)) VUINT32 iOffExpoMask[4][1];
        __declspec(align(16)) VUINT32 sBigThreshold[4][1];
        __declspec(align(16)) VUINT32 sC2[4][1];
        __declspec(align(16)) VUINT32 sC3[4][1];
        __declspec(align(16)) VUINT32 sHalf[4][1];
        __declspec(align(16)) VUINT32 sLargestFinite[4][1];
        __declspec(align(16)) VUINT32 sLittleThreshold[4][1];
        __declspec(align(16)) VUINT32 sSign[4][1];
        __declspec(align(16)) VUINT32 sThirtyOne[4][1];
        __declspec(align(16)) VUINT32 sTopMask11[4][1];
        __declspec(align(16)) VUINT32 sTopMask8[4][1];
        __declspec(align(16)) VUINT32 XScale[4][1];
        __declspec(align(16)) VUINT32 sLn2[4][1];
} __svml_sasinh_data_internal;
#endif
__svml_sasinh_data_internal:
        /*== SgnMask ==*/
        .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff
        /*== sOne = SP 1.0 ==*/
        .align 16
        .long 0x3f800000, 0x3f800000, 0x3f800000, 0x3f800000
        /*== sPoly[] = SP polynomial ==*/
        .align 16
        .long 0xbf000000, 0xbf000000, 0xbf000000, 0xbf000000 /* -5.0000000000000000000000000e-01 P0 */
        .long 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94, 0x3eaaaa94 /*  3.3333265781402587890625000e-01 P1 */
        .long 0xbe80058e, 0xbe80058e, 0xbe80058e, 0xbe80058e /* -2.5004237890243530273437500e-01 P2 */
        .long 0x3e4ce190, 0x3e4ce190, 0x3e4ce190, 0x3e4ce190 /*  2.0007920265197753906250000e-01 P3 */
        .long 0xbe28ad37, 0xbe28ad37, 0xbe28ad37, 0xbe28ad37 /* -1.6472326219081878662109375e-01 P4 */
        .long 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12, 0x3e0fcb12 /*  1.4042308926582336425781250e-01 P5 */
        .long 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3, 0xbe1ad9e3 /* -1.5122179687023162841796875e-01 P6 */
        .long 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed, 0x3e0d84ed /*  1.3820238411426544189453125e-01 P7 */
        /*== iBrkValue = SP 2/3 ==*/
        .align 16
        .long 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab, 0x3f2aaaab
        /*== iOffExpoMask = SP significand mask ==*/
        .align 16
        .long 0x007fffff, 0x007fffff, 0x007fffff, 0x007fffff
        /*== sBigThreshold ==*/
        .align 16
        .long 0x4E800000, 0x4E800000, 0x4E800000, 0x4E800000
        /*== sC2 ==*/
        .align 16
        .long 0x3EC00000, 0x3EC00000, 0x3EC00000, 0x3EC00000
        /*== sC3 ==*/
        .align 16
        .long 0x3EA00000, 0x3EA00000, 0x3EA00000, 0x3EA00000
        /*== sHalf ==*/
        .align 16
        .long 0x3F000000, 0x3F000000, 0x3F000000, 0x3F000000
        /*== sLargestFinite ==*/
        .align 16
        .long 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF
        /*== sLittleThreshold ==*/
        .align 16
        .long 0x3D800000, 0x3D800000, 0x3D800000, 0x3D800000
        /*== sSign ==*/
        .align 16
        .long 0x80000000, 0x80000000, 0x80000000, 0x80000000
        /*== sThirtyOne ==*/
        .align 16
        .long 0x41F80000, 0x41F80000, 0x41F80000, 0x41F80000
        /*== sTopMask11 ==*/
        .align 16
        .long 0xFFFFE000, 0xFFFFE000, 0xFFFFE000, 0xFFFFE000
        /*== sTopMask8 ==*/
        .align 16
        .long 0xFFFF0000, 0xFFFF0000, 0xFFFF0000, 0xFFFF0000
        /*== XScale ==*/
        .align 16
        .long 0x30800000, 0x30800000, 0x30800000, 0x30800000
        /*== sLn2 = SP ln(2) ==*/
        .align 16
        .long 0x3f317218, 0x3f317218, 0x3f317218, 0x3f317218
        .align 16
        .type	__svml_sasinh_data_internal,@object
        .size	__svml_sasinh_data_internal,.-__svml_sasinh_data_internal