asinhd2.h

Newlib 嵌入式 C库 标准实现代码

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/* PROLOG END TAG zYx                                              */
#ifdef __SPU__
#ifndef _ASINHD2_H_
#define _ASINHD2_H_	1

#include <spu_intrinsics.h>

#include "logd2.h"
#include "sqrtd2.h"

/*
 * FUNCTION
 *  vector double _asinhd2(vector double x)
 *
 * DESCRIPTION
 *  The asinhd2 function returns a vector containing the hyperbolic
 *  arcsines of the corresponding elements of the input vector.
 *
 *  We are using the formula:
 *    asinh = ln(|x| + sqrt(x^2 + 1))
 *  and the anti-symmetry of asinh.
 *
 *  For x near zero, we use the Taylor series:
 *
 *                infinity
 *                 ------
 *                  -   '  P  (0)
 *                   -      k-1    k
 *    asinh x =       -    -----  x
 *                   -       k
 *                  -   ,
 *                 ------
 *                 k = 1
 *
 *  Special Cases:
 *    asinh(+0)        returns +0
 *    asinh(-0)        returns -0
 *    asinh(+infinity) returns +infinity
 *    asinh(-infinity) returns -infinity
 *    asinh(NaN)       returns NaN
 *
 */

/*
 * Maclaurin Series Coefficients 
 * for x near 0.
 */
#define ASINH_MAC01     1.0000000000000000000000000000000000000000000000000000000000000000000000E0
#define ASINH_MAC03     -1.6666666666666666666666666666666666666666666666666666666666666666666667E-1
#define ASINH_MAC05     7.5000000000000000000000000000000000000000000000000000000000000000000000E-2
#define ASINH_MAC07     -4.4642857142857142857142857142857142857142857142857142857142857142857143E-2
#define ASINH_MAC09     3.0381944444444444444444444444444444444444444444444444444444444444444444E-2
#define ASINH_MAC11     -2.2372159090909090909090909090909090909090909090909090909090909090909091E-2
#define ASINH_MAC13     1.7352764423076923076923076923076923076923076923076923076923076923076923E-2
#define ASINH_MAC15     -1.3964843750000000000000000000000000000000000000000000000000000000000000E-2
#define ASINH_MAC17     1.1551800896139705882352941176470588235294117647058823529411764705882353E-2
#if 0
#define ASINH_MAC19     -9.7616095291940789473684210526315789473684210526315789473684210526315789E-3
#define ASINH_MAC21     8.3903358096168154761904761904761904761904761904761904761904761904761905E-3
#define ASINH_MAC23     -7.3125258735988451086956521739130434782608695652173913043478260869565217E-3
#define ASINH_MAC25     6.4472103118896484375000000000000000000000000000000000000000000000000000E-3
#define ASINH_MAC27     -5.7400376708419234664351851851851851851851851851851851851851851851851852E-3
#define ASINH_MAC29     5.1533096823199041958512931034482758620689655172413793103448275862068966E-3
#define ASINH_MAC31     -4.6601434869150961599042338709677419354838709677419354838709677419354839E-3
#define ASINH_MAC33     4.2409070936793630773370916193181818181818181818181818181818181818181818E-3
#define ASINH_MAC35     -3.8809645588376692363194056919642857142857142857142857142857142857142857E-3
#define ASINH_MAC37     3.5692053938259345454138678473395270270270270270270270270270270270270270E-3
#define ASINH_MAC39     -3.2970595034734847453924325796274038461538461538461538461538461538461538E-3
#define ASINH_MAC41     3.0578216492580306693548109473251714939024390243902439024390243902439024E-3
#define ASINH_MAC43     -2.8461784011089421678767647854117460029069767441860465116279069767441860E-3
#endif


static __inline vector double _asinhd2(vector double x)
{
    vec_double2 sign_mask = spu_splats(-0.0);
    vec_double2 oned      = spu_splats(1.0);
    vec_uchar16 dup_even  = ((vec_uchar16) { 0,1,2,3,  0,1,2,3, 8,9,10,11, 8,9,10,11 });
    vec_uint4   infminus1 = spu_splats(0x7FEFFFFFU);
    vec_uint4   isinfnan;
    vec_double2 xabs, xsqu;
    vec_uint4   xabshigh;
    /* Where we switch from maclaurin to formula */
    vec_float4  switch_approx = spu_splats(0.165f);
    vec_uint4   use_form;
    vec_float4  xf;
    vec_double2 result, fresult, mresult;


    xabs = spu_andc(x, sign_mask);
    xsqu = spu_mul(x, x);

    xf = spu_roundtf(xabs);
    xf = spu_shuffle(xf, xf, dup_even);

    /*
     * Formula:
     *   asinh = ln(|x| + sqrt(x^2 + 1))
     */
    fresult = _sqrtd2(spu_add(xsqu, oned));
    fresult = spu_add(xabs, fresult);
    fresult = _logd2(fresult);


    /*
     * Maclaurin Series approximation
     */
    mresult = spu_madd(xsqu, spu_splats(ASINH_MAC17), spu_splats(ASINH_MAC15));
    mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC13));
    mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC11));
    mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC09));
    mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC07));
    mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC05));
    mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC03));
    mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC01));
    mresult = spu_mul(xabs, mresult);


    /*
     * Choose between series and formula
     */
    use_form = spu_cmpgt(xf, switch_approx);
    result = spu_sel(mresult, fresult, (vec_ullong2)use_form);


    /* Special Cases */

    /* Infinity and NaN */
    xabshigh = (vec_uint4)spu_shuffle(xabs, xabs, dup_even);
    isinfnan = spu_cmpgt(xabshigh, infminus1);
    result = spu_sel(result, x, (vec_ullong2)isinfnan);


    /* Restore sign - asinh is an anti-symmetric */
    result = spu_sel(result, x, (vec_ullong2)sign_mask);

    return result;
}

#endif /* _ASINHD2_H_ */
#endif /* __SPU__ */