atanhf4.h

Newlib 嵌入式 C库 标准实现代码

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/* PROLOG END TAG zYx                                              */
#ifdef __SPU__
#ifndef _ATANHF4_H_
#define _ATANHF4_H_	1

#include <spu_intrinsics.h>
#include "logf4.h"

/*
 * FUNCTION
 *  vector float _atanhf4(vector float x)
 *
 * DESCRIPTION
 *  The atanhf4 function returns a vector containing the hyperbolic
 *  arctangents of the corresponding elements of the input vector.
 *
 *  We are using the formula:
 *    atanh x = 1/2 * ln((1 + x)/(1 - x)) = 1/2 * [ln(1+x) - ln(1-x)]
 *  and the anti-symmetry of atanh.
 *
 *  For x near 0, we use the Taylor series:
 *    atanh x = x + x^3/3 + x^5/5 + x^7/7 + x^9/9 + ...
 *
 *  Special Cases:
 *  - atanh(1)  =  HUGE_VALF
 *  - atanh(-1) = -HUGE_VALF
 *	- The result is undefined for x outside of the domain [-1,1],
 *	  since single-precision NaN is not supported on the SPU.
 *
 */

/*
 * Maclaurin Series Coefficients 
 * for x near 0.
 */
#define ATANH_MAC01 1.0000000000000000000000000000000000000000000000000000000000000000000000E0
#define ATANH_MAC03 3.3333333333333333333333333333333333333333333333333333333333333333333333E-1
#define ATANH_MAC05 2.0000000000000000000000000000000000000000000000000000000000000000000000E-1
#define ATANH_MAC07 1.4285714285714285714285714285714285714285714285714285714285714285714286E-1
#if 0
#define ATANH_MAC09 1.1111111111111111111111111111111111111111111111111111111111111111111111E-1
#define ATANH_MAC11 9.0909090909090909090909090909090909090909090909090909090909090909090909E-2
#define ATANH_MAC13 7.6923076923076923076923076923076923076923076923076923076923076923076923E-2
#define ATANH_MAC15 6.6666666666666666666666666666666666666666666666666666666666666666666667E-2
#define ATANH_MAC17 5.8823529411764705882352941176470588235294117647058823529411764705882353E-2
#define ATANH_MAC19 5.2631578947368421052631578947368421052631578947368421052631578947368421E-2
#define ATANH_MAC21 4.7619047619047619047619047619047619047619047619047619047619047619047619E-2
#define ATANH_MAC23 4.3478260869565217391304347826086956521739130434782608695652173913043478E-2
#define ATANH_MAC25 4.0000000000000000000000000000000000000000000000000000000000000000000000E-2
#define ATANH_MAC27 3.7037037037037037037037037037037037037037037037037037037037037037037037E-2
#define ATANH_MAC29 3.4482758620689655172413793103448275862068965517241379310344827586206897E-2
#endif


static __inline vector float _atanhf4(vector float x)
{
    vec_float4 sign_mask = spu_splats(-0.0f);
    vec_float4 onef      = spu_splats(1.0f);
    vec_float4 onehalff  = spu_splats(0.5f);
    vec_float4 result, fresult, mresult;;
    vec_float4 xabs, xsqu;
    /* Where we switch from maclaurin to formula */
    //vec_float4  switch_approx = spu_splats(0.4661f);
    vec_float4  switch_approx = spu_splats(0.165f);
    vec_uint4   use_form;

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

    /*
     * Formula:
     *   atanh = 1/2 * ln((1 + x)/(1 - x)) = 1/2 * [ln(1+x) - ln(1-x)]
     */
    fresult = spu_sub(_logf4(spu_add(onef, xabs)), _logf4(spu_sub(onef, xabs)));
    fresult = spu_mul(fresult, onehalff);


    /*
     * Taylor Series
     */
    mresult = spu_madd(xsqu, spu_splats((float)ATANH_MAC07), spu_splats((float)ATANH_MAC05));
    mresult = spu_madd(xsqu, mresult, spu_splats((float)ATANH_MAC03));
    mresult = spu_madd(xsqu, mresult, spu_splats((float)ATANH_MAC01));
    mresult = spu_mul(xabs, mresult);


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


    /* Preserve sign - atanh is anti-symmetric */
    result = spu_sel(result, x, (vec_uint4)sign_mask);

    return result;
}

#endif /* _ATANHF4_H_ */
#endif /* __SPU__ */