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IN NO EVENT SHALL THE COPYRIGHT OWNER OR */ /* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */ /* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */ /* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */ /* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */ /* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */ /* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */ /* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */ /* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /* -------------------------------------------------------------- */ /* PROLOG END TAG zYx */ #ifdef __SPU__ #ifndef _ATANHD2_H_ #define _ATANHD2_H_ 1 #include #include "logd2.h" /* * FUNCTION * vector double _atanhd2(vector double x) * * DESCRIPTION * The atanhd2 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) = Infinity * - atanh(-1) = -Infinity * - atanh(x) for |x| > 1 = NaN * */ /* * 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 #define ATANH_MAC09 1.1111111111111111111111111111111111111111111111111111111111111111111111E-1 #define ATANH_MAC11 9.0909090909090909090909090909090909090909090909090909090909090909090909E-2 #define ATANH_MAC13 7.6923076923076923076923076923076923076923076923076923076923076923076923E-2 #if 0 #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 #define ATANH_MAC31 3.2258064516129032258064516129032258064516129032258064516129032258064516E-2 #define ATANH_MAC33 3.0303030303030303030303030303030303030303030303030303030303030303030303E-2 #define ATANH_MAC35 2.8571428571428571428571428571428571428571428571428571428571428571428571E-2 #define ATANH_MAC37 2.7027027027027027027027027027027027027027027027027027027027027027027027E-2 #define ATANH_MAC39 2.5641025641025641025641025641025641025641025641025641025641025641025641E-2 #define ATANH_MAC41 2.4390243902439024390243902439024390243902439024390243902439024390243902E-2 #define ATANH_MAC43 2.3255813953488372093023255813953488372093023255813953488372093023255814E-2 #define ATANH_MAC45 2.2222222222222222222222222222222222222222222222222222222222222222222222E-2 #define ATANH_MAC47 2.1276595744680851063829787234042553191489361702127659574468085106382979E-2 #define ATANH_MAC49 2.0408163265306122448979591836734693877551020408163265306122448979591837E-2 #define ATANH_MAC51 1.9607843137254901960784313725490196078431372549019607843137254901960784E-2 #define ATANH_MAC53 1.8867924528301886792452830188679245283018867924528301886792452830188679E-2 #define ATANH_MAC55 1.8181818181818181818181818181818181818181818181818181818181818181818182E-2 #define ATANH_MAC57 1.7543859649122807017543859649122807017543859649122807017543859649122807E-2 #define ATANH_MAC59 1.6949152542372881355932203389830508474576271186440677966101694915254237E-2 #endif static __inline vector double _atanhd2(vector double x) { vec_uchar16 dup_even = ((vec_uchar16) { 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 }); vec_double2 sign_mask = spu_splats(-0.0); vec_double2 oned = spu_splats(1.0); vec_double2 onehalfd = spu_splats(0.5); vec_uint4 infminus1 = spu_splats(0x7FEFFFFFU); vec_uint4 isinfnan; vec_uint4 xabshigh; vec_double2 xabs, xsqu; /* Where we switch from maclaurin to formula */ vec_float4 switch_approx = spu_splats(0.08f); 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: * atanh = 1/2 * ln((1 + x)/(1 - x)) = 1/2 * [ln(1+x) - ln(1-x)] */ fresult = spu_sub(_logd2(spu_add(oned, xabs)), _logd2(spu_sub(oned, xabs))); fresult = spu_mul(fresult, onehalfd); /* * Taylor Series */ mresult = spu_madd(xsqu, spu_splats(ATANH_MAC13), spu_splats(ATANH_MAC11)); mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC09)); mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC07)); mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC05)); mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_MAC03)); mresult = spu_madd(xsqu, mresult, spu_splats(ATANH_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); /* 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 - atanh is an anti-symmetric */ result = spu_sel(result, x, (vec_ullong2)sign_mask); return result; } #endif /* _ATANHD2_H_ */ #endif /* __SPU__ */