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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 _ACOSHD2_H_ #define _ACOSHD2_H_ 1 #include #include "logd2.h" #include "sqrtd2.h" /* * FUNCTION * vector double _acoshd2(vector double x) * * DESCRIPTION * The acoshd2 function returns a vector containing the hyperbolic * arccosines of the corresponding elements of the input vector. * * We are using the formula: * acosh = ln(x + sqrt(x^2 - 1)) * * For x near one, we use the Taylor series: * * infinity * ------ * - ' * - k * acosh x = - C (x - 1) * - k * - , * ------ * k = 0 * * * Special Cases: * - acosh(1) = +0 * - acosh(NaN) = NaN * - acosh(Infinity) = Infinity * - acosh(x < 1) = NaN * */ /* * Taylor Series Coefficients * for x around 1. */ #define SDM_ACOSHD2_TAY01 1.000000000000000000000000000000000E0 /* 1 / 1 */ #define SDM_ACOSHD2_TAY02 -8.333333333333333333333333333333333E-2 /* 1 / 12 */ #define SDM_ACOSHD2_TAY03 1.875000000000000000000000000000000E-2 /* 3 / 160 */ #define SDM_ACOSHD2_TAY04 -5.580357142857142857142857142857142E-3 /* 5 / 896 */ #define SDM_ACOSHD2_TAY05 1.898871527777777777777777777777777E-3 /* 35 / 18432 */ #define SDM_ACOSHD2_TAY06 -6.991299715909090909090909090909090E-4 /* 63 / 90112 */ #define SDM_ACOSHD2_TAY07 2.711369441105769230769230769230769E-4 /* 231 / 851968 */ #define SDM_ACOSHD2_TAY08 -1.091003417968750000000000000000000E-4 /* 143 / 1310720 */ #define SDM_ACOSHD2_TAY09 4.512422225054572610294117647058823E-5 /* 6435 / 142606336 */ #define SDM_ACOSHD2_TAY10 -1.906564361170718544407894736842105E-5 /* 12155 / 637534208 */ #define SDM_ACOSHD2_TAY11 8.193687314078921363467261904761904E-6 /* 46189 / 5637144576 */ #define SDM_ACOSHD2_TAY12 -3.570569274218186088230298913043478E-6 /* 88179 / 24696061952 */ #define SDM_ACOSHD2_TAY13 1.574025955051183700561523437500000E-6 /* 676039 / 429496729600 */ #define SDM_ACOSHD2_TAY14 -7.006881922414457356488263165509259E-7 /* 1300075 / 1855425871872 */ #define SDM_ACOSHD2_TAY15 3.145330616650332150788142763335129E-7 /* 5014575 / 15942918602752 */ static __inline vector double _acoshd2(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 minus_oned = spu_splats(-1.0); vec_double2 twod = spu_splats(2.0); /* Where we switch from taylor to formula */ vec_float4 switch_approx = spu_splats(1.15f); vec_double2 result, fresult, mresult;; vec_double2 xminus1 = spu_add(x, minus_oned); vec_float4 xf = spu_roundtf(x); xf = spu_shuffle(xf, xf, dup_even); vec_ullong2 use_form = (vec_ullong2)spu_cmpgt(xf, switch_approx); vec_double2 sqrtargformula = spu_madd(x, x, minus_oned); vec_double2 sqrtargtaylor = spu_mul(xminus1, twod); vec_double2 sqrtarg = spu_sel(sqrtargtaylor, sqrtargformula, use_form); vec_double2 sqrtresult = _sqrtd2(sqrtarg); /* * Formula: * acosh = ln(x + sqrt(x^2 - 1)) */ fresult = spu_add(x, sqrtresult); fresult = _logd2(fresult); /* * Taylor Series */ mresult = spu_splats(SDM_ACOSHD2_TAY15); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY14)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY13)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY12)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY11)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY10)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY09)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY08)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY07)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY06)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY05)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY04)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY03)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY02)); mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY01)); mresult = spu_mul(mresult, sqrtresult); /* * Select series or formula */ result = spu_sel(mresult, fresult, use_form); return result; } #endif /* _ACOSHD2_H_ */ #endif /* __SPU__ */