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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 ACOSH_TAY01 1.0000000000000000000000000000000000000000000000000000000000000000000000E0 /* 1 / 1 */ #define ACOSH_TAY02 -8.3333333333333333333333333333333333333333333333333333333333333333333333E-2 /* 1 / 12 */ #define ACOSH_TAY03 1.8750000000000000000000000000000000000000000000000000000000000000000000E-2 /* 3 / 160 */ #define ACOSH_TAY04 -5.5803571428571428571428571428571428571428571428571428571428571428571429E-3 /* 5 / 896 */ #define ACOSH_TAY05 1.8988715277777777777777777777777777777777777777777777777777777777777778E-3 /* 35 / 18432 */ #define ACOSH_TAY06 -6.9912997159090909090909090909090909090909090909090909090909090909090909E-4 /* 63 / 90112 */ #define ACOSH_TAY07 2.7113694411057692307692307692307692307692307692307692307692307692307692E-4 /* 231 / 851968 */ #define ACOSH_TAY08 -1.0910034179687500000000000000000000000000000000000000000000000000000000E-4 /* 143 / 1310720 */ #define ACOSH_TAY09 4.5124222250545726102941176470588235294117647058823529411764705882352941E-5 /* 6435 / 142606336 */ #define ACOSH_TAY10 -1.9065643611707185444078947368421052631578947368421052631578947368421053E-5 /* 12155 / 637534208 */ #define ACOSH_TAY11 8.1936873140789213634672619047619047619047619047619047619047619047619048E-6 /* 46189 / 5637144576 */ #define ACOSH_TAY12 -3.5705692742181860882302989130434782608695652173913043478260869565217391E-6 /* 88179 / 24696061952 */ #define ACOSH_TAY13 1.5740259550511837005615234375000000000000000000000000000000000000000000E-6 /* 676039 / 429496729600 */ #define ACOSH_TAY14 -7.0068819224144573564882631655092592592592592592592592592592592592592593E-7 /* 1300075 / 1855425871872 */ #define ACOSH_TAY15 3.1453306166503321507881427633351293103448275862068965517241379310344828E-7 /* 5014575 / 15942918602752 */ #if 0 #define ACOSH_TAY16 -1.4221629293564136230176494967552923387096774193548387096774193548387097E-7 /* 9694845 / 68169720922112 */ #define ACOSH_TAY17 6.4711106776113328206437555226412686434659090909090909090909090909090909E-8 /* 100180065 / 1548112371908608 */ #define ACOSH_TAY18 -2.9609409781171182528071637664522443498883928571428571428571428571428571E-8 /* 116680311 / 3940649673949184 */ #define ACOSH_TAY19 1.3615438056281793767600509061201198680980785472972972972972972972972973E-8 /* 2268783825 / 166633186212708352 */ #endif 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); vec_double2 xminus1; vec_float4 xf; /* Where we switch from taylor to formula */ vec_float4 switch_approx = spu_splats(1.15f); vec_uint4 use_form; vec_double2 result, fresult, mresult;; xf = spu_roundtf(x); xf = spu_shuffle(xf, xf, dup_even); /* * Formula: * acosh = ln(x + sqrt(x^2 - 1)) */ fresult = _sqrtd2(spu_madd(x, x, minus_oned)); fresult = spu_add(x, fresult); fresult = _logd2(fresult); /* * Taylor Series */ xminus1 = spu_add(x, minus_oned); mresult = spu_madd(xminus1, spu_splats(ACOSH_TAY15), spu_splats(ACOSH_TAY14)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY13)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY12)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY11)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY10)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY09)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY08)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY07)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY06)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY05)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY04)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY03)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY02)); mresult = spu_madd(xminus1, mresult, spu_splats(ACOSH_TAY01)); mresult = spu_mul(mresult, _sqrtd2(spu_mul(xminus1, twod))); /* * Select series or formula */ use_form = spu_cmpgt(xf, switch_approx); result = spu_sel(mresult, fresult, (vec_ullong2)use_form); return result; } #endif /* _ACOSHD2_H_ */ #endif /* __SPU__ */