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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 _ATANHF4_H_ #define _ATANHF4_H_ 1 #include #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__ */