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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 _EXPD2_H_ #define _EXPD2_H_ 1 #include #include "floord2.h" #define LOG2E 1.4426950408889634073599 // 1/log(2) /* * FUNCTION * vector double _expd2(vector double x) * * DESCRIPTION * _expd2 computes e raised to the input x for * each of the element of the double word vector. * * Calculation is performed by reducing the input argument * to within a managable range, and then computing the power * series to the 11th degree. * * Range reduction is performed using the property: * * exp(x) = 2^n * exp(r) * * Values for "n" and "r" are determined such that: * * x = n * ln(2) + r, |r| <= ln(2)/2 * * n = floor( (x/ln(2)) + 1/2 ) * r = x - (n * ln(2)) * * To enhance the precision for "r", computation is performed * using a two part representation of ln(2). * * Once the input is reduced, the power series is computed: * * __12_ * \ * exp(x) = 1 + \ (x^i)/i! * / * /____ * i=2 * * The resulting value is scaled by 2^n and returned. * */ static __inline vector double _expd2(vector double x) { // log(2) in extended machine representable precision vec_double2 ln2_hi = spu_splats(6.9314575195312500E-1); // 3FE62E4000000000 vec_double2 ln2_lo = spu_splats(1.4286068203094172E-6); // 3EB7F7D1CF79ABCA // coefficients for the power series // vec_double2 f01 = spu_splats(1.00000000000000000000E0); // 1/(1!) vec_double2 f02 = spu_splats(5.00000000000000000000E-1); // 1/(2!) vec_double2 f03 = spu_splats(1.66666666666666666667E-1); // 1/(3!) vec_double2 f04 = spu_splats(4.16666666666666666667E-2); // 1/(4!) vec_double2 f05 = spu_splats(8.33333333333333333333E-3); // 1/(5!) vec_double2 f06 = spu_splats(1.38888888888888888889E-3); // 1/(6!) vec_double2 f07 = spu_splats(1.98412698412698412698E-4); // 1/(7!) vec_double2 f08 = spu_splats(2.48015873015873015873E-5); // 1/(8!) vec_double2 f09 = spu_splats(2.75573192239858906526E-6); // 1/(9!) vec_double2 f10 = spu_splats(2.75573192239858906526E-7); // 1/(10!) vec_double2 f11 = spu_splats(2.50521083854417187751E-8); // 1/(11!) vec_double2 f12 = spu_splats(2.08767569878680989792E-9); // 1/(12!) // rx = floor(1/2 + x/log(2)) vec_double2 rx = _floord2(spu_madd(x,spu_splats(LOG2E),spu_splats(0.5))); // extract the exponent of reduction vec_int4 exp = spu_convts(spu_roundtf(rx),0); // reduce the input to within [ -ln(2)/2 ... ln(2)/2 ] vec_double2 r; r = spu_nmsub(rx,ln2_hi,x); r = spu_nmsub(rx,ln2_lo,r); vec_double2 result; vec_double2 r2 = spu_mul(r,r); // Use Horner's method on the power series /* result = ((((c12*x + c11)*x + c10)*x + c9)*x + c8)*x + c7)*x + c6)*x^6 + ((((((c5*x + c4)*x + c3)*x + c2)*x + c1)*x + c0 */ #ifdef __SPU_EDP__ vec_double2 p1, p2, r4, r6; p1 = spu_madd(f12, r, f11); p2 = spu_madd(f05, r, f04); r4 = spu_mul(r2, r2); p1 = spu_madd(p1, r, f10); p2 = spu_madd(p2, r, f03); p1 = spu_madd(p1, r, f09); p2 = spu_madd(p2, r, f02); p1 = spu_madd(p1, r, f08); r6 = spu_mul(r2, r4); p1 = spu_madd(p1, r, f07); p2 = spu_madd(p2, r2, r); p1 = spu_madd(p1, r, f06); result = spu_madd(r6, p1, p2); result = spu_add(result, spu_splats(1.0)); #else result = spu_madd(r,f12,f11); result = spu_madd(result,r,f10); result = spu_madd(result,r,f09); result = spu_madd(result,r,f08); result = spu_madd(result,r,f07); result = spu_madd(result,r,f06); result = spu_madd(result,r,f05); result = spu_madd(result,r,f04); result = spu_madd(result,r,f03); result = spu_madd(result,r,f02); result = spu_madd(result,r2,r); result = spu_add(result,spu_splats(1.0)); #endif /* __SPU_EDP__ */ // Scale the result - basically a call to ldexpd2() vec_int4 e1, e2; vec_int4 min = spu_splats(-2044); vec_int4 max = spu_splats(2046); vec_uint4 cmp_min, cmp_max; vec_uint4 shift = (vec_uint4) { 20, 32, 20, 32 }; vec_double2 f1, f2; /* Clamp the specified exponent to the range -2044 to 2046. */ cmp_min = spu_cmpgt(exp, min); cmp_max = spu_cmpgt(exp, max); exp = spu_sel(min, exp, cmp_min); exp = spu_sel(exp, max, cmp_max); /* Generate the factors f1 = 2^e1 and f2 = 2^e2 */ e1 = spu_rlmaska(exp, -1); e2 = spu_sub(exp, e1); f1 = (vec_double2)spu_sl(spu_add(e1, 1023), shift); f2 = (vec_double2)spu_sl(spu_add(e2, 1023), shift); /* Compute the product x * 2^e1 * 2^e2 */ result = spu_mul(spu_mul(result, f1), f2); return result; } #endif /* _EXPD2_H_ */ #endif /* __SPU__ */