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| /* -------------------------------------------------------------- */ |
| /* PROLOG END TAG zYx */ |
| #ifdef __SPU__ |
| #ifndef _EXPD2_H_ |
| #define _EXPD2_H_ 1 |
| |
| #include <spu_intrinsics.h> |
| #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__ */ |
