diff options
Diffstat (limited to 'newlib/libm/machine/spu/headers/recipd2.h')
| -rw-r--r-- | newlib/libm/machine/spu/headers/recipd2.h | 115 |
1 files changed, 85 insertions, 30 deletions
diff --git a/newlib/libm/machine/spu/headers/recipd2.h b/newlib/libm/machine/spu/headers/recipd2.h index 0c701ec05..b53d4efc8 100644 --- a/newlib/libm/machine/spu/headers/recipd2.h +++ b/newlib/libm/machine/spu/headers/recipd2.h @@ -62,49 +62,104 @@ * preicision result. * * The Newton-Raphson iteration is of the form: - * X[i+1] = X[i] * (2.0 - b*X[i]) + * a) X[i+1] = X[i] * (2.0 - b*X[i]) + * or + * b) X[i+1] = X[i] + X[i]*(1.0 - X[i]*b) * where b is the input value to be inverted * + * The later (b) form improves the accuracy to 99.95% correctly rounded. */ -static __inline vector double _recipd2(vector double value_d) +static __inline vector double _recipd2(vector double value_in) { - vector unsigned long long expmask = (vector unsigned long long) { 0x7FF0000000000000ULL, 0x7FF0000000000000ULL }; - vector float x0; - vector float value; - vector float two = spu_splats(2.0f); - vector double two_d = spu_splats(2.0); - vector double x1, x2, x3; - vector double bias; - - /* Bias the divisor to correct for double precision floating + vec_float4 x0; + vec_float4 value; + vec_float4 one = spu_splats(1.0f); + vec_double2 one_d = spu_splats(1.0); + vec_double2 x1, x2, x3; + vec_double2 scale; + vec_double2 exp, value_d; + vec_ullong2 expmask = spu_splats(0x7FF0000000000000ULL); + vec_ullong2 is0inf; + +#ifdef __SPU_EDP__ + vec_ullong2 isdenorm; + vec_ullong2 expmask_minus1 = spu_splats(0x7FE0000000000000ULL); + + /* Determine special input values. For example, if the input is a denorm, infinity or 0 */ + + isdenorm = spu_testsv(value_in, (SPU_SV_POS_DENORM | SPU_SV_NEG_DENORM)); + is0inf = spu_testsv(value_in, (SPU_SV_NEG_ZERO | SPU_SV_POS_ZERO | + SPU_SV_NEG_INFINITY | SPU_SV_POS_INFINITY)); + + /* Scale the divisor to correct for double precision floating * point exponents that are out of single precision range. */ - bias = spu_xor(spu_and(value_d, (vector double)expmask), (vector double)expmask); + exp = spu_and(value_in, (vec_double2)expmask); + scale = spu_xor(exp, (vec_double2)spu_sel(expmask, expmask_minus1, isdenorm)); + value_d = spu_mul(value_in, scale); + value = spu_roundtf(value_d); - value = spu_roundtf(spu_mul(value_d, bias)); + /* Perform reciprocal with 1 single precision and 2 double precision + * Newton-Raphson iterations. + */ x0 = spu_re(value); - x1 = spu_extend(spu_mul(x0, spu_nmsub(value, x0, two))); - x1 = spu_mul(x1, bias); - x2 = spu_mul(x1, spu_nmsub(value_d, x1, two_d)); - x3 = spu_mul(x2, spu_nmsub(value_d, x2, two_d)); + x1 = spu_extend(spu_madd(spu_nmsub(value, x0, one), x0, x0)); + x2 = spu_madd(spu_nmsub(value_d, x1, one_d), x1, x1); + x3 = spu_madd(spu_nmsub(value_d, x2, one_d), x2, x2); + x3 = spu_sel(spu_mul(x3, scale), spu_xor(value_in, (vector double)expmask), is0inf); - /* Handle input = +/- infinity or +/-0. */ +#else /* !__SPU_EDP__ */ -#ifdef __SPU_EDP__ - vec_ullong2 is0inf = spu_testsv(value_d, SPU_SV_NEG_ZERO | SPU_SV_POS_ZERO | - SPU_SV_NEG_INFINITY | SPU_SV_POS_INFINITY); -#else - vec_double2 nzero = spu_splats(-0.0); - vec_double2 xabs = spu_andc(value_d, nzero); - vector unsigned char swap = (vector unsigned char) {4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11}; - vec_uint4 isinf = spu_cmpeq((vec_uint4)xabs, (vec_uint4)expmask); - vec_uint4 iszero = spu_cmpeq((vec_uint4)xabs, 0); + vec_uint4 isinf, iszero, isdenorm0; + vec_double2 value_abs; + vec_double2 sign = spu_splats(-0.0); + vec_double2 denorm_scale = (vec_double2)spu_splats(0x4330000000000000ULL); + vec_double2 exp_53 = (vec_double2)spu_splats(0x0350000000000000ULL); + vec_uchar16 splat_hi = (vec_uchar16){0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11}; + vec_uchar16 swap = (vec_uchar16){4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11}; + + value_abs = spu_andc(value_in, sign); + exp = spu_and(value_in, (vec_double2)expmask); + + /* Determine if the input is a special value. These include: + * denorm - then we must coerce it to a normal value. + * zero - then we must return an infinity + * infinity - then we must return a zero. + */ + isdenorm0 = spu_cmpeq(spu_shuffle((vec_uint4)exp, (vec_uint4)exp, splat_hi), 0); + + isinf = spu_cmpeq((vec_uint4)value_abs, (vec_uint4)expmask); + iszero = spu_cmpeq((vec_uint4)value_abs, 0); isinf = spu_and(isinf, spu_shuffle(isinf, isinf, swap)); iszero = spu_and(iszero, spu_shuffle(iszero, iszero, swap)); - vec_ullong2 is0inf = (vec_ullong2)spu_or(isinf, iszero); -#endif /* __SPU_EDP__ */ + is0inf = (vec_ullong2)spu_or(isinf, iszero); + + /* If the inputs is a denorm, we must first convert it to a normal number since + * arithmetic operations on denormals produces 0 on Cell/B.E. + */ + value_d = spu_sub(spu_or(value_abs, exp_53), exp_53); + value_d = spu_sel(value_abs, value_d, (vec_ullong2)isdenorm0); + + /* Scale the divisor to correct for double precision floating + * point exponents that are out of single precision range. + */ + scale = spu_xor(spu_and(value_d, (vec_double2)expmask), (vec_double2)expmask); + value_d = spu_mul(value_d, scale); + value = spu_roundtf(value_d); - x3 = spu_sel(x3, spu_xor(value_d, (vector double)expmask), is0inf); + /* Perform reciprocal with 1 single precision and 2 double precision + * Newton-Raphson iterations. The bias is removed after the single + * precision iteration. + */ + x0 = spu_re(value); + x1 = spu_extend(spu_madd(spu_nmsub(value, x0, one), x0, x0)); + x2 = spu_madd(spu_nmsub(value_d, x1, one_d), x1, x1); + x3 = spu_madd(spu_nmsub(value_d, x2, one_d), x2, x2); + x3 = spu_mul(x3, spu_sel(scale, value_in, (vec_ullong2)sign)); + x3 = spu_sel(x3, spu_mul(x3, denorm_scale), (vec_ullong2)isdenorm0); + x3 = spu_sel(x3, spu_xor(value_in, (vector double)expmask), is0inf); + +#endif /* __SPU_EDP__ */ return (x3); } |