diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/asin_sve.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/asin_sve.c | 74 |
1 files changed, 46 insertions, 28 deletions
diff --git a/sysdeps/aarch64/fpu/asin_sve.c b/sysdeps/aarch64/fpu/asin_sve.c index 9314466..975f408 100644 --- a/sysdeps/aarch64/fpu/asin_sve.c +++ b/sysdeps/aarch64/fpu/asin_sve.c @@ -18,45 +18,43 @@ <https://www.gnu.org/licenses/>. */ #include "sv_math.h" -#include "poly_sve_f64.h" static const struct data { - float64_t poly[12]; - float64_t pi_over_2f; + float64_t c1, c3, c5, c7, c9, c11; + float64_t c0, c2, c4, c6, c8, c10; + float64_t pi_over_2; } data = { /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on [ 0x1p-106, 0x1p-2 ], relative error: 0x1.c3d8e169p-57. */ - .poly = { 0x1.555555555554ep-3, 0x1.3333333337233p-4, - 0x1.6db6db67f6d9fp-5, 0x1.f1c71fbd29fbbp-6, - 0x1.6e8b264d467d6p-6, 0x1.1c5997c357e9dp-6, - 0x1.c86a22cd9389dp-7, 0x1.856073c22ebbep-7, - 0x1.fd1151acb6bedp-8, 0x1.087182f799c1dp-6, - -0x1.6602748120927p-7, 0x1.cfa0dd1f9478p-6, }, - .pi_over_2f = 0x1.921fb54442d18p+0, + .c0 = 0x1.555555555554ep-3, .c1 = 0x1.3333333337233p-4, + .c2 = 0x1.6db6db67f6d9fp-5, .c3 = 0x1.f1c71fbd29fbbp-6, + .c4 = 0x1.6e8b264d467d6p-6, .c5 = 0x1.1c5997c357e9dp-6, + .c6 = 0x1.c86a22cd9389dp-7, .c7 = 0x1.856073c22ebbep-7, + .c8 = 0x1.fd1151acb6bedp-8, .c9 = 0x1.087182f799c1dp-6, + .c10 = -0x1.6602748120927p-7, .c11 = 0x1.cfa0dd1f9478p-6, + .pi_over_2 = 0x1.921fb54442d18p+0, }; -#define P(i) sv_f64 (d->poly[i]) - /* Double-precision SVE implementation of vector asin(x). For |x| in [0, 0.5], use an order 11 polynomial P such that the final approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2). - The largest observed error in this region is 0.52 ulps, - _ZGVsMxv_asin(0x1.d95ae04998b6cp-2) got 0x1.ec13757305f27p-2 - want 0x1.ec13757305f26p-2. - - For |x| in [0.5, 1.0], use same approximation with a change of variable + The largest observed error in this region is 0.98 ulp: + _ZGVsMxv_asin (0x1.d98f6a748ed8ap-2) got 0x1.ec4eb661a73d3p-2 + want 0x1.ec4eb661a73d2p-2. - asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). + For |x| in [0.5, 1.0], use same approximation with a change of variable: + asin(x) = pi/2 - (y + y * z * P(z)), with z = (1-x)/2 and y = sqrt(z). - The largest observed error in this region is 2.69 ulps, - _ZGVsMxv_asin(0x1.044ac9819f573p-1) got 0x1.110d7e85fdd5p-1 - want 0x1.110d7e85fdd53p-1. */ + The largest observed error in this region is 2.66 ulp: + _ZGVsMxv_asin (0x1.04024f6e2a2fbp-1) got 0x1.10b9586f087a8p-1 + want 0x1.10b9586f087abp-1. */ svfloat64_t SV_NAME_D1 (asin) (svfloat64_t x, const svbool_t pg) { const struct data *d = ptr_barrier (&data); + svbool_t ptrue = svptrue_b64 (); svuint64_t sign = svand_x (pg, svreinterpret_u64 (x), 0x8000000000000000); svfloat64_t ax = svabs_x (pg, x); @@ -70,17 +68,37 @@ svfloat64_t SV_NAME_D1 (asin) (svfloat64_t x, const svbool_t pg) svfloat64_t z = svsqrt_m (ax, a_ge_half, z2); /* Use a single polynomial approximation P for both intervals. */ + svfloat64_t z3 = svmul_x (pg, z2, z); svfloat64_t z4 = svmul_x (pg, z2, z2); svfloat64_t z8 = svmul_x (pg, z4, z4); - svfloat64_t z16 = svmul_x (pg, z8, z8); - svfloat64_t p = sv_estrin_11_f64_x (pg, z2, z4, z8, z16, d->poly); + + svfloat64_t c13 = svld1rq (ptrue, &d->c1); + svfloat64_t c57 = svld1rq (ptrue, &d->c5); + svfloat64_t c911 = svld1rq (ptrue, &d->c9); + + /* Order-11 Estrin scheme. */ + svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), z2, c13, 0); + svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), z2, c13, 1); + svfloat64_t p03 = svmla_x (pg, p01, z4, p23); + + svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), z2, c57, 0); + svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), z2, c57, 1); + svfloat64_t p47 = svmla_x (pg, p45, z4, p67); + + svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), z2, c911, 0); + svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), z2, c911, 1); + svfloat64_t p811 = svmla_x (pg, p89, z4, p1011); + + svfloat64_t p411 = svmla_x (pg, p47, z8, p811); + svfloat64_t p = svmla_x (pg, p03, z8, p411); + /* Finalize polynomial: z + z * z2 * P(z2). */ - p = svmla_x (pg, z, svmul_x (pg, z, z2), p); + p = svmla_x (pg, z, z3, p); - /* asin(|x|) = Q(|x|) , for |x| < 0.5 - = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ - svfloat64_t y = svmad_m (a_ge_half, p, sv_f64 (-2.0), d->pi_over_2f); + /* asin(|x|) = Q(|x|), for |x| < 0.5 + = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ + svfloat64_t y = svmad_m (a_ge_half, p, sv_f64 (-2.0), d->pi_over_2); - /* Copy sign. */ + /* Reinsert the sign from the argument. */ return svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (y), sign)); } |