diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/acos_sve.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/acos_sve.c | 75 |
1 files changed, 47 insertions, 28 deletions
diff --git a/sysdeps/aarch64/fpu/acos_sve.c b/sysdeps/aarch64/fpu/acos_sve.c index 74e2f7d..104f0d7 100644 --- a/sysdeps/aarch64/fpu/acos_sve.c +++ b/sysdeps/aarch64/fpu/acos_sve.c @@ -18,20 +18,21 @@ <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, pi_over_2; + 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 = 0x1.921fb54442d18p+1, + .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, }; @@ -42,20 +43,21 @@ static const struct data acos(x) ~ pi/2 - (x + x^3 P(x^2)). - The largest observed error in this region is 1.18 ulps, - _ZGVsMxv_acos (0x1.fbc5fe28ee9e3p-2) got 0x1.0d4d0f55667f6p+0 - want 0x1.0d4d0f55667f7p+0. + The largest observed error in this region is 1.18 ulp: + _ZGVsMxv_acos (0x1.fbb7c9079b429p-2) got 0x1.0d51266607582p+0 + want 0x1.0d51266607583p+0. For |x| in [0.5, 1.0], use same approximation with a change of variable acos(x) = y + y * z * P(z), with z = (1-x)/2 and y = sqrt(z). - The largest observed error in this region is 1.52 ulps, - _ZGVsMxv_acos (0x1.24024271a500ap-1) got 0x1.ed82df4243f0dp-1 - want 0x1.ed82df4243f0bp-1. */ + The largest observed error in this region is 1.50 ulp: + _ZGVsMxv_acos (0x1.252a2cf3fb9acp-1) got 0x1.ec1a46aa82901p-1 + want 0x1.ec1a46aa829p-1. */ svfloat64_t SV_NAME_D1 (acos) (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); @@ -70,24 +72,41 @@ svfloat64_t SV_NAME_D1 (acos) (svfloat64_t x, const svbool_t pg) svfloat64_t z = svsqrt_m (ax, a_gt_half, z2); /* Use a single polynomial approximation P for both intervals. */ - 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 z3 = svmul_x (ptrue, z2, z); + svfloat64_t z4 = svmul_x (ptrue, z2, z2); + svfloat64_t z8 = svmul_x (ptrue, z4, z4); + + svfloat64_t c13 = svld1rq (ptrue, &d->c1); + svfloat64_t c57 = svld1rq (ptrue, &d->c5); + svfloat64_t c911 = svld1rq (ptrue, &d->c9); + + 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 = svmad_x (pg, p411, z8, p03); /* Finalize polynomial: z + z * z2 * P(z2). */ - p = svmla_x (pg, z, svmul_x (pg, z, z2), p); + p = svmad_x (pg, p, z3, z); /* acos(|x|) = pi/2 - sign(x) * Q(|x|), for |x| < 0.5 = 2 Q(|x|) , for 0.5 < x < 1.0 = pi - 2 Q(|x|) , for -1.0 < x < -0.5. */ - svfloat64_t y - = svreinterpret_f64 (svorr_x (pg, svreinterpret_u64 (p), sign)); - - svbool_t is_neg = svcmplt (pg, x, 0.0); - svfloat64_t off = svdup_f64_z (is_neg, d->pi); - svfloat64_t mul = svsel (a_gt_half, sv_f64 (2.0), sv_f64 (-1.0)); - svfloat64_t add = svsel (a_gt_half, off, sv_f64 (d->pi_over_2)); - - return svmla_x (pg, add, mul, y); + svfloat64_t mul = svreinterpret_f64 ( + svlsl_m (a_gt_half, svreinterpret_u64 (sv_f64 (1.0)), 10)); + mul = svreinterpret_f64 (sveor_x (ptrue, svreinterpret_u64 (mul), sign)); + svfloat64_t add = svreinterpret_f64 ( + svorr_x (ptrue, sign, svreinterpret_u64 (sv_f64 (d->pi_over_2)))); + add = svsub_m (a_gt_half, sv_f64 (d->pi_over_2), add); + + return svmsb_x (pg, p, mul, add); } |