diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/acos_advsimd.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/acos_advsimd.c | 56 |
1 files changed, 37 insertions, 19 deletions
diff --git a/sysdeps/aarch64/fpu/acos_advsimd.c b/sysdeps/aarch64/fpu/acos_advsimd.c index 7709b54..453f780 100644 --- a/sysdeps/aarch64/fpu/acos_advsimd.c +++ b/sysdeps/aarch64/fpu/acos_advsimd.c @@ -18,24 +18,23 @@ <https://www.gnu.org/licenses/>. */ #include "v_math.h" -#include "poly_advsimd_f64.h" static const struct data { - float64x2_t poly[12]; - float64x2_t pi, pi_over_2; + double c1, c3, c5, c7, c9, c11; + float64x2_t c0, c2, c4, c6, c8, c10; uint64x2_t abs_mask; + float64x2_t pi, 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 = { V2 (0x1.555555555554ep-3), V2 (0x1.3333333337233p-4), - V2 (0x1.6db6db67f6d9fp-5), V2 (0x1.f1c71fbd29fbbp-6), - V2 (0x1.6e8b264d467d6p-6), V2 (0x1.1c5997c357e9dp-6), - V2 (0x1.c86a22cd9389dp-7), V2 (0x1.856073c22ebbep-7), - V2 (0x1.fd1151acb6bedp-8), V2 (0x1.087182f799c1dp-6), - V2 (-0x1.6602748120927p-7), V2 (0x1.cfa0dd1f9478p-6), }, - .pi = V2 (0x1.921fb54442d18p+1), - .pi_over_2 = V2 (0x1.921fb54442d18p+0), + .c0 = V2 (0x1.555555555554ep-3), .c1 = 0x1.3333333337233p-4, + .c2 = V2 (0x1.6db6db67f6d9fp-5), .c3 = 0x1.f1c71fbd29fbbp-6, + .c4 = V2 (0x1.6e8b264d467d6p-6), .c5 = 0x1.1c5997c357e9dp-6, + .c6 = V2 (0x1.c86a22cd9389dp-7), .c7 = 0x1.856073c22ebbep-7, + .c8 = V2 (0x1.fd1151acb6bedp-8), .c9 = 0x1.087182f799c1dp-6, + .c10 = V2 (-0x1.6602748120927p-7), .c11 = 0x1.cfa0dd1f9478p-6, + .pi = V2 (0x1.921fb54442d18p+1), .pi_over_2 = V2 (0x1.921fb54442d18p+0), .abs_mask = V2 (0x7fffffffffffffff), }; @@ -63,7 +62,7 @@ special_case (float64x2_t x, float64x2_t y, uint64x2_t special) acos(x) ~ pi/2 - (x + x^3 P(x^2)). - The largest observed error in this region is 1.18 ulps, + The largest observed error in this region is 1.18 ulp: _ZGVnN2v_acos (0x1.fbab0a7c460f6p-2) got 0x1.0d54d1985c068p+0 want 0x1.0d54d1985c069p+0. @@ -71,9 +70,9 @@ special_case (float64x2_t x, float64x2_t y, uint64x2_t special) 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, - _ZGVnN2v_acos (0x1.23d362722f591p-1) got 0x1.edbbedf8a7d6ep-1 - want 0x1.edbbedf8a7d6cp-1. */ + The largest observed error in this region is 1.50 ulp: + _ZGVnN2v_acos (0x1.252a2cf3fb9acp-1) got 0x1.ec1a46aa82901p-1 + want 0x1.ec1a46aa829p-1. */ float64x2_t VPCS_ATTR V_NAME_D1 (acos) (float64x2_t x) { const struct data *d = ptr_barrier (&data); @@ -99,13 +98,32 @@ float64x2_t VPCS_ATTR V_NAME_D1 (acos) (float64x2_t x) float64x2_t z = vbslq_f64 (a_le_half, ax, vsqrtq_f64 (z2)); /* Use a single polynomial approximation P for both intervals. */ + float64x2_t z3 = vmulq_f64 (z2, z); float64x2_t z4 = vmulq_f64 (z2, z2); float64x2_t z8 = vmulq_f64 (z4, z4); - float64x2_t z16 = vmulq_f64 (z8, z8); - float64x2_t p = v_estrin_11_f64 (z2, z4, z8, z16, d->poly); - /* Finalize polynomial: z + z * z2 * P(z2). */ - p = vfmaq_f64 (z, vmulq_f64 (z, z2), p); + /* Order-11 Estrin. */ + float64x2_t c13 = vld1q_f64 (&d->c1); + float64x2_t c57 = vld1q_f64 (&d->c5); + float64x2_t c911 = vld1q_f64 (&d->c9); + + float64x2_t p01 = vfmaq_laneq_f64 (d->c0, z2, c13, 0); + float64x2_t p23 = vfmaq_laneq_f64 (d->c2, z2, c13, 1); + float64x2_t p03 = vfmaq_f64 (p01, z4, p23); + + float64x2_t p45 = vfmaq_laneq_f64 (d->c4, z2, c57, 0); + float64x2_t p67 = vfmaq_laneq_f64 (d->c6, z2, c57, 1); + float64x2_t p47 = vfmaq_f64 (p45, z4, p67); + + float64x2_t p89 = vfmaq_laneq_f64 (d->c8, z2, c911, 0); + float64x2_t p1011 = vfmaq_laneq_f64 (d->c10, z2, c911, 1); + float64x2_t p811 = vfmaq_f64 (p89, z4, p1011); + + float64x2_t p411 = vfmaq_f64 (p47, z8, p811); + float64x2_t p = vfmaq_f64 (p03, z8, p411); + + /* Finalize polynomial: z + z3 * P(z2). */ + p = vfmaq_f64 (z, z3, p); /* acos(|x|) = pi/2 - sign(x) * Q(|x|), for |x| < 0.5 = 2 Q(|x|) , for 0.5 < x < 1.0 |