diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/asinf_advsimd.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/asinf_advsimd.c | 31 |
1 files changed, 17 insertions, 14 deletions
diff --git a/sysdeps/aarch64/fpu/asinf_advsimd.c b/sysdeps/aarch64/fpu/asinf_advsimd.c index 52c7c0e..013936c 100644 --- a/sysdeps/aarch64/fpu/asinf_advsimd.c +++ b/sysdeps/aarch64/fpu/asinf_advsimd.c @@ -18,22 +18,21 @@ <https://www.gnu.org/licenses/>. */ #include "v_math.h" -#include "poly_advsimd_f32.h" static const struct data { - float32x4_t poly[5]; + float32x4_t c0, c2, c4; + float c1, c3; float32x4_t pi_over_2f; } data = { /* Polynomial approximation of (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x)) on [ 0x1p-24 0x1p-2 ] order = 4 rel error: 0x1.00a23bbp-29 . */ - .poly = { V4 (0x1.55555ep-3), V4 (0x1.33261ap-4), V4 (0x1.70d7dcp-5), - V4 (0x1.b059dp-6), V4 (0x1.3af7d8p-5) }, - .pi_over_2f = V4 (0x1.921fb6p+0f), + .c0 = V4 (0x1.55555ep-3f), .c1 = 0x1.33261ap-4f, + .c2 = V4 (0x1.70d7dcp-5f), .c3 = 0x1.b059dp-6f, + .c4 = V4 (0x1.3af7d8p-5f), .pi_over_2f = V4 (0x1.921fb6p+0f), }; #define AbsMask 0x7fffffff -#define Half 0x3f000000 #define One 0x3f800000 #define Small 0x39800000 /* 2^-12. */ @@ -47,11 +46,8 @@ special_case (float32x4_t x, float32x4_t y, uint32x4_t special) /* Single-precision implementation of vector asin(x). - For |x| < Small, approximate asin(x) by x. Small = 2^-12 for correct - rounding. If WANT_SIMD_EXCEPT = 0, Small = 0 and we proceed with the - following approximation. - For |x| in [Small, 0.5], use order 4 polynomial P such that the final + For |x| <0.5, use order 4 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 0.83 ulps, @@ -80,24 +76,31 @@ float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (asin) (float32x4_t x) #endif float32x4_t ax = vreinterpretq_f32_u32 (ia); - uint32x4_t a_lt_half = vcltq_u32 (ia, v_u32 (Half)); + uint32x4_t a_lt_half = vcaltq_f32 (x, v_f32 (0.5f)); /* Evaluate polynomial Q(x) = y + y * z * P(z) with z = x ^ 2 and y = |x| , if |x| < 0.5 z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5. */ float32x4_t z2 = vbslq_f32 (a_lt_half, vmulq_f32 (x, x), - vfmsq_n_f32 (v_f32 (0.5), ax, 0.5)); + vfmsq_n_f32 (v_f32 (0.5f), ax, 0.5f)); float32x4_t z = vbslq_f32 (a_lt_half, ax, vsqrtq_f32 (z2)); /* Use a single polynomial approximation P for both intervals. */ - float32x4_t p = v_horner_4_f32 (z2, d->poly); + + /* PW Horner 3 evaluation scheme. */ + float32x4_t z4 = vmulq_f32 (z2, z2); + float32x4_t c13 = vld1q_f32 (&d->c1); + float32x4_t p01 = vfmaq_laneq_f32 (d->c0, z2, c13, 0); + float32x4_t p23 = vfmaq_laneq_f32 (d->c2, z2, c13, 1); + float32x4_t p = vfmaq_f32 (p23, d->c4, z4); + p = vfmaq_f32 (p01, p, z4); /* Finalize polynomial: z + z * z2 * P(z2). */ p = vfmaq_f32 (z, vmulq_f32 (z, z2), p); /* asin(|x|) = Q(|x|) , for |x| < 0.5 = pi/2 - 2 Q(|x|), for |x| >= 0.5. */ float32x4_t y - = vbslq_f32 (a_lt_half, p, vfmsq_n_f32 (d->pi_over_2f, p, 2.0)); + = vbslq_f32 (a_lt_half, p, vfmsq_n_f32 (d->pi_over_2f, p, 2.0f)); /* Copy sign. */ return vbslq_f32 (v_u32 (AbsMask), y, x); |