diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/atan2f_advsimd.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/atan2f_advsimd.c | 64 |
1 files changed, 34 insertions, 30 deletions
diff --git a/sysdeps/aarch64/fpu/atan2f_advsimd.c b/sysdeps/aarch64/fpu/atan2f_advsimd.c index e65406f..75d8738 100644 --- a/sysdeps/aarch64/fpu/atan2f_advsimd.c +++ b/sysdeps/aarch64/fpu/atan2f_advsimd.c @@ -18,22 +18,22 @@ <https://www.gnu.org/licenses/>. */ #include "v_math.h" -#include "poly_advsimd_f32.h" static const struct data { - float32x4_t c0, pi_over_2, c4, c6, c2; + float32x4_t c0, c4, c6, c2; float c1, c3, c5, c7; uint32x4_t comp_const; + float32x4_t pi; } data = { /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on [2**-128, 1.0]. Generated using fpminimax between FLT_MIN and 1. */ - .c0 = V4 (-0x1.55555p-2f), .c1 = 0x1.99935ep-3f, - .c2 = V4 (-0x1.24051ep-3f), .c3 = 0x1.bd7368p-4f, - .c4 = V4 (-0x1.491f0ep-4f), .c5 = 0x1.93a2c0p-5f, - .c6 = V4 (-0x1.4c3c60p-6f), .c7 = 0x1.01fd88p-8f, - .pi_over_2 = V4 (0x1.921fb6p+0f), .comp_const = V4 (2 * 0x7f800000lu - 1), + .c0 = V4 (-0x1.5554dcp-2), .c1 = 0x1.9978ecp-3, + .c2 = V4 (-0x1.230a94p-3), .c3 = 0x1.b4debp-4, + .c4 = V4 (-0x1.3550dap-4), .c5 = 0x1.61eebp-5, + .c6 = V4 (-0x1.0c17d4p-6), .c7 = 0x1.7ea694p-9, + .pi = V4 (0x1.921fb6p+1f), .comp_const = V4 (2 * 0x7f800000lu - 1), }; #define SignMask v_u32 (0x80000000) @@ -54,13 +54,13 @@ static inline uint32x4_t zeroinfnan (uint32x4_t i, const struct data *d) { /* 2 * i - 1 >= 2 * 0x7f800000lu - 1. */ - return vcgeq_u32 (vsubq_u32 (vmulq_n_u32 (i, 2), v_u32 (1)), d->comp_const); + return vcgeq_u32 (vsubq_u32 (vshlq_n_u32 (i, 1), v_u32 (1)), d->comp_const); } /* Fast implementation of vector atan2f. Maximum observed error is - 2.95 ULP in [0x1.9300d6p+6 0x1.93c0c6p+6] x [0x1.8c2dbp+6 0x1.8cea6p+6]: - _ZGVnN4vv_atan2f (0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1 - want 0x1.967f00p-1. */ + 2.13 ULP in [0x1.9300d6p+6 0x1.93c0c6p+6] x [0x1.8c2dbp+6 0x1.8cea6p+6]: + _ZGVnN4vv_atan2f (0x1.14a9d4p-87, 0x1.0eb886p-87) got 0x1.97aea2p-1 + want 0x1.97ae9ep-1. */ float32x4_t VPCS_ATTR NOINLINE V_NAME_F2 (atan2) (float32x4_t y, float32x4_t x) { const struct data *d = ptr_barrier (&data); @@ -81,28 +81,31 @@ float32x4_t VPCS_ATTR NOINLINE V_NAME_F2 (atan2) (float32x4_t y, float32x4_t x) uint32x4_t pred_xlt0 = vcltzq_f32 (x); uint32x4_t pred_aygtax = vcgtq_f32 (ay, ax); - /* Set up z for call to atanf. */ - float32x4_t n = vbslq_f32 (pred_aygtax, vnegq_f32 (ax), ay); - float32x4_t q = vbslq_f32 (pred_aygtax, ay, ax); - float32x4_t z = vdivq_f32 (n, q); - - /* Work out the correct shift. */ + /* Set up z for evaluation of atanf. */ + float32x4_t num = vbslq_f32 (pred_aygtax, vnegq_f32 (ax), ay); + float32x4_t den = vbslq_f32 (pred_aygtax, ay, ax); + float32x4_t z = vdivq_f32 (num, den); + + /* Work out the correct shift for atan2: + Multiplication by pi is done later. + -pi when x < 0 and ax < ay + -pi/2 when x < 0 and ax > ay + 0 when x >= 0 and ax < ay + pi/2 when x >= 0 and ax > ay. */ float32x4_t shift = vreinterpretq_f32_u32 ( - vandq_u32 (pred_xlt0, vreinterpretq_u32_f32 (v_f32 (-2.0f)))); - shift = vbslq_f32 (pred_aygtax, vaddq_f32 (shift, v_f32 (1.0f)), shift); - shift = vmulq_f32 (shift, d->pi_over_2); - - /* Calculate the polynomial approximation. - Use 2-level Estrin scheme for P(z^2) with deg(P)=7. However, - a standard implementation using z8 creates spurious underflow - in the very last fma (when z^8 is small enough). - Therefore, we split the last fma into a mul and an fma. - Horner and single-level Estrin have higher errors that exceed - threshold. */ + vandq_u32 (pred_xlt0, vreinterpretq_u32_f32 (v_f32 (-1.0f)))); + float32x4_t shift2 = vreinterpretq_f32_u32 ( + vandq_u32 (pred_aygtax, vreinterpretq_u32_f32 (v_f32 (0.5f)))); + shift = vaddq_f32 (shift, shift2); + + /* Calculate the polynomial approximation. */ float32x4_t z2 = vmulq_f32 (z, z); + float32x4_t z3 = vmulq_f32 (z2, z); float32x4_t z4 = vmulq_f32 (z2, z2); + float32x4_t z8 = vmulq_f32 (z4, z4); float32x4_t c1357 = vld1q_f32 (&d->c1); + float32x4_t p01 = vfmaq_laneq_f32 (d->c0, z2, c1357, 0); float32x4_t p23 = vfmaq_laneq_f32 (d->c2, z2, c1357, 1); float32x4_t p45 = vfmaq_laneq_f32 (d->c4, z2, c1357, 2); @@ -110,10 +113,11 @@ float32x4_t VPCS_ATTR NOINLINE V_NAME_F2 (atan2) (float32x4_t y, float32x4_t x) float32x4_t p03 = vfmaq_f32 (p01, z4, p23); float32x4_t p47 = vfmaq_f32 (p45, z4, p67); - float32x4_t ret = vfmaq_f32 (p03, z4, vmulq_f32 (z4, p47)); + float32x4_t poly = vfmaq_f32 (p03, z8, p47); /* y = shift + z * P(z^2). */ - ret = vaddq_f32 (vfmaq_f32 (z, ret, vmulq_f32 (z2, z)), shift); + float32x4_t ret = vfmaq_f32 (z, shift, d->pi); + ret = vfmaq_f32 (ret, z3, poly); if (__glibc_unlikely (v_any_u32 (special_cases))) { |