diff options
Diffstat (limited to 'pl/math/v_atan2_3u.c')
| -rw-r--r-- | pl/math/v_atan2_3u.c | 117 |
1 files changed, 74 insertions, 43 deletions
diff --git a/pl/math/v_atan2_3u.c b/pl/math/v_atan2_3u.c index 6327fea8eb2c..f24667682dec 100644 --- a/pl/math/v_atan2_3u.c +++ b/pl/math/v_atan2_3u.c @@ -8,83 +8,114 @@ #include "v_math.h" #include "pl_sig.h" #include "pl_test.h" +#include "poly_advsimd_f64.h" -#if V_SUPPORTED - -#include "atan_common.h" +static const struct data +{ + float64x2_t pi_over_2; + float64x2_t poly[20]; +} data = { + /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on + the interval [2**-1022, 1.0]. */ + .poly = { V2 (-0x1.5555555555555p-2), V2 (0x1.99999999996c1p-3), + V2 (-0x1.2492492478f88p-3), V2 (0x1.c71c71bc3951cp-4), + V2 (-0x1.745d160a7e368p-4), V2 (0x1.3b139b6a88ba1p-4), + V2 (-0x1.11100ee084227p-4), V2 (0x1.e1d0f9696f63bp-5), + V2 (-0x1.aebfe7b418581p-5), V2 (0x1.842dbe9b0d916p-5), + V2 (-0x1.5d30140ae5e99p-5), V2 (0x1.338e31eb2fbbcp-5), + V2 (-0x1.00e6eece7de8p-5), V2 (0x1.860897b29e5efp-6), + V2 (-0x1.0051381722a59p-6), V2 (0x1.14e9dc19a4a4ep-7), + V2 (-0x1.d0062b42fe3bfp-9), V2 (0x1.17739e210171ap-10), + V2 (-0x1.ab24da7be7402p-13), V2 (0x1.358851160a528p-16), }, + .pi_over_2 = V2 (0x1.921fb54442d18p+0), +}; -#define PiOver2 v_f64 (0x1.921fb54442d18p+0) #define SignMask v_u64 (0x8000000000000000) /* Special cases i.e. 0, infinity, NaN (fall back to scalar calls). */ -VPCS_ATTR -NOINLINE static v_f64_t -specialcase (v_f64_t y, v_f64_t x, v_f64_t ret, v_u64_t cmp) +static float64x2_t VPCS_ATTR NOINLINE +special_case (float64x2_t y, float64x2_t x, float64x2_t ret, uint64x2_t cmp) { return v_call2_f64 (atan2, y, x, ret, cmp); } /* Returns 1 if input is the bit representation of 0, infinity or nan. */ -static inline v_u64_t -zeroinfnan (v_u64_t i) +static inline uint64x2_t +zeroinfnan (uint64x2_t i) { - return v_cond_u64 (2 * i - 1 >= v_u64 (2 * asuint64 (INFINITY) - 1)); + /* (2 * i - 1) >= (2 * asuint64 (INFINITY) - 1). */ + return vcgeq_u64 (vsubq_u64 (vaddq_u64 (i, i), v_u64 (1)), + v_u64 (2 * asuint64 (INFINITY) - 1)); } /* Fast implementation of vector atan2. Maximum observed error is 2.8 ulps: - v_atan2(0x1.9651a429a859ap+5, 0x1.953075f4ee26p+5) + _ZGVnN2vv_atan2 (0x1.9651a429a859ap+5, 0x1.953075f4ee26p+5) got 0x1.92d628ab678ccp-1 want 0x1.92d628ab678cfp-1. */ -VPCS_ATTR -v_f64_t V_NAME (atan2) (v_f64_t y, v_f64_t x) +float64x2_t VPCS_ATTR V_NAME_D2 (atan2) (float64x2_t y, float64x2_t x) { - v_u64_t ix = v_as_u64_f64 (x); - v_u64_t iy = v_as_u64_f64 (y); + const struct data *data_ptr = ptr_barrier (&data); - v_u64_t special_cases = zeroinfnan (ix) | zeroinfnan (iy); + uint64x2_t ix = vreinterpretq_u64_f64 (x); + uint64x2_t iy = vreinterpretq_u64_f64 (y); - v_u64_t sign_x = ix & SignMask; - v_u64_t sign_y = iy & SignMask; - v_u64_t sign_xy = sign_x ^ sign_y; + uint64x2_t special_cases = vorrq_u64 (zeroinfnan (ix), zeroinfnan (iy)); - v_f64_t ax = v_abs_f64 (x); - v_f64_t ay = v_abs_f64 (y); + uint64x2_t sign_x = vandq_u64 (ix, SignMask); + uint64x2_t sign_y = vandq_u64 (iy, SignMask); + uint64x2_t sign_xy = veorq_u64 (sign_x, sign_y); - v_u64_t pred_xlt0 = x < 0.0; - v_u64_t pred_aygtax = ay > ax; + float64x2_t ax = vabsq_f64 (x); + float64x2_t ay = vabsq_f64 (y); + + uint64x2_t pred_xlt0 = vcltzq_f64 (x); + uint64x2_t pred_aygtax = vcgtq_f64 (ay, ax); /* Set up z for call to atan. */ - v_f64_t n = v_sel_f64 (pred_aygtax, -ax, ay); - v_f64_t d = v_sel_f64 (pred_aygtax, ay, ax); - v_f64_t z = v_div_f64 (n, d); + float64x2_t n = vbslq_f64 (pred_aygtax, vnegq_f64 (ax), ay); + float64x2_t d = vbslq_f64 (pred_aygtax, ay, ax); + float64x2_t z = vdivq_f64 (n, d); /* Work out the correct shift. */ - v_f64_t shift = v_sel_f64 (pred_xlt0, v_f64 (-2.0), v_f64 (0.0)); - shift = v_sel_f64 (pred_aygtax, shift + 1.0, shift); - shift *= PiOver2; - - v_f64_t ret = eval_poly (z, z, shift); + float64x2_t shift = vreinterpretq_f64_u64 ( + vandq_u64 (pred_xlt0, vreinterpretq_u64_f64 (v_f64 (-2.0)))); + shift = vbslq_f64 (pred_aygtax, vaddq_f64 (shift, v_f64 (1.0)), shift); + shift = vmulq_f64 (shift, data_ptr->pi_over_2); + + /* Calculate the polynomial approximation. + Use split Estrin scheme for P(z^2) with deg(P)=19. Use split instead of + full scheme to avoid underflow in x^16. + The order 19 polynomial P approximates + (atan(sqrt(x))-sqrt(x))/x^(3/2). */ + float64x2_t z2 = vmulq_f64 (z, z); + float64x2_t x2 = vmulq_f64 (z2, z2); + float64x2_t x4 = vmulq_f64 (x2, x2); + float64x2_t x8 = vmulq_f64 (x4, x4); + float64x2_t ret + = vfmaq_f64 (v_estrin_7_f64 (z2, x2, x4, data_ptr->poly), + v_estrin_11_f64 (z2, x2, x4, x8, data_ptr->poly + 8), x8); + + /* Finalize. y = shift + z + z^3 * P(z^2). */ + ret = vfmaq_f64 (z, ret, vmulq_f64 (z2, z)); + ret = vaddq_f64 (ret, shift); /* Account for the sign of x and y. */ - ret = v_as_f64_u64 (v_as_u64_f64 (ret) ^ sign_xy); + ret = vreinterpretq_f64_u64 ( + veorq_u64 (vreinterpretq_u64_f64 (ret), sign_xy)); if (unlikely (v_any_u64 (special_cases))) - { - return specialcase (y, x, ret, special_cases); - } + return special_case (y, x, ret, special_cases); return ret; } -VPCS_ALIAS /* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */ PL_SIG (V, D, 2, atan2) // TODO tighten this once __v_atan2 is fixed -PL_TEST_ULP (V_NAME (atan2), 2.9) -PL_TEST_INTERVAL (V_NAME (atan2), -10.0, 10.0, 50000) -PL_TEST_INTERVAL (V_NAME (atan2), -1.0, 1.0, 40000) -PL_TEST_INTERVAL (V_NAME (atan2), 0.0, 1.0, 40000) -PL_TEST_INTERVAL (V_NAME (atan2), 1.0, 100.0, 40000) -PL_TEST_INTERVAL (V_NAME (atan2), 1e6, 1e32, 40000) -#endif +PL_TEST_ULP (V_NAME_D2 (atan2), 2.9) +PL_TEST_INTERVAL (V_NAME_D2 (atan2), -10.0, 10.0, 50000) +PL_TEST_INTERVAL (V_NAME_D2 (atan2), -1.0, 1.0, 40000) +PL_TEST_INTERVAL (V_NAME_D2 (atan2), 0.0, 1.0, 40000) +PL_TEST_INTERVAL (V_NAME_D2 (atan2), 1.0, 100.0, 40000) +PL_TEST_INTERVAL (V_NAME_D2 (atan2), 1e6, 1e32, 40000) |