diff options
Diffstat (limited to 'pl/math/v_atan_2u5.c')
| -rw-r--r-- | pl/math/v_atan_2u5.c | 98 |
1 files changed, 64 insertions, 34 deletions
diff --git a/pl/math/v_atan_2u5.c b/pl/math/v_atan_2u5.c index 0f3c2ccf2606..ba68cc3cc720 100644 --- a/pl/math/v_atan_2u5.c +++ b/pl/math/v_atan_2u5.c @@ -8,33 +8,51 @@ #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 + [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 AbsMask v_u64 (0x7fffffffffffffff) -#define TinyBound 0x3e1 /* top12(asuint64(0x1p-30)). */ -#define BigBound 0x434 /* top12(asuint64(0x1p53)). */ +#define SignMask v_u64 (0x8000000000000000) +#define TinyBound 0x3e10000000000000 /* asuint64(0x1p-30). */ +#define BigBound 0x4340000000000000 /* asuint64(0x1p53). */ /* Fast implementation of vector atan. Based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using z=1/x and shift = pi/2. Maximum observed error is 2.27 ulps: - __v_atan(0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1 - want 0x1.9225645bdd7c3p-1. */ -VPCS_ATTR -v_f64_t V_NAME (atan) (v_f64_t x) + _ZGVnN2v_atan (0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1 + want 0x1.9225645bdd7c3p-1. */ +float64x2_t VPCS_ATTR V_NAME_D1 (atan) (float64x2_t x) { + const struct data *d = ptr_barrier (&data); + /* Small cases, infs and nans are supported by our approximation technique, but do not set fenv flags correctly. Only trigger special case if we need fenv. */ - v_u64_t ix = v_as_u64_f64 (x); - v_u64_t sign = ix & ~AbsMask; + uint64x2_t ix = vreinterpretq_u64_f64 (x); + uint64x2_t sign = vandq_u64 (ix, SignMask); #if WANT_SIMD_EXCEPT - v_u64_t ia12 = (ix >> 52) & 0x7ff; - v_u64_t special = v_cond_u64 (ia12 - TinyBound > BigBound - TinyBound); + uint64x2_t ia12 = vandq_u64 (ix, v_u64 (0x7ff0000000000000)); + uint64x2_t special = vcgtq_u64 (vsubq_u64 (ia12, v_u64 (TinyBound)), + v_u64 (BigBound - TinyBound)); /* If any lane is special, fall back to the scalar routine for all lanes. */ if (unlikely (v_any_u64 (special))) return v_call_f64 (atan, x, v_f64 (0), v_u64 (-1)); @@ -44,31 +62,43 @@ v_f64_t V_NAME (atan) (v_f64_t x) y := arctan(x) for x < 1 y := pi/2 + arctan(-1/x) for x > 1 Hence, use z=-1/a if x>=1, otherwise z=a. */ - v_u64_t red = v_cagt_f64 (x, v_f64 (1.0)); + uint64x2_t red = vcagtq_f64 (x, v_f64 (1.0)); /* Avoid dependency in abs(x) in division (and comparison). */ - v_f64_t z = v_sel_f64 (red, v_div_f64 (v_f64 (-1.0), x), x); - v_f64_t shift = v_sel_f64 (red, PiOver2, v_f64 (0.0)); + float64x2_t z = vbslq_f64 (red, vdivq_f64 (v_f64 (1.0), x), x); + float64x2_t shift = vreinterpretq_f64_u64 ( + vandq_u64 (red, vreinterpretq_u64_f64 (d->pi_over_2))); /* Use absolute value only when needed (odd powers of z). */ - v_f64_t az = v_abs_f64 (z); - az = v_sel_f64 (red, -az, az); + float64x2_t az = vbslq_f64 ( + SignMask, vreinterpretq_f64_u64 (vandq_u64 (SignMask, red)), z); - /* Calculate the polynomial approximation. */ - v_f64_t y = eval_poly (z, az, shift); + /* 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 y + = vfmaq_f64 (v_estrin_7_f64 (z2, x2, x4, d->poly), + v_estrin_11_f64 (z2, x2, x4, x8, d->poly + 8), x8); + + /* Finalize. y = shift + z + z^3 * P(z^2). */ + y = vfmaq_f64 (az, y, vmulq_f64 (z2, az)); + y = vaddq_f64 (y, shift); /* y = atan(x) if x>0, -atan(-x) otherwise. */ - y = v_as_f64_u64 (v_as_u64_f64 (y) ^ sign); + y = vreinterpretq_f64_u64 (veorq_u64 (vreinterpretq_u64_f64 (y), sign)); return y; } -VPCS_ALIAS PL_SIG (V, D, 1, atan, -10.0, 10.0) -PL_TEST_ULP (V_NAME (atan), 1.78) -PL_TEST_EXPECT_FENV (V_NAME (atan), WANT_SIMD_EXCEPT) -PL_TEST_INTERVAL (V_NAME (atan), 0, 0x1p-30, 10000) -PL_TEST_INTERVAL (V_NAME (atan), -0, -0x1p-30, 1000) -PL_TEST_INTERVAL (V_NAME (atan), 0x1p-30, 0x1p53, 900000) -PL_TEST_INTERVAL (V_NAME (atan), -0x1p-30, -0x1p53, 90000) -PL_TEST_INTERVAL (V_NAME (atan), 0x1p53, inf, 10000) -PL_TEST_INTERVAL (V_NAME (atan), -0x1p53, -inf, 1000) - -#endif +PL_TEST_ULP (V_NAME_D1 (atan), 1.78) +PL_TEST_EXPECT_FENV (V_NAME_D1 (atan), WANT_SIMD_EXCEPT) +PL_TEST_INTERVAL (V_NAME_D1 (atan), 0, 0x1p-30, 10000) +PL_TEST_INTERVAL (V_NAME_D1 (atan), -0, -0x1p-30, 1000) +PL_TEST_INTERVAL (V_NAME_D1 (atan), 0x1p-30, 0x1p53, 900000) +PL_TEST_INTERVAL (V_NAME_D1 (atan), -0x1p-30, -0x1p53, 90000) +PL_TEST_INTERVAL (V_NAME_D1 (atan), 0x1p53, inf, 10000) +PL_TEST_INTERVAL (V_NAME_D1 (atan), -0x1p53, -inf, 1000) |