diff options
Diffstat (limited to 'pl/math/sv_atan2f_3u.c')
| -rw-r--r-- | pl/math/sv_atan2f_3u.c | 112 |
1 files changed, 63 insertions, 49 deletions
diff --git a/pl/math/sv_atan2f_3u.c b/pl/math/sv_atan2f_3u.c index f7674c441f2f..9ff73ecb74ba 100644 --- a/pl/math/sv_atan2f_3u.c +++ b/pl/math/sv_atan2f_3u.c @@ -8,87 +8,101 @@ #include "sv_math.h" #include "pl_sig.h" #include "pl_test.h" +#include "poly_sve_f32.h" -#if SV_SUPPORTED - -#include "sv_atanf_common.h" +static const struct data +{ + float32_t poly[8]; + float32_t pi_over_2; +} data = { + /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on + [2**-128, 1.0]. */ + .poly = { -0x1.55555p-2f, 0x1.99935ep-3f, -0x1.24051ep-3f, 0x1.bd7368p-4f, + -0x1.491f0ep-4f, 0x1.93a2c0p-5f, -0x1.4c3c60p-6f, 0x1.01fd88p-8f }, + .pi_over_2 = 0x1.921fb6p+0f, +}; -/* Useful constants. */ -#define PiOver2 sv_f32 (0x1.921fb6p+0f) #define SignMask sv_u32 (0x80000000) /* Special cases i.e. 0, infinity, nan (fall back to scalar calls). */ -static inline sv_f32_t -specialcase (sv_f32_t y, sv_f32_t x, sv_f32_t ret, const svbool_t cmp) +static inline svfloat32_t +special_case (svfloat32_t y, svfloat32_t x, svfloat32_t ret, + const svbool_t cmp) { return sv_call2_f32 (atan2f, y, x, ret, cmp); } -/* Returns a predicate indicating true if the input is the bit representation of - 0, infinity or nan. */ +/* Returns a predicate indicating true if the input is the bit representation + of 0, infinity or nan. */ static inline svbool_t -zeroinfnan (sv_u32_t i, const svbool_t pg) +zeroinfnan (svuint32_t i, const svbool_t pg) { - return svcmpge_u32 (pg, svsub_n_u32_x (pg, svlsl_n_u32_x (pg, i, 1), 1), - sv_u32 (2 * 0x7f800000lu - 1)); + return svcmpge (pg, svsub_x (pg, svlsl_x (pg, i, 1), 1), + sv_u32 (2 * 0x7f800000lu - 1)); } -/* Fast implementation of SVE atan2f 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 2.95 ULP: - __sv_atan2f(0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1 - want 0x1.967f00p-1. */ -sv_f32_t -__sv_atan2f_x (sv_f32_t y, sv_f32_t x, const svbool_t pg) +/* Fast implementation of SVE atan2f 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 2.95 ULP: + _ZGVsMxvv_atan2f (0x1.93836cp+6, 0x1.8cae1p+6) got 0x1.967f06p-1 + want 0x1.967f00p-1. */ +svfloat32_t SV_NAME_F2 (atan2) (svfloat32_t y, svfloat32_t x, const svbool_t pg) { - sv_u32_t ix = sv_as_u32_f32 (x); - sv_u32_t iy = sv_as_u32_f32 (y); + const struct data *data_ptr = ptr_barrier (&data); + + svuint32_t ix = svreinterpret_u32 (x); + svuint32_t iy = svreinterpret_u32 (y); svbool_t cmp_x = zeroinfnan (ix, pg); svbool_t cmp_y = zeroinfnan (iy, pg); - svbool_t cmp_xy = svorr_b_z (pg, cmp_x, cmp_y); + svbool_t cmp_xy = svorr_z (pg, cmp_x, cmp_y); - sv_u32_t sign_x = svand_u32_x (pg, ix, SignMask); - sv_u32_t sign_y = svand_u32_x (pg, iy, SignMask); - sv_u32_t sign_xy = sveor_u32_x (pg, sign_x, sign_y); + svuint32_t sign_x = svand_x (pg, ix, SignMask); + svuint32_t sign_y = svand_x (pg, iy, SignMask); + svuint32_t sign_xy = sveor_x (pg, sign_x, sign_y); - sv_f32_t ax = svabs_f32_x (pg, x); - sv_f32_t ay = svabs_f32_x (pg, y); + svfloat32_t ax = svabs_x (pg, x); + svfloat32_t ay = svabs_x (pg, y); - svbool_t pred_xlt0 = svcmplt_f32 (pg, x, sv_f32 (0.0)); - svbool_t pred_aygtax = svcmpgt_f32 (pg, ay, ax); + svbool_t pred_xlt0 = svcmplt (pg, x, 0.0); + svbool_t pred_aygtax = svcmpgt (pg, ay, ax); /* Set up z for call to atan. */ - sv_f32_t n = svsel_f32 (pred_aygtax, svneg_f32_x (pg, ax), ay); - sv_f32_t d = svsel_f32 (pred_aygtax, ay, ax); - sv_f32_t z = svdiv_f32_x (pg, n, d); + svfloat32_t n = svsel (pred_aygtax, svneg_x (pg, ax), ay); + svfloat32_t d = svsel (pred_aygtax, ay, ax); + svfloat32_t z = svdiv_x (pg, n, d); /* Work out the correct shift. */ - sv_f32_t shift = svsel_f32 (pred_xlt0, sv_f32 (-2.0), sv_f32 (0.0)); - shift = svsel_f32 (pred_aygtax, svadd_n_f32_x (pg, shift, 1.0), shift); - shift = svmul_f32_x (pg, shift, PiOver2); + svfloat32_t shift = svsel (pred_xlt0, sv_f32 (-2.0), sv_f32 (0.0)); + shift = svsel (pred_aygtax, svadd_x (pg, shift, 1.0), shift); + shift = svmul_x (pg, shift, sv_f32 (data_ptr->pi_over_2)); + + /* Use split Estrin scheme for P(z^2) with deg(P)=7. */ + svfloat32_t z2 = svmul_x (pg, z, z); + svfloat32_t z4 = svmul_x (pg, z2, z2); + svfloat32_t z8 = svmul_x (pg, z4, z4); - sv_f32_t ret = __sv_atanf_common (pg, pg, z, z, shift); + svfloat32_t ret = sv_estrin_7_f32_x (pg, z2, z4, z8, data_ptr->poly); + + /* ret = shift + z + z^3 * P(z^2). */ + svfloat32_t z3 = svmul_x (pg, z2, z); + ret = svmla_x (pg, z, z3, ret); + + ret = svadd_m (pg, ret, shift); /* Account for the sign of x and y. */ - ret = sv_as_f32_u32 (sveor_u32_x (pg, sv_as_u32_f32 (ret), sign_xy)); + ret = svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (ret), sign_xy)); if (unlikely (svptest_any (pg, cmp_xy))) - { - return specialcase (y, x, ret, cmp_xy); - } + return special_case (y, x, ret, cmp_xy); return ret; } -PL_ALIAS (__sv_atan2f_x, _ZGVsMxvv_atan2f) - /* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */ PL_SIG (SV, F, 2, atan2) -PL_TEST_ULP (__sv_atan2f, 2.45) -PL_TEST_INTERVAL (__sv_atan2f, -10.0, 10.0, 50000) -PL_TEST_INTERVAL (__sv_atan2f, -1.0, 1.0, 40000) -PL_TEST_INTERVAL (__sv_atan2f, 0.0, 1.0, 40000) -PL_TEST_INTERVAL (__sv_atan2f, 1.0, 100.0, 40000) -PL_TEST_INTERVAL (__sv_atan2f, 1e6, 1e32, 40000) -#endif +PL_TEST_ULP (SV_NAME_F2 (atan2), 2.45) +PL_TEST_INTERVAL (SV_NAME_F2 (atan2), 0.0, 1.0, 40000) +PL_TEST_INTERVAL (SV_NAME_F2 (atan2), 1.0, 100.0, 40000) +PL_TEST_INTERVAL (SV_NAME_F2 (atan2), 100, inf, 40000) +PL_TEST_INTERVAL (SV_NAME_F2 (atan2), -0, -inf, 40000) |