diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/atan2f_sve.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/atan2f_sve.c | 61 |
1 files changed, 38 insertions, 23 deletions
diff --git a/sysdeps/aarch64/fpu/atan2f_sve.c b/sysdeps/aarch64/fpu/atan2f_sve.c index 5f26e2a..4d93419 100644 --- a/sysdeps/aarch64/fpu/atan2f_sve.c +++ b/sysdeps/aarch64/fpu/atan2f_sve.c @@ -18,18 +18,18 @@ <https://www.gnu.org/licenses/>. */ #include "sv_math.h" -#include "poly_sve_f32.h" static const struct data { - float32_t poly[8]; + float32_t c0, c2, c4, c6; + float32_t c1, c3, c5, c7; 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, + .c0 = -0x1.5554dcp-2, .c1 = 0x1.9978ecp-3, .c2 = -0x1.230a94p-3, + .c3 = 0x1.b4debp-4, .c4 = -0x1.3550dap-4, .c5 = 0x1.61eebp-5, + .c6 = -0x1.0c17d4p-6, .c7 = 0x1.7ea694p-9, .pi_over_2 = 0x1.921fb6p+0f, }; /* Special cases i.e. 0, infinity, nan (fall back to scalar calls). */ @@ -51,12 +51,14 @@ zeroinfnan (svuint32_t i, 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) + observed error is 2.21 ULP: + _ZGVnN4vv_atan2f (0x1.a04aa8p+6, 0x1.9a274p+6) got 0x1.95ed3ap-1 + want 0x1.95ed36p-1. */ +svfloat32_t SV_NAME_F2 (atan2) (svfloat32_t y, svfloat32_t x, + const svbool_t pg) { - const struct data *data_ptr = ptr_barrier (&data); + const struct data *d = ptr_barrier (&data); + svbool_t ptrue = svptrue_b32 (); svuint32_t ix = svreinterpret_u32 (x); svuint32_t iy = svreinterpret_u32 (y); @@ -76,29 +78,42 @@ svfloat32_t SV_NAME_F2 (atan2) (svfloat32_t y, svfloat32_t x, const svbool_t pg) svbool_t pred_aygtax = svcmpgt (pg, ay, ax); - /* Set up z for call to atan. */ - 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. */ + /* Set up z for evaluation of atanf. */ + svfloat32_t num = svsel (pred_aygtax, svneg_x (pg, ax), ay); + svfloat32_t den = svsel (pred_aygtax, ay, ax); + svfloat32_t z = svdiv_x (ptrue, 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. */ svfloat32_t shift = svreinterpret_f32 (svlsr_x (pg, sign_x, 1)); shift = svsel (pred_aygtax, sv_f32 (1.0), shift); shift = svreinterpret_f32 (svorr_x (pg, sign_x, svreinterpret_u32 (shift))); - shift = svmul_x (pg, shift, sv_f32 (data_ptr->pi_over_2)); /* Use pure Estrin scheme for P(z^2) with deg(P)=7. */ - svfloat32_t z2 = svmul_x (pg, z, z); + svfloat32_t z2 = svmul_x (ptrue, z, z); + svfloat32_t z3 = svmul_x (pg, z2, z); svfloat32_t z4 = svmul_x (pg, z2, z2); svfloat32_t z8 = svmul_x (pg, z4, z4); - svfloat32_t ret = sv_estrin_7_f32_x (pg, z2, z4, z8, data_ptr->poly); + svfloat32_t odd_coeffs = svld1rq (ptrue, &d->c1); - /* ret = shift + z + z^3 * P(z^2). */ - svfloat32_t z3 = svmul_x (pg, z2, z); - ret = svmla_x (pg, z, z3, ret); + svfloat32_t p01 = svmla_lane (sv_f32 (d->c0), z2, odd_coeffs, 0); + svfloat32_t p23 = svmla_lane (sv_f32 (d->c2), z2, odd_coeffs, 1); + svfloat32_t p45 = svmla_lane (sv_f32 (d->c4), z2, odd_coeffs, 2); + svfloat32_t p67 = svmla_lane (sv_f32 (d->c6), z2, odd_coeffs, 3); - ret = svadd_m (pg, ret, shift); + svfloat32_t p03 = svmla_x (pg, p01, z4, p23); + svfloat32_t p47 = svmla_x (pg, p45, z4, p67); + + svfloat32_t poly = svmla_x (pg, p03, z8, p47); + + /* ret = shift + z + z^3 * P(z^2). */ + svfloat32_t ret = svmla_x (pg, z, shift, sv_f32 (d->pi_over_2)); + ret = svmla_x (pg, ret, z3, poly); /* Account for the sign of x and y. */ |