diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/atanf_sve.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/atanf_sve.c | 84 |
1 files changed, 49 insertions, 35 deletions
diff --git a/sysdeps/aarch64/fpu/atanf_sve.c b/sysdeps/aarch64/fpu/atanf_sve.c index 3a98d70..6558223 100644 --- a/sysdeps/aarch64/fpu/atanf_sve.c +++ b/sysdeps/aarch64/fpu/atanf_sve.c @@ -18,18 +18,26 @@ <https://www.gnu.org/licenses/>. */ #include "sv_math.h" -#include "poly_sve_f32.h" static const struct data { - float32_t poly[8]; - float32_t pi_over_2; + float32_t c1, c3, c5, c7; + float32_t c0, c2, c4, c6; + float32_t shift_val, neg_one; } 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/2, used as a shift value after reduction. */ + .shift_val = 0x1.921fb54442d18p+0, + .neg_one = -1.0f, }; #define SignMask (0x80000000) @@ -37,43 +45,49 @@ static const struct data /* Fast implementation of SVE atanf based on atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] using z=-1/x and shift = pi/2. - Largest observed error is 2.9 ULP, close to +/-1.0: - _ZGVsMxv_atanf (0x1.0468f6p+0) got -0x1.967f06p-1 - want -0x1.967fp-1. */ + Largest observed error is 2.12 ULP: + _ZGVsMxv_atanf (0x1.03d4cep+0) got 0x1.95ed3ap-1 + want 0x1.95ed36p-1. */ svfloat32_t SV_NAME_F1 (atan) (svfloat32_t x, const svbool_t pg) { const struct data *d = ptr_barrier (&data); + svbool_t ptrue = svptrue_b32 (); /* No need to trigger special case. Small cases, infs and nans are supported by our approximation technique. */ svuint32_t ix = svreinterpret_u32 (x); - svuint32_t sign = svand_x (pg, ix, SignMask); + svuint32_t sign = svand_x (ptrue, ix, SignMask); /* Argument reduction: 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. */ - svbool_t red = svacgt (pg, x, 1.0f); - /* Avoid dependency in abs(x) in division (and comparison). */ - svfloat32_t z = svsel (red, svdiv_x (pg, sv_f32 (1.0f), x), x); - /* Use absolute value only when needed (odd powers of z). */ - svfloat32_t az = svabs_x (pg, z); - az = svneg_m (az, red, az); - - /* 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); - - svfloat32_t y = sv_estrin_7_f32_x (pg, z2, z4, z8, d->poly); - - /* y = shift + z + z^3 * P(z^2). */ - svfloat32_t z3 = svmul_x (pg, z2, az); - y = svmla_x (pg, az, z3, y); - - /* Apply shift as indicated by 'red' predicate. */ - y = svadd_m (red, y, sv_f32 (d->pi_over_2)); - - /* y = atan(x) if x>0, -atan(-x) otherwise. */ - return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign)); + y := arctan(-1/x) + pi/2 for x > +1 + y := arctan(-1/x) - pi/2 for x < -1 + Hence, use z=-1/a if |x|>=|-1|, otherwise z=a. */ + svbool_t red = svacgt (pg, x, d->neg_one); + svfloat32_t z = svsel (red, svdiv_x (pg, sv_f32 (d->neg_one), x), x); + + /* Reinserts the sign bit of the argument to handle the case of x < -1. */ + svfloat32_t shift = svreinterpret_f32 ( + sveor_x (red, svreinterpret_u32 (sv_f32 (d->shift_val)), sign)); + + svfloat32_t z2 = svmul_x (ptrue, z, z); + svfloat32_t z3 = svmul_x (ptrue, z2, z); + svfloat32_t z4 = svmul_x (ptrue, z2, z2); + svfloat32_t z8 = svmul_x (ptrue, z4, z4); + + svfloat32_t odd_coeffs = svld1rq (ptrue, &d->c1); + + 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); + + svfloat32_t p03 = svmla_x (pg, p01, z4, p23); + svfloat32_t p47 = svmla_x (pg, p45, z4, p67); + + svfloat32_t y = svmla_x (pg, p03, z8, p47); + + /* shift + z + z^3 * P(z^2). */ + shift = svadd_m (red, z, shift); + return svmla_x (pg, shift, z3, y); } |