diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/atan_sve.c')
| -rw-r--r-- | sysdeps/aarch64/fpu/atan_sve.c | 104 |
1 files changed, 67 insertions, 37 deletions
diff --git a/sysdeps/aarch64/fpu/atan_sve.c b/sysdeps/aarch64/fpu/atan_sve.c index 3880ced..a6b0489 100644 --- a/sysdeps/aarch64/fpu/atan_sve.c +++ b/sysdeps/aarch64/fpu/atan_sve.c @@ -18,23 +18,26 @@ <https://www.gnu.org/licenses/>. */ #include "sv_math.h" -#include "poly_sve_f64.h" static const struct data { - float64_t poly[20]; - float64_t pi_over_2; + float64_t c0, c2, c4, c6, c8, c10, c12, c14, c16, c18; + float64_t c1, c3, c5, c7, c9, c11, c13, c15, c17, c19; + float64_t shift_val, neg_one; } data = { /* Coefficients of polynomial P such that atan(x)~x+x*P(x^2) on [2**-1022, 1.0]. */ - .poly = { -0x1.5555555555555p-2, 0x1.99999999996c1p-3, -0x1.2492492478f88p-3, - 0x1.c71c71bc3951cp-4, -0x1.745d160a7e368p-4, 0x1.3b139b6a88ba1p-4, - -0x1.11100ee084227p-4, 0x1.e1d0f9696f63bp-5, -0x1.aebfe7b418581p-5, - 0x1.842dbe9b0d916p-5, -0x1.5d30140ae5e99p-5, 0x1.338e31eb2fbbcp-5, - -0x1.00e6eece7de8p-5, 0x1.860897b29e5efp-6, -0x1.0051381722a59p-6, - 0x1.14e9dc19a4a4ep-7, -0x1.d0062b42fe3bfp-9, 0x1.17739e210171ap-10, - -0x1.ab24da7be7402p-13, 0x1.358851160a528p-16, }, - .pi_over_2 = 0x1.921fb54442d18p+0, + .c0 = -0x1.555555555552ap-2, .c1 = 0x1.9999999995aebp-3, + .c2 = -0x1.24924923923f6p-3, .c3 = 0x1.c71c7184288a2p-4, + .c4 = -0x1.745d11fb3d32bp-4, .c5 = 0x1.3b136a18051b9p-4, + .c6 = -0x1.110e6d985f496p-4, .c7 = 0x1.e1bcf7f08801dp-5, + .c8 = -0x1.ae644e28058c3p-5, .c9 = 0x1.82eeb1fed85c6p-5, + .c10 = -0x1.59d7f901566cbp-5, .c11 = 0x1.2c982855ab069p-5, + .c12 = -0x1.eb49592998177p-6, .c13 = 0x1.69d8b396e3d38p-6, + .c14 = -0x1.ca980345c4204p-7, .c15 = 0x1.dc050eafde0b3p-8, + .c16 = -0x1.7ea70755b8eccp-9, .c17 = 0x1.ba3da3de903e8p-11, + .c18 = -0x1.44a4b059b6f67p-13, .c19 = 0x1.c4a45029e5a91p-17, + .shift_val = 0x1.490fdaa22168cp+1, .neg_one = -1, }; /* Useful constants. */ @@ -43,15 +46,14 @@ static const struct data /* Fast implementation of SVE 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. Largest errors are close to 1. The maximum observed - error is 2.27 ulps: - _ZGVsMxv_atan (0x1.0005af27c23e9p+0) got 0x1.9225645bdd7c1p-1 - want 0x1.9225645bdd7c3p-1. */ + error is 2.08 ulps: + _ZGVsMxv_atan (0x1.000a7c56975e8p+0) got 0x1.922a3163e15c2p-1 + want 0x1.922a3163e15c4p-1. */ svfloat64_t SV_NAME_D1 (atan) (svfloat64_t x, const svbool_t pg) { const struct data *d = ptr_barrier (&data); - /* No need to trigger special case. Small cases, infs and nans - are supported by our approximation technique. */ + svbool_t ptrue = svptrue_b64 (); svuint64_t ix = svreinterpret_u64 (x); svuint64_t sign = svand_x (pg, ix, SignMask); @@ -59,32 +61,60 @@ svfloat64_t SV_NAME_D1 (atan) (svfloat64_t x, const svbool_t pg) 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, 1.0); - /* Avoid dependency in abs(x) in division (and comparison). */ - svfloat64_t z = svsel (red, svdivr_x (pg, x, 1.0), x); - /* Use absolute value only when needed (odd powers of z). */ - svfloat64_t az = svabs_x (pg, z); - az = svneg_m (az, red, az); + svbool_t red = svacgt (pg, x, d->neg_one); + svfloat64_t z = svsel (red, svdiv_x (pg, sv_f64 (d->neg_one), x), x); + + /* Reuse of -1.0f to reduce constant loads, + We need a shift value of 1/2, which is created via -1 + (1 + 1/2). */ + svfloat64_t shift + = svadd_z (red, sv_f64 (d->neg_one), sv_f64 (d->shift_val)); + + /* Reinserts the sign bit of the argument to handle the case of x < -1. */ + shift = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (shift), sign)); /* Use split Estrin scheme for P(z^2) with deg(P)=19. */ - svfloat64_t z2 = svmul_x (pg, z, z); - svfloat64_t x2 = svmul_x (pg, z2, z2); - svfloat64_t x4 = svmul_x (pg, x2, x2); - svfloat64_t x8 = svmul_x (pg, x4, x4); + svfloat64_t z2 = svmul_x (ptrue, z, z); + svfloat64_t z4 = svmul_x (ptrue, z2, z2); + svfloat64_t z8 = svmul_x (ptrue, z4, z4); + svfloat64_t z16 = svmul_x (ptrue, z8, z8); - svfloat64_t y - = svmla_x (pg, sv_estrin_7_f64_x (pg, z2, x2, x4, d->poly), - sv_estrin_11_f64_x (pg, z2, x2, x4, x8, d->poly + 8), x8); + /* Order-7 Estrin. */ + svfloat64_t c13 = svld1rq (ptrue, &d->c1); + svfloat64_t c57 = svld1rq (ptrue, &d->c5); - /* y = shift + z + z^3 * P(z^2). */ - svfloat64_t z3 = svmul_x (pg, z2, az); - y = svmla_x (pg, az, z3, y); + svfloat64_t p01 = svmla_lane (sv_f64 (d->c0), z2, c13, 0); + svfloat64_t p23 = svmla_lane (sv_f64 (d->c2), z2, c13, 1); + svfloat64_t p45 = svmla_lane (sv_f64 (d->c4), z2, c57, 0); + svfloat64_t p67 = svmla_lane (sv_f64 (d->c6), z2, c57, 1); + + svfloat64_t p03 = svmla_x (pg, p01, z4, p23); + svfloat64_t p47 = svmla_x (pg, p45, z4, p67); + svfloat64_t p07 = svmla_x (pg, p03, z8, p47); + + /* Order-11 Estrin. */ + svfloat64_t c911 = svld1rq (ptrue, &d->c9); + svfloat64_t c1315 = svld1rq (ptrue, &d->c13); + svfloat64_t c1719 = svld1rq (ptrue, &d->c17); - /* Apply shift as indicated by `red` predicate. */ - y = svadd_m (red, y, d->pi_over_2); + svfloat64_t p89 = svmla_lane (sv_f64 (d->c8), z2, c911, 0); + svfloat64_t p1011 = svmla_lane (sv_f64 (d->c10), z2, c911, 1); + svfloat64_t p811 = svmla_x (pg, p89, z4, p1011); - /* y = atan(x) if x>0, -atan(-x) otherwise. */ - y = svreinterpret_f64 (sveor_x (pg, svreinterpret_u64 (y), sign)); + svfloat64_t p1213 = svmla_lane (sv_f64 (d->c12), z2, c1315, 0); + svfloat64_t p1415 = svmla_lane (sv_f64 (d->c14), z2, c1315, 1); + svfloat64_t p1215 = svmla_x (pg, p1213, z4, p1415); - return y; + svfloat64_t p1617 = svmla_lane (sv_f64 (d->c16), z2, c1719, 0); + svfloat64_t p1819 = svmla_lane (sv_f64 (d->c18), z2, c1719, 1); + svfloat64_t p1619 = svmla_x (pg, p1617, z4, p1819); + + svfloat64_t p815 = svmla_x (pg, p811, z8, p1215); + svfloat64_t p819 = svmla_x (pg, p815, z16, p1619); + + svfloat64_t y = svmla_x (pg, p07, z16, p819); + + /* y = shift + z + z^3 * P(z^2). */ + shift = svadd_m (red, z, shift); + y = svmul_x (pg, z2, y); + return svmla_x (pg, shift, z, y); } |