diff options
Diffstat (limited to 'sysdeps/aarch64/fpu')
| -rw-r--r-- | sysdeps/aarch64/fpu/sin_advsimd.c | 10 | ||||
| -rw-r--r-- | sysdeps/aarch64/fpu/sin_sve.c | 106 | ||||
| -rw-r--r-- | sysdeps/aarch64/fpu/sinf_sve.c | 44 |
3 files changed, 87 insertions, 73 deletions
diff --git a/sysdeps/aarch64/fpu/sin_advsimd.c b/sysdeps/aarch64/fpu/sin_advsimd.c index 0389b334cc..3d87a1da79 100644 --- a/sysdeps/aarch64/fpu/sin_advsimd.c +++ b/sysdeps/aarch64/fpu/sin_advsimd.c @@ -24,7 +24,6 @@ static const struct data float64x2_t poly[7]; float64x2_t range_val, inv_pi, shift, pi_1, pi_2, pi_3; } data = { - /* Worst-case error is 2.8 ulp in [-pi/2, pi/2]. */ .poly = { V2 (-0x1.555555555547bp-3), V2 (0x1.1111111108a4dp-7), V2 (-0x1.a01a019936f27p-13), V2 (0x1.71de37a97d93ep-19), V2 (-0x1.ae633919987c6p-26), V2 (0x1.60e277ae07cecp-33), @@ -52,6 +51,15 @@ special_case (float64x2_t x, float64x2_t y, uint64x2_t odd, uint64x2_t cmp) return v_call_f64 (sin, x, y, cmp); } +/* Vector (AdvSIMD) sin approximation. + Maximum observed error in [-pi/2, pi/2], where argument is not reduced, + is 2.87 ULP: + _ZGVnN2v_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1 + want 0x1.fffffffa7dc05p-1 + Maximum observed error in the entire non-special domain ([-2^23, 2^23]) + is 3.22 ULP: + _ZGVnN2v_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3 + want 0x1.ffdcd125c84f8p-3. */ float64x2_t VPCS_ATTR V_NAME_D1 (sin) (float64x2_t x) { const struct data *d = ptr_barrier (&data); diff --git a/sysdeps/aarch64/fpu/sin_sve.c b/sysdeps/aarch64/fpu/sin_sve.c index c3f450d0ea..54c8dae286 100644 --- a/sysdeps/aarch64/fpu/sin_sve.c +++ b/sysdeps/aarch64/fpu/sin_sve.c @@ -21,20 +21,22 @@ static const struct data { - double inv_pi, half_pi, inv_pi_over_2, pi_over_2_1, pi_over_2_2, pi_over_2_3, - shift; + double inv_pi, pi_1, pi_2, pi_3, shift, range_val; + double poly[7]; } data = { - /* Polynomial coefficients are hard-wired in the FTMAD instruction. */ + .poly = { -0x1.555555555547bp-3, 0x1.1111111108a4dp-7, -0x1.a01a019936f27p-13, + 0x1.71de37a97d93ep-19, -0x1.ae633919987c6p-26, + 0x1.60e277ae07cecp-33, -0x1.9e9540300a1p-41, }, + .inv_pi = 0x1.45f306dc9c883p-2, - .half_pi = 0x1.921fb54442d18p+0, - .inv_pi_over_2 = 0x1.45f306dc9c882p-1, - .pi_over_2_1 = 0x1.921fb50000000p+0, - .pi_over_2_2 = 0x1.110b460000000p-26, - .pi_over_2_3 = 0x1.1a62633145c07p-54, - .shift = 0x1.8p52 + .pi_1 = 0x1.921fb54442d18p+1, + .pi_2 = 0x1.1a62633145c06p-53, + .pi_3 = 0x1.c1cd129024e09p-106, + .shift = 0x1.8p52, + .range_val = 0x1p23, }; -#define RangeVal 0x4160000000000000 /* asuint64 (0x1p23). */ +#define C(i) sv_f64 (d->poly[i]) static svfloat64_t NOINLINE special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp) @@ -42,56 +44,58 @@ special_case (svfloat64_t x, svfloat64_t y, svbool_t cmp) return sv_call_f64 (sin, x, y, cmp); } -/* A fast SVE implementation of sin based on trigonometric - instructions (FTMAD, FTSSEL, FTSMUL). - Maximum observed error in 2.52 ULP: - SV_NAME_D1 (sin)(0x1.2d2b00df69661p+19) got 0x1.10ace8f3e786bp-40 - want 0x1.10ace8f3e7868p-40. */ +/* A fast SVE implementation of sin. + Maximum observed error in [-pi/2, pi/2], where argument is not reduced, + is 2.87 ULP: + _ZGVsMxv_sin (0x1.921d5c6a07142p+0) got 0x1.fffffffa7dc02p-1 + want 0x1.fffffffa7dc05p-1 + Maximum observed error in the entire non-special domain ([-2^23, 2^23]) + is 3.22 ULP: + _ZGVsMxv_sin (0x1.5702447b6f17bp+22) got 0x1.ffdcd125c84fbp-3 + want 0x1.ffdcd125c84f8p-3. */ svfloat64_t SV_NAME_D1 (sin) (svfloat64_t x, const svbool_t pg) { const struct data *d = ptr_barrier (&data); - svfloat64_t r = svabs_f64_x (pg, x); - svuint64_t sign - = sveor_u64_x (pg, svreinterpret_u64_f64 (x), svreinterpret_u64_f64 (r)); - svbool_t cmp = svcmpge_n_u64 (pg, svreinterpret_u64_f64 (r), RangeVal); + /* Load some values in quad-word chunks to minimise memory access. */ + const svbool_t ptrue = svptrue_b64 (); + svfloat64_t shift = sv_f64 (d->shift); + svfloat64_t inv_pi_and_pi1 = svld1rq (ptrue, &d->inv_pi); + svfloat64_t pi2_and_pi3 = svld1rq (ptrue, &d->pi_2); - /* Load first two pio2-related constants to one vector. */ - svfloat64_t invpio2_and_pio2_1 - = svld1rq_f64 (svptrue_b64 (), &d->inv_pi_over_2); + /* n = rint(|x|/pi). */ + svfloat64_t n = svmla_lane (shift, x, inv_pi_and_pi1, 0); + svuint64_t odd = svlsl_x (pg, svreinterpret_u64 (n), 63); + n = svsub_x (pg, n, shift); - /* n = rint(|x|/(pi/2)). */ - svfloat64_t q = svmla_lane_f64 (sv_f64 (d->shift), r, invpio2_and_pio2_1, 0); - svfloat64_t n = svsub_n_f64_x (pg, q, d->shift); + /* r = |x| - n*(pi/2) (range reduction into -pi/2 .. pi/2). */ + svfloat64_t r = x; + r = svmls_lane (r, n, inv_pi_and_pi1, 1); + r = svmls_lane (r, n, pi2_and_pi3, 0); + r = svmls_lane (r, n, pi2_and_pi3, 1); - /* r = |x| - n*(pi/2) (range reduction into -pi/4 .. pi/4). */ - r = svmls_lane_f64 (r, n, invpio2_and_pio2_1, 1); - r = svmls_n_f64_x (pg, r, n, d->pi_over_2_2); - r = svmls_n_f64_x (pg, r, n, d->pi_over_2_3); + /* sin(r) poly approx. */ + svfloat64_t r2 = svmul_x (pg, r, r); + svfloat64_t r3 = svmul_x (pg, r2, r); + svfloat64_t r4 = svmul_x (pg, r2, r2); - /* Final multiplicative factor: 1.0 or x depending on bit #0 of q. */ - svfloat64_t f = svtssel_f64 (r, svreinterpret_u64_f64 (q)); + svfloat64_t t1 = svmla_x (pg, C (4), C (5), r2); + svfloat64_t t2 = svmla_x (pg, C (2), C (3), r2); + svfloat64_t t3 = svmla_x (pg, C (0), C (1), r2); - /* sin(r) poly approx. */ - svfloat64_t r2 = svtsmul_f64 (r, svreinterpret_u64_f64 (q)); - svfloat64_t y = sv_f64 (0.0); - y = svtmad_f64 (y, r2, 7); - y = svtmad_f64 (y, r2, 6); - y = svtmad_f64 (y, r2, 5); - y = svtmad_f64 (y, r2, 4); - y = svtmad_f64 (y, r2, 3); - y = svtmad_f64 (y, r2, 2); - y = svtmad_f64 (y, r2, 1); - y = svtmad_f64 (y, r2, 0); - - /* Apply factor. */ - y = svmul_f64_x (pg, f, y); - - /* sign = y^sign. */ - y = svreinterpret_f64_u64 ( - sveor_u64_x (pg, svreinterpret_u64_f64 (y), sign)); + svfloat64_t y = svmla_x (pg, t1, C (6), r4); + y = svmla_x (pg, t2, y, r4); + y = svmla_x (pg, t3, y, r4); + y = svmla_x (pg, r, y, r3); + svbool_t cmp = svacle (pg, x, d->range_val); + cmp = svnot_z (pg, cmp); if (__glibc_unlikely (svptest_any (pg, cmp))) - return special_case (x, y, cmp); - return y; + return special_case (x, + svreinterpret_f64 (sveor_z ( + svnot_z (pg, cmp), svreinterpret_u64 (y), odd)), + cmp); + + /* Copy sign. */ + return svreinterpret_f64 (sveor_z (pg, svreinterpret_u64 (y), odd)); } diff --git a/sysdeps/aarch64/fpu/sinf_sve.c b/sysdeps/aarch64/fpu/sinf_sve.c index 4d2ce7a846..590881c14b 100644 --- a/sysdeps/aarch64/fpu/sinf_sve.c +++ b/sysdeps/aarch64/fpu/sinf_sve.c @@ -23,7 +23,7 @@ static const struct data { float poly[4]; /* Pi-related values to be loaded as one quad-word and used with - svmla_lane_f32. */ + svmla_lane. */ float negpi1, negpi2, negpi3, invpi; float shift; } data = { @@ -57,40 +57,42 @@ svfloat32_t SV_NAME_F1 (sin) (svfloat32_t x, const svbool_t pg) { const struct data *d = ptr_barrier (&data); - svfloat32_t ax = svabs_f32_x (pg, x); - svuint32_t sign = sveor_u32_x (pg, svreinterpret_u32_f32 (x), - svreinterpret_u32_f32 (ax)); - svbool_t cmp = svcmpge_n_u32 (pg, svreinterpret_u32_f32 (ax), RangeVal); + svfloat32_t ax = svabs_x (pg, x); + svuint32_t sign + = sveor_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (ax)); + svbool_t cmp = svcmpge (pg, svreinterpret_u32 (ax), RangeVal); /* pi_vals are a quad-word of helper values - the first 3 elements contain -pi in extended precision, the last contains 1 / pi. */ - svfloat32_t pi_vals = svld1rq_f32 (svptrue_b32 (), &d->negpi1); + svfloat32_t pi_vals = svld1rq (svptrue_b32 (), &d->negpi1); /* n = rint(|x|/pi). */ - svfloat32_t n = svmla_lane_f32 (sv_f32 (d->shift), ax, pi_vals, 3); - svuint32_t odd = svlsl_n_u32_x (pg, svreinterpret_u32_f32 (n), 31); - n = svsub_n_f32_x (pg, n, d->shift); + svfloat32_t n = svmla_lane (sv_f32 (d->shift), ax, pi_vals, 3); + svuint32_t odd = svlsl_x (pg, svreinterpret_u32 (n), 31); + n = svsub_x (pg, n, d->shift); /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */ svfloat32_t r; - r = svmla_lane_f32 (ax, n, pi_vals, 0); - r = svmla_lane_f32 (r, n, pi_vals, 1); - r = svmla_lane_f32 (r, n, pi_vals, 2); + r = svmla_lane (ax, n, pi_vals, 0); + r = svmla_lane (r, n, pi_vals, 1); + r = svmla_lane (r, n, pi_vals, 2); /* sin(r) approx using a degree 9 polynomial from the Taylor series expansion. Note that only the odd terms of this are non-zero. */ - svfloat32_t r2 = svmul_f32_x (pg, r, r); + svfloat32_t r2 = svmul_x (pg, r, r); svfloat32_t y; - y = svmla_f32_x (pg, C (2), r2, C (3)); - y = svmla_f32_x (pg, C (1), r2, y); - y = svmla_f32_x (pg, C (0), r2, y); - y = svmla_f32_x (pg, r, r, svmul_f32_x (pg, y, r2)); + y = svmla_x (pg, C (2), r2, C (3)); + y = svmla_x (pg, C (1), r2, y); + y = svmla_x (pg, C (0), r2, y); + y = svmla_x (pg, r, r, svmul_x (pg, y, r2)); /* sign = y^sign^odd. */ - y = svreinterpret_f32_u32 (sveor_u32_x (pg, svreinterpret_u32_f32 (y), - sveor_u32_x (pg, sign, odd))); + sign = sveor_x (pg, sign, odd); if (__glibc_unlikely (svptest_any (pg, cmp))) - return special_case (x, y, cmp); - return y; + return special_case (x, + svreinterpret_f32 (sveor_x ( + svnot_z (pg, cmp), svreinterpret_u32 (y), sign)), + cmp); + return svreinterpret_f32 (sveor_x (pg, svreinterpret_u32 (y), sign)); } |