diff options
Diffstat (limited to 'sysdeps/aarch64/fpu/tanf_advsimd.c')
-rw-r--r-- | sysdeps/aarch64/fpu/tanf_advsimd.c | 129 |
1 files changed, 129 insertions, 0 deletions
diff --git a/sysdeps/aarch64/fpu/tanf_advsimd.c b/sysdeps/aarch64/fpu/tanf_advsimd.c new file mode 100644 index 0000000000..4c8a7f740e --- /dev/null +++ b/sysdeps/aarch64/fpu/tanf_advsimd.c @@ -0,0 +1,129 @@ +/* Single-precision vector (Advanced SIMD) tan function + + Copyright (C) 2023 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <https://www.gnu.org/licenses/>. */ + +#include "v_math.h" +#include "poly_advsimd_f32.h" + +static const struct data +{ + float32x4_t poly[6]; + float32x4_t neg_half_pi_1, neg_half_pi_2, neg_half_pi_3, two_over_pi, shift; +#if !WANT_SIMD_EXCEPT + float32x4_t range_val; +#endif +} data = { + /* Coefficients generated using FPMinimax. */ + .poly = { V4 (0x1.55555p-2f), V4 (0x1.11166p-3f), V4 (0x1.b88a78p-5f), + V4 (0x1.7b5756p-6f), V4 (0x1.4ef4cep-8f), V4 (0x1.0e1e74p-7f) }, + .neg_half_pi_1 = V4 (-0x1.921fb6p+0f), + .neg_half_pi_2 = V4 (0x1.777a5cp-25f), + .neg_half_pi_3 = V4 (0x1.ee59dap-50f), + .two_over_pi = V4 (0x1.45f306p-1f), + .shift = V4 (0x1.8p+23f), +#if !WANT_SIMD_EXCEPT + .range_val = V4 (0x1p15f), +#endif +}; + +#define RangeVal v_u32 (0x47000000) /* asuint32(0x1p15f). */ +#define TinyBound v_u32 (0x30000000) /* asuint32 (0x1p-31f). */ +#define Thresh v_u32 (0x16000000) /* asuint32(RangeVal) - TinyBound. */ + +/* Special cases (fall back to scalar calls). */ +static float32x4_t VPCS_ATTR NOINLINE +special_case (float32x4_t x, float32x4_t y, uint32x4_t cmp) +{ + return v_call_f32 (tanf, x, y, cmp); +} + +/* Use a full Estrin scheme to evaluate polynomial. */ +static inline float32x4_t +eval_poly (float32x4_t z, const struct data *d) +{ + float32x4_t z2 = vmulq_f32 (z, z); +#if WANT_SIMD_EXCEPT + /* Tiny z (<= 0x1p-31) will underflow when calculating z^4. If fp exceptions + are to be triggered correctly, sidestep this by fixing such lanes to 0. */ + uint32x4_t will_uflow + = vcleq_u32 (vreinterpretq_u32_f32 (vabsq_f32 (z)), TinyBound); + if (__glibc_unlikely (v_any_u32 (will_uflow))) + z2 = vbslq_f32 (will_uflow, v_f32 (0), z2); +#endif + float32x4_t z4 = vmulq_f32 (z2, z2); + return v_estrin_5_f32 (z, z2, z4, d->poly); +} + +/* Fast implementation of AdvSIMD tanf. + Maximum error is 3.45 ULP: + __v_tanf(-0x1.e5f0cap+13) got 0x1.ff9856p-1 + want 0x1.ff9850p-1. */ +float32x4_t VPCS_ATTR V_NAME_F1 (tan) (float32x4_t x) +{ + const struct data *d = ptr_barrier (&data); + float32x4_t special_arg = x; + + /* iax >= RangeVal means x, if not inf or NaN, is too large to perform fast + regression. */ +#if WANT_SIMD_EXCEPT + uint32x4_t iax = vreinterpretq_u32_f32 (vabsq_f32 (x)); + /* If fp exceptions are to be triggered correctly, also special-case tiny + input, as this will load to overflow later. Fix any special lanes to 1 to + prevent any exceptions being triggered. */ + uint32x4_t special = vcgeq_u32 (vsubq_u32 (iax, TinyBound), Thresh); + if (__glibc_unlikely (v_any_u32 (special))) + x = vbslq_f32 (special, v_f32 (1.0f), x); +#else + /* Otherwise, special-case large and special values. */ + uint32x4_t special = vcageq_f32 (x, d->range_val); +#endif + + /* n = rint(x/(pi/2)). */ + float32x4_t q = vfmaq_f32 (d->shift, d->two_over_pi, x); + float32x4_t n = vsubq_f32 (q, d->shift); + /* Determine if x lives in an interval, where |tan(x)| grows to infinity. */ + uint32x4_t pred_alt = vtstq_u32 (vreinterpretq_u32_f32 (q), v_u32 (1)); + + /* r = x - n * (pi/2) (range reduction into -pi./4 .. pi/4). */ + float32x4_t r; + r = vfmaq_f32 (x, d->neg_half_pi_1, n); + r = vfmaq_f32 (r, d->neg_half_pi_2, n); + r = vfmaq_f32 (r, d->neg_half_pi_3, n); + + /* If x lives in an interval, where |tan(x)| + - is finite, then use a polynomial approximation of the form + tan(r) ~ r + r^3 * P(r^2) = r + r * r^2 * P(r^2). + - grows to infinity then use symmetries of tangent and the identity + tan(r) = cotan(pi/2 - r) to express tan(x) as 1/tan(-r). Finally, use + the same polynomial approximation of tan as above. */ + + /* Invert sign of r if odd quadrant. */ + float32x4_t z = vmulq_f32 (r, vbslq_f32 (pred_alt, v_f32 (-1), v_f32 (1))); + + /* Evaluate polynomial approximation of tangent on [-pi/4, pi/4]. */ + float32x4_t z2 = vmulq_f32 (r, r); + float32x4_t p = eval_poly (z2, d); + float32x4_t y = vfmaq_f32 (z, vmulq_f32 (z, z2), p); + + /* Compute reciprocal and apply if required. */ + float32x4_t inv_y = vdivq_f32 (v_f32 (1.0f), y); + + if (__glibc_unlikely (v_any_u32 (special))) + return special_case (special_arg, vbslq_f32 (pred_alt, inv_y, y), special); + return vbslq_f32 (pred_alt, inv_y, y); +} |