/* Double-precision AdvSIMD inverse sin

   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_f64.h"

static const struct data
{
  float64x2_t poly[12];
  float64x2_t pi_over_2;
  uint64x2_t abs_mask;
} data = {
  /* Polynomial approximation of  (asin(sqrt(x)) - sqrt(x)) / (x * sqrt(x))
     on [ 0x1p-106, 0x1p-2 ], relative error: 0x1.c3d8e169p-57.  */
  .poly = { V2 (0x1.555555555554ep-3), V2 (0x1.3333333337233p-4),
	    V2 (0x1.6db6db67f6d9fp-5), V2 (0x1.f1c71fbd29fbbp-6),
	    V2 (0x1.6e8b264d467d6p-6), V2 (0x1.1c5997c357e9dp-6),
	    V2 (0x1.c86a22cd9389dp-7), V2 (0x1.856073c22ebbep-7),
	    V2 (0x1.fd1151acb6bedp-8), V2 (0x1.087182f799c1dp-6),
	    V2 (-0x1.6602748120927p-7), V2 (0x1.cfa0dd1f9478p-6), },
  .pi_over_2 = V2 (0x1.921fb54442d18p+0),
  .abs_mask = V2 (0x7fffffffffffffff),
};

#define AllMask v_u64 (0xffffffffffffffff)
#define One (0x3ff0000000000000)
#define Small (0x3e50000000000000) /* 2^-12.  */

#if WANT_SIMD_EXCEPT
static float64x2_t VPCS_ATTR NOINLINE
special_case (float64x2_t x, float64x2_t y, uint64x2_t special)
{
  return v_call_f64 (asin, x, y, special);
}
#endif

/* Double-precision implementation of vector asin(x).

   For |x| < Small, approximate asin(x) by x. Small = 2^-12 for correct
   rounding. If WANT_SIMD_EXCEPT = 0, Small = 0 and we proceed with the
   following approximation.

   For |x| in [Small, 0.5], use an order 11 polynomial P such that the final
   approximation is an odd polynomial: asin(x) ~ x + x^3 P(x^2).

   The largest observed error in this region is 1.01 ulps,
   _ZGVnN2v_asin (0x1.da9735b5a9277p-2) got 0x1.ed78525a927efp-2
				       want 0x1.ed78525a927eep-2.

   For |x| in [0.5, 1.0], use same approximation with a change of variable

     asin(x) = pi/2 - (y + y * z * P(z)), with  z = (1-x)/2 and y = sqrt(z).

   The largest observed error in this region is 2.69 ulps,
   _ZGVnN2v_asin (0x1.044ac9819f573p-1) got 0x1.110d7e85fdd5p-1
				       want 0x1.110d7e85fdd53p-1.  */
float64x2_t VPCS_ATTR V_NAME_D1 (asin) (float64x2_t x)
{
  const struct data *d = ptr_barrier (&data);

  float64x2_t ax = vabsq_f64 (x);

#if WANT_SIMD_EXCEPT
  /* Special values need to be computed with scalar fallbacks so
     that appropriate exceptions are raised.  */
  uint64x2_t special
      = vcgtq_u64 (vsubq_u64 (vreinterpretq_u64_f64 (ax), v_u64 (Small)),
		   v_u64 (One - Small));
  if (__glibc_unlikely (v_any_u64 (special)))
    return special_case (x, x, AllMask);
#endif

  uint64x2_t a_lt_half = vcltq_f64 (ax, v_f64 (0.5));

  /* Evaluate polynomial Q(x) = y + y * z * P(z) with
     z = x ^ 2 and y = |x|            , if |x| < 0.5
     z = (1 - |x|) / 2 and y = sqrt(z), if |x| >= 0.5.  */
  float64x2_t z2 = vbslq_f64 (a_lt_half, vmulq_f64 (x, x),
			      vfmsq_n_f64 (v_f64 (0.5), ax, 0.5));
  float64x2_t z = vbslq_f64 (a_lt_half, ax, vsqrtq_f64 (z2));

  /* Use a single polynomial approximation P for both intervals.  */
  float64x2_t z4 = vmulq_f64 (z2, z2);
  float64x2_t z8 = vmulq_f64 (z4, z4);
  float64x2_t z16 = vmulq_f64 (z8, z8);
  float64x2_t p = v_estrin_11_f64 (z2, z4, z8, z16, d->poly);

  /* Finalize polynomial: z + z * z2 * P(z2).  */
  p = vfmaq_f64 (z, vmulq_f64 (z, z2), p);

  /* asin(|x|) = Q(|x|)         , for |x| < 0.5
	       = pi/2 - 2 Q(|x|), for |x| >= 0.5.  */
  float64x2_t y = vbslq_f64 (a_lt_half, p, vfmsq_n_f64 (d->pi_over_2, p, 2.0));

  /* Copy sign.  */
  return vbslq_f64 (d->abs_mask, y, x);
}