/* Double-precision SVE expm1

   Copyright (C) 2023-2026 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 "sv_math.h"

#define FexpaBound 0x1.4cb5ecef28adap-3 /* 15*ln2/64.  */
#define SpecialBound 0x1.628c2855bfaddp+9 /* ln(2^(1023 + 1/128)).  */

static const struct data
{
  double c2, c4;
  double inv_ln2;
  double ln2_hi, ln2_lo;
  double c0, c1, c3;
  double shift, thres;
  uint64_t expm1_data[32];
} data = {
  /* Table emulating FEXPA - 1, for values of FEXPA close to 1.
  The table holds values of 2^(i/64) - 1, computed in arbitrary precision.
  The first half of the table stores values associated to i from 0 to 15.
  The second half of the table stores values associated to i from 0 to -15.  */
  .expm1_data = {
      0x0000000000000000, 0x3f864d1f3bc03077, 0x3f966c34c5615d0f, 0x3fa0e8a30eb37901,
      0x3fa6ab0d9f3121ec, 0x3fac7d865a7a3440, 0x3fb1301d0125b50a, 0x3fb429aaea92ddfb,
      0x3fb72b83c7d517ae, 0x3fba35beb6fcb754, 0x3fbd4873168b9aa8, 0x3fc031dc431466b2,
		  0x3fc1c3d373ab11c3, 0x3fc35a2b2f13e6e9, 0x3fc4f4efa8fef709, 0x3fc6942d3720185a,
      0x0000000000000000, 0xbfc331751ec3a814, 0xbfc20224341286e4, 0xbfc0cf85bed0f8b7,
      0xbfbf332113d56b1f, 0xbfbcc0768d4175a6, 0xbfba46f918837cb7, 0xbfb7c695afc3b424,
		  0xbfb53f391822dbc7, 0xbfb2b0cfe1266bd4, 0xbfb01b466423250a, 0xbfaafd11874c009e,
      0xbfa5b505d5b6f268, 0xbfa05e4119ea5d89, 0xbf95f134923757f3, 0xbf860f9f985bc9f4,
    },

  /* Generated using Remez, in [-log(2)/128, log(2)/128].  */
  .c0 = 0x1p-1,
  .c1 = 0x1.55555555548f9p-3,
  .c2 = 0x1.5555555554c22p-5,
  .c3 = 0x1.111123aaa2fb2p-7,
  .c4 = 0x1.6c16d77d98e5bp-10,
  .ln2_hi = 0x1.62e42fefa3800p-1,
  .ln2_lo = 0x1.ef35793c76730p-45,
  .inv_ln2 = 0x1.71547652b82fep+0,
  .shift = 0x1.800000000ffc0p+46, /* 1.5*2^46+1023.  */
  .thres = SpecialBound,
};

#define SpecialOffset 0x6000000000000000 /* 0x1p513.  */
/* SpecialBias1 + SpecialBias1 = asuint(1.0).  */
#define SpecialBias1 0x7000000000000000 /* 0x1p769.  */
#define SpecialBias2 0x3010000000000000 /* 0x1p-254.  */

static NOINLINE svfloat64_t
special_case (svbool_t pg, svfloat64_t y, svfloat64_t s, svfloat64_t p,
	      svfloat64_t n)
{
  /* s=2^n may overflow, break it up into s=s1*s2,
     such that exp = s + s*y can be computed as s1*(s2+s2*y)
     and s1*s1 overflows only if n>0.  */

  /* If n<=0 then set b to 0x6, 0 otherwise.  */
  svbool_t p_sign = svcmple (pg, n, 0.0); /* n <= 0.  */
  svuint64_t b
      = svdup_u64_z (p_sign, SpecialOffset); /* Inactive lanes set to 0.  */

  /* Set s1 to generate overflow depending on sign of exponent n,
     ie. s1 = 0x70...0 - b.  */
  svfloat64_t s1 = svreinterpret_f64 (svsubr_x (pg, b, SpecialBias1));
  /* Offset s to avoid overflow in final result if n is below threshold.
     ie. s2 = as_u64 (s) - 0x3010...0 + b.  */
  svfloat64_t s2 = svreinterpret_f64 (
      svadd_x (pg, svsub_x (pg, svreinterpret_u64 (s), SpecialBias2), b));

  /* |n| > 1280 => 2^(n) overflows.  */
  svbool_t p_cmp = svacgt (pg, n, 1280.0);

  svfloat64_t r1 = svmul_x (svptrue_b64 (), s1, s1);
  svfloat64_t r2 = svmla_x (pg, s2, s2, p);
  svfloat64_t r0 = svmul_x (svptrue_b64 (), r2, s1);

  svbool_t is_safe = svacle (pg, n, 1023); /* Only correct special lanes.  */
  return svsel (is_safe, y, svsub_x (pg, svsel (p_cmp, r1, r0), 1.0));
}

/* FEXPA based SVE expm1 algorithm.
   Maximum measured error is 2.81 + 0.5 ULP:
   _ZGVsMxv_expm1 (0x1.974060e619bfp-3) got 0x1.c290e5858bb53p-3
				       want 0x1.c290e5858bb5p-3.  */
svfloat64_t SV_NAME_D1 (expm1) (svfloat64_t x, svbool_t pg)
{
  const struct data *d = ptr_barrier (&data);

  svbool_t special = svacgt (pg, x, d->thres);

  svfloat64_t z = svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2);
  svuint64_t u = svreinterpret_u64 (z);
  svfloat64_t n = svsub_x (pg, z, d->shift);

  /* r = x - n * ln2, r is in [-ln2/128, ln2/128].  */
  svfloat64_t ln2 = svld1rq (svptrue_b64 (), &d->ln2_hi);
  svfloat64_t r = x;
  r = svmls_lane (r, n, ln2, 0);
  r = svmls_lane (r, n, ln2, 1);

  /* y = exp(r) - 1 ~= r + C0 r^2 + C1 r^3 + C2 r^4 + C3 r^5 + C4 r^6.  */
  svfloat64_t r2 = svmul_x (svptrue_b64 (), r, r);
  svfloat64_t c24 = svld1rq (svptrue_b64 (), &d->c2);

  svfloat64_t p;
  svfloat64_t c12 = svmla_lane (sv_f64 (d->c1), r, c24, 0);
  svfloat64_t c34 = svmla_lane (sv_f64 (d->c3), r, c24, 1);
  p = svmad_x (pg, c34, r2, c12);
  p = svmad_x (pg, p, r, sv_f64 (d->c0));
  p = svmad_x (pg, p, r2, r);

  svfloat64_t scale = svexpa (u);
  svfloat64_t scalem1 = svsub_x (pg, scale, sv_f64 (1.0));

  /* We want to construct expm1(x) = (scale - 1) + scale * poly.
     However, for values of scale close to 1, scale-1 causes large ULP errors
     due to cancellation.

     This can be circumvented by using a small lookup for scale-1
     when our input is below a certain bound, otherwise we can use FEXPA.

     This bound is based upon the table size:
	   Bound = (TableSize-1/64) * ln2.
     The current bound is based upon a table size of 16.  */
  svbool_t is_small = svaclt (pg, x, FexpaBound);

  if (svptest_any (pg, is_small))
    {
      /* Index via the input of FEXPA, but we only care about the lower 4 bits.
       */
      svuint64_t base_idx = svand_x (pg, u, 0xf);

      /* We can use the sign of x as a fifth bit to account for the asymmetry
	 of e^x around 0.  */
      svuint64_t signBit
	  = svlsl_x (pg, svlsr_x (pg, svreinterpret_u64 (x), 63), 4);
      svuint64_t idx = svorr_x (pg, base_idx, signBit);

      /* Lookup values for scale - 1 for small x.  */
      svfloat64_t lookup = svreinterpret_f64 (
	  svld1_gather_index (is_small, d->expm1_data, idx));

      /* Select the appropriate scale - 1 value based on x.  */
      scalem1 = svsel (is_small, lookup, scalem1);
    }

  svfloat64_t y = svmla_x (pg, scalem1, scale, p);

  /* FEXPA returns nan for large inputs so we special case those.  */
  if (__glibc_unlikely (svptest_any (pg, special)))
    {
      /* FEXPA zeroes the sign bit, however the sign is meaningful to the
          special case function so needs to be copied.
          e = sign bit of u << 46.  */
      svuint64_t e = svand_x (pg, svlsl_x (pg, u, 46), 0x8000000000000000);
      /* Copy sign to s.  */
      scale = svreinterpret_f64 (svadd_x (pg, e, svreinterpret_u64 (scale)));
      return special_case (pg, y, scale, p, n);
    }

  /* return expm1 = (scale - 1) + (scale * poly).  */
  return y;
}
