expm1.c

/*
 * Double-precision vector exp(x) - 1 function.
 *
 * Copyright (c) 2022-2024, Arm Limited.
 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
 */

#include "v_math.h"
#include "test_sig.h"
#include "test_defs.h"
#include "v_expm1_inline.h"

static const struct data
{
  struct v_expm1_data d;
#if WANT_SIMD_EXCEPT
  uint64x2_t thresh, tiny_bound;
#else
  float64x2_t oflow_bound;
#endif
} data = {
  .d = V_EXPM1_DATA,
#if WANT_SIMD_EXCEPT
  /* asuint64(oflow_bound) - asuint64(0x1p-51), shifted left by 1 for abs
     compare.  */
  .thresh = V2 (0x78c56fa6d34b552),
  /* asuint64(0x1p-51) << 1.  */
  .tiny_bound = V2 (0x3cc0000000000000 << 1),
#else
  /* Value above which expm1(x) should overflow. Absolute value of the
     underflow bound is greater than this, so it catches both cases - there is
     a small window where fallbacks are triggered unnecessarily.  */
  .oflow_bound = V2 (0x1.62b7d369a5aa9p+9),
#endif
};

static float64x2_t VPCS_ATTR NOINLINE
special_case (float64x2_t x, uint64x2_t special, const struct data *d)
{
  return v_call_f64 (expm1, x, expm1_inline (v_zerofy_f64 (x, special), &d->d),
		     special);
}

/* Double-precision vector exp(x) - 1 function.
   The maximum error observed error is 2.05 ULP:
  _ZGVnN2v_expm1(0x1.6329669eb8c87p-2) got 0x1.a8897eef87b34p-2
				      want 0x1.a8897eef87b32p-2.  */
float64x2_t VPCS_ATTR V_NAME_D1 (expm1) (float64x2_t x)
{
  const struct data *d = ptr_barrier (&data);

#if WANT_SIMD_EXCEPT
  uint64x2_t ix = vreinterpretq_u64_f64 (x);
  /* If fp exceptions are to be triggered correctly, fall back to scalar for
     |x| < 2^-51, |x| > oflow_bound, Inf & NaN. Add ix to itself for
     shift-left by 1, and compare with thresh which was left-shifted offline -
     this is effectively an absolute compare.  */
  uint64x2_t special
      = vcgeq_u64 (vsubq_u64 (vaddq_u64 (ix, ix), d->tiny_bound), d->thresh);
#else
  /* Large input, NaNs and Infs.  */
  uint64x2_t special = vcageq_f64 (x, d->oflow_bound);
#endif

  if (unlikely (v_any_u64 (special)))
    return special_case (x, special, d);

  /* expm1(x) ~= p * t + (t - 1).  */
  return expm1_inline (x, &d->d);
}

TEST_SIG (V, D, 1, expm1, -9.9, 9.9)
TEST_ULP (V_NAME_D1 (expm1), 1.56)
TEST_DISABLE_FENV_IF_NOT (V_NAME_D1 (expm1), WANT_SIMD_EXCEPT)
TEST_SYM_INTERVAL (V_NAME_D1 (expm1), 0, 0x1p-51, 1000)
TEST_SYM_INTERVAL (V_NAME_D1 (expm1), 0x1p-51, 0x1.62b7d369a5aa9p+9, 100000)
TEST_SYM_INTERVAL (V_NAME_D1 (expm1), 0x1.62b7d369a5aa9p+9, inf, 100)