expm1f.c

/*
 * Single-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_expm1f_inline.h"

static const struct data
{
  struct v_expm1f_data d;
#if WANT_SIMD_EXCEPT
  uint32x4_t thresh;
#else
  float32x4_t oflow_bound;
#endif
} data = {
  .d = V_EXPM1F_DATA,
#if !WANT_SIMD_EXCEPT
  /* Value above which expm1f(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 = V4 (0x1.5ebc4p+6),
#else
  /* asuint(oflow_bound) - asuint(0x1p-23), shifted left by 1 for absolute
     compare.  */
  .thresh = V4 (0x1d5ebc40),
#endif
};

/* asuint(0x1p-23), shifted by 1 for abs compare.  */
#define TinyBound v_u32 (0x34000000 << 1)

static float32x4_t VPCS_ATTR NOINLINE
special_case (float32x4_t x, uint32x4_t special, const struct data *d)
{
  return v_call_f32 (
      expm1f, x, expm1f_inline (v_zerofy_f32 (x, special), &d->d), special);
}

/* Single-precision vector exp(x) - 1 function.
   The maximum error is 1.62 ULP:
   _ZGVnN4v_expm1f(0x1.85f83p-2) got 0x1.da9f4p-2
				want 0x1.da9f44p-2.  */
float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (expm1) (float32x4_t x)
{
  const struct data *d = ptr_barrier (&data);

#if WANT_SIMD_EXCEPT
  uint32x4_t ix = vreinterpretq_u32_f32 (x);
  /* If fp exceptions are to be triggered correctly, fall back to scalar for
     |x| < 2^-23, |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.  */
  uint32x4_t special
      = vcgeq_u32 (vsubq_u32 (vaddq_u32 (ix, ix), TinyBound), d->thresh);
#else
  /* Handles very large values (+ve and -ve), +/-NaN, +/-Inf.  */
  uint32x4_t special = vcagtq_f32 (x, d->oflow_bound);
#endif

  if (unlikely (v_any_u32 (special)))
    return special_case (x, special, d);

  /* expm1(x) ~= p * t + (t - 1).  */
  return expm1f_inline (x, &d->d);
}

HALF_WIDTH_ALIAS_F1 (expm1)

TEST_SIG (V, F, 1, expm1, -9.9, 9.9)
TEST_ULP (V_NAME_F1 (expm1), 1.13)
TEST_DISABLE_FENV_IF_NOT (V_NAME_F1 (expm1), WANT_SIMD_EXCEPT)
TEST_SYM_INTERVAL (V_NAME_F1 (expm1), 0, 0x1p-23, 1000)
TEST_INTERVAL (V_NAME_F1 (expm1), -0x1p-23, 0x1.5ebc4p+6, 1000000)
TEST_INTERVAL (V_NAME_F1 (expm1), -0x1p-23, -0x1.9bbabcp+6, 1000000)
TEST_INTERVAL (V_NAME_F1 (expm1), 0x1.5ebc4p+6, inf, 1000)
TEST_INTERVAL (V_NAME_F1 (expm1), -0x1.9bbabcp+6, -inf, 1000)