atanh.c

/*
 * Double-precision SVE atanh(x) function.
 *
 * Copyright (c) 2023-2024, Arm Limited.
 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
 */

#include "sv_math.h"
#include "test_sig.h"
#include "test_defs.h"

#define WANT_SV_LOG1P_K0_SHORTCUT 0
#include "sv_log1p_inline.h"

#define One (0x3ff0000000000000)
#define Half (0x3fe0000000000000)

static svfloat64_t NOINLINE
special_case (svfloat64_t x, svfloat64_t y, svbool_t special)
{
  return sv_call_f64 (atanh, x, y, special);
}

/* SVE approximation for double-precision atanh, based on log1p.
   The greatest observed error is 2.81 ULP:
   _ZGVsMxv_atanh(0x1.ffae6288b601p-6) got 0x1.ffd8ff31b5019p-6
				      want 0x1.ffd8ff31b501cp-6.  */
svfloat64_t SV_NAME_D1 (atanh) (svfloat64_t x, const svbool_t pg)
{

  svfloat64_t ax = svabs_x (pg, x);
  svuint64_t iax = svreinterpret_u64 (ax);
  svuint64_t sign = sveor_x (pg, svreinterpret_u64 (x), iax);
  svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, Half));

  /* It is special if iax >= 1.  */
  svbool_t special = svacge (pg, x, 1.0);

  /* Computation is performed based on the following sequence of equality:
	(1+x)/(1-x) = 1 + 2x/(1-x).  */
  svfloat64_t y;
  y = svadd_x (pg, ax, ax);
  y = svdiv_x (pg, y, svsub_x (pg, sv_f64 (1), ax));
  /* ln((1+x)/(1-x)) = ln(1+2x/(1-x)) = ln(1 + y).  */
  y = sv_log1p_inline (y, pg);

  if (unlikely (svptest_any (pg, special)))
    return special_case (x, svmul_x (pg, halfsign, y), special);
  return svmul_x (pg, halfsign, y);
}

TEST_SIG (SV, D, 1, atanh, -1.0, 1.0)
TEST_ULP (SV_NAME_D1 (atanh), 3.32)
TEST_DISABLE_FENV (SV_NAME_D1 (atanh))
TEST_SYM_INTERVAL (SV_NAME_D1 (atanh), 0, 0x1p-23, 10000)
TEST_SYM_INTERVAL (SV_NAME_D1 (atanh), 0x1p-23, 1, 90000)
TEST_SYM_INTERVAL (SV_NAME_D1 (atanh), 1, inf, 100)
/* atanh is asymptotic at 1, which is the default control value - have to set
   -c 0 specially to ensure fp exceptions are triggered correctly (choice of
   control lane is irrelevant if fp exceptions are disabled).  */
TEST_CONTROL_VALUE (SV_NAME_D1 (atanh), 0)
CLOSE_SVE_ATTR