acosh.c

/*
 * Double-precision SVE acosh(x) function.
 * Copyright (c) 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 1
#include "sv_log1p_inline.h"

#define One (0x3ff0000000000000)
#define Thres (0x1ff0000000000000) /* asuint64 (0x1p511) - One.  */

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

/* SVE approximation for double-precision acosh, based on log1p.
   The largest observed error is 3.19 ULP in the region where the
   argument to log1p falls in the k=0 interval, i.e. x close to 1:
   SV_NAME_D1 (acosh)(0x1.1e4388d4ca821p+0) got 0x1.ed23399f5137p-2
					   want 0x1.ed23399f51373p-2.  */
svfloat64_t SV_NAME_D1 (acosh) (svfloat64_t x, const svbool_t pg)
{
  /* (ix - One) >= (BigBound - One).  */
  svuint64_t ix = svreinterpret_u64 (x);
  svbool_t special = svcmpge (pg, svsub_x (pg, ix, One), Thres);

  svfloat64_t xm1 = svsub_x (pg, x, 1.0);
  svfloat64_t u = svmul_x (pg, xm1, svadd_x (pg, x, 1.0));
  svfloat64_t y = svadd_x (pg, xm1, svsqrt_x (pg, u));

  /* Fall back to scalar routine for special lanes.  */
  if (unlikely (svptest_any (pg, special)))
    return special_case (x, sv_log1p_inline (y, pg), special);
  return sv_log1p_inline (y, pg);
}

TEST_SIG (SV, D, 1, acosh, 1.0, 10.0)
TEST_ULP (SV_NAME_D1 (acosh), 2.69)
TEST_DISABLE_FENV (SV_NAME_D1 (acosh))
TEST_INTERVAL (SV_NAME_D1 (acosh), 1, 0x1p511, 90000)
TEST_INTERVAL (SV_NAME_D1 (acosh), 0x1p511, inf, 10000)
TEST_INTERVAL (SV_NAME_D1 (acosh), 0, 1, 1000)
TEST_INTERVAL (SV_NAME_D1 (acosh), -0, -inf, 10000)
CLOSE_SVE_ATTR