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/*
* Double-precision SVE atanh(x) function.
*
* Copyright (c) 2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "sv_math.h"
#include "pl_sig.h"
#include "pl_test.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 = svcmpge (pg, iax, One);
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);
}
PL_SIG (SV, D, 1, atanh, -1.0, 1.0)
PL_TEST_ULP (SV_NAME_D1 (atanh), 3.32)
/* 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). */
PL_TEST_SYM_INTERVAL_C (SV_NAME_D1 (atanh), 0, 0x1p-23, 10000, 0)
PL_TEST_SYM_INTERVAL_C (SV_NAME_D1 (atanh), 0x1p-23, 1, 90000, 0)
PL_TEST_SYM_INTERVAL_C (SV_NAME_D1 (atanh), 1, inf, 100, 0)
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