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/*
* Single-precision atanh(x) function.
*
* Copyright (c) 2022-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "math_config.h"
#include "mathlib.h"
#include "pl_sig.h"
#include "pl_test.h"
#define AbsMask 0x7fffffff
#define Half 0x3f000000
#define One 0x3f800000
#define Four 0x40800000
#define Ln2 0x1.62e43p-1f
#define TinyBound 0x39800000 /* 0x1p-12, below which atanhf(x) rounds to x. */
#define C(i) __log1pf_data.coeffs[i]
static inline float
eval_poly (float m)
{
/* Approximate log(1+m) on [-0.25, 0.5] using Estrin scheme. */
float p_12 = fmaf (m, C (1), C (0));
float p_34 = fmaf (m, C (3), C (2));
float p_56 = fmaf (m, C (5), C (4));
float p_78 = fmaf (m, C (7), C (6));
float m2 = m * m;
float p_02 = fmaf (m2, p_12, m);
float p_36 = fmaf (m2, p_56, p_34);
float p_79 = fmaf (m2, C (8), p_78);
float m4 = m2 * m2;
float p_06 = fmaf (m4, p_36, p_02);
return fmaf (m4 * p_79, m4, p_06);
}
static inline float
log1pf_inline (float x)
{
/* Helper for calculating log(x + 1). Copied from log1pf_2u1.c, with no
special-case handling. See that file for details of the algorithm. */
float m = x + 1.0f;
int k = (asuint (m) - 0x3f400000) & 0xff800000;
float s = asfloat (Four - k);
float m_scale = asfloat (asuint (x) - k) + fmaf (0.25f, s, -1.0f);
float p = eval_poly (m_scale);
float scale_back = (float) k * 0x1.0p-23f;
return fmaf (scale_back, Ln2, p);
}
/* Approximation for single-precision inverse tanh(x), using a simplified
version of log1p. Maximum error is 3.08 ULP:
atanhf(0x1.ff0d5p-5) got 0x1.ffb768p-5
want 0x1.ffb76ep-5. */
float
atanhf (float x)
{
uint32_t ix = asuint (x);
uint32_t iax = ix & AbsMask;
uint32_t sign = ix & ~AbsMask;
if (unlikely (iax < TinyBound))
return x;
if (iax == One)
return __math_divzero (sign);
if (unlikely (iax > One))
return __math_invalidf (x);
float halfsign = asfloat (Half | sign);
float ax = asfloat (iax);
return halfsign * log1pf_inline ((2 * ax) / (1 - ax));
}
PL_SIG (S, F, 1, atanh, -1.0, 1.0)
PL_TEST_ULP (atanhf, 2.59)
PL_TEST_INTERVAL (atanhf, 0, 0x1p-12, 500)
PL_TEST_INTERVAL (atanhf, 0x1p-12, 1, 200000)
PL_TEST_INTERVAL (atanhf, 1, inf, 1000)
PL_TEST_INTERVAL (atanhf, -0, -0x1p-12, 500)
PL_TEST_INTERVAL (atanhf, -0x1p-12, -1, 200000)
PL_TEST_INTERVAL (atanhf, -1, -inf, 1000)
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