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/*
* Single-precision atan(x) function.
*
* Copyright (c) 2022-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "atanf_common.h"
#include "pl_sig.h"
#include "pl_test.h"
#define PiOver2 0x1.921fb6p+0f
#define AbsMask 0x7fffffff
#define TinyBound 0x30800000 /* asuint(0x1p-30). */
#define BigBound 0x4e800000 /* asuint(0x1p30). */
#define One 0x3f800000
/* Approximation of single-precision atan(x) based on
atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1]
using z=-1/x and shift = pi/2.
Maximum error is 2.88 ulps:
atanf(0x1.0565ccp+0) got 0x1.97771p-1
want 0x1.97770ap-1. */
float
atanf (float x)
{
uint32_t ix = asuint (x);
uint32_t sign = ix & ~AbsMask;
uint32_t ia = ix & AbsMask;
if (unlikely (ia < TinyBound))
/* Avoid underflow by returning x. */
return x;
if (unlikely (ia > BigBound))
{
if (ia > 0x7f800000)
/* Propagate NaN. */
return __math_invalidf (x);
/* atan(x) rounds to PiOver2 for large x. */
return asfloat (asuint (PiOver2) ^ sign);
}
float z, az, shift;
if (ia > One)
{
/* For x > 1, use atan(x) = pi / 2 + atan(-1 / x). */
z = -1.0f / x;
shift = PiOver2;
/* Use absolute value only when needed (odd powers of z). */
az = -fabsf (z);
}
else
{
/* For x < 1, approximate atan(x) directly. */
z = x;
az = asfloat (ia);
shift = 0;
}
/* Calculate polynomial, shift + z + z^3 * P(z^2). */
float y = eval_poly (z, az, shift);
/* Copy sign. */
return asfloat (asuint (y) ^ sign);
}
PL_SIG (S, F, 1, atan, -10.0, 10.0)
PL_TEST_ULP (atanf, 2.38)
PL_TEST_INTERVAL (atanf, 0, 0x1p-30, 5000)
PL_TEST_INTERVAL (atanf, -0, -0x1p-30, 5000)
PL_TEST_INTERVAL (atanf, 0x1p-30, 1, 40000)
PL_TEST_INTERVAL (atanf, -0x1p-30, -1, 40000)
PL_TEST_INTERVAL (atanf, 1, 0x1p30, 40000)
PL_TEST_INTERVAL (atanf, -1, -0x1p30, 40000)
PL_TEST_INTERVAL (atanf, 0x1p30, inf, 1000)
PL_TEST_INTERVAL (atanf, -0x1p30, -inf, 1000)
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