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