79 lines
2.2 KiB
C
79 lines
2.2 KiB
C
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/*
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* Single-precision asinh(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 "estrinf.h"
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#include "math_config.h"
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#include "pl_sig.h"
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#include "pl_test.h"
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#define AbsMask (0x7fffffff)
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#define SqrtFltMax (0x1.749e96p+10f)
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#define Ln2 (0x1.62e4p-1f)
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#define One (0x3f8)
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#define ExpM12 (0x398)
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#define C(i) __asinhf_data.coeffs[i]
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float
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optr_aor_log_f32 (float);
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/* asinhf approximation using a variety of approaches on different intervals:
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|x| < 2^-12: Return x. Function is exactly rounded in this region.
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|x| < 1.0: Use custom order-8 polynomial. The largest observed
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error in this region is 1.3ulps:
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asinhf(0x1.f0f74cp-1) got 0x1.b88de4p-1 want 0x1.b88de2p-1.
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|x| <= SqrtFltMax: Calculate the result directly using the
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definition of asinh(x) = ln(x + sqrt(x*x + 1)). The largest
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observed error in this region is 1.99ulps.
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asinhf(0x1.00e358p+0) got 0x1.c4849ep-1 want 0x1.c484a2p-1.
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|x| > SqrtFltMax: We cannot square x without overflow at a low
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cost. At very large x, asinh(x) ~= ln(2x). At huge x we cannot
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even double x without overflow, so calculate this as ln(x) +
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ln(2). This largest observed error in this region is 3.39ulps.
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asinhf(0x1.749e9ep+10) got 0x1.fffff8p+2 want 0x1.fffffep+2. */
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float
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asinhf (float x)
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{
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uint32_t ix = asuint (x);
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uint32_t ia = ix & AbsMask;
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uint32_t ia12 = ia >> 20;
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float ax = asfloat (ia);
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uint32_t sign = ix & ~AbsMask;
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if (unlikely (ia12 < ExpM12 || ia == 0x7f800000))
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return x;
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if (unlikely (ia12 >= 0x7f8))
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return __math_invalidf (x);
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if (ia12 < One)
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{
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float x2 = ax * ax;
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float p = ESTRIN_7 (ax, x2, x2 * x2, C);
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float y = fmaf (x2, p, ax);
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return asfloat (asuint (y) | sign);
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}
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if (unlikely (ax > SqrtFltMax))
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{
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return asfloat (asuint (optr_aor_log_f32 (ax) + Ln2) | sign);
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}
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return asfloat (asuint (optr_aor_log_f32 (ax + sqrtf (ax * ax + 1))) | sign);
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}
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PL_SIG (S, F, 1, asinh, -10.0, 10.0)
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PL_TEST_ULP (asinhf, 2.9)
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PL_TEST_INTERVAL (asinhf, 0, 0x1p-12, 5000)
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PL_TEST_INTERVAL (asinhf, 0x1p-12, 1.0, 50000)
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PL_TEST_INTERVAL (asinhf, 1.0, 0x1p11, 50000)
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PL_TEST_INTERVAL (asinhf, 0x1p11, 0x1p127, 20000)
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