83 lines
2.4 KiB
C
83 lines
2.4 KiB
C
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/*
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* Double-precision tanh(x) function.
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*
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* Copyright (c) 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 "math_config.h"
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#include "estrin.h"
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#include "pl_sig.h"
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#include "pl_test.h"
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#define AbsMask 0x7fffffffffffffff
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#define InvLn2 0x1.71547652b82fep0
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#define Ln2hi 0x1.62e42fefa39efp-1
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#define Ln2lo 0x1.abc9e3b39803fp-56
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#define Shift 0x1.8p52
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#define C(i) __expm1_poly[i]
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#define BoringBound 0x403241bf835f9d5f /* asuint64 (0x1.241bf835f9d5fp+4). */
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#define TinyBound 0x3e40000000000000 /* asuint64 (0x1p-27). */
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#define One 0x3ff0000000000000
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static inline double
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expm1_inline (double x)
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{
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/* Helper routine for calculating exp(x) - 1. Copied from expm1_2u5.c, with
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several simplifications:
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- No special-case handling for tiny or special values.
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- Simpler combination of p and t in final stage of the algorithm.
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- Use shift-and-add instead of ldexp to calculate t. */
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/* Reduce argument: f in [-ln2/2, ln2/2], i is exact. */
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double j = fma (InvLn2, x, Shift) - Shift;
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int64_t i = j;
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double f = fma (j, -Ln2hi, x);
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f = fma (j, -Ln2lo, f);
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/* Approximate expm1(f) using polynomial. */
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double f2 = f * f;
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double f4 = f2 * f2;
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double p = fma (f2, ESTRIN_10 (f, f2, f4, f4 * f4, C), f);
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/* t = 2 ^ i. */
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double t = asdouble ((uint64_t) (i + 1023) << 52);
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/* expm1(x) = p * t + (t - 1). */
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return fma (p, t, t - 1);
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}
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/* Approximation for double-precision tanh(x), using a simplified version of
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expm1. The greatest observed error is 2.75 ULP:
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tanh(-0x1.c143c3a44e087p-3) got -0x1.ba31ba4691ab7p-3
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want -0x1.ba31ba4691ab4p-3. */
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double
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tanh (double x)
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{
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uint64_t ix = asuint64 (x);
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uint64_t ia = ix & AbsMask;
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uint64_t sign = ix & ~AbsMask;
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if (unlikely (ia > BoringBound))
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{
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if (ia > 0x7ff0000000000000)
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return __math_invalid (x);
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return asdouble (One | sign);
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}
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if (unlikely (ia < TinyBound))
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return x;
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/* tanh(x) = (e^2x - 1) / (e^2x + 1). */
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double q = expm1_inline (2 * x);
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return q / (q + 2);
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}
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PL_SIG (S, D, 1, tanh, -10.0, 10.0)
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PL_TEST_ULP (tanh, 2.26)
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PL_TEST_INTERVAL (tanh, 0, TinyBound, 1000)
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PL_TEST_INTERVAL (tanh, -0, -TinyBound, 1000)
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PL_TEST_INTERVAL (tanh, TinyBound, BoringBound, 100000)
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PL_TEST_INTERVAL (tanh, -TinyBound, -BoringBound, 100000)
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PL_TEST_INTERVAL (tanh, BoringBound, inf, 1000)
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PL_TEST_INTERVAL (tanh, -BoringBound, -inf, 1000)
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