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https://github.com/freebsd/freebsd-src
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072a4ba82a
Sponsored by: Arm Ltd
87 lines
2.6 KiB
C
87 lines
2.6 KiB
C
/*
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* Double-precision atanh(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 "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 Half 0x3fe0000000000000
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#define One 0x3ff0000000000000
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#define Ln2Hi 0x1.62e42fefa3800p-1
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#define Ln2Lo 0x1.ef35793c76730p-45
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#define OneMHfRt2Top \
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0x00095f62 /* top32(asuint64(1)) - top32(asuint64(sqrt(2)/2)). */
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#define OneTop12 0x3ff
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#define HfRt2Top 0x3fe6a09e /* top32(asuint64(sqrt(2)/2)). */
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#define BottomMask 0xffffffff
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#define C(i) __log1p_data.coeffs[i]
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static inline double
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log1p_inline (double x)
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{
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/* Helper for calculating log(1 + x) using order-18 polynomial on a reduced
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interval. Copied from log1p_2u.c, with no special-case handling. See that
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file for details of the algorithm. */
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double m = x + 1;
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uint64_t mi = asuint64 (m);
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/* Decompose x + 1 into (f + 1) * 2^k, with k chosen such that f is in
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[sqrt(2)/2, sqrt(2)]. */
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uint32_t u = (mi >> 32) + OneMHfRt2Top;
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int32_t k = (int32_t) (u >> 20) - OneTop12;
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uint32_t utop = (u & 0x000fffff) + HfRt2Top;
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uint64_t u_red = ((uint64_t) utop << 32) | (mi & BottomMask);
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double f = asdouble (u_red) - 1;
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/* Correction term for round-off in f. */
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double cm = (x - (m - 1)) / m;
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/* Approximate log1p(f) with polynomial. */
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double f2 = f * f;
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double f4 = f2 * f2;
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double f8 = f4 * f4;
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double p = fma (f, ESTRIN_18 (f, f2, f4, f8, f8 * f8, C) * f, f);
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/* Recombine log1p(x) = k*log2 + log1p(f) + c/m. */
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double kd = k;
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double y = fma (Ln2Lo, kd, cm);
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return y + fma (Ln2Hi, kd, p);
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}
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/* Approximation for double-precision inverse tanh(x), using a simplified
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version of log1p. Greatest observed error is 3.00 ULP:
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atanh(0x1.e58f3c108d714p-4) got 0x1.e7da77672a647p-4
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want 0x1.e7da77672a64ap-4. */
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double
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atanh (double x)
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{
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uint64_t ix = asuint64 (x);
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uint64_t sign = ix & ~AbsMask;
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uint64_t ia = ix & AbsMask;
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if (unlikely (ia == One))
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return __math_divzero (sign >> 32);
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if (unlikely (ia > One))
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return __math_invalid (x);
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double halfsign = asdouble (Half | sign);
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double ax = asdouble (ia);
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return halfsign * log1p_inline ((2 * ax) / (1 - ax));
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}
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PL_SIG (S, D, 1, atanh, -1.0, 1.0)
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PL_TEST_ULP (atanh, 3.00)
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PL_TEST_INTERVAL (atanh, 0, 0x1p-23, 10000)
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PL_TEST_INTERVAL (atanh, -0, -0x1p-23, 10000)
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PL_TEST_INTERVAL (atanh, 0x1p-23, 1, 90000)
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PL_TEST_INTERVAL (atanh, -0x1p-23, -1, 90000)
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PL_TEST_INTERVAL (atanh, 1, inf, 100)
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PL_TEST_INTERVAL (atanh, -1, -inf, 100)
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