67 lines
2.1 KiB
C
67 lines
2.1 KiB
C
/*
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* Double-precision cosh(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 "pl_sig.h"
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#include "pl_test.h"
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#define AbsMask 0x7fffffffffffffff
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#define SpecialBound \
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0x40861da04cbafe44 /* 0x1.61da04cbafe44p+9, above which exp overflows. */
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double
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__exp_dd (double, double);
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static double
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specialcase (double x, uint64_t iax)
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{
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if (iax == 0x7ff0000000000000)
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return INFINITY;
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if (iax > 0x7ff0000000000000)
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return __math_invalid (x);
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/* exp overflows above SpecialBound. At this magnitude cosh(x) is dominated by
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exp(x), so we can approximate cosh(x) by (exp(|x|/2)) ^ 2 / 2. */
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double t = __exp_dd (asdouble (iax) / 2, 0);
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return (0.5 * t) * t;
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}
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/* Approximation for double-precision cosh(x).
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cosh(x) = (exp(x) + exp(-x)) / 2.
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The greatest observed error is in the special region, 1.93 ULP:
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cosh(0x1.628af341989dap+9) got 0x1.fdf28623ef921p+1021
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want 0x1.fdf28623ef923p+1021.
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The greatest observed error in the non-special region is 1.03 ULP:
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cosh(0x1.502cd8e56ab3bp+0) got 0x1.fe54962842d0ep+0
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want 0x1.fe54962842d0fp+0. */
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double
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cosh (double x)
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{
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uint64_t ix = asuint64 (x);
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uint64_t iax = ix & AbsMask;
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/* exp overflows a little bit before cosh, so use special-case handler for the
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gap, as well as special values. */
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if (unlikely (iax >= SpecialBound))
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return specialcase (x, iax);
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double ax = asdouble (iax);
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/* Use double-precision exp helper to calculate exp(x), then:
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cosh(x) = exp(|x|) / 2 + 1 / (exp(|x| * 2). */
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double t = __exp_dd (ax, 0);
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return 0.5 * t + 0.5 / t;
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}
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PL_SIG (S, D, 1, cosh, -10.0, 10.0)
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PL_TEST_ULP (cosh, 1.43)
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PL_TEST_INTERVAL (cosh, 0, 0x1.61da04cbafe44p+9, 100000)
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PL_TEST_INTERVAL (cosh, -0, -0x1.61da04cbafe44p+9, 100000)
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PL_TEST_INTERVAL (cosh, 0x1.61da04cbafe44p+9, 0x1p10, 1000)
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PL_TEST_INTERVAL (cosh, -0x1.61da04cbafe44p+9, -0x1p10, 1000)
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PL_TEST_INTERVAL (cosh, 0x1p10, inf, 100)
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PL_TEST_INTERVAL (cosh, -0x1p10, -inf, 100)
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