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72 lines
2.2 KiB
C
72 lines
2.2 KiB
C
/*
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* Single-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 0x7fffffff
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#define TinyBound 0x20000000 /* 0x1p-63: Round to 1 below this. */
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#define SpecialBound \
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0x42ad496c /* 0x1.5a92d8p+6: expf overflows above this, so have to use \
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special case. */
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float
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optr_aor_exp_f32 (float);
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static NOINLINE float
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specialcase (float x, uint32_t iax)
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{
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if (iax == 0x7f800000)
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return INFINITY;
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if (iax > 0x7f800000)
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return __math_invalidf (x);
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if (iax <= TinyBound)
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/* For tiny x, avoid underflow by just returning 1. */
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return 1;
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/* Otherwise SpecialBound <= |x| < Inf. x is too large to calculate exp(x)
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without overflow, so use exp(|x|/2) instead. For large x cosh(x) is
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dominated by exp(x), so return:
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cosh(x) ~= (exp(|x|/2))^2 / 2. */
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float t = optr_aor_exp_f32 (asfloat (iax) / 2);
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return (0.5 * t) * t;
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}
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/* Approximation for single-precision cosh(x) using exp.
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cosh(x) = (exp(x) + exp(-x)) / 2.
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The maximum error is 1.89 ULP, observed for |x| > SpecialBound:
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coshf(0x1.65898cp+6) got 0x1.f00aep+127 want 0x1.f00adcp+127.
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The maximum error observed for TinyBound < |x| < SpecialBound is 1.02 ULP:
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coshf(0x1.50a3cp+0) got 0x1.ff21dcp+0 want 0x1.ff21dap+0. */
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float
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coshf (float x)
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{
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uint32_t ix = asuint (x);
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uint32_t iax = ix & AbsMask;
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float ax = asfloat (iax);
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if (unlikely (iax <= TinyBound || iax >= SpecialBound))
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{
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/* x is tiny, large or special. */
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return specialcase (x, iax);
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}
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/* Compute cosh using the definition:
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coshf(x) = exp(x) / 2 + exp(-x) / 2. */
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float t = optr_aor_exp_f32 (ax);
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return 0.5f * t + 0.5f / t;
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}
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PL_SIG (S, F, 1, cosh, -10.0, 10.0)
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PL_TEST_ULP (coshf, 1.89)
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PL_TEST_INTERVAL (coshf, 0, 0x1p-63, 100)
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PL_TEST_INTERVAL (coshf, 0, 0x1.5a92d8p+6, 80000)
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PL_TEST_INTERVAL (coshf, 0x1.5a92d8p+6, inf, 2000)
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PL_TEST_INTERVAL (coshf, -0, -0x1p-63, 100)
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PL_TEST_INTERVAL (coshf, -0, -0x1.5a92d8p+6, 80000)
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PL_TEST_INTERVAL (coshf, -0x1.5a92d8p+6, -inf, 2000)
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