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/*
* Single-precision cosh(x) function.
*
* Copyright (c) 2022-2023, Arm Limited.
* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
*/
#include "math_config.h"
#include "pl_sig.h"
#include "pl_test.h"
#define AbsMask 0x7fffffff
#define TinyBound 0x20000000 /* 0x1p-63: Round to 1 below this. */
#define SpecialBound \
0x42ad496c /* 0x1.5a92d8p+6: expf overflows above this, so have to use \
special case. */
float
optr_aor_exp_f32 (float);
static NOINLINE float
specialcase (float x, uint32_t iax)
{
if (iax == 0x7f800000)
return INFINITY;
if (iax > 0x7f800000)
return __math_invalidf (x);
if (iax <= TinyBound)
/* For tiny x, avoid underflow by just returning 1. */
return 1;
/* Otherwise SpecialBound <= |x| < Inf. x is too large to calculate exp(x)
without overflow, so use exp(|x|/2) instead. For large x cosh(x) is
dominated by exp(x), so return:
cosh(x) ~= (exp(|x|/2))^2 / 2. */
float t = optr_aor_exp_f32 (asfloat (iax) / 2);
return (0.5 * t) * t;
}
/* Approximation for single-precision cosh(x) using exp.
cosh(x) = (exp(x) + exp(-x)) / 2.
The maximum error is 1.89 ULP, observed for |x| > SpecialBound:
coshf(0x1.65898cp+6) got 0x1.f00aep+127 want 0x1.f00adcp+127.
The maximum error observed for TinyBound < |x| < SpecialBound is 1.02 ULP:
coshf(0x1.50a3cp+0) got 0x1.ff21dcp+0 want 0x1.ff21dap+0. */
float
coshf (float x)
{
uint32_t ix = asuint (x);
uint32_t iax = ix & AbsMask;
float ax = asfloat (iax);
if (unlikely (iax <= TinyBound || iax >= SpecialBound))
{
/* x is tiny, large or special. */
return specialcase (x, iax);
}
/* Compute cosh using the definition:
coshf(x) = exp(x) / 2 + exp(-x) / 2. */
float t = optr_aor_exp_f32 (ax);
return 0.5f * t + 0.5f / t;
}
PL_SIG (S, F, 1, cosh, -10.0, 10.0)
PL_TEST_ULP (coshf, 1.89)
PL_TEST_INTERVAL (coshf, 0, 0x1p-63, 100)
PL_TEST_INTERVAL (coshf, 0, 0x1.5a92d8p+6, 80000)
PL_TEST_INTERVAL (coshf, 0x1.5a92d8p+6, inf, 2000)
PL_TEST_INTERVAL (coshf, -0, -0x1p-63, 100)
PL_TEST_INTERVAL (coshf, -0, -0x1.5a92d8p+6, 80000)
PL_TEST_INTERVAL (coshf, -0x1.5a92d8p+6, -inf, 2000)
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