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Diffstat (limited to 'pl/math/coshf_1u9.c')
-rw-r--r-- | pl/math/coshf_1u9.c | 71 |
1 files changed, 71 insertions, 0 deletions
diff --git a/pl/math/coshf_1u9.c b/pl/math/coshf_1u9.c new file mode 100644 index 0000000..c125c92 --- /dev/null +++ b/pl/math/coshf_1u9.c @@ -0,0 +1,71 @@ +/* + * 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) |