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Diffstat (limited to 'pl/math/v_cosh_2u.c')
-rw-r--r-- | pl/math/v_cosh_2u.c | 96 |
1 files changed, 96 insertions, 0 deletions
diff --git a/pl/math/v_cosh_2u.c b/pl/math/v_cosh_2u.c new file mode 100644 index 0000000..0a9fbf8 --- /dev/null +++ b/pl/math/v_cosh_2u.c @@ -0,0 +1,96 @@ +/* + * Double-precision vector cosh(x) function. + * + * Copyright (c) 2022-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include "v_math.h" +#include "pl_sig.h" +#include "pl_test.h" +#include "v_exp_tail.h" + +#define C1 v_f64 (C1_scal) +#define C2 v_f64 (C2_scal) +#define C3 v_f64 (C3_scal) +#define InvLn2 v_f64 (InvLn2_scal) +#define Ln2hi v_f64 (Ln2hi_scal) +#define Ln2lo v_f64 (Ln2lo_scal) +#define IndexMask v_u64 (IndexMask_scal) +#define Shift v_f64 (Shift_scal) +#define Thres v_f64 (Thres_scal) + +#define AbsMask 0x7fffffffffffffff +#define Half v_f64 (0.5) +#define SpecialBound \ + 0x4086000000000000 /* 0x1.6p9, above which exp overflows. */ + +#if V_SUPPORTED + +static inline v_f64_t +exp_inline (v_f64_t x) +{ + /* Helper for approximating exp(x). Copied from v_exp_tail, with no + special-case handling or tail. */ + + /* n = round(x/(ln2/N)). */ + v_f64_t z = v_fma_f64 (x, InvLn2, Shift); + v_u64_t u = v_as_u64_f64 (z); + v_f64_t n = z - Shift; + + /* r = x - n*ln2/N. */ + v_f64_t r = x; + r = v_fma_f64 (-Ln2hi, n, r); + r = v_fma_f64 (-Ln2lo, n, r); + + v_u64_t e = u << (52 - V_EXP_TAIL_TABLE_BITS); + v_u64_t i = u & IndexMask; + + /* y = tail + exp(r) - 1 ~= r + C1 r^2 + C2 r^3 + C3 r^4. */ + v_f64_t y = v_fma_f64 (C3, r, C2); + y = v_fma_f64 (y, r, C1); + y = v_fma_f64 (y, r, v_f64 (1)) * r; + + /* s = 2^(n/N). */ + u = v_lookup_u64 (Tab, i); + v_f64_t s = v_as_f64_u64 (u + e); + + return v_fma_f64 (y, s, s); +} + +/* Approximation for vector double-precision cosh(x) using exp_inline. + cosh(x) = (exp(x) + exp(-x)) / 2. + The greatest observed error is in the scalar fall-back region, so is the same + as the scalar routine, 1.93 ULP: + __v_cosh(0x1.628af341989dap+9) got 0x1.fdf28623ef921p+1021 + want 0x1.fdf28623ef923p+1021. + + The greatest observed error in the non-special region is 1.54 ULP: + __v_cosh(0x1.8e205b6ecacf7p+2) got 0x1.f711dcb0c77afp+7 + want 0x1.f711dcb0c77b1p+7. */ +VPCS_ATTR v_f64_t V_NAME (cosh) (v_f64_t x) +{ + v_u64_t ix = v_as_u64_f64 (x); + v_u64_t iax = ix & AbsMask; + v_u64_t special = v_cond_u64 (iax > SpecialBound); + + /* If any inputs are special, fall back to scalar for all lanes. */ + if (unlikely (v_any_u64 (special))) + return v_call_f64 (cosh, x, x, v_u64 (-1)); + + v_f64_t ax = v_as_f64_u64 (iax); + /* Up to the point that exp overflows, we can use it to calculate cosh by + exp(|x|) / 2 + 1 / (2 * exp(|x|)). */ + v_f64_t t = exp_inline (ax); + return t * Half + Half / t; +} +VPCS_ALIAS + +PL_SIG (V, D, 1, cosh, -10.0, 10.0) +PL_TEST_ULP (V_NAME (cosh), 1.43) +PL_TEST_EXPECT_FENV_ALWAYS (V_NAME (cosh)) +PL_TEST_INTERVAL (V_NAME (cosh), 0, 0x1.6p9, 100000) +PL_TEST_INTERVAL (V_NAME (cosh), -0, -0x1.6p9, 100000) +PL_TEST_INTERVAL (V_NAME (cosh), 0x1.6p9, inf, 1000) +PL_TEST_INTERVAL (V_NAME (cosh), -0x1.6p9, -inf, 1000) +#endif |