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Diffstat (limited to 'pl/math/v_expm1_2u5.c')
| -rw-r--r-- | pl/math/v_expm1_2u5.c | 113 |
1 files changed, 113 insertions, 0 deletions
diff --git a/pl/math/v_expm1_2u5.c b/pl/math/v_expm1_2u5.c new file mode 100644 index 0000000..4b491d1 --- /dev/null +++ b/pl/math/v_expm1_2u5.c @@ -0,0 +1,113 @@ +/* + * Double-precision vector exp(x) - 1 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" + +#if V_SUPPORTED + +#define InvLn2 v_f64 (0x1.71547652b82fep0) +#define MLn2hi v_f64 (-0x1.62e42fefa39efp-1) +#define MLn2lo v_f64 (-0x1.abc9e3b39803fp-56) +#define Shift v_f64 (0x1.8p52) +#define TinyBound \ + 0x3cc0000000000000 /* 0x1p-51, below which expm1(x) is within 2 ULP of x. */ +#define SpecialBound \ + 0x40862b7d369a5aa9 /* 0x1.62b7d369a5aa9p+9. For |x| > SpecialBound, the \ + final stage of the algorithm overflows so fall back to \ + scalar. */ +#define AbsMask 0x7fffffffffffffff +#define One 0x3ff0000000000000 + +#define C(i) v_f64 (__expm1_poly[i]) + +static inline v_f64_t +eval_poly (v_f64_t f, v_f64_t f2) +{ + /* Evaluate custom polynomial using Estrin scheme. */ + v_f64_t p_01 = v_fma_f64 (f, C (1), C (0)); + v_f64_t p_23 = v_fma_f64 (f, C (3), C (2)); + v_f64_t p_45 = v_fma_f64 (f, C (5), C (4)); + v_f64_t p_67 = v_fma_f64 (f, C (7), C (6)); + v_f64_t p_89 = v_fma_f64 (f, C (9), C (8)); + + v_f64_t p_03 = v_fma_f64 (f2, p_23, p_01); + v_f64_t p_47 = v_fma_f64 (f2, p_67, p_45); + v_f64_t p_8a = v_fma_f64 (f2, C (10), p_89); + + v_f64_t f4 = f2 * f2; + v_f64_t p_07 = v_fma_f64 (f4, p_47, p_03); + return v_fma_f64 (f4 * f4, p_8a, p_07); +} + +/* Double-precision vector exp(x) - 1 function. + The maximum error observed error is 2.18 ULP: + __v_expm1(0x1.634ba0c237d7bp-2) got 0x1.a8b9ea8d66e22p-2 + want 0x1.a8b9ea8d66e2p-2. */ +VPCS_ATTR +v_f64_t V_NAME (expm1) (v_f64_t x) +{ + v_u64_t ix = v_as_u64_f64 (x); + v_u64_t ax = ix & AbsMask; + +#if WANT_SIMD_EXCEPT + /* If fp exceptions are to be triggered correctly, fall back to the scalar + variant for all lanes if any of them should trigger an exception. */ + v_u64_t special = v_cond_u64 ((ax >= SpecialBound) | (ax <= TinyBound)); + if (unlikely (v_any_u64 (special))) + return v_call_f64 (expm1, x, x, v_u64 (-1)); +#else + /* Large input, NaNs and Infs. */ + v_u64_t special + = v_cond_u64 ((ax >= SpecialBound) | (ix == 0x8000000000000000)); +#endif + + /* Reduce argument to smaller range: + Let i = round(x / ln2) + and f = x - i * ln2, then f is in [-ln2/2, ln2/2]. + exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 + where 2^i is exact because i is an integer. */ + v_f64_t j = v_fma_f64 (InvLn2, x, Shift) - Shift; + v_s64_t i = v_to_s64_f64 (j); + v_f64_t f = v_fma_f64 (j, MLn2hi, x); + f = v_fma_f64 (j, MLn2lo, f); + + /* Approximate expm1(f) using polynomial. + Taylor expansion for expm1(x) has the form: + x + ax^2 + bx^3 + cx^4 .... + So we calculate the polynomial P(f) = a + bf + cf^2 + ... + and assemble the approximation expm1(f) ~= f + f^2 * P(f). */ + v_f64_t f2 = f * f; + v_f64_t p = v_fma_f64 (f2, eval_poly (f, f2), f); + + /* Assemble the result. + expm1(x) ~= 2^i * (p + 1) - 1 + Let t = 2^i. */ + v_f64_t t = v_as_f64_u64 (v_as_u64_s64 (i << 52) + One); + /* expm1(x) ~= p * t + (t - 1). */ + v_f64_t y = v_fma_f64 (p, t, t - 1); + +#if !WANT_SIMD_EXCEPT + if (unlikely (v_any_u64 (special))) + return v_call_f64 (expm1, x, y, special); +#endif + + return y; +} +VPCS_ALIAS + +PL_SIG (V, D, 1, expm1, -9.9, 9.9) +PL_TEST_ULP (V_NAME (expm1), 1.68) +PL_TEST_EXPECT_FENV (V_NAME (expm1), WANT_SIMD_EXCEPT) +PL_TEST_INTERVAL (V_NAME (expm1), 0, 0x1p-51, 1000) +PL_TEST_INTERVAL (V_NAME (expm1), -0, -0x1p-51, 1000) +PL_TEST_INTERVAL (V_NAME (expm1), 0x1p-51, 0x1.63108c75a1937p+9, 100000) +PL_TEST_INTERVAL (V_NAME (expm1), -0x1p-51, -0x1.740bf7c0d927dp+9, 100000) +PL_TEST_INTERVAL (V_NAME (expm1), 0x1.63108c75a1937p+9, inf, 100) +PL_TEST_INTERVAL (V_NAME (expm1), -0x1.740bf7c0d927dp+9, -inf, 100) +#endif |