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Diffstat (limited to 'pl/math/cbrt_2u.c')
-rw-r--r-- | pl/math/cbrt_2u.c | 69 |
1 files changed, 0 insertions, 69 deletions
diff --git a/pl/math/cbrt_2u.c b/pl/math/cbrt_2u.c deleted file mode 100644 index 80be83c4470c..000000000000 --- a/pl/math/cbrt_2u.c +++ /dev/null @@ -1,69 +0,0 @@ -/* - * Double-precision cbrt(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" - -PL_SIG (S, D, 1, cbrt, -10.0, 10.0) - -#define AbsMask 0x7fffffffffffffff -#define TwoThirds 0x1.5555555555555p-1 - -#define C(i) __cbrt_data.poly[i] -#define T(i) __cbrt_data.table[i] - -/* Approximation for double-precision cbrt(x), using low-order polynomial and - two Newton iterations. Greatest observed error is 1.79 ULP. Errors repeat - according to the exponent, for instance an error observed for double value - m * 2^e will be observed for any input m * 2^(e + 3*i), where i is an - integer. - cbrt(0x1.fffff403f0bc6p+1) got 0x1.965fe72821e9bp+0 - want 0x1.965fe72821e99p+0. */ -double -cbrt (double x) -{ - uint64_t ix = asuint64 (x); - uint64_t iax = ix & AbsMask; - uint64_t sign = ix & ~AbsMask; - - if (unlikely (iax == 0 || iax == 0x7ff0000000000000)) - return x; - - /* |x| = m * 2^e, where m is in [0.5, 1.0]. - We can easily decompose x into m and e using frexp. */ - int e; - double m = frexp (asdouble (iax), &e); - - /* Calculate rough approximation for cbrt(m) in [0.5, 1.0], starting point for - Newton iterations. */ - double p_01 = fma (C (1), m, C (0)); - double p_23 = fma (C (3), m, C (2)); - double p = fma (p_23, m * m, p_01); - - /* Two iterations of Newton's method for iteratively approximating cbrt. */ - double m_by_3 = m / 3; - double a = fma (TwoThirds, p, m_by_3 / (p * p)); - a = fma (TwoThirds, a, m_by_3 / (a * a)); - - /* Assemble the result by the following: - - cbrt(x) = cbrt(m) * 2 ^ (e / 3). - - Let t = (2 ^ (e / 3)) / (2 ^ round(e / 3)). - - Then we know t = 2 ^ (i / 3), where i is the remainder from e / 3. - i is an integer in [-2, 2], so t can be looked up in the table T. - Hence the result is assembled as: - - cbrt(x) = cbrt(m) * t * 2 ^ round(e / 3) * sign. - Which can be done easily using ldexp. */ - return asdouble (asuint64 (ldexp (a * T (2 + e % 3), e / 3)) | sign); -} - -PL_TEST_ULP (cbrt, 1.30) -PL_TEST_SYM_INTERVAL (cbrt, 0, inf, 1000000) |