aboutsummaryrefslogtreecommitdiff
path: root/pl/math/cbrt_2u.c
diff options
context:
space:
mode:
Diffstat (limited to 'pl/math/cbrt_2u.c')
-rw-r--r--pl/math/cbrt_2u.c69
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)