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Diffstat (limited to 'pl/math/acos_2u.c')
| -rw-r--r-- | pl/math/acos_2u.c | 100 |
1 files changed, 0 insertions, 100 deletions
diff --git a/pl/math/acos_2u.c b/pl/math/acos_2u.c deleted file mode 100644 index 9ec6894f1d81..000000000000 --- a/pl/math/acos_2u.c +++ /dev/null @@ -1,100 +0,0 @@ -/* - * Double-precision acos(x) function. - * - * Copyright (c) 2023, Arm Limited. - * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception - */ - -#include "math_config.h" -#include "poly_scalar_f64.h" -#include "pl_sig.h" -#include "pl_test.h" - -#define AbsMask (0x7fffffffffffffff) -#define Half (0x3fe0000000000000) -#define One (0x3ff0000000000000) -#define PiOver2 (0x1.921fb54442d18p+0) -#define Pi (0x1.921fb54442d18p+1) -#define Small (0x3c90000000000000) /* 2^-53. */ -#define Small16 (0x3c90) -#define QNaN (0x7ff8) - -/* Fast implementation of double-precision acos(x) based on polynomial - approximation of double-precision asin(x). - - For x < Small, approximate acos(x) by pi/2 - x. Small = 2^-53 for correct - rounding. - - For |x| in [Small, 0.5], use the trigonometric identity - - acos(x) = pi/2 - asin(x) - - and use an order 11 polynomial P such that the final approximation of asin is - an odd polynomial: asin(x) ~ x + x^3 * P(x^2). - - The largest observed error in this region is 1.18 ulps, - acos(0x1.fbab0a7c460f6p-2) got 0x1.0d54d1985c068p+0 - want 0x1.0d54d1985c069p+0. - - For |x| in [0.5, 1.0], use the following development of acos(x) near x = 1 - - acos(x) ~ pi/2 - 2 * sqrt(z) (1 + z * P(z)) - - where z = (1-x)/2, z is near 0 when x approaches 1, and P contributes to the - approximation of asin near 0. - - The largest observed error in this region is 1.52 ulps, - acos(0x1.23d362722f591p-1) got 0x1.edbbedf8a7d6ep-1 - want 0x1.edbbedf8a7d6cp-1. - - For x in [-1.0, -0.5], use this other identity to deduce the negative inputs - from their absolute value: acos(x) = pi - acos(-x). */ -double -acos (double x) -{ - uint64_t ix = asuint64 (x); - uint64_t ia = ix & AbsMask; - uint64_t ia16 = ia >> 48; - double ax = asdouble (ia); - uint64_t sign = ix & ~AbsMask; - - /* Special values and invalid range. */ - if (unlikely (ia16 == QNaN)) - return x; - if (ia > One) - return __math_invalid (x); - if (ia16 < Small16) - return PiOver2 - x; - - /* Evaluate polynomial Q(|x|) = z + z * z2 * P(z2) with - z2 = x ^ 2 and z = |x| , if |x| < 0.5 - z2 = (1 - |x|) / 2 and z = sqrt(z2), if |x| >= 0.5. */ - double z2 = ax < 0.5 ? x * x : fma (-0.5, ax, 0.5); - double z = ax < 0.5 ? ax : sqrt (z2); - - /* Use a single polynomial approximation P for both intervals. */ - double z4 = z2 * z2; - double z8 = z4 * z4; - double z16 = z8 * z8; - double p = estrin_11_f64 (z2, z4, z8, z16, __asin_poly); - - /* Finalize polynomial: z + z * z2 * P(z2). */ - p = fma (z * z2, p, z); - - /* acos(|x|) = pi/2 - sign(x) * Q(|x|), for |x| < 0.5 - = pi - 2 Q(|x|), for -1.0 < x <= -0.5 - = 2 Q(|x|) , for -0.5 < x < 0.0. */ - if (ax < 0.5) - return PiOver2 - asdouble (asuint64 (p) | sign); - - return (x <= -0.5) ? fma (-2.0, p, Pi) : 2.0 * p; -} - -PL_SIG (S, D, 1, acos, -1.0, 1.0) -PL_TEST_ULP (acos, 1.02) -PL_TEST_INTERVAL (acos, 0, Small, 5000) -PL_TEST_INTERVAL (acos, Small, 0.5, 50000) -PL_TEST_INTERVAL (acos, 0.5, 1.0, 50000) -PL_TEST_INTERVAL (acos, 1.0, 0x1p11, 50000) -PL_TEST_INTERVAL (acos, 0x1p11, inf, 20000) -PL_TEST_INTERVAL (acos, -0, -inf, 20000) |
