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Diffstat (limited to 'pl/math/acosf_1u4.c')
-rw-r--r-- | pl/math/acosf_1u4.c | 99 |
1 files changed, 0 insertions, 99 deletions
diff --git a/pl/math/acosf_1u4.c b/pl/math/acosf_1u4.c deleted file mode 100644 index 6dde422ef85a..000000000000 --- a/pl/math/acosf_1u4.c +++ /dev/null @@ -1,99 +0,0 @@ -/* - * Single-precision acos(x) function. - * - * Copyright (c) 2023, Arm Limited. - * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception - */ - -#include "poly_scalar_f32.h" -#include "math_config.h" -#include "pl_sig.h" -#include "pl_test.h" - -#define AbsMask (0x7fffffff) -#define Half (0x3f000000) -#define One (0x3f800000) -#define PiOver2f (0x1.921fb6p+0f) -#define Pif (0x1.921fb6p+1f) -#define Small (0x32800000) /* 2^-26. */ -#define Small12 (0x328) -#define QNaN (0x7fc) - -/* Fast implementation of single-precision acos(x) based on polynomial - approximation of single-precision asin(x). - - For x < Small, approximate acos(x) by pi/2 - x. Small = 2^-26 for correct - rounding. - - For |x| in [Small, 0.5], use the trigonometric identity - - acos(x) = pi/2 - asin(x) - - and use an order 4 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 1.16 ulps, - acosf(0x1.ffbeccp-2) got 0x1.0c27f8p+0 want 0x1.0c27f6p+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 1.32 ulps, - acosf(0x1.15ba56p-1) got 0x1.feb33p-1 want 0x1.feb32ep-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) - - The largest observed error in this region is 1.28 ulps, - acosf(-0x1.002072p-1) got 0x1.0c1e84p+1 want 0x1.0c1e82p+1. */ -float -acosf (float x) -{ - uint32_t ix = asuint (x); - uint32_t ia = ix & AbsMask; - uint32_t ia12 = ia >> 20; - float ax = asfloat (ia); - uint32_t sign = ix & ~AbsMask; - - /* Special values and invalid range. */ - if (unlikely (ia12 == QNaN)) - return x; - if (ia > One) - return __math_invalidf (x); - if (ia12 < Small12) - return PiOver2f - 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. */ - float z2 = ax < 0.5 ? x * x : fmaf (-0.5f, ax, 0.5f); - float z = ax < 0.5 ? ax : sqrtf (z2); - - /* Use a single polynomial approximation P for both intervals. */ - float p = horner_4_f32 (z2, __asinf_poly); - /* Finalize polynomial: z + z * z2 * P(z2). */ - p = fmaf (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 PiOver2f - asfloat (asuint (p) | sign); - - return (x <= -0.5) ? fmaf (-2.0f, p, Pif) : 2.0f * p; -} - -PL_SIG (S, F, 1, acos, -1.0, 1.0) -PL_TEST_ULP (acosf, 0.82) -PL_TEST_INTERVAL (acosf, 0, Small, 5000) -PL_TEST_INTERVAL (acosf, Small, 0.5, 50000) -PL_TEST_INTERVAL (acosf, 0.5, 1.0, 50000) -PL_TEST_INTERVAL (acosf, 1.0, 0x1p11, 50000) -PL_TEST_INTERVAL (acosf, 0x1p11, inf, 20000) -PL_TEST_INTERVAL (acosf, -0, -inf, 20000) |