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Diffstat (limited to 'contrib/arm-optimized-routines/pl/math/atanf_2u9.c')
-rw-r--r--contrib/arm-optimized-routines/pl/math/atanf_2u9.c72
1 files changed, 72 insertions, 0 deletions
diff --git a/contrib/arm-optimized-routines/pl/math/atanf_2u9.c b/contrib/arm-optimized-routines/pl/math/atanf_2u9.c
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index 000000000000..ba6f68089de1
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+++ b/contrib/arm-optimized-routines/pl/math/atanf_2u9.c
@@ -0,0 +1,72 @@
+/*
+ * Single-precision atan(x) function.
+ *
+ * Copyright (c) 2022-2023, Arm Limited.
+ * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+ */
+
+#include "atanf_common.h"
+#include "pl_sig.h"
+#include "pl_test.h"
+
+#define PiOver2 0x1.921fb6p+0f
+#define AbsMask 0x7fffffff
+#define TinyBound 0x30800000 /* asuint(0x1p-30). */
+#define BigBound 0x4e800000 /* asuint(0x1p30). */
+#define One 0x3f800000
+
+/* Approximation of single-precision atan(x) based on
+ atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1]
+ using z=-1/x and shift = pi/2.
+ Maximum error is 2.88 ulps:
+ atanf(0x1.0565ccp+0) got 0x1.97771p-1
+ want 0x1.97770ap-1. */
+float
+atanf (float x)
+{
+ uint32_t ix = asuint (x);
+ uint32_t sign = ix & ~AbsMask;
+ uint32_t ia = ix & AbsMask;
+
+ if (unlikely (ia < TinyBound))
+ /* Avoid underflow by returning x. */
+ return x;
+
+ if (unlikely (ia > BigBound))
+ {
+ if (ia > 0x7f800000)
+ /* Propagate NaN. */
+ return __math_invalidf (x);
+ /* atan(x) rounds to PiOver2 for large x. */
+ return asfloat (asuint (PiOver2) ^ sign);
+ }
+
+ float z, az, shift;
+ if (ia > One)
+ {
+ /* For x > 1, use atan(x) = pi / 2 + atan(-1 / x). */
+ z = -1.0f / x;
+ shift = PiOver2;
+ /* Use absolute value only when needed (odd powers of z). */
+ az = -fabsf (z);
+ }
+ else
+ {
+ /* For x < 1, approximate atan(x) directly. */
+ z = x;
+ az = asfloat (ia);
+ shift = 0;
+ }
+
+ /* Calculate polynomial, shift + z + z^3 * P(z^2). */
+ float y = eval_poly (z, az, shift);
+ /* Copy sign. */
+ return asfloat (asuint (y) ^ sign);
+}
+
+PL_SIG (S, F, 1, atan, -10.0, 10.0)
+PL_TEST_ULP (atanf, 2.38)
+PL_TEST_SYM_INTERVAL (atanf, 0, 0x1p-30, 5000)
+PL_TEST_SYM_INTERVAL (atanf, 0x1p-30, 1, 40000)
+PL_TEST_SYM_INTERVAL (atanf, 1, 0x1p30, 40000)
+PL_TEST_SYM_INTERVAL (atanf, 0x1p30, inf, 1000)