84 lines
2.7 KiB
C
84 lines
2.7 KiB
C
/*
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* Single-precision vector atan(x) function.
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*
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* Copyright (c) 2021-2023, Arm Limited.
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* SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
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*/
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#include "v_math.h"
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#include "pl_sig.h"
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#include "pl_test.h"
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#if V_SUPPORTED
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#include "atanf_common.h"
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#define PiOver2 v_f32 (0x1.921fb6p+0f)
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#define AbsMask v_u32 (0x7fffffff)
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#define TinyBound 0x308 /* top12(asuint(0x1p-30)). */
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#define BigBound 0x4e8 /* top12(asuint(0x1p30)). */
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#if WANT_SIMD_EXCEPT
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static NOINLINE v_f32_t
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specialcase (v_f32_t x, v_f32_t y, v_u32_t special)
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{
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return v_call_f32 (atanf, x, y, special);
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}
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#endif
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/* Fast implementation of vector atanf based on
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atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1]
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using z=-1/x and shift = pi/2. Maximum observed error is 2.9ulps:
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v_atanf(0x1.0468f6p+0) got 0x1.967f06p-1 want 0x1.967fp-1. */
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VPCS_ATTR
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v_f32_t V_NAME (atanf) (v_f32_t x)
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{
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/* Small cases, infs and nans are supported by our approximation technique,
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but do not set fenv flags correctly. Only trigger special case if we need
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fenv. */
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v_u32_t ix = v_as_u32_f32 (x);
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v_u32_t sign = ix & ~AbsMask;
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#if WANT_SIMD_EXCEPT
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v_u32_t ia12 = (ix >> 20) & 0x7ff;
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v_u32_t special = v_cond_u32 (ia12 - TinyBound > BigBound - TinyBound);
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/* If any lane is special, fall back to the scalar routine for all lanes. */
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if (unlikely (v_any_u32 (special)))
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return specialcase (x, x, v_u32 (-1));
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#endif
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/* Argument reduction:
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y := arctan(x) for x < 1
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y := pi/2 + arctan(-1/x) for x > 1
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Hence, use z=-1/a if x>=1, otherwise z=a. */
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v_u32_t red = v_cagt_f32 (x, v_f32 (1.0));
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/* Avoid dependency in abs(x) in division (and comparison). */
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v_f32_t z = v_sel_f32 (red, v_div_f32 (v_f32 (-1.0f), x), x);
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v_f32_t shift = v_sel_f32 (red, PiOver2, v_f32 (0.0f));
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/* Use absolute value only when needed (odd powers of z). */
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v_f32_t az = v_abs_f32 (z);
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az = v_sel_f32 (red, -az, az);
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/* Calculate the polynomial approximation. */
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v_f32_t y = eval_poly (z, az, shift);
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/* y = atan(x) if x>0, -atan(-x) otherwise. */
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y = v_as_f32_u32 (v_as_u32_f32 (y) ^ sign);
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return y;
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}
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VPCS_ALIAS
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PL_SIG (V, F, 1, atan, -10.0, 10.0)
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PL_TEST_ULP (V_NAME (atanf), 2.5)
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PL_TEST_EXPECT_FENV (V_NAME (atanf), WANT_SIMD_EXCEPT)
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PL_TEST_INTERVAL (V_NAME (atanf), 0, 0x1p-30, 5000)
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PL_TEST_INTERVAL (V_NAME (atanf), -0, -0x1p-30, 5000)
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PL_TEST_INTERVAL (V_NAME (atanf), 0x1p-30, 1, 40000)
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PL_TEST_INTERVAL (V_NAME (atanf), -0x1p-30, -1, 40000)
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PL_TEST_INTERVAL (V_NAME (atanf), 1, 0x1p30, 40000)
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PL_TEST_INTERVAL (V_NAME (atanf), -1, -0x1p30, 40000)
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PL_TEST_INTERVAL (V_NAME (atanf), 0x1p30, inf, 1000)
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PL_TEST_INTERVAL (V_NAME (atanf), -0x1p30, -inf, 1000)
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#endif
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