llvm-project

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/*
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 * Double-precision vector cos function.
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 *
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 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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 * See https://llvm.org/LICENSE.txt for license information.
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 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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 */
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#include "mathlib.h"
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#include "v_math.h"
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#if V_SUPPORTED
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static const double Poly[] = {
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/* worst-case error is 3.5 ulp.
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   abs error: 0x1.be222a58p-53 in [-pi/2, pi/2].  */
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-0x1.9f4a9c8b21dc9p-41,
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 0x1.60e88a10163f2p-33,
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-0x1.ae6361b7254e7p-26,
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 0x1.71de382e8d62bp-19,
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-0x1.a01a019aeb4ffp-13,
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 0x1.111111110b25ep-7,
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-0x1.55555555554c3p-3,
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};
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#define C7 v_f64 (Poly[0])
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#define C6 v_f64 (Poly[1])
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#define C5 v_f64 (Poly[2])
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#define C4 v_f64 (Poly[3])
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#define C3 v_f64 (Poly[4])
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#define C2 v_f64 (Poly[5])
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#define C1 v_f64 (Poly[6])
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#define InvPi v_f64 (0x1.45f306dc9c883p-2)
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#define HalfPi v_f64 (0x1.921fb54442d18p+0)
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#define Pi1 v_f64 (0x1.921fb54442d18p+1)
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#define Pi2 v_f64 (0x1.1a62633145c06p-53)
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#define Pi3 v_f64 (0x1.c1cd129024e09p-106)
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#define Shift v_f64 (0x1.8p52)
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#define RangeVal v_f64 (0x1p23)
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#define AbsMask v_u64 (0x7fffffffffffffff)
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VPCS_ATTR
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__attribute__ ((noinline)) static v_f64_t
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specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
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{
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  return v_call_f64 (cos, x, y, cmp);
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}
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VPCS_ATTR
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v_f64_t
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V_NAME(cos) (v_f64_t x)
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{
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  v_f64_t n, r, r2, y;
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  v_u64_t odd, cmp;
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  r = v_as_f64_u64 (v_as_u64_f64 (x) & AbsMask);
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  cmp = v_cond_u64 (v_as_u64_f64 (r) >= v_as_u64_f64 (RangeVal));
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  /* n = rint((|x|+pi/2)/pi) - 0.5.  */
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  n = v_fma_f64 (InvPi, r + HalfPi, Shift);
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  odd = v_as_u64_f64 (n) << 63;
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  n -= Shift;
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  n -= v_f64 (0.5);
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  /* r = |x| - n*pi  (range reduction into -pi/2 .. pi/2).  */
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  r = v_fma_f64 (-Pi1, n, r);
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  r = v_fma_f64 (-Pi2, n, r);
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  r = v_fma_f64 (-Pi3, n, r);
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  /* sin(r) poly approx.  */
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  r2 = r * r;
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  y = v_fma_f64 (C7, r2, C6);
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  y = v_fma_f64 (y, r2, C5);
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  y = v_fma_f64 (y, r2, C4);
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  y = v_fma_f64 (y, r2, C3);
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  y = v_fma_f64 (y, r2, C2);
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  y = v_fma_f64 (y, r2, C1);
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  y = v_fma_f64 (y * r2, r, r);
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  /* sign.  */
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  y = v_as_f64_u64 (v_as_u64_f64 (y) ^ odd);
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  if (unlikely (v_any_u64 (cmp)))
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    return specialcase (x, y, cmp);
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  return y;
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}
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VPCS_ALIAS
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#endif
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