llvm-project

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/*
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 * Single-precision vector e^x 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 float Poly[] = {
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  /* maxerr: 1.45358 +0.5 ulp.  */
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  0x1.0e4020p-7f,
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  0x1.573e2ep-5f,
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  0x1.555e66p-3f,
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  0x1.fffdb6p-2f,
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  0x1.ffffecp-1f,
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};
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#define C0 v_f32 (Poly[0])
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#define C1 v_f32 (Poly[1])
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#define C2 v_f32 (Poly[2])
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#define C3 v_f32 (Poly[3])
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#define C4 v_f32 (Poly[4])
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#define Shift v_f32 (0x1.8p23f)
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#define InvLn2 v_f32 (0x1.715476p+0f)
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#define Ln2hi v_f32 (0x1.62e4p-1f)
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#define Ln2lo v_f32 (0x1.7f7d1cp-20f)
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VPCS_ATTR
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static v_f32_t
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specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn, v_u32_t cmp1, v_f32_t scale)
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{
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  /* 2^n may overflow, break it up into s1*s2.  */
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  v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x82000000);
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  v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
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  v_f32_t s2 = v_as_f32_u32 (e - b);
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  v_u32_t cmp2 = v_cond_u32 (absn > v_f32 (192.0f));
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  v_u32_t r2 = v_as_u32_f32 (s1 * s1);
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  v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1);
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  /* Similar to r1 but avoids double rounding in the subnormal range.  */
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  v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale));
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  return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0));
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}
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VPCS_ATTR
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v_f32_t
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V_NAME(expf) (v_f32_t x)
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{
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  v_f32_t n, r, r2, scale, p, q, poly, absn, z;
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  v_u32_t cmp, e;
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  /* exp(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
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     x = ln2*n + r, with r in [-ln2/2, ln2/2].  */
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#if 1
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  z = v_fma_f32 (x, InvLn2, Shift);
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  n = z - Shift;
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  r = v_fma_f32 (n, -Ln2hi, x);
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  r = v_fma_f32 (n, -Ln2lo, r);
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  e = v_as_u32_f32 (z) << 23;
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#else
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  z = x * InvLn2;
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  n = v_round_f32 (z);
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  r = v_fma_f32 (n, -Ln2hi, x);
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  r = v_fma_f32 (n, -Ln2lo, r);
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  e = v_as_u32_s32 (v_round_s32 (z)) << 23;
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#endif
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  scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
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  absn = v_abs_f32 (n);
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  cmp = v_cond_u32 (absn > v_f32 (126.0f));
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  r2 = r * r;
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  p = v_fma_f32 (C0, r, C1);
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  q = v_fma_f32 (C2, r, C3);
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  q = v_fma_f32 (p, r2, q);
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  p = C4 * r;
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  poly = v_fma_f32 (q, r2, p);
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  if (unlikely (v_any_u32 (cmp)))
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    return specialcase (poly, n, e, absn, cmp, scale);
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  return v_fma_f32 (poly, scale, scale);
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}
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VPCS_ALIAS
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#endif
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