libc/AOR_v20.02/math/v_exp2f_1u.c

   1 /*
   2  * Single-precision vector 2^x function.
   3  *
   4  * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   5  * See https://llvm.org/LICENSE.txt for license information.
   6  * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   7  */
   8
   9 #include "mathlib.h"
  10 #include "v_math.h"
  11 #if V_SUPPORTED
  12
  13 static const float Poly[] = {
  14   /*  maxerr: 0.878 ulp.  */
  15   0x1.416b5ep-13f, 0x1.5f082ep-10f, 0x1.3b2dep-7f, 0x1.c6af7cp-5f, 0x1.ebfbdcp-3f, 0x1.62e43p-1f
  16 };
  17 #define C0 v_f32 (Poly[0])
  18 #define C1 v_f32 (Poly[1])
  19 #define C2 v_f32 (Poly[2])
  20 #define C3 v_f32 (Poly[3])
  21 #define C4 v_f32 (Poly[4])
  22 #define C5 v_f32 (Poly[5])
  23
  24 #define Shift v_f32 (0x1.8p23f)
  25 #define InvLn2 v_f32 (0x1.715476p+0f)
  26 #define Ln2hi v_f32 (0x1.62e4p-1f)
  27 #define Ln2lo v_f32 (0x1.7f7d1cp-20f)
  28
  29 VPCS_ATTR
  30 static v_f32_t
  31 specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn)
  32 {
  33   /* 2^n may overflow, break it up into s1*s2.  */
  34   v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x83000000);
  35   v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b);
  36   v_f32_t s2 = v_as_f32_u32 (e - b);
  37   v_u32_t cmp = v_cond_u32 (absn > v_f32 (192.0f));
  38   v_f32_t r1 = s1 * s1;
  39   v_f32_t r0 = poly * s1 * s2;
  40   return v_as_f32_u32 ((cmp & v_as_u32_f32 (r1)) | (~cmp & v_as_u32_f32 (r0)));
  41 }
  42
  43 VPCS_ATTR
  44 v_f32_t
  45 V_NAME(exp2f_1u) (v_f32_t x)
  46 {
  47   v_f32_t n, r, scale, poly, absn;
  48   v_u32_t cmp, e;
  49
  50   /* exp2(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)]
  51      x = n + r, with r in [-1/2, 1/2].  */
  52 #if 0
  53   v_f32_t z;
  54   z = x + Shift;
  55   n = z - Shift;
  56   r = x - n;
  57   e = v_as_u32_f32 (z) << 23;
  58 #else
  59   n = v_round_f32 (x);
  60   r = x - n;
  61   e = v_as_u32_s32 (v_round_s32 (x)) << 23;
  62 #endif
  63   scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
  64   absn = v_abs_f32 (n);
  65   cmp = v_cond_u32 (absn > v_f32 (126.0f));
  66   poly = v_fma_f32 (C0, r, C1);
  67   poly = v_fma_f32 (poly, r, C2);
  68   poly = v_fma_f32 (poly, r, C3);
  69   poly = v_fma_f32 (poly, r, C4);
  70   poly = v_fma_f32 (poly, r, C5);
  71   poly = v_fma_f32 (poly, r, v_f32 (1.0f));
  72   if (unlikely (v_any_u32 (cmp)))
  73     return specialcase (poly, n, e, absn);
  74   return scale * poly;
  75 }
  76 #endif