libc/AOR_v20.02/math/v_exp2f.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: 1.962 ulp.  */
  15   0x1.59977ap-10f,
  16   0x1.3ce9e4p-7f,
  17   0x1.c6bd32p-5f,
  18   0x1.ebf9bcp-3f,
  19   0x1.62e422p-1f,
  20 };
  21 #define C0 v_f32 (Poly[0])
  22 #define C1 v_f32 (Poly[1])
  23 #define C2 v_f32 (Poly[2])
  24 #define C3 v_f32 (Poly[3])
  25 #define C4 v_f32 (Poly[4])
  26
  27 #define Shift v_f32 (0x1.8p23f)
  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, v_u32_t cmp1, v_f32_t scale)
  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 (0x82000000);
  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 cmp2 = v_cond_u32 (absn > v_f32 (192.0f));
  38   v_u32_t r2 = v_as_u32_f32 (s1 * s1);
  39   v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1);
  40   /* Similar to r1 but avoids double rounding in the subnormal range.  */
  41   v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale));
  42   return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0));
  43 }
  44
  45 VPCS_ATTR
  46 v_f32_t
  47 V_NAME(exp2f) (v_f32_t x)
  48 {
  49   v_f32_t n, r, r2, scale, p, q, poly, absn;
  50   v_u32_t cmp, e;
  51
  52   /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)]
  53      x = n + r, with r in [-1/2, 1/2].  */
  54 #if 0
  55   v_f32_t z;
  56   z = x + Shift;
  57   n = z - Shift;
  58   r = x - n;
  59   e = v_as_u32_f32 (z) << 23;
  60 #else
  61   n = v_round_f32 (x);
  62   r = x - n;
  63   e = v_as_u32_s32 (v_round_s32 (x)) << 23;
  64 #endif
  65   scale = v_as_f32_u32 (e + v_u32 (0x3f800000));
  66   absn = v_abs_f32 (n);
  67   cmp = v_cond_u32 (absn > v_f32 (126.0f));
  68   r2 = r * r;
  69   p = v_fma_f32 (C0, r, C1);
  70   q = v_fma_f32 (C2, r, C3);
  71   q = v_fma_f32 (p, r2, q);
  72   p = C4 * r;
  73   poly = v_fma_f32 (q, r2, p);
  74   if (unlikely (v_any_u32 (cmp)))
  75     return specialcase (poly, n, e, absn, cmp, scale);
  76   return v_fma_f32 (poly, scale, scale);
  77 }
  78 VPCS_ALIAS
  79 #endif