libc/AOR_v20.02/math/exp2f.c

   1 /*
   2  * Single-precision 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 <math.h>
  10 #include <stdint.h>
  11 #include "math_config.h"
  12
  13 /*
  14 EXP2F_TABLE_BITS = 5
  15 EXP2F_POLY_ORDER = 3
  16
  17 ULP error: 0.502 (nearest rounding.)
  18 Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.)
  19 Wrong count: 168353 (all nearest rounding wrong results with fma.)
  20 Non-nearest ULP error: 1 (rounded ULP error)
  21 */
  22
  23 #define N (1 << EXP2F_TABLE_BITS)
  24 #define T __exp2f_data.tab
  25 #define C __exp2f_data.poly
  26 #define SHIFT __exp2f_data.shift_scaled
  27
  28 static inline uint32_t
  29 top12 (float x)
  30 {
  31   return asuint (x) >> 20;
  32 }
  33
  34 float
  35 exp2f (float x)
  36 {
  37   uint32_t abstop;
  38   uint64_t ki, t;
  39   /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
  40   double_t kd, xd, z, r, r2, y, s;
  41
  42   xd = (double_t) x;
  43   abstop = top12 (x) & 0x7ff;
  44   if (unlikely (abstop >= top12 (128.0f)))
  45     {
  46       /* |x| >= 128 or x is nan.  */
  47       if (asuint (x) == asuint (-INFINITY))
  48         return 0.0f;
  49       if (abstop >= top12 (INFINITY))
  50         return x + x;
  51       if (x > 0.0f)
  52         return __math_oflowf (0);
  53       if (x <= -150.0f)
  54         return __math_uflowf (0);
  55 #if WANT_ERRNO_UFLOW
  56       if (x < -149.0f)
  57         return __math_may_uflowf (0);
  58 #endif
  59     }
  60
  61   /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k.  */
  62   kd = eval_as_double (xd + SHIFT);
  63   ki = asuint64 (kd);
  64   kd -= SHIFT; /* k/N for int k.  */
  65   r = xd - kd;
  66
  67   /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
  68   t = T[ki % N];
  69   t += ki << (52 - EXP2F_TABLE_BITS);
  70   s = asdouble (t);
  71   z = C[0] * r + C[1];
  72   r2 = r * r;
  73   y = C[2] * r + 1;
  74   y = z * r2 + y;
  75   y = y * s;
  76   return eval_as_float (y);
  77 }
  78 #if USE_GLIBC_ABI
  79 strong_alias (exp2f, __exp2f_finite)
  80 hidden_alias (exp2f, __ieee754_exp2f)
  81 #endif