src/math/exp2f.c

   1 /*
   2  * Single-precision 2^x function.
   3  *
   4  * Copyright (c) 2017-2018, Arm Limited.
   5  * SPDX-License-Identifier: MIT
   6  */
   7
   8 #include <math.h>
   9 #include <stdint.h>
  10 #include "libm.h"
  11 #include "exp2f_data.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 top12(float x)
  29 {
  30         return asuint(x) >> 20;
  31 }
  32
  33 float exp2f(float x)
  34 {
  35         uint32_t abstop;
  36         uint64_t ki, t;
  37         double_t kd, xd, z, r, r2, y, s;
  38
  39         xd = (double_t)x;
  40         abstop = top12(x) & 0x7ff;
  41         if (predict_false(abstop >= top12(128.0f))) {
  42                 /* |x| >= 128 or x is nan.  */
  43                 if (asuint(x) == asuint(-INFINITY))
  44                         return 0.0f;
  45                 if (abstop >= top12(INFINITY))
  46                         return x + x;
  47                 if (x > 0.0f)
  48                         return __math_oflowf(0);
  49                 if (x <= -150.0f)
  50                         return __math_uflowf(0);
  51         }
  52
  53         /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k.  */
  54         kd = eval_as_double(xd + SHIFT);
  55         ki = asuint64(kd);
  56         kd -= SHIFT; /* k/N for int k.  */
  57         r = xd - kd;
  58
  59         /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
  60         t = T[ki % N];
  61         t += ki << (52 - EXP2F_TABLE_BITS);
  62         s = asdouble(t);
  63         z = C[0] * r + C[1];
  64         r2 = r * r;
  65         y = C[2] * r + 1;
  66         y = z * r2 + y;
  67         y = y * s;
  68         return eval_as_float(y);
  69 }