exp2f.c raw

   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  }
  70