expf.c raw

   1  /*
   2   * Single-precision e^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 [-ln2/64, ln2/64] (before rounding.)
  19  Wrong count: 170635 (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 InvLn2N __exp2f_data.invln2_scaled
  25  #define T __exp2f_data.tab
  26  #define C __exp2f_data.poly_scaled
  27  
  28  static inline uint32_t top12(float x)
  29  {
  30  	return asuint(x) >> 20;
  31  }
  32  
  33  float expf(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(88.0f))) {
  42  		/* |x| >= 88 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 > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
  48  			return __math_oflowf(0);
  49  		if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
  50  			return __math_uflowf(0);
  51  	}
  52  
  53  	/* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k.  */
  54  	z = InvLn2N * xd;
  55  
  56  	/* Round and convert z to int, the result is in [-150*N, 128*N] and
  57  	   ideally ties-to-even rule is used, otherwise the magnitude of r
  58  	   can be bigger which gives larger approximation error.  */
  59  #if TOINT_INTRINSICS
  60  	kd = roundtoint(z);
  61  	ki = converttoint(z);
  62  #else
  63  # define SHIFT __exp2f_data.shift
  64  	kd = eval_as_double(z + SHIFT);
  65  	ki = asuint64(kd);
  66  	kd -= SHIFT;
  67  #endif
  68  	r = z - kd;
  69  
  70  	/* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
  71  	t = T[ki % N];
  72  	t += ki << (52 - EXP2F_TABLE_BITS);
  73  	s = asdouble(t);
  74  	z = C[0] * r + C[1];
  75  	r2 = r * r;
  76  	y = C[2] * r + 1;
  77  	y = z * r2 + y;
  78  	y = y * s;
  79  	return eval_as_float(y);
  80  }
  81