expm1f.c raw

   1  /* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
   2  /*
   3   * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
   4   */
   5  /*
   6   * ====================================================
   7   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8   *
   9   * Developed at SunPro, a Sun Microsystems, Inc. business.
  10   * Permission to use, copy, modify, and distribute this
  11   * software is freely granted, provided that this notice
  12   * is preserved.
  13   * ====================================================
  14   */
  15  
  16  #include "libm.h"
  17  
  18  static const float
  19  ln2_hi      = 6.9313812256e-01, /* 0x3f317180 */
  20  ln2_lo      = 9.0580006145e-06, /* 0x3717f7d1 */
  21  invln2      = 1.4426950216e+00, /* 0x3fb8aa3b */
  22  /*
  23   * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
  24   * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
  25   * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
  26   */
  27  Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
  28  Q2 =  1.5807170421e-3; /*  0xcf3010.0p-33 */
  29  
  30  float expm1f(float x)
  31  {
  32  	float_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
  33  	union {float f; uint32_t i;} u = {x};
  34  	uint32_t hx = u.i & 0x7fffffff;
  35  	int k, sign = u.i >> 31;
  36  
  37  	/* filter out huge and non-finite argument */
  38  	if (hx >= 0x4195b844) {  /* if |x|>=27*ln2 */
  39  		if (hx > 0x7f800000)  /* NaN */
  40  			return x;
  41  		if (sign)
  42  			return -1;
  43  		if (hx > 0x42b17217) { /* x > log(FLT_MAX) */
  44  			x *= 0x1p127f;
  45  			return x;
  46  		}
  47  	}
  48  
  49  	/* argument reduction */
  50  	if (hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  51  		if (hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  52  			if (!sign) {
  53  				hi = x - ln2_hi;
  54  				lo = ln2_lo;
  55  				k =  1;
  56  			} else {
  57  				hi = x + ln2_hi;
  58  				lo = -ln2_lo;
  59  				k = -1;
  60  			}
  61  		} else {
  62  			k  = invln2*x + (sign ? -0.5f : 0.5f);
  63  			t  = k;
  64  			hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
  65  			lo = t*ln2_lo;
  66  		}
  67  		x = hi-lo;
  68  		c = (hi-x)-lo;
  69  	} else if (hx < 0x33000000) {  /* when |x|<2**-25, return x */
  70  		if (hx < 0x00800000)
  71  			FORCE_EVAL(x*x);
  72  		return x;
  73  	} else
  74  		k = 0;
  75  
  76  	/* x is now in primary range */
  77  	hfx = 0.5f*x;
  78  	hxs = x*hfx;
  79  	r1 = 1.0f+hxs*(Q1+hxs*Q2);
  80  	t  = 3.0f - r1*hfx;
  81  	e  = hxs*((r1-t)/(6.0f - x*t));
  82  	if (k == 0)  /* c is 0 */
  83  		return x - (x*e-hxs);
  84  	e  = x*(e-c) - c;
  85  	e -= hxs;
  86  	/* exp(x) ~ 2^k (x_reduced - e + 1) */
  87  	if (k == -1)
  88  		return 0.5f*(x-e) - 0.5f;
  89  	if (k == 1) {
  90  		if (x < -0.25f)
  91  			return -2.0f*(e-(x+0.5f));
  92  		return 1.0f + 2.0f*(x-e);
  93  	}
  94  	u.i = (0x7f+k)<<23;  /* 2^k */
  95  	twopk = u.f;
  96  	if (k < 0 || k > 56) {   /* suffice to return exp(x)-1 */
  97  		y = x - e + 1.0f;
  98  		if (k == 128)
  99  			y = y*2.0f*0x1p127f;
 100  		else
 101  			y = y*twopk;
 102  		return y - 1.0f;
 103  	}
 104  	u.i = (0x7f-k)<<23;  /* 2^-k */
 105  	if (k < 23)
 106  		y = (x-e+(1-u.f))*twopk;
 107  	else
 108  		y = (x-(e+u.f)+1)*twopk;
 109  	return y;
 110  }
 111