1  /* s_log1pf.c -- float version of s_log1p.c.
       2   */
       3  
       4  /*
       5   * ====================================================
       6   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       7   *
       8   * Developed at SunPro, a Sun Microsystems, Inc. business.
       9   * Permission to use, copy, modify, and distribute this
      10   * software is freely granted, provided that this notice
      11   * is preserved.
      12   * ====================================================
      13   */
      14  
      15  #include <float.h>
      16  #include <math.h>
      17  #include <math-barriers.h>
      18  #include <math_private.h>
      19  #include <math-underflow.h>
      20  #include <libc-diag.h>
      21  
      22  static const float
      23  ln2_hi =   6.9313812256e-01,	/* 0x3f317180 */
      24  ln2_lo =   9.0580006145e-06,	/* 0x3717f7d1 */
      25  two25 =    3.355443200e+07,	/* 0x4c000000 */
      26  Lp1 = 6.6666668653e-01,	/* 3F2AAAAB */
      27  Lp2 = 4.0000000596e-01,	/* 3ECCCCCD */
      28  Lp3 = 2.8571429849e-01, /* 3E924925 */
      29  Lp4 = 2.2222198546e-01, /* 3E638E29 */
      30  Lp5 = 1.8183572590e-01, /* 3E3A3325 */
      31  Lp6 = 1.5313838422e-01, /* 3E1CD04F */
      32  Lp7 = 1.4798198640e-01; /* 3E178897 */
      33  
      34  static const float zero = 0.0;
      35  
      36  float
      37  __log1pf(float x)
      38  {
      39  	float hfsq,f,c,s,z,R,u;
      40  	int32_t k,hx,hu,ax;
      41  
      42  	GET_FLOAT_WORD(hx,x);
      43  	ax = hx&0x7fffffff;
      44  
      45  	k = 1;
      46  	if (hx < 0x3ed413d7) {			/* x < 0.41422  */
      47  	    if(ax>=0x3f800000) {		/* x <= -1.0 */
      48  		if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=-inf */
      49  		else return (x-x)/(x-x);	/* log1p(x<-1)=NaN */
      50  	    }
      51  	    if(ax<0x31000000) {			/* |x| < 2**-29 */
      52  		math_force_eval(two25+x);	/* raise inexact */
      53  		if (ax<0x24800000)		/* |x| < 2**-54 */
      54  		  {
      55  		    math_check_force_underflow (x);
      56  		    return x;
      57  		  }
      58  		else
      59  		    return x - x*x*(float)0.5;
      60  	    }
      61  	    if(hx>0||hx<=((int32_t)0xbe95f61f)) {
      62  		k=0;f=x;hu=1;}	/* -0.2929<x<0.41422 */
      63  	}
      64  	if (hx >= 0x7f800000) return x+x;
      65  	if(k!=0) {
      66  	    if(hx<0x5a000000) {
      67  		u  = (float)1.0+x;
      68  		GET_FLOAT_WORD(hu,u);
      69  		k  = (hu>>23)-127;
      70  		/* correction term */
      71  		c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
      72  		c /= u;
      73  	    } else {
      74  		u  = x;
      75  		GET_FLOAT_WORD(hu,u);
      76  		k  = (hu>>23)-127;
      77  		c  = 0;
      78  	    }
      79  	    hu &= 0x007fffff;
      80  	    if(hu<0x3504f7) {
      81  		SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
      82  	    } else {
      83  		k += 1;
      84  		SET_FLOAT_WORD(u,hu|0x3f000000);	/* normalize u/2 */
      85  		hu = (0x00800000-hu)>>2;
      86  	    }
      87  	    f = u-(float)1.0;
      88  	}
      89  	hfsq=(float)0.5*f*f;
      90  	if(hu==0) {	/* |f| < 2**-20 */
      91  	    if(f==zero) {
      92  		if(k==0) return zero;
      93  		else {c += k*ln2_lo; return k*ln2_hi+c;}
      94  	    }
      95  	    R = hfsq*(1.0f-0.66666666666666666f*f);
      96  	    if(k==0) return f-R; else
      97  		     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
      98  	}
      99  	s = f/((float)2.0+f);
     100  	z = s*s;
     101  	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
     102  	if (k == 0)
     103  	  return f - (hfsq - s * (hfsq + R));
     104  	else
     105  	  {
     106  	    /* With GCC 7 when compiling with -Os the compiler warns
     107  	       that c might be used uninitialized.  This can't be true
     108  	       because k must be 0 for c to be uninitialized and we
     109  	       handled that computation earlier without using c.  */
     110  	    DIAG_PUSH_NEEDS_COMMENT;
     111  	    DIAG_IGNORE_Os_NEEDS_COMMENT (7, "-Wmaybe-uninitialized");
     112  	    return k * ln2_hi - ((hfsq - (s * (hfsq + R)
     113  					  + (k * ln2_lo + c))) - f);
     114  	    DIAG_POP_NEEDS_COMMENT;
     115  	  }
     116  }