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  1. /* ef_exp.c -- float version of e_exp.c.
  2.  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
  3.  */
  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 "fdlibm.h"
  17.  
  18. #ifdef __v810__
  19. #define const
  20. #endif
  21.  
  22. #ifdef __STDC__
  23. static const float
  24. #else
  25. static float
  26. #endif
  27. one     = 1.0,
  28. halF[2] = {0.5,-0.5,},
  29. huge    = 1.0e+30,
  30. twom100 = 7.8886090522e-31,      /* 2**-100=0x0d800000 */
  31. ln2HI[2]   ={ 6.9313812256e-01,         /* 0x3f317180 */
  32.              -6.9313812256e-01,},       /* 0xbf317180 */
  33. ln2LO[2]   ={ 9.0580006145e-06,         /* 0x3717f7d1 */
  34.              -9.0580006145e-06,},       /* 0xb717f7d1 */
  35. invln2 =  1.4426950216e+00,             /* 0x3fb8aa3b */
  36. P1   =  1.6666667163e-01, /* 0x3e2aaaab */
  37. P2   = -2.7777778450e-03, /* 0xbb360b61 */
  38. P3   =  6.6137559770e-05, /* 0x388ab355 */
  39. P4   = -1.6533901999e-06, /* 0xb5ddea0e */
  40. P5   =  4.1381369442e-08; /* 0x3331bb4c */
  41.  
  42. #ifdef __STDC__
  43.         float __ieee754_expf(float x)   /* default IEEE double exp */
  44. #else
  45.         float __ieee754_expf(x) /* default IEEE double exp */
  46.         float x;
  47. #endif
  48. {
  49.         float y,hi,lo,c,t;
  50.         __int32_t k = 0,xsb,sx;
  51.         __uint32_t hx;
  52.  
  53.         GET_FLOAT_WORD(sx,x);
  54.         xsb = (sx>>31)&1;               /* sign bit of x */
  55.         hx = sx & 0x7fffffff;           /* high word of |x| */
  56.  
  57.     /* filter out non-finite argument */
  58.         if(FLT_UWORD_IS_NAN(hx))
  59.             return x+x;         /* NaN */
  60.         if(FLT_UWORD_IS_INFINITE(hx))
  61.             return (xsb==0)? x:0.0;             /* exp(+-inf)={inf,0} */
  62.         if(sx > FLT_UWORD_LOG_MAX)
  63.             return huge*huge; /* overflow */
  64.         if(sx < 0 && hx > FLT_UWORD_LOG_MIN)
  65.             return twom100*twom100; /* underflow */
  66.        
  67.     /* argument reduction */
  68.         if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
  69.             if(hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
  70.                 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
  71.             } else {
  72.                 k  = invln2*x+halF[xsb];
  73.                 t  = k;
  74.                 hi = x - t*ln2HI[0];    /* t*ln2HI is exact here */
  75.                 lo = t*ln2LO[0];
  76.             }
  77.             x  = hi - lo;
  78.         }
  79.         else if(hx < 0x31800000)  {     /* when |x|<2**-28 */
  80.             if(huge+x>one) return one+x;/* trigger inexact */
  81.         }
  82.  
  83.     /* x is now in primary range */
  84.         t  = x*x;
  85.         c  = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
  86.         if(k==0)        return one-((x*c)/(c-(float)2.0)-x);
  87.         else            y = one-((lo-(x*c)/((float)2.0-c))-hi);
  88.         if(k >= -125) {
  89.             __uint32_t hy;
  90.             GET_FLOAT_WORD(hy,y);
  91.             SET_FLOAT_WORD(y,hy+(k<<23));       /* add k to y's exponent */
  92.             return y;
  93.         } else {
  94.             __uint32_t hy;
  95.             GET_FLOAT_WORD(hy,y);
  96.             SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
  97.             return y*twom100;
  98.         }
  99. }
  100.