newlib/libm/common/s_rint.c

   1
   2 /* @(#)s_rint.c 5.1 93/09/24 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  */
  13 /*
  14 FUNCTION
  15 <<rint>>, <<rintf>>---round to integer
  16 INDEX
  17         rint
  18 INDEX
  19         rintf
  20
  21 SYNOPSIS
  22         #include <math.h>
  23         double rint(double <[x]>);
  24         float rintf(float <[x]>);
  25
  26 DESCRIPTION
  27         The <<rint>> functions round their argument to an integer value in
  28         floating-point format, using the current rounding direction.  They
  29         raise the "inexact" floating-point exception if the result differs
  30         in value from the argument.  See the <<nearbyint>> functions for the
  31         same function with the "inexact" floating-point exception never being
  32         raised.  Newlib does not directly support floating-point exceptions.
  33         The <<rint>> functions are written so that the "inexact" exception is
  34         raised in hardware implementations that support it, even though Newlib
  35         does not provide access.
  36
  37 RETURNS
  38 <[x]> rounded to an integral value, using the current rounding direction.
  39
  40 PORTABILITY
  41 ANSI C, POSIX
  42
  43 SEEALSO
  44 <<nearbyint>>, <<round>>
  45
  46 */
  47
  48 /*
  49  * rint(x)
  50  * Return x rounded to integral value according to the prevailing
  51  * rounding mode.
  52  * Method:
  53  *      Using floating addition.
  54  *      Whenever a fraction is present, if the second or any following bit after
  55  *      the radix point is set, limit to the second radix point to avoid
  56  *      possible double rounding in the TWO52 +- steps (in case guard bits are
  57  *      used).  Specifically, if have any, chop off bits past the 2nd place and
  58  *      set the second place.
  59  *      (e.g.   2.0625=0b10.0001 => 0b10.01=2.25;
  60  *              2.3125=0b10.011  => 0b10.01=2.25;
  61  *              1.5625= 0b1.1001 =>  0b1.11=1.75;
  62  *              1.9375= 0b1.1111 =>  0b1.11=1.75.
  63  *      Pseudo-code:  if(x.frac & ~0b0.10) x.frac = (x.frac & 0b0.11) | 0b0.01;).
  64  * Exception:
  65  *      Inexact flag raised if x not equal to rint(x).
  66  */
  67
  68 #include "fdlibm.h"
  69
  70 #ifndef _DOUBLE_IS_32BITS
  71
  72 #ifdef __STDC__
  73 static const double
  74 #else
  75 static double
  76 #endif
  77 TWO52[2]={
  78   4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
  79  -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
  80 };
  81
  82 #ifdef __STDC__
  83         double rint(double x)
  84 #else
  85         double rint(x)
  86         double x;
  87 #endif
  88 {
  89         __int32_t i0,j0,sx;
  90         __uint32_t i,i1;
  91         double t;
  92         volatile double w;
  93         EXTRACT_WORDS(i0,i1,x);
  94         sx = (i0>>31)&1;                /* sign */
  95         j0 = ((i0>>20)&0x7ff)-0x3ff;    /* exponent */
  96         if(j0<20) {                     /* no integral bits in LS part */
  97             if(j0<0) {                  /* x is fractional or 0 */
  98                 if(((i0&0x7fffffff)|i1)==0) return x;   /* x == 0 */
  99                 i1 |= (i0&0x0fffff);
 100                 i0 &= 0xfffe0000;
 101                 i0 |= ((i1|-i1)>>12)&0x80000;
 102                 SET_HIGH_WORD(x,i0);
 103                 w = TWO52[sx]+x;
 104                 t =  w-TWO52[sx];
 105                 GET_HIGH_WORD(i0,t);
 106                 SET_HIGH_WORD(t,(i0&0x7fffffff)|(sx<<31));
 107                 return t;
 108             } else {                    /* x has integer and maybe fraction */
 109                 i = (0x000fffff)>>j0;
 110                 if(((i0&i)|i1)==0) return x; /* x is integral */
 111                 i>>=1;
 112                 if(((i0&i)|i1)!=0) {
 113                     /* 2nd or any later bit after radix is set */
 114                     if(j0==19) i1 = 0x80000000; else i1 = 0;
 115                     i0 = (i0&(~i))|((0x40000)>>j0);
 116                 }
 117             }
 118         } else if (j0>51) {
 119             if(j0==0x400) return x+x;   /* inf or NaN */
 120             else return x;              /* x is integral */
 121         } else {
 122             i = ((__uint32_t)(0xffffffff))>>(j0-20);
 123             if((i1&i)==0) return x;     /* x is integral */
 124             i>>=1;
 125             if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20));
 126         }
 127         INSERT_WORDS(x,i0,i1);
 128         w = TWO52[sx]+x;
 129         return w-TWO52[sx];
 130 }
 131
 132 #endif /* _DOUBLE_IS_32BITS */