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