sysdeps/ieee754/ldbl-128ibm/math_ldbl.h

   1 #ifndef _MATH_PRIVATE_H_
   2 #error "Never use <math_ldbl.h> directly; include <math_private.h> instead."
   3 #endif
   4
   5 #include <sysdeps/ieee754/ldbl-128/math_ldbl.h>
   6 #include <ieee754.h>
   7
   8 static inline void
   9 ldbl_extract_mantissa (int64_t *hi64, u_int64_t *lo64, int *exp, long double x)
  10 {
  11   /* We have 105 bits of mantissa plus one implicit digit.  Since
  12      106 bits are representable we use the first implicit digit for
  13      the number before the decimal point and the second implicit bit
  14      as bit 53 of the mantissa.  */
  15   unsigned long long hi, lo;
  16   int ediff;
  17   union ibm_extended_long_double eldbl;
  18   eldbl.d = x;
  19   *exp = eldbl.ieee.exponent - IBM_EXTENDED_LONG_DOUBLE_BIAS;
  20
  21   lo = ((long long)eldbl.ieee.mantissa2 << 32) | eldbl.ieee.mantissa3;
  22   hi = ((long long)eldbl.ieee.mantissa0 << 32) | eldbl.ieee.mantissa1;
  23   /* If the lower double is not a denomal or zero then set the hidden
  24      53rd bit.  */
  25   if (eldbl.ieee.exponent2 > 0x001)
  26     {
  27       lo |= (1ULL << 52);
  28       lo = lo << 7; /* pre-shift lo to match ieee854.  */
  29       /* The lower double is normalized separately from the upper.  We
  30          may need to adjust the lower manitissa to reflect this.  */
  31       ediff = eldbl.ieee.exponent - eldbl.ieee.exponent2;
  32       if (ediff > 53)
  33         lo = lo >> (ediff-53);
  34     }
  35   hi |= (1ULL << 52);
  36
  37   if ((eldbl.ieee.negative != eldbl.ieee.negative2)
  38       && ((eldbl.ieee.exponent2 != 0) && (lo != 0LL)))
  39     {
  40       hi--;
  41       lo = (1ULL << 60) - lo;
  42       if (hi < (1ULL << 52))
  43         {
  44           /* we have a borrow from the hidden bit, so shift left 1.  */
  45           hi = (hi << 1) | (lo >> 59);
  46           lo = 0xfffffffffffffffLL & (lo << 1);
  47           *exp = *exp - 1;
  48         }
  49     }
  50   *lo64 = (hi << 60) | lo;
  51   *hi64 = hi >> 4;
  52 }
  53
  54 static inline long double
  55 ldbl_insert_mantissa (int sign, int exp, int64_t hi64, u_int64_t lo64)
  56 {
  57   union ibm_extended_long_double u;
  58   unsigned long hidden2, lzcount;
  59   unsigned long long hi, lo;
  60
  61   u.ieee.negative = sign;
  62   u.ieee.negative2 = sign;
  63   u.ieee.exponent = exp + IBM_EXTENDED_LONG_DOUBLE_BIAS;
  64   u.ieee.exponent2 = exp-53 + IBM_EXTENDED_LONG_DOUBLE_BIAS;
  65   /* Expect 113 bits (112 bits + hidden) right justified in two longs.
  66      The low order 53 bits (52 + hidden) go into the lower double */
  67   lo = (lo64 >> 7)& ((1ULL << 53) - 1);
  68   hidden2 = (lo64 >> 59) &  1ULL;
  69   /* The high order 53 bits (52 + hidden) go into the upper double */
  70   hi = (lo64 >> 60) & ((1ULL << 11) - 1);
  71   hi |= (hi64 << 4);
  72
  73   if (lo != 0LL)
  74     {
  75       /* hidden2 bit of low double controls rounding of the high double.
  76          If hidden2 is '1' then round up hi and adjust lo (2nd mantissa)
  77          plus change the sign of the low double to compensate.  */
  78       if (hidden2)
  79         {
  80           hi++;
  81           u.ieee.negative2 = !sign;
  82           lo = (1ULL << 53) - lo;
  83         }
  84       /* The hidden bit of the lo mantissa is zero so we need to
  85          normalize the it for the low double.  Shift it left until the
  86          hidden bit is '1' then adjust the 2nd exponent accordingly.  */
  87
  88       if (sizeof (lo) == sizeof (long))
  89         lzcount = __builtin_clzl (lo);
  90       else if ((lo >> 32) != 0)
  91         lzcount = __builtin_clzl ((long) (lo >> 32));
  92       else
  93         lzcount = __builtin_clzl ((long) lo) + 32;
  94       lzcount = lzcount - 11;
  95       if (lzcount > 0)
  96         {
  97           int expnt2 = u.ieee.exponent2 - lzcount;
  98           if (expnt2 >= 1)
  99             {
 100               /* Not denormal.  Normalize and set low exponent.  */
 101               lo = lo << lzcount;
 102               u.ieee.exponent2 = expnt2;
 103             }
 104           else
 105             {
 106               /* Is denormal.  */
 107               lo = lo << (lzcount + expnt2);
 108               u.ieee.exponent2 = 0;
 109             }
 110         }
 111     }
 112   else
 113     {
 114       u.ieee.negative2 = 0;
 115       u.ieee.exponent2 = 0;
 116     }
 117
 118   u.ieee.mantissa3 = lo & ((1ULL << 32) - 1);
 119   u.ieee.mantissa2 = (lo >> 32) & ((1ULL << 20) - 1);
 120   u.ieee.mantissa1 = hi & ((1ULL << 32) - 1);
 121   u.ieee.mantissa0 = (hi >> 32) & ((1ULL << 20) - 1);
 122   return u.d;
 123 }
 124
 125 /* Handy utility functions to pack/unpack/cononicalize and find the nearbyint
 126    of long double implemented as double double.  */
 127 static inline long double
 128 ldbl_pack (double a, double aa)
 129 {
 130   union ibm_extended_long_double u;
 131   u.dd[0] = a;
 132   u.dd[1] = aa;
 133   return u.d;
 134 }
 135
 136 static inline void
 137 ldbl_unpack (long double l, double *a, double *aa)
 138 {
 139   union ibm_extended_long_double u;
 140   u.d = l;
 141   *a = u.dd[0];
 142   *aa = u.dd[1];
 143 }
 144
 145
 146 /* Convert a finite long double to canonical form.
 147    Does not handle +/-Inf properly.  */
 148 static inline void
 149 ldbl_canonicalize (double *a, double *aa)
 150 {
 151   double xh, xl;
 152
 153   xh = *a + *aa;
 154   xl = (*a - xh) + *aa;
 155   *a = xh;
 156   *aa = xl;
 157 }
 158
 159 /* Simple inline nearbyint (double) function .
 160    Only works in the default rounding mode
 161    but is useful in long double rounding functions.  */
 162 static inline double
 163 ldbl_nearbyint (double a)
 164 {
 165   double two52 = 0x10000000000000LL;
 166
 167   if (__builtin_expect ((__builtin_fabs (a) < two52), 1))
 168     {
 169       if (__builtin_expect ((a > 0.0), 1))
 170         {
 171           a += two52;
 172           a -= two52;
 173         }
 174       else if (__builtin_expect ((a < 0.0), 1))
 175         {
 176           a = two52 - a;
 177           a = -(a - two52);
 178         }
 179     }
 180   return a;
 181 }