newlib/libm/ld/e_fmodl.c

   1 /* @(#)e_fmod.c 1.3 95/01/18 */
   2 /*-
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 #include <sys/cdefs.h>
  14 __FBSDID("$FreeBSD$");
  15
  16 #include <float.h>
  17 #include <stdint.h>
  18
  19 #include "fpmath.h"
  20 #include "math.h"
  21 #include "math_private.h"
  22
  23 #define BIAS (LDBL_MAX_EXP - 1)
  24
  25 #if LDBL_MANL_SIZE > 32
  26 typedef uint64_t manl_t;
  27 #else
  28 typedef uint32_t manl_t;
  29 #endif
  30
  31 #if LDBL_MANH_SIZE > 32
  32 typedef uint64_t manh_t;
  33 #else
  34 typedef uint32_t manh_t;
  35 #endif
  36
  37 /*
  38  * These macros add and remove an explicit integer bit in front of the
  39  * fractional mantissa, if the architecture doesn't have such a bit by
  40  * default already.
  41  */
  42 #ifdef LDBL_IMPLICIT_NBIT
  43 #define SET_NBIT(hx)    ((hx) | (1ULL << LDBL_MANH_SIZE))
  44 #define HFRAC_BITS      LDBL_MANH_SIZE
  45 #else
  46 #define SET_NBIT(hx)    (hx)
  47 #define HFRAC_BITS      (LDBL_MANH_SIZE - 1)
  48 #endif
  49
  50 #define MANL_SHIFT      (LDBL_MANL_SIZE - 1)
  51
  52 static const long double one = 1.0, Zero[] = {0.0, -0.0,};
  53
  54 /*
  55  * fmodl(x,y)
  56  * Return x mod y in exact arithmetic
  57  * Method: shift and subtract
  58  *
  59  * Assumptions:
  60  * - The low part of the mantissa fits in a manl_t exactly.
  61  * - The high part of the mantissa fits in an int64_t with enough room
  62  *   for an explicit integer bit in front of the fractional bits.
  63  */
  64 long double
  65 fmodl(long double x, long double y)
  66 {
  67         union IEEEl2bits ux, uy;
  68         int64_t hx,hz;  /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
  69         manh_t hy;
  70         manl_t lx,ly,lz;
  71         int ix,iy,n,sx;
  72
  73         ux.e = x;
  74         uy.e = y;
  75         sx = ux.bits.sign;
  76
  77     /* purge off exception values */
  78         if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
  79            (ux.bits.exp == BIAS + LDBL_MAX_EXP) ||       /* or x not finite */
  80            (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
  81             ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
  82             return nan_mix_op(x, y, *)/nan_mix_op(x, y, *);
  83         if(ux.bits.exp<=uy.bits.exp) {
  84             if((ux.bits.exp<uy.bits.exp) ||
  85                (ux.bits.manh<=uy.bits.manh &&
  86                 (ux.bits.manh<uy.bits.manh ||
  87                  ux.bits.manl<uy.bits.manl))) {
  88                 return x;               /* |x|<|y| return x or x-y */
  89             }
  90             if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
  91                 return Zero[sx];        /* |x|=|y| return x*0*/
  92             }
  93         }
  94
  95     /* determine ix = ilogb(x) */
  96         if(ux.bits.exp == 0) {  /* subnormal x */
  97             ux.e *= 0x1.0p512;
  98             ix = ux.bits.exp - (BIAS + 512);
  99         } else {
 100             ix = ux.bits.exp - BIAS;
 101         }
 102
 103     /* determine iy = ilogb(y) */
 104         if(uy.bits.exp == 0) {  /* subnormal y */
 105             uy.e *= 0x1.0p512;
 106             iy = uy.bits.exp - (BIAS + 512);
 107         } else {
 108             iy = uy.bits.exp - BIAS;
 109         }
 110
 111     /* set up {hx,lx}, {hy,ly} and align y to x */
 112         hx = SET_NBIT(ux.bits.manh);
 113         hy = SET_NBIT(uy.bits.manh);
 114         lx = ux.bits.manl;
 115         ly = uy.bits.manl;
 116
 117     /* fix point fmod */
 118         n = ix - iy;
 119
 120         while(n--) {
 121             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 122             if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
 123             else {
 124                 if ((hz|lz)==0)         /* return sign(x)*0 */
 125                     return Zero[sx];
 126                 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
 127             }
 128         }
 129         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 130         if(hz>=0) {hx=hz;lx=lz;}
 131
 132     /* convert back to floating value and restore the sign */
 133         if((hx|lx)==0)                  /* return sign(x)*0 */
 134             return Zero[sx];
 135         while(hx<(1ULL<<HFRAC_BITS)) {  /* normalize x */
 136             hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
 137             iy -= 1;
 138         }
 139         ux.bits.manh = hx; /* The mantissa is truncated here if needed. */
 140         ux.bits.manl = lx;
 141         if (iy < LDBL_MIN_EXP) {
 142             ux.bits.exp = iy + (BIAS + 512);
 143             ux.e *= 0x1p-512;
 144         } else {
 145             ux.bits.exp = iy + BIAS;
 146         }
 147         x = ux.e * one;         /* create necessary signal */
 148         return x;               /* exact output */
 149 }