lib/libm/src/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 __RCSID("$NetBSD: e_fmodl.c,v 1.2 2013/11/14 15:25:22 martin Exp $");
  15 #if 0
  16 __FBSDID("$FreeBSD: head/lib/msun/src/e_fmodl.c 181063 2008-07-31 20:09:47Z das $");
  17 #endif
  18
  19 #include "namespace.h"
  20
  21 #include <float.h>
  22 #include <stdint.h>
  23
  24 #include "math.h"
  25 #include "math_private.h"
  26 #include <machine/ieee.h>
  27
  28 #ifdef __HAVE_LONG_DOUBLE
  29
  30 #define BIAS (LDBL_MAX_EXP - 1)
  31
  32 #if EXT_FRACLBITS > 32
  33 typedef uint64_t manl_t;
  34 #else
  35 typedef uint32_t manl_t;
  36 #endif
  37
  38 #if EXT_FRACHBITS > 32
  39 typedef uint64_t manh_t;
  40 #else
  41 typedef uint32_t manh_t;
  42 #endif
  43
  44 /*
  45  * These macros add and remove an explicit integer bit in front of the
  46  * fractional mantissa, if the architecture doesn't have such a bit by
  47  * default already.
  48  */
  49 #ifdef LDBL_IMPLICIT_NBIT
  50 #define SET_NBIT(hx)    ((hx) | (1ULL << EXT_FRACHBITS))
  51 #define HFRAC_BITS      EXT_FRACHBITS
  52 #define LDBL_NBIT       0
  53 #else
  54 #define SET_NBIT(hx)    (hx)
  55 #define HFRAC_BITS      (EXT_FRACHBITS - 1)
  56 #endif
  57
  58 #define MANL_SHIFT      (EXT_FRACLBITS - 1)
  59
  60 static const long double one = 1.0, Zero[] = {0.0, -0.0,};
  61
  62 /*
  63  * fmodl(x,y)
  64  * Return x mod y in exact arithmetic
  65  * Method: shift and subtract
  66  *
  67  * Assumptions:
  68  * - The low part of the mantissa fits in a manl_t exactly.
  69  * - The high part of the mantissa fits in an int64_t with enough room
  70  *   for an explicit integer bit in front of the fractional bits.
  71  */
  72 long double
  73 __ieee754_fmodl(long double x, long double y)
  74 {
  75         union ieee_ext_u ux = { .extu_ld = x, };
  76         union ieee_ext_u uy = { .extu_ld = y, };
  77         int64_t hx,hz;  /* We need a carry bit even if EXT_FRACHBITS is 32. */
  78         manh_t hy;
  79         manl_t lx,ly,lz;
  80         int ix,iy,n,sx;
  81
  82         sx = ux.extu_sign;
  83
  84     /* purge off exception values */
  85         if((uy.extu_exp|uy.extu_frach|uy.extu_fracl)==0 || /* y=0 */
  86            (ux.extu_exp == BIAS + LDBL_MAX_EXP) ||       /* or x not finite */
  87            (uy.extu_exp == BIAS + LDBL_MAX_EXP &&
  88             ((uy.extu_frach&~LDBL_NBIT)|uy.extu_fracl)!=0)) /* or y is NaN */
  89             return (x*y)/(x*y);
  90         if(ux.extu_exp<=uy.extu_exp) {
  91             if((ux.extu_exp<uy.extu_exp) ||
  92                (ux.extu_frach<=uy.extu_frach &&
  93                 (ux.extu_frach<uy.extu_frach ||
  94                  ux.extu_fracl<uy.extu_fracl))) {
  95                 return x;               /* |x|<|y| return x or x-y */
  96             }
  97             if(ux.extu_frach==uy.extu_frach && ux.extu_fracl==uy.extu_fracl) {
  98                 return Zero[sx];        /* |x|=|y| return x*0*/
  99             }
 100         }
 101
 102     /* determine ix = ilogb(x) */
 103         if(ux.extu_exp == 0) {  /* subnormal x */
 104             ux.extu_ld *= 0x1.0p512;
 105             ix = ux.extu_exp - (BIAS + 512);
 106         } else {
 107             ix = ux.extu_exp - BIAS;
 108         }
 109
 110     /* determine iy = ilogb(y) */
 111         if(uy.extu_exp == 0) {  /* subnormal y */
 112             uy.extu_ld *= 0x1.0p512;
 113             iy = uy.extu_exp - (BIAS + 512);
 114         } else {
 115             iy = uy.extu_exp - BIAS;
 116         }
 117
 118     /* set up {hx,lx}, {hy,ly} and align y to x */
 119         hx = SET_NBIT(ux.extu_frach);
 120         hy = SET_NBIT(uy.extu_frach);
 121         lx = ux.extu_fracl;
 122         ly = uy.extu_fracl;
 123
 124     /* fix point fmod */
 125         n = ix - iy;
 126
 127         while(n--) {
 128             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 129             if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
 130             else {
 131                 if ((hz|lz)==0)         /* return sign(x)*0 */
 132                     return Zero[sx];
 133                 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
 134             }
 135         }
 136         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 137         if(hz>=0) {hx=hz;lx=lz;}
 138
 139     /* convert back to floating value and restore the sign */
 140         if((hx|lx)==0)                  /* return sign(x)*0 */
 141             return Zero[sx];
 142         while(hx<(1LL<<HFRAC_BITS)) {   /* normalize x */
 143             hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
 144             iy -= 1;
 145         }
 146         ux.extu_frach = hx; /* The mantissa is truncated here if needed. */
 147         ux.extu_fracl = lx;
 148         if (iy < LDBL_MIN_EXP) {
 149             ux.extu_exp = iy + (BIAS + 512);
 150             ux.extu_ld *= 0x1p-512;
 151         } else {
 152             ux.extu_exp = iy + BIAS;
 153         }
 154         x = ux.extu_ld * one;   /* create necessary signal */
 155         return x;               /* exact output */
 156 }
 157
 158 #endif /* __HAVE_LONG_DOUBLE */