1 /* @(#)e_fmod.c 1.3 95/01/18 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
12 * FreeBSD SVN: 181063 (2008-07-31)
20 #include "math_private.h"
22 #define BIAS (LDBL_MAX_EXP - 1)
24 #if LDBL_MANL_SIZE > 32
25 typedef uint64_t manl_t;
27 typedef uint32_t manl_t;
30 #if LDBL_MANH_SIZE > 32
31 typedef uint64_t manh_t;
33 typedef uint32_t manh_t;
37 * These macros add and remove an explicit integer bit in front of the
38 * fractional mantissa, if the architecture doesn't have such a bit by
41 #ifdef LDBL_IMPLICIT_NBIT
42 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE))
43 #define HFRAC_BITS LDBL_MANH_SIZE
45 #define SET_NBIT(hx) (hx)
46 #define HFRAC_BITS (LDBL_MANH_SIZE - 1)
49 #define MANL_SHIFT (LDBL_MANL_SIZE - 1)
51 static const long double one = 1.0, Zero[] = {0.0, -0.0,};
55 * Return x mod y in exact arithmetic
56 * Method: shift and subtract
59 * - The low part of the mantissa fits in a manl_t exactly.
60 * - The high part of the mantissa fits in an int64_t with enough room
61 * for an explicit integer bit in front of the fractional bits.
64 fmodl(long double x, long double y)
66 union IEEEl2bits ux, uy;
67 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
76 /* purge off exception values */
77 if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
78 (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
79 (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
80 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
82 if(ux.bits.exp<=uy.bits.exp) {
83 if((ux.bits.exp<uy.bits.exp) ||
84 (ux.bits.manh<=uy.bits.manh &&
85 (ux.bits.manh<uy.bits.manh ||
86 ux.bits.manl<uy.bits.manl))) {
87 return x; /* |x|<|y| return x or x-y */
89 if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
90 return Zero[sx]; /* |x|=|y| return x*0*/
94 /* determine ix = ilogb(x) */
95 if(ux.bits.exp == 0) { /* subnormal x */
97 ix = ux.bits.exp - (BIAS + 512);
99 ix = ux.bits.exp - BIAS;
102 /* determine iy = ilogb(y) */
103 if(uy.bits.exp == 0) { /* subnormal y */
105 iy = uy.bits.exp - (BIAS + 512);
107 iy = uy.bits.exp - BIAS;
110 /* set up {hx,lx}, {hy,ly} and align y to x */
111 hx = SET_NBIT(ux.bits.manh);
112 hy = SET_NBIT(uy.bits.manh);
120 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
121 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
123 if ((hz|lz)==0) /* return sign(x)*0 */
125 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
128 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
129 if(hz>=0) {hx=hz;lx=lz;}
131 /* convert back to floating value and restore the sign */
132 if((hx|lx)==0) /* return sign(x)*0 */
134 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */
135 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
138 ux.bits.manh = hx; /* The mantissa is truncated here if needed. */
140 if (iy < LDBL_MIN_EXP) {
141 ux.bits.exp = iy + (BIAS + 512);
144 ux.bits.exp = iy + BIAS;
146 x = ux.e * one; /* create necessary signal */
147 return x; /* exact output */