1 /* @(#)e_fmod.c 1.3 95/01/18 */
2 /* $FreeBSD: head/lib/msun/src/e_fmodl.c 181063 2008-07-31 20:09:47Z das $ */
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
11 * ====================================================
19 #include "math_private.h"
21 #define BIAS (LDBL_MAX_EXP - 1)
23 #if LDBL_MANL_SIZE > 32
24 typedef uint64_t manl_t;
26 typedef uint32_t manl_t;
29 #if LDBL_MANH_SIZE > 32
30 typedef uint64_t manh_t;
32 typedef uint32_t manh_t;
36 * These macros add and remove an explicit integer bit in front of the
37 * fractional mantissa, if the architecture doesn't have such a bit by
40 #ifdef LDBL_IMPLICIT_NBIT
41 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE))
42 #define HFRAC_BITS LDBL_MANH_SIZE
44 #define SET_NBIT(hx) (hx)
45 #define HFRAC_BITS (LDBL_MANH_SIZE - 1)
48 #define MANL_SHIFT (LDBL_MANL_SIZE - 1)
50 static const long double one = 1.0, Zero[] = {0.0, -0.0,};
54 * Return x mod y in exact arithmetic
55 * Method: shift and subtract
58 * - The low part of the mantissa fits in a manl_t exactly.
59 * - The high part of the mantissa fits in an int64_t with enough room
60 * for an explicit integer bit in front of the fractional bits.
63 fmodl(long double x, long double y)
65 union IEEEl2bits ux, uy;
66 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
75 /* purge off exception values */
76 if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
77 (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
78 (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
79 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
81 if(ux.bits.exp<=uy.bits.exp) {
82 if((ux.bits.exp<uy.bits.exp) ||
83 (ux.bits.manh<=uy.bits.manh &&
84 (ux.bits.manh<uy.bits.manh ||
85 ux.bits.manl<uy.bits.manl))) {
86 return x; /* |x|<|y| return x or x-y */
88 if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
89 return Zero[sx]; /* |x|=|y| return x*0*/
93 /* determine ix = ilogb(x) */
94 if(ux.bits.exp == 0) { /* subnormal x */
96 ix = ux.bits.exp - (BIAS + 512);
98 ix = ux.bits.exp - BIAS;
101 /* determine iy = ilogb(y) */
102 if(uy.bits.exp == 0) { /* subnormal y */
104 iy = uy.bits.exp - (BIAS + 512);
106 iy = uy.bits.exp - BIAS;
109 /* set up {hx,lx}, {hy,ly} and align y to x */
110 hx = SET_NBIT(ux.bits.manh);
111 hy = SET_NBIT(uy.bits.manh);
119 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
120 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
122 if ((hz|lz)==0) /* return sign(x)*0 */
124 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
127 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
128 if(hz>=0) {hx=hz;lx=lz;}
130 /* convert back to floating value and restore the sign */
131 if((hx|lx)==0) /* return sign(x)*0 */
133 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */
134 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
137 ux.bits.manh = hx; /* The mantissa is truncated here if needed. */
139 if (iy < LDBL_MIN_EXP) {
140 ux.bits.exp = iy + (BIAS + 512);
143 ux.bits.exp = iy + BIAS;
145 x = ux.e * one; /* create necessary signal */
146 return x; /* exact output */