1 /*
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
5  * Developed at SunPro, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  *
11  * From: @(#)s_floor.c 5.1 93/09/24
12  */
13 
14 #include <sys/cdefs.h>
15 __FBSDID("$FreeBSD$");
16 
17 /*
18  * floorl(x)
19  * Return x rounded toward -inf to integral value
20  * Method:
21  *	Bit twiddling.
22  * Exception:
23  *	Inexact flag raised if x not equal to floorl(x).
24  */
25 
26 #include <float.h>
27 #include <math.h>
28 #include <stdint.h>
29 
30 #include "fpmath.h"
31 
32 #ifdef LDBL_IMPLICIT_NBIT
33 #define	MANH_SIZE	(LDBL_MANH_SIZE + 1)
34 #define	INC_MANH(u, c)	do {					\
35 	uint64_t o = u.bits.manh;				\
36 	u.bits.manh += (c);					\
37 	if (u.bits.manh < o)					\
38 		u.bits.exp++;					\
39 } while (0)
40 #else
41 #define	MANH_SIZE	LDBL_MANH_SIZE
42 #define	INC_MANH(u, c)	do {					\
43 	uint64_t o = u.bits.manh;				\
44 	u.bits.manh += (c);					\
45 	if (u.bits.manh < o) {					\
46 		u.bits.exp++;					\
47 		u.bits.manh |= 1llu << (LDBL_MANH_SIZE - 1);	\
48 	}							\
49 } while (0)
50 #endif
51 
52 static const long double huge = 1.0e300;
53 
54 long double
floorl(long double x)55 floorl(long double x)
56 {
57 	union IEEEl2bits u = { .e = x };
58 	int e = u.bits.exp - LDBL_MAX_EXP + 1;
59 
60 	if (e < MANH_SIZE - 1) {
61 		if (e < 0) {			/* raise inexact if x != 0 */
62 			if (huge + x > 0.0)
63 				if (u.bits.exp > 0 ||
64 				    (u.bits.manh | u.bits.manl) != 0)
65 					u.e = u.bits.sign ? -1.0 : 0.0;
66 		} else {
67 			uint64_t m = ((1llu << MANH_SIZE) - 1) >> (e + 1);
68 			if (((u.bits.manh & m) | u.bits.manl) == 0)
69 				return (x);	/* x is integral */
70 			if (u.bits.sign) {
71 #ifdef LDBL_IMPLICIT_NBIT
72 				if (e == 0)
73 					u.bits.exp++;
74 				else
75 #endif
76 				INC_MANH(u, 1llu << (MANH_SIZE - e - 1));
77 			}
78 			if (huge + x > 0.0) {	/* raise inexact flag */
79 				u.bits.manh &= ~m;
80 				u.bits.manl = 0;
81 			}
82 		}
83 	} else if (e < LDBL_MANT_DIG - 1) {
84 		uint64_t m = (uint64_t)-1 >> (64 - LDBL_MANT_DIG + e + 1);
85 		if ((u.bits.manl & m) == 0)
86 			return (x);	/* x is integral */
87 		if (u.bits.sign) {
88 			if (e == MANH_SIZE - 1)
89 				INC_MANH(u, 1);
90 			else {
91 				uint64_t o = u.bits.manl;
92 				u.bits.manl += 1llu << (LDBL_MANT_DIG - e - 1);
93 				if (u.bits.manl < o)	/* got a carry */
94 					INC_MANH(u, 1);
95 			}
96 		}
97 		if (huge + x > 0.0)		/* raise inexact flag */
98 			u.bits.manl &= ~m;
99 	}
100 	return (u.e);
101 }
102