e_sqrtl.c revision 1.5 
1/*-
2 * Copyright (c) 2007 Steven G. Kargl
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 *    notice unmodified, this list of conditions, and the following
10 *    disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 *    notice, this list of conditions and the following disclaimer in the
13 *    documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
16 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
19 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25 */
26
27#include <sys/cdefs.h>
28#if 0
29__FBSDID("$FreeBSD: head/lib/msun/src/e_sqrtl.c 176720 2008-03-02 01:47:58Z das $");
30#endif
31__RCSID("$NetBSD: e_sqrtl.c,v 1.5 2016/08/26 08:31:17 christos Exp $");
32
33#include <machine/ieee.h>
34#include <float.h>
35
36#include "math.h"
37#include "math_private.h"
38
39#ifdef __HAVE_LONG_DOUBLE
40
41#define __TEST_FENV
42#include <fenv.h>
43
44#ifdef LDBL_IMPLICIT_NBIT
45#define	LDBL_NBIT	0
46#endif
47
48#ifdef __HAVE_FENV
49
50/* Return (x + ulp) for normal positive x. Assumes no overflow. */
51static inline long double
52inc(long double x)
53{
54	union ieee_ext_u ux = { .extu_ld = x, };
55
56	if (++ux.extu_fracl == 0) {
57		if (++ux.extu_frach == 0) {
58			ux.extu_exp++;
59			ux.extu_frach |= LDBL_NBIT;
60		}
61	}
62	return (ux.extu_ld);
63}
64
65/* Return (x - ulp) for normal positive x. Assumes no underflow. */
66static inline long double
67dec(long double x)
68{
69	union ieee_ext_u ux = { .extu_ld = x, };
70
71	if (ux.extu_fracl-- == 0) {
72		if (ux.extu_frach-- == LDBL_NBIT) {
73			ux.extu_exp--;
74			ux.extu_frach |= LDBL_NBIT;
75		}
76	}
77	return (ux.extu_ld);
78}
79
80/*
81 * This is slow, but simple and portable. You should use hardware sqrt
82 * if possible.
83 */
84
85long double
86__ieee754_sqrtl(long double x)
87{
88	union ieee_ext_u ux = { .extu_ld = x, };
89	int k, r;
90	long double lo, xn;
91	fenv_t env;
92
93	/* If x = NaN, then sqrt(x) = NaN. */
94	/* If x = Inf, then sqrt(x) = Inf. */
95	/* If x = -Inf, then sqrt(x) = NaN. */
96	if (ux.extu_exp == LDBL_MAX_EXP * 2 - 1)
97		return (x * x + x);
98
99	/* If x = +-0, then sqrt(x) = +-0. */
100	if ((ux.extu_frach | ux.extu_fracl | ux.extu_exp) == 0)
101		return (x);
102
103	/* If x < 0, then raise invalid and return NaN */
104	if (ux.extu_sign)
105		return ((x - x) / (x - x));
106
107	feholdexcept(&env);
108
109	if (ux.extu_exp == 0) {
110		/* Adjust subnormal numbers. */
111		ux.extu_ld *= 0x1.0p514;
112		k = -514;
113	} else {
114		k = 0;
115	}
116	/*
117	 * ux.extu_ld is a normal number, so break it into ux.extu_ld = e*2^n where
118	 * ux.extu_ld = (2*e)*2^2k for odd n and ux.extu_ld = (4*e)*2^2k for even n.
119	 */
120	if ((ux.extu_exp - EXT_EXP_BIAS) & 1) {	/* n is even.     */
121		k += ux.extu_exp - EXT_EXP_BIAS - 1; /* 2k = n - 2.   */
122		ux.extu_exp = EXT_EXP_BIAS + 1;	/* ux.extu_ld in [2,4). */
123	} else {
124		k += ux.extu_exp - EXT_EXP_BIAS;	/* 2k = n - 1.   */
125		ux.extu_exp = EXT_EXP_BIAS;	/* ux.extu_ld in [1,2). */
126	}
127
128	/*
129	 * Newton's iteration.
130	 * Split ux.extu_ld into a high and low part to achieve additional precision.
131	 */
132	xn = sqrt(ux.extu_ld);			/* 53-bit estimate of sqrtl(x). */
133#if LDBL_MANT_DIG > 100
134	xn = (xn + (ux.extu_ld / xn)) * 0.5;	/* 106-bit estimate. */
135#endif
136	lo = ux.extu_ld;
137	ux.extu_fracl = 0;		/* Zero out lower bits. */
138	lo = (lo - ux.extu_ld) / xn;	/* Low bits divided by xn. */
139	xn = xn + (ux.extu_ld / xn);	/* High portion of estimate. */
140	ux.extu_ld = xn + lo;		/* Combine everything. */
141	ux.extu_exp += (k >> 1) - 1;
142
143	feclearexcept(FE_INEXACT);
144	r = fegetround();
145	fesetround(FE_TOWARDZERO);	/* Set to round-toward-zero. */
146	xn = x / ux.extu_ld;		/* Chopped quotient (inexact?). */
147
148	if (!fetestexcept(FE_INEXACT)) { /* Quotient is exact. */
149		if (xn == ux.extu_ld) {
150			fesetenv(&env);
151			return (ux.extu_ld);
152		}
153		/* Round correctly for inputs like x = y**2 - ulp. */
154		xn = dec(xn);		/* xn = xn - ulp. */
155	}
156
157	if (r == FE_TONEAREST) {
158		xn = inc(xn);		/* xn = xn + ulp. */
159	} else if (r == FE_UPWARD) {
160		ux.extu_ld = inc(ux.extu_ld);	/* ux.extu_ld = ux.extu_ld + ulp. */
161		xn = inc(xn);		/* xn  = xn + ulp. */
162	}
163	ux.extu_ld = ux.extu_ld + xn;		/* Chopped sum. */
164	feupdateenv(&env);	/* Restore env and raise inexact */
165	ux.extu_exp--;
166	return (ux.extu_ld);
167}
168
169#else /* !__HAVE_FENV */
170
171/*
172 * No fenv support:
173 * poor man's version: just use double
174 */
175long double
176__ieee754_sqrtl(long double x)
177{
178	return __ieee754_sqrt((double)x);
179}
180
181#endif /* __HAVE_FENV */
182
183#endif /* __HAVE_LONG_DOUBLE */
184