ipiq: Add simple IPI latency measure sysctls (2)
[dragonfly.git] / lib / libm / src / s_fmal.c
CommitLineData
1a3b704c
JM
1/*-
2 * Copyright (c) 2005-2011 David Schultz <das@FreeBSD.ORG>
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, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 *
01429808 26 * $FreeBSD: head/lib/msun/src/s_fmal.c 252170 2013-06-24 19:12:17Z eadler $
1a3b704c
JM
27 */
28
29#include <fenv.h>
30#include <float.h>
31#include <math.h>
32
33#include "fpmath.h"
34
35/*
36 * A struct dd represents a floating-point number with twice the precision
37 * of a long double. We maintain the invariant that "hi" stores the high-order
38 * bits of the result.
39 */
40struct dd {
41 long double hi;
42 long double lo;
43};
44
45/*
46 * Compute a+b exactly, returning the exact result in a struct dd. We assume
47 * that both a and b are finite, but make no assumptions about their relative
48 * magnitudes.
49 */
50static inline struct dd
51dd_add(long double a, long double b)
52{
53 struct dd ret;
54 long double s;
55
56 ret.hi = a + b;
57 s = ret.hi - a;
58 ret.lo = (a - (ret.hi - s)) + (b - s);
59 return (ret);
60}
61
62/*
63 * Compute a+b, with a small tweak: The least significant bit of the
64 * result is adjusted into a sticky bit summarizing all the bits that
65 * were lost to rounding. This adjustment negates the effects of double
66 * rounding when the result is added to another number with a higher
67 * exponent. For an explanation of round and sticky bits, see any reference
68 * on FPU design, e.g.,
69 *
70 * J. Coonen. An Implementation Guide to a Proposed Standard for
71 * Floating-Point Arithmetic. Computer, vol. 13, no. 1, Jan 1980.
72 */
73static inline long double
74add_adjusted(long double a, long double b)
75{
76 struct dd sum;
77 union IEEEl2bits u;
78
79 sum = dd_add(a, b);
80 if (sum.lo != 0) {
81 u.e = sum.hi;
82 if ((u.bits.manl & 1) == 0)
83 sum.hi = nextafterl(sum.hi, INFINITY * sum.lo);
84 }
85 return (sum.hi);
86}
87
88/*
89 * Compute ldexp(a+b, scale) with a single rounding error. It is assumed
90 * that the result will be subnormal, and care is taken to ensure that
91 * double rounding does not occur.
92 */
93static inline long double
94add_and_denormalize(long double a, long double b, int scale)
95{
96 struct dd sum;
97 int bits_lost;
98 union IEEEl2bits u;
99
100 sum = dd_add(a, b);
101
102 /*
103 * If we are losing at least two bits of accuracy to denormalization,
104 * then the first lost bit becomes a round bit, and we adjust the
105 * lowest bit of sum.hi to make it a sticky bit summarizing all the
106 * bits in sum.lo. With the sticky bit adjusted, the hardware will
107 * break any ties in the correct direction.
108 *
109 * If we are losing only one bit to denormalization, however, we must
110 * break the ties manually.
111 */
112 if (sum.lo != 0) {
113 u.e = sum.hi;
114 bits_lost = -u.bits.exp - scale + 1;
01429808 115 if ((bits_lost != 1) ^ (int)(u.bits.manl & 1))
1a3b704c
JM
116 sum.hi = nextafterl(sum.hi, INFINITY * sum.lo);
117 }
118 return (ldexp(sum.hi, scale));
119}
120
121/*
122 * Compute a*b exactly, returning the exact result in a struct dd. We assume
123 * that both a and b are normalized, so no underflow or overflow will occur.
124 * The current rounding mode must be round-to-nearest.
125 */
126static inline struct dd
127dd_mul(long double a, long double b)
128{
129#if LDBL_MANT_DIG == 64
130 static const long double split = 0x1p32L + 1.0;
131#elif LDBL_MANT_DIG == 113
132 static const long double split = 0x1p57L + 1.0;
133#endif
134 struct dd ret;
135 long double ha, hb, la, lb, p, q;
136
137 p = a * split;
138 ha = a - p;
139 ha += p;
140 la = a - ha;
141
142 p = b * split;
143 hb = b - p;
144 hb += p;
145 lb = b - hb;
146
147 p = ha * hb;
148 q = ha * lb + la * hb;
149
150 ret.hi = p + q;
151 ret.lo = p - ret.hi + q + la * lb;
152 return (ret);
153}
154
155/*
156 * Fused multiply-add: Compute x * y + z with a single rounding error.
157 *
158 * We use scaling to avoid overflow/underflow, along with the
159 * canonical precision-doubling technique adapted from:
160 *
161 * Dekker, T. A Floating-Point Technique for Extending the
162 * Available Precision. Numer. Math. 18, 224-242 (1971).
163 */
164long double
165fmal(long double x, long double y, long double z)
166{
167 long double xs, ys, zs, adj;
168 struct dd xy, r;
169 int oround;
170 int ex, ey, ez;
171 int spread;
172
173 /*
174 * Handle special cases. The order of operations and the particular
175 * return values here are crucial in handling special cases involving
176 * infinities, NaNs, overflows, and signed zeroes correctly.
177 */
178 if (x == 0.0 || y == 0.0)
179 return (x * y + z);
180 if (z == 0.0)
181 return (x * y);
182 if (!isfinite(x) || !isfinite(y))
183 return (x * y + z);
184 if (!isfinite(z))
185 return (z);
186
187 xs = frexpl(x, &ex);
188 ys = frexpl(y, &ey);
189 zs = frexpl(z, &ez);
190 oround = fegetround();
191 spread = ex + ey - ez;
192
193 /*
194 * If x * y and z are many orders of magnitude apart, the scaling
195 * will overflow, so we handle these cases specially. Rounding
196 * modes other than FE_TONEAREST are painful.
197 */
198 if (spread < -LDBL_MANT_DIG) {
199 feraiseexcept(FE_INEXACT);
200 if (!isnormal(z))
201 feraiseexcept(FE_UNDERFLOW);
202 switch (oround) {
203 case FE_TONEAREST:
204 return (z);
205 case FE_TOWARDZERO:
6ff43c94 206 if (x > 0.0 ^ y < 0.0 ^ z < 0.0)
1a3b704c
JM
207 return (z);
208 else
209 return (nextafterl(z, 0));
210 case FE_DOWNWARD:
6ff43c94 211 if (x > 0.0 ^ y < 0.0)
1a3b704c
JM
212 return (z);
213 else
214 return (nextafterl(z, -INFINITY));
215 default: /* FE_UPWARD */
6ff43c94 216 if (x > 0.0 ^ y < 0.0)
1a3b704c
JM
217 return (nextafterl(z, INFINITY));
218 else
219 return (z);
220 }
221 }
222 if (spread <= LDBL_MANT_DIG * 2)
223 zs = ldexpl(zs, -spread);
224 else
225 zs = copysignl(LDBL_MIN, zs);
226
227 fesetround(FE_TONEAREST);
6ff43c94
PA
228 /* work around clang bug 8100 */
229 volatile long double vxs = xs;
1a3b704c
JM
230
231 /*
232 * Basic approach for round-to-nearest:
233 *
234 * (xy.hi, xy.lo) = x * y (exact)
235 * (r.hi, r.lo) = xy.hi + z (exact)
236 * adj = xy.lo + r.lo (inexact; low bit is sticky)
237 * result = r.hi + adj (correctly rounded)
238 */
6ff43c94 239 xy = dd_mul(vxs, ys);
1a3b704c
JM
240 r = dd_add(xy.hi, zs);
241
242 spread = ex + ey;
243
244 if (r.hi == 0.0) {
245 /*
246 * When the addends cancel to 0, ensure that the result has
247 * the correct sign.
248 */
249 fesetround(oround);
250 volatile long double vzs = zs; /* XXX gcc CSE bug workaround */
251 return (xy.hi + vzs + ldexpl(xy.lo, spread));
252 }
253
254 if (oround != FE_TONEAREST) {
255 /*
256 * There is no need to worry about double rounding in directed
257 * rounding modes.
258 */
259 fesetround(oround);
6ff43c94
PA
260 /* work around clang bug 8100 */
261 volatile long double vrlo = r.lo;
262 adj = vrlo + xy.lo;
1a3b704c
JM
263 return (ldexpl(r.hi + adj, spread));
264 }
265
266 adj = add_adjusted(r.lo, xy.lo);
267 if (spread + ilogbl(r.hi) > -16383)
268 return (ldexpl(r.hi + adj, spread));
269 else
270 return (add_and_denormalize(r.hi, adj, spread));
271}