s_clogf.c revision 334654 
1/*-
2 * Copyright (c) 2013 Bruce D. Evans
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__FBSDID("$FreeBSD: stable/11/lib/msun/src/s_clogf.c 334654 2018-06-05 13:46:18Z kib $");
29
30#include <complex.h>
31#include <float.h>
32
33#include "fpmath.h"
34#include "math.h"
35#include "math_private.h"
36
37#define	MANT_DIG	FLT_MANT_DIG
38#define	MAX_EXP		FLT_MAX_EXP
39#define	MIN_EXP		FLT_MIN_EXP
40
41static const float
42ln2f_hi =  6.9314575195e-1,		/*  0xb17200.0p-24 */
43ln2f_lo =  1.4286067653e-6;		/*  0xbfbe8e.0p-43 */
44
45float complex
46clogf(float complex z)
47{
48	float_t ax, ax2h, ax2l, axh, axl, ay, ay2h, ay2l, ayh, ayl, sh, sl, t;
49	float x, y, v;
50	uint32_t hax, hay;
51	int kx, ky;
52
53	x = crealf(z);
54	y = cimagf(z);
55	v = atan2f(y, x);
56
57	ax = fabsf(x);
58	ay = fabsf(y);
59	if (ax < ay) {
60		t = ax;
61		ax = ay;
62		ay = t;
63	}
64
65	GET_FLOAT_WORD(hax, ax);
66	kx = (hax >> 23) - 127;
67	GET_FLOAT_WORD(hay, ay);
68	ky = (hay >> 23) - 127;
69
70	/* Handle NaNs and Infs using the general formula. */
71	if (kx == MAX_EXP || ky == MAX_EXP)
72		return (CMPLXF(logf(hypotf(x, y)), v));
73
74	/* Avoid spurious underflow, and reduce inaccuracies when ax is 1. */
75	if (hax == 0x3f800000) {
76		if (ky < (MIN_EXP - 1) / 2)
77			return (CMPLXF((ay / 2) * ay, v));
78		return (CMPLXF(log1pf(ay * ay) / 2, v));
79	}
80
81	/* Avoid underflow when ax is not small.  Also handle zero args. */
82	if (kx - ky > MANT_DIG || hay == 0)
83		return (CMPLXF(logf(ax), v));
84
85	/* Avoid overflow. */
86	if (kx >= MAX_EXP - 1)
87		return (CMPLXF(logf(hypotf(x * 0x1p-126F, y * 0x1p-126F)) +
88		    (MAX_EXP - 2) * ln2f_lo + (MAX_EXP - 2) * ln2f_hi, v));
89	if (kx >= (MAX_EXP - 1) / 2)
90		return (CMPLXF(logf(hypotf(x, y)), v));
91
92	/* Reduce inaccuracies and avoid underflow when ax is denormal. */
93	if (kx <= MIN_EXP - 2)
94		return (CMPLXF(logf(hypotf(x * 0x1p127F, y * 0x1p127F)) +
95		    (MIN_EXP - 2) * ln2f_lo + (MIN_EXP - 2) * ln2f_hi, v));
96
97	/* Avoid remaining underflows (when ax is small but not denormal). */
98	if (ky < (MIN_EXP - 1) / 2 + MANT_DIG)
99		return (CMPLXF(logf(hypotf(x, y)), v));
100
101	/* Calculate ax*ax and ay*ay exactly using Dekker's algorithm. */
102	t = (float)(ax * (0x1p12F + 1));
103	axh = (float)(ax - t) + t;
104	axl = ax - axh;
105	ax2h = ax * ax;
106	ax2l = axh * axh - ax2h + 2 * axh * axl + axl * axl;
107	t = (float)(ay * (0x1p12F + 1));
108	ayh = (float)(ay - t) + t;
109	ayl = ay - ayh;
110	ay2h = ay * ay;
111	ay2l = ayh * ayh - ay2h + 2 * ayh * ayl + ayl * ayl;
112
113	/*
114	 * When log(|z|) is far from 1, accuracy in calculating the sum
115	 * of the squares is not very important since log() reduces
116	 * inaccuracies.  We depended on this to use the general
117	 * formula when log(|z|) is very far from 1.  When log(|z|) is
118	 * moderately far from 1, we go through the extra-precision
119	 * calculations to reduce branches and gain a little accuracy.
120	 *
121	 * When |z| is near 1, we subtract 1 and use log1p() and don't
122	 * leave it to log() to subtract 1, since we gain at least 1 bit
123	 * of accuracy in this way.
124	 *
125	 * When |z| is very near 1, subtracting 1 can cancel almost
126	 * 3*MANT_DIG bits.  We arrange that subtracting 1 is exact in
127	 * doubled precision, and then do the rest of the calculation
128	 * in sloppy doubled precision.  Although large cancellations
129	 * often lose lots of accuracy, here the final result is exact
130	 * in doubled precision if the large calculation occurs (because
131	 * then it is exact in tripled precision and the cancellation
132	 * removes enough bits to fit in doubled precision).  Thus the
133	 * result is accurate in sloppy doubled precision, and the only
134	 * significant loss of accuracy is when it is summed and passed
135	 * to log1p().
136	 */
137	sh = ax2h;
138	sl = ay2h;
139	_2sumF(sh, sl);
140	if (sh < 0.5F || sh >= 3)
141		return (CMPLXF(logf(ay2l + ax2l + sl + sh) / 2, v));
142	sh -= 1;
143	_2sum(sh, sl);
144	_2sum(ax2l, ay2l);
145	/* Briggs-Kahan algorithm (except we discard the final low term): */
146	_2sum(sh, ax2l);
147	_2sum(sl, ay2l);
148	t = ax2l + sl;
149	_2sumF(sh, t);
150	return (CMPLXF(log1pf(ay2l + t + sh) / 2, v));
151}
152