/[cmucl]/src/lisp/e_rem_pio2.c
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Contents of /src/lisp/e_rem_pio2.c

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Revision 1.2 - (show annotations)
Fri Apr 11 07:49:46 2008 UTC (6 years ago) by cshapiro
Branch: MAIN
CVS Tags: sparc-tramp-assem-base, post-merge-intl-branch, merged-unicode-utf16-extfmt-2009-06-11, unicode-utf16-extfmt-2009-03-27, snapshot-2008-08, snapshot-2008-09, sse2-packed-2008-11-12, snapshot-2008-05, snapshot-2008-06, snapshot-2008-07, intl-branch-working-2010-02-19-1000, unicode-string-buffer-impl-base, sse2-base, release-20b-pre1, release-20b-pre2, unicode-string-buffer-base, sse2-packed-base, sparc-tramp-assem-2010-07-19, amd64-dd-start, release-19f-pre1, snapshot-2008-12, snapshot-2008-11, intl-2-branch-base, GIT-CONVERSION, unicode-utf16-sync-2008-12, cross-sol-x86-merged, label-2009-03-16, release-19f-base, merge-sse2-packed, merge-with-19f, intl-branch-working-2010-02-11-1000, unicode-snapshot-2009-05, unicode-snapshot-2009-06, unicode-utf16-sync-2008-07, unicode-utf16-sync-2008-09, unicode-utf16-extfmts-sync-2008-12, RELEASE_20b, unicode-utf16-sync-label-2009-03-16, RELEASE_19f, release-20a-base, cross-sol-x86-base, unicode-utf16-char-support-2009-03-26, unicode-utf16-char-support-2009-03-25, unicode-utf16-extfmts-pre-sync-2008-11, snapshot-2008-10, snapshot-2010-12, snapshot-2010-11, unicode-utf16-sync-2008-11, snapshot-2011-09, snapshot-2011-06, snapshot-2011-07, snapshot-2011-04, snapshot-2011-02, snapshot-2011-03, snapshot-2011-01, pre-merge-intl-branch, snapshot-2010-05, snapshot-2010-04, snapshot-2010-07, snapshot-2010-06, snapshot-2010-01, snapshot-2010-03, snapshot-2010-02, snapshot-2010-08, label-2009-03-25, cross-sol-x86-2010-12-20, sse2-checkpoint-2008-10-01, intl-branch-2010-03-18-1300, sse2-merge-with-2008-11, sse2-merge-with-2008-10, RELEASE_20a, release-20a-pre1, snapshot-2009-11, snapshot-2009-12, unicode-utf16-extfmt-2009-06-11, portable-clx-import-2009-06-16, unicode-utf16-string-support, cross-sparc-branch-base, intl-branch-base, unicode-utf16-base, portable-clx-base, snapshot-2009-08, snapshot-2009-02, snapshot-2009-01, snapshot-2009-07, snapshot-2009-05, snapshot-2009-04, HEAD
Branch point for: RELEASE-19F-BRANCH, portable-clx-branch, cross-sparc-branch, RELEASE-20B-BRANCH, unicode-string-buffer-branch, sparc-tramp-assem-branch, sse2-packed-branch, RELEASE-20A-BRANCH, amd64-dd-branch, unicode-string-buffer-impl-branch, intl-branch, unicode-utf16-branch, cross-sol-x86-branch, sse2-branch, intl-2-branch, unicode-utf16-extfmt-branch
Changes since 1.1: +12 -23 lines
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Retrieve the constituent words of a double through a union instead of
casts and pointer arithmetic.  This code now compiles correctly on GCC
version 4 without disabling the default assumption of strict aliasing
rules.  Also, remove lots of dead code associated with parts of fdlibm
that have not been imported into the runtime.
1
2 /* @(#)e_rem_pio2.c 1.4 95/01/18 */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
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
10 * is preserved.
11 * ====================================================
12 *
13 */
14
15 /* __ieee754_rem_pio2(x,y)
16 *
17 * return the remainder of x rem pi/2 in y[0]+y[1]
18 * use __kernel_rem_pio2()
19 */
20
21 #include "fdlibm.h"
22
23 /*
24 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
25 */
26 static const int two_over_pi[] = {
27 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
28 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
29 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
30 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
31 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
32 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
33 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
34 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
35 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
36 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
37 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
38 };
39
40 static const int npio2_hw[] = {
41 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
42 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
43 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
44 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
45 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
46 0x404858EB, 0x404921FB,
47 };
48
49 /*
50 * invpio2: 53 bits of 2/pi
51 * pio2_1: first 33 bit of pi/2
52 * pio2_1t: pi/2 - pio2_1
53 * pio2_2: second 33 bit of pi/2
54 * pio2_2t: pi/2 - (pio2_1+pio2_2)
55 * pio2_3: third 33 bit of pi/2
56 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
57 */
58
59 static const double
60 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
61 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
62 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
63 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
64 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
65 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
66 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
67 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
68 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
69 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
70
71 int __ieee754_rem_pio2(double x, double *y)
72 {
73 double z,w,t,r,fn;
74 double tx[3];
75 int e0,i,j,nx,n,ix,hx;
76 union { int i[2]; double d; } ux,uy0,uz;
77
78 ux.d = x;
79 hx = ux.i[HIWORD]; /* high word of x */
80 ix = hx&0x7fffffff;
81 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
82 {y[0] = x; y[1] = 0; return 0;}
83 if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
84 if(hx>0) {
85 z = x - pio2_1;
86 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
87 y[0] = z - pio2_1t;
88 y[1] = (z-y[0])-pio2_1t;
89 } else { /* near pi/2, use 33+33+53 bit pi */
90 z -= pio2_2;
91 y[0] = z - pio2_2t;
92 y[1] = (z-y[0])-pio2_2t;
93 }
94 return 1;
95 } else { /* negative x */
96 z = x + pio2_1;
97 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
98 y[0] = z + pio2_1t;
99 y[1] = (z-y[0])+pio2_1t;
100 } else { /* near pi/2, use 33+33+53 bit pi */
101 z += pio2_2;
102 y[0] = z + pio2_2t;
103 y[1] = (z-y[0])+pio2_2t;
104 }
105 return -1;
106 }
107 }
108 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
109 t = fabs(x);
110 n = (int) (t*invpio2+half);
111 fn = (double)n;
112 r = t-fn*pio2_1;
113 w = fn*pio2_1t; /* 1st round good to 85 bit */
114 if(n<32&&ix!=npio2_hw[n-1]) {
115 y[0] = r-w; /* quick check no cancellation */
116 } else {
117 j = ix>>20;
118 y[0] = r-w;
119 uy0.d = y[0];
120 i = j-((uy0.i[HIWORD]>>20)&0x7ff);
121 if(i>16) { /* 2nd iteration needed, good to 118 */
122 t = r;
123 w = fn*pio2_2;
124 r = t-w;
125 w = fn*pio2_2t-((t-r)-w);
126 y[0] = r-w;
127 uy0.d = y[0];
128 i = j-((uy0.i[HIWORD]>>20)&0x7ff);
129 if(i>49) { /* 3rd iteration need, 151 bits acc */
130 t = r; /* will cover all possible cases */
131 w = fn*pio2_3;
132 r = t-w;
133 w = fn*pio2_3t-((t-r)-w);
134 y[0] = r-w;
135 }
136 }
137 }
138 y[1] = (r-y[0])-w;
139 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
140 else return n;
141 }
142 /*
143 * all other (large) arguments
144 */
145 if(ix>=0x7ff00000) { /* x is inf or NaN */
146 y[0]=y[1]=x-x; return 0;
147 }
148 /* set z = scalbn(|x|,ilogb(x)-23) */
149 ux.d = x;
150 uz.i[LOWORD] = ux.i[LOWORD];
151 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
152 uz.i[HIWORD] = ix - (e0<<20);
153 z = uz.d;
154 for(i=0;i<2;i++) {
155 tx[i] = (double)((int)(z));
156 z = (z-tx[i])*two24;
157 }
158 tx[2] = z;
159 nx = 3;
160 while(tx[nx-1]==zero) nx--; /* skip zero term */
161 n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
162 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
163 return n;
164 }

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