Mercurial > sdl-ios-xcode

annotate src/libm/e_rem_pio2.c @ 5246:189b1bdb7baf

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Surfaces aren't in hardware memory anymore!
author Sam Lantinga <slouken@libsdl.org>
date Thu, 10 Feb 2011 05:10:05 -0800
parents dc1eb82ffdaa
children
rev   line source
2756
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
1 /* @(#)e_rem_pio2.c 5.1 93/09/24 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
2 /*
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
3 * ====================================================
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
5 *
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
7 * Permission to use, copy, modify, and distribute this
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
8 * software is freely granted, provided that this notice
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
9 * is preserved.
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
10 * ====================================================
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
11 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
12
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
13 #if defined(LIBM_SCCS) && !defined(lint)
3162
dc1eb82ffdaa Von: Thomas Zimmermann
Sam Lantinga <slouken@libsdl.org>
parents: 2756
diff changeset
14 static const char rcsid[] =
2756
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
15 "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
16 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
17
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
18 /* __ieee754_rem_pio2(x,y)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
19 *
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
20 * return the remainder of x rem pi/2 in y[0]+y[1]
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
21 * use __kernel_rem_pio2()
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
22 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
23
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
24 #include "math.h"
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
25 #include "math_private.h"
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
26
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
27 libm_hidden_proto(fabs)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
28
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
29 /*
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
30 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
31 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
32 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
33 static const int32_t two_over_pi[] = {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
34 #else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
35 static int32_t two_over_pi[] = {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
36 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
37 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
38 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
39 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
40 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
41 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
42 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
43 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
44 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
45 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
46 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
47 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
48 };
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
49
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
50 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
51 static const int32_t npio2_hw[] = {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
52 #else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
53 static int32_t npio2_hw[] = {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
54 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
55 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
56 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
57 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
58 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
59 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
60 0x404858EB, 0x404921FB,
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
61 };
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
62
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
63 /*
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
64 * invpio2: 53 bits of 2/pi
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
65 * pio2_1: first 33 bit of pi/2
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
66 * pio2_1t: pi/2 - pio2_1
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
67 * pio2_2: second 33 bit of pi/2
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
68 * pio2_2t: pi/2 - (pio2_1+pio2_2)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
69 * pio2_3: third 33 bit of pi/2
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
70 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
71 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
72
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
73 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
74 static const double
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
75 #else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
76 static double
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
77 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
78 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
79 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
80 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
81 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
82 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
83 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
84 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
85 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
86 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
87 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
88
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
89 #ifdef __STDC__
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
90 int32_t attribute_hidden
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
91 __ieee754_rem_pio2(double x, double *y)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
92 #else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
93 int32_t attribute_hidden
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
94 __ieee754_rem_pio2(x, y)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
95 double x, y[];
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
96 #endif
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
97 {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
98 double z = 0.0, w, t, r, fn;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
99 double tx[3];
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
100 int32_t e0, i, j, nx, n, ix, hx;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
101 u_int32_t low;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
102
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
103 GET_HIGH_WORD(hx, x); /* high word of x */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
104 ix = hx & 0x7fffffff;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
105 if (ix <= 0x3fe921fb) { /* |x| ~<= pi/4 , no need for reduction */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
106 y[0] = x;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
107 y[1] = 0;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
108 return 0;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
109 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
110 if (ix < 0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
111 if (hx > 0) {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
112 z = x - pio2_1;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
113 if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
114 y[0] = z - pio2_1t;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
115 y[1] = (z - y[0]) - pio2_1t;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
116 } else { /* near pi/2, use 33+33+53 bit pi */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
117 z -= pio2_2;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
118 y[0] = z - pio2_2t;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
119 y[1] = (z - y[0]) - pio2_2t;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
120 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
121 return 1;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
122 } else { /* negative x */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
123 z = x + pio2_1;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
124 if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
125 y[0] = z + pio2_1t;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
126 y[1] = (z - y[0]) + pio2_1t;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
127 } else { /* near pi/2, use 33+33+53 bit pi */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
128 z += pio2_2;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
129 y[0] = z + pio2_2t;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
130 y[1] = (z - y[0]) + pio2_2t;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
131 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
132 return -1;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
133 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
134 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
135 if (ix <= 0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
136 t = fabs(x);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
137 n = (int32_t) (t * invpio2 + half);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
138 fn = (double) n;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
139 r = t - fn * pio2_1;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
140 w = fn * pio2_1t; /* 1st round good to 85 bit */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
141 if (n < 32 && ix != npio2_hw[n - 1]) {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
142 y[0] = r - w; /* quick check no cancellation */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
143 } else {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
144 u_int32_t high;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
145 j = ix >> 20;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
146 y[0] = r - w;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
147 GET_HIGH_WORD(high, y[0]);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
148 i = j - ((high >> 20) & 0x7ff);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
149 if (i > 16) { /* 2nd iteration needed, good to 118 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
150 t = r;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
151 w = fn * pio2_2;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
152 r = t - w;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
153 w = fn * pio2_2t - ((t - r) - w);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
154 y[0] = r - w;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
155 GET_HIGH_WORD(high, y[0]);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
156 i = j - ((high >> 20) & 0x7ff);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
157 if (i > 49) { /* 3rd iteration need, 151 bits acc */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
158 t = r; /* will cover all possible cases */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
159 w = fn * pio2_3;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
160 r = t - w;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
161 w = fn * pio2_3t - ((t - r) - w);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
162 y[0] = r - w;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
163 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
164 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
165 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
166 y[1] = (r - y[0]) - w;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
167 if (hx < 0) {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
168 y[0] = -y[0];
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
169 y[1] = -y[1];
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
170 return -n;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
171 } else
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
172 return n;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
173 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
174 /*
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
175 * all other (large) arguments
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
176 */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
177 if (ix >= 0x7ff00000) { /* x is inf or NaN */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
178 y[0] = y[1] = x - x;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
179 return 0;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
180 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
181 /* set z = scalbn(|x|,ilogb(x)-23) */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
182 GET_LOW_WORD(low, x);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
183 SET_LOW_WORD(z, low);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
184 e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
185 SET_HIGH_WORD(z, ix - ((int32_t) (e0 << 20)));
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
186 for (i = 0; i < 2; i++) {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
187 tx[i] = (double) ((int32_t) (z));
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
188 z = (z - tx[i]) * two24;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
189 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
190 tx[2] = z;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
191 nx = 3;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
192 while (tx[nx - 1] == zero)
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
193 nx--; /* skip zero term */
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
194 n = __kernel_rem_pio2(tx, y, e0, nx, 2, two_over_pi);
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
195 if (hx < 0) {
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
196 y[0] = -y[0];
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
197 y[1] = -y[1];
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
198 return -n;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
199 }
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
200 return n;
a98604b691c8 Expanded the libm support and put it into a separate directory.
Sam Lantinga <slouken@libsdl.org>
parents:
diff changeset
201 }