1 #ifdef NOT_NEEDED_ANYMORE
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
11 * ====================================================
14 /* __ieee754_rem_pio2(x,y)
16 * return the remainder of x rem pi/2 in y[0]+y[1]
17 * use __kernel_rem_pio2()
21 #include <math_private.h>
24 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
26 static const int32_t 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,
40 static const int32_t 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,
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)
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 */
72 __ieee754_rem_pio2 (double x
, double *y
)
74 double z
, w
, t
, r
, fn
;
76 int32_t e0
, i
, j
, nx
, n
, ix
, hx
;
79 GET_HIGH_WORD (hx
, x
); /* high word of x */
81 if (ix
<= 0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
83 y
[0] = x
; y
[1] = 0; return 0;
85 if (ix
< 0x4002d97c) /* |x| < 3pi/4, special case with n=+-1 */
90 if (ix
!= 0x3ff921fb) /* 33+53 bit pi is good enough */
93 y
[1] = (z
- y
[0]) - pio2_1t
;
95 else /* near pi/2, use 33+33+53 bit pi */
99 y
[1] = (z
- y
[0]) - pio2_2t
;
103 else /* negative x */
106 if (ix
!= 0x3ff921fb) /* 33+53 bit pi is good enough */
109 y
[1] = (z
- y
[0]) + pio2_1t
;
111 else /* near pi/2, use 33+33+53 bit pi */
115 y
[1] = (z
- y
[0]) + pio2_2t
;
120 if (ix
<= 0x413921fb) /* |x| ~<= 2^19*(pi/2), medium size */
123 n
= (int32_t) (t
* invpio2
+ half
);
126 w
= fn
* pio2_1t
; /* 1st round good to 85 bit */
127 if (n
< 32 && ix
!= npio2_hw
[n
- 1])
129 y
[0] = r
- w
; /* quick check no cancellation */
136 GET_HIGH_WORD (high
, y
[0]);
137 i
= j
- ((high
>> 20) & 0x7ff);
138 if (i
> 16) /* 2nd iteration needed, good to 118 */
143 w
= fn
* pio2_2t
- ((t
- r
) - w
);
145 GET_HIGH_WORD (high
, y
[0]);
146 i
= j
- ((high
>> 20) & 0x7ff);
147 if (i
> 49) /* 3rd iteration need, 151 bits acc */
149 t
= r
; /* will cover all possible cases */
152 w
= fn
* pio2_3t
- ((t
- r
) - w
);
157 y
[1] = (r
- y
[0]) - w
;
160 y
[0] = -y
[0]; y
[1] = -y
[1]; return -n
;
166 * all other (large) arguments
168 if (ix
>= 0x7ff00000) /* x is inf or NaN */
170 y
[0] = y
[1] = x
- x
; return 0;
172 /* set z = scalbn(|x|,ilogb(x)-23) */
173 GET_LOW_WORD (low
, x
);
174 SET_LOW_WORD (z
, low
);
175 e0
= (ix
>> 20) - 1046; /* e0 = ilogb(z)-23; */
176 SET_HIGH_WORD (z
, ix
- ((int32_t) (e0
<< 20)));
177 for (i
= 0; i
< 2; i
++)
179 tx
[i
] = (double) ((int32_t) (z
));
180 z
= (z
- tx
[i
]) * two24
;
184 while (tx
[nx
- 1] == zero
)
185 nx
--; /* skip zero term */
186 n
= __kernel_rem_pio2 (tx
, y
, e0
, nx
, 2, two_over_pi
);
189 y
[0] = -y
[0]; y
[1] = -y
[1]; return -n
;