1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
|
/*
* Copyright 2023 Siemens
*
* The authors hereby grant permission to use, copy, modify, distribute,
* and license this software and its documentation for any purpose, provided
* that existing copyright notices are retained in all copies and that this
* notice is included verbatim in any distributions. No written agreement,
* license, or royalty fee is required for any of the authorized uses.
* Modifications to this software may be copyrighted by their authors
* and need not follow the licensing terms described here, provided that
* the new terms are clearly indicated on the first page of each file where
* they apply.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* Based on newlib/libm/math/kf_tan.c in Newlib. */
#include "amdgcnmach.h"
static const double
pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
T[] = {
3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
-1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
};
#if defined (__has_builtin) && __has_builtin (__builtin_gcn_fabsv)
static v64df
v64df_kernel_tan (v64df x, v64df y, v64si iy, v64di __mask)
{
FUNCTION_INIT (v64df);
v64si hx;
GET_HIGH_WORD(hx, x, NO_COND);
v64si ix = hx & 0x7fffffff; /* high word of |x| */
VECTOR_IF (ix < 0x3e300000, cond) /* x < 2**-28 */
VECTOR_IF2(__builtin_convertvector (x, v64si)==0, cond2, cond) /* generate inexact */
v64si low;
GET_LOW_WORD (low, x, cond2);
VECTOR_RETURN (1.0 / __builtin_gcn_fabsv (x), ((ix|low)|(iy+1))==0);
VECTOR_RETURN (x, cond2 & (iy == 1));
v64df z, w;
z = w = x + y;
SET_LOW_WORD (z, VECTOR_INIT (0.0), cond2);
v64df v = y - (z - x);
v64df t, a;
t = a = -1.0 / w;
SET_LOW_WORD(t, VECTOR_INIT (0.0), cond2);
v64df s = 1.0 + t * z;
VECTOR_RETURN ( t + a * (s + t * v), cond2);
VECTOR_ENDIF
VECTOR_ENDIF
VECTOR_IF(ix>=0x3FE59428, cond) /* |x|>=0.6744 */
VECTOR_COND_MOVE (x, -x, cond & (hx < 0));
VECTOR_COND_MOVE (y, -y, cond & (hx < 0));
v64df z = pio4-x;
v64df w = pio4lo-y;
VECTOR_COND_MOVE (x, z+w, cond);
VECTOR_COND_MOVE (y, VECTOR_INIT (0.0), cond);
VECTOR_ENDIF
v64df z = x*x;
v64df w = z*z;
/* Break x^5*(T[1]+x^2*T[2]+...) into
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
*/
v64df r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
v64df v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
v64df s = z*x;
r = y + z*(s*(r+v)+y);
r += T[0]*s;
w = x+r;
VECTOR_IF(ix>=0x3FE59428, cond)
v = __builtin_convertvector (iy, v64df);
VECTOR_RETURN (__builtin_convertvector (1-((hx>>30)&2), v64df)
* (v-2.0*(x-(w*w/(w+v)-r))), cond);
VECTOR_ENDIF
VECTOR_RETURN (w, iy == 1);
/* if allow error up to 2 ulp,
simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
z = w;
SET_LOW_WORD (z, VECTOR_INIT (0), NO_COND);
v = r - (z - x); /* z+v = r+x */
v64df a, t;
t = a = -1.0/w; /* a = -1.0/w */
SET_LOW_WORD(t, VECTOR_INIT (0), NO_COND);
s = 1.0+t*z;
VECTOR_RETURN (t+a*(s+t*v), NO_COND);
FUNCTION_RETURN;
}
static v64si
v64df_rem_pio2 (v64df x, v64df *y)
{
v64df r = x * __INV_PI_OVER_TWO_2_24;
v64si n = (__builtin_convertvector (r, v64si) + 0x800000) >> 24;
x = x - __builtin_convertvector (n, v64df) * __PI_OVER_TWO;
y[0] = x;
y[1] = x - y[0];
return n;
}
DEF_VD_MATH_FUNC (v64df, tan, v64df x)
{
FUNCTION_INIT (v64df);
v64si ix;
GET_HIGH_WORD (ix, x, NO_COND);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
VECTOR_RETURN (v64df_kernel_tan (x, VECTOR_INIT (0.0), VECTOR_INIT (1), __mask),
ix <= 0x3fe921fb);
/* tan(Inf or NaN) is NaN */
VECTOR_RETURN (x-x, ix >= 0x7ff00000); /* NaN */
/* argument reduction needed */
v64df y[2];
v64si n = v64df_rem_pio2 (x,y);
VECTOR_RETURN (v64df_kernel_tan (y[0], y[1], 1-((n&1)<<1), __mask), // 1 -- n even
NO_COND); // -1 -- n odd
FUNCTION_RETURN;
}
DEF_VARIANTS (tan, df, df)
#endif
|
