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
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
|
/*========================== begin_copyright_notice ============================
Copyright (C) 2024 Intel Corporation
SPDX-License-Identifier: MIT
============================= end_copyright_notice ===========================*/
#include "../imf.h"
#pragma OPENCL FP_CONTRACT OFF
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_large_x = {0x49800000u};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_small_x = {0x39800000u};
// largest norm
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_largest_norm = {0x7f7fffffu};
// log(2)
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_ln2l = {0xb102e308u};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_ln2h = {0x3f317218u};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_c9 = {0xbd3bc2cau};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_c8 = {0x3dd8bd42u};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_c7 = {0xbe075e7fu};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_c6 = {0x3e1445e9u};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_c5 = {0xbe2a6712u};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_c4 = {0x3e4cb1a3u};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_c3 = {0xbe800059u};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_c2 = {0x3eaaaae2u};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_c1 = {0xbf000000u};
static __constant union {
unsigned int w;
float f;
int i;
} __sasinh_ha_c0 = {0x3f800000u};
static __constant float __sasinh_ha_fc0[] = {
0x1.fffffep-1, 0x1.dcd7b4p-25, // HI + LO: 0.99999994 + 5.5511784e-08
// [0x3f7fffff + 0x336e6bda]
};
static __constant float __sasinh_ha_fln2[] = {
0x1.62e42ep-1, 0x1.efa39ep-25, // HI + LO: 0.69314712 + 5.7699989e-08
// [0x3f317217 + 0x3377d1cf]
};
__attribute__((always_inline)) inline int
__ocl_svml_internal_sasinh_ha(float *a, float *r) {
int nRet = 0;
float x = *a;
float x2h, z2h, x2l, z2l, A, B, Bh, Sh, S0h, Sl, RS, E, Yhh;
float Bl, poly, R, Rl, R0, exponf;
union {
unsigned int w;
float f;
int i;
} Yh, Yl, res, xin, sgn, xa, two_expon;
int expon, e23, iexpon_corr;
x2h = __spirv_ocl_fma(x, x, 0.0f);
z2h = x2h + 1.0f;
A = __spirv_ocl_fmax(x2h, 1.0f);
B = __spirv_ocl_fmin(x2h, 1.0f);
x2l = __spirv_ocl_fma(x, x, (-x2h));
Bh = z2h - A;
Bl = B - Bh;
z2l = x2l + Bl;
RS = 1.0f / __spirv_ocl_sqrt(z2h);
S0h = __spirv_ocl_fma(z2h, RS, 0.0f);
// rsqrt(z2h)*0.5
RS *= 0.5f;
// (1+x^2) - Sh^2
E = __spirv_ocl_fma((-S0h), S0h, z2h);
E = E + z2l;
// sqrt(1+x^2)_low
Sl = __spirv_ocl_fma(E, RS, 0.0f);
Sh = S0h + Sl;
Yhh = Sh - S0h;
Sl = Sl - Yhh;
xa.f = __spirv_ocl_fabs(x);
// |x| + Sh + Sl
Yh.f = xa.f + Sh;
Yhh = Yh.f - Sh;
Yl.f = xa.f - Yhh;
Yl.f = Yl.f + Sl;
// set Yh, Yl for large |x|
// will use exponent correction in log computation, for large x
Yh.f = (xa.f < __sasinh_ha_large_x.f) ? Yh.f : xa.f * 0.5f;
Yl.f = (xa.f < __sasinh_ha_large_x.f) ? Yl.f : 0;
// fixup needed for x near largest normal
iexpon_corr = (xa.f < __sasinh_ha_large_x.f) ? 0 : 2;
// expon(Yh) + 2
expon = ((Yh.w + 0x00400000) >> 23) - 0x7f;
// new expon
e23 = expon << 23;
// 2^(-expon)
two_expon.w = 0x3f800000 - e23;
// Yl * 2^(-expon)
Yl.f *= two_expon.f;
// Yh * 2^(-expon-2)
Yh.w -= e23;
// reduced argument
R0 = Yh.f - 1.0f;
R = Yl.f + R0;
// add exponent correction
expon += iexpon_corr;
// log() polynomial
poly = __spirv_ocl_fma(__sasinh_ha_c9.f, R,
__sasinh_ha_c8.f);
poly = __spirv_ocl_fma(poly, R, __sasinh_ha_c7.f);
poly = __spirv_ocl_fma(poly, R, __sasinh_ha_c6.f);
poly = __spirv_ocl_fma(poly, R, __sasinh_ha_c5.f);
poly = __spirv_ocl_fma(poly, R, __sasinh_ha_c4.f);
poly = __spirv_ocl_fma(poly, R, __sasinh_ha_c3.f);
poly = __spirv_ocl_fma(poly, R, __sasinh_ha_c2.f);
poly = __spirv_ocl_fma(poly, R, __sasinh_ha_c1.f);
float fR[2], fPoly[2], fExpon[2];
fR[0] = R0;
fR[1] = Yl.f;
fPoly[0] = poly;
fPoly[1] = 0.0f;
fExpon[0] = __sasinh_ha_fln2[0];
fExpon[1] = __sasinh_ha_fln2[1];
{
float __ph, __phl;
__ph = __spirv_ocl_fma(fPoly[0], fR[0], 0.0f);
__phl = __spirv_ocl_fma(fPoly[0], fR[0], -__ph);
fPoly[1] = __spirv_ocl_fma(fPoly[1], fR[0], __phl);
fPoly[1] =
__spirv_ocl_fma(fPoly[0], fR[1], fPoly[1]);
fPoly[0] = __ph;
};
{
float __ph, __ahl, __ahh;
__ph = __spirv_ocl_fma(fPoly[0], 1.0f,
__sasinh_ha_fc0[0]);
__ahh =
__spirv_ocl_fma(__ph, 1.0f, -__sasinh_ha_fc0[0]);
__ahl = __spirv_ocl_fma(fPoly[0], 1.0f, -__ahh);
fPoly[1] = (fPoly[1] + __sasinh_ha_fc0[1]) + __ahl;
fPoly[0] = __ph;
};
;
{
float __ph, __phl;
__ph = __spirv_ocl_fma(fExpon[0], expon, 0.0f);
__phl = __spirv_ocl_fma(fExpon[0], expon, -__ph);
fExpon[1] = __spirv_ocl_fma(fExpon[1], expon, __phl);
fExpon[0] = __ph;
};
{
float __ph, __phl;
__ph = __spirv_ocl_fma(fPoly[0], fR[0], 0.0f);
__phl = __spirv_ocl_fma(fPoly[0], fR[0], -__ph);
fPoly[1] = __spirv_ocl_fma(fPoly[1], fR[0], __phl);
fPoly[1] =
__spirv_ocl_fma(fPoly[0], fR[1], fPoly[1]);
fPoly[0] = __ph;
};
{
float __ph, __ahl, __ahh;
__ph = __spirv_ocl_fma(fPoly[0], 1.0f, fExpon[0]);
__ahh = __spirv_ocl_fma(__ph, 1.0f, -fExpon[0]);
__ahl = __spirv_ocl_fma(fPoly[0], 1.0f, -__ahh);
fPoly[1] = (fPoly[1] + fExpon[1]) + __ahl;
fPoly[0] = __ph;
};
;
res.f = fPoly[0] + fPoly[1];
xin.f = x;
sgn.w = xin.w ^ xa.w;
res.w ^= sgn.w;
// fixup for small or Inf/NaN
res.f = ((xa.f < __sasinh_ha_small_x.f) | (xa.w > __sasinh_ha_largest_norm.w))
? (x + sgn.f)
: res.f;
*r = res.f;
return nRet;
}
float __ocl_svml_asinhf_ha(float x) {
float r;
__ocl_svml_internal_sasinh_ha(&x, &r);
return r;
}
|
