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
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
|
.file "sqrtf.s"
// Copyright (c) 2000 - 2003, Intel Corporation
// All rights reserved.
//
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
//*********************************************************************
// History:
//
// 02/02/00 Initial version
// 04/04/00 Unwind support added
// 08/15/00 Bundle added after call to __libm_error_support to properly
// set [the previously overwritten] GR_Parameter_RESULT.
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/10/03 Reordered header: .section, .global, .proc, .align
//
//*********************************************************************
//
// Function: Combined sqrtf(x), where
// _
// sqrtf(x) = |x, for single precision x values
//
//********************************************************************
//
// Accuracy: Correctly Rounded
//
//********************************************************************
//
// Resources Used:
//
// Floating-Point Registers: f8 (Input and Return Value)
// f7 -f14
//
// General Purpose Registers:
// r32-r36 (Locals)
// r37-r40 (Used to pass arguments to error handling routine)
//
// Predicate Registers: p6, p7, p8
//
//********************************************************************
//
// IEEE Special Conditions:
//
// All faults and exceptions should be raised correctly.
// sqrtf(QNaN) = QNaN
// sqrtf(SNaN) = QNaN
// sqrtf(+/-0) = +/-0
// sqrtf(negative) = QNaN and error handling is called
//
//********************************************************************
//
// Implementation:
//
// Modified Newton-Raphson Algorithm
//
//********************************************************************
GR_SAVE_B0 = r34
GR_SAVE_PFS = r33
GR_SAVE_GP = r35
GR_Parameter_X = r37
GR_Parameter_Y = r38
GR_Parameter_RESULT = r39
GR_Parameter_TAG = r40
FR_X = f13
FR_Y = f0
FR_RESULT = f8
.section .text
GLOBAL_IEEE754_ENTRY(sqrtf)
{ .mlx
// BEGIN SINGLE PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM
alloc r32= ar.pfs,0,5,4,0
// exponent of +1/2 in r2
movl r2 = 0x0fffe
} { .mfi
// +1/2 in f12
nop.m 0
frsqrta.s0 f7,p6=f8
nop.i 0;;
} { .mfi
setf.exp f12 = r2
// Step (1)
// y0 = 1/sqrt(a) in f7
fclass.m.unc p7,p8 = f8,0x3A
nop.i 0
} { .mfi
nop.m 0
// Make a copy of x just in case
mov f13 = f8
nop.i 0;;
} { .mfi
nop.m 0
// Step (2)
// H0 = 1/2 * y0 in f9
(p6) fma.s1 f9=f12,f7,f0
nop.i 0
} { .mfi
nop.m 0
// Step (3)
// S0 = a * y0 in f7
(p6) fma.s1 f7=f8,f7,f0
nop.i 0;;
} { .mfi
nop.m 0
// Step (4)
// d = 1/2 - S0 * H0 in f10
(p6) fnma.s1 f10=f7,f9,f12
nop.i 0
} { .mfi
nop.m 0
// Step (0'')
// 3/2 = 1 + 1/2 in f12
(p6) fma.s1 f12=f12,f1,f1
nop.i 0;;
} { .mfi
nop.m 0
// Step (5)
// e = 1 + 3/2 * d in f12
(p6) fma.s1 f12=f12,f10,f1
nop.i 0
} { .mfi
nop.m 0
// Step (6)
// T0 = d * S0 in f11
(p6) fma.s1 f11=f10,f7,f0
nop.i 0;;
} { .mfi
nop.m 0
// Step (7)
// G0 = d * H0 in f10
(p6) fma.s1 f10=f10,f9,f0
nop.i 0;;
} { .mfi
nop.m 0
// Step (8)
// S1 = S0 + e * T0 in f7
(p6) fma.s.s1 f7=f12,f11,f7
nop.i 0;;
} { .mfi
nop.m 0
// Step (9)
// H1 = H0 + e * G0 in f12
(p6) fma.s1 f12=f12,f10,f9
nop.i 0;;
} { .mfi
nop.m 0
// Step (10)
// d1 = a - S1 * S1 in f9
(p6) fnma.s1 f9=f7,f7,f8
nop.i 0;;
} { .mfb
nop.m 0
// Step (11)
// S = S1 + d1 * H1 in f7
(p6) fma.s.s0 f8=f9,f12,f7
(p6) br.ret.sptk b0 ;;
// END SINGLE PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM
} { .mfb
nop.m 0
mov f8 = f7
(p8) br.ret.sptk b0 ;;
}
//
// This branch includes all those special values that are not negative,
// with the result equal to frcpa(x)
//
GLOBAL_IEEE754_END(sqrtf)
libm_alias_float_other (__sqrt, sqrt)
LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mii
add GR_Parameter_Y=-32,sp // Parameter 2 value
mov GR_Parameter_TAG = 50
.save ar.pfs,GR_SAVE_PFS
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
}
{ .mfi
.fframe 64
add sp=-64,sp // Create new stack
nop.f 0
mov GR_SAVE_GP=gp // Save gp
};;
{ .mmi
stfs [GR_Parameter_Y] = FR_Y,16 // Store Parameter 2 on stack
add GR_Parameter_X = 16,sp // Parameter 1 address
.save b0, GR_SAVE_B0
mov GR_SAVE_B0=b0 // Save b0
};;
.body
{ .mib
stfs [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
add GR_Parameter_RESULT = 0,GR_Parameter_Y
nop.b 0 // Parameter 3 address
}
{ .mib
stfs [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
add GR_Parameter_Y = -16,GR_Parameter_Y
br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
nop.m 0
nop.m 0
add GR_Parameter_RESULT = 48,sp
};;
{ .mmi
ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
add sp = 64,sp // Restore stack pointer
mov b0 = GR_SAVE_B0 // Restore return address
};;
{ .mib
mov gp = GR_SAVE_GP // Restore gp
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
br.ret.sptk b0 // Return
};;
LOCAL_LIBM_END(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#
|
