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
|
.file "round.s"
// Copyright (c) 2000 - 2003, Intel Corporation
// All rights reserved.
//
// Contributed 2000 by the Intel Numerics Group, Intel Corporation
//
// 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
//==============================================================
// 10/25/00 Initial version
// 06/14/01 Changed cmp to an equivalent form
// 05/20/02 Cleaned up namespace and sf0 syntax
// 01/20/03 Improved performance and reduced code size
// 04/18/03 Eliminate possible WAW dependency warning
//==============================================================
// API
//==============================================================
// double round(double x)
//==============================================================
// general input registers:
// r14 - r19
rSignexp = r14
rExp = r15
rExpMask = r16
rBigexp = r17
rExpHalf = r18
rExpMHalf = r19
// floating-point registers:
// f8 - f13
fXtruncInt = f9
fNormX = f10
fHalf = f11
fMHalf = f12
fRem = f13
// predicate registers used:
// p6 - p10
// Overview of operation
//==============================================================
// double round(double x)
// Return an integer value (represented as a double) that is x
// rounded to nearest integer, halfway cases rounded away from
// zero.
// if x>0 result = trunc(x+0.5)
// if x<0 result = trunc(x-0.5)
//
//==============================================================
// double_extended
// if the exponent is > 1003e => 3F(true) = 63(decimal)
// we have a significand of 64 bits 1.63-bits.
// If we multiply by 2^63, we no longer have a fractional part
// So input is an integer value already.
// double
// if the exponent is >= 10033 => 34(true) = 52(decimal)
// 34 + 3ff = 433
// we have a significand of 53 bits 1.52-bits. (implicit 1)
// If we multiply by 2^52, we no longer have a fractional part
// So input is an integer value already.
// single
// if the exponent is > 10016 => 17(true) = 23(decimal)
// we have a significand of 24 bits 1.23-bits. (implicit 1)
// If we multiply by 2^23, we no longer have a fractional part
// So input is an integer value already.
.section .text
GLOBAL_LIBM_ENTRY(round)
{ .mfi
getf.exp rSignexp = f8 // Get signexp, recompute if unorm
fcvt.fx.trunc.s1 fXtruncInt = f8 // Convert to int in significand
addl rBigexp = 0x10033, r0 // Set exponent at which is integer
}
{ .mfi
mov rExpHalf = 0x0FFFE // Form sign and exponent of 0.5
fnorm.s1 fNormX = f8 // Normalize input
mov rExpMask = 0x1FFFF // Form exponent mask
}
;;
{ .mmf
setf.exp fHalf = rExpHalf // Form 0.5
mov rExpMHalf = 0x2FFFE // Form sign and exponent of -0.5
fclass.m p7,p0 = f8, 0x0b // Test x unorm
}
;;
{ .mfb
setf.exp fMHalf = rExpMHalf // Form -0.5
fclass.m p6,p0 = f8, 0x1e3 // Test x natval, nan, inf
(p7) br.cond.spnt ROUND_UNORM // Branch if x unorm
}
;;
ROUND_COMMON:
// Return here from ROUND_UNORM
{ .mfi
nop.m 0
fcmp.lt.s1 p8,p9 = f8, f0 // Test if x < 0
nop.i 0
}
{ .mfb
and rExp = rSignexp, rExpMask // Get biased exponent
(p6) fma.d.s0 f8 = f8, f1, f0 // Result if x natval, nan, inf
(p6) br.ret.spnt b0 // Exit if x natval, nan, inf
}
;;
{ .mfi
cmp.lt p6,p0 = rExp, rExpHalf // Is |x| < 0.5?
fcvt.xf f8 = fXtruncInt // Pre-Result if 0.5 <= |x| < 2^52
cmp.ge p7,p0 = rExp, rBigexp // Is |x| >= 2^52?
}
{ .mfi
cmp.lt p10,p0 = rExp, rExpHalf // Is |x| < 0.5?
nop.f 0
nop.i 0
}
;;
// We must correct result if |x| < 0.5, or |x| >= 2^52
.pred.rel "mutex",p6,p7
{ .mfi
nop.m 0
(p6) fmerge.s f8 = fNormX, f0 // If |x| < 0.5, result sgn(x)*0
nop.i 0
}
{ .mfb
(p7) cmp.eq p10,p0 = r0, r0 // Also turn on p10 if |x| >= 2^52
(p7) fma.d.s0 f8 = fNormX, f1, f0 // If |x| >= 2^52, result x
(p10) br.ret.spnt b0 // Exit |x| < 0.5 or |x| >= 2^52
}
;;
// Here if 0.5 <= |x| < 2^52
{ .mfi
nop.m 0
fms.s1 fRem = fNormX, f1, f8 // Get remainder = x - trunc(x)
nop.i 0
}
;;
{ .mfi
nop.m 0
(p8) fcmp.le.s1 p8,p0 = fRem, fMHalf
nop.i 0
}
{ .mfi
nop.m 0
(p9) fcmp.ge.s1 p9,p0 = fRem, fHalf
nop.i 0
}
;;
// If x < 0 and remainder <= -0.5, then subtract 1 from result
// If x > 0 and remainder >= +0.5, then add 1 to result
.pred.rel "mutex",p8,p9
{ .mfi
nop.m 0
(p8) fms.d.s0 f8 = f8, f1, f1
nop.i 0
}
{ .mfb
nop.m 0
(p9) fma.d.s0 f8 = f8, f1, f1
br.ret.sptk b0
}
;;
ROUND_UNORM:
// Here if x unorm
{ .mfb
getf.exp rSignexp = fNormX // Get signexp, recompute if unorm
fcmp.eq.s0 p7,p0 = f8, f0 // Dummy op to set denormal flag
br.cond.sptk ROUND_COMMON // Return to main path
}
;;
GLOBAL_LIBM_END(round)
|
