aboutsummaryrefslogtreecommitdiff
path: root/sysdeps/ia64/fpu/e_sqrtl.S
blob: 6aa402150f0aa74aa9040a767290953cd5cd9f71 (plain)
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
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
.file "sqrtl.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:
// 02/02/00 (hand-optimized)
// 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 sqrtl(x), where
//                         _
//             sqrtl(x) = |x, for double-extended precision x values
//
//********************************************************************
//
// 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.
//    sqrtl(QNaN) = QNaN
//    sqrtl(SNaN) = QNaN
//    sqrtl(+/-0) = +/-0
//    sqrtl(negative) = QNaN and error handling is called
//
//********************************************************************
//
// Implementation:
//
//  Modified Newton-Raphson Algorithm
//
//********************************************************************

GR_SAVE_PFS         = r33
GR_SAVE_B0          = r34
GR_SAVE_GP          = r35
GR_Parameter_X      = r37
GR_Parameter_Y      = r38
GR_Parameter_RESULT = r39
GR_Parameter_TAG    = r40

FR_X                = f15
FR_Y                = f0
FR_RESULT           = f8

.section .text
GLOBAL_IEEE754_ENTRY(sqrtl)
{ .mlx
alloc r32= ar.pfs,0,5,4,0
  // exponent of +1/2 in r2
  movl r2 = 0x0fffe;;
} { .mfi
  // +1/2 in f10
  setf.exp f12 = r2
  // Step (1)
  // y0 = 1/sqrt(a) in f7
  frsqrta.s0 f7,p6=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
  // Make copy input x
  mov f13=f8
  nop.i 0
} { .mfi
  nop.m 0
  fclass.m.unc p7,p8 = f8,0x3A
  nop.i 0;;
} { .mfi
  nop.m 0
  // Step (4)
  // d0 = 1/2 - S0 * H0 in f10
  (p6) fnma.s1 f10=f7,f9,f12
  nop.i 0;;
}
{ .mfi
  nop.m 0
       mov f15=f8
  nop.i 0;;
} { .mfi
  nop.m 0
  // Step (5)
  // H1 = H0 + d0 * H0 in f9
  (p6) fma.s1 f9=f10,f9,f9
  nop.i 0
} { .mfi
  nop.m 0
  // Step (6)
  // S1 = S0 + d0 * S0 in f7
  (p6) fma.s1 f7=f10,f7,f7
  nop.i 0;;
} { .mfi
  nop.m 0
  // Step (7)
  // d1 = 1/2 - S1 * H1 in f10
  (p6) fnma.s1 f10=f7,f9,f12
  nop.i 0;;
} { .mfi
  nop.m 0
  // Step (8)
  // H2 = H1 + d1 * H1 in f9
  (p6) fma.s1 f9=f10,f9,f9
  nop.i 0
} { .mfi
  nop.m 0
  // Step (9)
  // S2 = S1 + d1 * S1 in f7
  (p6) fma.s1 f7=f10,f7,f7
  nop.i 0;;
} { .mfi
  nop.m 0
  // Step (10)
  // d2 = 1/2 - S2 * H2 in f10
  (p6) fnma.s1 f10=f7,f9,f12
  nop.i 0
} { .mfi
  nop.m 0
  // Step (11)
  // e2 = a - S2 * S2 in f12
  (p6) fnma.s1 f12=f7,f7,f8
  nop.i 0;;
} { .mfi
  nop.m 0
  // Step (12)
  // S3 = S2 + d2 * S2 in f7
  (p6) fma.s1 f7=f12,f9,f7
  nop.i 0
} { .mfi
  nop.m 0
  // Step (13)
  // H3 = H2 + d2 * H2 in f9
  (p6) fma.s1 f9=f10,f9,f9
  nop.i 0;;
} { .mfi
  nop.m 0
  // Step (14)
  // e3 = a - S3 * S3 in f12
  (p6) fnma.s1 f12=f7,f7,f8
  nop.i 0;;
} { .mfb
  nop.m 0
  // Step (15)
  // S = S3 + e3 * H3 in f7
  (p6) fma.s0 f8=f12,f9,f7
  (p6) br.ret.sptk b0 ;;
}
{ .mfb
       mov GR_Parameter_TAG    = 48
       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)
//


// END DOUBLE EXTENDED PRECISION MINIMUM LATENCY SQUARE ROOT ALGORITHM
GLOBAL_IEEE754_END(sqrtl)

LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mfi
        add   GR_Parameter_Y=-32,sp             // Parameter 2 value
        nop.f 0
.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
        stfe [GR_Parameter_Y] = FR_Y,16         // Save 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
        stfe [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
        stfe [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
        ldfe  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#