1.file "hypotl.s"
2
3
4// Copyright (c) 2000 - 2003, Intel Corporation
5// All rights reserved.
6//
7//
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9// modification, are permitted provided that the following conditions are
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13// notice, this list of conditions and the following disclaimer.
14//
15// * Redistributions in binary form must reproduce the above copyright
16// notice, this list of conditions and the following disclaimer in the
17// documentation and/or other materials provided with the distribution.
18//
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20// products derived from this software without specific prior written
21// permission.
22
23// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
24// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
25// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
26// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
27// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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32// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
33// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
34//
35// Intel Corporation is the author of this code, and requests that all
36// problem reports or change requests be submitted to it directly at
37// http://www.intel.com/software/products/opensource/libraries/num.htm.
38//
39//*********************************************************************
40//
41// History:
42// 02/02/00 hand-optimized
43// 04/04/00 Unwind support added
44// 06/20/00 new version
45// 08/15/00 Bundle added after call to __libm_error_support to properly
46//          set [the previously overwritten] GR_Parameter_RESULT.
47// 05/20/02 Cleaned up namespace and sf0 syntax
48// 02/10/03 Reordered header: .section, .global, .proc, .align
49//
50//*********************************************************************
51//                           ___________
52// Function:   hypotl(x,y) = |(x^2 + y^2) = for double extended values
53//             x and y
54//             Also provides cabsl functionality.
55//
56//*********************************************************************
57//
58// Resources Used:
59//
60//    Floating-Point Registers: f8  (Input and Return Value)
61//                              f9  (Input)
62//                              f6 -f15, f32-f34
63//
64//    General Purpose Registers:
65//      r2-r3   (Scratch)
66//      r32-r36 (Locals)
67//      r37-r40 (Used to pass arguments to error handling routine)
68//
69//    Predicate Registers:      p6 - p10
70//
71//*********************************************************************
72//
73// IEEE Special Conditions:
74//
75//    All faults and exceptions should be raised correctly.
76//    Overflow can occur.
77//    hypotl(Infinity and anything) = +Infinity
78//    hypotl(QNaN and anything) = QNaN
79//    hypotl(SNaN and anything ) = QNaN
80//
81//*********************************************************************
82//
83// Implementation:
84//  x2 = x * x   in double-extended
85//  y2 = y * y   in double-extended
86//  temp = x2 + y2   in double-extended
87//  sqrt(temp) rounded to double extended
88//
89//*********************************************************************
90
91GR_SAVE_PFS         = r33
92GR_SAVE_B0          = r34
93GR_SAVE_GP          = r35
94GR_Parameter_X      = r36
95GR_Parameter_Y      = r37
96GR_Parameter_RESULT = r38
97GR_Parameter_TAG    = r39
98
99FR_X                = f32
100FR_Y                = f33
101FR_RESULT           = f8
102
103.section .text
104
105LOCAL_LIBM_ENTRY(cabsl)
106LOCAL_LIBM_END(cabsl)
107
108GLOBAL_IEEE754_ENTRY(hypotl)
109{.mfi
110  alloc r32= ar.pfs,0,4,4,0
111  // Compute x*x
112  fma.s1 f10=f8,f8,f0
113  // r2=bias-1
114  mov r2=0xfffe
115}
116{.mfi
117  nop.m 0
118  // y*y
119  fma.s1 f11=f9,f9,f0
120  nop.i 0;;
121}
122
123{ .mfi
124     nop.m 0
125//   Check if x is an Inf - if so return Inf even
126//   if y is a NaN (C9X)
127     fclass.m.unc p7, p6 = f8, 0x023
128     nop.i 0
129}
130{.mfi
131	nop.m 0
132	// if possible overflow, copy f8 to f32
133	// set Denormal, if necessary
134	// (p8)
135	fma.s0 f32=f8,f1,f0
136    nop.i 0;;
137}
138{ .mfi
139     nop.m 0
140//   Check if y is an Inf - if so return Inf even
141//   if x is a NaN (C9X)
142     fclass.m.unc p8, p9 = f9, 0x023
143	 nop.i 0
144}
145{ .mfi
146     nop.m 999
147//   For x=inf, multiply y by 1 to raise invalid on y an SNaN
148//   (p7) fma.s0 f9=f9,f1,f0
149     // copy f9 to f33; set Denormal, if necessary
150	 fma.s0 f33=f9,f1,f0
151     nop.i 0;;
152}
153{.mfi
154  nop.m 0
155  // is y Zero ?
156  (p6) fclass.m p6,p0=f9,0x7
157  nop.i 0;;
158}
159
160{.mfi
161  // f7=0.5
162  setf.exp f7=r2
163  // a=x2+y2
164  fma.s1 f12=f10,f1,f11
165  nop.i 0
166}
167{.mfi
168  mov r2=0x408c  //0000
169  // dx=x*x-x2
170  fms.s1 f13=f8,f8,f10
171  nop.i 0;;
172}
173{.mfi
174  nop.m 0
175  // is x Zero ?
176  (p9) fclass.m p9,p0=f8,0x7
177  shl r2=r2,16
178}
179{.mfi
180  nop.m 0
181  // dy=y*y-y2
182  fms.s1 f14=f9,f9,f11
183  nop.i 0;;
184}
185
186{.mfi
187  nop.m 0
188  // x not NaN ?
189  (p6) fclass.m p7,p0=f8,0x3f
190  nop.i 0
191}
192{.mfi
193  nop.m 0
194  // f6=2
195  fma.s1 f6=f1,f1,f1
196  nop.i 0;;
197}
198
199{.mfi
200  nop.m 0
201  // f34=min(x2,y2)
202  famin.s1 f34=f10,f11
203  nop.i 0
204}
205{.mfb
206  nop.m 0
207  // f10=max(x2,y2)
208  famax.s1 f10=f11,f10
209  nop.b 0;; //
210}
211
212{.mfi
213  nop.m 0
214  // y not NaN ?
215  (p9) fclass.m p8,p0=f9,0x3f
216  nop.i 0;;
217}
218{.mfb
219  // f9=35/8
220  setf.s f9=r2
221  // if f8=Infinity or f9=Zero, return |f8|
222  (p7) fmerge.s f8=f0,f32
223  (p7) br.ret.spnt b0;;
224}
225
226
227{.mfi
228  nop.m 0
229  // z0=frsqrta(a)
230  frsqrta.s1 f8,p6=f12
231  nop.i 0;;
232}
233{ .mfi
234     nop.m 0
235//   Identify Natvals, Infs, NaNs, and Zeros
236//   and return result
237     fclass.m.unc p7, p0 = f12, 0x1E7
238     nop.i 0
239}
240{.mfi
241  // get exponent of x^2+y^2
242  getf.exp r3=f12
243  // dxy=dx+dy
244  fma.s1 f13=f13,f1,f14
245  nop.i 0;;
246}
247
248{.mfb
249  // 2*emax-2
250  mov r2=0x17ffb
251  // if f9=Infinity or f8=Zero, return |f9|
252  (p8) fmerge.s f8=f0,f33
253  (p8) br.ret.spnt b0
254}
255{.mfi
256  nop.m 0
257  // dd=a-max(x2,y2)
258  fnma.s1 f10=f10,f1,f12
259  nop.i 0;;
260}
261
262{.mfi
263  nop.m 0
264  // S0=a*z0
265  (p6) fma.s1 f14=f12,f8,f0
266  nop.i 0
267}
268{.mfi
269  nop.m 0
270  // H0=0.5*z0
271  (p6) fma.s1 f15=f8,f7,f0
272  nop.i 0;;
273}
274
275{.mfb
276  nop.m 0
277  // if special case, set f8
278  (p7) mov f8=f12
279  (p7) br.ret.spnt b0
280}
281{.mfi
282  nop.m 0
283  // da=min(x2,y2)-dd
284  fnma.s1 f10=f10,f1,f34
285  nop.i 0;;
286}
287{.mfi
288  nop.m 0
289  // f6=5/2
290  fma.s1 f6=f7,f1,f6
291  nop.i 0
292}
293{.mfi
294  nop.m 0
295  // f11=3/2
296  fma.s1 f11=f7,f1,f1
297  nop.i 0;;
298}
299
300{.mfi
301  nop.m 0
302  // d=0.5-S0*H0
303  (p6) fnma.s1 f7=f14,f15,f7
304  nop.i 0;;
305}
306
307{.mfi
308  nop.m 0
309  // P1=3/2*d+1
310  (p6) fma.s1 f11=f11,f7,f1
311  nop.i 0
312}
313{.mfi
314  nop.m 0
315  // P2=35/8*d+5/2
316  (p6) fma.s1 f9=f9,f7,f6
317  nop.i 0;;
318}
319{.mfi
320  nop.m 0
321  // d2=d*d
322  (p6) fma.s1 f34=f7,f7,f0
323  nop.i 0;;
324}
325
326{.mfi
327  nop.m 0
328  // T0=d*S0
329  (p6) fma.s1 f6=f7,f14,f0
330  nop.i 0
331}
332{.mfi
333  nop.m 0
334  // G0=d*H0
335  (p6) fma.s1 f7=f7,f15,f0
336  nop.i 0;;
337}
338{.mfi
339  nop.m 0
340  // P=d2*P2+P1
341  (p6) fma.s1 f11=f34,f9,f11
342  nop.i 0;;
343}
344
345{.mfi
346  nop.m 0
347  // S1=p*T0+S0
348  (p6) fma.s1 f14=f11,f6,f14
349  nop.i 0
350}
351{.mfi
352  nop.m 0
353  // H1=p*G0+H0
354  (p6) fma.s1 f15=f11,f7,f15
355  nop.i 0;;
356}
357
358
359{.mfi
360  nop.m 0
361  // e1=a-S1*S1
362  (p6) fnma.s1 f7=f14,f14,f12
363  nop.i 0
364}
365{.mfi
366  // Is x^2 + y^2 well less than the overflow
367  // threshold?
368  (p6) cmp.lt.unc p7, p8 =  r3,r2
369  // c=dxy+da
370  (p6) fma.s1 f13=f13,f1,f10
371  nop.i 0;;
372}
373
374{.mfi
375  nop.m 0
376  // e=e1+c
377  (p6) fma.s1 f13=f7,f1,f13
378  nop.i 0;;
379}
380
381{.mfb
382  nop.m 0
383  // S=e*H1+S1
384  fma.s0 f8=f13,f15,f14
385  // No overflow in this case
386  (p7) br.ret.sptk b0;;
387}
388
389{ .mfi
390     nop.m 0
391(p8) fsetc.s2 0x7F,0x42
392     // Possible overflow path, must detect by
393     // Setting widest range exponent with prevailing
394     // rounding mode.
395     nop.i 0 ;;
396}
397
398
399{ .mfi
400   // bias+0x4000 (bias+EMAX+1)
401   (p8) mov r2=0x13fff
402   // S=e*H1+S1
403   (p8) fma.s2 f12=f13,f15,f14
404   nop.i 0 ;;
405}
406{ .mfi
407(p8) setf.exp f11 = r2
408(p8) fsetc.s2 0x7F,0x40
409//   Restore Original Mode in S2
410     nop.i 0 ;;
411}
412{ .mfi
413     nop.m 0
414(p8) fcmp.lt.unc.s1 p9, p10 =  f12, f11
415     nop.i 0 ;;
416}
417{ .mib
418     nop.m 0
419     mov GR_Parameter_TAG = 45;
420	 // No overflow
421(p9) br.ret.sptk b0;;
422}
423GLOBAL_IEEE754_END(hypotl)
424libm_alias_ldouble_other (__hypot, hypot)
425
426LOCAL_LIBM_ENTRY(__libm_error_region)
427.prologue
428{ .mfi
429        add   GR_Parameter_Y=-32,sp             // Parameter 2 value
430        nop.f 0
431.save   ar.pfs,GR_SAVE_PFS
432        mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
433}
434{ .mfi
435.fframe 64
436        add sp=-64,sp                           // Create new stack
437        nop.f 0
438        mov GR_SAVE_GP=gp                       // Save gp
439};;
440{ .mmi
441        stfe [GR_Parameter_Y] = FR_Y,16         // Save Parameter 2 on stack
442        add GR_Parameter_X = 16,sp              // Parameter 1 address
443.save   b0, GR_SAVE_B0
444        mov GR_SAVE_B0=b0                       // Save b0
445};;
446.body
447{ .mib
448        stfe [GR_Parameter_X] = FR_X            // Store Parameter 1 on stack
449        add   GR_Parameter_RESULT = 0,GR_Parameter_Y
450        nop.b 0                                 // Parameter 3 address
451}
452{ .mib
453        stfe [GR_Parameter_Y] = FR_RESULT      // Store Parameter 3 on stack
454        add   GR_Parameter_Y = -16,GR_Parameter_Y
455        br.call.sptk b0=__libm_error_support#  // Call error handling function
456};;
457{ .mmi
458        nop.m 0
459        nop.m 0
460        add   GR_Parameter_RESULT = 48,sp
461};;
462{ .mmi
463        ldfe  f8 = [GR_Parameter_RESULT]       // Get return result off stack
464.restore sp
465        add   sp = 64,sp                       // Restore stack pointer
466        mov   b0 = GR_SAVE_B0                  // Restore return address
467};;
468{ .mib
469        mov   gp = GR_SAVE_GP                  // Restore gp
470        mov   ar.pfs = GR_SAVE_PFS             // Restore ar.pfs
471        br.ret.sptk     b0                     // Return
472};;
473LOCAL_LIBM_END(__libm_error_region#)
474.type   __libm_error_support#,@function
475.global __libm_error_support#
476