| blob | 7cd3f7834c0f07e8f90c04e2b87f422fc73f8959 |
1 .file "log1pl.s"
3 // Copyright (C) 2000, 2001, Intel Corporation
4 // All rights reserved.
5 //
6 // Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
7 // and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
8 //
9 // Redistribution and use in source and binary forms, with or without
10 // modification, are permitted provided that the following conditions are
11 // met:
12 //
13 // * Redistributions of source code must retain the above copyright
14 // notice, this list of conditions and the following disclaimer.
15 //
16 // * Redistributions in binary form must reproduce the above copyright
17 // notice, this list of conditions and the following disclaimer in the
18 // documentation and/or other materials provided with the distribution.
19 //
20 // * The name of Intel Corporation may not be used to endorse or promote
21 // products derived from this software without specific prior written
22 // permission.
23 //
24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
25 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
28 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
29 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
30 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
31 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
32 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
33 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
34 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
35 //
36 // Intel Corporation is the author of this code, and requests that all
37 // problem reports or change requests be submitted to it directly at
38 // http://developer.intel.com/opensource.
39 //
40 // *********************************************************************
41 //
42 // History:
43 // 2/02/00 hand-optimized
44 // 4/04/00 Unwind support added
45 // 8/15/00 Bundle added after call to __libm_error_support to properly
46 // set [the previously overwritten] GR_Parameter_RESULT.
47 //
48 // *********************************************************************
49 //
50 // *********************************************************************
51 //
52 // Function: Combined logl(x), log1pl(x), and log10l(x) where
53 // logl(x) = ln(x), for double-extended precision x values
54 // log1pl(x) = ln(x+1), for double-extended precision x values
55 // log10l(x) = log (x), for double-extended precision x values
56 // 10
57 //
58 // *********************************************************************
59 //
60 // Resources Used:
61 //
62 // Floating-Point Registers: f8 (Input and Return Value)
63 // f9,f33-f55,f99
64 //
65 // General Purpose Registers:
66 // r32-r53
67 // r54-r57 (Used to pass arguments to error handling routine)
68 //
69 // Predicate Registers: p6-p15
70 //
71 // *********************************************************************
72 //
73 // IEEE Special Conditions:
74 //
75 // Denormal fault raised on denormal inputs
76 // Overflow exceptions cannot occur
77 // Underflow exceptions raised when appropriate for log1p
78 // (Error Handling Routine called for underflow)
79 // Inexact raised when appropriate by algorithm
80 //
81 // logl(inf) = inf
82 // logl(-inf) = QNaN
83 // logl(+/-0) = -inf
84 // logl(SNaN) = QNaN
85 // logl(QNaN) = QNaN
86 // logl(EM_special Values) = QNaN
87 // log1pl(inf) = inf
88 // log1pl(-inf) = QNaN
89 // log1pl(+/-0) = +/-0
90 // log1pl(-1) = -inf
91 // log1pl(SNaN) = QNaN
92 // log1pl(QNaN) = QNaN
93 // log1pl(EM_special Values) = QNaN
94 // log10l(inf) = inf
95 // log10l(-inf) = QNaN
96 // log10l(+/-0) = -inf
97 // log10l(SNaN) = QNaN
98 // log10l(QNaN) = QNaN
99 // log10l(EM_special Values) = QNaN
100 //
101 // *********************************************************************
102 //
103 // Computation is based on the following kernel.
104 //
105 // ker_log_64( in_FR : X,
106 // in_FR : E,
107 // in_FR : Em1,
108 // in_GR : Expo_Range,
109 // out_FR : Y_hi,
110 // out_FR : Y_lo,
111 // out_FR : Scale,
112 // out_PR : Safe )
113 //
114 // Overview
115 //
116 // The method consists of three cases.
117 //
118 // If |X+Em1| < 2^(-80) use case log1pl_small;
119 // elseif |X+Em1| < 2^(-7) use case log_near1;
120 // else use case log_regular;
121 //
122 // Case log1pl_small:
123 //
124 // logl( 1 + (X+Em1) ) can be approximated by (X+Em1).
125 //
126 // Case log_near1:
127 //
128 // logl( 1 + (X+Em1) ) can be approximated by a simple polynomial
129 // in W = X+Em1. This polynomial resembles the truncated Taylor
130 // series W - W^/2 + W^3/3 - ...
131 //
132 // Case log_regular:
133 //
134 // Here we use a table lookup method. The basic idea is that in
135 // order to compute logl(Arg) for an argument Arg in [1,2), we
136 // construct a value G such that G*Arg is close to 1 and that
137 // logl(1/G) is obtainable easily from a table of values calculated
138 // beforehand. Thus
139 //
140 // logl(Arg) = logl(1/G) + logl(G*Arg)
141 // = logl(1/G) + logl(1 + (G*Arg - 1))
142 //
143 // Because |G*Arg - 1| is small, the second term on the right hand
144 // side can be approximated by a short polynomial. We elaborate
145 // this method in four steps.
146 //
147 // Step 0: Initialization
148 //
149 // We need to calculate logl( E + X ). Obtain N, S_hi, S_lo such that
150 //
151 // E + X = 2^N * ( S_hi + S_lo ) exactly
152 //
153 // where S_hi in [1,2) and S_lo is a correction to S_hi in the sense
154 // that |S_lo| <= ulp(S_hi).
155 //
156 // Step 1: Argument Reduction
157 //
158 // Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate
159 //
160 // G := G_1 * G_2 * G_3
161 // r := (G * S_hi - 1) + G * S_lo
162 //
163 // These G_j's have the property that the product is exactly
164 // representable and that |r| < 2^(-12) as a result.
165 //
166 // Step 2: Approximation
167 //
168 //
169 // logl(1 + r) is approximated by a short polynomial poly(r).
170 //
171 // Step 3: Reconstruction
172 //
173 //
174 // Finally, logl( E + X ) is given by
175 //
176 // logl( E + X ) = logl( 2^N * (S_hi + S_lo) )
177 // ~=~ N*logl(2) + logl(1/G) + logl(1 + r)
178 // ~=~ N*logl(2) + logl(1/G) + poly(r).
179 //
180 // **** Algorithm ****
181 //
182 // Case log1pl_small:
183 //
184 // Although logl(1 + (X+Em1)) is basically X+Em1, we would like to
185 // preserve the inexactness nature as well as consistent behavior
186 // under different rounding modes. Note that this case can only be
187 // taken if E is set to be 1.0. In this case, Em1 is zero, and that
188 // X can be very tiny and thus the final result can possibly underflow.
189 // Thus, we compare X against a threshold that is dependent on the
190 // input Expo_Range. If |X| is smaller than this threshold, we set
191 // SAFE to be FALSE.
192 //
193 // The result is returned as Y_hi, Y_lo, and in the case of SAFE
194 // is FALSE, an additional value Scale is also returned.
195 //
196 // W := X + Em1
197 // Threshold := Threshold_Table( Expo_Range )
198 // Tiny := Tiny_Table( Expo_Range )
199 //
200 // If ( |W| > Threshold ) then
201 // Y_hi := W
202 // Y_lo := -W*W
203 // Else
204 // Y_hi := W
205 // Y_lo := -Tiny
206 // Scale := 2^(-100)
207 // Safe := FALSE
208 // EndIf
209 //
210 //
211 // One may think that Y_lo should be -W*W/2; however, it does not matter
212 // as Y_lo will be rounded off completely except for the correct effect in
213 // directed rounding. Clearly -W*W is simplier to compute. Moreover,
214 // because of the difference in exponent value, Y_hi + Y_lo or
215 // Y_hi + Scale*Y_lo is always inexact.
216 //
217 // Case log_near1:
218 //
219 // Here we compute a simple polynomial. To exploit parallelism, we split
220 // the polynomial into two portions.
221 //
222 // W := X + Em1
223 // Wsq := W * W
224 // W4 := Wsq*Wsq
225 // W6 := W4*Wsq
226 // Y_hi := W + Wsq*(P_1 + W*(P_2 + W*(P_3 + W*P_4))
227 // Y_lo := W6*(P_5 + W*(P_6 + W*(P_7 + W*P_8)))
228 // set lsb(Y_lo) to be 1
229 //
230 // Case log_regular:
231 //
232 // We present the algorithm in four steps.
233 //
234 // Step 0. Initialization
235 // ----------------------
236 //
237 // Z := X + E
238 // N := unbaised exponent of Z
239 // S_hi := 2^(-N) * Z
240 // S_lo := 2^(-N) * { (max(X,E)-Z) + min(X,E) }
241 //
242 // Note that S_lo is always 0 for the case E = 0.
243 //
244 // Step 1. Argument Reduction
245 // --------------------------
246 //
247 // Let
248 //
249 // Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63
250 //
251 // We obtain G_1, G_2, G_3 by the following steps.
252 //
253 //
254 // Define X_0 := 1.d_1 d_2 ... d_14. This is extracted
255 // from S_hi.
256 //
257 // Define A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated
258 // to lsb = 2^(-4).
259 //
260 // Define index_1 := [ d_1 d_2 d_3 d_4 ].
261 //
262 // Fetch Z_1 := (1/A_1) rounded UP in fixed point with
263 // fixed point lsb = 2^(-15).
264 // Z_1 looks like z_0.z_1 z_2 ... z_15
265 // Note that the fetching is done using index_1.
266 // A_1 is actually not needed in the implementation
267 // and is used here only to explain how is the value
268 // Z_1 defined.
269 //
270 // Fetch G_1 := (1/A_1) truncated to 21 sig. bits.
271 // floating pt. Again, fetching is done using index_1. A_1
272 // explains how G_1 is defined.
273 //
274 // Calculate X_1 := X_0 * Z_1 truncated to lsb = 2^(-14)
275 // = 1.0 0 0 0 d_5 ... d_14
276 // This is accomplised by integer multiplication.
277 // It is proved that X_1 indeed always begin
278 // with 1.0000 in fixed point.
279 //
280 //
281 // Define A_2 := 1.0 0 0 0 d_5 d_6 d_7 d_8. This is X_1
282 // truncated to lsb = 2^(-8). Similar to A_1,
283 // A_2 is not needed in actual implementation. It
284 // helps explain how some of the values are defined.
285 //
286 // Define index_2 := [ d_5 d_6 d_7 d_8 ].
287 //
288 // Fetch Z_2 := (1/A_2) rounded UP in fixed point with
289 // fixed point lsb = 2^(-15). Fetch done using index_2.
290 // Z_2 looks like z_0.z_1 z_2 ... z_15
291 //
292 // Fetch G_2 := (1/A_2) truncated to 21 sig. bits.
293 // floating pt.
294 //
295 // Calculate X_2 := X_1 * Z_2 truncated to lsb = 2^(-14)
296 // = 1.0 0 0 0 0 0 0 0 d_9 d_10 ... d_14
297 // This is accomplised by integer multiplication.
298 // It is proved that X_2 indeed always begin
299 // with 1.00000000 in fixed point.
300 //
301 //
302 // Define A_3 := 1.0 0 0 0 0 0 0 0 d_9 d_10 d_11 d_12 d_13 1.
303 // This is 2^(-14) + X_2 truncated to lsb = 2^(-13).
304 //
305 // Define index_3 := [ d_9 d_10 d_11 d_12 d_13 ].
306 //
307 // Fetch G_3 := (1/A_3) truncated to 21 sig. bits.
308 // floating pt. Fetch is done using index_3.
309 //
310 // Compute G := G_1 * G_2 * G_3.
311 //
312 // This is done exactly since each of G_j only has 21 sig. bits.
313 //
314 // Compute
315 //
316 // r := (G*S_hi - 1) + G*S_lo using 2 FMA operations.
317 //
318 // thus, r approximates G*(S_hi+S_lo) - 1 to within a couple of
319 // rounding errors.
320 //
321 //
322 // Step 2. Approximation
323 // ---------------------
324 //
325 // This step computes an approximation to logl( 1 + r ) where r is the
326 // reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13);
327 // thus logl(1+r) can be approximated by a short polynomial:
328 //
329 // logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5
330 //
331 //
332 // Step 3. Reconstruction
333 // ----------------------
334 //
335 // This step computes the desired result of logl(X+E):
336 //
337 // logl(X+E) = logl( 2^N * (S_hi + S_lo) )
338 // = N*logl(2) + logl( S_hi + S_lo )
339 // = N*logl(2) + logl(1/G) +
340 // logl(1 + C*(S_hi+S_lo) - 1 )
341 //
342 // logl(2), logl(1/G_j) are stored as pairs of (single,double) numbers:
343 // log2_hi, log2_lo, log1byGj_hi, log1byGj_lo. The high parts are
344 // single-precision numbers and the low parts are double precision
345 // numbers. These have the property that
346 //
347 // N*log2_hi + SUM ( log1byGj_hi )
348 //
349 // is computable exactly in double-extended precision (64 sig. bits).
350 // Finally
351 //
352 // Y_hi := N*log2_hi + SUM ( log1byGj_hi )
353 // Y_lo := poly_hi + [ poly_lo +
354 // ( SUM ( log1byGj_lo ) + N*log2_lo ) ]
355 // set lsb(Y_lo) to be 1
356 //
358 #include "libm_support.h"
360 #ifdef _LIBC
361 .rodata
362 #else
363 .data
364 #endif
366 // P_7, P_6, P_5, P_4, P_3, P_2, and P_1
368 .align 64
369 Constants_P:
370 ASM_TYPE_DIRECTIVE(Constants_P,@object)
371 data4 0xEFD62B15,0xE3936754,0x00003FFB,0x00000000
372 data4 0xA5E56381,0x8003B271,0x0000BFFC,0x00000000
373 data4 0x73282DB0,0x9249248C,0x00003FFC,0x00000000
374 data4 0x47305052,0xAAAAAA9F,0x0000BFFC,0x00000000
375 data4 0xCCD17FC9,0xCCCCCCCC,0x00003FFC,0x00000000
376 data4 0x00067ED5,0x80000000,0x0000BFFD,0x00000000
377 data4 0xAAAAAAAA,0xAAAAAAAA,0x00003FFD,0x00000000
378 data4 0xFFFFFFFE,0xFFFFFFFF,0x0000BFFD,0x00000000
379 ASM_SIZE_DIRECTIVE(Constants_P)
381 // log2_hi, log2_lo, Q_4, Q_3, Q_2, and Q_1
383 .align 64
384 Constants_Q:
385 ASM_TYPE_DIRECTIVE(Constants_Q,@object)
386 data4 0x00000000,0xB1721800,0x00003FFE,0x00000000
387 data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000
388 data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000
389 data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000
390 data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000
391 data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000
392 ASM_SIZE_DIRECTIVE(Constants_Q)
394 // Z1 - 16 bit fixed, G1 and H1 - IEEE single
396 .align 64
397 Constants_Z_G_H_h1:
398 ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h1,@object)
399 data4 0x00008000,0x3F800000,0x00000000,0x00000000,0x00000000,0x00000000
400 data4 0x00007879,0x3F70F0F0,0x3D785196,0x00000000,0x617D741C,0x3DA163A6
401 data4 0x000071C8,0x3F638E38,0x3DF13843,0x00000000,0xCBD3D5BB,0x3E2C55E6
402 data4 0x00006BCB,0x3F579430,0x3E2FF9A0,0x00000000,0xD86EA5E7,0xBE3EB0BF
403 data4 0x00006667,0x3F4CCCC8,0x3E647FD6,0x00000000,0x86B12760,0x3E2E6A8C
404 data4 0x00006187,0x3F430C30,0x3E8B3AE7,0x00000000,0x5C0739BA,0x3E47574C
405 data4 0x00005D18,0x3F3A2E88,0x3EA30C68,0x00000000,0x13E8AF2F,0x3E20E30F
406 data4 0x0000590C,0x3F321640,0x3EB9CEC8,0x00000000,0xF2C630BD,0xBE42885B
407 data4 0x00005556,0x3F2AAAA8,0x3ECF9927,0x00000000,0x97E577C6,0x3E497F34
408 data4 0x000051EC,0x3F23D708,0x3EE47FC5,0x00000000,0xA6B0A5AB,0x3E3E6A6E
409 data4 0x00004EC5,0x3F1D89D8,0x3EF8947D,0x00000000,0xD328D9BE,0xBDF43E3C
410 data4 0x00004BDB,0x3F17B420,0x3F05F3A1,0x00000000,0x0ADB090A,0x3E4094C3
411 data4 0x00004925,0x3F124920,0x3F0F4303,0x00000000,0xFC1FE510,0xBE28FBB2
412 data4 0x0000469F,0x3F0D3DC8,0x3F183EBF,0x00000000,0x10FDE3FA,0x3E3A7895
413 data4 0x00004445,0x3F088888,0x3F20EC80,0x00000000,0x7CC8C98F,0x3E508CE5
414 data4 0x00004211,0x3F042108,0x3F29516A,0x00000000,0xA223106C,0xBE534874
415 ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h1)
417 // Z2 - 16 bit fixed, G2 and H2 - IEEE single
419 .align 64
420 Constants_Z_G_H_h2:
421 ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h2,@object)
422 data4 0x00008000,0x3F800000,0x00000000,0x00000000,0x00000000,0x00000000
423 data4 0x00007F81,0x3F7F00F8,0x3B7F875D,0x00000000,0x22C42273,0x3DB5A116
424 data4 0x00007F02,0x3F7E03F8,0x3BFF015B,0x00000000,0x21F86ED3,0x3DE620CF
425 data4 0x00007E85,0x3F7D08E0,0x3C3EE393,0x00000000,0x484F34ED,0xBDAFA07E
426 data4 0x00007E08,0x3F7C0FC0,0x3C7E0586,0x00000000,0x3860BCF6,0xBDFE07F0
427 data4 0x00007D8D,0x3F7B1880,0x3C9E75D2,0x00000000,0xA78093D6,0x3DEA370F
428 data4 0x00007D12,0x3F7A2328,0x3CBDC97A,0x00000000,0x72A753D0,0x3DFF5791
429 data4 0x00007C98,0x3F792FB0,0x3CDCFE47,0x00000000,0xA7EF896B,0x3DFEBE6C
430 data4 0x00007C20,0x3F783E08,0x3CFC15D0,0x00000000,0x409ECB43,0x3E0CF156
431 data4 0x00007BA8,0x3F774E38,0x3D0D874D,0x00000000,0xFFEF71DF,0xBE0B6F97
432 data4 0x00007B31,0x3F766038,0x3D1CF49B,0x00000000,0x5D59EEE8,0xBE080483
433 data4 0x00007ABB,0x3F757400,0x3D2C531D,0x00000000,0xA9192A74,0x3E1F91E9
434 data4 0x00007A45,0x3F748988,0x3D3BA322,0x00000000,0xBF72A8CD,0xBE139A06
435 data4 0x000079D1,0x3F73A0D0,0x3D4AE46F,0x00000000,0xF8FBA6CF,0x3E1D9202
436 data4 0x0000795D,0x3F72B9D0,0x3D5A1756,0x00000000,0xBA796223,0xBE1DCCC4
437 data4 0x000078EB,0x3F71D488,0x3D693B9D,0x00000000,0xB6B7C239,0xBE049391
438 ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h2)
440 // G3 and H3 - IEEE single and h3 -IEEE double
442 .align 64
443 Constants_Z_G_H_h3:
444 ASM_TYPE_DIRECTIVE(Constants_Z_G_H_h3,@object)
445 data4 0x3F7FFC00,0x38800100,0x562224CD,0x3D355595
446 data4 0x3F7FF400,0x39400480,0x06136FF6,0x3D8200A2
447 data4 0x3F7FEC00,0x39A00640,0xE8DE9AF0,0x3DA4D68D
448 data4 0x3F7FE400,0x39E00C41,0xB10238DC,0xBD8B4291
449 data4 0x3F7FDC00,0x3A100A21,0x3B1952CA,0xBD89CCB8
450 data4 0x3F7FD400,0x3A300F22,0x1DC46826,0xBDB10707
451 data4 0x3F7FCC08,0x3A4FF51C,0xF43307DB,0x3DB6FCB9
452 data4 0x3F7FC408,0x3A6FFC1D,0x62DC7872,0xBD9B7C47
453 data4 0x3F7FBC10,0x3A87F20B,0x3F89154A,0xBDC3725E
454 data4 0x3F7FB410,0x3A97F68B,0x62B9D392,0xBD93519D
455 data4 0x3F7FAC18,0x3AA7EB86,0x0F21BD9D,0x3DC18441
456 data4 0x3F7FA420,0x3AB7E101,0x2245E0A6,0xBDA64B95
457 data4 0x3F7F9C20,0x3AC7E701,0xAABB34B8,0x3DB4B0EC
458 data4 0x3F7F9428,0x3AD7DD7B,0x6DC40A7E,0x3D992337
459 data4 0x3F7F8C30,0x3AE7D474,0x4F2083D3,0x3DC6E17B
460 data4 0x3F7F8438,0x3AF7CBED,0x811D4394,0x3DAE314B
461 data4 0x3F7F7C40,0x3B03E1F3,0xB08F2DB1,0xBDD46F21
462 data4 0x3F7F7448,0x3B0BDE2F,0x6D34522B,0xBDDC30A4
463 data4 0x3F7F6C50,0x3B13DAAA,0xB1F473DB,0x3DCB0070
464 data4 0x3F7F6458,0x3B1BD766,0x6AD282FD,0xBDD65DDC
465 data4 0x3F7F5C68,0x3B23CC5C,0xF153761A,0xBDCDAB83
466 data4 0x3F7F5470,0x3B2BC997,0x341D0F8F,0xBDDADA40
467 data4 0x3F7F4C78,0x3B33C711,0xEBC394E8,0x3DCD1BD7
468 data4 0x3F7F4488,0x3B3BBCC6,0x52E3E695,0xBDC3532B
469 data4 0x3F7F3C90,0x3B43BAC0,0xE846B3DE,0xBDA3961E
470 data4 0x3F7F34A0,0x3B4BB0F4,0x785778D4,0xBDDADF06
471 data4 0x3F7F2CA8,0x3B53AF6D,0xE55CE212,0x3DCC3ED1
472 data4 0x3F7F24B8,0x3B5BA620,0x9E382C15,0xBDBA3103
473 data4 0x3F7F1CC8,0x3B639D12,0x5C5AF197,0x3D635A0B
474 data4 0x3F7F14D8,0x3B6B9444,0x71D34EFC,0xBDDCCB19
475 data4 0x3F7F0CE0,0x3B7393BC,0x52CD7ADA,0x3DC74502
476 data4 0x3F7F04F0,0x3B7B8B6D,0x7D7F2A42,0xBDB68F17
477 ASM_SIZE_DIRECTIVE(Constants_Z_G_H_h3)
479 //
480 // Exponent Thresholds and Tiny Thresholds
481 // for 8, 11, 15, and 17 bit exponents
482 //
483 // Expo_Range Value
484 //
485 // 0 (8 bits) 2^(-126)
486 // 1 (11 bits) 2^(-1022)
487 // 2 (15 bits) 2^(-16382)
488 // 3 (17 bits) 2^(-16382)
489 //
490 // Tiny_Table
491 // ----------
492 // Expo_Range Value
493 //
494 // 0 (8 bits) 2^(-16382)
495 // 1 (11 bits) 2^(-16382)
496 // 2 (15 bits) 2^(-16382)
497 // 3 (17 bits) 2^(-16382)
498 //
500 .align 64
501 Constants_Threshold:
502 ASM_TYPE_DIRECTIVE(Constants_Threshold,@object)
503 data4 0x00000000,0x80000000,0x00003F81,0x00000000
504 data4 0x00000000,0x80000000,0x00000001,0x00000000
505 data4 0x00000000,0x80000000,0x00003C01,0x00000000
506 data4 0x00000000,0x80000000,0x00000001,0x00000000
507 data4 0x00000000,0x80000000,0x00000001,0x00000000
508 data4 0x00000000,0x80000000,0x00000001,0x00000000
509 data4 0x00000000,0x80000000,0x00000001,0x00000000
510 data4 0x00000000,0x80000000,0x00000001,0x00000000
511 ASM_SIZE_DIRECTIVE(Constants_Threshold)
513 .align 64
514 Constants_1_by_LN10:
515 ASM_TYPE_DIRECTIVE(Constants_1_by_LN10,@object)
516 data4 0x37287195,0xDE5BD8A9,0x00003FFD,0x00000000
517 data4 0xACCF70C8,0xD56EAABE,0x00003FBB,0x00000000
518 ASM_SIZE_DIRECTIVE(Constants_1_by_LN10)
520 FR_Input_X = f8
521 FR_Neg_One = f9
522 FR_E = f33
523 FR_Em1 = f34
524 FR_Y_hi = f34
525 // Shared with Em1
526 FR_Y_lo = f35
527 FR_Scale = f36
528 FR_X_Prime = f37
529 FR_Z = f38
530 FR_S_hi = f38
531 // Shared with Z
532 FR_W = f39
533 FR_G = f40
534 FR_wsq = f40
535 // Shared with G
536 FR_H = f41
537 FR_w4 = f41
538 // Shared with H
539 FR_h = f42
540 FR_w6 = f42
541 // Shared with h
542 FR_G_tmp = f43
543 FR_poly_lo = f43
544 // Shared with G_tmp
545 FR_P8 = f43
546 // Shared with G_tmp
547 FR_H_tmp = f44
548 FR_poly_hi = f44
549 // Shared with H_tmp
550 FR_P7 = f44
551 // Shared with H_tmp
552 FR_h_tmp = f45
553 FR_rsq = f45
554 // Shared with h_tmp
555 FR_P6 = f45
556 // Shared with h_tmp
557 FR_abs_W = f46
558 FR_r = f46
559 // Shared with abs_W
560 FR_AA = f47
561 FR_log2_hi = f47
562 // Shared with AA
563 FR_BB = f48
564 FR_log2_lo = f48
565 // Shared with BB
566 FR_S_lo = f49
567 FR_two_negN = f50
568 FR_float_N = f51
569 FR_Q4 = f52
570 FR_dummy = f52
571 // Shared with Q4
572 FR_P4 = f52
573 // Shared with Q4
574 FR_Threshold = f52
575 // Shared with Q4
576 FR_Q3 = f53
577 FR_P3 = f53
578 // Shared with Q3
579 FR_Tiny = f53
580 // Shared with Q3
581 FR_Q2 = f54
582 FR_P2 = f54
583 // Shared with Q2
584 FR_1LN10_hi = f54
585 // Shared with Q2
586 FR_Q1 = f55
587 FR_P1 = f55
588 // Shared with Q1
589 FR_1LN10_lo = f55
590 // Shared with Q1
591 FR_P5 = f98
592 FR_SCALE = f98
593 FR_Output_X_tmp = f99
595 GR_Expo_Range = r32
596 GR_Table_Base = r34
597 GR_Table_Base1 = r35
598 GR_Table_ptr = r36
599 GR_Index2 = r37
600 GR_signif = r38
601 GR_X_0 = r39
602 GR_X_1 = r40
603 GR_X_2 = r41
604 GR_Z_1 = r42
605 GR_Z_2 = r43
606 GR_N = r44
607 GR_Bias = r45
608 GR_M = r46
609 GR_ScaleN = r47
610 GR_Index3 = r48
611 GR_Perturb = r49
612 GR_Table_Scale = r50
614 //
615 // Added for unwind support
616 //
618 GR_SAVE_PFS = r51
619 GR_SAVE_B0 = r52
620 GR_SAVE_GP = r53
621 GR_Parameter_X = r54
622 GR_Parameter_Y = r55
623 GR_Parameter_RESULT = r56
624 GR_Parameter_TAG = r57
626 FR_X = f8
627 FR_Y = f0
628 FR_RESULT = f99
630 .section .text
631 .proc logl#
632 .global logl#
633 .align 64
634 logl:
635 #ifdef _LIBC
636 .global __ieee754_logl
637 __ieee754_logl:
638 #endif
639 { .mfi
640 alloc r32 = ar.pfs,0,22,4,0
641 (p0) fnorm.s1 FR_X_Prime = FR_Input_X
642 (p0) cmp.eq.unc p7, p0 = r0, r0
643 }
644 { .mfi
645 (p0) cmp.ne.unc p14, p0 = r0, r0
646 (p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3
647 (p0) cmp.ne.unc p15, p0 = r0, r0 ;;
648 }
649 { .mfi
650 nop.m 0
651 (p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF
652 nop.i 0
653 }
654 { .mfi
655 nop.m 999
656 (p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, f0
657 nop.i 0
658 }
659 { .mfi
660 nop.m 999
661 (p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, f0
662 nop.i 0
663 }
664 { .mfi
665 nop.m 999
666 (p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f1
667 nop.i 999 ;;
668 }
669 { .mfi
670 nop.m 999
671 (p0) fsub.s1 FR_Em1 = f0,f1
672 nop.i 999
673 }
674 { .mfb
675 nop.m 999
676 (p0) fadd FR_E = f0,f0
677 //
678 // Create E = 0 and Em1 = -1
679 // Check for X == 1, meaning logl(1)
680 // Check for X < 0, meaning logl(negative)
681 // Check for X == 0, meaning logl(0)
682 // Identify NatVals, NaNs, Infs.
683 // Identify EM unsupporteds.
684 // Identify Negative values - us S1 so as
685 // not to raise denormal operand exception
686 // Set p15 to false for log
687 // Set p14 to false for log
688 // Set p7 true for log and log1p
689 //
690 (p0) br.cond.sptk L(LOGL_BEGIN) ;;
691 }
693 .endp logl
694 ASM_SIZE_DIRECTIVE(logl)
696 .section .text
697 .proc log10l#
698 .global log10l#
699 .align 64
700 log10l:
701 #ifdef _LIBC
702 .global __ieee754_log10l
703 __ieee754_log10l:
704 #endif
705 { .mfi
706 alloc r32 = ar.pfs,0,22,4,0
707 (p0) fadd FR_E = f0,f0
708 nop.i 0
709 }
710 { .mfi
711 nop.m 0
712 (p0) fsub.s1 FR_Em1 = f0,f1
713 nop.i 0
714 }
715 { .mfi
716 (p0) cmp.ne.unc p15, p0 = r0, r0
717 (p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f1
718 nop.i 0
719 }
720 { .mfi
721 (p0) cmp.eq.unc p14, p0 = r0, r0
722 (p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, f0
723 (p0) cmp.ne.unc p7, p0 = r0, r0 ;;
724 }
725 { .mfi
726 nop.m 999
727 (p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, f0
728 nop.i 999
729 }
730 { .mfi
731 nop.m 999
732 (p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF
733 nop.i 999 ;;
734 }
735 { .mfi
736 nop.m 999
737 (p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3
738 nop.i 999
739 }
740 { .mfb
741 nop.m 999
742 (p0) fnorm.s1 FR_X_Prime = FR_Input_X
743 //
744 // Create E = 0 and Em1 = -1
745 // Check for X == 1, meaning logl(1)
746 // Check for X < 0, meaning logl(negative)
747 // Check for X == 0, meaning logl(0)
748 // Identify NatVals, NaNs, Infs.
749 // Identify EM unsupporteds.
750 // Identify Negative values - us S1 so as
751 // Identify Negative values - us S1 so as
752 // not to raise denormal operand exception
753 // Set p15 to false for log10
754 // Set p14 to true for log10
755 // Set p7 to false for log10
756 //
757 (p0) br.cond.sptk L(LOGL_BEGIN) ;;
758 }
760 .endp log10l
761 ASM_SIZE_DIRECTIVE(log10l)
763 .section .text
764 .proc log1pl#
765 .global log1pl#
766 .align 64
767 log1pl:
768 #ifdef _LIBC
769 .global __log1pl
770 __log1pl:
771 #endif
772 { .mfi
773 alloc r32 = ar.pfs,0,22,4,0
774 (p0) fsub.s1 FR_Neg_One = f0,f1
775 (p0) cmp.eq.unc p7, p0 = r0, r0
776 }
777 { .mfi
778 (p0) cmp.ne.unc p14, p0 = r0, r0
779 (p0) fnorm.s1 FR_X_Prime = FR_Input_X
780 (p0) cmp.eq.unc p15, p0 = r0, r0 ;;
781 }
782 { .mfi
783 nop.m 0
784 (p0) fclass.m.unc p6, p0 = FR_Input_X, 0x1E3
785 nop.i 0
786 }
787 { .mfi
788 nop.m 999
789 (p0) fclass.nm.unc p10, p0 = FR_Input_X, 0x1FF
790 nop.i 0
791 }
792 { .mfi
793 nop.m 999
794 (p0) fcmp.eq.unc.s1 p9, p0 = FR_Input_X, f0
795 nop.i 0
796 }
797 { .mfi
798 nop.m 999
799 (p0) fadd FR_Em1 = f0,f0
800 nop.i 999 ;;
801 }
802 { .mfi
803 nop.m 999
804 (p0) fadd FR_E = f0,f1
805 nop.i 999 ;;
806 }
807 { .mfi
808 nop.m 999
809 (p0) fcmp.eq.unc.s1 p8, p0 = FR_Input_X, FR_Neg_One
810 nop.i 999
811 }
812 { .mfi
813 nop.m 999
814 (p0) fcmp.lt.unc.s1 p13, p0 = FR_Input_X, FR_Neg_One
815 nop.i 999
816 }
817 L(LOGL_BEGIN):
818 { .mfi
819 nop.m 999
820 (p0) fadd.s1 FR_Z = FR_X_Prime, FR_E
821 nop.i 999
822 }
823 { .mlx
824 nop.m 999
825 (p0) movl GR_Table_Scale = 0x0000000000000018 ;;
826 }
827 { .mmi
828 nop.m 999
829 nop.m 999
830 //
831 // Create E = 1 and Em1 = 0
832 // Check for X == 0, meaning logl(1+0)
833 // Check for X < -1, meaning logl(negative)
834 // Check for X == -1, meaning logl(0)
835 // Normalize x
836 // Identify NatVals, NaNs, Infs.
837 // Identify EM unsupporteds.
838 // Identify Negative values - us S1 so as
839 // not to raise denormal operand exception
840 // Set p15 to true for log1p
841 // Set p14 to false for log1p
842 // Set p7 true for log and log1p
843 //
844 (p0) addl GR_Table_Base = @ltoff(Constants_Z_G_H_h1#),gp
845 }
846 { .mfi
847 nop.m 999
848 (p0) fmax.s1 FR_AA = FR_X_Prime, FR_E
849 nop.i 999 ;;
850 }
851 { .mfi
852 ld8 GR_Table_Base = [GR_Table_Base]
853 (p0) fmin.s1 FR_BB = FR_X_Prime, FR_E
854 nop.i 999
855 }
856 { .mfb
857 nop.m 999
858 (p0) fadd.s1 FR_W = FR_X_Prime, FR_Em1
859 //
860 // Begin load of constants base
861 // FR_Z = Z = |x| + E
862 // FR_W = W = |x| + Em1
863 // AA = fmax(|x|,E)
864 // BB = fmin(|x|,E)
865 //
866 (p6) br.cond.spnt L(LOGL_64_special) ;;
867 }
868 { .mib
869 nop.m 999
870 nop.i 999
871 (p10) br.cond.spnt L(LOGL_64_unsupported) ;;
872 }
873 { .mib
874 nop.m 999
875 nop.i 999
876 (p13) br.cond.spnt L(LOGL_64_negative) ;;
877 }
878 { .mib
879 (p0) getf.sig GR_signif = FR_Z
880 nop.i 999
881 (p9) br.cond.spnt L(LOGL_64_one) ;;
882 }
883 { .mib
884 nop.m 999
885 nop.i 999
886 (p8) br.cond.spnt L(LOGL_64_zero) ;;
887 }
888 { .mfi
889 (p0) getf.exp GR_N = FR_Z
890 //
891 // Raise possible denormal operand exception
892 // Create Bias
893 //
894 // This function computes ln( x + e )
895 // Input FR 1: FR_X = FR_Input_X
896 // Input FR 2: FR_E = FR_E
897 // Input FR 3: FR_Em1 = FR_Em1
898 // Input GR 1: GR_Expo_Range = GR_Expo_Range = 1
899 // Output FR 4: FR_Y_hi
900 // Output FR 5: FR_Y_lo
901 // Output FR 6: FR_Scale
902 // Output PR 7: PR_Safe
903 //
904 (p0) fsub.s1 FR_S_lo = FR_AA, FR_Z
905 //
906 // signif = getf.sig(Z)
907 // abs_W = fabs(w)
908 //
909 (p0) extr.u GR_Table_ptr = GR_signif, 59, 4 ;;
910 }
911 { .mfi
912 nop.m 999
913 (p0) fmerge.se FR_S_hi = f1,FR_Z
914 (p0) extr.u GR_X_0 = GR_signif, 49, 15
915 }
916 { .mmi
917 nop.m 999
918 nop.m 999
919 (p0) addl GR_Table_Base1 = @ltoff(Constants_Z_G_H_h2#),gp ;;
920 }
921 { .mlx
922 ld8 GR_Table_Base1 = [GR_Table_Base1]
923 (p0) movl GR_Bias = 0x000000000000FFFF ;;
924 }
925 { .mfi
926 nop.m 999
927 (p0) fabs FR_abs_W = FR_W
928 (p0) pmpyshr2.u GR_Table_ptr = GR_Table_ptr,GR_Table_Scale,0
929 }
930 { .mfi
931 nop.m 999
932 //
933 // Branch out for special input values
934 //
935 (p0) fcmp.lt.unc.s0 p8, p0 = FR_Input_X, f0
936 nop.i 999 ;;
937 }
938 { .mfi
939 nop.m 999
940 //
941 // X_0 = extr.u(signif,49,15)
942 // Index1 = extr.u(signif,59,4)
943 //
944 (p0) fadd.s1 FR_S_lo = FR_S_lo, FR_BB
945 nop.i 999 ;;
946 }
947 { .mii
948 nop.m 999
949 nop.i 999 ;;
950 //
951 // Offset_to_Z1 = 24 * Index1
952 // For performance, don't use result
953 // for 3 or 4 cycles.
954 //
955 (p0) add GR_Table_ptr = GR_Table_ptr, GR_Table_Base ;;
956 }
957 //
958 // Add Base to Offset for Z1
959 // Create Bias
960 { .mmi
961 (p0) ld4 GR_Z_1 = [GR_Table_ptr],4 ;;
962 (p0) ldfs FR_G = [GR_Table_ptr],4
963 nop.i 999 ;;
964 }
965 { .mmi
966 (p0) ldfs FR_H = [GR_Table_ptr],8 ;;
967 (p0) ldfd FR_h = [GR_Table_ptr],0
968 (p0) pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15
969 }
970 //
971 // Load Z_1
972 // Get Base of Table2
973 //
974 { .mfi
975 (p0) getf.exp GR_M = FR_abs_W
976 nop.f 999
977 nop.i 999 ;;
978 }
979 { .mii
980 nop.m 999
981 nop.i 999 ;;
982 //
983 // M = getf.exp(abs_W)
984 // S_lo = AA - Z
985 // X_1 = pmpyshr2(X_0,Z_1,15)
986 //
987 (p0) sub GR_M = GR_M, GR_Bias ;;
988 }
989 //
990 // M = M - Bias
991 // Load G1
992 // N = getf.exp(Z)
993 //
994 { .mii
995 (p0) cmp.gt.unc p11, p0 = -80, GR_M
996 (p0) cmp.gt.unc p12, p0 = -7, GR_M ;;
997 (p0) extr.u GR_Index2 = GR_X_1, 6, 4 ;;
998 }
999 { .mib
1000 nop.m 999
1001 //
1002 // if -80 > M, set p11
1003 // Index2 = extr.u(X_1,6,4)
1004 // if -7 > M, set p12
1005 // Load H1
1006 //
1007 (p0) pmpyshr2.u GR_Index2 = GR_Index2,GR_Table_Scale,0
1008 (p11) br.cond.spnt L(log1pl_small) ;;
1009 }
1010 { .mib
1011 nop.m 999
1012 nop.i 999
1013 (p12) br.cond.spnt L(log1pl_near) ;;
1014 }
1015 { .mii
1016 (p0) sub GR_N = GR_N, GR_Bias
1017 //
1018 // poly_lo = r * poly_lo
1019 //
1020 (p0) add GR_Perturb = 0x1, r0 ;;
1021 (p0) sub GR_ScaleN = GR_Bias, GR_N
1022 }
1023 { .mii
1024 (p0) setf.sig FR_float_N = GR_N
1025 nop.i 999 ;;
1026 //
1027 // Prepare Index2 - pmpyshr2.u(X_1,Z_2,15)
1028 // Load h1
1029 // S_lo = S_lo + BB
1030 // Branch for -80 > M
1031 //
1032 (p0) add GR_Index2 = GR_Index2, GR_Table_Base1
1033 }
1034 { .mmi
1035 (p0) setf.exp FR_two_negN = GR_ScaleN
1036 nop.m 999
1037 (p0) addl GR_Table_Base = @ltoff(Constants_Z_G_H_h3#),gp ;;
1038 }
1039 //
1040 // Index2 points to Z2
1041 // Branch for -7 > M
1042 //
1043 { .mmb
1044 (p0) ld4 GR_Z_2 = [GR_Index2],4
1045 (p0) ld8 GR_Table_Base = [GR_Table_Base]
1046 nop.b 999 ;;
1047 }
1048 (p0) nop.i 999
1049 //
1050 // Load Z_2
1051 // N = N - Bias
1052 // Tablebase points to Table3
1053 //
1054 { .mmi
1055 (p0) ldfs FR_G_tmp = [GR_Index2],4 ;;
1056 //
1057 // Load G_2
1058 // pmpyshr2 X_2= (X_1,Z_2,15)
1059 // float_N = setf.sig(N)
1060 // ScaleN = Bias - N
1061 //
1062 (p0) ldfs FR_H_tmp = [GR_Index2],8
1063 nop.i 999 ;;
1064 }
1065 //
1066 // Load H_2
1067 // two_negN = setf.exp(scaleN)
1068 // G = G_1 * G_2
1069 //
1070 { .mfi
1071 (p0) ldfd FR_h_tmp = [GR_Index2],0
1072 nop.f 999
1073 (p0) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 ;;
1074 }
1075 { .mii
1076 nop.m 999
1077 (p0) extr.u GR_Index3 = GR_X_2, 1, 5 ;;
1078 //
1079 // Load h_2
1080 // H = H_1 + H_2
1081 // h = h_1 + h_2
1082 // Index3 = extr.u(X_2,1,5)
1083 //
1084 (p0) shladd GR_Index3 = GR_Index3,4,GR_Table_Base
1085 }
1086 { .mmi
1087 nop.m 999
1088 nop.m 999
1089 //
1090 // float_N = fcvt.xf(float_N)
1091 // load G3
1092 //
1093 (p0) addl GR_Table_Base = @ltoff(Constants_Q#),gp ;;
1094 }
1095 { .mmi
1096 nop.m 999
1097 ld8 GR_Table_Base = [GR_Table_Base]
1098 nop.i 999
1099 };;
1101 { .mfi
1102 (p0) ldfe FR_log2_hi = [GR_Table_Base],16
1103 (p0) fmpy.s1 FR_S_lo = FR_S_lo, FR_two_negN
1104 nop.i 999 ;;
1105 }
1106 { .mmf
1107 nop.m 999
1108 //
1109 // G = G3 * G
1110 // Load h3
1111 // Load log2_hi
1112 // H = H + H3
1113 //
1114 (p0) ldfe FR_log2_lo = [GR_Table_Base],16
1115 (p0) fmpy.s1 FR_G = FR_G, FR_G_tmp ;;
1116 }
1117 { .mmf
1118 (p0) ldfs FR_G_tmp = [GR_Index3],4
1119 //
1120 // h = h + h3
1121 // r = G * S_hi + 1
1122 // Load log2_lo
1123 //
1124 (p0) ldfe FR_Q4 = [GR_Table_Base],16
1125 (p0) fadd.s1 FR_h = FR_h, FR_h_tmp ;;
1126 }
1127 { .mfi
1128 (p0) ldfe FR_Q3 = [GR_Table_Base],16
1129 (p0) fadd.s1 FR_H = FR_H, FR_H_tmp
1130 nop.i 999 ;;
1131 }
1132 { .mmf
1133 (p0) ldfs FR_H_tmp = [GR_Index3],4
1134 (p0) ldfe FR_Q2 = [GR_Table_Base],16
1135 //
1136 // Comput Index for Table3
1137 // S_lo = S_lo * two_negN
1138 //
1139 (p0) fcvt.xf FR_float_N = FR_float_N ;;
1140 }
1141 //
1142 // If S_lo == 0, set p8 false
1143 // Load H3
1144 // Load ptr to table of polynomial coeff.
1145 //
1146 { .mmf
1147 (p0) ldfd FR_h_tmp = [GR_Index3],0
1148 (p0) ldfe FR_Q1 = [GR_Table_Base],0
1149 (p0) fcmp.eq.unc.s1 p0, p8 = FR_S_lo, f0 ;;
1150 }
1151 { .mfi
1152 nop.m 999
1153 (p0) fmpy.s1 FR_G = FR_G, FR_G_tmp
1154 nop.i 999 ;;
1155 }
1156 { .mfi
1157 nop.m 999
1158 (p0) fadd.s1 FR_H = FR_H, FR_H_tmp
1159 nop.i 999 ;;
1160 }
1161 { .mfi
1162 nop.m 999
1163 (p0) fms.s1 FR_r = FR_G, FR_S_hi, f1
1164 nop.i 999
1165 }
1166 { .mfi
1167 nop.m 999
1168 (p0) fadd.s1 FR_h = FR_h, FR_h_tmp
1169 nop.i 999 ;;
1170 }
1171 { .mfi
1172 nop.m 999
1173 (p0) fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H
1174 nop.i 999 ;;
1175 }
1176 { .mfi
1177 nop.m 999
1178 //
1179 // Load Q4
1180 // Load Q3
1181 // Load Q2
1182 // Load Q1
1183 //
1184 (p8) fma.s1 FR_r = FR_G, FR_S_lo, FR_r
1185 nop.i 999
1186 }
1187 { .mfi
1188 nop.m 999
1189 //
1190 // poly_lo = r * Q4 + Q3
1191 // rsq = r* r
1192 //
1193 (p0) fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h
1194 nop.i 999 ;;
1195 }
1196 { .mfi
1197 nop.m 999
1198 //
1199 // If (S_lo!=0) r = s_lo * G + r
1200 //
1201 (p0) fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3
1202 nop.i 999
1203 }
1204 //
1205 // Create a 0x00000....01
1206 // poly_lo = poly_lo * rsq + h
1207 //
1208 { .mfi
1209 (p0) setf.sig FR_dummy = GR_Perturb
1210 (p0) fmpy.s1 FR_rsq = FR_r, FR_r
1211 nop.i 999 ;;
1212 }
1213 { .mfi
1214 nop.m 999
1215 //
1216 // h = N * log2_lo + h
1217 // Y_hi = n * log2_hi + H
1218 //
1219 (p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2
1220 nop.i 999
1221 }
1222 { .mfi
1223 nop.m 999
1224 (p0) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r
1225 nop.i 999 ;;
1226 }
1227 { .mfi
1228 nop.m 999
1229 //
1230 // poly_lo = r * poly_o + Q2
1231 // poly_hi = Q1 * rsq + r
1232 //
1233 (p0) fmpy.s1 FR_poly_lo = FR_poly_lo, FR_r
1234 nop.i 999 ;;
1235 }
1236 { .mfi
1237 nop.m 999
1238 (p0) fma.s1 FR_poly_lo = FR_poly_lo, FR_rsq, FR_h
1239 nop.i 999 ;;
1240 }
1241 { .mfb
1242 nop.m 999
1243 (p0) fadd.s1 FR_Y_lo = FR_poly_hi, FR_poly_lo
1244 //
1245 // Create the FR for a binary "or"
1246 // Y_lo = poly_hi + poly_lo
1247 //
1248 // (p0) for FR_dummy = FR_Y_lo,FR_dummy ;;
1249 //
1250 // Turn the lsb of Y_lo ON
1251 //
1252 // (p0) fmerge.se FR_Y_lo = FR_Y_lo,FR_dummy ;;
1253 //
1254 // Merge the new lsb into Y_lo, for alone doesn't
1255 //
1256 (p0) br.cond.sptk LOGL_main ;;
1257 }
1258 L(log1pl_near):
1259 { .mmi
1260 nop.m 999
1261 nop.m 999
1262 // /*******************************************************/
1263 // /*********** Branch log1pl_near ************************/
1264 // /*******************************************************/
1265 (p0) addl GR_Table_Base = @ltoff(Constants_P#),gp ;;
1266 }
1267 { .mmi
1268 nop.m 999
1269 ld8 GR_Table_Base = [GR_Table_Base]
1270 nop.i 999
1271 };;
1272 //
1273 // Load base address of poly. coeff.
1274 //
1275 { .mmb
1276 (p0) add GR_Table_ptr = 0x40,GR_Table_Base
1277 //
1278 // Address tables with separate pointers
1279 //
1280 (p0) ldfe FR_P8 = [GR_Table_Base],16
1281 nop.b 999 ;;
1282 }
1283 { .mmb
1284 (p0) ldfe FR_P4 = [GR_Table_ptr],16
1285 //
1286 // Load P4
1287 // Load P8
1288 //
1289 (p0) ldfe FR_P7 = [GR_Table_Base],16
1290 nop.b 999 ;;
1291 }
1292 { .mmf
1293 (p0) ldfe FR_P3 = [GR_Table_ptr],16
1294 //
1295 // Load P3
1296 // Load P7
1297 //
1298 (p0) ldfe FR_P6 = [GR_Table_Base],16
1299 (p0) fmpy.s1 FR_wsq = FR_W, FR_W ;;
1300 }
1301 { .mfi
1302 (p0) ldfe FR_P2 = [GR_Table_ptr],16
1303 nop.f 999
1304 nop.i 999 ;;
1305 }
1306 { .mfi
1307 nop.m 999
1308 (p0) fma.s1 FR_Y_hi = FR_W, FR_P4, FR_P3
1309 nop.i 999
1310 }
1311 //
1312 // Load P2
1313 // Load P6
1314 // Wsq = w * w
1315 // Y_hi = p4 * w + p3
1316 //
1317 { .mfi
1318 (p0) ldfe FR_P5 = [GR_Table_Base],16
1319 (p0) fma.s1 FR_Y_lo = FR_W, FR_P8, FR_P7
1320 nop.i 999 ;;
1321 }
1322 { .mfi
1323 (p0) ldfe FR_P1 = [GR_Table_ptr],16
1324 //
1325 // Load P1
1326 // Load P5
1327 // Y_lo = p8 * w + P7
1328 //
1329 (p0) fmpy.s1 FR_w4 = FR_wsq, FR_wsq
1330 nop.i 999 ;;
1331 }
1332 { .mfi
1333 nop.m 999
1334 (p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P2
1335 nop.i 999
1336 }
1337 { .mfi
1338 nop.m 999
1339 (p0) fma.s1 FR_Y_lo = FR_W, FR_Y_lo, FR_P6
1340 (p0) add GR_Perturb = 0x1, r0 ;;
1341 }
1342 { .mfi
1343 nop.m 999
1344 //
1345 // w4 = w2 * w2
1346 // Y_hi = y_hi * w + p2
1347 // Y_lo = y_lo * w + p6
1348 // Create perturbation bit
1349 //
1350 (p0) fmpy.s1 FR_w6 = FR_w4, FR_wsq
1351 nop.i 999 ;;
1352 }
1353 { .mfi
1354 nop.m 999
1355 (p0) fma.s1 FR_Y_hi = FR_W, FR_Y_hi, FR_P1
1356 nop.i 999
1357 }
1358 //
1359 // Y_hi = y_hi * w + p1
1360 // w6 = w4 * w2
1361 //
1362 { .mfi
1363 (p0) setf.sig FR_Q4 = GR_Perturb
1364 (p0) fma.s1 FR_Y_lo = FR_W, FR_Y_lo, FR_P5
1365 nop.i 999 ;;
1366 }
1367 { .mfi
1368 nop.m 999
1369 (p0) fma.s1 FR_dummy = FR_wsq,FR_Y_hi, f0
1370 nop.i 999
1371 }
1372 { .mfi
1373 nop.m 999
1374 (p0) fma.s1 FR_Y_hi = FR_W,f1,f0
1375 nop.i 999
1376 };;
1377 { .mfb
1378 nop.m 999
1379 //
1380 // Y_hi = w
1381 // Y_lo = y_lo * w + p5
1382 //
1383 (p0) fma.s1 FR_Y_lo = FR_w6, FR_Y_lo,FR_dummy
1384 //
1385 // Y_lo = y_lo * w6 + y_high order part.
1386 //
1387 // performance
1388 //
1389 (p0) br.cond.sptk LOGL_main ;;
1390 }
1391 L(log1pl_small):
1392 { .mmi
1393 nop.m 999
1394 // /*******************************************************/
1395 // /*********** Branch log1pl_small ***********************/
1396 // /*******************************************************/
1397 (p0) addl GR_Table_Base = @ltoff(Constants_Threshold#),gp
1398 }
1399 { .mfi
1400 nop.m 999
1401 (p0) mov FR_Em1 = FR_W
1402 (p0) cmp.eq.unc p7, p0 = r0, r0 ;;
1403 }
1404 { .mlx
1405 ld8 GR_Table_Base = [GR_Table_Base]
1406 (p0) movl GR_Expo_Range = 0x0000000000000004 ;;
1407 }
1408 //
1409 // Set Safe to true
1410 // Set Expo_Range = 0 for single
1411 // Set Expo_Range = 2 for double
1412 // Set Expo_Range = 4 for double-extended
1413 //
1414 { .mmi
1415 (p0) shladd GR_Table_Base = GR_Expo_Range,4,GR_Table_Base ;;
1416 (p0) ldfe FR_Threshold = [GR_Table_Base],16
1417 nop.i 999
1418 }
1419 { .mlx
1420 nop.m 999
1421 (p0) movl GR_Bias = 0x000000000000FF9B ;;
1422 }
1423 { .mfi
1424 (p0) ldfe FR_Tiny = [GR_Table_Base],0
1425 nop.f 999
1426 nop.i 999 ;;
1427 }
1428 { .mfi
1429 nop.m 999
1430 (p0) fcmp.gt.unc.s1 p13, p12 = FR_abs_W, FR_Threshold
1431 nop.i 999 ;;
1432 }
1433 { .mfi
1434 nop.m 999
1435 (p13) fnmpy.s1 FR_Y_lo = FR_W, FR_W
1436 nop.i 999
1437 }
1438 { .mfi
1439 nop.m 999
1440 (p13) fadd FR_SCALE = f0, f1
1441 nop.i 999 ;;
1442 }
1443 { .mfi
1444 nop.m 999
1445 (p12) fsub.s1 FR_Y_lo = f0, FR_Tiny
1446 (p12) cmp.ne.unc p7, p0 = r0, r0
1447 }
1448 { .mfi
1449 (p12) setf.exp FR_SCALE = GR_Bias
1450 nop.f 999
1451 nop.i 999 ;;
1452 }
1453 { .mfb
1454 nop.m 999
1455 //
1456 // Set p7 to SAFE = FALSE
1457 // Set Scale = 2^-100
1458 //
1459 (p0) fma.s0 f8 = FR_Y_lo,FR_SCALE,FR_Y_hi
1460 (p0) br.ret.sptk b0 ;;
1461 }
1462 L(LOGL_64_one):
1463 { .mfb
1464 nop.m 999
1465 (p0) fmpy.s0 f8 = FR_Input_X, f0
1466 (p0) br.ret.sptk b0 ;;
1467 }
1468 //
1469 // Raise divide by zero for +/-0 input.
1470 //
1471 L(LOGL_64_zero):
1472 { .mfi
1473 (p0) mov GR_Parameter_TAG = 0
1474 //
1475 // If we have logl(1), log10l(1) or log1pl(0), return 0.
1476 //
1477 (p0) fsub.s0 FR_Output_X_tmp = f0, f1
1478 nop.i 999 ;;
1479 }
1480 { .mii
1481 (p14) mov GR_Parameter_TAG = 6
1482 nop.i 999 ;;
1483 (p15) mov GR_Parameter_TAG = 138 ;;
1484 }
1485 { .mfb
1486 nop.m 999
1487 (p0) frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0
1488 (p0) br.cond.sptk __libm_error_region ;;
1489 }
1490 { .mfb
1491 nop.m 999
1492 //
1493 // Report that logl(0) computed
1494 // { .mfb
1495 (p0) mov FR_Input_X = FR_Output_X_tmp
1496 (p0) br.ret.sptk b0 ;;
1497 }
1499 L(LOGL_64_special):
1500 { .mfi
1501 nop.m 999
1502 //
1503 // Return -Inf or value from handler.
1504 //
1505 (p0) fclass.m.unc p7, p0 = FR_Input_X, 0x1E1
1506 nop.i 999 ;;
1507 }
1508 { .mfb
1509 nop.m 999
1510 //
1511 // Check for Natval, QNan, SNaN, +Inf
1512 //
1513 (p7) fmpy.s0 f8 = FR_Input_X, f1
1514 //
1515 // For SNaN raise invalid and return QNaN.
1516 // For QNaN raise invalid and return QNaN.
1517 // For +Inf return +Inf.
1518 //
1519 (p7) br.ret.sptk b0 ;;
1520 }
1521 //
1522 // For -Inf raise invalid and return QNaN.
1523 //
1524 { .mii
1525 (p0) mov GR_Parameter_TAG = 1
1526 nop.i 999 ;;
1527 (p14) mov GR_Parameter_TAG = 7 ;;
1528 }
1529 { .mfi
1530 (p15) mov GR_Parameter_TAG = 139
1531 nop.f 999
1532 nop.i 999 ;;
1533 }
1534 { .mfb
1535 nop.m 999
1536 (p0) fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0
1537 (p0) br.cond.sptk __libm_error_region ;;
1538 }
1539 //
1540 // Report that logl(-Inf) computed
1541 // Report that log10l(-Inf) computed
1542 // Report that log1p(-Inf) computed
1543 //
1544 { .mfb
1545 nop.m 0
1546 (p0) mov FR_Input_X = FR_Output_X_tmp
1547 (p0) br.ret.sptk b0 ;;
1548 }
1549 L(LOGL_64_unsupported):
1550 { .mfb
1551 nop.m 999
1552 //
1553 // Return generated NaN or other value .
1554 //
1555 (p0) fmpy.s0 f8 = FR_Input_X, f0
1556 (p0) br.ret.sptk b0 ;;
1557 }
1558 L(LOGL_64_negative):
1559 { .mfi
1560 nop.m 999
1561 //
1562 // Deal with x < 0 in a special way
1563 //
1564 (p0) frcpa.s0 FR_Output_X_tmp, p8 = f0, f0
1565 //
1566 // Deal with x < 0 in a special way - raise
1567 // invalid and produce QNaN indefinite.
1568 //
1569 (p0) mov GR_Parameter_TAG = 1 ;;
1570 }
1571 { .mii
1572 (p14) mov GR_Parameter_TAG = 7
1573 nop.i 999 ;;
1574 (p15) mov GR_Parameter_TAG = 139
1575 }
1576 .endp log1pl
1577 ASM_SIZE_DIRECTIVE(log1pl)
1579 .proc __libm_error_region
1580 __libm_error_region:
1581 .prologue
1582 { .mfi
1583 add GR_Parameter_Y=-32,sp // Parameter 2 value
1584 nop.f 0
1585 .save ar.pfs,GR_SAVE_PFS
1586 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
1587 }
1588 { .mfi
1589 .fframe 64
1590 add sp=-64,sp // Create new stack
1591 nop.f 0
1592 mov GR_SAVE_GP=gp // Save gp
1593 };;
1594 { .mmi
1595 stfe [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack
1596 add GR_Parameter_X = 16,sp // Parameter 1 address
1597 .save b0, GR_SAVE_B0
1598 mov GR_SAVE_B0=b0 // Save b0
1599 };;
1600 .body
1601 { .mib
1602 stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
1603 add GR_Parameter_RESULT = 0,GR_Parameter_Y
1604 nop.b 0 // Parameter 3 address
1605 }
1606 { .mib
1607 stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
1608 add GR_Parameter_Y = -16,GR_Parameter_Y
1609 br.call.sptk b0=__libm_error_support# // Call error handling function
1610 };;
1611 { .mmi
1612 nop.m 0
1613 nop.m 0
1614 add GR_Parameter_RESULT = 48,sp
1615 };;
1616 { .mmi
1617 ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
1618 .restore sp
1619 add sp = 64,sp // Restore stack pointer
1620 mov b0 = GR_SAVE_B0 // Restore return address
1621 };;
1622 { .mib
1623 mov gp = GR_SAVE_GP // Restore gp
1624 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
1625 br.ret.sptk b0 // Return
1626 };;
1628 .endp __libm_error_region
1629 ASM_SIZE_DIRECTIVE(__libm_error_region)
1631 .proc LOGL_main
1632 LOGL_main:
1633 { .mfi
1634 nop.m 999
1635 //
1636 // kernel_log_64 computes ln(X + E)
1637 //
1638 (p7) fadd.s0 FR_Input_X = FR_Y_lo,FR_Y_hi
1639 nop.i 0
1640 }
1641 { .mmi
1642 nop.m 999
1643 nop.m 999
1644 (p14) addl GR_Table_Base = @ltoff(Constants_1_by_LN10#),gp ;;
1645 }
1646 { .mmi
1647 nop.m 999
1648 (p14) ld8 GR_Table_Base = [GR_Table_Base]
1649 nop.i 999
1650 };;
1652 { .mmi
1653 (p14) ldfe FR_1LN10_hi = [GR_Table_Base],16 ;;
1654 (p14) ldfe FR_1LN10_lo = [GR_Table_Base]
1655 nop.i 999 ;;
1656 }
1657 { .mfi
1658 nop.m 999
1659 (p14) fmpy.s1 FR_Output_X_tmp = FR_Y_lo,FR_1LN10_hi
1660 nop.i 999 ;;
1661 }
1662 { .mfi
1663 nop.m 999
1664 (p14) fma.s1 FR_Output_X_tmp = FR_Y_hi,FR_1LN10_lo,FR_Output_X_tmp
1665 nop.i 999 ;;
1666 }
1667 { .mfb
1668 nop.m 999
1669 (p14) fma.s0 FR_Input_X = FR_Y_hi,FR_1LN10_hi,FR_Output_X_tmp
1670 (p0) br.ret.sptk b0 ;;
1671 }
1672 .endp LOGL_main
1673 ASM_SIZE_DIRECTIVE(LOGL_main)
1675 .type __libm_error_support#,@function
1676 .global __libm_error_support#