1 /**************************************************************************
3 * Copyright 2009-2010 VMware, Inc.
6 * Permission is hereby granted, free of charge, to any person obtaining a
7 * copy of this software and associated documentation files (the
8 * "Software"), to deal in the Software without restriction, including
9 * without limitation the rights to use, copy, modify, merge, publish,
10 * distribute, sub license, and/or sell copies of the Software, and to
11 * permit persons to whom the Software is furnished to do so, subject to
12 * the following conditions:
14 * The above copyright notice and this permission notice (including the
15 * next paragraph) shall be included in all copies or substantial portions
18 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
19 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
20 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT.
21 * IN NO EVENT SHALL VMWARE AND/OR ITS SUPPLIERS BE LIABLE FOR
22 * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
23 * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
24 * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
26 **************************************************************************/
33 * LLVM IR doesn't support all basic arithmetic operations we care about (most
34 * notably min/max and saturated operations), and it is often necessary to
35 * resort machine-specific intrinsics directly. The functions here hide all
36 * these implementation details from the other modules.
38 * We also do simple expressions simplification here. Reasons are:
39 * - it is very easy given we have all necessary information readily available
40 * - LLVM optimization passes fail to simplify several vector expressions
41 * - We often know value constraints which the optimization passes have no way
42 * of knowing, such as when source arguments are known to be in [0, 1] range.
44 * @author Jose Fonseca <jfonseca@vmware.com>
50 #include "util/u_memory.h"
51 #include "util/u_debug.h"
52 #include "util/u_math.h"
53 #include "util/u_string.h"
54 #include "util/u_cpu_detect.h"
56 #include "lp_bld_type.h"
57 #include "lp_bld_const.h"
58 #include "lp_bld_init.h"
59 #include "lp_bld_intr.h"
60 #include "lp_bld_logic.h"
61 #include "lp_bld_pack.h"
62 #include "lp_bld_debug.h"
63 #include "lp_bld_bitarit.h"
64 #include "lp_bld_arit.h"
67 #define EXP_POLY_DEGREE 5
69 #define LOG_POLY_DEGREE 4
74 * No checks for special case values of a or b = 1 or 0 are done.
77 lp_build_min_simple(struct lp_build_context
*bld
,
81 const struct lp_type type
= bld
->type
;
82 const char *intrinsic
= NULL
;
83 unsigned intr_size
= 0;
86 assert(lp_check_value(type
, a
));
87 assert(lp_check_value(type
, b
));
89 /* TODO: optimize the constant case */
91 if (type
.floating
&& util_cpu_caps
.has_sse
) {
92 if (type
.width
== 32) {
93 if (type
.length
== 1) {
94 intrinsic
= "llvm.x86.sse.min.ss";
97 else if (type
.length
<= 4 || !util_cpu_caps
.has_avx
) {
98 intrinsic
= "llvm.x86.sse.min.ps";
102 intrinsic
= "llvm.x86.avx.min.ps.256";
106 if (type
.width
== 64 && util_cpu_caps
.has_sse2
) {
107 if (type
.length
== 1) {
108 intrinsic
= "llvm.x86.sse2.min.sd";
111 else if (type
.length
== 2 || !util_cpu_caps
.has_avx
) {
112 intrinsic
= "llvm.x86.sse2.min.pd";
116 intrinsic
= "llvm.x86.avx.min.pd.256";
121 else if (type
.floating
&& util_cpu_caps
.has_altivec
) {
122 if (type
.width
== 32 && type
.length
== 4) {
123 intrinsic
= "llvm.ppc.altivec.vminfp";
126 } else if (util_cpu_caps
.has_sse2
&& type
.length
>= 2) {
128 if ((type
.width
== 8 || type
.width
== 16) &&
129 (type
.width
* type
.length
<= 64) &&
130 (gallivm_debug
& GALLIVM_DEBUG_PERF
)) {
131 debug_printf("%s: inefficient code, bogus shuffle due to packing\n",
134 if (type
.width
== 8 && !type
.sign
) {
135 intrinsic
= "llvm.x86.sse2.pminu.b";
137 else if (type
.width
== 16 && type
.sign
) {
138 intrinsic
= "llvm.x86.sse2.pmins.w";
140 if (util_cpu_caps
.has_sse4_1
) {
141 if (type
.width
== 8 && type
.sign
) {
142 intrinsic
= "llvm.x86.sse41.pminsb";
144 if (type
.width
== 16 && !type
.sign
) {
145 intrinsic
= "llvm.x86.sse41.pminuw";
147 if (type
.width
== 32 && !type
.sign
) {
148 intrinsic
= "llvm.x86.sse41.pminud";
150 if (type
.width
== 32 && type
.sign
) {
151 intrinsic
= "llvm.x86.sse41.pminsd";
154 } else if (util_cpu_caps
.has_altivec
) {
156 if (type
.width
== 8) {
158 intrinsic
= "llvm.ppc.altivec.vminub";
160 intrinsic
= "llvm.ppc.altivec.vminsb";
162 } else if (type
.width
== 16) {
164 intrinsic
= "llvm.ppc.altivec.vminuh";
166 intrinsic
= "llvm.ppc.altivec.vminsh";
168 } else if (type
.width
== 32) {
170 intrinsic
= "llvm.ppc.altivec.vminuw";
172 intrinsic
= "llvm.ppc.altivec.vminsw";
178 return lp_build_intrinsic_binary_anylength(bld
->gallivm
, intrinsic
,
183 cond
= lp_build_cmp(bld
, PIPE_FUNC_LESS
, a
, b
);
184 return lp_build_select(bld
, cond
, a
, b
);
190 * No checks for special case values of a or b = 1 or 0 are done.
193 lp_build_max_simple(struct lp_build_context
*bld
,
197 const struct lp_type type
= bld
->type
;
198 const char *intrinsic
= NULL
;
199 unsigned intr_size
= 0;
202 assert(lp_check_value(type
, a
));
203 assert(lp_check_value(type
, b
));
205 /* TODO: optimize the constant case */
207 if (type
.floating
&& util_cpu_caps
.has_sse
) {
208 if (type
.width
== 32) {
209 if (type
.length
== 1) {
210 intrinsic
= "llvm.x86.sse.max.ss";
213 else if (type
.length
<= 4 || !util_cpu_caps
.has_avx
) {
214 intrinsic
= "llvm.x86.sse.max.ps";
218 intrinsic
= "llvm.x86.avx.max.ps.256";
222 if (type
.width
== 64 && util_cpu_caps
.has_sse2
) {
223 if (type
.length
== 1) {
224 intrinsic
= "llvm.x86.sse2.max.sd";
227 else if (type
.length
== 2 || !util_cpu_caps
.has_avx
) {
228 intrinsic
= "llvm.x86.sse2.max.pd";
232 intrinsic
= "llvm.x86.avx.max.pd.256";
237 else if (type
.floating
&& util_cpu_caps
.has_altivec
) {
238 if (type
.width
== 32 || type
.length
== 4) {
239 intrinsic
= "llvm.ppc.altivec.vmaxfp";
242 } else if (util_cpu_caps
.has_sse2
&& type
.length
>= 2) {
244 if ((type
.width
== 8 || type
.width
== 16) &&
245 (type
.width
* type
.length
<= 64) &&
246 (gallivm_debug
& GALLIVM_DEBUG_PERF
)) {
247 debug_printf("%s: inefficient code, bogus shuffle due to packing\n",
250 if (type
.width
== 8 && !type
.sign
) {
251 intrinsic
= "llvm.x86.sse2.pmaxu.b";
254 else if (type
.width
== 16 && type
.sign
) {
255 intrinsic
= "llvm.x86.sse2.pmaxs.w";
257 if (util_cpu_caps
.has_sse4_1
) {
258 if (type
.width
== 8 && type
.sign
) {
259 intrinsic
= "llvm.x86.sse41.pmaxsb";
261 if (type
.width
== 16 && !type
.sign
) {
262 intrinsic
= "llvm.x86.sse41.pmaxuw";
264 if (type
.width
== 32 && !type
.sign
) {
265 intrinsic
= "llvm.x86.sse41.pmaxud";
267 if (type
.width
== 32 && type
.sign
) {
268 intrinsic
= "llvm.x86.sse41.pmaxsd";
271 } else if (util_cpu_caps
.has_altivec
) {
273 if (type
.width
== 8) {
275 intrinsic
= "llvm.ppc.altivec.vmaxub";
277 intrinsic
= "llvm.ppc.altivec.vmaxsb";
279 } else if (type
.width
== 16) {
281 intrinsic
= "llvm.ppc.altivec.vmaxuh";
283 intrinsic
= "llvm.ppc.altivec.vmaxsh";
285 } else if (type
.width
== 32) {
287 intrinsic
= "llvm.ppc.altivec.vmaxuw";
289 intrinsic
= "llvm.ppc.altivec.vmaxsw";
295 return lp_build_intrinsic_binary_anylength(bld
->gallivm
, intrinsic
,
300 cond
= lp_build_cmp(bld
, PIPE_FUNC_GREATER
, a
, b
);
301 return lp_build_select(bld
, cond
, a
, b
);
306 * Generate 1 - a, or ~a depending on bld->type.
309 lp_build_comp(struct lp_build_context
*bld
,
312 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
313 const struct lp_type type
= bld
->type
;
315 assert(lp_check_value(type
, a
));
322 if(type
.norm
&& !type
.floating
&& !type
.fixed
&& !type
.sign
) {
323 if(LLVMIsConstant(a
))
324 return LLVMConstNot(a
);
326 return LLVMBuildNot(builder
, a
, "");
329 if(LLVMIsConstant(a
))
331 return LLVMConstFSub(bld
->one
, a
);
333 return LLVMConstSub(bld
->one
, a
);
336 return LLVMBuildFSub(builder
, bld
->one
, a
, "");
338 return LLVMBuildSub(builder
, bld
->one
, a
, "");
346 lp_build_add(struct lp_build_context
*bld
,
350 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
351 const struct lp_type type
= bld
->type
;
354 assert(lp_check_value(type
, a
));
355 assert(lp_check_value(type
, b
));
361 if(a
== bld
->undef
|| b
== bld
->undef
)
365 const char *intrinsic
= NULL
;
367 if(a
== bld
->one
|| b
== bld
->one
)
370 if (type
.width
* type
.length
== 128 &&
371 !type
.floating
&& !type
.fixed
) {
372 if(util_cpu_caps
.has_sse2
) {
374 intrinsic
= type
.sign
? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
376 intrinsic
= type
.sign
? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
377 } else if (util_cpu_caps
.has_altivec
) {
379 intrinsic
= type
.sign
? "llvm.ppc.altivec.vaddsbs" : "llvm.ppc.altivec.vaddubs";
381 intrinsic
= type
.sign
? "llvm.ppc.altivec.vaddsws" : "llvm.ppc.altivec.vadduws";
386 return lp_build_intrinsic_binary(builder
, intrinsic
, lp_build_vec_type(bld
->gallivm
, bld
->type
), a
, b
);
389 if(LLVMIsConstant(a
) && LLVMIsConstant(b
))
391 res
= LLVMConstFAdd(a
, b
);
393 res
= LLVMConstAdd(a
, b
);
396 res
= LLVMBuildFAdd(builder
, a
, b
, "");
398 res
= LLVMBuildAdd(builder
, a
, b
, "");
400 /* clamp to ceiling of 1.0 */
401 if(bld
->type
.norm
&& (bld
->type
.floating
|| bld
->type
.fixed
))
402 res
= lp_build_min_simple(bld
, res
, bld
->one
);
404 /* XXX clamp to floor of -1 or 0??? */
410 /** Return the scalar sum of the elements of a.
411 * Should avoid this operation whenever possible.
414 lp_build_horizontal_add(struct lp_build_context
*bld
,
417 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
418 const struct lp_type type
= bld
->type
;
419 LLVMValueRef index
, res
;
421 LLVMValueRef shuffles1
[LP_MAX_VECTOR_LENGTH
/ 2];
422 LLVMValueRef shuffles2
[LP_MAX_VECTOR_LENGTH
/ 2];
423 LLVMValueRef vecres
, elem2
;
425 assert(lp_check_value(type
, a
));
427 if (type
.length
== 1) {
431 assert(!bld
->type
.norm
);
434 * for byte vectors can do much better with psadbw.
435 * Using repeated shuffle/adds here. Note with multiple vectors
436 * this can be done more efficiently as outlined in the intel
437 * optimization manual.
438 * Note: could cause data rearrangement if used with smaller element
443 length
= type
.length
/ 2;
445 LLVMValueRef vec1
, vec2
;
446 for (i
= 0; i
< length
; i
++) {
447 shuffles1
[i
] = lp_build_const_int32(bld
->gallivm
, i
);
448 shuffles2
[i
] = lp_build_const_int32(bld
->gallivm
, i
+ length
);
450 vec1
= LLVMBuildShuffleVector(builder
, vecres
, vecres
,
451 LLVMConstVector(shuffles1
, length
), "");
452 vec2
= LLVMBuildShuffleVector(builder
, vecres
, vecres
,
453 LLVMConstVector(shuffles2
, length
), "");
455 vecres
= LLVMBuildFAdd(builder
, vec1
, vec2
, "");
458 vecres
= LLVMBuildAdd(builder
, vec1
, vec2
, "");
460 length
= length
>> 1;
463 /* always have vector of size 2 here */
466 index
= lp_build_const_int32(bld
->gallivm
, 0);
467 res
= LLVMBuildExtractElement(builder
, vecres
, index
, "");
468 index
= lp_build_const_int32(bld
->gallivm
, 1);
469 elem2
= LLVMBuildExtractElement(builder
, vecres
, index
, "");
472 res
= LLVMBuildFAdd(builder
, res
, elem2
, "");
474 res
= LLVMBuildAdd(builder
, res
, elem2
, "");
480 * Return the horizontal sums of 4 float vectors as a float4 vector.
481 * This uses the technique as outlined in Intel Optimization Manual.
484 lp_build_horizontal_add4x4f(struct lp_build_context
*bld
,
487 struct gallivm_state
*gallivm
= bld
->gallivm
;
488 LLVMBuilderRef builder
= gallivm
->builder
;
489 LLVMValueRef shuffles
[4];
491 LLVMValueRef sumtmp
[2], shuftmp
[2];
493 /* lower half of regs */
494 shuffles
[0] = lp_build_const_int32(gallivm
, 0);
495 shuffles
[1] = lp_build_const_int32(gallivm
, 1);
496 shuffles
[2] = lp_build_const_int32(gallivm
, 4);
497 shuffles
[3] = lp_build_const_int32(gallivm
, 5);
498 tmp
[0] = LLVMBuildShuffleVector(builder
, src
[0], src
[1],
499 LLVMConstVector(shuffles
, 4), "");
500 tmp
[2] = LLVMBuildShuffleVector(builder
, src
[2], src
[3],
501 LLVMConstVector(shuffles
, 4), "");
503 /* upper half of regs */
504 shuffles
[0] = lp_build_const_int32(gallivm
, 2);
505 shuffles
[1] = lp_build_const_int32(gallivm
, 3);
506 shuffles
[2] = lp_build_const_int32(gallivm
, 6);
507 shuffles
[3] = lp_build_const_int32(gallivm
, 7);
508 tmp
[1] = LLVMBuildShuffleVector(builder
, src
[0], src
[1],
509 LLVMConstVector(shuffles
, 4), "");
510 tmp
[3] = LLVMBuildShuffleVector(builder
, src
[2], src
[3],
511 LLVMConstVector(shuffles
, 4), "");
513 sumtmp
[0] = LLVMBuildFAdd(builder
, tmp
[0], tmp
[1], "");
514 sumtmp
[1] = LLVMBuildFAdd(builder
, tmp
[2], tmp
[3], "");
516 shuffles
[0] = lp_build_const_int32(gallivm
, 0);
517 shuffles
[1] = lp_build_const_int32(gallivm
, 2);
518 shuffles
[2] = lp_build_const_int32(gallivm
, 4);
519 shuffles
[3] = lp_build_const_int32(gallivm
, 6);
520 shuftmp
[0] = LLVMBuildShuffleVector(builder
, sumtmp
[0], sumtmp
[1],
521 LLVMConstVector(shuffles
, 4), "");
523 shuffles
[0] = lp_build_const_int32(gallivm
, 1);
524 shuffles
[1] = lp_build_const_int32(gallivm
, 3);
525 shuffles
[2] = lp_build_const_int32(gallivm
, 5);
526 shuffles
[3] = lp_build_const_int32(gallivm
, 7);
527 shuftmp
[1] = LLVMBuildShuffleVector(builder
, sumtmp
[0], sumtmp
[1],
528 LLVMConstVector(shuffles
, 4), "");
530 return LLVMBuildFAdd(builder
, shuftmp
[0], shuftmp
[1], "");
535 * partially horizontally add 2-4 float vectors with length nx4,
536 * i.e. only four adjacent values in each vector will be added,
537 * assuming values are really grouped in 4 which also determines
540 * Return a vector of the same length as the initial vectors,
541 * with the excess elements (if any) being undefined.
542 * The element order is independent of number of input vectors.
543 * For 3 vectors x0x1x2x3x4x5x6x7, y0y1y2y3y4y5y6y7, z0z1z2z3z4z5z6z7
544 * the output order thus will be
545 * sumx0-x3,sumy0-y3,sumz0-z3,undef,sumx4-x7,sumy4-y7,sumz4z7,undef
548 lp_build_hadd_partial4(struct lp_build_context
*bld
,
549 LLVMValueRef vectors
[],
552 struct gallivm_state
*gallivm
= bld
->gallivm
;
553 LLVMBuilderRef builder
= gallivm
->builder
;
554 LLVMValueRef ret_vec
;
556 const char *intrinsic
= NULL
;
558 assert(num_vecs
>= 2 && num_vecs
<= 4);
559 assert(bld
->type
.floating
);
561 /* only use this with at least 2 vectors, as it is sort of expensive
562 * (depending on cpu) and we always need two horizontal adds anyway,
563 * so a shuffle/add approach might be better.
569 tmp
[2] = num_vecs
> 2 ? vectors
[2] : vectors
[0];
570 tmp
[3] = num_vecs
> 3 ? vectors
[3] : vectors
[0];
572 if (util_cpu_caps
.has_sse3
&& bld
->type
.width
== 32 &&
573 bld
->type
.length
== 4) {
574 intrinsic
= "llvm.x86.sse3.hadd.ps";
576 else if (util_cpu_caps
.has_avx
&& bld
->type
.width
== 32 &&
577 bld
->type
.length
== 8) {
578 intrinsic
= "llvm.x86.avx.hadd.ps.256";
581 tmp
[0] = lp_build_intrinsic_binary(builder
, intrinsic
,
582 lp_build_vec_type(gallivm
, bld
->type
),
585 tmp
[1] = lp_build_intrinsic_binary(builder
, intrinsic
,
586 lp_build_vec_type(gallivm
, bld
->type
),
592 return lp_build_intrinsic_binary(builder
, intrinsic
,
593 lp_build_vec_type(gallivm
, bld
->type
),
597 if (bld
->type
.length
== 4) {
598 ret_vec
= lp_build_horizontal_add4x4f(bld
, tmp
);
601 LLVMValueRef partres
[LP_MAX_VECTOR_LENGTH
/4];
603 unsigned num_iter
= bld
->type
.length
/ 4;
604 struct lp_type parttype
= bld
->type
;
606 for (j
= 0; j
< num_iter
; j
++) {
607 LLVMValueRef partsrc
[4];
609 for (i
= 0; i
< 4; i
++) {
610 partsrc
[i
] = lp_build_extract_range(gallivm
, tmp
[i
], j
*4, 4);
612 partres
[j
] = lp_build_horizontal_add4x4f(bld
, partsrc
);
614 ret_vec
= lp_build_concat(gallivm
, partres
, parttype
, num_iter
);
623 lp_build_sub(struct lp_build_context
*bld
,
627 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
628 const struct lp_type type
= bld
->type
;
631 assert(lp_check_value(type
, a
));
632 assert(lp_check_value(type
, b
));
636 if(a
== bld
->undef
|| b
== bld
->undef
)
642 const char *intrinsic
= NULL
;
647 if (type
.width
* type
.length
== 128 &&
648 !type
.floating
&& !type
.fixed
) {
649 if (util_cpu_caps
.has_sse2
) {
651 intrinsic
= type
.sign
? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
653 intrinsic
= type
.sign
? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
654 } else if (util_cpu_caps
.has_altivec
) {
656 intrinsic
= type
.sign
? "llvm.ppc.altivec.vsubsbs" : "llvm.ppc.altivec.vsububs";
658 intrinsic
= type
.sign
? "llvm.ppc.altivec.vsubsws" : "llvm.ppc.altivec.vsubuws";
663 return lp_build_intrinsic_binary(builder
, intrinsic
, lp_build_vec_type(bld
->gallivm
, bld
->type
), a
, b
);
666 if(LLVMIsConstant(a
) && LLVMIsConstant(b
))
668 res
= LLVMConstFSub(a
, b
);
670 res
= LLVMConstSub(a
, b
);
673 res
= LLVMBuildFSub(builder
, a
, b
, "");
675 res
= LLVMBuildSub(builder
, a
, b
, "");
677 if(bld
->type
.norm
&& (bld
->type
.floating
|| bld
->type
.fixed
))
678 res
= lp_build_max_simple(bld
, res
, bld
->zero
);
686 * Normalized multiplication.
688 * There are several approaches here (using 8-bit normalized multiplication as
693 * makes the following approximation to the division (Sree)
695 * a*b/255 ~= (a*(b + 1)) >> 256
697 * which is the fastest method that satisfies the following OpenGL criteria
699 * 0*0 = 0 and 255*255 = 255
703 * takes the geometric series approximation to the division
705 * t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
707 * in this case just the first two terms to fit in 16bit arithmetic
709 * t/255 ~= (t + (t >> 8)) >> 8
711 * note that just by itself it doesn't satisfies the OpenGL criteria, as
712 * 255*255 = 254, so the special case b = 255 must be accounted or roundoff
715 * - geometric series plus rounding
717 * when using a geometric series division instead of truncating the result
718 * use roundoff in the approximation (Jim Blinn)
720 * t/255 ~= (t + (t >> 8) + 0x80) >> 8
722 * achieving the exact results
724 * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
725 * ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
726 * @sa Michael Herf, The "double blend trick", May 2000,
727 * http://www.stereopsis.com/doubleblend.html
730 lp_build_mul_norm(struct gallivm_state
*gallivm
,
731 struct lp_type wide_type
,
732 LLVMValueRef a
, LLVMValueRef b
)
734 LLVMBuilderRef builder
= gallivm
->builder
;
735 struct lp_build_context bld
;
741 assert(!wide_type
.floating
);
742 assert(lp_check_value(wide_type
, a
));
743 assert(lp_check_value(wide_type
, b
));
745 lp_build_context_init(&bld
, gallivm
, wide_type
);
747 bits
= wide_type
.width
/ 2;
748 if (wide_type
.sign
) {
752 shift
= lp_build_const_int_vec(gallivm
, wide_type
, bits
);
756 /* a*b/255 ~= (a*(b + 1)) >> 256 */
757 /* XXX: This would not work for signed types */
758 assert(!wide_type
.sign
);
759 b
= LLVMBuildAdd(builder
, b
, lp_build_const_int_vec(gallium
, wide_type
, 1), "");
760 ab
= LLVMBuildMul(builder
, a
, b
, "");
764 /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
765 ab
= LLVMBuildMul(builder
, a
, b
, "");
766 ab
= LLVMBuildAdd(builder
, ab
, LLVMBuildLShr(builder
, ab
, shift
, ""), "");
768 /* Add rounding term */
769 half
= lp_build_const_int_vec(gallivm
, wide_type
, 1 << (bits
- 1));
770 if (wide_type
.sign
) {
771 LLVMValueRef minus_half
= LLVMBuildNeg(builder
, half
, "");
772 LLVMValueRef sign
= lp_build_shr_imm(&bld
, half
, wide_type
.width
- 1);
773 half
= lp_build_select(&bld
, sign
, minus_half
, half
);
775 ab
= LLVMBuildAdd(builder
, ab
, half
, "");
779 ab
= LLVMBuildLShr(builder
, ab
, shift
, "");
788 lp_build_mul(struct lp_build_context
*bld
,
792 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
793 const struct lp_type type
= bld
->type
;
797 assert(lp_check_value(type
, a
));
798 assert(lp_check_value(type
, b
));
808 if(a
== bld
->undef
|| b
== bld
->undef
)
811 if (!type
.floating
&& !type
.fixed
&& type
.norm
) {
812 struct lp_type wide_type
= lp_wider_type(type
);
813 LLVMValueRef al
, ah
, bl
, bh
, abl
, abh
, ab
;
815 lp_build_unpack2(bld
->gallivm
, type
, wide_type
, a
, &al
, &ah
);
816 lp_build_unpack2(bld
->gallivm
, type
, wide_type
, b
, &bl
, &bh
);
818 /* PMULLW, PSRLW, PADDW */
819 abl
= lp_build_mul_norm(bld
->gallivm
, wide_type
, al
, bl
);
820 abh
= lp_build_mul_norm(bld
->gallivm
, wide_type
, ah
, bh
);
822 ab
= lp_build_pack2(bld
->gallivm
, wide_type
, type
, abl
, abh
);
828 shift
= lp_build_const_int_vec(bld
->gallivm
, type
, type
.width
/2);
832 if(LLVMIsConstant(a
) && LLVMIsConstant(b
)) {
834 res
= LLVMConstFMul(a
, b
);
836 res
= LLVMConstMul(a
, b
);
839 res
= LLVMConstAShr(res
, shift
);
841 res
= LLVMConstLShr(res
, shift
);
846 res
= LLVMBuildFMul(builder
, a
, b
, "");
848 res
= LLVMBuildMul(builder
, a
, b
, "");
851 res
= LLVMBuildAShr(builder
, res
, shift
, "");
853 res
= LLVMBuildLShr(builder
, res
, shift
, "");
862 * Small vector x scale multiplication optimization.
865 lp_build_mul_imm(struct lp_build_context
*bld
,
869 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
872 assert(lp_check_value(bld
->type
, a
));
881 return lp_build_negate(bld
, a
);
883 if(b
== 2 && bld
->type
.floating
)
884 return lp_build_add(bld
, a
, a
);
886 if(util_is_power_of_two(b
)) {
887 unsigned shift
= ffs(b
) - 1;
889 if(bld
->type
.floating
) {
892 * Power of two multiplication by directly manipulating the exponent.
894 * XXX: This might not be always faster, it will introduce a small error
895 * for multiplication by zero, and it will produce wrong results
898 unsigned mantissa
= lp_mantissa(bld
->type
);
899 factor
= lp_build_const_int_vec(bld
->gallivm
, bld
->type
, (unsigned long long)shift
<< mantissa
);
900 a
= LLVMBuildBitCast(builder
, a
, lp_build_int_vec_type(bld
->type
), "");
901 a
= LLVMBuildAdd(builder
, a
, factor
, "");
902 a
= LLVMBuildBitCast(builder
, a
, lp_build_vec_type(bld
->gallivm
, bld
->type
), "");
907 factor
= lp_build_const_vec(bld
->gallivm
, bld
->type
, shift
);
908 return LLVMBuildShl(builder
, a
, factor
, "");
912 factor
= lp_build_const_vec(bld
->gallivm
, bld
->type
, (double)b
);
913 return lp_build_mul(bld
, a
, factor
);
921 lp_build_div(struct lp_build_context
*bld
,
925 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
926 const struct lp_type type
= bld
->type
;
928 assert(lp_check_value(type
, a
));
929 assert(lp_check_value(type
, b
));
934 return lp_build_rcp(bld
, b
);
939 if(a
== bld
->undef
|| b
== bld
->undef
)
942 if(LLVMIsConstant(a
) && LLVMIsConstant(b
)) {
944 return LLVMConstFDiv(a
, b
);
946 return LLVMConstSDiv(a
, b
);
948 return LLVMConstUDiv(a
, b
);
951 if(((util_cpu_caps
.has_sse
&& type
.width
== 32 && type
.length
== 4) ||
952 (util_cpu_caps
.has_avx
&& type
.width
== 32 && type
.length
== 8)) &&
954 return lp_build_mul(bld
, a
, lp_build_rcp(bld
, b
));
957 return LLVMBuildFDiv(builder
, a
, b
, "");
959 return LLVMBuildSDiv(builder
, a
, b
, "");
961 return LLVMBuildUDiv(builder
, a
, b
, "");
966 * Linear interpolation helper.
968 * @param normalized whether we are interpolating normalized values,
969 * encoded in normalized integers, twice as wide.
971 * @sa http://www.stereopsis.com/doubleblend.html
973 static INLINE LLVMValueRef
974 lp_build_lerp_simple(struct lp_build_context
*bld
,
980 unsigned half_width
= bld
->type
.width
/2;
981 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
985 assert(lp_check_value(bld
->type
, x
));
986 assert(lp_check_value(bld
->type
, v0
));
987 assert(lp_check_value(bld
->type
, v1
));
989 delta
= lp_build_sub(bld
, v1
, v0
);
991 res
= lp_build_mul(bld
, x
, delta
);
994 if (bld
->type
.sign
) {
995 res
= lp_build_shr_imm(bld
, res
, half_width
- 1);
997 res
= lp_build_shr_imm(bld
, res
, half_width
);
1001 res
= lp_build_add(bld
, v0
, res
);
1003 if ((normalized
&& !bld
->type
.sign
) || bld
->type
.fixed
) {
1004 /* We need to mask out the high order bits when lerping 8bit normalized colors stored on 16bits */
1005 /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
1006 * but it will be wrong for true fixed point use cases. Basically we need
1007 * a more powerful lp_type, capable of further distinguishing the values
1008 * interpretation from the value storage. */
1009 res
= LLVMBuildAnd(builder
, res
, lp_build_const_int_vec(bld
->gallivm
, bld
->type
, (1 << half_width
) - 1), "");
1017 * Linear interpolation.
1020 lp_build_lerp(struct lp_build_context
*bld
,
1025 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1026 const struct lp_type type
= bld
->type
;
1029 assert(lp_check_value(type
, x
));
1030 assert(lp_check_value(type
, v0
));
1031 assert(lp_check_value(type
, v1
));
1034 struct lp_type wide_type
;
1035 struct lp_build_context wide_bld
;
1036 LLVMValueRef xl
, xh
, v0l
, v0h
, v1l
, v1h
, resl
, resh
;
1040 assert(type
.length
>= 2);
1043 * Create a wider integer type, enough to hold the
1044 * intermediate result of the multiplication.
1046 memset(&wide_type
, 0, sizeof wide_type
);
1047 wide_type
.sign
= type
.sign
;
1048 wide_type
.width
= type
.width
*2;
1049 wide_type
.length
= type
.length
/2;
1051 lp_build_context_init(&wide_bld
, bld
->gallivm
, wide_type
);
1053 lp_build_unpack2(bld
->gallivm
, type
, wide_type
, x
, &xl
, &xh
);
1054 lp_build_unpack2(bld
->gallivm
, type
, wide_type
, v0
, &v0l
, &v0h
);
1055 lp_build_unpack2(bld
->gallivm
, type
, wide_type
, v1
, &v1l
, &v1h
);
1058 * Scale x from [0, 255] to [0, 256]
1061 bits
= type
.width
- 1;
1066 shift
= lp_build_const_int_vec(bld
->gallivm
, wide_type
, bits
- 1);
1068 xl
= lp_build_add(&wide_bld
, xl
,
1069 LLVMBuildAShr(builder
, xl
, shift
, ""));
1070 xh
= lp_build_add(&wide_bld
, xh
,
1071 LLVMBuildAShr(builder
, xh
, shift
, ""));
1077 resl
= lp_build_lerp_simple(&wide_bld
, xl
, v0l
, v1l
, TRUE
);
1078 resh
= lp_build_lerp_simple(&wide_bld
, xh
, v0h
, v1h
, TRUE
);
1080 res
= lp_build_pack2(bld
->gallivm
, wide_type
, type
, resl
, resh
);
1082 res
= lp_build_lerp_simple(bld
, x
, v0
, v1
, FALSE
);
1090 lp_build_lerp_2d(struct lp_build_context
*bld
,
1098 LLVMValueRef v0
= lp_build_lerp(bld
, x
, v00
, v01
);
1099 LLVMValueRef v1
= lp_build_lerp(bld
, x
, v10
, v11
);
1100 return lp_build_lerp(bld
, y
, v0
, v1
);
1105 * Generate min(a, b)
1106 * Do checks for special cases.
1109 lp_build_min(struct lp_build_context
*bld
,
1113 assert(lp_check_value(bld
->type
, a
));
1114 assert(lp_check_value(bld
->type
, b
));
1116 if(a
== bld
->undef
|| b
== bld
->undef
)
1122 if (bld
->type
.norm
) {
1123 if (!bld
->type
.sign
) {
1124 if (a
== bld
->zero
|| b
== bld
->zero
) {
1134 return lp_build_min_simple(bld
, a
, b
);
1139 * Generate max(a, b)
1140 * Do checks for special cases.
1143 lp_build_max(struct lp_build_context
*bld
,
1147 assert(lp_check_value(bld
->type
, a
));
1148 assert(lp_check_value(bld
->type
, b
));
1150 if(a
== bld
->undef
|| b
== bld
->undef
)
1156 if(bld
->type
.norm
) {
1157 if(a
== bld
->one
|| b
== bld
->one
)
1159 if (!bld
->type
.sign
) {
1160 if (a
== bld
->zero
) {
1163 if (b
== bld
->zero
) {
1169 return lp_build_max_simple(bld
, a
, b
);
1174 * Generate clamp(a, min, max)
1175 * Do checks for special cases.
1178 lp_build_clamp(struct lp_build_context
*bld
,
1183 assert(lp_check_value(bld
->type
, a
));
1184 assert(lp_check_value(bld
->type
, min
));
1185 assert(lp_check_value(bld
->type
, max
));
1187 a
= lp_build_min(bld
, a
, max
);
1188 a
= lp_build_max(bld
, a
, min
);
1197 lp_build_abs(struct lp_build_context
*bld
,
1200 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1201 const struct lp_type type
= bld
->type
;
1202 LLVMTypeRef vec_type
= lp_build_vec_type(bld
->gallivm
, type
);
1204 assert(lp_check_value(type
, a
));
1210 /* Mask out the sign bit */
1211 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(bld
->gallivm
, type
);
1212 unsigned long long absMask
= ~(1ULL << (type
.width
- 1));
1213 LLVMValueRef mask
= lp_build_const_int_vec(bld
->gallivm
, type
, ((unsigned long long) absMask
));
1214 a
= LLVMBuildBitCast(builder
, a
, int_vec_type
, "");
1215 a
= LLVMBuildAnd(builder
, a
, mask
, "");
1216 a
= LLVMBuildBitCast(builder
, a
, vec_type
, "");
1220 if(type
.width
*type
.length
== 128 && util_cpu_caps
.has_ssse3
) {
1221 switch(type
.width
) {
1223 return lp_build_intrinsic_unary(builder
, "llvm.x86.ssse3.pabs.b.128", vec_type
, a
);
1225 return lp_build_intrinsic_unary(builder
, "llvm.x86.ssse3.pabs.w.128", vec_type
, a
);
1227 return lp_build_intrinsic_unary(builder
, "llvm.x86.ssse3.pabs.d.128", vec_type
, a
);
1230 else if (type
.width
*type
.length
== 256 && util_cpu_caps
.has_ssse3
&&
1231 (gallivm_debug
& GALLIVM_DEBUG_PERF
) &&
1232 (type
.width
== 8 || type
.width
== 16 || type
.width
== 32)) {
1233 debug_printf("%s: inefficient code, should split vectors manually\n",
1237 return lp_build_max(bld
, a
, LLVMBuildNeg(builder
, a
, ""));
1242 lp_build_negate(struct lp_build_context
*bld
,
1245 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1247 assert(lp_check_value(bld
->type
, a
));
1249 #if HAVE_LLVM >= 0x0207
1250 if (bld
->type
.floating
)
1251 a
= LLVMBuildFNeg(builder
, a
, "");
1254 a
= LLVMBuildNeg(builder
, a
, "");
1260 /** Return -1, 0 or +1 depending on the sign of a */
1262 lp_build_sgn(struct lp_build_context
*bld
,
1265 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1266 const struct lp_type type
= bld
->type
;
1270 assert(lp_check_value(type
, a
));
1272 /* Handle non-zero case */
1274 /* if not zero then sign must be positive */
1277 else if(type
.floating
) {
1278 LLVMTypeRef vec_type
;
1279 LLVMTypeRef int_type
;
1283 unsigned long long maskBit
= (unsigned long long)1 << (type
.width
- 1);
1285 int_type
= lp_build_int_vec_type(bld
->gallivm
, type
);
1286 vec_type
= lp_build_vec_type(bld
->gallivm
, type
);
1287 mask
= lp_build_const_int_vec(bld
->gallivm
, type
, maskBit
);
1289 /* Take the sign bit and add it to 1 constant */
1290 sign
= LLVMBuildBitCast(builder
, a
, int_type
, "");
1291 sign
= LLVMBuildAnd(builder
, sign
, mask
, "");
1292 one
= LLVMConstBitCast(bld
->one
, int_type
);
1293 res
= LLVMBuildOr(builder
, sign
, one
, "");
1294 res
= LLVMBuildBitCast(builder
, res
, vec_type
, "");
1298 /* signed int/norm/fixed point */
1299 /* could use psign with sse3 and appropriate vectors here */
1300 LLVMValueRef minus_one
= lp_build_const_vec(bld
->gallivm
, type
, -1.0);
1301 cond
= lp_build_cmp(bld
, PIPE_FUNC_GREATER
, a
, bld
->zero
);
1302 res
= lp_build_select(bld
, cond
, bld
->one
, minus_one
);
1306 cond
= lp_build_cmp(bld
, PIPE_FUNC_EQUAL
, a
, bld
->zero
);
1307 res
= lp_build_select(bld
, cond
, bld
->zero
, res
);
1314 * Set the sign of float vector 'a' according to 'sign'.
1315 * If sign==0, return abs(a).
1316 * If sign==1, return -abs(a);
1317 * Other values for sign produce undefined results.
1320 lp_build_set_sign(struct lp_build_context
*bld
,
1321 LLVMValueRef a
, LLVMValueRef sign
)
1323 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1324 const struct lp_type type
= bld
->type
;
1325 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(bld
->gallivm
, type
);
1326 LLVMTypeRef vec_type
= lp_build_vec_type(bld
->gallivm
, type
);
1327 LLVMValueRef shift
= lp_build_const_int_vec(bld
->gallivm
, type
, type
.width
- 1);
1328 LLVMValueRef mask
= lp_build_const_int_vec(bld
->gallivm
, type
,
1329 ~((unsigned long long) 1 << (type
.width
- 1)));
1330 LLVMValueRef val
, res
;
1332 assert(type
.floating
);
1333 assert(lp_check_value(type
, a
));
1335 /* val = reinterpret_cast<int>(a) */
1336 val
= LLVMBuildBitCast(builder
, a
, int_vec_type
, "");
1337 /* val = val & mask */
1338 val
= LLVMBuildAnd(builder
, val
, mask
, "");
1339 /* sign = sign << shift */
1340 sign
= LLVMBuildShl(builder
, sign
, shift
, "");
1341 /* res = val | sign */
1342 res
= LLVMBuildOr(builder
, val
, sign
, "");
1343 /* res = reinterpret_cast<float>(res) */
1344 res
= LLVMBuildBitCast(builder
, res
, vec_type
, "");
1351 * Convert vector of (or scalar) int to vector of (or scalar) float.
1354 lp_build_int_to_float(struct lp_build_context
*bld
,
1357 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1358 const struct lp_type type
= bld
->type
;
1359 LLVMTypeRef vec_type
= lp_build_vec_type(bld
->gallivm
, type
);
1361 assert(type
.floating
);
1363 return LLVMBuildSIToFP(builder
, a
, vec_type
, "");
1367 arch_rounding_available(const struct lp_type type
)
1369 if ((util_cpu_caps
.has_sse4_1
&&
1370 (type
.length
== 1 || type
.width
*type
.length
== 128)) ||
1371 (util_cpu_caps
.has_avx
&& type
.width
*type
.length
== 256))
1373 else if ((util_cpu_caps
.has_altivec
&&
1374 (type
.width
== 32 && type
.length
== 4)))
1380 enum lp_build_round_mode
1382 LP_BUILD_ROUND_NEAREST
= 0,
1383 LP_BUILD_ROUND_FLOOR
= 1,
1384 LP_BUILD_ROUND_CEIL
= 2,
1385 LP_BUILD_ROUND_TRUNCATE
= 3
1389 * Helper for SSE4.1's ROUNDxx instructions.
1391 * NOTE: In the SSE4.1's nearest mode, if two values are equally close, the
1392 * result is the even value. That is, rounding 2.5 will be 2.0, and not 3.0.
1394 static INLINE LLVMValueRef
1395 lp_build_round_sse41(struct lp_build_context
*bld
,
1397 enum lp_build_round_mode mode
)
1399 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1400 const struct lp_type type
= bld
->type
;
1401 LLVMTypeRef i32t
= LLVMInt32TypeInContext(bld
->gallivm
->context
);
1402 const char *intrinsic
;
1405 assert(type
.floating
);
1407 assert(lp_check_value(type
, a
));
1408 assert(util_cpu_caps
.has_sse4_1
);
1410 if (type
.length
== 1) {
1411 LLVMTypeRef vec_type
;
1413 LLVMValueRef args
[3];
1414 LLVMValueRef index0
= LLVMConstInt(i32t
, 0, 0);
1416 switch(type
.width
) {
1418 intrinsic
= "llvm.x86.sse41.round.ss";
1421 intrinsic
= "llvm.x86.sse41.round.sd";
1428 vec_type
= LLVMVectorType(bld
->elem_type
, 4);
1430 undef
= LLVMGetUndef(vec_type
);
1433 args
[1] = LLVMBuildInsertElement(builder
, undef
, a
, index0
, "");
1434 args
[2] = LLVMConstInt(i32t
, mode
, 0);
1436 res
= lp_build_intrinsic(builder
, intrinsic
,
1437 vec_type
, args
, Elements(args
));
1439 res
= LLVMBuildExtractElement(builder
, res
, index0
, "");
1442 if (type
.width
* type
.length
== 128) {
1443 switch(type
.width
) {
1445 intrinsic
= "llvm.x86.sse41.round.ps";
1448 intrinsic
= "llvm.x86.sse41.round.pd";
1456 assert(type
.width
* type
.length
== 256);
1457 assert(util_cpu_caps
.has_avx
);
1459 switch(type
.width
) {
1461 intrinsic
= "llvm.x86.avx.round.ps.256";
1464 intrinsic
= "llvm.x86.avx.round.pd.256";
1472 res
= lp_build_intrinsic_binary(builder
, intrinsic
,
1474 LLVMConstInt(i32t
, mode
, 0));
1481 static INLINE LLVMValueRef
1482 lp_build_iround_nearest_sse2(struct lp_build_context
*bld
,
1485 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1486 const struct lp_type type
= bld
->type
;
1487 LLVMTypeRef i32t
= LLVMInt32TypeInContext(bld
->gallivm
->context
);
1488 LLVMTypeRef ret_type
= lp_build_int_vec_type(bld
->gallivm
, type
);
1489 const char *intrinsic
;
1492 assert(type
.floating
);
1493 /* using the double precision conversions is a bit more complicated */
1494 assert(type
.width
== 32);
1496 assert(lp_check_value(type
, a
));
1497 assert(util_cpu_caps
.has_sse2
);
1499 /* This is relying on MXCSR rounding mode, which should always be nearest. */
1500 if (type
.length
== 1) {
1501 LLVMTypeRef vec_type
;
1504 LLVMValueRef index0
= LLVMConstInt(i32t
, 0, 0);
1506 vec_type
= LLVMVectorType(bld
->elem_type
, 4);
1508 intrinsic
= "llvm.x86.sse.cvtss2si";
1510 undef
= LLVMGetUndef(vec_type
);
1512 arg
= LLVMBuildInsertElement(builder
, undef
, a
, index0
, "");
1514 res
= lp_build_intrinsic_unary(builder
, intrinsic
,
1518 if (type
.width
* type
.length
== 128) {
1519 intrinsic
= "llvm.x86.sse2.cvtps2dq";
1522 assert(type
.width
*type
.length
== 256);
1523 assert(util_cpu_caps
.has_avx
);
1525 intrinsic
= "llvm.x86.avx.cvt.ps2dq.256";
1527 res
= lp_build_intrinsic_unary(builder
, intrinsic
,
1537 static INLINE LLVMValueRef
1538 lp_build_round_altivec(struct lp_build_context
*bld
,
1540 enum lp_build_round_mode mode
)
1542 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1543 const struct lp_type type
= bld
->type
;
1544 const char *intrinsic
= NULL
;
1546 assert(type
.floating
);
1548 assert(lp_check_value(type
, a
));
1549 assert(util_cpu_caps
.has_altivec
);
1552 case LP_BUILD_ROUND_NEAREST
:
1553 intrinsic
= "llvm.ppc.altivec.vrfin";
1555 case LP_BUILD_ROUND_FLOOR
:
1556 intrinsic
= "llvm.ppc.altivec.vrfim";
1558 case LP_BUILD_ROUND_CEIL
:
1559 intrinsic
= "llvm.ppc.altivec.vrfip";
1561 case LP_BUILD_ROUND_TRUNCATE
:
1562 intrinsic
= "llvm.ppc.altivec.vrfiz";
1566 return lp_build_intrinsic_unary(builder
, intrinsic
, bld
->vec_type
, a
);
1569 static INLINE LLVMValueRef
1570 lp_build_round_arch(struct lp_build_context
*bld
,
1572 enum lp_build_round_mode mode
)
1574 if (util_cpu_caps
.has_sse4_1
)
1575 return lp_build_round_sse41(bld
, a
, mode
);
1576 else /* (util_cpu_caps.has_altivec) */
1577 return lp_build_round_altivec(bld
, a
, mode
);
1581 * Return the integer part of a float (vector) value (== round toward zero).
1582 * The returned value is a float (vector).
1583 * Ex: trunc(-1.5) = -1.0
1586 lp_build_trunc(struct lp_build_context
*bld
,
1589 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1590 const struct lp_type type
= bld
->type
;
1592 assert(type
.floating
);
1593 assert(lp_check_value(type
, a
));
1595 if (arch_rounding_available(type
)) {
1596 return lp_build_round_arch(bld
, a
, LP_BUILD_ROUND_TRUNCATE
);
1599 LLVMTypeRef vec_type
= lp_build_vec_type(bld
->gallivm
, type
);
1600 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(bld
->gallivm
, type
);
1602 res
= LLVMBuildFPToSI(builder
, a
, int_vec_type
, "");
1603 res
= LLVMBuildSIToFP(builder
, res
, vec_type
, "");
1610 * Return float (vector) rounded to nearest integer (vector). The returned
1611 * value is a float (vector).
1612 * Ex: round(0.9) = 1.0
1613 * Ex: round(-1.5) = -2.0
1616 lp_build_round(struct lp_build_context
*bld
,
1619 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1620 const struct lp_type type
= bld
->type
;
1622 assert(type
.floating
);
1623 assert(lp_check_value(type
, a
));
1625 if (arch_rounding_available(type
)) {
1626 return lp_build_round_arch(bld
, a
, LP_BUILD_ROUND_NEAREST
);
1629 LLVMTypeRef vec_type
= lp_build_vec_type(bld
->gallivm
, type
);
1631 res
= lp_build_iround(bld
, a
);
1632 res
= LLVMBuildSIToFP(builder
, res
, vec_type
, "");
1639 * Return floor of float (vector), result is a float (vector)
1640 * Ex: floor(1.1) = 1.0
1641 * Ex: floor(-1.1) = -2.0
1644 lp_build_floor(struct lp_build_context
*bld
,
1647 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1648 const struct lp_type type
= bld
->type
;
1650 assert(type
.floating
);
1651 assert(lp_check_value(type
, a
));
1653 if (arch_rounding_available(type
)) {
1654 return lp_build_round_arch(bld
, a
, LP_BUILD_ROUND_FLOOR
);
1657 LLVMTypeRef vec_type
= lp_build_vec_type(bld
->gallivm
, type
);
1659 res
= lp_build_ifloor(bld
, a
);
1660 res
= LLVMBuildSIToFP(builder
, res
, vec_type
, "");
1667 * Return ceiling of float (vector), returning float (vector).
1668 * Ex: ceil( 1.1) = 2.0
1669 * Ex: ceil(-1.1) = -1.0
1672 lp_build_ceil(struct lp_build_context
*bld
,
1675 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1676 const struct lp_type type
= bld
->type
;
1678 assert(type
.floating
);
1679 assert(lp_check_value(type
, a
));
1681 if (arch_rounding_available(type
)) {
1682 return lp_build_round_arch(bld
, a
, LP_BUILD_ROUND_CEIL
);
1685 LLVMTypeRef vec_type
= lp_build_vec_type(bld
->gallivm
, type
);
1687 res
= lp_build_iceil(bld
, a
);
1688 res
= LLVMBuildSIToFP(builder
, res
, vec_type
, "");
1695 * Return fractional part of 'a' computed as a - floor(a)
1696 * Typically used in texture coord arithmetic.
1699 lp_build_fract(struct lp_build_context
*bld
,
1702 assert(bld
->type
.floating
);
1703 return lp_build_sub(bld
, a
, lp_build_floor(bld
, a
));
1708 * Prevent returning a fractional part of 1.0 for very small negative values of
1709 * 'a' by clamping against 0.99999(9).
1711 static inline LLVMValueRef
1712 clamp_fract(struct lp_build_context
*bld
, LLVMValueRef fract
)
1716 /* this is the largest number smaller than 1.0 representable as float */
1717 max
= lp_build_const_vec(bld
->gallivm
, bld
->type
,
1718 1.0 - 1.0/(1LL << (lp_mantissa(bld
->type
) + 1)));
1719 return lp_build_min(bld
, fract
, max
);
1724 * Same as lp_build_fract, but guarantees that the result is always smaller
1728 lp_build_fract_safe(struct lp_build_context
*bld
,
1731 return clamp_fract(bld
, lp_build_fract(bld
, a
));
1736 * Return the integer part of a float (vector) value (== round toward zero).
1737 * The returned value is an integer (vector).
1738 * Ex: itrunc(-1.5) = -1
1741 lp_build_itrunc(struct lp_build_context
*bld
,
1744 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1745 const struct lp_type type
= bld
->type
;
1746 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(bld
->gallivm
, type
);
1748 assert(type
.floating
);
1749 assert(lp_check_value(type
, a
));
1751 return LLVMBuildFPToSI(builder
, a
, int_vec_type
, "");
1756 * Return float (vector) rounded to nearest integer (vector). The returned
1757 * value is an integer (vector).
1758 * Ex: iround(0.9) = 1
1759 * Ex: iround(-1.5) = -2
1762 lp_build_iround(struct lp_build_context
*bld
,
1765 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1766 const struct lp_type type
= bld
->type
;
1767 LLVMTypeRef int_vec_type
= bld
->int_vec_type
;
1770 assert(type
.floating
);
1772 assert(lp_check_value(type
, a
));
1774 if ((util_cpu_caps
.has_sse2
&&
1775 ((type
.width
== 32) && (type
.length
== 1 || type
.length
== 4))) ||
1776 (util_cpu_caps
.has_avx
&& type
.width
== 32 && type
.length
== 8)) {
1777 return lp_build_iround_nearest_sse2(bld
, a
);
1779 if (arch_rounding_available(type
)) {
1780 res
= lp_build_round_arch(bld
, a
, LP_BUILD_ROUND_NEAREST
);
1785 half
= lp_build_const_vec(bld
->gallivm
, type
, 0.5);
1788 LLVMTypeRef vec_type
= bld
->vec_type
;
1789 LLVMValueRef mask
= lp_build_const_int_vec(bld
->gallivm
, type
,
1790 (unsigned long long)1 << (type
.width
- 1));
1794 sign
= LLVMBuildBitCast(builder
, a
, int_vec_type
, "");
1795 sign
= LLVMBuildAnd(builder
, sign
, mask
, "");
1798 half
= LLVMBuildBitCast(builder
, half
, int_vec_type
, "");
1799 half
= LLVMBuildOr(builder
, sign
, half
, "");
1800 half
= LLVMBuildBitCast(builder
, half
, vec_type
, "");
1803 res
= LLVMBuildFAdd(builder
, a
, half
, "");
1806 res
= LLVMBuildFPToSI(builder
, res
, int_vec_type
, "");
1813 * Return floor of float (vector), result is an int (vector)
1814 * Ex: ifloor(1.1) = 1.0
1815 * Ex: ifloor(-1.1) = -2.0
1818 lp_build_ifloor(struct lp_build_context
*bld
,
1821 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1822 const struct lp_type type
= bld
->type
;
1823 LLVMTypeRef int_vec_type
= bld
->int_vec_type
;
1826 assert(type
.floating
);
1827 assert(lp_check_value(type
, a
));
1831 if (arch_rounding_available(type
)) {
1832 res
= lp_build_round_arch(bld
, a
, LP_BUILD_ROUND_FLOOR
);
1835 /* Take the sign bit and add it to 1 constant */
1836 LLVMTypeRef vec_type
= bld
->vec_type
;
1837 unsigned mantissa
= lp_mantissa(type
);
1838 LLVMValueRef mask
= lp_build_const_int_vec(bld
->gallivm
, type
,
1839 (unsigned long long)1 << (type
.width
- 1));
1841 LLVMValueRef offset
;
1843 /* sign = a < 0 ? ~0 : 0 */
1844 sign
= LLVMBuildBitCast(builder
, a
, int_vec_type
, "");
1845 sign
= LLVMBuildAnd(builder
, sign
, mask
, "");
1846 sign
= LLVMBuildAShr(builder
, sign
,
1847 lp_build_const_int_vec(bld
->gallivm
, type
,
1851 /* offset = -0.99999(9)f */
1852 offset
= lp_build_const_vec(bld
->gallivm
, type
,
1853 -(double)(((unsigned long long)1 << mantissa
) - 10)/((unsigned long long)1 << mantissa
));
1854 offset
= LLVMConstBitCast(offset
, int_vec_type
);
1856 /* offset = a < 0 ? offset : 0.0f */
1857 offset
= LLVMBuildAnd(builder
, offset
, sign
, "");
1858 offset
= LLVMBuildBitCast(builder
, offset
, vec_type
, "ifloor.offset");
1860 res
= LLVMBuildFAdd(builder
, res
, offset
, "ifloor.res");
1864 /* round to nearest (toward zero) */
1865 res
= LLVMBuildFPToSI(builder
, res
, int_vec_type
, "ifloor.res");
1872 * Return ceiling of float (vector), returning int (vector).
1873 * Ex: iceil( 1.1) = 2
1874 * Ex: iceil(-1.1) = -1
1877 lp_build_iceil(struct lp_build_context
*bld
,
1880 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1881 const struct lp_type type
= bld
->type
;
1882 LLVMTypeRef int_vec_type
= bld
->int_vec_type
;
1885 assert(type
.floating
);
1886 assert(lp_check_value(type
, a
));
1888 if (arch_rounding_available(type
)) {
1889 res
= lp_build_round_arch(bld
, a
, LP_BUILD_ROUND_CEIL
);
1892 LLVMTypeRef vec_type
= bld
->vec_type
;
1893 unsigned mantissa
= lp_mantissa(type
);
1894 LLVMValueRef offset
;
1896 /* offset = 0.99999(9)f */
1897 offset
= lp_build_const_vec(bld
->gallivm
, type
,
1898 (double)(((unsigned long long)1 << mantissa
) - 10)/((unsigned long long)1 << mantissa
));
1901 LLVMValueRef mask
= lp_build_const_int_vec(bld
->gallivm
, type
,
1902 (unsigned long long)1 << (type
.width
- 1));
1905 /* sign = a < 0 ? 0 : ~0 */
1906 sign
= LLVMBuildBitCast(builder
, a
, int_vec_type
, "");
1907 sign
= LLVMBuildAnd(builder
, sign
, mask
, "");
1908 sign
= LLVMBuildAShr(builder
, sign
,
1909 lp_build_const_int_vec(bld
->gallivm
, type
,
1912 sign
= LLVMBuildNot(builder
, sign
, "iceil.not");
1914 /* offset = a < 0 ? 0.0 : offset */
1915 offset
= LLVMConstBitCast(offset
, int_vec_type
);
1916 offset
= LLVMBuildAnd(builder
, offset
, sign
, "");
1917 offset
= LLVMBuildBitCast(builder
, offset
, vec_type
, "iceil.offset");
1920 res
= LLVMBuildFAdd(builder
, a
, offset
, "iceil.res");
1923 /* round to nearest (toward zero) */
1924 res
= LLVMBuildFPToSI(builder
, res
, int_vec_type
, "iceil.res");
1931 * Combined ifloor() & fract().
1933 * Preferred to calling the functions separately, as it will ensure that the
1934 * strategy (floor() vs ifloor()) that results in less redundant work is used.
1937 lp_build_ifloor_fract(struct lp_build_context
*bld
,
1939 LLVMValueRef
*out_ipart
,
1940 LLVMValueRef
*out_fpart
)
1942 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1943 const struct lp_type type
= bld
->type
;
1946 assert(type
.floating
);
1947 assert(lp_check_value(type
, a
));
1949 if (arch_rounding_available(type
)) {
1951 * floor() is easier.
1954 ipart
= lp_build_floor(bld
, a
);
1955 *out_fpart
= LLVMBuildFSub(builder
, a
, ipart
, "fpart");
1956 *out_ipart
= LLVMBuildFPToSI(builder
, ipart
, bld
->int_vec_type
, "ipart");
1960 * ifloor() is easier.
1963 *out_ipart
= lp_build_ifloor(bld
, a
);
1964 ipart
= LLVMBuildSIToFP(builder
, *out_ipart
, bld
->vec_type
, "ipart");
1965 *out_fpart
= LLVMBuildFSub(builder
, a
, ipart
, "fpart");
1971 * Same as lp_build_ifloor_fract, but guarantees that the fractional part is
1972 * always smaller than one.
1975 lp_build_ifloor_fract_safe(struct lp_build_context
*bld
,
1977 LLVMValueRef
*out_ipart
,
1978 LLVMValueRef
*out_fpart
)
1980 lp_build_ifloor_fract(bld
, a
, out_ipart
, out_fpart
);
1981 *out_fpart
= clamp_fract(bld
, *out_fpart
);
1986 lp_build_sqrt(struct lp_build_context
*bld
,
1989 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
1990 const struct lp_type type
= bld
->type
;
1991 LLVMTypeRef vec_type
= lp_build_vec_type(bld
->gallivm
, type
);
1994 assert(lp_check_value(type
, a
));
1996 /* TODO: optimize the constant case */
1998 assert(type
.floating
);
1999 if (type
.length
== 1) {
2000 util_snprintf(intrinsic
, sizeof intrinsic
, "llvm.sqrt.f%u", type
.width
);
2003 util_snprintf(intrinsic
, sizeof intrinsic
, "llvm.sqrt.v%uf%u", type
.length
, type
.width
);
2006 return lp_build_intrinsic_unary(builder
, intrinsic
, vec_type
, a
);
2011 * Do one Newton-Raphson step to improve reciprocate precision:
2013 * x_{i+1} = x_i * (2 - a * x_i)
2015 * XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
2016 * +/-Inf, giving NaN instead. Certain applications rely on this behavior,
2017 * such as Google Earth, which does RCP(RSQRT(0.0) when drawing the Earth's
2018 * halo. It would be necessary to clamp the argument to prevent this.
2021 * - http://en.wikipedia.org/wiki/Division_(digital)#Newton.E2.80.93Raphson_division
2022 * - http://softwarecommunity.intel.com/articles/eng/1818.htm
2024 static INLINE LLVMValueRef
2025 lp_build_rcp_refine(struct lp_build_context
*bld
,
2029 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
2030 LLVMValueRef two
= lp_build_const_vec(bld
->gallivm
, bld
->type
, 2.0);
2033 res
= LLVMBuildFMul(builder
, a
, rcp_a
, "");
2034 res
= LLVMBuildFSub(builder
, two
, res
, "");
2035 res
= LLVMBuildFMul(builder
, rcp_a
, res
, "");
2042 lp_build_rcp(struct lp_build_context
*bld
,
2045 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
2046 const struct lp_type type
= bld
->type
;
2048 assert(lp_check_value(type
, a
));
2057 assert(type
.floating
);
2059 if(LLVMIsConstant(a
))
2060 return LLVMConstFDiv(bld
->one
, a
);
2063 * We don't use RCPPS because:
2064 * - it only has 10bits of precision
2065 * - it doesn't even get the reciprocate of 1.0 exactly
2066 * - doing Newton-Rapshon steps yields wrong (NaN) values for 0.0 or Inf
2067 * - for recent processors the benefit over DIVPS is marginal, a case
2070 * We could still use it on certain processors if benchmarks show that the
2071 * RCPPS plus necessary workarounds are still preferrable to DIVPS; or for
2072 * particular uses that require less workarounds.
2075 if (FALSE
&& ((util_cpu_caps
.has_sse
&& type
.width
== 32 && type
.length
== 4) ||
2076 (util_cpu_caps
.has_avx
&& type
.width
== 32 && type
.length
== 8))){
2077 const unsigned num_iterations
= 0;
2080 const char *intrinsic
= NULL
;
2082 if (type
.length
== 4) {
2083 intrinsic
= "llvm.x86.sse.rcp.ps";
2086 intrinsic
= "llvm.x86.avx.rcp.ps.256";
2089 res
= lp_build_intrinsic_unary(builder
, intrinsic
, bld
->vec_type
, a
);
2091 for (i
= 0; i
< num_iterations
; ++i
) {
2092 res
= lp_build_rcp_refine(bld
, a
, res
);
2098 return LLVMBuildFDiv(builder
, bld
->one
, a
, "");
2103 * Do one Newton-Raphson step to improve rsqrt precision:
2105 * x_{i+1} = 0.5 * x_i * (3.0 - a * x_i * x_i)
2107 * See also Intel 64 and IA-32 Architectures Optimization Manual.
2109 static INLINE LLVMValueRef
2110 lp_build_rsqrt_refine(struct lp_build_context
*bld
,
2112 LLVMValueRef rsqrt_a
)
2114 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
2115 LLVMValueRef half
= lp_build_const_vec(bld
->gallivm
, bld
->type
, 0.5);
2116 LLVMValueRef three
= lp_build_const_vec(bld
->gallivm
, bld
->type
, 3.0);
2119 res
= LLVMBuildFMul(builder
, rsqrt_a
, rsqrt_a
, "");
2120 res
= LLVMBuildFMul(builder
, a
, res
, "");
2121 res
= LLVMBuildFSub(builder
, three
, res
, "");
2122 res
= LLVMBuildFMul(builder
, rsqrt_a
, res
, "");
2123 res
= LLVMBuildFMul(builder
, half
, res
, "");
2130 * Generate 1/sqrt(a).
2131 * Result is undefined for values < 0, infinity for +0.
2134 lp_build_rsqrt(struct lp_build_context
*bld
,
2137 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
2138 const struct lp_type type
= bld
->type
;
2140 assert(lp_check_value(type
, a
));
2142 assert(type
.floating
);
2145 * This should be faster but all denormals will end up as infinity.
2147 if (0 && ((util_cpu_caps
.has_sse
&& type
.width
== 32 && type
.length
== 4) ||
2148 (util_cpu_caps
.has_avx
&& type
.width
== 32 && type
.length
== 8))) {
2149 const unsigned num_iterations
= 1;
2152 const char *intrinsic
= NULL
;
2154 if (type
.length
== 4) {
2155 intrinsic
= "llvm.x86.sse.rsqrt.ps";
2158 intrinsic
= "llvm.x86.avx.rsqrt.ps.256";
2160 if (num_iterations
) {
2162 * Newton-Raphson will result in NaN instead of infinity for zero,
2163 * and NaN instead of zero for infinity.
2164 * Also, need to ensure rsqrt(1.0) == 1.0.
2165 * All numbers smaller than FLT_MIN will result in +infinity
2166 * (rsqrtps treats all denormals as zero).
2169 * Certain non-c99 compilers don't know INFINITY and might not support
2170 * hacks to evaluate it at compile time neither.
2172 const unsigned posinf_int
= 0x7F800000;
2174 LLVMValueRef flt_min
= lp_build_const_vec(bld
->gallivm
, type
, FLT_MIN
);
2175 LLVMValueRef inf
= lp_build_const_int_vec(bld
->gallivm
, type
, posinf_int
);
2177 inf
= LLVMBuildBitCast(builder
, inf
, lp_build_vec_type(bld
->gallivm
, type
), "");
2179 res
= lp_build_intrinsic_unary(builder
, intrinsic
, bld
->vec_type
, a
);
2181 for (i
= 0; i
< num_iterations
; ++i
) {
2182 res
= lp_build_rsqrt_refine(bld
, a
, res
);
2184 cmp
= lp_build_compare(bld
->gallivm
, type
, PIPE_FUNC_LESS
, a
, flt_min
);
2185 res
= lp_build_select(bld
, cmp
, inf
, res
);
2186 cmp
= lp_build_compare(bld
->gallivm
, type
, PIPE_FUNC_EQUAL
, a
, inf
);
2187 res
= lp_build_select(bld
, cmp
, bld
->zero
, res
);
2188 cmp
= lp_build_compare(bld
->gallivm
, type
, PIPE_FUNC_EQUAL
, a
, bld
->one
);
2189 res
= lp_build_select(bld
, cmp
, bld
->one
, res
);
2192 /* rsqrt(1.0) != 1.0 here */
2193 res
= lp_build_intrinsic_unary(builder
, intrinsic
, bld
->vec_type
, a
);
2200 return lp_build_rcp(bld
, lp_build_sqrt(bld
, a
));
2205 * Generate sin(a) using SSE2
2208 lp_build_sin(struct lp_build_context
*bld
,
2211 struct gallivm_state
*gallivm
= bld
->gallivm
;
2212 LLVMBuilderRef builder
= gallivm
->builder
;
2213 struct lp_type int_type
= lp_int_type(bld
->type
);
2214 LLVMBuilderRef b
= builder
;
2217 * take the absolute value,
2218 * x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
2221 LLVMValueRef inv_sig_mask
= lp_build_const_int_vec(gallivm
, bld
->type
, ~0x80000000);
2222 LLVMValueRef a_v4si
= LLVMBuildBitCast(b
, a
, bld
->int_vec_type
, "a_v4si");
2224 LLVMValueRef absi
= LLVMBuildAnd(b
, a_v4si
, inv_sig_mask
, "absi");
2225 LLVMValueRef x_abs
= LLVMBuildBitCast(b
, absi
, bld
->vec_type
, "x_abs");
2228 * extract the sign bit (upper one)
2229 * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
2231 LLVMValueRef sig_mask
= lp_build_const_int_vec(gallivm
, bld
->type
, 0x80000000);
2232 LLVMValueRef sign_bit_i
= LLVMBuildAnd(b
, a_v4si
, sig_mask
, "sign_bit_i");
2236 * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
2239 LLVMValueRef FOPi
= lp_build_const_vec(gallivm
, bld
->type
, 1.27323954473516);
2240 LLVMValueRef scale_y
= LLVMBuildFMul(b
, x_abs
, FOPi
, "scale_y");
2243 * store the integer part of y in mm0
2244 * emm2 = _mm_cvttps_epi32(y);
2247 LLVMValueRef emm2_i
= LLVMBuildFPToSI(b
, scale_y
, bld
->int_vec_type
, "emm2_i");
2250 * j=(j+1) & (~1) (see the cephes sources)
2251 * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
2254 LLVMValueRef all_one
= lp_build_const_int_vec(gallivm
, bld
->type
, 1);
2255 LLVMValueRef emm2_add
= LLVMBuildAdd(b
, emm2_i
, all_one
, "emm2_add");
2257 * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
2259 LLVMValueRef inv_one
= lp_build_const_int_vec(gallivm
, bld
->type
, ~1);
2260 LLVMValueRef emm2_and
= LLVMBuildAnd(b
, emm2_add
, inv_one
, "emm2_and");
2263 * y = _mm_cvtepi32_ps(emm2);
2265 LLVMValueRef y_2
= LLVMBuildSIToFP(b
, emm2_and
, bld
->vec_type
, "y_2");
2267 /* get the swap sign flag
2268 * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
2270 LLVMValueRef pi32_4
= lp_build_const_int_vec(gallivm
, bld
->type
, 4);
2271 LLVMValueRef emm0_and
= LLVMBuildAnd(b
, emm2_add
, pi32_4
, "emm0_and");
2274 * emm2 = _mm_slli_epi32(emm0, 29);
2276 LLVMValueRef const_29
= lp_build_const_int_vec(gallivm
, bld
->type
, 29);
2277 LLVMValueRef swap_sign_bit
= LLVMBuildShl(b
, emm0_and
, const_29
, "swap_sign_bit");
2280 * get the polynom selection mask
2281 * there is one polynom for 0 <= x <= Pi/4
2282 * and another one for Pi/4<x<=Pi/2
2283 * Both branches will be computed.
2285 * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
2286 * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
2289 LLVMValueRef pi32_2
= lp_build_const_int_vec(gallivm
, bld
->type
, 2);
2290 LLVMValueRef emm2_3
= LLVMBuildAnd(b
, emm2_and
, pi32_2
, "emm2_3");
2291 LLVMValueRef poly_mask
= lp_build_compare(gallivm
,
2292 int_type
, PIPE_FUNC_EQUAL
,
2293 emm2_3
, lp_build_const_int_vec(gallivm
, bld
->type
, 0));
2295 * sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
2297 LLVMValueRef sign_bit_1
= LLVMBuildXor(b
, sign_bit_i
, swap_sign_bit
, "sign_bit");
2300 * _PS_CONST(minus_cephes_DP1, -0.78515625);
2301 * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
2302 * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
2304 LLVMValueRef DP1
= lp_build_const_vec(gallivm
, bld
->type
, -0.78515625);
2305 LLVMValueRef DP2
= lp_build_const_vec(gallivm
, bld
->type
, -2.4187564849853515625e-4);
2306 LLVMValueRef DP3
= lp_build_const_vec(gallivm
, bld
->type
, -3.77489497744594108e-8);
2309 * The magic pass: "Extended precision modular arithmetic"
2310 * x = ((x - y * DP1) - y * DP2) - y * DP3;
2311 * xmm1 = _mm_mul_ps(y, xmm1);
2312 * xmm2 = _mm_mul_ps(y, xmm2);
2313 * xmm3 = _mm_mul_ps(y, xmm3);
2315 LLVMValueRef xmm1
= LLVMBuildFMul(b
, y_2
, DP1
, "xmm1");
2316 LLVMValueRef xmm2
= LLVMBuildFMul(b
, y_2
, DP2
, "xmm2");
2317 LLVMValueRef xmm3
= LLVMBuildFMul(b
, y_2
, DP3
, "xmm3");
2320 * x = _mm_add_ps(x, xmm1);
2321 * x = _mm_add_ps(x, xmm2);
2322 * x = _mm_add_ps(x, xmm3);
2325 LLVMValueRef x_1
= LLVMBuildFAdd(b
, x_abs
, xmm1
, "x_1");
2326 LLVMValueRef x_2
= LLVMBuildFAdd(b
, x_1
, xmm2
, "x_2");
2327 LLVMValueRef x_3
= LLVMBuildFAdd(b
, x_2
, xmm3
, "x_3");
2330 * Evaluate the first polynom (0 <= x <= Pi/4)
2332 * z = _mm_mul_ps(x,x);
2334 LLVMValueRef z
= LLVMBuildFMul(b
, x_3
, x_3
, "z");
2337 * _PS_CONST(coscof_p0, 2.443315711809948E-005);
2338 * _PS_CONST(coscof_p1, -1.388731625493765E-003);
2339 * _PS_CONST(coscof_p2, 4.166664568298827E-002);
2341 LLVMValueRef coscof_p0
= lp_build_const_vec(gallivm
, bld
->type
, 2.443315711809948E-005);
2342 LLVMValueRef coscof_p1
= lp_build_const_vec(gallivm
, bld
->type
, -1.388731625493765E-003);
2343 LLVMValueRef coscof_p2
= lp_build_const_vec(gallivm
, bld
->type
, 4.166664568298827E-002);
2346 * y = *(v4sf*)_ps_coscof_p0;
2347 * y = _mm_mul_ps(y, z);
2349 LLVMValueRef y_3
= LLVMBuildFMul(b
, z
, coscof_p0
, "y_3");
2350 LLVMValueRef y_4
= LLVMBuildFAdd(b
, y_3
, coscof_p1
, "y_4");
2351 LLVMValueRef y_5
= LLVMBuildFMul(b
, y_4
, z
, "y_5");
2352 LLVMValueRef y_6
= LLVMBuildFAdd(b
, y_5
, coscof_p2
, "y_6");
2353 LLVMValueRef y_7
= LLVMBuildFMul(b
, y_6
, z
, "y_7");
2354 LLVMValueRef y_8
= LLVMBuildFMul(b
, y_7
, z
, "y_8");
2358 * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
2359 * y = _mm_sub_ps(y, tmp);
2360 * y = _mm_add_ps(y, *(v4sf*)_ps_1);
2362 LLVMValueRef half
= lp_build_const_vec(gallivm
, bld
->type
, 0.5);
2363 LLVMValueRef tmp
= LLVMBuildFMul(b
, z
, half
, "tmp");
2364 LLVMValueRef y_9
= LLVMBuildFSub(b
, y_8
, tmp
, "y_8");
2365 LLVMValueRef one
= lp_build_const_vec(gallivm
, bld
->type
, 1.0);
2366 LLVMValueRef y_10
= LLVMBuildFAdd(b
, y_9
, one
, "y_9");
2369 * _PS_CONST(sincof_p0, -1.9515295891E-4);
2370 * _PS_CONST(sincof_p1, 8.3321608736E-3);
2371 * _PS_CONST(sincof_p2, -1.6666654611E-1);
2373 LLVMValueRef sincof_p0
= lp_build_const_vec(gallivm
, bld
->type
, -1.9515295891E-4);
2374 LLVMValueRef sincof_p1
= lp_build_const_vec(gallivm
, bld
->type
, 8.3321608736E-3);
2375 LLVMValueRef sincof_p2
= lp_build_const_vec(gallivm
, bld
->type
, -1.6666654611E-1);
2378 * Evaluate the second polynom (Pi/4 <= x <= 0)
2380 * y2 = *(v4sf*)_ps_sincof_p0;
2381 * y2 = _mm_mul_ps(y2, z);
2382 * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
2383 * y2 = _mm_mul_ps(y2, z);
2384 * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
2385 * y2 = _mm_mul_ps(y2, z);
2386 * y2 = _mm_mul_ps(y2, x);
2387 * y2 = _mm_add_ps(y2, x);
2390 LLVMValueRef y2_3
= LLVMBuildFMul(b
, z
, sincof_p0
, "y2_3");
2391 LLVMValueRef y2_4
= LLVMBuildFAdd(b
, y2_3
, sincof_p1
, "y2_4");
2392 LLVMValueRef y2_5
= LLVMBuildFMul(b
, y2_4
, z
, "y2_5");
2393 LLVMValueRef y2_6
= LLVMBuildFAdd(b
, y2_5
, sincof_p2
, "y2_6");
2394 LLVMValueRef y2_7
= LLVMBuildFMul(b
, y2_6
, z
, "y2_7");
2395 LLVMValueRef y2_8
= LLVMBuildFMul(b
, y2_7
, x_3
, "y2_8");
2396 LLVMValueRef y2_9
= LLVMBuildFAdd(b
, y2_8
, x_3
, "y2_9");
2399 * select the correct result from the two polynoms
2401 * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
2402 * y = _mm_andnot_ps(xmm3, y);
2403 * y = _mm_add_ps(y,y2);
2405 LLVMValueRef y2_i
= LLVMBuildBitCast(b
, y2_9
, bld
->int_vec_type
, "y2_i");
2406 LLVMValueRef y_i
= LLVMBuildBitCast(b
, y_10
, bld
->int_vec_type
, "y_i");
2407 LLVMValueRef y2_and
= LLVMBuildAnd(b
, y2_i
, poly_mask
, "y2_and");
2408 LLVMValueRef inv
= lp_build_const_int_vec(gallivm
, bld
->type
, ~0);
2409 LLVMValueRef poly_mask_inv
= LLVMBuildXor(b
, poly_mask
, inv
, "poly_mask_inv");
2410 LLVMValueRef y_and
= LLVMBuildAnd(b
, y_i
, poly_mask_inv
, "y_and");
2411 LLVMValueRef y_combine
= LLVMBuildAdd(b
, y_and
, y2_and
, "y_combine");
2415 * y = _mm_xor_ps(y, sign_bit);
2417 LLVMValueRef y_sign
= LLVMBuildXor(b
, y_combine
, sign_bit_1
, "y_sin");
2418 LLVMValueRef y_result
= LLVMBuildBitCast(b
, y_sign
, bld
->vec_type
, "y_result");
2424 * Generate cos(a) using SSE2
2427 lp_build_cos(struct lp_build_context
*bld
,
2430 struct gallivm_state
*gallivm
= bld
->gallivm
;
2431 LLVMBuilderRef builder
= gallivm
->builder
;
2432 struct lp_type int_type
= lp_int_type(bld
->type
);
2433 LLVMBuilderRef b
= builder
;
2436 * take the absolute value,
2437 * x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
2440 LLVMValueRef inv_sig_mask
= lp_build_const_int_vec(gallivm
, bld
->type
, ~0x80000000);
2441 LLVMValueRef a_v4si
= LLVMBuildBitCast(b
, a
, bld
->int_vec_type
, "a_v4si");
2443 LLVMValueRef absi
= LLVMBuildAnd(b
, a_v4si
, inv_sig_mask
, "absi");
2444 LLVMValueRef x_abs
= LLVMBuildBitCast(b
, absi
, bld
->vec_type
, "x_abs");
2448 * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
2451 LLVMValueRef FOPi
= lp_build_const_vec(gallivm
, bld
->type
, 1.27323954473516);
2452 LLVMValueRef scale_y
= LLVMBuildFMul(b
, x_abs
, FOPi
, "scale_y");
2455 * store the integer part of y in mm0
2456 * emm2 = _mm_cvttps_epi32(y);
2459 LLVMValueRef emm2_i
= LLVMBuildFPToSI(b
, scale_y
, bld
->int_vec_type
, "emm2_i");
2462 * j=(j+1) & (~1) (see the cephes sources)
2463 * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
2466 LLVMValueRef all_one
= lp_build_const_int_vec(gallivm
, bld
->type
, 1);
2467 LLVMValueRef emm2_add
= LLVMBuildAdd(b
, emm2_i
, all_one
, "emm2_add");
2469 * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
2471 LLVMValueRef inv_one
= lp_build_const_int_vec(gallivm
, bld
->type
, ~1);
2472 LLVMValueRef emm2_and
= LLVMBuildAnd(b
, emm2_add
, inv_one
, "emm2_and");
2475 * y = _mm_cvtepi32_ps(emm2);
2477 LLVMValueRef y_2
= LLVMBuildSIToFP(b
, emm2_and
, bld
->vec_type
, "y_2");
2481 * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
2483 LLVMValueRef const_2
= lp_build_const_int_vec(gallivm
, bld
->type
, 2);
2484 LLVMValueRef emm2_2
= LLVMBuildSub(b
, emm2_and
, const_2
, "emm2_2");
2487 /* get the swap sign flag
2488 * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
2490 LLVMValueRef inv
= lp_build_const_int_vec(gallivm
, bld
->type
, ~0);
2491 LLVMValueRef emm0_not
= LLVMBuildXor(b
, emm2_2
, inv
, "emm0_not");
2492 LLVMValueRef pi32_4
= lp_build_const_int_vec(gallivm
, bld
->type
, 4);
2493 LLVMValueRef emm0_and
= LLVMBuildAnd(b
, emm0_not
, pi32_4
, "emm0_and");
2496 * emm2 = _mm_slli_epi32(emm0, 29);
2498 LLVMValueRef const_29
= lp_build_const_int_vec(gallivm
, bld
->type
, 29);
2499 LLVMValueRef sign_bit
= LLVMBuildShl(b
, emm0_and
, const_29
, "sign_bit");
2502 * get the polynom selection mask
2503 * there is one polynom for 0 <= x <= Pi/4
2504 * and another one for Pi/4<x<=Pi/2
2505 * Both branches will be computed.
2507 * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
2508 * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
2511 LLVMValueRef pi32_2
= lp_build_const_int_vec(gallivm
, bld
->type
, 2);
2512 LLVMValueRef emm2_3
= LLVMBuildAnd(b
, emm2_2
, pi32_2
, "emm2_3");
2513 LLVMValueRef poly_mask
= lp_build_compare(gallivm
,
2514 int_type
, PIPE_FUNC_EQUAL
,
2515 emm2_3
, lp_build_const_int_vec(gallivm
, bld
->type
, 0));
2518 * _PS_CONST(minus_cephes_DP1, -0.78515625);
2519 * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
2520 * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
2522 LLVMValueRef DP1
= lp_build_const_vec(gallivm
, bld
->type
, -0.78515625);
2523 LLVMValueRef DP2
= lp_build_const_vec(gallivm
, bld
->type
, -2.4187564849853515625e-4);
2524 LLVMValueRef DP3
= lp_build_const_vec(gallivm
, bld
->type
, -3.77489497744594108e-8);
2527 * The magic pass: "Extended precision modular arithmetic"
2528 * x = ((x - y * DP1) - y * DP2) - y * DP3;
2529 * xmm1 = _mm_mul_ps(y, xmm1);
2530 * xmm2 = _mm_mul_ps(y, xmm2);
2531 * xmm3 = _mm_mul_ps(y, xmm3);
2533 LLVMValueRef xmm1
= LLVMBuildFMul(b
, y_2
, DP1
, "xmm1");
2534 LLVMValueRef xmm2
= LLVMBuildFMul(b
, y_2
, DP2
, "xmm2");
2535 LLVMValueRef xmm3
= LLVMBuildFMul(b
, y_2
, DP3
, "xmm3");
2538 * x = _mm_add_ps(x, xmm1);
2539 * x = _mm_add_ps(x, xmm2);
2540 * x = _mm_add_ps(x, xmm3);
2543 LLVMValueRef x_1
= LLVMBuildFAdd(b
, x_abs
, xmm1
, "x_1");
2544 LLVMValueRef x_2
= LLVMBuildFAdd(b
, x_1
, xmm2
, "x_2");
2545 LLVMValueRef x_3
= LLVMBuildFAdd(b
, x_2
, xmm3
, "x_3");
2548 * Evaluate the first polynom (0 <= x <= Pi/4)
2550 * z = _mm_mul_ps(x,x);
2552 LLVMValueRef z
= LLVMBuildFMul(b
, x_3
, x_3
, "z");
2555 * _PS_CONST(coscof_p0, 2.443315711809948E-005);
2556 * _PS_CONST(coscof_p1, -1.388731625493765E-003);
2557 * _PS_CONST(coscof_p2, 4.166664568298827E-002);
2559 LLVMValueRef coscof_p0
= lp_build_const_vec(gallivm
, bld
->type
, 2.443315711809948E-005);
2560 LLVMValueRef coscof_p1
= lp_build_const_vec(gallivm
, bld
->type
, -1.388731625493765E-003);
2561 LLVMValueRef coscof_p2
= lp_build_const_vec(gallivm
, bld
->type
, 4.166664568298827E-002);
2564 * y = *(v4sf*)_ps_coscof_p0;
2565 * y = _mm_mul_ps(y, z);
2567 LLVMValueRef y_3
= LLVMBuildFMul(b
, z
, coscof_p0
, "y_3");
2568 LLVMValueRef y_4
= LLVMBuildFAdd(b
, y_3
, coscof_p1
, "y_4");
2569 LLVMValueRef y_5
= LLVMBuildFMul(b
, y_4
, z
, "y_5");
2570 LLVMValueRef y_6
= LLVMBuildFAdd(b
, y_5
, coscof_p2
, "y_6");
2571 LLVMValueRef y_7
= LLVMBuildFMul(b
, y_6
, z
, "y_7");
2572 LLVMValueRef y_8
= LLVMBuildFMul(b
, y_7
, z
, "y_8");
2576 * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
2577 * y = _mm_sub_ps(y, tmp);
2578 * y = _mm_add_ps(y, *(v4sf*)_ps_1);
2580 LLVMValueRef half
= lp_build_const_vec(gallivm
, bld
->type
, 0.5);
2581 LLVMValueRef tmp
= LLVMBuildFMul(b
, z
, half
, "tmp");
2582 LLVMValueRef y_9
= LLVMBuildFSub(b
, y_8
, tmp
, "y_8");
2583 LLVMValueRef one
= lp_build_const_vec(gallivm
, bld
->type
, 1.0);
2584 LLVMValueRef y_10
= LLVMBuildFAdd(b
, y_9
, one
, "y_9");
2587 * _PS_CONST(sincof_p0, -1.9515295891E-4);
2588 * _PS_CONST(sincof_p1, 8.3321608736E-3);
2589 * _PS_CONST(sincof_p2, -1.6666654611E-1);
2591 LLVMValueRef sincof_p0
= lp_build_const_vec(gallivm
, bld
->type
, -1.9515295891E-4);
2592 LLVMValueRef sincof_p1
= lp_build_const_vec(gallivm
, bld
->type
, 8.3321608736E-3);
2593 LLVMValueRef sincof_p2
= lp_build_const_vec(gallivm
, bld
->type
, -1.6666654611E-1);
2596 * Evaluate the second polynom (Pi/4 <= x <= 0)
2598 * y2 = *(v4sf*)_ps_sincof_p0;
2599 * y2 = _mm_mul_ps(y2, z);
2600 * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
2601 * y2 = _mm_mul_ps(y2, z);
2602 * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
2603 * y2 = _mm_mul_ps(y2, z);
2604 * y2 = _mm_mul_ps(y2, x);
2605 * y2 = _mm_add_ps(y2, x);
2608 LLVMValueRef y2_3
= LLVMBuildFMul(b
, z
, sincof_p0
, "y2_3");
2609 LLVMValueRef y2_4
= LLVMBuildFAdd(b
, y2_3
, sincof_p1
, "y2_4");
2610 LLVMValueRef y2_5
= LLVMBuildFMul(b
, y2_4
, z
, "y2_5");
2611 LLVMValueRef y2_6
= LLVMBuildFAdd(b
, y2_5
, sincof_p2
, "y2_6");
2612 LLVMValueRef y2_7
= LLVMBuildFMul(b
, y2_6
, z
, "y2_7");
2613 LLVMValueRef y2_8
= LLVMBuildFMul(b
, y2_7
, x_3
, "y2_8");
2614 LLVMValueRef y2_9
= LLVMBuildFAdd(b
, y2_8
, x_3
, "y2_9");
2617 * select the correct result from the two polynoms
2619 * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
2620 * y = _mm_andnot_ps(xmm3, y);
2621 * y = _mm_add_ps(y,y2);
2623 LLVMValueRef y2_i
= LLVMBuildBitCast(b
, y2_9
, bld
->int_vec_type
, "y2_i");
2624 LLVMValueRef y_i
= LLVMBuildBitCast(b
, y_10
, bld
->int_vec_type
, "y_i");
2625 LLVMValueRef y2_and
= LLVMBuildAnd(b
, y2_i
, poly_mask
, "y2_and");
2626 LLVMValueRef poly_mask_inv
= LLVMBuildXor(b
, poly_mask
, inv
, "poly_mask_inv");
2627 LLVMValueRef y_and
= LLVMBuildAnd(b
, y_i
, poly_mask_inv
, "y_and");
2628 LLVMValueRef y_combine
= LLVMBuildAdd(b
, y_and
, y2_and
, "y_combine");
2632 * y = _mm_xor_ps(y, sign_bit);
2634 LLVMValueRef y_sign
= LLVMBuildXor(b
, y_combine
, sign_bit
, "y_sin");
2635 LLVMValueRef y_result
= LLVMBuildBitCast(b
, y_sign
, bld
->vec_type
, "y_result");
2641 * Generate pow(x, y)
2644 lp_build_pow(struct lp_build_context
*bld
,
2648 /* TODO: optimize the constant case */
2649 if (gallivm_debug
& GALLIVM_DEBUG_PERF
&&
2650 LLVMIsConstant(x
) && LLVMIsConstant(y
)) {
2651 debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2655 return lp_build_exp2(bld
, lp_build_mul(bld
, lp_build_log2(bld
, x
), y
));
2663 lp_build_exp(struct lp_build_context
*bld
,
2666 /* log2(e) = 1/log(2) */
2667 LLVMValueRef log2e
= lp_build_const_vec(bld
->gallivm
, bld
->type
,
2668 1.4426950408889634);
2670 assert(lp_check_value(bld
->type
, x
));
2672 return lp_build_exp2(bld
, lp_build_mul(bld
, log2e
, x
));
2680 lp_build_log(struct lp_build_context
*bld
,
2684 LLVMValueRef log2
= lp_build_const_vec(bld
->gallivm
, bld
->type
,
2685 0.69314718055994529);
2687 assert(lp_check_value(bld
->type
, x
));
2689 return lp_build_mul(bld
, log2
, lp_build_log2(bld
, x
));
2694 * Generate polynomial.
2695 * Ex: coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
2698 lp_build_polynomial(struct lp_build_context
*bld
,
2700 const double *coeffs
,
2701 unsigned num_coeffs
)
2703 const struct lp_type type
= bld
->type
;
2704 LLVMValueRef even
= NULL
, odd
= NULL
;
2708 assert(lp_check_value(bld
->type
, x
));
2710 /* TODO: optimize the constant case */
2711 if (gallivm_debug
& GALLIVM_DEBUG_PERF
&&
2712 LLVMIsConstant(x
)) {
2713 debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2718 * Calculate odd and even terms seperately to decrease data dependency
2720 * c[0] + x^2 * c[2] + x^4 * c[4] ...
2721 * + x * (c[1] + x^2 * c[3] + x^4 * c[5]) ...
2723 x2
= lp_build_mul(bld
, x
, x
);
2725 for (i
= num_coeffs
; i
--; ) {
2728 coeff
= lp_build_const_vec(bld
->gallivm
, type
, coeffs
[i
]);
2732 even
= lp_build_add(bld
, coeff
, lp_build_mul(bld
, x2
, even
));
2737 odd
= lp_build_add(bld
, coeff
, lp_build_mul(bld
, x2
, odd
));
2744 return lp_build_add(bld
, lp_build_mul(bld
, odd
, x
), even
);
2753 * Minimax polynomial fit of 2**x, in range [0, 1[
2755 const double lp_build_exp2_polynomial
[] = {
2756 #if EXP_POLY_DEGREE == 5
2757 0.999999925063526176901,
2758 0.693153073200168932794,
2759 0.240153617044375388211,
2760 0.0558263180532956664775,
2761 0.00898934009049466391101,
2762 0.00187757667519147912699
2763 #elif EXP_POLY_DEGREE == 4
2764 1.00000259337069434683,
2765 0.693003834469974940458,
2766 0.24144275689150793076,
2767 0.0520114606103070150235,
2768 0.0135341679161270268764
2769 #elif EXP_POLY_DEGREE == 3
2770 0.999925218562710312959,
2771 0.695833540494823811697,
2772 0.226067155427249155588,
2773 0.0780245226406372992967
2774 #elif EXP_POLY_DEGREE == 2
2775 1.00172476321474503578,
2776 0.657636275736077639316,
2777 0.33718943461968720704
2785 lp_build_exp2_approx(struct lp_build_context
*bld
,
2787 LLVMValueRef
*p_exp2_int_part
,
2788 LLVMValueRef
*p_frac_part
,
2789 LLVMValueRef
*p_exp2
)
2791 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
2792 const struct lp_type type
= bld
->type
;
2793 LLVMTypeRef vec_type
= lp_build_vec_type(bld
->gallivm
, type
);
2794 LLVMValueRef ipart
= NULL
;
2795 LLVMValueRef fpart
= NULL
;
2796 LLVMValueRef expipart
= NULL
;
2797 LLVMValueRef expfpart
= NULL
;
2798 LLVMValueRef res
= NULL
;
2800 assert(lp_check_value(bld
->type
, x
));
2802 if(p_exp2_int_part
|| p_frac_part
|| p_exp2
) {
2803 /* TODO: optimize the constant case */
2804 if (gallivm_debug
& GALLIVM_DEBUG_PERF
&&
2805 LLVMIsConstant(x
)) {
2806 debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2810 assert(type
.floating
&& type
.width
== 32);
2812 x
= lp_build_min(bld
, x
, lp_build_const_vec(bld
->gallivm
, type
, 129.0));
2813 x
= lp_build_max(bld
, x
, lp_build_const_vec(bld
->gallivm
, type
, -126.99999));
2815 /* ipart = floor(x) */
2816 /* fpart = x - ipart */
2817 lp_build_ifloor_fract(bld
, x
, &ipart
, &fpart
);
2820 if(p_exp2_int_part
|| p_exp2
) {
2821 /* expipart = (float) (1 << ipart) */
2822 expipart
= LLVMBuildAdd(builder
, ipart
,
2823 lp_build_const_int_vec(bld
->gallivm
, type
, 127), "");
2824 expipart
= LLVMBuildShl(builder
, expipart
,
2825 lp_build_const_int_vec(bld
->gallivm
, type
, 23), "");
2826 expipart
= LLVMBuildBitCast(builder
, expipart
, vec_type
, "");
2830 expfpart
= lp_build_polynomial(bld
, fpart
, lp_build_exp2_polynomial
,
2831 Elements(lp_build_exp2_polynomial
));
2833 res
= LLVMBuildFMul(builder
, expipart
, expfpart
, "");
2837 *p_exp2_int_part
= expipart
;
2840 *p_frac_part
= fpart
;
2848 lp_build_exp2(struct lp_build_context
*bld
,
2852 lp_build_exp2_approx(bld
, x
, NULL
, NULL
, &res
);
2858 * Extract the exponent of a IEEE-754 floating point value.
2860 * Optionally apply an integer bias.
2862 * Result is an integer value with
2864 * ifloor(log2(x)) + bias
2867 lp_build_extract_exponent(struct lp_build_context
*bld
,
2871 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
2872 const struct lp_type type
= bld
->type
;
2873 unsigned mantissa
= lp_mantissa(type
);
2876 assert(type
.floating
);
2878 assert(lp_check_value(bld
->type
, x
));
2880 x
= LLVMBuildBitCast(builder
, x
, bld
->int_vec_type
, "");
2882 res
= LLVMBuildLShr(builder
, x
,
2883 lp_build_const_int_vec(bld
->gallivm
, type
, mantissa
), "");
2884 res
= LLVMBuildAnd(builder
, res
,
2885 lp_build_const_int_vec(bld
->gallivm
, type
, 255), "");
2886 res
= LLVMBuildSub(builder
, res
,
2887 lp_build_const_int_vec(bld
->gallivm
, type
, 127 - bias
), "");
2894 * Extract the mantissa of the a floating.
2896 * Result is a floating point value with
2898 * x / floor(log2(x))
2901 lp_build_extract_mantissa(struct lp_build_context
*bld
,
2904 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
2905 const struct lp_type type
= bld
->type
;
2906 unsigned mantissa
= lp_mantissa(type
);
2907 LLVMValueRef mantmask
= lp_build_const_int_vec(bld
->gallivm
, type
,
2908 (1ULL << mantissa
) - 1);
2909 LLVMValueRef one
= LLVMConstBitCast(bld
->one
, bld
->int_vec_type
);
2912 assert(lp_check_value(bld
->type
, x
));
2914 assert(type
.floating
);
2916 x
= LLVMBuildBitCast(builder
, x
, bld
->int_vec_type
, "");
2918 /* res = x / 2**ipart */
2919 res
= LLVMBuildAnd(builder
, x
, mantmask
, "");
2920 res
= LLVMBuildOr(builder
, res
, one
, "");
2921 res
= LLVMBuildBitCast(builder
, res
, bld
->vec_type
, "");
2929 * Minimax polynomial fit of log2((1.0 + sqrt(x))/(1.0 - sqrt(x)))/sqrt(x) ,for x in range of [0, 1/9[
2930 * These coefficients can be generate with
2931 * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
2933 const double lp_build_log2_polynomial
[] = {
2934 #if LOG_POLY_DEGREE == 5
2935 2.88539008148777786488L,
2936 0.961796878841293367824L,
2937 0.577058946784739859012L,
2938 0.412914355135828735411L,
2939 0.308591899232910175289L,
2940 0.352376952300281371868L,
2941 #elif LOG_POLY_DEGREE == 4
2942 2.88539009343309178325L,
2943 0.961791550404184197881L,
2944 0.577440339438736392009L,
2945 0.403343858251329912514L,
2946 0.406718052498846252698L,
2947 #elif LOG_POLY_DEGREE == 3
2948 2.88538959748872753838L,
2949 0.961932915889597772928L,
2950 0.571118517972136195241L,
2951 0.493997535084709500285L,
2958 * See http://www.devmaster.net/forums/showthread.php?p=43580
2959 * http://en.wikipedia.org/wiki/Logarithm#Calculation
2960 * http://www.nezumi.demon.co.uk/consult/logx.htm
2963 lp_build_log2_approx(struct lp_build_context
*bld
,
2965 LLVMValueRef
*p_exp
,
2966 LLVMValueRef
*p_floor_log2
,
2967 LLVMValueRef
*p_log2
)
2969 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
2970 const struct lp_type type
= bld
->type
;
2971 LLVMTypeRef vec_type
= lp_build_vec_type(bld
->gallivm
, type
);
2972 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(bld
->gallivm
, type
);
2974 LLVMValueRef expmask
= lp_build_const_int_vec(bld
->gallivm
, type
, 0x7f800000);
2975 LLVMValueRef mantmask
= lp_build_const_int_vec(bld
->gallivm
, type
, 0x007fffff);
2976 LLVMValueRef one
= LLVMConstBitCast(bld
->one
, int_vec_type
);
2978 LLVMValueRef i
= NULL
;
2979 LLVMValueRef y
= NULL
;
2980 LLVMValueRef z
= NULL
;
2981 LLVMValueRef exp
= NULL
;
2982 LLVMValueRef mant
= NULL
;
2983 LLVMValueRef logexp
= NULL
;
2984 LLVMValueRef logmant
= NULL
;
2985 LLVMValueRef res
= NULL
;
2987 assert(lp_check_value(bld
->type
, x
));
2989 if(p_exp
|| p_floor_log2
|| p_log2
) {
2990 /* TODO: optimize the constant case */
2991 if (gallivm_debug
& GALLIVM_DEBUG_PERF
&&
2992 LLVMIsConstant(x
)) {
2993 debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2997 assert(type
.floating
&& type
.width
== 32);
3000 * We don't explicitly handle denormalized numbers. They will yield a
3001 * result in the neighbourhood of -127, which appears to be adequate
3005 i
= LLVMBuildBitCast(builder
, x
, int_vec_type
, "");
3007 /* exp = (float) exponent(x) */
3008 exp
= LLVMBuildAnd(builder
, i
, expmask
, "");
3011 if(p_floor_log2
|| p_log2
) {
3012 logexp
= LLVMBuildLShr(builder
, exp
, lp_build_const_int_vec(bld
->gallivm
, type
, 23), "");
3013 logexp
= LLVMBuildSub(builder
, logexp
, lp_build_const_int_vec(bld
->gallivm
, type
, 127), "");
3014 logexp
= LLVMBuildSIToFP(builder
, logexp
, vec_type
, "");
3018 /* mant = 1 + (float) mantissa(x) */
3019 mant
= LLVMBuildAnd(builder
, i
, mantmask
, "");
3020 mant
= LLVMBuildOr(builder
, mant
, one
, "");
3021 mant
= LLVMBuildBitCast(builder
, mant
, vec_type
, "");
3023 /* y = (mant - 1) / (mant + 1) */
3024 y
= lp_build_div(bld
,
3025 lp_build_sub(bld
, mant
, bld
->one
),
3026 lp_build_add(bld
, mant
, bld
->one
)
3030 z
= lp_build_mul(bld
, y
, y
);
3033 logmant
= lp_build_polynomial(bld
, z
, lp_build_log2_polynomial
,
3034 Elements(lp_build_log2_polynomial
));
3036 /* logmant = y * P(z) */
3037 logmant
= lp_build_mul(bld
, y
, logmant
);
3039 res
= lp_build_add(bld
, logmant
, logexp
);
3043 exp
= LLVMBuildBitCast(builder
, exp
, vec_type
, "");
3048 *p_floor_log2
= logexp
;
3056 lp_build_log2(struct lp_build_context
*bld
,
3060 lp_build_log2_approx(bld
, x
, NULL
, NULL
, &res
);
3066 * Faster (and less accurate) log2.
3068 * log2(x) = floor(log2(x)) - 1 + x / 2**floor(log2(x))
3070 * Piece-wise linear approximation, with exact results when x is a
3073 * See http://www.flipcode.com/archives/Fast_log_Function.shtml
3076 lp_build_fast_log2(struct lp_build_context
*bld
,
3079 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
3083 assert(lp_check_value(bld
->type
, x
));
3085 assert(bld
->type
.floating
);
3087 /* ipart = floor(log2(x)) - 1 */
3088 ipart
= lp_build_extract_exponent(bld
, x
, -1);
3089 ipart
= LLVMBuildSIToFP(builder
, ipart
, bld
->vec_type
, "");
3091 /* fpart = x / 2**ipart */
3092 fpart
= lp_build_extract_mantissa(bld
, x
);
3095 return LLVMBuildFAdd(builder
, ipart
, fpart
, "");
3100 * Fast implementation of iround(log2(x)).
3102 * Not an approximation -- it should give accurate results all the time.
3105 lp_build_ilog2(struct lp_build_context
*bld
,
3108 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
3109 LLVMValueRef sqrt2
= lp_build_const_vec(bld
->gallivm
, bld
->type
, M_SQRT2
);
3112 assert(bld
->type
.floating
);
3114 assert(lp_check_value(bld
->type
, x
));
3116 /* x * 2^(0.5) i.e., add 0.5 to the log2(x) */
3117 x
= LLVMBuildFMul(builder
, x
, sqrt2
, "");
3119 /* ipart = floor(log2(x) + 0.5) */
3120 ipart
= lp_build_extract_exponent(bld
, x
, 0);
3126 lp_build_mod(struct lp_build_context
*bld
,
3130 LLVMBuilderRef builder
= bld
->gallivm
->builder
;
3132 const struct lp_type type
= bld
->type
;
3134 assert(lp_check_value(type
, x
));
3135 assert(lp_check_value(type
, y
));
3138 res
= LLVMBuildFRem(builder
, x
, y
, "");
3140 res
= LLVMBuildSRem(builder
, x
, y
, "");
3142 res
= LLVMBuildURem(builder
, x
, y
, "");