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>
48 #include "util/u_memory.h"
49 #include "util/u_debug.h"
50 #include "util/u_math.h"
51 #include "util/u_string.h"
52 #include "util/u_cpu_detect.h"
54 #include "lp_bld_type.h"
55 #include "lp_bld_const.h"
56 #include "lp_bld_intr.h"
57 #include "lp_bld_logic.h"
58 #include "lp_bld_pack.h"
59 #include "lp_bld_debug.h"
60 #include "lp_bld_arit.h"
63 #define EXP_POLY_DEGREE 3
65 #define LOG_POLY_DEGREE 5
70 * No checks for special case values of a or b = 1 or 0 are done.
73 lp_build_min_simple(struct lp_build_context
*bld
,
77 const struct lp_type type
= bld
->type
;
78 const char *intrinsic
= NULL
;
81 assert(lp_check_value(type
, a
));
82 assert(lp_check_value(type
, b
));
84 /* TODO: optimize the constant case */
86 if(type
.width
* type
.length
== 128) {
88 if(type
.width
== 32 && util_cpu_caps
.has_sse
)
89 intrinsic
= "llvm.x86.sse.min.ps";
90 if(type
.width
== 64 && util_cpu_caps
.has_sse2
)
91 intrinsic
= "llvm.x86.sse2.min.pd";
94 if(type
.width
== 8 && !type
.sign
&& util_cpu_caps
.has_sse2
)
95 intrinsic
= "llvm.x86.sse2.pminu.b";
96 if(type
.width
== 8 && type
.sign
&& util_cpu_caps
.has_sse4_1
)
97 intrinsic
= "llvm.x86.sse41.pminsb";
98 if(type
.width
== 16 && !type
.sign
&& util_cpu_caps
.has_sse4_1
)
99 intrinsic
= "llvm.x86.sse41.pminuw";
100 if(type
.width
== 16 && type
.sign
&& util_cpu_caps
.has_sse2
)
101 intrinsic
= "llvm.x86.sse2.pmins.w";
102 if(type
.width
== 32 && !type
.sign
&& util_cpu_caps
.has_sse4_1
)
103 intrinsic
= "llvm.x86.sse41.pminud";
104 if(type
.width
== 32 && type
.sign
&& util_cpu_caps
.has_sse4_1
)
105 intrinsic
= "llvm.x86.sse41.pminsd";
110 return lp_build_intrinsic_binary(bld
->builder
, intrinsic
, lp_build_vec_type(bld
->type
), a
, b
);
112 cond
= lp_build_cmp(bld
, PIPE_FUNC_LESS
, a
, b
);
113 return lp_build_select(bld
, cond
, a
, b
);
119 * No checks for special case values of a or b = 1 or 0 are done.
122 lp_build_max_simple(struct lp_build_context
*bld
,
126 const struct lp_type type
= bld
->type
;
127 const char *intrinsic
= NULL
;
130 assert(lp_check_value(type
, a
));
131 assert(lp_check_value(type
, b
));
133 /* TODO: optimize the constant case */
135 if(type
.width
* type
.length
== 128) {
137 if(type
.width
== 32 && util_cpu_caps
.has_sse
)
138 intrinsic
= "llvm.x86.sse.max.ps";
139 if(type
.width
== 64 && util_cpu_caps
.has_sse2
)
140 intrinsic
= "llvm.x86.sse2.max.pd";
143 if(type
.width
== 8 && !type
.sign
&& util_cpu_caps
.has_sse2
)
144 intrinsic
= "llvm.x86.sse2.pmaxu.b";
145 if(type
.width
== 8 && type
.sign
&& util_cpu_caps
.has_sse4_1
)
146 intrinsic
= "llvm.x86.sse41.pmaxsb";
147 if(type
.width
== 16 && !type
.sign
&& util_cpu_caps
.has_sse4_1
)
148 intrinsic
= "llvm.x86.sse41.pmaxuw";
149 if(type
.width
== 16 && type
.sign
&& util_cpu_caps
.has_sse2
)
150 intrinsic
= "llvm.x86.sse2.pmaxs.w";
151 if(type
.width
== 32 && !type
.sign
&& util_cpu_caps
.has_sse4_1
)
152 intrinsic
= "llvm.x86.sse41.pmaxud";
153 if(type
.width
== 32 && type
.sign
&& util_cpu_caps
.has_sse4_1
)
154 intrinsic
= "llvm.x86.sse41.pmaxsd";
159 return lp_build_intrinsic_binary(bld
->builder
, intrinsic
, lp_build_vec_type(bld
->type
), a
, b
);
161 cond
= lp_build_cmp(bld
, PIPE_FUNC_GREATER
, a
, b
);
162 return lp_build_select(bld
, cond
, a
, b
);
167 * Generate 1 - a, or ~a depending on bld->type.
170 lp_build_comp(struct lp_build_context
*bld
,
173 const struct lp_type type
= bld
->type
;
175 assert(lp_check_value(type
, a
));
182 if(type
.norm
&& !type
.floating
&& !type
.fixed
&& !type
.sign
) {
183 if(LLVMIsConstant(a
))
184 return LLVMConstNot(a
);
186 return LLVMBuildNot(bld
->builder
, a
, "");
189 if(LLVMIsConstant(a
))
191 return LLVMConstFSub(bld
->one
, a
);
193 return LLVMConstSub(bld
->one
, a
);
196 return LLVMBuildFSub(bld
->builder
, bld
->one
, a
, "");
198 return LLVMBuildSub(bld
->builder
, bld
->one
, a
, "");
206 lp_build_add(struct lp_build_context
*bld
,
210 const struct lp_type type
= bld
->type
;
213 assert(lp_check_value(type
, a
));
214 assert(lp_check_value(type
, b
));
220 if(a
== bld
->undef
|| b
== bld
->undef
)
224 const char *intrinsic
= NULL
;
226 if(a
== bld
->one
|| b
== bld
->one
)
229 if(util_cpu_caps
.has_sse2
&&
230 type
.width
* type
.length
== 128 &&
231 !type
.floating
&& !type
.fixed
) {
233 intrinsic
= type
.sign
? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
235 intrinsic
= type
.sign
? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
239 return lp_build_intrinsic_binary(bld
->builder
, intrinsic
, lp_build_vec_type(bld
->type
), a
, b
);
242 if(LLVMIsConstant(a
) && LLVMIsConstant(b
))
244 res
= LLVMConstFAdd(a
, b
);
246 res
= LLVMConstAdd(a
, b
);
249 res
= LLVMBuildFAdd(bld
->builder
, a
, b
, "");
251 res
= LLVMBuildAdd(bld
->builder
, a
, b
, "");
253 /* clamp to ceiling of 1.0 */
254 if(bld
->type
.norm
&& (bld
->type
.floating
|| bld
->type
.fixed
))
255 res
= lp_build_min_simple(bld
, res
, bld
->one
);
257 /* XXX clamp to floor of -1 or 0??? */
263 /** Return the scalar sum of the elements of a */
265 lp_build_sum_vector(struct lp_build_context
*bld
,
268 const struct lp_type type
= bld
->type
;
269 LLVMValueRef index
, res
;
272 assert(lp_check_value(type
, a
));
274 if (type
.length
== 1) {
278 assert(!bld
->type
.norm
);
280 index
= LLVMConstInt(LLVMInt32Type(), 0, 0);
281 res
= LLVMBuildExtractElement(bld
->builder
, a
, index
, "");
283 for (i
= 1; i
< type
.length
; i
++) {
284 index
= LLVMConstInt(LLVMInt32Type(), i
, 0);
286 res
= LLVMBuildFAdd(bld
->builder
, res
,
287 LLVMBuildExtractElement(bld
->builder
,
291 res
= LLVMBuildAdd(bld
->builder
, res
,
292 LLVMBuildExtractElement(bld
->builder
,
305 lp_build_sub(struct lp_build_context
*bld
,
309 const struct lp_type type
= bld
->type
;
312 assert(lp_check_value(type
, a
));
313 assert(lp_check_value(type
, b
));
317 if(a
== bld
->undef
|| b
== bld
->undef
)
323 const char *intrinsic
= NULL
;
328 if(util_cpu_caps
.has_sse2
&&
329 type
.width
* type
.length
== 128 &&
330 !type
.floating
&& !type
.fixed
) {
332 intrinsic
= type
.sign
? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
334 intrinsic
= type
.sign
? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
338 return lp_build_intrinsic_binary(bld
->builder
, intrinsic
, lp_build_vec_type(bld
->type
), a
, b
);
341 if(LLVMIsConstant(a
) && LLVMIsConstant(b
))
343 res
= LLVMConstFSub(a
, b
);
345 res
= LLVMConstSub(a
, b
);
348 res
= LLVMBuildFSub(bld
->builder
, a
, b
, "");
350 res
= LLVMBuildSub(bld
->builder
, a
, b
, "");
352 if(bld
->type
.norm
&& (bld
->type
.floating
|| bld
->type
.fixed
))
353 res
= lp_build_max_simple(bld
, res
, bld
->zero
);
360 * Normalized 8bit multiplication.
364 * makes the following approximation to the division (Sree)
366 * a*b/255 ~= (a*(b + 1)) >> 256
368 * which is the fastest method that satisfies the following OpenGL criteria
370 * 0*0 = 0 and 255*255 = 255
374 * takes the geometric series approximation to the division
376 * t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
378 * in this case just the first two terms to fit in 16bit arithmetic
380 * t/255 ~= (t + (t >> 8)) >> 8
382 * note that just by itself it doesn't satisfies the OpenGL criteria, as
383 * 255*255 = 254, so the special case b = 255 must be accounted or roundoff
386 * - geometric series plus rounding
388 * when using a geometric series division instead of truncating the result
389 * use roundoff in the approximation (Jim Blinn)
391 * t/255 ~= (t + (t >> 8) + 0x80) >> 8
393 * achieving the exact results
395 * @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
396 * ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
397 * @sa Michael Herf, The "double blend trick", May 2000,
398 * http://www.stereopsis.com/doubleblend.html
401 lp_build_mul_u8n(LLVMBuilderRef builder
,
402 struct lp_type i16_type
,
403 LLVMValueRef a
, LLVMValueRef b
)
408 assert(!i16_type
.floating
);
409 assert(lp_check_value(i16_type
, a
));
410 assert(lp_check_value(i16_type
, b
));
412 c8
= lp_build_const_int_vec(i16_type
, 8);
416 /* a*b/255 ~= (a*(b + 1)) >> 256 */
417 b
= LLVMBuildAdd(builder
, b
, lp_build_const_int_vec(i16_type
, 1), "");
418 ab
= LLVMBuildMul(builder
, a
, b
, "");
422 /* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
423 ab
= LLVMBuildMul(builder
, a
, b
, "");
424 ab
= LLVMBuildAdd(builder
, ab
, LLVMBuildLShr(builder
, ab
, c8
, ""), "");
425 ab
= LLVMBuildAdd(builder
, ab
, lp_build_const_int_vec(i16_type
, 0x80), "");
429 ab
= LLVMBuildLShr(builder
, ab
, c8
, "");
439 lp_build_mul(struct lp_build_context
*bld
,
443 const struct lp_type type
= bld
->type
;
447 assert(lp_check_value(type
, a
));
448 assert(lp_check_value(type
, b
));
458 if(a
== bld
->undef
|| b
== bld
->undef
)
461 if(!type
.floating
&& !type
.fixed
&& type
.norm
) {
462 if(type
.width
== 8) {
463 struct lp_type i16_type
= lp_wider_type(type
);
464 LLVMValueRef al
, ah
, bl
, bh
, abl
, abh
, ab
;
466 lp_build_unpack2(bld
->builder
, type
, i16_type
, a
, &al
, &ah
);
467 lp_build_unpack2(bld
->builder
, type
, i16_type
, b
, &bl
, &bh
);
469 /* PMULLW, PSRLW, PADDW */
470 abl
= lp_build_mul_u8n(bld
->builder
, i16_type
, al
, bl
);
471 abh
= lp_build_mul_u8n(bld
->builder
, i16_type
, ah
, bh
);
473 ab
= lp_build_pack2(bld
->builder
, i16_type
, type
, abl
, abh
);
483 shift
= lp_build_const_int_vec(type
, type
.width
/2);
487 if(LLVMIsConstant(a
) && LLVMIsConstant(b
)) {
489 res
= LLVMConstFMul(a
, b
);
491 res
= LLVMConstMul(a
, b
);
494 res
= LLVMConstAShr(res
, shift
);
496 res
= LLVMConstLShr(res
, shift
);
501 res
= LLVMBuildFMul(bld
->builder
, a
, b
, "");
503 res
= LLVMBuildMul(bld
->builder
, a
, b
, "");
506 res
= LLVMBuildAShr(bld
->builder
, res
, shift
, "");
508 res
= LLVMBuildLShr(bld
->builder
, res
, shift
, "");
517 * Small vector x scale multiplication optimization.
520 lp_build_mul_imm(struct lp_build_context
*bld
,
526 assert(lp_check_value(bld
->type
, a
));
535 return lp_build_negate(bld
, a
);
537 if(b
== 2 && bld
->type
.floating
)
538 return lp_build_add(bld
, a
, a
);
540 if(util_is_power_of_two(b
)) {
541 unsigned shift
= ffs(b
) - 1;
543 if(bld
->type
.floating
) {
546 * Power of two multiplication by directly manipulating the mantissa.
548 * XXX: This might not be always faster, it will introduce a small error
549 * for multiplication by zero, and it will produce wrong results
552 unsigned mantissa
= lp_mantissa(bld
->type
);
553 factor
= lp_build_const_int_vec(bld
->type
, (unsigned long long)shift
<< mantissa
);
554 a
= LLVMBuildBitCast(bld
->builder
, a
, lp_build_int_vec_type(bld
->type
), "");
555 a
= LLVMBuildAdd(bld
->builder
, a
, factor
, "");
556 a
= LLVMBuildBitCast(bld
->builder
, a
, lp_build_vec_type(bld
->type
), "");
561 factor
= lp_build_const_vec(bld
->type
, shift
);
562 return LLVMBuildShl(bld
->builder
, a
, factor
, "");
566 factor
= lp_build_const_vec(bld
->type
, (double)b
);
567 return lp_build_mul(bld
, a
, factor
);
575 lp_build_div(struct lp_build_context
*bld
,
579 const struct lp_type type
= bld
->type
;
581 assert(lp_check_value(type
, a
));
582 assert(lp_check_value(type
, b
));
587 return lp_build_rcp(bld
, b
);
592 if(a
== bld
->undef
|| b
== bld
->undef
)
595 if(LLVMIsConstant(a
) && LLVMIsConstant(b
)) {
597 return LLVMConstFDiv(a
, b
);
599 return LLVMConstSDiv(a
, b
);
601 return LLVMConstUDiv(a
, b
);
604 if(util_cpu_caps
.has_sse
&& type
.width
== 32 && type
.length
== 4)
605 return lp_build_mul(bld
, a
, lp_build_rcp(bld
, b
));
608 return LLVMBuildFDiv(bld
->builder
, a
, b
, "");
610 return LLVMBuildSDiv(bld
->builder
, a
, b
, "");
612 return LLVMBuildUDiv(bld
->builder
, a
, b
, "");
617 * Linear interpolation -- without any checks.
619 * @sa http://www.stereopsis.com/doubleblend.html
621 static INLINE LLVMValueRef
622 lp_build_lerp_simple(struct lp_build_context
*bld
,
630 assert(lp_check_value(bld
->type
, x
));
631 assert(lp_check_value(bld
->type
, v0
));
632 assert(lp_check_value(bld
->type
, v1
));
634 delta
= lp_build_sub(bld
, v1
, v0
);
636 res
= lp_build_mul(bld
, x
, delta
);
638 res
= lp_build_add(bld
, v0
, res
);
640 if (bld
->type
.fixed
) {
641 /* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
642 * but it will be wrong for other uses. Basically we need a more
643 * powerful lp_type, capable of further distinguishing the values
644 * interpretation from the value storage. */
645 res
= LLVMBuildAnd(bld
->builder
, res
, lp_build_const_int_vec(bld
->type
, (1 << bld
->type
.width
/2) - 1), "");
653 * Linear interpolation.
656 lp_build_lerp(struct lp_build_context
*bld
,
661 const struct lp_type type
= bld
->type
;
664 assert(lp_check_value(type
, x
));
665 assert(lp_check_value(type
, v0
));
666 assert(lp_check_value(type
, v1
));
669 struct lp_type wide_type
;
670 struct lp_build_context wide_bld
;
671 LLVMValueRef xl
, xh
, v0l
, v0h
, v1l
, v1h
, resl
, resh
;
674 assert(type
.length
>= 2);
678 * Create a wider type, enough to hold the intermediate result of the
681 memset(&wide_type
, 0, sizeof wide_type
);
682 wide_type
.fixed
= TRUE
;
683 wide_type
.width
= type
.width
*2;
684 wide_type
.length
= type
.length
/2;
686 lp_build_context_init(&wide_bld
, bld
->builder
, wide_type
);
688 lp_build_unpack2(bld
->builder
, type
, wide_type
, x
, &xl
, &xh
);
689 lp_build_unpack2(bld
->builder
, type
, wide_type
, v0
, &v0l
, &v0h
);
690 lp_build_unpack2(bld
->builder
, type
, wide_type
, v1
, &v1l
, &v1h
);
693 * Scale x from [0, 255] to [0, 256]
696 shift
= lp_build_const_int_vec(wide_type
, type
.width
- 1);
698 xl
= lp_build_add(&wide_bld
, xl
,
699 LLVMBuildAShr(bld
->builder
, xl
, shift
, ""));
700 xh
= lp_build_add(&wide_bld
, xh
,
701 LLVMBuildAShr(bld
->builder
, xh
, shift
, ""));
707 resl
= lp_build_lerp_simple(&wide_bld
, xl
, v0l
, v1l
);
708 resh
= lp_build_lerp_simple(&wide_bld
, xh
, v0h
, v1h
);
710 res
= lp_build_pack2(bld
->builder
, wide_type
, type
, resl
, resh
);
712 res
= lp_build_lerp_simple(bld
, x
, v0
, v1
);
720 lp_build_lerp_2d(struct lp_build_context
*bld
,
728 LLVMValueRef v0
= lp_build_lerp(bld
, x
, v00
, v01
);
729 LLVMValueRef v1
= lp_build_lerp(bld
, x
, v10
, v11
);
730 return lp_build_lerp(bld
, y
, v0
, v1
);
736 * Do checks for special cases.
739 lp_build_min(struct lp_build_context
*bld
,
743 assert(lp_check_value(bld
->type
, a
));
744 assert(lp_check_value(bld
->type
, b
));
746 if(a
== bld
->undef
|| b
== bld
->undef
)
753 if(a
== bld
->zero
|| b
== bld
->zero
)
761 return lp_build_min_simple(bld
, a
, b
);
767 * Do checks for special cases.
770 lp_build_max(struct lp_build_context
*bld
,
774 assert(lp_check_value(bld
->type
, a
));
775 assert(lp_check_value(bld
->type
, b
));
777 if(a
== bld
->undef
|| b
== bld
->undef
)
784 if(a
== bld
->one
|| b
== bld
->one
)
792 return lp_build_max_simple(bld
, a
, b
);
797 * Generate clamp(a, min, max)
798 * Do checks for special cases.
801 lp_build_clamp(struct lp_build_context
*bld
,
806 assert(lp_check_value(bld
->type
, a
));
807 assert(lp_check_value(bld
->type
, min
));
808 assert(lp_check_value(bld
->type
, max
));
810 a
= lp_build_min(bld
, a
, max
);
811 a
= lp_build_max(bld
, a
, min
);
820 lp_build_abs(struct lp_build_context
*bld
,
823 const struct lp_type type
= bld
->type
;
824 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
826 assert(lp_check_value(type
, a
));
832 /* Mask out the sign bit */
833 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(type
);
834 unsigned long long absMask
= ~(1ULL << (type
.width
- 1));
835 LLVMValueRef mask
= lp_build_const_int_vec(type
, ((unsigned long long) absMask
));
836 a
= LLVMBuildBitCast(bld
->builder
, a
, int_vec_type
, "");
837 a
= LLVMBuildAnd(bld
->builder
, a
, mask
, "");
838 a
= LLVMBuildBitCast(bld
->builder
, a
, vec_type
, "");
842 if(type
.width
*type
.length
== 128 && util_cpu_caps
.has_ssse3
) {
845 return lp_build_intrinsic_unary(bld
->builder
, "llvm.x86.ssse3.pabs.b.128", vec_type
, a
);
847 return lp_build_intrinsic_unary(bld
->builder
, "llvm.x86.ssse3.pabs.w.128", vec_type
, a
);
849 return lp_build_intrinsic_unary(bld
->builder
, "llvm.x86.ssse3.pabs.d.128", vec_type
, a
);
853 return lp_build_max(bld
, a
, LLVMBuildNeg(bld
->builder
, a
, ""));
858 lp_build_negate(struct lp_build_context
*bld
,
861 assert(lp_check_value(bld
->type
, a
));
863 #if HAVE_LLVM >= 0x0207
864 if (bld
->type
.floating
)
865 a
= LLVMBuildFNeg(bld
->builder
, a
, "");
868 a
= LLVMBuildNeg(bld
->builder
, a
, "");
874 /** Return -1, 0 or +1 depending on the sign of a */
876 lp_build_sgn(struct lp_build_context
*bld
,
879 const struct lp_type type
= bld
->type
;
883 assert(lp_check_value(type
, a
));
885 /* Handle non-zero case */
887 /* if not zero then sign must be positive */
890 else if(type
.floating
) {
891 LLVMTypeRef vec_type
;
892 LLVMTypeRef int_type
;
896 unsigned long long maskBit
= (unsigned long long)1 << (type
.width
- 1);
898 int_type
= lp_build_int_vec_type(type
);
899 vec_type
= lp_build_vec_type(type
);
900 mask
= lp_build_const_int_vec(type
, maskBit
);
902 /* Take the sign bit and add it to 1 constant */
903 sign
= LLVMBuildBitCast(bld
->builder
, a
, int_type
, "");
904 sign
= LLVMBuildAnd(bld
->builder
, sign
, mask
, "");
905 one
= LLVMConstBitCast(bld
->one
, int_type
);
906 res
= LLVMBuildOr(bld
->builder
, sign
, one
, "");
907 res
= LLVMBuildBitCast(bld
->builder
, res
, vec_type
, "");
911 LLVMValueRef minus_one
= lp_build_const_vec(type
, -1.0);
912 cond
= lp_build_cmp(bld
, PIPE_FUNC_GREATER
, a
, bld
->zero
);
913 res
= lp_build_select(bld
, cond
, bld
->one
, minus_one
);
917 cond
= lp_build_cmp(bld
, PIPE_FUNC_EQUAL
, a
, bld
->zero
);
918 res
= lp_build_select(bld
, cond
, bld
->zero
, res
);
925 * Set the sign of float vector 'a' according to 'sign'.
926 * If sign==0, return abs(a).
927 * If sign==1, return -abs(a);
928 * Other values for sign produce undefined results.
931 lp_build_set_sign(struct lp_build_context
*bld
,
932 LLVMValueRef a
, LLVMValueRef sign
)
934 const struct lp_type type
= bld
->type
;
935 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(type
);
936 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
937 LLVMValueRef shift
= lp_build_const_int_vec(type
, type
.width
- 1);
938 LLVMValueRef mask
= lp_build_const_int_vec(type
,
939 ~((unsigned long long) 1 << (type
.width
- 1)));
940 LLVMValueRef val
, res
;
942 assert(type
.floating
);
943 assert(lp_check_value(type
, a
));
945 /* val = reinterpret_cast<int>(a) */
946 val
= LLVMBuildBitCast(bld
->builder
, a
, int_vec_type
, "");
947 /* val = val & mask */
948 val
= LLVMBuildAnd(bld
->builder
, val
, mask
, "");
949 /* sign = sign << shift */
950 sign
= LLVMBuildShl(bld
->builder
, sign
, shift
, "");
951 /* res = val | sign */
952 res
= LLVMBuildOr(bld
->builder
, val
, sign
, "");
953 /* res = reinterpret_cast<float>(res) */
954 res
= LLVMBuildBitCast(bld
->builder
, res
, vec_type
, "");
961 * Convert vector of (or scalar) int to vector of (or scalar) float.
964 lp_build_int_to_float(struct lp_build_context
*bld
,
967 const struct lp_type type
= bld
->type
;
968 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
970 assert(type
.floating
);
972 return LLVMBuildSIToFP(bld
->builder
, a
, vec_type
, "");
977 enum lp_build_round_sse41_mode
979 LP_BUILD_ROUND_SSE41_NEAREST
= 0,
980 LP_BUILD_ROUND_SSE41_FLOOR
= 1,
981 LP_BUILD_ROUND_SSE41_CEIL
= 2,
982 LP_BUILD_ROUND_SSE41_TRUNCATE
= 3
986 static INLINE LLVMValueRef
987 lp_build_round_sse41(struct lp_build_context
*bld
,
989 enum lp_build_round_sse41_mode mode
)
991 const struct lp_type type
= bld
->type
;
992 LLVMTypeRef i32t
= LLVMInt32Type();
993 const char *intrinsic
;
996 assert(type
.floating
);
998 assert(lp_check_value(type
, a
));
999 assert(util_cpu_caps
.has_sse4_1
);
1001 if (type
.length
== 1) {
1002 LLVMTypeRef vec_type
;
1004 LLVMValueRef args
[3];
1005 LLVMValueRef index0
= LLVMConstInt(i32t
, 0, 0);
1007 switch(type
.width
) {
1009 intrinsic
= "llvm.x86.sse41.round.ss";
1012 intrinsic
= "llvm.x86.sse41.round.sd";
1019 vec_type
= LLVMVectorType(bld
->elem_type
, 4);
1021 undef
= LLVMGetUndef(vec_type
);
1024 args
[1] = LLVMBuildInsertElement(bld
->builder
, undef
, a
, index0
, "");
1025 args
[2] = LLVMConstInt(i32t
, mode
, 0);
1027 res
= lp_build_intrinsic(bld
->builder
, intrinsic
,
1028 vec_type
, args
, Elements(args
));
1030 res
= LLVMBuildExtractElement(bld
->builder
, res
, index0
, "");
1033 assert(type
.width
*type
.length
== 128);
1035 switch(type
.width
) {
1037 intrinsic
= "llvm.x86.sse41.round.ps";
1040 intrinsic
= "llvm.x86.sse41.round.pd";
1047 res
= lp_build_intrinsic_binary(bld
->builder
, intrinsic
,
1049 LLVMConstInt(i32t
, mode
, 0));
1057 * Return the integer part of a float (vector) value. The returned value is
1059 * Ex: trunc(-1.5) = 1.0
1062 lp_build_trunc(struct lp_build_context
*bld
,
1065 const struct lp_type type
= bld
->type
;
1067 assert(type
.floating
);
1068 assert(lp_check_value(type
, a
));
1070 if (util_cpu_caps
.has_sse4_1
&&
1071 (type
.length
== 1 || type
.width
*type
.length
== 128)) {
1072 return lp_build_round_sse41(bld
, a
, LP_BUILD_ROUND_SSE41_TRUNCATE
);
1075 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
1076 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(type
);
1078 res
= LLVMBuildFPToSI(bld
->builder
, a
, int_vec_type
, "");
1079 res
= LLVMBuildSIToFP(bld
->builder
, res
, vec_type
, "");
1086 * Return float (vector) rounded to nearest integer (vector). The returned
1087 * value is a float (vector).
1088 * Ex: round(0.9) = 1.0
1089 * Ex: round(-1.5) = -2.0
1092 lp_build_round(struct lp_build_context
*bld
,
1095 const struct lp_type type
= bld
->type
;
1097 assert(type
.floating
);
1098 assert(lp_check_value(type
, a
));
1100 if (util_cpu_caps
.has_sse4_1
&&
1101 (type
.length
== 1 || type
.width
*type
.length
== 128)) {
1102 return lp_build_round_sse41(bld
, a
, LP_BUILD_ROUND_SSE41_NEAREST
);
1105 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
1107 res
= lp_build_iround(bld
, a
);
1108 res
= LLVMBuildSIToFP(bld
->builder
, res
, vec_type
, "");
1115 * Return floor of float (vector), result is a float (vector)
1116 * Ex: floor(1.1) = 1.0
1117 * Ex: floor(-1.1) = -2.0
1120 lp_build_floor(struct lp_build_context
*bld
,
1123 const struct lp_type type
= bld
->type
;
1125 assert(type
.floating
);
1126 assert(lp_check_value(type
, a
));
1128 if (util_cpu_caps
.has_sse4_1
&&
1129 (type
.length
== 1 || type
.width
*type
.length
== 128)) {
1130 return lp_build_round_sse41(bld
, a
, LP_BUILD_ROUND_SSE41_FLOOR
);
1133 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
1135 res
= lp_build_ifloor(bld
, a
);
1136 res
= LLVMBuildSIToFP(bld
->builder
, res
, vec_type
, "");
1143 * Return ceiling of float (vector), returning float (vector).
1144 * Ex: ceil( 1.1) = 2.0
1145 * Ex: ceil(-1.1) = -1.0
1148 lp_build_ceil(struct lp_build_context
*bld
,
1151 const struct lp_type type
= bld
->type
;
1153 assert(type
.floating
);
1154 assert(lp_check_value(type
, a
));
1156 if (util_cpu_caps
.has_sse4_1
&&
1157 (type
.length
== 1 || type
.width
*type
.length
== 128)) {
1158 return lp_build_round_sse41(bld
, a
, LP_BUILD_ROUND_SSE41_CEIL
);
1161 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
1163 res
= lp_build_iceil(bld
, a
);
1164 res
= LLVMBuildSIToFP(bld
->builder
, res
, vec_type
, "");
1171 * Return fractional part of 'a' computed as a - floor(a)
1172 * Typically used in texture coord arithmetic.
1175 lp_build_fract(struct lp_build_context
*bld
,
1178 assert(bld
->type
.floating
);
1179 return lp_build_sub(bld
, a
, lp_build_floor(bld
, a
));
1184 * Return the integer part of a float (vector) value. The returned value is
1185 * an integer (vector).
1186 * Ex: itrunc(-1.5) = 1
1189 lp_build_itrunc(struct lp_build_context
*bld
,
1192 const struct lp_type type
= bld
->type
;
1193 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(type
);
1195 assert(type
.floating
);
1196 assert(lp_check_value(type
, a
));
1198 return LLVMBuildFPToSI(bld
->builder
, a
, int_vec_type
, "");
1203 * Return float (vector) rounded to nearest integer (vector). The returned
1204 * value is an integer (vector).
1205 * Ex: iround(0.9) = 1
1206 * Ex: iround(-1.5) = -2
1209 lp_build_iround(struct lp_build_context
*bld
,
1212 const struct lp_type type
= bld
->type
;
1213 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(type
);
1216 assert(type
.floating
);
1218 assert(lp_check_value(type
, a
));
1220 if (util_cpu_caps
.has_sse4_1
&&
1221 (type
.length
== 1 || type
.width
*type
.length
== 128)) {
1222 res
= lp_build_round_sse41(bld
, a
, LP_BUILD_ROUND_SSE41_NEAREST
);
1225 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
1226 LLVMValueRef mask
= lp_build_const_int_vec(type
, (unsigned long long)1 << (type
.width
- 1));
1231 sign
= LLVMBuildBitCast(bld
->builder
, a
, int_vec_type
, "");
1232 sign
= LLVMBuildAnd(bld
->builder
, sign
, mask
, "");
1235 half
= lp_build_const_vec(type
, 0.5);
1236 half
= LLVMBuildBitCast(bld
->builder
, half
, int_vec_type
, "");
1237 half
= LLVMBuildOr(bld
->builder
, sign
, half
, "");
1238 half
= LLVMBuildBitCast(bld
->builder
, half
, vec_type
, "");
1240 res
= LLVMBuildFAdd(bld
->builder
, a
, half
, "");
1243 res
= LLVMBuildFPToSI(bld
->builder
, res
, int_vec_type
, "");
1250 * Return floor of float (vector), result is an int (vector)
1251 * Ex: ifloor(1.1) = 1.0
1252 * Ex: ifloor(-1.1) = -2.0
1255 lp_build_ifloor(struct lp_build_context
*bld
,
1258 const struct lp_type type
= bld
->type
;
1259 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(type
);
1262 assert(type
.floating
);
1263 assert(lp_check_value(type
, a
));
1265 if (util_cpu_caps
.has_sse4_1
&&
1266 (type
.length
== 1 || type
.width
*type
.length
== 128)) {
1267 res
= lp_build_round_sse41(bld
, a
, LP_BUILD_ROUND_SSE41_FLOOR
);
1270 /* Take the sign bit and add it to 1 constant */
1271 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
1272 unsigned mantissa
= lp_mantissa(type
);
1273 LLVMValueRef mask
= lp_build_const_int_vec(type
, (unsigned long long)1 << (type
.width
- 1));
1275 LLVMValueRef offset
;
1277 /* sign = a < 0 ? ~0 : 0 */
1278 sign
= LLVMBuildBitCast(bld
->builder
, a
, int_vec_type
, "");
1279 sign
= LLVMBuildAnd(bld
->builder
, sign
, mask
, "");
1280 sign
= LLVMBuildAShr(bld
->builder
, sign
, lp_build_const_int_vec(type
, type
.width
- 1), "ifloor.sign");
1282 /* offset = -0.99999(9)f */
1283 offset
= lp_build_const_vec(type
, -(double)(((unsigned long long)1 << mantissa
) - 10)/((unsigned long long)1 << mantissa
));
1284 offset
= LLVMConstBitCast(offset
, int_vec_type
);
1286 /* offset = a < 0 ? offset : 0.0f */
1287 offset
= LLVMBuildAnd(bld
->builder
, offset
, sign
, "");
1288 offset
= LLVMBuildBitCast(bld
->builder
, offset
, vec_type
, "ifloor.offset");
1290 res
= LLVMBuildFAdd(bld
->builder
, a
, offset
, "ifloor.res");
1293 /* round to nearest (toward zero) */
1294 res
= LLVMBuildFPToSI(bld
->builder
, res
, int_vec_type
, "ifloor.res");
1301 * Return ceiling of float (vector), returning int (vector).
1302 * Ex: iceil( 1.1) = 2
1303 * Ex: iceil(-1.1) = -1
1306 lp_build_iceil(struct lp_build_context
*bld
,
1309 const struct lp_type type
= bld
->type
;
1310 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(type
);
1313 assert(type
.floating
);
1314 assert(lp_check_value(type
, a
));
1316 if (util_cpu_caps
.has_sse4_1
&&
1317 (type
.length
== 1 || type
.width
*type
.length
== 128)) {
1318 res
= lp_build_round_sse41(bld
, a
, LP_BUILD_ROUND_SSE41_CEIL
);
1321 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
1322 unsigned mantissa
= lp_mantissa(type
);
1323 LLVMValueRef mask
= lp_build_const_int_vec(type
, (unsigned long long)1 << (type
.width
- 1));
1325 LLVMValueRef offset
;
1327 /* sign = a < 0 ? 0 : ~0 */
1328 sign
= LLVMBuildBitCast(bld
->builder
, a
, int_vec_type
, "");
1329 sign
= LLVMBuildAnd(bld
->builder
, sign
, mask
, "");
1330 sign
= LLVMBuildAShr(bld
->builder
, sign
, lp_build_const_int_vec(type
, type
.width
- 1), "iceil.sign");
1331 sign
= LLVMBuildNot(bld
->builder
, sign
, "iceil.not");
1333 /* offset = 0.99999(9)f */
1334 offset
= lp_build_const_vec(type
, (double)(((unsigned long long)1 << mantissa
) - 10)/((unsigned long long)1 << mantissa
));
1335 offset
= LLVMConstBitCast(offset
, int_vec_type
);
1337 /* offset = a < 0 ? 0.0 : offset */
1338 offset
= LLVMBuildAnd(bld
->builder
, offset
, sign
, "");
1339 offset
= LLVMBuildBitCast(bld
->builder
, offset
, vec_type
, "iceil.offset");
1341 res
= LLVMBuildFAdd(bld
->builder
, a
, offset
, "iceil.res");
1344 /* round to nearest (toward zero) */
1345 res
= LLVMBuildFPToSI(bld
->builder
, res
, int_vec_type
, "iceil.res");
1352 lp_build_sqrt(struct lp_build_context
*bld
,
1355 const struct lp_type type
= bld
->type
;
1356 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
1359 assert(lp_check_value(type
, a
));
1361 /* TODO: optimize the constant case */
1362 /* TODO: optimize the constant case */
1364 assert(type
.floating
);
1365 util_snprintf(intrinsic
, sizeof intrinsic
, "llvm.sqrt.v%uf%u", type
.length
, type
.width
);
1367 return lp_build_intrinsic_unary(bld
->builder
, intrinsic
, vec_type
, a
);
1372 * Do one Newton-Raphson step to improve reciprocate precision:
1374 * x_{i+1} = x_i * (2 - a * x_i)
1376 * XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
1377 * +/-Inf, giving NaN instead. Certain applications rely on this behavior,
1378 * such as Google Earth, which does RCP(RSQRT(0.0) when drawing the Earth's
1379 * halo. It would be necessary to clamp the argument to prevent this.
1382 * - http://en.wikipedia.org/wiki/Division_(digital)#Newton.E2.80.93Raphson_division
1383 * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1385 static INLINE LLVMValueRef
1386 lp_build_rcp_refine(struct lp_build_context
*bld
,
1390 LLVMValueRef two
= lp_build_const_vec(bld
->type
, 2.0);
1393 res
= LLVMBuildFMul(bld
->builder
, a
, rcp_a
, "");
1394 res
= LLVMBuildFSub(bld
->builder
, two
, res
, "");
1395 res
= LLVMBuildFMul(bld
->builder
, rcp_a
, res
, "");
1402 lp_build_rcp(struct lp_build_context
*bld
,
1405 const struct lp_type type
= bld
->type
;
1407 assert(lp_check_value(type
, a
));
1416 assert(type
.floating
);
1418 if(LLVMIsConstant(a
))
1419 return LLVMConstFDiv(bld
->one
, a
);
1422 * We don't use RCPPS because:
1423 * - it only has 10bits of precision
1424 * - it doesn't even get the reciprocate of 1.0 exactly
1425 * - doing Newton-Rapshon steps yields wrong (NaN) values for 0.0 or Inf
1426 * - for recent processors the benefit over DIVPS is marginal, a case
1429 * We could still use it on certain processors if benchmarks show that the
1430 * RCPPS plus necessary workarounds are still preferrable to DIVPS; or for
1431 * particular uses that require less workarounds.
1434 if (FALSE
&& util_cpu_caps
.has_sse
&& type
.width
== 32 && type
.length
== 4) {
1435 const unsigned num_iterations
= 0;
1439 res
= lp_build_intrinsic_unary(bld
->builder
, "llvm.x86.sse.rcp.ps", bld
->vec_type
, a
);
1441 for (i
= 0; i
< num_iterations
; ++i
) {
1442 res
= lp_build_rcp_refine(bld
, a
, res
);
1448 return LLVMBuildFDiv(bld
->builder
, bld
->one
, a
, "");
1453 * Do one Newton-Raphson step to improve rsqrt precision:
1455 * x_{i+1} = 0.5 * x_i * (3.0 - a * x_i * x_i)
1458 * - http://softwarecommunity.intel.com/articles/eng/1818.htm
1460 static INLINE LLVMValueRef
1461 lp_build_rsqrt_refine(struct lp_build_context
*bld
,
1463 LLVMValueRef rsqrt_a
)
1465 LLVMValueRef half
= lp_build_const_vec(bld
->type
, 0.5);
1466 LLVMValueRef three
= lp_build_const_vec(bld
->type
, 3.0);
1469 res
= LLVMBuildFMul(bld
->builder
, rsqrt_a
, rsqrt_a
, "");
1470 res
= LLVMBuildFMul(bld
->builder
, a
, res
, "");
1471 res
= LLVMBuildFSub(bld
->builder
, three
, res
, "");
1472 res
= LLVMBuildFMul(bld
->builder
, rsqrt_a
, res
, "");
1473 res
= LLVMBuildFMul(bld
->builder
, half
, res
, "");
1480 * Generate 1/sqrt(a)
1483 lp_build_rsqrt(struct lp_build_context
*bld
,
1486 const struct lp_type type
= bld
->type
;
1488 assert(lp_check_value(type
, a
));
1490 assert(type
.floating
);
1492 if (util_cpu_caps
.has_sse
&& type
.width
== 32 && type
.length
== 4) {
1493 const unsigned num_iterations
= 0;
1497 res
= lp_build_intrinsic_unary(bld
->builder
, "llvm.x86.sse.rsqrt.ps", bld
->vec_type
, a
);
1499 for (i
= 0; i
< num_iterations
; ++i
) {
1500 res
= lp_build_rsqrt_refine(bld
, a
, res
);
1506 return lp_build_rcp(bld
, lp_build_sqrt(bld
, a
));
1510 static inline LLVMValueRef
1511 lp_build_const_v4si(unsigned long value
)
1513 LLVMValueRef element
= LLVMConstInt(LLVMInt32Type(), value
, 0);
1514 LLVMValueRef elements
[4] = { element
, element
, element
, element
};
1515 return LLVMConstVector(elements
, 4);
1518 static inline LLVMValueRef
1519 lp_build_const_v4sf(float value
)
1521 LLVMValueRef element
= LLVMConstReal(LLVMFloatType(), value
);
1522 LLVMValueRef elements
[4] = { element
, element
, element
, element
};
1523 return LLVMConstVector(elements
, 4);
1528 * Generate sin(a) using SSE2
1531 lp_build_sin(struct lp_build_context
*bld
,
1534 struct lp_type int_type
= lp_int_type(bld
->type
);
1535 LLVMBuilderRef b
= bld
->builder
;
1536 LLVMTypeRef v4sf
= LLVMVectorType(LLVMFloatType(), 4);
1537 LLVMTypeRef v4si
= LLVMVectorType(LLVMInt32Type(), 4);
1540 * take the absolute value,
1541 * x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1544 LLVMValueRef inv_sig_mask
= lp_build_const_v4si(~0x80000000);
1545 LLVMValueRef a_v4si
= LLVMBuildBitCast(b
, a
, v4si
, "a_v4si");
1547 LLVMValueRef absi
= LLVMBuildAnd(b
, a_v4si
, inv_sig_mask
, "absi");
1548 LLVMValueRef x_abs
= LLVMBuildBitCast(b
, absi
, v4sf
, "x_abs");
1551 * extract the sign bit (upper one)
1552 * sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
1554 LLVMValueRef sig_mask
= lp_build_const_v4si(0x80000000);
1555 LLVMValueRef sign_bit_i
= LLVMBuildAnd(b
, a_v4si
, sig_mask
, "sign_bit_i");
1559 * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1562 LLVMValueRef FOPi
= lp_build_const_v4sf(1.27323954473516);
1563 LLVMValueRef scale_y
= LLVMBuildFMul(b
, x_abs
, FOPi
, "scale_y");
1566 * store the integer part of y in mm0
1567 * emm2 = _mm_cvttps_epi32(y);
1570 LLVMValueRef emm2_i
= LLVMBuildFPToSI(b
, scale_y
, v4si
, "emm2_i");
1573 * j=(j+1) & (~1) (see the cephes sources)
1574 * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1577 LLVMValueRef all_one
= lp_build_const_v4si(1);
1578 LLVMValueRef emm2_add
= LLVMBuildAdd(b
, emm2_i
, all_one
, "emm2_add");
1580 * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1582 LLVMValueRef inv_one
= lp_build_const_v4si(~1);
1583 LLVMValueRef emm2_and
= LLVMBuildAnd(b
, emm2_add
, inv_one
, "emm2_and");
1586 * y = _mm_cvtepi32_ps(emm2);
1588 LLVMValueRef y_2
= LLVMBuildSIToFP(b
, emm2_and
, v4sf
, "y_2");
1590 /* get the swap sign flag
1591 * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
1593 LLVMValueRef pi32_4
= lp_build_const_v4si(4);
1594 LLVMValueRef emm0_and
= LLVMBuildAnd(b
, emm2_add
, pi32_4
, "emm0_and");
1597 * emm2 = _mm_slli_epi32(emm0, 29);
1599 LLVMValueRef const_29
= lp_build_const_v4si(29);
1600 LLVMValueRef swap_sign_bit
= LLVMBuildShl(b
, emm0_and
, const_29
, "swap_sign_bit");
1603 * get the polynom selection mask
1604 * there is one polynom for 0 <= x <= Pi/4
1605 * and another one for Pi/4<x<=Pi/2
1606 * Both branches will be computed.
1608 * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1609 * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1612 LLVMValueRef pi32_2
= lp_build_const_v4si(2);
1613 LLVMValueRef emm2_3
= LLVMBuildAnd(b
, emm2_and
, pi32_2
, "emm2_3");
1614 LLVMValueRef poly_mask
= lp_build_compare(b
, int_type
, PIPE_FUNC_EQUAL
,
1615 emm2_3
, lp_build_const_v4si(0));
1617 * sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
1619 LLVMValueRef sign_bit_1
= LLVMBuildXor(b
, sign_bit_i
, swap_sign_bit
, "sign_bit");
1622 * _PS_CONST(minus_cephes_DP1, -0.78515625);
1623 * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1624 * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1626 LLVMValueRef DP1
= lp_build_const_v4sf(-0.78515625);
1627 LLVMValueRef DP2
= lp_build_const_v4sf(-2.4187564849853515625e-4);
1628 LLVMValueRef DP3
= lp_build_const_v4sf(-3.77489497744594108e-8);
1631 * The magic pass: "Extended precision modular arithmetic"
1632 * x = ((x - y * DP1) - y * DP2) - y * DP3;
1633 * xmm1 = _mm_mul_ps(y, xmm1);
1634 * xmm2 = _mm_mul_ps(y, xmm2);
1635 * xmm3 = _mm_mul_ps(y, xmm3);
1637 LLVMValueRef xmm1
= LLVMBuildFMul(b
, y_2
, DP1
, "xmm1");
1638 LLVMValueRef xmm2
= LLVMBuildFMul(b
, y_2
, DP2
, "xmm2");
1639 LLVMValueRef xmm3
= LLVMBuildFMul(b
, y_2
, DP3
, "xmm3");
1642 * x = _mm_add_ps(x, xmm1);
1643 * x = _mm_add_ps(x, xmm2);
1644 * x = _mm_add_ps(x, xmm3);
1647 LLVMValueRef x_1
= LLVMBuildFAdd(b
, x_abs
, xmm1
, "x_1");
1648 LLVMValueRef x_2
= LLVMBuildFAdd(b
, x_1
, xmm2
, "x_2");
1649 LLVMValueRef x_3
= LLVMBuildFAdd(b
, x_2
, xmm3
, "x_3");
1652 * Evaluate the first polynom (0 <= x <= Pi/4)
1654 * z = _mm_mul_ps(x,x);
1656 LLVMValueRef z
= LLVMBuildFMul(b
, x_3
, x_3
, "z");
1659 * _PS_CONST(coscof_p0, 2.443315711809948E-005);
1660 * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1661 * _PS_CONST(coscof_p2, 4.166664568298827E-002);
1663 LLVMValueRef coscof_p0
= lp_build_const_v4sf(2.443315711809948E-005);
1664 LLVMValueRef coscof_p1
= lp_build_const_v4sf(-1.388731625493765E-003);
1665 LLVMValueRef coscof_p2
= lp_build_const_v4sf(4.166664568298827E-002);
1668 * y = *(v4sf*)_ps_coscof_p0;
1669 * y = _mm_mul_ps(y, z);
1671 LLVMValueRef y_3
= LLVMBuildFMul(b
, z
, coscof_p0
, "y_3");
1672 LLVMValueRef y_4
= LLVMBuildFAdd(b
, y_3
, coscof_p1
, "y_4");
1673 LLVMValueRef y_5
= LLVMBuildFMul(b
, y_4
, z
, "y_5");
1674 LLVMValueRef y_6
= LLVMBuildFAdd(b
, y_5
, coscof_p2
, "y_6");
1675 LLVMValueRef y_7
= LLVMBuildFMul(b
, y_6
, z
, "y_7");
1676 LLVMValueRef y_8
= LLVMBuildFMul(b
, y_7
, z
, "y_8");
1680 * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1681 * y = _mm_sub_ps(y, tmp);
1682 * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1684 LLVMValueRef half
= lp_build_const_v4sf(0.5);
1685 LLVMValueRef tmp
= LLVMBuildFMul(b
, z
, half
, "tmp");
1686 LLVMValueRef y_9
= LLVMBuildFSub(b
, y_8
, tmp
, "y_8");
1687 LLVMValueRef one
= lp_build_const_v4sf(1.0);
1688 LLVMValueRef y_10
= LLVMBuildFAdd(b
, y_9
, one
, "y_9");
1691 * _PS_CONST(sincof_p0, -1.9515295891E-4);
1692 * _PS_CONST(sincof_p1, 8.3321608736E-3);
1693 * _PS_CONST(sincof_p2, -1.6666654611E-1);
1695 LLVMValueRef sincof_p0
= lp_build_const_v4sf(-1.9515295891E-4);
1696 LLVMValueRef sincof_p1
= lp_build_const_v4sf(8.3321608736E-3);
1697 LLVMValueRef sincof_p2
= lp_build_const_v4sf(-1.6666654611E-1);
1700 * Evaluate the second polynom (Pi/4 <= x <= 0)
1702 * y2 = *(v4sf*)_ps_sincof_p0;
1703 * y2 = _mm_mul_ps(y2, z);
1704 * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1705 * y2 = _mm_mul_ps(y2, z);
1706 * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1707 * y2 = _mm_mul_ps(y2, z);
1708 * y2 = _mm_mul_ps(y2, x);
1709 * y2 = _mm_add_ps(y2, x);
1712 LLVMValueRef y2_3
= LLVMBuildFMul(b
, z
, sincof_p0
, "y2_3");
1713 LLVMValueRef y2_4
= LLVMBuildFAdd(b
, y2_3
, sincof_p1
, "y2_4");
1714 LLVMValueRef y2_5
= LLVMBuildFMul(b
, y2_4
, z
, "y2_5");
1715 LLVMValueRef y2_6
= LLVMBuildFAdd(b
, y2_5
, sincof_p2
, "y2_6");
1716 LLVMValueRef y2_7
= LLVMBuildFMul(b
, y2_6
, z
, "y2_7");
1717 LLVMValueRef y2_8
= LLVMBuildFMul(b
, y2_7
, x_3
, "y2_8");
1718 LLVMValueRef y2_9
= LLVMBuildFAdd(b
, y2_8
, x_3
, "y2_9");
1721 * select the correct result from the two polynoms
1723 * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1724 * y = _mm_andnot_ps(xmm3, y);
1725 * y = _mm_add_ps(y,y2);
1727 LLVMValueRef y2_i
= LLVMBuildBitCast(b
, y2_9
, v4si
, "y2_i");
1728 LLVMValueRef y_i
= LLVMBuildBitCast(b
, y_10
, v4si
, "y_i");
1729 LLVMValueRef y2_and
= LLVMBuildAnd(b
, y2_i
, poly_mask
, "y2_and");
1730 LLVMValueRef inv
= lp_build_const_v4si(~0);
1731 LLVMValueRef poly_mask_inv
= LLVMBuildXor(b
, poly_mask
, inv
, "poly_mask_inv");
1732 LLVMValueRef y_and
= LLVMBuildAnd(b
, y_i
, poly_mask_inv
, "y_and");
1733 LLVMValueRef y_combine
= LLVMBuildAdd(b
, y_and
, y2_and
, "y_combine");
1737 * y = _mm_xor_ps(y, sign_bit);
1739 LLVMValueRef y_sign
= LLVMBuildXor(b
, y_combine
, sign_bit_1
, "y_sin");
1740 LLVMValueRef y_result
= LLVMBuildBitCast(b
, y_sign
, v4sf
, "y_result");
1746 * Generate cos(a) using SSE2
1749 lp_build_cos(struct lp_build_context
*bld
,
1752 struct lp_type int_type
= lp_int_type(bld
->type
);
1753 LLVMBuilderRef b
= bld
->builder
;
1754 LLVMTypeRef v4sf
= LLVMVectorType(LLVMFloatType(), 4);
1755 LLVMTypeRef v4si
= LLVMVectorType(LLVMInt32Type(), 4);
1758 * take the absolute value,
1759 * x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
1762 LLVMValueRef inv_sig_mask
= lp_build_const_v4si(~0x80000000);
1763 LLVMValueRef a_v4si
= LLVMBuildBitCast(b
, a
, v4si
, "a_v4si");
1765 LLVMValueRef absi
= LLVMBuildAnd(b
, a_v4si
, inv_sig_mask
, "absi");
1766 LLVMValueRef x_abs
= LLVMBuildBitCast(b
, absi
, v4sf
, "x_abs");
1770 * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
1773 LLVMValueRef FOPi
= lp_build_const_v4sf(1.27323954473516);
1774 LLVMValueRef scale_y
= LLVMBuildFMul(b
, x_abs
, FOPi
, "scale_y");
1777 * store the integer part of y in mm0
1778 * emm2 = _mm_cvttps_epi32(y);
1781 LLVMValueRef emm2_i
= LLVMBuildFPToSI(b
, scale_y
, v4si
, "emm2_i");
1784 * j=(j+1) & (~1) (see the cephes sources)
1785 * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
1788 LLVMValueRef all_one
= lp_build_const_v4si(1);
1789 LLVMValueRef emm2_add
= LLVMBuildAdd(b
, emm2_i
, all_one
, "emm2_add");
1791 * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
1793 LLVMValueRef inv_one
= lp_build_const_v4si(~1);
1794 LLVMValueRef emm2_and
= LLVMBuildAnd(b
, emm2_add
, inv_one
, "emm2_and");
1797 * y = _mm_cvtepi32_ps(emm2);
1799 LLVMValueRef y_2
= LLVMBuildSIToFP(b
, emm2_and
, v4sf
, "y_2");
1803 * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
1805 LLVMValueRef const_2
= lp_build_const_v4si(2);
1806 LLVMValueRef emm2_2
= LLVMBuildSub(b
, emm2_and
, const_2
, "emm2_2");
1809 /* get the swap sign flag
1810 * emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
1812 LLVMValueRef inv
= lp_build_const_v4si(~0);
1813 LLVMValueRef emm0_not
= LLVMBuildXor(b
, emm2_2
, inv
, "emm0_not");
1814 LLVMValueRef pi32_4
= lp_build_const_v4si(4);
1815 LLVMValueRef emm0_and
= LLVMBuildAnd(b
, emm0_not
, pi32_4
, "emm0_and");
1818 * emm2 = _mm_slli_epi32(emm0, 29);
1820 LLVMValueRef const_29
= lp_build_const_v4si(29);
1821 LLVMValueRef sign_bit
= LLVMBuildShl(b
, emm0_and
, const_29
, "sign_bit");
1824 * get the polynom selection mask
1825 * there is one polynom for 0 <= x <= Pi/4
1826 * and another one for Pi/4<x<=Pi/2
1827 * Both branches will be computed.
1829 * emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
1830 * emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
1833 LLVMValueRef pi32_2
= lp_build_const_v4si(2);
1834 LLVMValueRef emm2_3
= LLVMBuildAnd(b
, emm2_2
, pi32_2
, "emm2_3");
1835 LLVMValueRef poly_mask
= lp_build_compare(b
, int_type
, PIPE_FUNC_EQUAL
,
1836 emm2_3
, lp_build_const_v4si(0));
1839 * _PS_CONST(minus_cephes_DP1, -0.78515625);
1840 * _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
1841 * _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
1843 LLVMValueRef DP1
= lp_build_const_v4sf(-0.78515625);
1844 LLVMValueRef DP2
= lp_build_const_v4sf(-2.4187564849853515625e-4);
1845 LLVMValueRef DP3
= lp_build_const_v4sf(-3.77489497744594108e-8);
1848 * The magic pass: "Extended precision modular arithmetic"
1849 * x = ((x - y * DP1) - y * DP2) - y * DP3;
1850 * xmm1 = _mm_mul_ps(y, xmm1);
1851 * xmm2 = _mm_mul_ps(y, xmm2);
1852 * xmm3 = _mm_mul_ps(y, xmm3);
1854 LLVMValueRef xmm1
= LLVMBuildFMul(b
, y_2
, DP1
, "xmm1");
1855 LLVMValueRef xmm2
= LLVMBuildFMul(b
, y_2
, DP2
, "xmm2");
1856 LLVMValueRef xmm3
= LLVMBuildFMul(b
, y_2
, DP3
, "xmm3");
1859 * x = _mm_add_ps(x, xmm1);
1860 * x = _mm_add_ps(x, xmm2);
1861 * x = _mm_add_ps(x, xmm3);
1864 LLVMValueRef x_1
= LLVMBuildFAdd(b
, x_abs
, xmm1
, "x_1");
1865 LLVMValueRef x_2
= LLVMBuildFAdd(b
, x_1
, xmm2
, "x_2");
1866 LLVMValueRef x_3
= LLVMBuildFAdd(b
, x_2
, xmm3
, "x_3");
1869 * Evaluate the first polynom (0 <= x <= Pi/4)
1871 * z = _mm_mul_ps(x,x);
1873 LLVMValueRef z
= LLVMBuildFMul(b
, x_3
, x_3
, "z");
1876 * _PS_CONST(coscof_p0, 2.443315711809948E-005);
1877 * _PS_CONST(coscof_p1, -1.388731625493765E-003);
1878 * _PS_CONST(coscof_p2, 4.166664568298827E-002);
1880 LLVMValueRef coscof_p0
= lp_build_const_v4sf(2.443315711809948E-005);
1881 LLVMValueRef coscof_p1
= lp_build_const_v4sf(-1.388731625493765E-003);
1882 LLVMValueRef coscof_p2
= lp_build_const_v4sf(4.166664568298827E-002);
1885 * y = *(v4sf*)_ps_coscof_p0;
1886 * y = _mm_mul_ps(y, z);
1888 LLVMValueRef y_3
= LLVMBuildFMul(b
, z
, coscof_p0
, "y_3");
1889 LLVMValueRef y_4
= LLVMBuildFAdd(b
, y_3
, coscof_p1
, "y_4");
1890 LLVMValueRef y_5
= LLVMBuildFMul(b
, y_4
, z
, "y_5");
1891 LLVMValueRef y_6
= LLVMBuildFAdd(b
, y_5
, coscof_p2
, "y_6");
1892 LLVMValueRef y_7
= LLVMBuildFMul(b
, y_6
, z
, "y_7");
1893 LLVMValueRef y_8
= LLVMBuildFMul(b
, y_7
, z
, "y_8");
1897 * tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
1898 * y = _mm_sub_ps(y, tmp);
1899 * y = _mm_add_ps(y, *(v4sf*)_ps_1);
1901 LLVMValueRef half
= lp_build_const_v4sf(0.5);
1902 LLVMValueRef tmp
= LLVMBuildFMul(b
, z
, half
, "tmp");
1903 LLVMValueRef y_9
= LLVMBuildFSub(b
, y_8
, tmp
, "y_8");
1904 LLVMValueRef one
= lp_build_const_v4sf(1.0);
1905 LLVMValueRef y_10
= LLVMBuildFAdd(b
, y_9
, one
, "y_9");
1908 * _PS_CONST(sincof_p0, -1.9515295891E-4);
1909 * _PS_CONST(sincof_p1, 8.3321608736E-3);
1910 * _PS_CONST(sincof_p2, -1.6666654611E-1);
1912 LLVMValueRef sincof_p0
= lp_build_const_v4sf(-1.9515295891E-4);
1913 LLVMValueRef sincof_p1
= lp_build_const_v4sf(8.3321608736E-3);
1914 LLVMValueRef sincof_p2
= lp_build_const_v4sf(-1.6666654611E-1);
1917 * Evaluate the second polynom (Pi/4 <= x <= 0)
1919 * y2 = *(v4sf*)_ps_sincof_p0;
1920 * y2 = _mm_mul_ps(y2, z);
1921 * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
1922 * y2 = _mm_mul_ps(y2, z);
1923 * y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
1924 * y2 = _mm_mul_ps(y2, z);
1925 * y2 = _mm_mul_ps(y2, x);
1926 * y2 = _mm_add_ps(y2, x);
1929 LLVMValueRef y2_3
= LLVMBuildFMul(b
, z
, sincof_p0
, "y2_3");
1930 LLVMValueRef y2_4
= LLVMBuildFAdd(b
, y2_3
, sincof_p1
, "y2_4");
1931 LLVMValueRef y2_5
= LLVMBuildFMul(b
, y2_4
, z
, "y2_5");
1932 LLVMValueRef y2_6
= LLVMBuildFAdd(b
, y2_5
, sincof_p2
, "y2_6");
1933 LLVMValueRef y2_7
= LLVMBuildFMul(b
, y2_6
, z
, "y2_7");
1934 LLVMValueRef y2_8
= LLVMBuildFMul(b
, y2_7
, x_3
, "y2_8");
1935 LLVMValueRef y2_9
= LLVMBuildFAdd(b
, y2_8
, x_3
, "y2_9");
1938 * select the correct result from the two polynoms
1940 * y2 = _mm_and_ps(xmm3, y2); //, xmm3);
1941 * y = _mm_andnot_ps(xmm3, y);
1942 * y = _mm_add_ps(y,y2);
1944 LLVMValueRef y2_i
= LLVMBuildBitCast(b
, y2_9
, v4si
, "y2_i");
1945 LLVMValueRef y_i
= LLVMBuildBitCast(b
, y_10
, v4si
, "y_i");
1946 LLVMValueRef y2_and
= LLVMBuildAnd(b
, y2_i
, poly_mask
, "y2_and");
1947 LLVMValueRef poly_mask_inv
= LLVMBuildXor(b
, poly_mask
, inv
, "poly_mask_inv");
1948 LLVMValueRef y_and
= LLVMBuildAnd(b
, y_i
, poly_mask_inv
, "y_and");
1949 LLVMValueRef y_combine
= LLVMBuildAdd(b
, y_and
, y2_and
, "y_combine");
1953 * y = _mm_xor_ps(y, sign_bit);
1955 LLVMValueRef y_sign
= LLVMBuildXor(b
, y_combine
, sign_bit
, "y_sin");
1956 LLVMValueRef y_result
= LLVMBuildBitCast(b
, y_sign
, v4sf
, "y_result");
1962 * Generate pow(x, y)
1965 lp_build_pow(struct lp_build_context
*bld
,
1969 /* TODO: optimize the constant case */
1970 if (gallivm_debug
& GALLIVM_DEBUG_PERF
&&
1971 LLVMIsConstant(x
) && LLVMIsConstant(y
)) {
1972 debug_printf("%s: inefficient/imprecise constant arithmetic\n",
1976 return lp_build_exp2(bld
, lp_build_mul(bld
, lp_build_log2(bld
, x
), y
));
1984 lp_build_exp(struct lp_build_context
*bld
,
1987 /* log2(e) = 1/log(2) */
1988 LLVMValueRef log2e
= lp_build_const_vec(bld
->type
, 1.4426950408889634);
1990 assert(lp_check_value(bld
->type
, x
));
1992 return lp_build_mul(bld
, log2e
, lp_build_exp2(bld
, x
));
2000 lp_build_log(struct lp_build_context
*bld
,
2004 LLVMValueRef log2
= lp_build_const_vec(bld
->type
, 0.69314718055994529);
2006 assert(lp_check_value(bld
->type
, x
));
2008 return lp_build_mul(bld
, log2
, lp_build_exp2(bld
, x
));
2013 * Generate polynomial.
2014 * Ex: coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
2017 lp_build_polynomial(struct lp_build_context
*bld
,
2019 const double *coeffs
,
2020 unsigned num_coeffs
)
2022 const struct lp_type type
= bld
->type
;
2023 LLVMValueRef res
= NULL
;
2026 assert(lp_check_value(bld
->type
, x
));
2028 /* TODO: optimize the constant case */
2029 if (gallivm_debug
& GALLIVM_DEBUG_PERF
&&
2030 LLVMIsConstant(x
)) {
2031 debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2035 for (i
= num_coeffs
; i
--; ) {
2038 coeff
= lp_build_const_vec(type
, coeffs
[i
]);
2041 res
= lp_build_add(bld
, coeff
, lp_build_mul(bld
, x
, res
));
2054 * Minimax polynomial fit of 2**x, in range [0, 1[
2056 const double lp_build_exp2_polynomial
[] = {
2057 #if EXP_POLY_DEGREE == 5
2058 0.999999999690134838155,
2059 0.583974334321735217258,
2060 0.164553105719676828492,
2061 0.0292811063701710962255,
2062 0.00354944426657875141846,
2063 0.000296253726543423377365
2064 #elif EXP_POLY_DEGREE == 4
2065 1.00000001502262084505,
2066 0.563586057338685991394,
2067 0.150436017652442413623,
2068 0.0243220604213317927308,
2069 0.0025359088446580436489
2070 #elif EXP_POLY_DEGREE == 3
2071 0.999925218562710312959,
2072 0.695833540494823811697,
2073 0.226067155427249155588,
2074 0.0780245226406372992967
2075 #elif EXP_POLY_DEGREE == 2
2076 1.00172476321474503578,
2077 0.657636275736077639316,
2078 0.33718943461968720704
2086 lp_build_exp2_approx(struct lp_build_context
*bld
,
2088 LLVMValueRef
*p_exp2_int_part
,
2089 LLVMValueRef
*p_frac_part
,
2090 LLVMValueRef
*p_exp2
)
2092 const struct lp_type type
= bld
->type
;
2093 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
2094 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(type
);
2095 LLVMValueRef ipart
= NULL
;
2096 LLVMValueRef fpart
= NULL
;
2097 LLVMValueRef expipart
= NULL
;
2098 LLVMValueRef expfpart
= NULL
;
2099 LLVMValueRef res
= NULL
;
2101 assert(lp_check_value(bld
->type
, x
));
2103 if(p_exp2_int_part
|| p_frac_part
|| p_exp2
) {
2104 /* TODO: optimize the constant case */
2105 if (gallivm_debug
& GALLIVM_DEBUG_PERF
&&
2106 LLVMIsConstant(x
)) {
2107 debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2111 assert(type
.floating
&& type
.width
== 32);
2113 x
= lp_build_min(bld
, x
, lp_build_const_vec(type
, 129.0));
2114 x
= lp_build_max(bld
, x
, lp_build_const_vec(type
, -126.99999));
2116 /* ipart = floor(x) */
2117 ipart
= lp_build_floor(bld
, x
);
2119 /* fpart = x - ipart */
2120 fpart
= LLVMBuildFSub(bld
->builder
, x
, ipart
, "");
2123 if(p_exp2_int_part
|| p_exp2
) {
2124 /* expipart = (float) (1 << ipart) */
2125 ipart
= LLVMBuildFPToSI(bld
->builder
, ipart
, int_vec_type
, "");
2126 expipart
= LLVMBuildAdd(bld
->builder
, ipart
, lp_build_const_int_vec(type
, 127), "");
2127 expipart
= LLVMBuildShl(bld
->builder
, expipart
, lp_build_const_int_vec(type
, 23), "");
2128 expipart
= LLVMBuildBitCast(bld
->builder
, expipart
, vec_type
, "");
2132 expfpart
= lp_build_polynomial(bld
, fpart
, lp_build_exp2_polynomial
,
2133 Elements(lp_build_exp2_polynomial
));
2135 res
= LLVMBuildFMul(bld
->builder
, expipart
, expfpart
, "");
2139 *p_exp2_int_part
= expipart
;
2142 *p_frac_part
= fpart
;
2150 lp_build_exp2(struct lp_build_context
*bld
,
2154 lp_build_exp2_approx(bld
, x
, NULL
, NULL
, &res
);
2160 * Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
2161 * These coefficients can be generate with
2162 * http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
2164 const double lp_build_log2_polynomial
[] = {
2165 #if LOG_POLY_DEGREE == 6
2166 3.11578814719469302614,
2167 -3.32419399085241980044,
2168 2.59883907202499966007,
2169 -1.23152682416275988241,
2170 0.318212422185251071475,
2171 -0.0344359067839062357313
2172 #elif LOG_POLY_DEGREE == 5
2173 2.8882704548164776201,
2174 -2.52074962577807006663,
2175 1.48116647521213171641,
2176 -0.465725644288844778798,
2177 0.0596515482674574969533
2178 #elif LOG_POLY_DEGREE == 4
2179 2.61761038894603480148,
2180 -1.75647175389045657003,
2181 0.688243882994381274313,
2182 -0.107254423828329604454
2183 #elif LOG_POLY_DEGREE == 3
2184 2.28330284476918490682,
2185 -1.04913055217340124191,
2186 0.204446009836232697516
2194 * See http://www.devmaster.net/forums/showthread.php?p=43580
2197 lp_build_log2_approx(struct lp_build_context
*bld
,
2199 LLVMValueRef
*p_exp
,
2200 LLVMValueRef
*p_floor_log2
,
2201 LLVMValueRef
*p_log2
)
2203 const struct lp_type type
= bld
->type
;
2204 LLVMTypeRef vec_type
= lp_build_vec_type(type
);
2205 LLVMTypeRef int_vec_type
= lp_build_int_vec_type(type
);
2207 LLVMValueRef expmask
= lp_build_const_int_vec(type
, 0x7f800000);
2208 LLVMValueRef mantmask
= lp_build_const_int_vec(type
, 0x007fffff);
2209 LLVMValueRef one
= LLVMConstBitCast(bld
->one
, int_vec_type
);
2211 LLVMValueRef i
= NULL
;
2212 LLVMValueRef exp
= NULL
;
2213 LLVMValueRef mant
= NULL
;
2214 LLVMValueRef logexp
= NULL
;
2215 LLVMValueRef logmant
= NULL
;
2216 LLVMValueRef res
= NULL
;
2218 assert(lp_check_value(bld
->type
, x
));
2220 if(p_exp
|| p_floor_log2
|| p_log2
) {
2221 /* TODO: optimize the constant case */
2222 if (gallivm_debug
& GALLIVM_DEBUG_PERF
&&
2223 LLVMIsConstant(x
)) {
2224 debug_printf("%s: inefficient/imprecise constant arithmetic\n",
2228 assert(type
.floating
&& type
.width
== 32);
2230 i
= LLVMBuildBitCast(bld
->builder
, x
, int_vec_type
, "");
2232 /* exp = (float) exponent(x) */
2233 exp
= LLVMBuildAnd(bld
->builder
, i
, expmask
, "");
2236 if(p_floor_log2
|| p_log2
) {
2237 logexp
= LLVMBuildLShr(bld
->builder
, exp
, lp_build_const_int_vec(type
, 23), "");
2238 logexp
= LLVMBuildSub(bld
->builder
, logexp
, lp_build_const_int_vec(type
, 127), "");
2239 logexp
= LLVMBuildSIToFP(bld
->builder
, logexp
, vec_type
, "");
2243 /* mant = (float) mantissa(x) */
2244 mant
= LLVMBuildAnd(bld
->builder
, i
, mantmask
, "");
2245 mant
= LLVMBuildOr(bld
->builder
, mant
, one
, "");
2246 mant
= LLVMBuildBitCast(bld
->builder
, mant
, vec_type
, "");
2248 logmant
= lp_build_polynomial(bld
, mant
, lp_build_log2_polynomial
,
2249 Elements(lp_build_log2_polynomial
));
2251 /* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
2252 logmant
= LLVMBuildFMul(bld
->builder
, logmant
, LLVMBuildFSub(bld
->builder
, mant
, bld
->one
, ""), "");
2254 res
= LLVMBuildFAdd(bld
->builder
, logmant
, logexp
, "");
2258 exp
= LLVMBuildBitCast(bld
->builder
, exp
, vec_type
, "");
2263 *p_floor_log2
= logexp
;
2271 lp_build_log2(struct lp_build_context
*bld
,
2275 lp_build_log2_approx(bld
, x
, NULL
, NULL
, &res
);