/**************************************************************************
*
* Copyright 2009-2010 VMware, Inc.
* All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sub license, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice (including the
* next paragraph) shall be included in all copies or substantial portions
* of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT.
* IN NO EVENT SHALL VMWARE AND/OR ITS SUPPLIERS BE LIABLE FOR
* ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
**************************************************************************/
/**
* @file
* Helper
*
* LLVM IR doesn't support all basic arithmetic operations we care about (most
* notably min/max and saturated operations), and it is often necessary to
* resort machine-specific intrinsics directly. The functions here hide all
* these implementation details from the other modules.
*
* We also do simple expressions simplification here. Reasons are:
* - it is very easy given we have all necessary information readily available
* - LLVM optimization passes fail to simplify several vector expressions
* - We often know value constraints which the optimization passes have no way
* of knowing, such as when source arguments are known to be in [0, 1] range.
*
* @author Jose Fonseca <jfonseca@vmware.com>
*/
#include "util/u_memory.h"
#include "util/u_debug.h"
#include "util/u_math.h"
#include "util/u_string.h"
#include "util/u_cpu_detect.h"
#include "lp_bld_type.h"
#include "lp_bld_const.h"
#include "lp_bld_intr.h"
#include "lp_bld_logic.h"
#include "lp_bld_pack.h"
#include "lp_bld_debug.h"
#include "lp_bld_arit.h"
#define EXP_POLY_DEGREE 3
#define LOG_POLY_DEGREE 5
/**
* Generate min(a, b)
* No checks for special case values of a or b = 1 or 0 are done.
*/
static LLVMValueRef
lp_build_min_simple(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef b)
{
const struct lp_type type = bld->type;
const char *intrinsic = NULL;
LLVMValueRef cond;
assert(lp_check_value(type, a));
assert(lp_check_value(type, b));
/* TODO: optimize the constant case */
if(type.width * type.length == 128) {
if(type.floating) {
if(type.width == 32 && util_cpu_caps.has_sse)
intrinsic = "llvm.x86.sse.min.ps";
if(type.width == 64 && util_cpu_caps.has_sse2)
intrinsic = "llvm.x86.sse2.min.pd";
}
else {
if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
intrinsic = "llvm.x86.sse2.pminu.b";
if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
intrinsic = "llvm.x86.sse41.pminsb";
if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
intrinsic = "llvm.x86.sse41.pminuw";
if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
intrinsic = "llvm.x86.sse2.pmins.w";
if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
intrinsic = "llvm.x86.sse41.pminud";
if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
intrinsic = "llvm.x86.sse41.pminsd";
}
}
if(intrinsic)
return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
cond = lp_build_cmp(bld, PIPE_FUNC_LESS, a, b);
return lp_build_select(bld, cond, a, b);
}
/**
* Generate max(a, b)
* No checks for special case values of a or b = 1 or 0 are done.
*/
static LLVMValueRef
lp_build_max_simple(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef b)
{
const struct lp_type type = bld->type;
const char *intrinsic = NULL;
LLVMValueRef cond;
assert(lp_check_value(type, a));
assert(lp_check_value(type, b));
/* TODO: optimize the constant case */
if(type.width * type.length == 128) {
if(type.floating) {
if(type.width == 32 && util_cpu_caps.has_sse)
intrinsic = "llvm.x86.sse.max.ps";
if(type.width == 64 && util_cpu_caps.has_sse2)
intrinsic = "llvm.x86.sse2.max.pd";
}
else {
if(type.width == 8 && !type.sign && util_cpu_caps.has_sse2)
intrinsic = "llvm.x86.sse2.pmaxu.b";
if(type.width == 8 && type.sign && util_cpu_caps.has_sse4_1)
intrinsic = "llvm.x86.sse41.pmaxsb";
if(type.width == 16 && !type.sign && util_cpu_caps.has_sse4_1)
intrinsic = "llvm.x86.sse41.pmaxuw";
if(type.width == 16 && type.sign && util_cpu_caps.has_sse2)
intrinsic = "llvm.x86.sse2.pmaxs.w";
if(type.width == 32 && !type.sign && util_cpu_caps.has_sse4_1)
intrinsic = "llvm.x86.sse41.pmaxud";
if(type.width == 32 && type.sign && util_cpu_caps.has_sse4_1)
intrinsic = "llvm.x86.sse41.pmaxsd";
}
}
if(intrinsic)
return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, b);
return lp_build_select(bld, cond, a, b);
}
/**
* Generate 1 - a, or ~a depending on bld->type.
*/
LLVMValueRef
lp_build_comp(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
assert(lp_check_value(type, a));
if(a == bld->one)
return bld->zero;
if(a == bld->zero)
return bld->one;
if(type.norm && !type.floating && !type.fixed && !type.sign) {
if(LLVMIsConstant(a))
return LLVMConstNot(a);
else
return LLVMBuildNot(bld->builder, a, "");
}
if(LLVMIsConstant(a))
if (type.floating)
return LLVMConstFSub(bld->one, a);
else
return LLVMConstSub(bld->one, a);
else
if (type.floating)
return LLVMBuildFSub(bld->builder, bld->one, a, "");
else
return LLVMBuildSub(bld->builder, bld->one, a, "");
}
/**
* Generate a + b
*/
LLVMValueRef
lp_build_add(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef b)
{
const struct lp_type type = bld->type;
LLVMValueRef res;
assert(lp_check_value(type, a));
assert(lp_check_value(type, b));
if(a == bld->zero)
return b;
if(b == bld->zero)
return a;
if(a == bld->undef || b == bld->undef)
return bld->undef;
if(bld->type.norm) {
const char *intrinsic = NULL;
if(a == bld->one || b == bld->one)
return bld->one;
if(util_cpu_caps.has_sse2 &&
type.width * type.length == 128 &&
!type.floating && !type.fixed) {
if(type.width == 8)
intrinsic = type.sign ? "llvm.x86.sse2.padds.b" : "llvm.x86.sse2.paddus.b";
if(type.width == 16)
intrinsic = type.sign ? "llvm.x86.sse2.padds.w" : "llvm.x86.sse2.paddus.w";
}
if(intrinsic)
return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
}
if(LLVMIsConstant(a) && LLVMIsConstant(b))
if (type.floating)
res = LLVMConstFAdd(a, b);
else
res = LLVMConstAdd(a, b);
else
if (type.floating)
res = LLVMBuildFAdd(bld->builder, a, b, "");
else
res = LLVMBuildAdd(bld->builder, a, b, "");
/* clamp to ceiling of 1.0 */
if(bld->type.norm && (bld->type.floating || bld->type.fixed))
res = lp_build_min_simple(bld, res, bld->one);
/* XXX clamp to floor of -1 or 0??? */
return res;
}
/** Return the scalar sum of the elements of a */
LLVMValueRef
lp_build_sum_vector(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
LLVMValueRef index, res;
unsigned i;
assert(lp_check_value(type, a));
if (type.length == 1) {
return a;
}
assert(!bld->type.norm);
index = LLVMConstInt(LLVMInt32Type(), 0, 0);
res = LLVMBuildExtractElement(bld->builder, a, index, "");
for (i = 1; i < type.length; i++) {
index = LLVMConstInt(LLVMInt32Type(), i, 0);
if (type.floating)
res = LLVMBuildFAdd(bld->builder, res,
LLVMBuildExtractElement(bld->builder,
a, index, ""),
"");
else
res = LLVMBuildAdd(bld->builder, res,
LLVMBuildExtractElement(bld->builder,
a, index, ""),
"");
}
return res;
}
/**
* Generate a - b
*/
LLVMValueRef
lp_build_sub(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef b)
{
const struct lp_type type = bld->type;
LLVMValueRef res;
assert(lp_check_value(type, a));
assert(lp_check_value(type, b));
if(b == bld->zero)
return a;
if(a == bld->undef || b == bld->undef)
return bld->undef;
if(a == b)
return bld->zero;
if(bld->type.norm) {
const char *intrinsic = NULL;
if(b == bld->one)
return bld->zero;
if(util_cpu_caps.has_sse2 &&
type.width * type.length == 128 &&
!type.floating && !type.fixed) {
if(type.width == 8)
intrinsic = type.sign ? "llvm.x86.sse2.psubs.b" : "llvm.x86.sse2.psubus.b";
if(type.width == 16)
intrinsic = type.sign ? "llvm.x86.sse2.psubs.w" : "llvm.x86.sse2.psubus.w";
}
if(intrinsic)
return lp_build_intrinsic_binary(bld->builder, intrinsic, lp_build_vec_type(bld->type), a, b);
}
if(LLVMIsConstant(a) && LLVMIsConstant(b))
if (type.floating)
res = LLVMConstFSub(a, b);
else
res = LLVMConstSub(a, b);
else
if (type.floating)
res = LLVMBuildFSub(bld->builder, a, b, "");
else
res = LLVMBuildSub(bld->builder, a, b, "");
if(bld->type.norm && (bld->type.floating || bld->type.fixed))
res = lp_build_max_simple(bld, res, bld->zero);
return res;
}
/**
* Normalized 8bit multiplication.
*
* - alpha plus one
*
* makes the following approximation to the division (Sree)
*
* a*b/255 ~= (a*(b + 1)) >> 256
*
* which is the fastest method that satisfies the following OpenGL criteria
*
* 0*0 = 0 and 255*255 = 255
*
* - geometric series
*
* takes the geometric series approximation to the division
*
* t/255 = (t >> 8) + (t >> 16) + (t >> 24) ..
*
* in this case just the first two terms to fit in 16bit arithmetic
*
* t/255 ~= (t + (t >> 8)) >> 8
*
* note that just by itself it doesn't satisfies the OpenGL criteria, as
* 255*255 = 254, so the special case b = 255 must be accounted or roundoff
* must be used
*
* - geometric series plus rounding
*
* when using a geometric series division instead of truncating the result
* use roundoff in the approximation (Jim Blinn)
*
* t/255 ~= (t + (t >> 8) + 0x80) >> 8
*
* achieving the exact results
*
* @sa Alvy Ray Smith, Image Compositing Fundamentals, Tech Memo 4, Aug 15, 1995,
* ftp://ftp.alvyray.com/Acrobat/4_Comp.pdf
* @sa Michael Herf, The "double blend trick", May 2000,
* http://www.stereopsis.com/doubleblend.html
*/
static LLVMValueRef
lp_build_mul_u8n(LLVMBuilderRef builder,
struct lp_type i16_type,
LLVMValueRef a, LLVMValueRef b)
{
LLVMValueRef c8;
LLVMValueRef ab;
assert(!i16_type.floating);
assert(lp_check_value(i16_type, a));
assert(lp_check_value(i16_type, b));
c8 = lp_build_const_int_vec(i16_type, 8);
#if 0
/* a*b/255 ~= (a*(b + 1)) >> 256 */
b = LLVMBuildAdd(builder, b, lp_build_const_int_vec(i16_type, 1), "");
ab = LLVMBuildMul(builder, a, b, "");
#else
/* ab/255 ~= (ab + (ab >> 8) + 0x80) >> 8 */
ab = LLVMBuildMul(builder, a, b, "");
ab = LLVMBuildAdd(builder, ab, LLVMBuildLShr(builder, ab, c8, ""), "");
ab = LLVMBuildAdd(builder, ab, lp_build_const_int_vec(i16_type, 0x80), "");
#endif
ab = LLVMBuildLShr(builder, ab, c8, "");
return ab;
}
/**
* Generate a * b
*/
LLVMValueRef
lp_build_mul(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef b)
{
const struct lp_type type = bld->type;
LLVMValueRef shift;
LLVMValueRef res;
assert(lp_check_value(type, a));
assert(lp_check_value(type, b));
if(a == bld->zero)
return bld->zero;
if(a == bld->one)
return b;
if(b == bld->zero)
return bld->zero;
if(b == bld->one)
return a;
if(a == bld->undef || b == bld->undef)
return bld->undef;
if(!type.floating && !type.fixed && type.norm) {
if(type.width == 8) {
struct lp_type i16_type = lp_wider_type(type);
LLVMValueRef al, ah, bl, bh, abl, abh, ab;
lp_build_unpack2(bld->builder, type, i16_type, a, &al, &ah);
lp_build_unpack2(bld->builder, type, i16_type, b, &bl, &bh);
/* PMULLW, PSRLW, PADDW */
abl = lp_build_mul_u8n(bld->builder, i16_type, al, bl);
abh = lp_build_mul_u8n(bld->builder, i16_type, ah, bh);
ab = lp_build_pack2(bld->builder, i16_type, type, abl, abh);
return ab;
}
/* FIXME */
assert(0);
}
if(type.fixed)
shift = lp_build_const_int_vec(type, type.width/2);
else
shift = NULL;
if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
if (type.floating)
res = LLVMConstFMul(a, b);
else
res = LLVMConstMul(a, b);
if(shift) {
if(type.sign)
res = LLVMConstAShr(res, shift);
else
res = LLVMConstLShr(res, shift);
}
}
else {
if (type.floating)
res = LLVMBuildFMul(bld->builder, a, b, "");
else
res = LLVMBuildMul(bld->builder, a, b, "");
if(shift) {
if(type.sign)
res = LLVMBuildAShr(bld->builder, res, shift, "");
else
res = LLVMBuildLShr(bld->builder, res, shift, "");
}
}
return res;
}
/**
* Small vector x scale multiplication optimization.
*/
LLVMValueRef
lp_build_mul_imm(struct lp_build_context *bld,
LLVMValueRef a,
int b)
{
LLVMValueRef factor;
assert(lp_check_value(bld->type, a));
if(b == 0)
return bld->zero;
if(b == 1)
return a;
if(b == -1)
return lp_build_negate(bld, a);
if(b == 2 && bld->type.floating)
return lp_build_add(bld, a, a);
if(util_is_power_of_two(b)) {
unsigned shift = ffs(b) - 1;
if(bld->type.floating) {
#if 0
/*
* Power of two multiplication by directly manipulating the mantissa.
*
* XXX: This might not be always faster, it will introduce a small error
* for multiplication by zero, and it will produce wrong results
* for Inf and NaN.
*/
unsigned mantissa = lp_mantissa(bld->type);
factor = lp_build_const_int_vec(bld->type, (unsigned long long)shift << mantissa);
a = LLVMBuildBitCast(bld->builder, a, lp_build_int_vec_type(bld->type), "");
a = LLVMBuildAdd(bld->builder, a, factor, "");
a = LLVMBuildBitCast(bld->builder, a, lp_build_vec_type(bld->type), "");
return a;
#endif
}
else {
factor = lp_build_const_vec(bld->type, shift);
return LLVMBuildShl(bld->builder, a, factor, "");
}
}
factor = lp_build_const_vec(bld->type, (double)b);
return lp_build_mul(bld, a, factor);
}
/**
* Generate a / b
*/
LLVMValueRef
lp_build_div(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef b)
{
const struct lp_type type = bld->type;
assert(lp_check_value(type, a));
assert(lp_check_value(type, b));
if(a == bld->zero)
return bld->zero;
if(a == bld->one)
return lp_build_rcp(bld, b);
if(b == bld->zero)
return bld->undef;
if(b == bld->one)
return a;
if(a == bld->undef || b == bld->undef)
return bld->undef;
if(LLVMIsConstant(a) && LLVMIsConstant(b)) {
if (type.floating)
return LLVMConstFDiv(a, b);
else if (type.sign)
return LLVMConstSDiv(a, b);
else
return LLVMConstUDiv(a, b);
}
if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4)
return lp_build_mul(bld, a, lp_build_rcp(bld, b));
if (type.floating)
return LLVMBuildFDiv(bld->builder, a, b, "");
else if (type.sign)
return LLVMBuildSDiv(bld->builder, a, b, "");
else
return LLVMBuildUDiv(bld->builder, a, b, "");
}
/**
* Linear interpolation -- without any checks.
*
* @sa http://www.stereopsis.com/doubleblend.html
*/
static INLINE LLVMValueRef
lp_build_lerp_simple(struct lp_build_context *bld,
LLVMValueRef x,
LLVMValueRef v0,
LLVMValueRef v1)
{
LLVMValueRef delta;
LLVMValueRef res;
assert(lp_check_value(bld->type, x));
assert(lp_check_value(bld->type, v0));
assert(lp_check_value(bld->type, v1));
delta = lp_build_sub(bld, v1, v0);
res = lp_build_mul(bld, x, delta);
res = lp_build_add(bld, v0, res);
if (bld->type.fixed) {
/* XXX: This step is necessary for lerping 8bit colors stored on 16bits,
* but it will be wrong for other uses. Basically we need a more
* powerful lp_type, capable of further distinguishing the values
* interpretation from the value storage. */
res = LLVMBuildAnd(bld->builder, res, lp_build_const_int_vec(bld->type, (1 << bld->type.width/2) - 1), "");
}
return res;
}
/**
* Linear interpolation.
*/
LLVMValueRef
lp_build_lerp(struct lp_build_context *bld,
LLVMValueRef x,
LLVMValueRef v0,
LLVMValueRef v1)
{
const struct lp_type type = bld->type;
LLVMValueRef res;
assert(lp_check_value(type, x));
assert(lp_check_value(type, v0));
assert(lp_check_value(type, v1));
if (type.norm) {
struct lp_type wide_type;
struct lp_build_context wide_bld;
LLVMValueRef xl, xh, v0l, v0h, v1l, v1h, resl, resh;
LLVMValueRef shift;
assert(type.length >= 2);
assert(!type.sign);
/*
* Create a wider type, enough to hold the intermediate result of the
* multiplication.
*/
memset(&wide_type, 0, sizeof wide_type);
wide_type.fixed = TRUE;
wide_type.width = type.width*2;
wide_type.length = type.length/2;
lp_build_context_init(&wide_bld, bld->builder, wide_type);
lp_build_unpack2(bld->builder, type, wide_type, x, &xl, &xh);
lp_build_unpack2(bld->builder, type, wide_type, v0, &v0l, &v0h);
lp_build_unpack2(bld->builder, type, wide_type, v1, &v1l, &v1h);
/*
* Scale x from [0, 255] to [0, 256]
*/
shift = lp_build_const_int_vec(wide_type, type.width - 1);
xl = lp_build_add(&wide_bld, xl,
LLVMBuildAShr(bld->builder, xl, shift, ""));
xh = lp_build_add(&wide_bld, xh,
LLVMBuildAShr(bld->builder, xh, shift, ""));
/*
* Lerp both halves.
*/
resl = lp_build_lerp_simple(&wide_bld, xl, v0l, v1l);
resh = lp_build_lerp_simple(&wide_bld, xh, v0h, v1h);
res = lp_build_pack2(bld->builder, wide_type, type, resl, resh);
} else {
res = lp_build_lerp_simple(bld, x, v0, v1);
}
return res;
}
LLVMValueRef
lp_build_lerp_2d(struct lp_build_context *bld,
LLVMValueRef x,
LLVMValueRef y,
LLVMValueRef v00,
LLVMValueRef v01,
LLVMValueRef v10,
LLVMValueRef v11)
{
LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01);
LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11);
return lp_build_lerp(bld, y, v0, v1);
}
/**
* Generate min(a, b)
* Do checks for special cases.
*/
LLVMValueRef
lp_build_min(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef b)
{
assert(lp_check_value(bld->type, a));
assert(lp_check_value(bld->type, b));
if(a == bld->undef || b == bld->undef)
return bld->undef;
if(a == b)
return a;
if(bld->type.norm) {
if(a == bld->zero || b == bld->zero)
return bld->zero;
if(a == bld->one)
return b;
if(b == bld->one)
return a;
}
return lp_build_min_simple(bld, a, b);
}
/**
* Generate max(a, b)
* Do checks for special cases.
*/
LLVMValueRef
lp_build_max(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef b)
{
assert(lp_check_value(bld->type, a));
assert(lp_check_value(bld->type, b));
if(a == bld->undef || b == bld->undef)
return bld->undef;
if(a == b)
return a;
if(bld->type.norm) {
if(a == bld->one || b == bld->one)
return bld->one;
if(a == bld->zero)
return b;
if(b == bld->zero)
return a;
}
return lp_build_max_simple(bld, a, b);
}
/**
* Generate clamp(a, min, max)
* Do checks for special cases.
*/
LLVMValueRef
lp_build_clamp(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef min,
LLVMValueRef max)
{
assert(lp_check_value(bld->type, a));
assert(lp_check_value(bld->type, min));
assert(lp_check_value(bld->type, max));
a = lp_build_min(bld, a, max);
a = lp_build_max(bld, a, min);
return a;
}
/**
* Generate abs(a)
*/
LLVMValueRef
lp_build_abs(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
LLVMTypeRef vec_type = lp_build_vec_type(type);
assert(lp_check_value(type, a));
if(!type.sign)
return a;
if(type.floating) {
/* Mask out the sign bit */
LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
unsigned long long absMask = ~(1ULL << (type.width - 1));
LLVMValueRef mask = lp_build_const_int_vec(type, ((unsigned long long) absMask));
a = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
a = LLVMBuildAnd(bld->builder, a, mask, "");
a = LLVMBuildBitCast(bld->builder, a, vec_type, "");
return a;
}
if(type.width*type.length == 128 && util_cpu_caps.has_ssse3) {
switch(type.width) {
case 8:
return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a);
case 16:
return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a);
case 32:
return lp_build_intrinsic_unary(bld->builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a);
}
}
return lp_build_max(bld, a, LLVMBuildNeg(bld->builder, a, ""));
}
LLVMValueRef
lp_build_negate(struct lp_build_context *bld,
LLVMValueRef a)
{
assert(lp_check_value(bld->type, a));
#if HAVE_LLVM >= 0x0207
if (bld->type.floating)
a = LLVMBuildFNeg(bld->builder, a, "");
else
#endif
a = LLVMBuildNeg(bld->builder, a, "");
return a;
}
/** Return -1, 0 or +1 depending on the sign of a */
LLVMValueRef
lp_build_sgn(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
LLVMValueRef cond;
LLVMValueRef res;
assert(lp_check_value(type, a));
/* Handle non-zero case */
if(!type.sign) {
/* if not zero then sign must be positive */
res = bld->one;
}
else if(type.floating) {
LLVMTypeRef vec_type;
LLVMTypeRef int_type;
LLVMValueRef mask;
LLVMValueRef sign;
LLVMValueRef one;
unsigned long long maskBit = (unsigned long long)1 << (type.width - 1);
int_type = lp_build_int_vec_type(type);
vec_type = lp_build_vec_type(type);
mask = lp_build_const_int_vec(type, maskBit);
/* Take the sign bit and add it to 1 constant */
sign = LLVMBuildBitCast(bld->builder, a, int_type, "");
sign = LLVMBuildAnd(bld->builder, sign, mask, "");
one = LLVMConstBitCast(bld->one, int_type);
res = LLVMBuildOr(bld->builder, sign, one, "");
res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
}
else
{
LLVMValueRef minus_one = lp_build_const_vec(type, -1.0);
cond = lp_build_cmp(bld, PIPE_FUNC_GREATER, a, bld->zero);
res = lp_build_select(bld, cond, bld->one, minus_one);
}
/* Handle zero */
cond = lp_build_cmp(bld, PIPE_FUNC_EQUAL, a, bld->zero);
res = lp_build_select(bld, cond, bld->zero, res);
return res;
}
/**
* Set the sign of float vector 'a' according to 'sign'.
* If sign==0, return abs(a).
* If sign==1, return -abs(a);
* Other values for sign produce undefined results.
*/
LLVMValueRef
lp_build_set_sign(struct lp_build_context *bld,
LLVMValueRef a, LLVMValueRef sign)
{
const struct lp_type type = bld->type;
LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
LLVMTypeRef vec_type = lp_build_vec_type(type);
LLVMValueRef shift = lp_build_const_int_vec(type, type.width - 1);
LLVMValueRef mask = lp_build_const_int_vec(type,
~((unsigned long long) 1 << (type.width - 1)));
LLVMValueRef val, res;
assert(type.floating);
assert(lp_check_value(type, a));
/* val = reinterpret_cast<int>(a) */
val = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
/* val = val & mask */
val = LLVMBuildAnd(bld->builder, val, mask, "");
/* sign = sign << shift */
sign = LLVMBuildShl(bld->builder, sign, shift, "");
/* res = val | sign */
res = LLVMBuildOr(bld->builder, val, sign, "");
/* res = reinterpret_cast<float>(res) */
res = LLVMBuildBitCast(bld->builder, res, vec_type, "");
return res;
}
/**
* Convert vector of (or scalar) int to vector of (or scalar) float.
*/
LLVMValueRef
lp_build_int_to_float(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
LLVMTypeRef vec_type = lp_build_vec_type(type);
assert(type.floating);
return LLVMBuildSIToFP(bld->builder, a, vec_type, "");
}
enum lp_build_round_sse41_mode
{
LP_BUILD_ROUND_SSE41_NEAREST = 0,
LP_BUILD_ROUND_SSE41_FLOOR = 1,
LP_BUILD_ROUND_SSE41_CEIL = 2,
LP_BUILD_ROUND_SSE41_TRUNCATE = 3
};
static INLINE LLVMValueRef
lp_build_round_sse41(struct lp_build_context *bld,
LLVMValueRef a,
enum lp_build_round_sse41_mode mode)
{
const struct lp_type type = bld->type;
LLVMTypeRef i32t = LLVMInt32Type();
const char *intrinsic;
LLVMValueRef res;
assert(type.floating);
assert(lp_check_value(type, a));
assert(util_cpu_caps.has_sse4_1);
if (type.length == 1) {
LLVMTypeRef vec_type;
LLVMValueRef undef;
LLVMValueRef args[3];
LLVMValueRef index0 = LLVMConstInt(i32t, 0, 0);
switch(type.width) {
case 32:
intrinsic = "llvm.x86.sse41.round.ss";
break;
case 64:
intrinsic = "llvm.x86.sse41.round.sd";
break;
default:
assert(0);
return bld->undef;
}
vec_type = LLVMVectorType(bld->elem_type, 4);
undef = LLVMGetUndef(vec_type);
args[0] = undef;
args[1] = LLVMBuildInsertElement(bld->builder, undef, a, index0, "");
args[2] = LLVMConstInt(i32t, mode, 0);
res = lp_build_intrinsic(bld->builder, intrinsic,
vec_type, args, Elements(args));
res = LLVMBuildExtractElement(bld->builder, res, index0, "");
}
else {
assert(type.width*type.length == 128);
switch(type.width) {
case 32:
intrinsic = "llvm.x86.sse41.round.ps";
break;
case 64:
intrinsic = "llvm.x86.sse41.round.pd";
break;
default:
assert(0);
return bld->undef;
}
res = lp_build_intrinsic_binary(bld->builder, intrinsic,
bld->vec_type, a,
LLVMConstInt(i32t, mode, 0));
}
return res;
}
static INLINE LLVMValueRef
lp_build_iround_nearest_sse2(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
LLVMTypeRef i32t = LLVMInt32Type();
LLVMTypeRef ret_type = lp_build_int_vec_type(type);
const char *intrinsic;
LLVMValueRef res;
assert(type.floating);
/* using the double precision conversions is a bit more complicated */
assert(type.width == 32);
assert(lp_check_value(type, a));
assert(util_cpu_caps.has_sse2);
/* This is relying on MXCSR rounding mode, which should always be nearest. */
if (type.length == 1) {
LLVMTypeRef vec_type;
LLVMValueRef undef;
LLVMValueRef arg;
LLVMValueRef index0 = LLVMConstInt(i32t, 0, 0);
vec_type = LLVMVectorType(bld->elem_type, 4);
intrinsic = "llvm.x86.sse.cvtss2si";
undef = LLVMGetUndef(vec_type);
arg = LLVMBuildInsertElement(bld->builder, undef, a, index0, "");
res = lp_build_intrinsic_unary(bld->builder, intrinsic,
ret_type, arg);
}
else {
assert(type.width*type.length == 128);
intrinsic = "llvm.x86.sse2.cvtps2dq";
res = lp_build_intrinsic_unary(bld->builder, intrinsic,
ret_type, a);
}
return res;
}
/**
* Return the integer part of a float (vector) value (== round toward zero).
* The returned value is a float (vector).
* Ex: trunc(-1.5) = -1.0
*/
LLVMValueRef
lp_build_trunc(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
assert(type.floating);
assert(lp_check_value(type, a));
if (util_cpu_caps.has_sse4_1 &&
(type.length == 1 || type.width*type.length == 128)) {
return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_TRUNCATE);
}
else {
LLVMTypeRef vec_type = lp_build_vec_type(type);
LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
LLVMValueRef res;
res = LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
return res;
}
}
/**
* Return float (vector) rounded to nearest integer (vector). The returned
* value is a float (vector).
* Ex: round(0.9) = 1.0
* Ex: round(-1.5) = -2.0
*/
LLVMValueRef
lp_build_round(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
assert(type.floating);
assert(lp_check_value(type, a));
if (util_cpu_caps.has_sse4_1 &&
(type.length == 1 || type.width*type.length == 128)) {
return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
}
else {
LLVMTypeRef vec_type = lp_build_vec_type(type);
LLVMValueRef res;
res = lp_build_iround(bld, a);
res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
return res;
}
}
/**
* Return floor of float (vector), result is a float (vector)
* Ex: floor(1.1) = 1.0
* Ex: floor(-1.1) = -2.0
*/
LLVMValueRef
lp_build_floor(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
assert(type.floating);
assert(lp_check_value(type, a));
if (util_cpu_caps.has_sse4_1 &&
(type.length == 1 || type.width*type.length == 128)) {
return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
}
else {
LLVMTypeRef vec_type = lp_build_vec_type(type);
LLVMValueRef res;
res = lp_build_ifloor(bld, a);
res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
return res;
}
}
/**
* Return ceiling of float (vector), returning float (vector).
* Ex: ceil( 1.1) = 2.0
* Ex: ceil(-1.1) = -1.0
*/
LLVMValueRef
lp_build_ceil(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
assert(type.floating);
assert(lp_check_value(type, a));
if (util_cpu_caps.has_sse4_1 &&
(type.length == 1 || type.width*type.length == 128)) {
return lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
}
else {
LLVMTypeRef vec_type = lp_build_vec_type(type);
LLVMValueRef res;
res = lp_build_iceil(bld, a);
res = LLVMBuildSIToFP(bld->builder, res, vec_type, "");
return res;
}
}
/**
* Return fractional part of 'a' computed as a - floor(a)
* Typically used in texture coord arithmetic.
*/
LLVMValueRef
lp_build_fract(struct lp_build_context *bld,
LLVMValueRef a)
{
assert(bld->type.floating);
return lp_build_sub(bld, a, lp_build_floor(bld, a));
}
/**
* Return the integer part of a float (vector) value (== round toward zero).
* The returned value is an integer (vector).
* Ex: itrunc(-1.5) = -1
*/
LLVMValueRef
lp_build_itrunc(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
assert(type.floating);
assert(lp_check_value(type, a));
return LLVMBuildFPToSI(bld->builder, a, int_vec_type, "");
}
/**
* Return float (vector) rounded to nearest integer (vector). The returned
* value is an integer (vector).
* Ex: iround(0.9) = 1
* Ex: iround(-1.5) = -2
*/
LLVMValueRef
lp_build_iround(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
LLVMTypeRef int_vec_type = bld->int_vec_type;
LLVMValueRef res;
assert(type.floating);
assert(lp_check_value(type, a));
if (util_cpu_caps.has_sse2 &&
((type.width == 32) && (type.length == 1 || type.length == 4))) {
return lp_build_iround_nearest_sse2(bld, a);
}
else if (util_cpu_caps.has_sse4_1 &&
(type.length == 1 || type.width*type.length == 128)) {
res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_NEAREST);
}
else {
LLVMValueRef half;
half = lp_build_const_vec(type, 0.5);
if (type.sign) {
LLVMTypeRef vec_type = bld->vec_type;
LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
LLVMValueRef sign;
/* get sign bit */
sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
sign = LLVMBuildAnd(bld->builder, sign, mask, "");
/* sign * 0.5 */
half = LLVMBuildBitCast(bld->builder, half, int_vec_type, "");
half = LLVMBuildOr(bld->builder, sign, half, "");
half = LLVMBuildBitCast(bld->builder, half, vec_type, "");
}
res = LLVMBuildFAdd(bld->builder, a, half, "");
}
res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "");
return res;
}
/**
* Return floor of float (vector), result is an int (vector)
* Ex: ifloor(1.1) = 1.0
* Ex: ifloor(-1.1) = -2.0
*/
LLVMValueRef
lp_build_ifloor(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
LLVMTypeRef int_vec_type = bld->int_vec_type;
LLVMValueRef res;
assert(type.floating);
assert(lp_check_value(type, a));
if (util_cpu_caps.has_sse4_1 &&
(type.length == 1 || type.width*type.length == 128)) {
res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_FLOOR);
}
else {
res = a;
if (type.sign) {
/* Take the sign bit and add it to 1 constant */
LLVMTypeRef vec_type = bld->vec_type;
unsigned mantissa = lp_mantissa(type);
LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
LLVMValueRef sign;
LLVMValueRef offset;
/* sign = a < 0 ? ~0 : 0 */
sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
sign = LLVMBuildAnd(bld->builder, sign, mask, "");
sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "ifloor.sign");
/* offset = -0.99999(9)f */
offset = lp_build_const_vec(type, -(double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
offset = LLVMConstBitCast(offset, int_vec_type);
/* offset = a < 0 ? offset : 0.0f */
offset = LLVMBuildAnd(bld->builder, offset, sign, "");
offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "ifloor.offset");
res = LLVMBuildFAdd(bld->builder, res, offset, "ifloor.res");
}
}
/* round to nearest (toward zero) */
res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "ifloor.res");
return res;
}
/**
* Return ceiling of float (vector), returning int (vector).
* Ex: iceil( 1.1) = 2
* Ex: iceil(-1.1) = -1
*/
LLVMValueRef
lp_build_iceil(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
LLVMTypeRef int_vec_type = bld->int_vec_type;
LLVMValueRef res;
assert(type.floating);
assert(lp_check_value(type, a));
if (util_cpu_caps.has_sse4_1 &&
(type.length == 1 || type.width*type.length == 128)) {
res = lp_build_round_sse41(bld, a, LP_BUILD_ROUND_SSE41_CEIL);
}
else {
LLVMTypeRef vec_type = bld->vec_type;
unsigned mantissa = lp_mantissa(type);
LLVMValueRef offset;
/* offset = 0.99999(9)f */
offset = lp_build_const_vec(type, (double)(((unsigned long long)1 << mantissa) - 10)/((unsigned long long)1 << mantissa));
if (type.sign) {
LLVMValueRef mask = lp_build_const_int_vec(type, (unsigned long long)1 << (type.width - 1));
LLVMValueRef sign;
/* sign = a < 0 ? 0 : ~0 */
sign = LLVMBuildBitCast(bld->builder, a, int_vec_type, "");
sign = LLVMBuildAnd(bld->builder, sign, mask, "");
sign = LLVMBuildAShr(bld->builder, sign, lp_build_const_int_vec(type, type.width - 1), "iceil.sign");
sign = LLVMBuildNot(bld->builder, sign, "iceil.not");
/* offset = a < 0 ? 0.0 : offset */
offset = LLVMConstBitCast(offset, int_vec_type);
offset = LLVMBuildAnd(bld->builder, offset, sign, "");
offset = LLVMBuildBitCast(bld->builder, offset, vec_type, "iceil.offset");
}
res = LLVMBuildFAdd(bld->builder, a, offset, "iceil.res");
}
/* round to nearest (toward zero) */
res = LLVMBuildFPToSI(bld->builder, res, int_vec_type, "iceil.res");
return res;
}
/**
* Combined ifloor() & fract().
*
* Preferred to calling the functions separately, as it will ensure that the
* stratergy (floor() vs ifloor()) that results in less redundant work is used.
*/
void
lp_build_ifloor_fract(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef *out_ipart,
LLVMValueRef *out_fpart)
{
const struct lp_type type = bld->type;
LLVMValueRef ipart;
assert(type.floating);
assert(lp_check_value(type, a));
if (util_cpu_caps.has_sse4_1 &&
(type.length == 1 || type.width*type.length == 128)) {
/*
* floor() is easier.
*/
ipart = lp_build_floor(bld, a);
*out_fpart = LLVMBuildFSub(bld->builder, a, ipart, "fpart");
*out_ipart = LLVMBuildFPToSI(bld->builder, ipart, bld->int_vec_type, "ipart");
}
else {
/*
* ifloor() is easier.
*/
*out_ipart = lp_build_ifloor(bld, a);
ipart = LLVMBuildSIToFP(bld->builder, *out_ipart, bld->vec_type, "ipart");
*out_fpart = LLVMBuildFSub(bld->builder, a, ipart, "fpart");
}
}
LLVMValueRef
lp_build_sqrt(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
LLVMTypeRef vec_type = lp_build_vec_type(type);
char intrinsic[32];
assert(lp_check_value(type, a));
/* TODO: optimize the constant case */
/* TODO: optimize the constant case */
assert(type.floating);
util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width);
return lp_build_intrinsic_unary(bld->builder, intrinsic, vec_type, a);
}
/**
* Do one Newton-Raphson step to improve reciprocate precision:
*
* x_{i+1} = x_i * (2 - a * x_i)
*
* XXX: Unfortunately this won't give IEEE-754 conformant results for 0 or
* +/-Inf, giving NaN instead. Certain applications rely on this behavior,
* such as Google Earth, which does RCP(RSQRT(0.0) when drawing the Earth's
* halo. It would be necessary to clamp the argument to prevent this.
*
* See also:
* - http://en.wikipedia.org/wiki/Division_(digital)#Newton.E2.80.93Raphson_division
* - http://softwarecommunity.intel.com/articles/eng/1818.htm
*/
static INLINE LLVMValueRef
lp_build_rcp_refine(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef rcp_a)
{
LLVMValueRef two = lp_build_const_vec(bld->type, 2.0);
LLVMValueRef res;
res = LLVMBuildFMul(bld->builder, a, rcp_a, "");
res = LLVMBuildFSub(bld->builder, two, res, "");
res = LLVMBuildFMul(bld->builder, rcp_a, res, "");
return res;
}
LLVMValueRef
lp_build_rcp(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
assert(lp_check_value(type, a));
if(a == bld->zero)
return bld->undef;
if(a == bld->one)
return bld->one;
if(a == bld->undef)
return bld->undef;
assert(type.floating);
if(LLVMIsConstant(a))
return LLVMConstFDiv(bld->one, a);
/*
* We don't use RCPPS because:
* - it only has 10bits of precision
* - it doesn't even get the reciprocate of 1.0 exactly
* - doing Newton-Rapshon steps yields wrong (NaN) values for 0.0 or Inf
* - for recent processors the benefit over DIVPS is marginal, a case
* depedent
*
* We could still use it on certain processors if benchmarks show that the
* RCPPS plus necessary workarounds are still preferrable to DIVPS; or for
* particular uses that require less workarounds.
*/
if (FALSE && util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
const unsigned num_iterations = 0;
LLVMValueRef res;
unsigned i;
res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rcp.ps", bld->vec_type, a);
for (i = 0; i < num_iterations; ++i) {
res = lp_build_rcp_refine(bld, a, res);
}
return res;
}
return LLVMBuildFDiv(bld->builder, bld->one, a, "");
}
/**
* Do one Newton-Raphson step to improve rsqrt precision:
*
* x_{i+1} = 0.5 * x_i * (3.0 - a * x_i * x_i)
*
* See also:
* - http://softwarecommunity.intel.com/articles/eng/1818.htm
*/
static INLINE LLVMValueRef
lp_build_rsqrt_refine(struct lp_build_context *bld,
LLVMValueRef a,
LLVMValueRef rsqrt_a)
{
LLVMValueRef half = lp_build_const_vec(bld->type, 0.5);
LLVMValueRef three = lp_build_const_vec(bld->type, 3.0);
LLVMValueRef res;
res = LLVMBuildFMul(bld->builder, rsqrt_a, rsqrt_a, "");
res = LLVMBuildFMul(bld->builder, a, res, "");
res = LLVMBuildFSub(bld->builder, three, res, "");
res = LLVMBuildFMul(bld->builder, rsqrt_a, res, "");
res = LLVMBuildFMul(bld->builder, half, res, "");
return res;
}
/**
* Generate 1/sqrt(a)
*/
LLVMValueRef
lp_build_rsqrt(struct lp_build_context *bld,
LLVMValueRef a)
{
const struct lp_type type = bld->type;
assert(lp_check_value(type, a));
assert(type.floating);
if (util_cpu_caps.has_sse && type.width == 32 && type.length == 4) {
const unsigned num_iterations = 0;
LLVMValueRef res;
unsigned i;
res = lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", bld->vec_type, a);
for (i = 0; i < num_iterations; ++i) {
res = lp_build_rsqrt_refine(bld, a, res);
}
return res;
}
return lp_build_rcp(bld, lp_build_sqrt(bld, a));
}
static inline LLVMValueRef
lp_build_const_v4si(unsigned long value)
{
LLVMValueRef element = LLVMConstInt(LLVMInt32Type(), value, 0);
LLVMValueRef elements[4] = { element, element, element, element };
return LLVMConstVector(elements, 4);
}
static inline LLVMValueRef
lp_build_const_v4sf(float value)
{
LLVMValueRef element = LLVMConstReal(LLVMFloatType(), value);
LLVMValueRef elements[4] = { element, element, element, element };
return LLVMConstVector(elements, 4);
}
/**
* Generate sin(a) using SSE2
*/
LLVMValueRef
lp_build_sin(struct lp_build_context *bld,
LLVMValueRef a)
{
struct lp_type int_type = lp_int_type(bld->type);
LLVMBuilderRef b = bld->builder;
LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
/*
* take the absolute value,
* x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
*/
LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
/*
* extract the sign bit (upper one)
* sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask);
*/
LLVMValueRef sig_mask = lp_build_const_v4si(0x80000000);
LLVMValueRef sign_bit_i = LLVMBuildAnd(b, a_v4si, sig_mask, "sign_bit_i");
/*
* scale by 4/Pi
* y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
*/
LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
/*
* store the integer part of y in mm0
* emm2 = _mm_cvttps_epi32(y);
*/
LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
/*
* j=(j+1) & (~1) (see the cephes sources)
* emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
*/
LLVMValueRef all_one = lp_build_const_v4si(1);
LLVMValueRef emm2_add = LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
/*
* emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
*/
LLVMValueRef inv_one = lp_build_const_v4si(~1);
LLVMValueRef emm2_and = LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
/*
* y = _mm_cvtepi32_ps(emm2);
*/
LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
/* get the swap sign flag
* emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4);
*/
LLVMValueRef pi32_4 = lp_build_const_v4si(4);
LLVMValueRef emm0_and = LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and");
/*
* emm2 = _mm_slli_epi32(emm0, 29);
*/
LLVMValueRef const_29 = lp_build_const_v4si(29);
LLVMValueRef swap_sign_bit = LLVMBuildShl(b, emm0_and, const_29, "swap_sign_bit");
/*
* get the polynom selection mask
* there is one polynom for 0 <= x <= Pi/4
* and another one for Pi/4<x<=Pi/2
* Both branches will be computed.
*
* emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
* emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
*/
LLVMValueRef pi32_2 = lp_build_const_v4si(2);
LLVMValueRef emm2_3 = LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3");
LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
emm2_3, lp_build_const_v4si(0));
/*
* sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
*/
LLVMValueRef sign_bit_1 = LLVMBuildXor(b, sign_bit_i, swap_sign_bit, "sign_bit");
/*
* _PS_CONST(minus_cephes_DP1, -0.78515625);
* _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
* _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
*/
LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
/*
* The magic pass: "Extended precision modular arithmetic"
* x = ((x - y * DP1) - y * DP2) - y * DP3;
* xmm1 = _mm_mul_ps(y, xmm1);
* xmm2 = _mm_mul_ps(y, xmm2);
* xmm3 = _mm_mul_ps(y, xmm3);
*/
LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
/*
* x = _mm_add_ps(x, xmm1);
* x = _mm_add_ps(x, xmm2);
* x = _mm_add_ps(x, xmm3);
*/
LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
/*
* Evaluate the first polynom (0 <= x <= Pi/4)
*
* z = _mm_mul_ps(x,x);
*/
LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
/*
* _PS_CONST(coscof_p0, 2.443315711809948E-005);
* _PS_CONST(coscof_p1, -1.388731625493765E-003);
* _PS_CONST(coscof_p2, 4.166664568298827E-002);
*/
LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
/*
* y = *(v4sf*)_ps_coscof_p0;
* y = _mm_mul_ps(y, z);
*/
LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
/*
* tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
* y = _mm_sub_ps(y, tmp);
* y = _mm_add_ps(y, *(v4sf*)_ps_1);
*/
LLVMValueRef half = lp_build_const_v4sf(0.5);
LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
LLVMValueRef one = lp_build_const_v4sf(1.0);
LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
/*
* _PS_CONST(sincof_p0, -1.9515295891E-4);
* _PS_CONST(sincof_p1, 8.3321608736E-3);
* _PS_CONST(sincof_p2, -1.6666654611E-1);
*/
LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
/*
* Evaluate the second polynom (Pi/4 <= x <= 0)
*
* y2 = *(v4sf*)_ps_sincof_p0;
* y2 = _mm_mul_ps(y2, z);
* y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
* y2 = _mm_mul_ps(y2, z);
* y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
* y2 = _mm_mul_ps(y2, z);
* y2 = _mm_mul_ps(y2, x);
* y2 = _mm_add_ps(y2, x);
*/
LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
/*
* select the correct result from the two polynoms
* xmm3 = poly_mask;
* y2 = _mm_and_ps(xmm3, y2); //, xmm3);
* y = _mm_andnot_ps(xmm3, y);
* y = _mm_add_ps(y,y2);
*/
LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
LLVMValueRef inv = lp_build_const_v4si(~0);
LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
/*
* update the sign
* y = _mm_xor_ps(y, sign_bit);
*/
LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit_1, "y_sin");
LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
return y_result;
}
/**
* Generate cos(a) using SSE2
*/
LLVMValueRef
lp_build_cos(struct lp_build_context *bld,
LLVMValueRef a)
{
struct lp_type int_type = lp_int_type(bld->type);
LLVMBuilderRef b = bld->builder;
LLVMTypeRef v4sf = LLVMVectorType(LLVMFloatType(), 4);
LLVMTypeRef v4si = LLVMVectorType(LLVMInt32Type(), 4);
/*
* take the absolute value,
* x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask);
*/
LLVMValueRef inv_sig_mask = lp_build_const_v4si(~0x80000000);
LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, v4si, "a_v4si");
LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi");
LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, v4sf, "x_abs");
/*
* scale by 4/Pi
* y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI);
*/
LLVMValueRef FOPi = lp_build_const_v4sf(1.27323954473516);
LLVMValueRef scale_y = LLVMBuildFMul(b, x_abs, FOPi, "scale_y");
/*
* store the integer part of y in mm0
* emm2 = _mm_cvttps_epi32(y);
*/
LLVMValueRef emm2_i = LLVMBuildFPToSI(b, scale_y, v4si, "emm2_i");
/*
* j=(j+1) & (~1) (see the cephes sources)
* emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1);
*/
LLVMValueRef all_one = lp_build_const_v4si(1);
LLVMValueRef emm2_add = LLVMBuildAdd(b, emm2_i, all_one, "emm2_add");
/*
* emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1);
*/
LLVMValueRef inv_one = lp_build_const_v4si(~1);
LLVMValueRef emm2_and = LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and");
/*
* y = _mm_cvtepi32_ps(emm2);
*/
LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, v4sf, "y_2");
/*
* emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2);
*/
LLVMValueRef const_2 = lp_build_const_v4si(2);
LLVMValueRef emm2_2 = LLVMBuildSub(b, emm2_and, const_2, "emm2_2");
/* get the swap sign flag
* emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4);
*/
LLVMValueRef inv = lp_build_const_v4si(~0);
LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not");
LLVMValueRef pi32_4 = lp_build_const_v4si(4);
LLVMValueRef emm0_and = LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and");
/*
* emm2 = _mm_slli_epi32(emm0, 29);
*/
LLVMValueRef const_29 = lp_build_const_v4si(29);
LLVMValueRef sign_bit = LLVMBuildShl(b, emm0_and, const_29, "sign_bit");
/*
* get the polynom selection mask
* there is one polynom for 0 <= x <= Pi/4
* and another one for Pi/4<x<=Pi/2
* Both branches will be computed.
*
* emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2);
* emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
*/
LLVMValueRef pi32_2 = lp_build_const_v4si(2);
LLVMValueRef emm2_3 = LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3");
LLVMValueRef poly_mask = lp_build_compare(b, int_type, PIPE_FUNC_EQUAL,
emm2_3, lp_build_const_v4si(0));
/*
* _PS_CONST(minus_cephes_DP1, -0.78515625);
* _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4);
* _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8);
*/
LLVMValueRef DP1 = lp_build_const_v4sf(-0.78515625);
LLVMValueRef DP2 = lp_build_const_v4sf(-2.4187564849853515625e-4);
LLVMValueRef DP3 = lp_build_const_v4sf(-3.77489497744594108e-8);
/*
* The magic pass: "Extended precision modular arithmetic"
* x = ((x - y * DP1) - y * DP2) - y * DP3;
* xmm1 = _mm_mul_ps(y, xmm1);
* xmm2 = _mm_mul_ps(y, xmm2);
* xmm3 = _mm_mul_ps(y, xmm3);
*/
LLVMValueRef xmm1 = LLVMBuildFMul(b, y_2, DP1, "xmm1");
LLVMValueRef xmm2 = LLVMBuildFMul(b, y_2, DP2, "xmm2");
LLVMValueRef xmm3 = LLVMBuildFMul(b, y_2, DP3, "xmm3");
/*
* x = _mm_add_ps(x, xmm1);
* x = _mm_add_ps(x, xmm2);
* x = _mm_add_ps(x, xmm3);
*/
LLVMValueRef x_1 = LLVMBuildFAdd(b, x_abs, xmm1, "x_1");
LLVMValueRef x_2 = LLVMBuildFAdd(b, x_1, xmm2, "x_2");
LLVMValueRef x_3 = LLVMBuildFAdd(b, x_2, xmm3, "x_3");
/*
* Evaluate the first polynom (0 <= x <= Pi/4)
*
* z = _mm_mul_ps(x,x);
*/
LLVMValueRef z = LLVMBuildFMul(b, x_3, x_3, "z");
/*
* _PS_CONST(coscof_p0, 2.443315711809948E-005);
* _PS_CONST(coscof_p1, -1.388731625493765E-003);
* _PS_CONST(coscof_p2, 4.166664568298827E-002);
*/
LLVMValueRef coscof_p0 = lp_build_const_v4sf(2.443315711809948E-005);
LLVMValueRef coscof_p1 = lp_build_const_v4sf(-1.388731625493765E-003);
LLVMValueRef coscof_p2 = lp_build_const_v4sf(4.166664568298827E-002);
/*
* y = *(v4sf*)_ps_coscof_p0;
* y = _mm_mul_ps(y, z);
*/
LLVMValueRef y_3 = LLVMBuildFMul(b, z, coscof_p0, "y_3");
LLVMValueRef y_4 = LLVMBuildFAdd(b, y_3, coscof_p1, "y_4");
LLVMValueRef y_5 = LLVMBuildFMul(b, y_4, z, "y_5");
LLVMValueRef y_6 = LLVMBuildFAdd(b, y_5, coscof_p2, "y_6");
LLVMValueRef y_7 = LLVMBuildFMul(b, y_6, z, "y_7");
LLVMValueRef y_8 = LLVMBuildFMul(b, y_7, z, "y_8");
/*
* tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5);
* y = _mm_sub_ps(y, tmp);
* y = _mm_add_ps(y, *(v4sf*)_ps_1);
*/
LLVMValueRef half = lp_build_const_v4sf(0.5);
LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp");
LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8");
LLVMValueRef one = lp_build_const_v4sf(1.0);
LLVMValueRef y_10 = LLVMBuildFAdd(b, y_9, one, "y_9");
/*
* _PS_CONST(sincof_p0, -1.9515295891E-4);
* _PS_CONST(sincof_p1, 8.3321608736E-3);
* _PS_CONST(sincof_p2, -1.6666654611E-1);
*/
LLVMValueRef sincof_p0 = lp_build_const_v4sf(-1.9515295891E-4);
LLVMValueRef sincof_p1 = lp_build_const_v4sf(8.3321608736E-3);
LLVMValueRef sincof_p2 = lp_build_const_v4sf(-1.6666654611E-1);
/*
* Evaluate the second polynom (Pi/4 <= x <= 0)
*
* y2 = *(v4sf*)_ps_sincof_p0;
* y2 = _mm_mul_ps(y2, z);
* y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1);
* y2 = _mm_mul_ps(y2, z);
* y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2);
* y2 = _mm_mul_ps(y2, z);
* y2 = _mm_mul_ps(y2, x);
* y2 = _mm_add_ps(y2, x);
*/
LLVMValueRef y2_3 = LLVMBuildFMul(b, z, sincof_p0, "y2_3");
LLVMValueRef y2_4 = LLVMBuildFAdd(b, y2_3, sincof_p1, "y2_4");
LLVMValueRef y2_5 = LLVMBuildFMul(b, y2_4, z, "y2_5");
LLVMValueRef y2_6 = LLVMBuildFAdd(b, y2_5, sincof_p2, "y2_6");
LLVMValueRef y2_7 = LLVMBuildFMul(b, y2_6, z, "y2_7");
LLVMValueRef y2_8 = LLVMBuildFMul(b, y2_7, x_3, "y2_8");
LLVMValueRef y2_9 = LLVMBuildFAdd(b, y2_8, x_3, "y2_9");
/*
* select the correct result from the two polynoms
* xmm3 = poly_mask;
* y2 = _mm_and_ps(xmm3, y2); //, xmm3);
* y = _mm_andnot_ps(xmm3, y);
* y = _mm_add_ps(y,y2);
*/
LLVMValueRef y2_i = LLVMBuildBitCast(b, y2_9, v4si, "y2_i");
LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, v4si, "y_i");
LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and");
LLVMValueRef poly_mask_inv = LLVMBuildXor(b, poly_mask, inv, "poly_mask_inv");
LLVMValueRef y_and = LLVMBuildAnd(b, y_i, poly_mask_inv, "y_and");
LLVMValueRef y_combine = LLVMBuildAdd(b, y_and, y2_and, "y_combine");
/*
* update the sign
* y = _mm_xor_ps(y, sign_bit);
*/
LLVMValueRef y_sign = LLVMBuildXor(b, y_combine, sign_bit, "y_sin");
LLVMValueRef y_result = LLVMBuildBitCast(b, y_sign, v4sf, "y_result");
return y_result;
}
/**
* Generate pow(x, y)
*/
LLVMValueRef
lp_build_pow(struct lp_build_context *bld,
LLVMValueRef x,
LLVMValueRef y)
{
/* TODO: optimize the constant case */
if (gallivm_debug & GALLIVM_DEBUG_PERF &&
LLVMIsConstant(x) && LLVMIsConstant(y)) {
debug_printf("%s: inefficient/imprecise constant arithmetic\n",
__FUNCTION__);
}
return lp_build_exp2(bld, lp_build_mul(bld, lp_build_log2(bld, x), y));
}
/**
* Generate exp(x)
*/
LLVMValueRef
lp_build_exp(struct lp_build_context *bld,
LLVMValueRef x)
{
/* log2(e) = 1/log(2) */
LLVMValueRef log2e = lp_build_const_vec(bld->type, 1.4426950408889634);
assert(lp_check_value(bld->type, x));
return lp_build_mul(bld, log2e, lp_build_exp2(bld, x));
}
/**
* Generate log(x)
*/
LLVMValueRef
lp_build_log(struct lp_build_context *bld,
LLVMValueRef x)
{
/* log(2) */
LLVMValueRef log2 = lp_build_const_vec(bld->type, 0.69314718055994529);
assert(lp_check_value(bld->type, x));
return lp_build_mul(bld, log2, lp_build_exp2(bld, x));
}
/**
* Generate polynomial.
* Ex: coeffs[0] + x * coeffs[1] + x^2 * coeffs[2].
*/
static LLVMValueRef
lp_build_polynomial(struct lp_build_context *bld,
LLVMValueRef x,
const double *coeffs,
unsigned num_coeffs)
{
const struct lp_type type = bld->type;
LLVMValueRef res = NULL;
unsigned i;
assert(lp_check_value(bld->type, x));
/* TODO: optimize the constant case */
if (gallivm_debug & GALLIVM_DEBUG_PERF &&
LLVMIsConstant(x)) {
debug_printf("%s: inefficient/imprecise constant arithmetic\n",
__FUNCTION__);
}
for (i = num_coeffs; i--; ) {
LLVMValueRef coeff;
coeff = lp_build_const_vec(type, coeffs[i]);
if(res)
res = lp_build_add(bld, coeff, lp_build_mul(bld, x, res));
else
res = coeff;
}
if(res)
return res;
else
return bld->undef;
}
/**
* Minimax polynomial fit of 2**x, in range [0, 1[
*/
const double lp_build_exp2_polynomial[] = {
#if EXP_POLY_DEGREE == 5
0.999999999690134838155,
0.583974334321735217258,
0.164553105719676828492,
0.0292811063701710962255,
0.00354944426657875141846,
0.000296253726543423377365
#elif EXP_POLY_DEGREE == 4
1.00000001502262084505,
0.563586057338685991394,
0.150436017652442413623,
0.0243220604213317927308,
0.0025359088446580436489
#elif EXP_POLY_DEGREE == 3
0.999925218562710312959,
0.695833540494823811697,
0.226067155427249155588,
0.0780245226406372992967
#elif EXP_POLY_DEGREE == 2
1.00172476321474503578,
0.657636275736077639316,
0.33718943461968720704
#else
#error
#endif
};
void
lp_build_exp2_approx(struct lp_build_context *bld,
LLVMValueRef x,
LLVMValueRef *p_exp2_int_part,
LLVMValueRef *p_frac_part,
LLVMValueRef *p_exp2)
{
const struct lp_type type = bld->type;
LLVMTypeRef vec_type = lp_build_vec_type(type);
LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
LLVMValueRef ipart = NULL;
LLVMValueRef fpart = NULL;
LLVMValueRef expipart = NULL;
LLVMValueRef expfpart = NULL;
LLVMValueRef res = NULL;
assert(lp_check_value(bld->type, x));
if(p_exp2_int_part || p_frac_part || p_exp2) {
/* TODO: optimize the constant case */
if (gallivm_debug & GALLIVM_DEBUG_PERF &&
LLVMIsConstant(x)) {
debug_printf("%s: inefficient/imprecise constant arithmetic\n",
__FUNCTION__);
}
assert(type.floating && type.width == 32);
x = lp_build_min(bld, x, lp_build_const_vec(type, 129.0));
x = lp_build_max(bld, x, lp_build_const_vec(type, -126.99999));
/* ipart = floor(x) */
ipart = lp_build_floor(bld, x);
/* fpart = x - ipart */
fpart = LLVMBuildFSub(bld->builder, x, ipart, "");
}
if(p_exp2_int_part || p_exp2) {
/* expipart = (float) (1 << ipart) */
ipart = LLVMBuildFPToSI(bld->builder, ipart, int_vec_type, "");
expipart = LLVMBuildAdd(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
expipart = LLVMBuildShl(bld->builder, expipart, lp_build_const_int_vec(type, 23), "");
expipart = LLVMBuildBitCast(bld->builder, expipart, vec_type, "");
}
if(p_exp2) {
expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial,
Elements(lp_build_exp2_polynomial));
res = LLVMBuildFMul(bld->builder, expipart, expfpart, "");
}
if(p_exp2_int_part)
*p_exp2_int_part = expipart;
if(p_frac_part)
*p_frac_part = fpart;
if(p_exp2)
*p_exp2 = res;
}
LLVMValueRef
lp_build_exp2(struct lp_build_context *bld,
LLVMValueRef x)
{
LLVMValueRef res;
lp_build_exp2_approx(bld, x, NULL, NULL, &res);
return res;
}
/**
* Minimax polynomial fit of log2(x)/(x - 1), for x in range [1, 2[
* These coefficients can be generate with
* http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
*/
const double lp_build_log2_polynomial[] = {
#if LOG_POLY_DEGREE == 6
3.11578814719469302614,
-3.32419399085241980044,
2.59883907202499966007,
-1.23152682416275988241,
0.318212422185251071475,
-0.0344359067839062357313
#elif LOG_POLY_DEGREE == 5
2.8882704548164776201,
-2.52074962577807006663,
1.48116647521213171641,
-0.465725644288844778798,
0.0596515482674574969533
#elif LOG_POLY_DEGREE == 4
2.61761038894603480148,
-1.75647175389045657003,
0.688243882994381274313,
-0.107254423828329604454
#elif LOG_POLY_DEGREE == 3
2.28330284476918490682,
-1.04913055217340124191,
0.204446009836232697516
#else
#error
#endif
};
/**
* See http://www.devmaster.net/forums/showthread.php?p=43580
*/
void
lp_build_log2_approx(struct lp_build_context *bld,
LLVMValueRef x,
LLVMValueRef *p_exp,
LLVMValueRef *p_floor_log2,
LLVMValueRef *p_log2)
{
const struct lp_type type = bld->type;
LLVMTypeRef vec_type = lp_build_vec_type(type);
LLVMTypeRef int_vec_type = lp_build_int_vec_type(type);
LLVMValueRef expmask = lp_build_const_int_vec(type, 0x7f800000);
LLVMValueRef mantmask = lp_build_const_int_vec(type, 0x007fffff);
LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
LLVMValueRef i = NULL;
LLVMValueRef exp = NULL;
LLVMValueRef mant = NULL;
LLVMValueRef logexp = NULL;
LLVMValueRef logmant = NULL;
LLVMValueRef res = NULL;
assert(lp_check_value(bld->type, x));
if(p_exp || p_floor_log2 || p_log2) {
/* TODO: optimize the constant case */
if (gallivm_debug & GALLIVM_DEBUG_PERF &&
LLVMIsConstant(x)) {
debug_printf("%s: inefficient/imprecise constant arithmetic\n",
__FUNCTION__);
}
assert(type.floating && type.width == 32);
i = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
/* exp = (float) exponent(x) */
exp = LLVMBuildAnd(bld->builder, i, expmask, "");
}
if(p_floor_log2 || p_log2) {
logexp = LLVMBuildLShr(bld->builder, exp, lp_build_const_int_vec(type, 23), "");
logexp = LLVMBuildSub(bld->builder, logexp, lp_build_const_int_vec(type, 127), "");
logexp = LLVMBuildSIToFP(bld->builder, logexp, vec_type, "");
}
if(p_log2) {
/* mant = (float) mantissa(x) */
mant = LLVMBuildAnd(bld->builder, i, mantmask, "");
mant = LLVMBuildOr(bld->builder, mant, one, "");
mant = LLVMBuildBitCast(bld->builder, mant, vec_type, "");
logmant = lp_build_polynomial(bld, mant, lp_build_log2_polynomial,
Elements(lp_build_log2_polynomial));
/* This effectively increases the polynomial degree by one, but ensures that log2(1) == 0*/
logmant = LLVMBuildFMul(bld->builder, logmant, LLVMBuildFSub(bld->builder, mant, bld->one, ""), "");
res = LLVMBuildFAdd(bld->builder, logmant, logexp, "");
}
if(p_exp) {
exp = LLVMBuildBitCast(bld->builder, exp, vec_type, "");
*p_exp = exp;
}
if(p_floor_log2)
*p_floor_log2 = logexp;
if(p_log2)
*p_log2 = res;
}
LLVMValueRef
lp_build_log2(struct lp_build_context *bld,
LLVMValueRef x)
{
LLVMValueRef res;
lp_build_log2_approx(bld, x, NULL, NULL, &res);
return res;
}
/**
* Faster (and less accurate) log2.
*
* log2(x) = floor(log2(x)) + frac(x)
*
* See http://www.flipcode.com/archives/Fast_log_Function.shtml
*/
LLVMValueRef
lp_build_fast_log2(struct lp_build_context *bld,
LLVMValueRef x)
{
const struct lp_type type = bld->type;
LLVMTypeRef vec_type = bld->vec_type;
LLVMTypeRef int_vec_type = bld->int_vec_type;
unsigned mantissa = lp_mantissa(type);
LLVMValueRef mantmask = lp_build_const_int_vec(type, (1ULL << mantissa) - 1);
LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type);
LLVMValueRef ipart;
LLVMValueRef fpart;
assert(lp_check_value(bld->type, x));
assert(type.floating);
x = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
/* ipart = floor(log2(x)) - 1 */
ipart = LLVMBuildLShr(bld->builder, x, lp_build_const_int_vec(type, mantissa), "");
ipart = LLVMBuildAnd(bld->builder, ipart, lp_build_const_int_vec(type, 255), "");
ipart = LLVMBuildSub(bld->builder, ipart, lp_build_const_int_vec(type, 128), "");
ipart = LLVMBuildSIToFP(bld->builder, ipart, vec_type, "");
/* fpart = 1.0 + frac(x) */
fpart = LLVMBuildAnd(bld->builder, x, mantmask, "");
fpart = LLVMBuildOr(bld->builder, fpart, one, "");
fpart = LLVMBuildBitCast(bld->builder, fpart, vec_type, "");
/* floor(log2(x)) + frac(x) */
return LLVMBuildFAdd(bld->builder, ipart, fpart, "");
}
/**
* Fast implementation of iround(log2(x)).
*
* Not an approximation -- it should give accurate results all the time.
*/
LLVMValueRef
lp_build_ilog2(struct lp_build_context *bld,
LLVMValueRef x)
{
const struct lp_type type = bld->type;
LLVMTypeRef int_vec_type = bld->int_vec_type;
unsigned mantissa = lp_mantissa(type);
LLVMValueRef sqrt2 = lp_build_const_vec(type, 1.4142135623730951);
LLVMValueRef ipart;
assert(lp_check_value(bld->type, x));
assert(type.floating);
/* x * 2^(0.5) i.e., add 0.5 to the log2(x) */
x = LLVMBuildFMul(bld->builder, x, sqrt2, "");
x = LLVMBuildBitCast(bld->builder, x, int_vec_type, "");
/* ipart = floor(log2(x) + 0.5) */
ipart = LLVMBuildLShr(bld->builder, x, lp_build_const_int_vec(type, mantissa), "");
ipart = LLVMBuildAnd(bld->builder, ipart, lp_build_const_int_vec(type, 255), "");
ipart = LLVMBuildSub(bld->builder, ipart, lp_build_const_int_vec(type, 127), "");
return ipart;
}