/************************************************************************** * * 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 */ #include #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_init.h" #include "lp_bld_intr.h" #include "lp_bld_logic.h" #include "lp_bld_pack.h" #include "lp_bld_debug.h" #include "lp_bld_bitarit.h" #include "lp_bld_arit.h" #define EXP_POLY_DEGREE 5 #define LOG_POLY_DEGREE 4 /** * 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; unsigned intr_size = 0; LLVMValueRef cond; assert(lp_check_value(type, a)); assert(lp_check_value(type, b)); /* TODO: optimize the constant case */ if (type.floating && util_cpu_caps.has_sse) { if (type.width == 32) { if (type.length == 1) { intrinsic = "llvm.x86.sse.min.ss"; intr_size = 128; } else if (type.length <= 4 || !util_cpu_caps.has_avx) { intrinsic = "llvm.x86.sse.min.ps"; intr_size = 128; } else { intrinsic = "llvm.x86.avx.min.ps.256"; intr_size = 256; } } if (type.width == 64 && util_cpu_caps.has_sse2) { if (type.length == 1) { intrinsic = "llvm.x86.sse2.min.sd"; intr_size = 128; } else if (type.length == 2 || !util_cpu_caps.has_avx) { intrinsic = "llvm.x86.sse2.min.pd"; intr_size = 128; } else { intrinsic = "llvm.x86.avx.min.pd.256"; intr_size = 256; } } } else if (type.floating && util_cpu_caps.has_altivec) { if (type.width == 32 && type.length == 4) { intrinsic = "llvm.ppc.altivec.vminfp"; intr_size = 128; } } else if (util_cpu_caps.has_sse2 && type.length >= 2) { intr_size = 128; if ((type.width == 8 || type.width == 16) && (type.width * type.length <= 64) && (gallivm_debug & GALLIVM_DEBUG_PERF)) { debug_printf("%s: inefficient code, bogus shuffle due to packing\n", __FUNCTION__); } if (type.width == 8 && !type.sign) { intrinsic = "llvm.x86.sse2.pminu.b"; } else if (type.width == 16 && type.sign) { intrinsic = "llvm.x86.sse2.pmins.w"; } if (util_cpu_caps.has_sse4_1) { if (type.width == 8 && type.sign) { intrinsic = "llvm.x86.sse41.pminsb"; } if (type.width == 16 && !type.sign) { intrinsic = "llvm.x86.sse41.pminuw"; } if (type.width == 32 && !type.sign) { intrinsic = "llvm.x86.sse41.pminud"; } if (type.width == 32 && type.sign) { intrinsic = "llvm.x86.sse41.pminsd"; } } } else if (util_cpu_caps.has_altivec) { intr_size = 128; if (type.width == 8) { if (!type.sign) { intrinsic = "llvm.ppc.altivec.vminub"; } else { intrinsic = "llvm.ppc.altivec.vminsb"; } } else if (type.width == 16) { if (!type.sign) { intrinsic = "llvm.ppc.altivec.vminuh"; } else { intrinsic = "llvm.ppc.altivec.vminsh"; } } else if (type.width == 32) { if (!type.sign) { intrinsic = "llvm.ppc.altivec.vminuw"; } else { intrinsic = "llvm.ppc.altivec.vminsw"; } } } if(intrinsic) { return lp_build_intrinsic_binary_anylength(bld->gallivm, intrinsic, type, intr_size, 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; unsigned intr_size = 0; LLVMValueRef cond; assert(lp_check_value(type, a)); assert(lp_check_value(type, b)); /* TODO: optimize the constant case */ if (type.floating && util_cpu_caps.has_sse) { if (type.width == 32) { if (type.length == 1) { intrinsic = "llvm.x86.sse.max.ss"; intr_size = 128; } else if (type.length <= 4 || !util_cpu_caps.has_avx) { intrinsic = "llvm.x86.sse.max.ps"; intr_size = 128; } else { intrinsic = "llvm.x86.avx.max.ps.256"; intr_size = 256; } } if (type.width == 64 && util_cpu_caps.has_sse2) { if (type.length == 1) { intrinsic = "llvm.x86.sse2.max.sd"; intr_size = 128; } else if (type.length == 2 || !util_cpu_caps.has_avx) { intrinsic = "llvm.x86.sse2.max.pd"; intr_size = 128; } else { intrinsic = "llvm.x86.avx.max.pd.256"; intr_size = 256; } } } else if (type.floating && util_cpu_caps.has_altivec) { if (type.width == 32 || type.length == 4) { intrinsic = "llvm.ppc.altivec.vmaxfp"; intr_size = 128; } } else if (util_cpu_caps.has_sse2 && type.length >= 2) { intr_size = 128; if ((type.width == 8 || type.width == 16) && (type.width * type.length <= 64) && (gallivm_debug & GALLIVM_DEBUG_PERF)) { debug_printf("%s: inefficient code, bogus shuffle due to packing\n", __FUNCTION__); } if (type.width == 8 && !type.sign) { intrinsic = "llvm.x86.sse2.pmaxu.b"; intr_size = 128; } else if (type.width == 16 && type.sign) { intrinsic = "llvm.x86.sse2.pmaxs.w"; } if (util_cpu_caps.has_sse4_1) { if (type.width == 8 && type.sign) { intrinsic = "llvm.x86.sse41.pmaxsb"; } if (type.width == 16 && !type.sign) { intrinsic = "llvm.x86.sse41.pmaxuw"; } if (type.width == 32 && !type.sign) { intrinsic = "llvm.x86.sse41.pmaxud"; } if (type.width == 32 && type.sign) { intrinsic = "llvm.x86.sse41.pmaxsd"; } } } else if (util_cpu_caps.has_altivec) { intr_size = 128; if (type.width == 8) { if (!type.sign) { intrinsic = "llvm.ppc.altivec.vmaxub"; } else { intrinsic = "llvm.ppc.altivec.vmaxsb"; } } else if (type.width == 16) { if (!type.sign) { intrinsic = "llvm.ppc.altivec.vmaxuh"; } else { intrinsic = "llvm.ppc.altivec.vmaxsh"; } } else if (type.width == 32) { if (!type.sign) { intrinsic = "llvm.ppc.altivec.vmaxuw"; } else { intrinsic = "llvm.ppc.altivec.vmaxsw"; } } } if(intrinsic) { return lp_build_intrinsic_binary_anylength(bld->gallivm, intrinsic, type, intr_size, 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) { LLVMBuilderRef builder = bld->gallivm->builder; 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(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(builder, bld->one, a, ""); else return LLVMBuildSub(builder, bld->one, a, ""); } /** * Generate a + b */ LLVMValueRef lp_build_add(struct lp_build_context *bld, LLVMValueRef a, LLVMValueRef b) { LLVMBuilderRef builder = bld->gallivm->builder; 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 (type.width * type.length == 128 && !type.floating && !type.fixed) { if(util_cpu_caps.has_sse2) { 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"; } else if (util_cpu_caps.has_altivec) { if(type.width == 8) intrinsic = type.sign ? "llvm.ppc.altivec.vaddsbs" : "llvm.ppc.altivec.vaddubs"; if(type.width == 16) intrinsic = type.sign ? "llvm.ppc.altivec.vaddshs" : "llvm.ppc.altivec.vadduhs"; } } if(intrinsic) return lp_build_intrinsic_binary(builder, intrinsic, lp_build_vec_type(bld->gallivm, bld->type), a, b); } /* TODO: handle signed case */ if(type.norm && !type.floating && !type.fixed && !type.sign) a = lp_build_min_simple(bld, a, lp_build_comp(bld, b)); if(LLVMIsConstant(a) && LLVMIsConstant(b)) if (type.floating) res = LLVMConstFAdd(a, b); else res = LLVMConstAdd(a, b); else if (type.floating) res = LLVMBuildFAdd(builder, a, b, ""); else res = LLVMBuildAdd(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. * Should avoid this operation whenever possible. */ LLVMValueRef lp_build_horizontal_add(struct lp_build_context *bld, LLVMValueRef a) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; LLVMValueRef index, res; unsigned i, length; LLVMValueRef shuffles1[LP_MAX_VECTOR_LENGTH / 2]; LLVMValueRef shuffles2[LP_MAX_VECTOR_LENGTH / 2]; LLVMValueRef vecres, elem2; assert(lp_check_value(type, a)); if (type.length == 1) { return a; } assert(!bld->type.norm); /* * for byte vectors can do much better with psadbw. * Using repeated shuffle/adds here. Note with multiple vectors * this can be done more efficiently as outlined in the intel * optimization manual. * Note: could cause data rearrangement if used with smaller element * sizes. */ vecres = a; length = type.length / 2; while (length > 1) { LLVMValueRef vec1, vec2; for (i = 0; i < length; i++) { shuffles1[i] = lp_build_const_int32(bld->gallivm, i); shuffles2[i] = lp_build_const_int32(bld->gallivm, i + length); } vec1 = LLVMBuildShuffleVector(builder, vecres, vecres, LLVMConstVector(shuffles1, length), ""); vec2 = LLVMBuildShuffleVector(builder, vecres, vecres, LLVMConstVector(shuffles2, length), ""); if (type.floating) { vecres = LLVMBuildFAdd(builder, vec1, vec2, ""); } else { vecres = LLVMBuildAdd(builder, vec1, vec2, ""); } length = length >> 1; } /* always have vector of size 2 here */ assert(length == 1); index = lp_build_const_int32(bld->gallivm, 0); res = LLVMBuildExtractElement(builder, vecres, index, ""); index = lp_build_const_int32(bld->gallivm, 1); elem2 = LLVMBuildExtractElement(builder, vecres, index, ""); if (type.floating) res = LLVMBuildFAdd(builder, res, elem2, ""); else res = LLVMBuildAdd(builder, res, elem2, ""); return res; } /** * Return the horizontal sums of 4 float vectors as a float4 vector. * This uses the technique as outlined in Intel Optimization Manual. */ static LLVMValueRef lp_build_horizontal_add4x4f(struct lp_build_context *bld, LLVMValueRef src[4]) { struct gallivm_state *gallivm = bld->gallivm; LLVMBuilderRef builder = gallivm->builder; LLVMValueRef shuffles[4]; LLVMValueRef tmp[4]; LLVMValueRef sumtmp[2], shuftmp[2]; /* lower half of regs */ shuffles[0] = lp_build_const_int32(gallivm, 0); shuffles[1] = lp_build_const_int32(gallivm, 1); shuffles[2] = lp_build_const_int32(gallivm, 4); shuffles[3] = lp_build_const_int32(gallivm, 5); tmp[0] = LLVMBuildShuffleVector(builder, src[0], src[1], LLVMConstVector(shuffles, 4), ""); tmp[2] = LLVMBuildShuffleVector(builder, src[2], src[3], LLVMConstVector(shuffles, 4), ""); /* upper half of regs */ shuffles[0] = lp_build_const_int32(gallivm, 2); shuffles[1] = lp_build_const_int32(gallivm, 3); shuffles[2] = lp_build_const_int32(gallivm, 6); shuffles[3] = lp_build_const_int32(gallivm, 7); tmp[1] = LLVMBuildShuffleVector(builder, src[0], src[1], LLVMConstVector(shuffles, 4), ""); tmp[3] = LLVMBuildShuffleVector(builder, src[2], src[3], LLVMConstVector(shuffles, 4), ""); sumtmp[0] = LLVMBuildFAdd(builder, tmp[0], tmp[1], ""); sumtmp[1] = LLVMBuildFAdd(builder, tmp[2], tmp[3], ""); shuffles[0] = lp_build_const_int32(gallivm, 0); shuffles[1] = lp_build_const_int32(gallivm, 2); shuffles[2] = lp_build_const_int32(gallivm, 4); shuffles[3] = lp_build_const_int32(gallivm, 6); shuftmp[0] = LLVMBuildShuffleVector(builder, sumtmp[0], sumtmp[1], LLVMConstVector(shuffles, 4), ""); shuffles[0] = lp_build_const_int32(gallivm, 1); shuffles[1] = lp_build_const_int32(gallivm, 3); shuffles[2] = lp_build_const_int32(gallivm, 5); shuffles[3] = lp_build_const_int32(gallivm, 7); shuftmp[1] = LLVMBuildShuffleVector(builder, sumtmp[0], sumtmp[1], LLVMConstVector(shuffles, 4), ""); return LLVMBuildFAdd(builder, shuftmp[0], shuftmp[1], ""); } /* * partially horizontally add 2-4 float vectors with length nx4, * i.e. only four adjacent values in each vector will be added, * assuming values are really grouped in 4 which also determines * output order. * * Return a vector of the same length as the initial vectors, * with the excess elements (if any) being undefined. * The element order is independent of number of input vectors. * For 3 vectors x0x1x2x3x4x5x6x7, y0y1y2y3y4y5y6y7, z0z1z2z3z4z5z6z7 * the output order thus will be * sumx0-x3,sumy0-y3,sumz0-z3,undef,sumx4-x7,sumy4-y7,sumz4z7,undef */ LLVMValueRef lp_build_hadd_partial4(struct lp_build_context *bld, LLVMValueRef vectors[], unsigned num_vecs) { struct gallivm_state *gallivm = bld->gallivm; LLVMBuilderRef builder = gallivm->builder; LLVMValueRef ret_vec; LLVMValueRef tmp[4]; const char *intrinsic = NULL; assert(num_vecs >= 2 && num_vecs <= 4); assert(bld->type.floating); /* only use this with at least 2 vectors, as it is sort of expensive * (depending on cpu) and we always need two horizontal adds anyway, * so a shuffle/add approach might be better. */ tmp[0] = vectors[0]; tmp[1] = vectors[1]; tmp[2] = num_vecs > 2 ? vectors[2] : vectors[0]; tmp[3] = num_vecs > 3 ? vectors[3] : vectors[0]; if (util_cpu_caps.has_sse3 && bld->type.width == 32 && bld->type.length == 4) { intrinsic = "llvm.x86.sse3.hadd.ps"; } else if (util_cpu_caps.has_avx && bld->type.width == 32 && bld->type.length == 8) { intrinsic = "llvm.x86.avx.hadd.ps.256"; } if (intrinsic) { tmp[0] = lp_build_intrinsic_binary(builder, intrinsic, lp_build_vec_type(gallivm, bld->type), tmp[0], tmp[1]); if (num_vecs > 2) { tmp[1] = lp_build_intrinsic_binary(builder, intrinsic, lp_build_vec_type(gallivm, bld->type), tmp[2], tmp[3]); } else { tmp[1] = tmp[0]; } return lp_build_intrinsic_binary(builder, intrinsic, lp_build_vec_type(gallivm, bld->type), tmp[0], tmp[1]); } if (bld->type.length == 4) { ret_vec = lp_build_horizontal_add4x4f(bld, tmp); } else { LLVMValueRef partres[LP_MAX_VECTOR_LENGTH/4]; unsigned j; unsigned num_iter = bld->type.length / 4; struct lp_type parttype = bld->type; parttype.length = 4; for (j = 0; j < num_iter; j++) { LLVMValueRef partsrc[4]; unsigned i; for (i = 0; i < 4; i++) { partsrc[i] = lp_build_extract_range(gallivm, tmp[i], j*4, 4); } partres[j] = lp_build_horizontal_add4x4f(bld, partsrc); } ret_vec = lp_build_concat(gallivm, partres, parttype, num_iter); } return ret_vec; } /** * Generate a - b */ LLVMValueRef lp_build_sub(struct lp_build_context *bld, LLVMValueRef a, LLVMValueRef b) { LLVMBuilderRef builder = bld->gallivm->builder; 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 (type.width * type.length == 128 && !type.floating && !type.fixed) { if (util_cpu_caps.has_sse2) { 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"; } else if (util_cpu_caps.has_altivec) { if(type.width == 8) intrinsic = type.sign ? "llvm.ppc.altivec.vsubsbs" : "llvm.ppc.altivec.vsububs"; if(type.width == 16) intrinsic = type.sign ? "llvm.ppc.altivec.vsubshs" : "llvm.ppc.altivec.vsubuhs"; } } if(intrinsic) return lp_build_intrinsic_binary(builder, intrinsic, lp_build_vec_type(bld->gallivm, bld->type), a, b); } /* TODO: handle signed case */ if(type.norm && !type.floating && !type.fixed && !type.sign) a = lp_build_max_simple(bld, 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(builder, a, b, ""); else res = LLVMBuildSub(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 multiplication. * * There are several approaches for (using 8-bit normalized multiplication as * an example): * * - 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 of * * 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_norm(struct gallivm_state *gallivm, struct lp_type wide_type, LLVMValueRef a, LLVMValueRef b) { LLVMBuilderRef builder = gallivm->builder; struct lp_build_context bld; unsigned n; LLVMValueRef half; LLVMValueRef ab; assert(!wide_type.floating); assert(lp_check_value(wide_type, a)); assert(lp_check_value(wide_type, b)); lp_build_context_init(&bld, gallivm, wide_type); n = wide_type.width / 2; if (wide_type.sign) { --n; } /* * TODO: for 16bits normalized SSE2 vectors we could consider using PMULHUW * http://ssp.impulsetrain.com/2011/07/03/multiplying-normalized-16-bit-numbers-with-sse2/ */ /* * a*b / (2**n - 1) ~= (a*b + (a*b >> n) + half) >> n */ ab = LLVMBuildMul(builder, a, b, ""); ab = LLVMBuildAdd(builder, ab, lp_build_shr_imm(&bld, ab, n), ""); /* * half = sgn(ab) * 0.5 * (2 ** n) = sgn(ab) * (1 << (n - 1)) */ half = lp_build_const_int_vec(gallivm, wide_type, 1 << (n - 1)); if (wide_type.sign) { LLVMValueRef minus_half = LLVMBuildNeg(builder, half, ""); LLVMValueRef sign = lp_build_shr_imm(&bld, ab, wide_type.width - 1); half = lp_build_select(&bld, sign, minus_half, half); } ab = LLVMBuildAdd(builder, ab, half, ""); /* Final division */ ab = lp_build_shr_imm(&bld, ab, n); return ab; } /** * Generate a * b */ LLVMValueRef lp_build_mul(struct lp_build_context *bld, LLVMValueRef a, LLVMValueRef b) { LLVMBuilderRef builder = bld->gallivm->builder; 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) { struct lp_type wide_type = lp_wider_type(type); LLVMValueRef al, ah, bl, bh, abl, abh, ab; lp_build_unpack2(bld->gallivm, type, wide_type, a, &al, &ah); lp_build_unpack2(bld->gallivm, type, wide_type, b, &bl, &bh); /* PMULLW, PSRLW, PADDW */ abl = lp_build_mul_norm(bld->gallivm, wide_type, al, bl); abh = lp_build_mul_norm(bld->gallivm, wide_type, ah, bh); ab = lp_build_pack2(bld->gallivm, wide_type, type, abl, abh); return ab; } if(type.fixed) shift = lp_build_const_int_vec(bld->gallivm, 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(builder, a, b, ""); else res = LLVMBuildMul(builder, a, b, ""); if(shift) { if(type.sign) res = LLVMBuildAShr(builder, res, shift, ""); else res = LLVMBuildLShr(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) { LLVMBuilderRef builder = bld->gallivm->builder; 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 exponent. * * 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->gallivm, bld->type, (unsigned long long)shift << mantissa); a = LLVMBuildBitCast(builder, a, lp_build_int_vec_type(bld->type), ""); a = LLVMBuildAdd(builder, a, factor, ""); a = LLVMBuildBitCast(builder, a, lp_build_vec_type(bld->gallivm, bld->type), ""); return a; #endif } else { factor = lp_build_const_vec(bld->gallivm, bld->type, shift); return LLVMBuildShl(builder, a, factor, ""); } } factor = lp_build_const_vec(bld->gallivm, 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) { LLVMBuilderRef builder = bld->gallivm->builder; 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) || (util_cpu_caps.has_avx && type.width == 32 && type.length == 8)) && type.floating) return lp_build_mul(bld, a, lp_build_rcp(bld, b)); if (type.floating) return LLVMBuildFDiv(builder, a, b, ""); else if (type.sign) return LLVMBuildSDiv(builder, a, b, ""); else return LLVMBuildUDiv(builder, a, b, ""); } /** * Linear interpolation helper. * * @param normalized whether we are interpolating normalized values, * encoded in normalized integers, twice as wide. * * @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, unsigned flags) { unsigned half_width = bld->type.width/2; LLVMBuilderRef builder = bld->gallivm->builder; 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); if (flags & LP_BLD_LERP_WIDE_NORMALIZED) { if (!bld->type.sign) { if (!(flags & LP_BLD_LERP_PRESCALED_WEIGHTS)) { /* * Scale x from [0, 2**n - 1] to [0, 2**n] by adding the * most-significant-bit to the lowest-significant-bit, so that * later we can just divide by 2**n instead of 2**n - 1. */ x = lp_build_add(bld, x, lp_build_shr_imm(bld, x, half_width - 1)); } /* (x * delta) >> n */ res = lp_build_mul(bld, x, delta); res = lp_build_shr_imm(bld, res, half_width); } else { /* * The rescaling trick above doesn't work for signed numbers, so * use the 2**n - 1 divison approximation in lp_build_mul_norm * instead. */ assert(!(flags & LP_BLD_LERP_PRESCALED_WEIGHTS)); res = lp_build_mul_norm(bld->gallivm, bld->type, x, delta); } } else { assert(!(flags & LP_BLD_LERP_PRESCALED_WEIGHTS)); res = lp_build_mul(bld, x, delta); } res = lp_build_add(bld, v0, res); if (((flags & LP_BLD_LERP_WIDE_NORMALIZED) && !bld->type.sign) || bld->type.fixed) { /* We need to mask out the high order bits when lerping 8bit normalized colors stored on 16bits */ /* XXX: This step is necessary for lerping 8bit colors stored on 16bits, * but it will be wrong for true fixed point use cases. Basically we need * a more powerful lp_type, capable of further distinguishing the values * interpretation from the value storage. */ res = LLVMBuildAnd(builder, res, lp_build_const_int_vec(bld->gallivm, bld->type, (1 << half_width) - 1), ""); } return res; } /** * Linear interpolation. */ LLVMValueRef lp_build_lerp(struct lp_build_context *bld, LLVMValueRef x, LLVMValueRef v0, LLVMValueRef v1, unsigned flags) { 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)); assert(!(flags & LP_BLD_LERP_WIDE_NORMALIZED)); if (type.norm) { struct lp_type wide_type; struct lp_build_context wide_bld; LLVMValueRef xl, xh, v0l, v0h, v1l, v1h, resl, resh; assert(type.length >= 2); /* * Create a wider integer type, enough to hold the * intermediate result of the multiplication. */ memset(&wide_type, 0, sizeof wide_type); wide_type.sign = type.sign; wide_type.width = type.width*2; wide_type.length = type.length/2; lp_build_context_init(&wide_bld, bld->gallivm, wide_type); lp_build_unpack2(bld->gallivm, type, wide_type, x, &xl, &xh); lp_build_unpack2(bld->gallivm, type, wide_type, v0, &v0l, &v0h); lp_build_unpack2(bld->gallivm, type, wide_type, v1, &v1l, &v1h); /* * Lerp both halves. */ flags |= LP_BLD_LERP_WIDE_NORMALIZED; resl = lp_build_lerp_simple(&wide_bld, xl, v0l, v1l, flags); resh = lp_build_lerp_simple(&wide_bld, xh, v0h, v1h, flags); res = lp_build_pack2(bld->gallivm, wide_type, type, resl, resh); } else { res = lp_build_lerp_simple(bld, x, v0, v1, flags); } return res; } /** * Bilinear interpolation. * * Values indices are in v_{yx}. */ LLVMValueRef lp_build_lerp_2d(struct lp_build_context *bld, LLVMValueRef x, LLVMValueRef y, LLVMValueRef v00, LLVMValueRef v01, LLVMValueRef v10, LLVMValueRef v11, unsigned flags) { LLVMValueRef v0 = lp_build_lerp(bld, x, v00, v01, flags); LLVMValueRef v1 = lp_build_lerp(bld, x, v10, v11, flags); return lp_build_lerp(bld, y, v0, v1, flags); } LLVMValueRef lp_build_lerp_3d(struct lp_build_context *bld, LLVMValueRef x, LLVMValueRef y, LLVMValueRef z, LLVMValueRef v000, LLVMValueRef v001, LLVMValueRef v010, LLVMValueRef v011, LLVMValueRef v100, LLVMValueRef v101, LLVMValueRef v110, LLVMValueRef v111, unsigned flags) { LLVMValueRef v0 = lp_build_lerp_2d(bld, x, y, v000, v001, v010, v011, flags); LLVMValueRef v1 = lp_build_lerp_2d(bld, x, y, v100, v101, v110, v111, flags); return lp_build_lerp(bld, z, v0, v1, flags); } /** * 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 (!bld->type.sign) { 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 (!bld->type.sign) { 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) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, 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(bld->gallivm, type); unsigned long long absMask = ~(1ULL << (type.width - 1)); LLVMValueRef mask = lp_build_const_int_vec(bld->gallivm, type, ((unsigned long long) absMask)); a = LLVMBuildBitCast(builder, a, int_vec_type, ""); a = LLVMBuildAnd(builder, a, mask, ""); a = LLVMBuildBitCast(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(builder, "llvm.x86.ssse3.pabs.b.128", vec_type, a); case 16: return lp_build_intrinsic_unary(builder, "llvm.x86.ssse3.pabs.w.128", vec_type, a); case 32: return lp_build_intrinsic_unary(builder, "llvm.x86.ssse3.pabs.d.128", vec_type, a); } } else if (type.width*type.length == 256 && util_cpu_caps.has_ssse3 && (gallivm_debug & GALLIVM_DEBUG_PERF) && (type.width == 8 || type.width == 16 || type.width == 32)) { debug_printf("%s: inefficient code, should split vectors manually\n", __FUNCTION__); } return lp_build_max(bld, a, LLVMBuildNeg(builder, a, "")); } LLVMValueRef lp_build_negate(struct lp_build_context *bld, LLVMValueRef a) { LLVMBuilderRef builder = bld->gallivm->builder; assert(lp_check_value(bld->type, a)); #if HAVE_LLVM >= 0x0207 if (bld->type.floating) a = LLVMBuildFNeg(builder, a, ""); else #endif a = LLVMBuildNeg(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) { LLVMBuilderRef builder = bld->gallivm->builder; 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(bld->gallivm, type); vec_type = lp_build_vec_type(bld->gallivm, type); mask = lp_build_const_int_vec(bld->gallivm, type, maskBit); /* Take the sign bit and add it to 1 constant */ sign = LLVMBuildBitCast(builder, a, int_type, ""); sign = LLVMBuildAnd(builder, sign, mask, ""); one = LLVMConstBitCast(bld->one, int_type); res = LLVMBuildOr(builder, sign, one, ""); res = LLVMBuildBitCast(builder, res, vec_type, ""); } else { /* signed int/norm/fixed point */ /* could use psign with sse3 and appropriate vectors here */ LLVMValueRef minus_one = lp_build_const_vec(bld->gallivm, 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) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type); LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type); LLVMValueRef shift = lp_build_const_int_vec(bld->gallivm, type, type.width - 1); LLVMValueRef mask = lp_build_const_int_vec(bld->gallivm, type, ~((unsigned long long) 1 << (type.width - 1))); LLVMValueRef val, res; assert(type.floating); assert(lp_check_value(type, a)); /* val = reinterpret_cast(a) */ val = LLVMBuildBitCast(builder, a, int_vec_type, ""); /* val = val & mask */ val = LLVMBuildAnd(builder, val, mask, ""); /* sign = sign << shift */ sign = LLVMBuildShl(builder, sign, shift, ""); /* res = val | sign */ res = LLVMBuildOr(builder, val, sign, ""); /* res = reinterpret_cast(res) */ res = LLVMBuildBitCast(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) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type); assert(type.floating); return LLVMBuildSIToFP(builder, a, vec_type, ""); } static boolean arch_rounding_available(const struct lp_type type) { if ((util_cpu_caps.has_sse4_1 && (type.length == 1 || type.width*type.length == 128)) || (util_cpu_caps.has_avx && type.width*type.length == 256)) return TRUE; else if ((util_cpu_caps.has_altivec && (type.width == 32 && type.length == 4))) return TRUE; return FALSE; } enum lp_build_round_mode { LP_BUILD_ROUND_NEAREST = 0, LP_BUILD_ROUND_FLOOR = 1, LP_BUILD_ROUND_CEIL = 2, LP_BUILD_ROUND_TRUNCATE = 3 }; /** * Helper for SSE4.1's ROUNDxx instructions. * * NOTE: In the SSE4.1's nearest mode, if two values are equally close, the * result is the even value. That is, rounding 2.5 will be 2.0, and not 3.0. */ static INLINE LLVMValueRef lp_build_round_sse41(struct lp_build_context *bld, LLVMValueRef a, enum lp_build_round_mode mode) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; LLVMTypeRef i32t = LLVMInt32TypeInContext(bld->gallivm->context); 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(builder, undef, a, index0, ""); args[2] = LLVMConstInt(i32t, mode, 0); res = lp_build_intrinsic(builder, intrinsic, vec_type, args, Elements(args)); res = LLVMBuildExtractElement(builder, res, index0, ""); } else { if (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; } } else { assert(type.width * type.length == 256); assert(util_cpu_caps.has_avx); switch(type.width) { case 32: intrinsic = "llvm.x86.avx.round.ps.256"; break; case 64: intrinsic = "llvm.x86.avx.round.pd.256"; break; default: assert(0); return bld->undef; } } res = lp_build_intrinsic_binary(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) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; LLVMTypeRef i32t = LLVMInt32TypeInContext(bld->gallivm->context); LLVMTypeRef ret_type = lp_build_int_vec_type(bld->gallivm, 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(builder, undef, a, index0, ""); res = lp_build_intrinsic_unary(builder, intrinsic, ret_type, arg); } else { if (type.width* type.length == 128) { intrinsic = "llvm.x86.sse2.cvtps2dq"; } else { assert(type.width*type.length == 256); assert(util_cpu_caps.has_avx); intrinsic = "llvm.x86.avx.cvt.ps2dq.256"; } res = lp_build_intrinsic_unary(builder, intrinsic, ret_type, a); } return res; } /* */ static INLINE LLVMValueRef lp_build_round_altivec(struct lp_build_context *bld, LLVMValueRef a, enum lp_build_round_mode mode) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; const char *intrinsic = NULL; assert(type.floating); assert(lp_check_value(type, a)); assert(util_cpu_caps.has_altivec); switch (mode) { case LP_BUILD_ROUND_NEAREST: intrinsic = "llvm.ppc.altivec.vrfin"; break; case LP_BUILD_ROUND_FLOOR: intrinsic = "llvm.ppc.altivec.vrfim"; break; case LP_BUILD_ROUND_CEIL: intrinsic = "llvm.ppc.altivec.vrfip"; break; case LP_BUILD_ROUND_TRUNCATE: intrinsic = "llvm.ppc.altivec.vrfiz"; break; } return lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a); } static INLINE LLVMValueRef lp_build_round_arch(struct lp_build_context *bld, LLVMValueRef a, enum lp_build_round_mode mode) { if (util_cpu_caps.has_sse4_1) return lp_build_round_sse41(bld, a, mode); else /* (util_cpu_caps.has_altivec) */ return lp_build_round_altivec(bld, a, mode); } /** * 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) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; assert(type.floating); assert(lp_check_value(type, a)); if (arch_rounding_available(type)) { return lp_build_round_arch(bld, a, LP_BUILD_ROUND_TRUNCATE); } else { const struct lp_type type = bld->type; struct lp_type inttype; struct lp_build_context intbld; LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 2^24); LLVMValueRef trunc, res, anosign, mask; LLVMTypeRef int_vec_type = bld->int_vec_type; LLVMTypeRef vec_type = bld->vec_type; assert(type.width == 32); /* might want to handle doubles at some point */ inttype = type; inttype.floating = 0; lp_build_context_init(&intbld, bld->gallivm, inttype); /* round by truncation */ trunc = LLVMBuildFPToSI(builder, a, int_vec_type, ""); res = LLVMBuildSIToFP(builder, trunc, vec_type, "floor.trunc"); /* mask out sign bit */ anosign = lp_build_abs(bld, a); /* * mask out all values if anosign > 2^24 * This should work both for large ints (all rounding is no-op for them * because such floats are always exact) as well as special cases like * NaNs, Infs (taking advantage of the fact they use max exponent). * (2^24 is arbitrary anything between 2^24 and 2^31 should work.) */ anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, ""); cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, ""); mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval); return lp_build_select(bld, mask, a, 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) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; assert(type.floating); assert(lp_check_value(type, a)); if (arch_rounding_available(type)) { return lp_build_round_arch(bld, a, LP_BUILD_ROUND_NEAREST); } else { const struct lp_type type = bld->type; struct lp_type inttype; struct lp_build_context intbld; LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 2^24); LLVMValueRef res, anosign, mask; LLVMTypeRef int_vec_type = bld->int_vec_type; LLVMTypeRef vec_type = bld->vec_type; assert(type.width == 32); /* might want to handle doubles at some point */ inttype = type; inttype.floating = 0; lp_build_context_init(&intbld, bld->gallivm, inttype); res = lp_build_iround(bld, a); res = LLVMBuildSIToFP(builder, res, vec_type, ""); /* mask out sign bit */ anosign = lp_build_abs(bld, a); /* * mask out all values if anosign > 2^24 * This should work both for large ints (all rounding is no-op for them * because such floats are always exact) as well as special cases like * NaNs, Infs (taking advantage of the fact they use max exponent). * (2^24 is arbitrary anything between 2^24 and 2^31 should work.) */ anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, ""); cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, ""); mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval); return lp_build_select(bld, mask, a, 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) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; assert(type.floating); assert(lp_check_value(type, a)); if (arch_rounding_available(type)) { return lp_build_round_arch(bld, a, LP_BUILD_ROUND_FLOOR); } else { const struct lp_type type = bld->type; struct lp_type inttype; struct lp_build_context intbld; LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 2^24); LLVMValueRef trunc, res, anosign, mask; LLVMTypeRef int_vec_type = bld->int_vec_type; LLVMTypeRef vec_type = bld->vec_type; assert(type.width == 32); /* might want to handle doubles at some point */ inttype = type; inttype.floating = 0; lp_build_context_init(&intbld, bld->gallivm, inttype); /* round by truncation */ trunc = LLVMBuildFPToSI(builder, a, int_vec_type, ""); res = LLVMBuildSIToFP(builder, trunc, vec_type, "floor.trunc"); if (type.sign) { LLVMValueRef tmp; /* * fix values if rounding is wrong (for non-special cases) * - this is the case if trunc > a */ mask = lp_build_cmp(bld, PIPE_FUNC_GREATER, res, a); /* tmp = trunc > a ? 1.0 : 0.0 */ tmp = LLVMBuildBitCast(builder, bld->one, int_vec_type, ""); tmp = lp_build_and(&intbld, mask, tmp); tmp = LLVMBuildBitCast(builder, tmp, vec_type, ""); res = lp_build_sub(bld, res, tmp); } /* mask out sign bit */ anosign = lp_build_abs(bld, a); /* * mask out all values if anosign > 2^24 * This should work both for large ints (all rounding is no-op for them * because such floats are always exact) as well as special cases like * NaNs, Infs (taking advantage of the fact they use max exponent). * (2^24 is arbitrary anything between 2^24 and 2^31 should work.) */ anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, ""); cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, ""); mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval); return lp_build_select(bld, mask, a, 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) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; assert(type.floating); assert(lp_check_value(type, a)); if (arch_rounding_available(type)) { return lp_build_round_arch(bld, a, LP_BUILD_ROUND_CEIL); } else { const struct lp_type type = bld->type; struct lp_type inttype; struct lp_build_context intbld; LLVMValueRef cmpval = lp_build_const_vec(bld->gallivm, type, 2^24); LLVMValueRef trunc, res, anosign, mask, tmp; LLVMTypeRef int_vec_type = bld->int_vec_type; LLVMTypeRef vec_type = bld->vec_type; assert(type.width == 32); /* might want to handle doubles at some point */ inttype = type; inttype.floating = 0; lp_build_context_init(&intbld, bld->gallivm, inttype); /* round by truncation */ trunc = LLVMBuildFPToSI(builder, a, int_vec_type, ""); trunc = LLVMBuildSIToFP(builder, trunc, vec_type, "ceil.trunc"); /* * fix values if rounding is wrong (for non-special cases) * - this is the case if trunc < a */ mask = lp_build_cmp(bld, PIPE_FUNC_LESS, trunc, a); /* tmp = trunc < a ? 1.0 : 0.0 */ tmp = LLVMBuildBitCast(builder, bld->one, int_vec_type, ""); tmp = lp_build_and(&intbld, mask, tmp); tmp = LLVMBuildBitCast(builder, tmp, vec_type, ""); res = lp_build_add(bld, trunc, tmp); /* mask out sign bit */ anosign = lp_build_abs(bld, a); /* * mask out all values if anosign > 2^24 * This should work both for large ints (all rounding is no-op for them * because such floats are always exact) as well as special cases like * NaNs, Infs (taking advantage of the fact they use max exponent). * (2^24 is arbitrary anything between 2^24 and 2^31 should work.) */ anosign = LLVMBuildBitCast(builder, anosign, int_vec_type, ""); cmpval = LLVMBuildBitCast(builder, cmpval, int_vec_type, ""); mask = lp_build_cmp(&intbld, PIPE_FUNC_GREATER, anosign, cmpval); return lp_build_select(bld, mask, a, 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)); } /** * Prevent returning a fractional part of 1.0 for very small negative values of * 'a' by clamping against 0.99999(9). */ static inline LLVMValueRef clamp_fract(struct lp_build_context *bld, LLVMValueRef fract) { LLVMValueRef max; /* this is the largest number smaller than 1.0 representable as float */ max = lp_build_const_vec(bld->gallivm, bld->type, 1.0 - 1.0/(1LL << (lp_mantissa(bld->type) + 1))); return lp_build_min(bld, fract, max); } /** * Same as lp_build_fract, but guarantees that the result is always smaller * than one. */ LLVMValueRef lp_build_fract_safe(struct lp_build_context *bld, LLVMValueRef a) { return clamp_fract(bld, lp_build_fract(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) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type); assert(type.floating); assert(lp_check_value(type, a)); return LLVMBuildFPToSI(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) { LLVMBuilderRef builder = bld->gallivm->builder; 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))) || (util_cpu_caps.has_avx && type.width == 32 && type.length == 8)) { return lp_build_iround_nearest_sse2(bld, a); } if (arch_rounding_available(type)) { res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_NEAREST); } else { LLVMValueRef half; half = lp_build_const_vec(bld->gallivm, type, 0.5); if (type.sign) { LLVMTypeRef vec_type = bld->vec_type; LLVMValueRef mask = lp_build_const_int_vec(bld->gallivm, type, (unsigned long long)1 << (type.width - 1)); LLVMValueRef sign; /* get sign bit */ sign = LLVMBuildBitCast(builder, a, int_vec_type, ""); sign = LLVMBuildAnd(builder, sign, mask, ""); /* sign * 0.5 */ half = LLVMBuildBitCast(builder, half, int_vec_type, ""); half = LLVMBuildOr(builder, sign, half, ""); half = LLVMBuildBitCast(builder, half, vec_type, ""); } res = LLVMBuildFAdd(builder, a, half, ""); } res = LLVMBuildFPToSI(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) { LLVMBuilderRef builder = bld->gallivm->builder; 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)); res = a; if (type.sign) { if (arch_rounding_available(type)) { res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_FLOOR); } else { struct lp_type inttype; struct lp_build_context intbld; LLVMValueRef trunc, itrunc, mask; assert(type.floating); assert(lp_check_value(type, a)); inttype = type; inttype.floating = 0; lp_build_context_init(&intbld, bld->gallivm, inttype); /* round by truncation */ itrunc = LLVMBuildFPToSI(builder, a, int_vec_type, ""); trunc = LLVMBuildSIToFP(builder, itrunc, bld->vec_type, "ifloor.trunc"); /* * fix values if rounding is wrong (for non-special cases) * - this is the case if trunc > a * The results of doing this with NaNs, very large values etc. * are undefined but this seems to be the case anyway. */ mask = lp_build_cmp(bld, PIPE_FUNC_GREATER, trunc, a); /* cheapie minus one with mask since the mask is minus one / zero */ return lp_build_add(&intbld, itrunc, mask); } } /* round to nearest (toward zero) */ res = LLVMBuildFPToSI(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) { LLVMBuilderRef builder = bld->gallivm->builder; 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 (arch_rounding_available(type)) { res = lp_build_round_arch(bld, a, LP_BUILD_ROUND_CEIL); } else { struct lp_type inttype; struct lp_build_context intbld; LLVMValueRef trunc, itrunc, mask; assert(type.floating); assert(lp_check_value(type, a)); inttype = type; inttype.floating = 0; lp_build_context_init(&intbld, bld->gallivm, inttype); /* round by truncation */ itrunc = LLVMBuildFPToSI(builder, a, int_vec_type, ""); trunc = LLVMBuildSIToFP(builder, itrunc, bld->vec_type, "iceil.trunc"); /* * fix values if rounding is wrong (for non-special cases) * - this is the case if trunc < a * The results of doing this with NaNs, very large values etc. * are undefined but this seems to be the case anyway. */ mask = lp_build_cmp(bld, PIPE_FUNC_LESS, trunc, a); /* cheapie plus one with mask since the mask is minus one / zero */ return lp_build_sub(&intbld, itrunc, mask); } /* round to nearest (toward zero) */ res = LLVMBuildFPToSI(builder, res, int_vec_type, "iceil.res"); return res; } /** * Combined ifloor() & fract(). * * Preferred to calling the functions separately, as it will ensure that the * strategy (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) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; LLVMValueRef ipart; assert(type.floating); assert(lp_check_value(type, a)); if (arch_rounding_available(type)) { /* * floor() is easier. */ ipart = lp_build_floor(bld, a); *out_fpart = LLVMBuildFSub(builder, a, ipart, "fpart"); *out_ipart = LLVMBuildFPToSI(builder, ipart, bld->int_vec_type, "ipart"); } else { /* * ifloor() is easier. */ *out_ipart = lp_build_ifloor(bld, a); ipart = LLVMBuildSIToFP(builder, *out_ipart, bld->vec_type, "ipart"); *out_fpart = LLVMBuildFSub(builder, a, ipart, "fpart"); } } /** * Same as lp_build_ifloor_fract, but guarantees that the fractional part is * always smaller than one. */ void lp_build_ifloor_fract_safe(struct lp_build_context *bld, LLVMValueRef a, LLVMValueRef *out_ipart, LLVMValueRef *out_fpart) { lp_build_ifloor_fract(bld, a, out_ipart, out_fpart); *out_fpart = clamp_fract(bld, *out_fpart); } LLVMValueRef lp_build_sqrt(struct lp_build_context *bld, LLVMValueRef a) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type); char intrinsic[32]; assert(lp_check_value(type, a)); /* TODO: optimize the constant case */ assert(type.floating); if (type.length == 1) { util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.f%u", type.width); } else { util_snprintf(intrinsic, sizeof intrinsic, "llvm.sqrt.v%uf%u", type.length, type.width); } return lp_build_intrinsic_unary(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) { LLVMBuilderRef builder = bld->gallivm->builder; LLVMValueRef two = lp_build_const_vec(bld->gallivm, bld->type, 2.0); LLVMValueRef res; res = LLVMBuildFMul(builder, a, rcp_a, ""); res = LLVMBuildFSub(builder, two, res, ""); res = LLVMBuildFMul(builder, rcp_a, res, ""); return res; } LLVMValueRef lp_build_rcp(struct lp_build_context *bld, LLVMValueRef a) { LLVMBuilderRef builder = bld->gallivm->builder; 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 * dependent * * 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) || (util_cpu_caps.has_avx && type.width == 32 && type.length == 8))){ const unsigned num_iterations = 0; LLVMValueRef res; unsigned i; const char *intrinsic = NULL; if (type.length == 4) { intrinsic = "llvm.x86.sse.rcp.ps"; } else { intrinsic = "llvm.x86.avx.rcp.ps.256"; } res = lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a); for (i = 0; i < num_iterations; ++i) { res = lp_build_rcp_refine(bld, a, res); } return res; } return LLVMBuildFDiv(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 Intel 64 and IA-32 Architectures Optimization Manual. */ static INLINE LLVMValueRef lp_build_rsqrt_refine(struct lp_build_context *bld, LLVMValueRef a, LLVMValueRef rsqrt_a) { LLVMBuilderRef builder = bld->gallivm->builder; LLVMValueRef half = lp_build_const_vec(bld->gallivm, bld->type, 0.5); LLVMValueRef three = lp_build_const_vec(bld->gallivm, bld->type, 3.0); LLVMValueRef res; res = LLVMBuildFMul(builder, rsqrt_a, rsqrt_a, ""); res = LLVMBuildFMul(builder, a, res, ""); res = LLVMBuildFSub(builder, three, res, ""); res = LLVMBuildFMul(builder, rsqrt_a, res, ""); res = LLVMBuildFMul(builder, half, res, ""); return res; } /** * Generate 1/sqrt(a). * Result is undefined for values < 0, infinity for +0. */ LLVMValueRef lp_build_rsqrt(struct lp_build_context *bld, LLVMValueRef a) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; assert(lp_check_value(type, a)); assert(type.floating); /* * This should be faster but all denormals will end up as infinity. */ if (0 && ((util_cpu_caps.has_sse && type.width == 32 && type.length == 4) || (util_cpu_caps.has_avx && type.width == 32 && type.length == 8))) { const unsigned num_iterations = 1; LLVMValueRef res; unsigned i; const char *intrinsic = NULL; if (type.length == 4) { intrinsic = "llvm.x86.sse.rsqrt.ps"; } else { intrinsic = "llvm.x86.avx.rsqrt.ps.256"; } if (num_iterations) { /* * Newton-Raphson will result in NaN instead of infinity for zero, * and NaN instead of zero for infinity. * Also, need to ensure rsqrt(1.0) == 1.0. * All numbers smaller than FLT_MIN will result in +infinity * (rsqrtps treats all denormals as zero). */ /* * Certain non-c99 compilers don't know INFINITY and might not support * hacks to evaluate it at compile time neither. */ const unsigned posinf_int = 0x7F800000; LLVMValueRef cmp; LLVMValueRef flt_min = lp_build_const_vec(bld->gallivm, type, FLT_MIN); LLVMValueRef inf = lp_build_const_int_vec(bld->gallivm, type, posinf_int); inf = LLVMBuildBitCast(builder, inf, lp_build_vec_type(bld->gallivm, type), ""); res = lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a); for (i = 0; i < num_iterations; ++i) { res = lp_build_rsqrt_refine(bld, a, res); } cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_LESS, a, flt_min); res = lp_build_select(bld, cmp, inf, res); cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_EQUAL, a, inf); res = lp_build_select(bld, cmp, bld->zero, res); cmp = lp_build_compare(bld->gallivm, type, PIPE_FUNC_EQUAL, a, bld->one); res = lp_build_select(bld, cmp, bld->one, res); } else { /* rsqrt(1.0) != 1.0 here */ res = lp_build_intrinsic_unary(builder, intrinsic, bld->vec_type, a); } return res; } return lp_build_rcp(bld, lp_build_sqrt(bld, a)); } /** * Generate sin(a) using SSE2 */ LLVMValueRef lp_build_sin(struct lp_build_context *bld, LLVMValueRef a) { struct gallivm_state *gallivm = bld->gallivm; LLVMBuilderRef builder = gallivm->builder; struct lp_type int_type = lp_int_type(bld->type); LLVMBuilderRef b = builder; /* * take the absolute value, * x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask); */ LLVMValueRef inv_sig_mask = lp_build_const_int_vec(gallivm, bld->type, ~0x80000000); LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, bld->int_vec_type, "a_v4si"); LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi"); LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, bld->vec_type, "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_int_vec(gallivm, bld->type, 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_vec(gallivm, bld->type, 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, bld->int_vec_type, "emm2_i"); /* * j=(j+1) & (~1) (see the cephes sources) * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1); */ LLVMValueRef all_one = lp_build_const_int_vec(gallivm, bld->type, 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_int_vec(gallivm, bld->type, ~1); LLVMValueRef emm2_and = LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and"); /* * y = _mm_cvtepi32_ps(emm2); */ LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, bld->vec_type, "y_2"); /* get the swap sign flag * emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4); */ LLVMValueRef pi32_4 = lp_build_const_int_vec(gallivm, bld->type, 4); LLVMValueRef emm0_and = LLVMBuildAnd(b, emm2_add, pi32_4, "emm0_and"); /* * emm2 = _mm_slli_epi32(emm0, 29); */ LLVMValueRef const_29 = lp_build_const_int_vec(gallivm, bld->type, 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/4type, 2); LLVMValueRef emm2_3 = LLVMBuildAnd(b, emm2_and, pi32_2, "emm2_3"); LLVMValueRef poly_mask = lp_build_compare(gallivm, int_type, PIPE_FUNC_EQUAL, emm2_3, lp_build_const_int_vec(gallivm, bld->type, 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_vec(gallivm, bld->type, -0.78515625); LLVMValueRef DP2 = lp_build_const_vec(gallivm, bld->type, -2.4187564849853515625e-4); LLVMValueRef DP3 = lp_build_const_vec(gallivm, bld->type, -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_vec(gallivm, bld->type, 2.443315711809948E-005); LLVMValueRef coscof_p1 = lp_build_const_vec(gallivm, bld->type, -1.388731625493765E-003); LLVMValueRef coscof_p2 = lp_build_const_vec(gallivm, bld->type, 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_vec(gallivm, bld->type, 0.5); LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp"); LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8"); LLVMValueRef one = lp_build_const_vec(gallivm, bld->type, 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_vec(gallivm, bld->type, -1.9515295891E-4); LLVMValueRef sincof_p1 = lp_build_const_vec(gallivm, bld->type, 8.3321608736E-3); LLVMValueRef sincof_p2 = lp_build_const_vec(gallivm, bld->type, -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, bld->int_vec_type, "y2_i"); LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, bld->int_vec_type, "y_i"); LLVMValueRef y2_and = LLVMBuildAnd(b, y2_i, poly_mask, "y2_and"); LLVMValueRef inv = lp_build_const_int_vec(gallivm, bld->type, ~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, bld->vec_type, "y_result"); return y_result; } /** * Generate cos(a) using SSE2 */ LLVMValueRef lp_build_cos(struct lp_build_context *bld, LLVMValueRef a) { struct gallivm_state *gallivm = bld->gallivm; LLVMBuilderRef builder = gallivm->builder; struct lp_type int_type = lp_int_type(bld->type); LLVMBuilderRef b = builder; /* * take the absolute value, * x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask); */ LLVMValueRef inv_sig_mask = lp_build_const_int_vec(gallivm, bld->type, ~0x80000000); LLVMValueRef a_v4si = LLVMBuildBitCast(b, a, bld->int_vec_type, "a_v4si"); LLVMValueRef absi = LLVMBuildAnd(b, a_v4si, inv_sig_mask, "absi"); LLVMValueRef x_abs = LLVMBuildBitCast(b, absi, bld->vec_type, "x_abs"); /* * scale by 4/Pi * y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI); */ LLVMValueRef FOPi = lp_build_const_vec(gallivm, bld->type, 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, bld->int_vec_type, "emm2_i"); /* * j=(j+1) & (~1) (see the cephes sources) * emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1); */ LLVMValueRef all_one = lp_build_const_int_vec(gallivm, bld->type, 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_int_vec(gallivm, bld->type, ~1); LLVMValueRef emm2_and = LLVMBuildAnd(b, emm2_add, inv_one, "emm2_and"); /* * y = _mm_cvtepi32_ps(emm2); */ LLVMValueRef y_2 = LLVMBuildSIToFP(b, emm2_and, bld->vec_type, "y_2"); /* * emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2); */ LLVMValueRef const_2 = lp_build_const_int_vec(gallivm, bld->type, 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_int_vec(gallivm, bld->type, ~0); LLVMValueRef emm0_not = LLVMBuildXor(b, emm2_2, inv, "emm0_not"); LLVMValueRef pi32_4 = lp_build_const_int_vec(gallivm, bld->type, 4); LLVMValueRef emm0_and = LLVMBuildAnd(b, emm0_not, pi32_4, "emm0_and"); /* * emm2 = _mm_slli_epi32(emm0, 29); */ LLVMValueRef const_29 = lp_build_const_int_vec(gallivm, bld->type, 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/4type, 2); LLVMValueRef emm2_3 = LLVMBuildAnd(b, emm2_2, pi32_2, "emm2_3"); LLVMValueRef poly_mask = lp_build_compare(gallivm, int_type, PIPE_FUNC_EQUAL, emm2_3, lp_build_const_int_vec(gallivm, bld->type, 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_vec(gallivm, bld->type, -0.78515625); LLVMValueRef DP2 = lp_build_const_vec(gallivm, bld->type, -2.4187564849853515625e-4); LLVMValueRef DP3 = lp_build_const_vec(gallivm, bld->type, -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_vec(gallivm, bld->type, 2.443315711809948E-005); LLVMValueRef coscof_p1 = lp_build_const_vec(gallivm, bld->type, -1.388731625493765E-003); LLVMValueRef coscof_p2 = lp_build_const_vec(gallivm, bld->type, 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_vec(gallivm, bld->type, 0.5); LLVMValueRef tmp = LLVMBuildFMul(b, z, half, "tmp"); LLVMValueRef y_9 = LLVMBuildFSub(b, y_8, tmp, "y_8"); LLVMValueRef one = lp_build_const_vec(gallivm, bld->type, 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_vec(gallivm, bld->type, -1.9515295891E-4); LLVMValueRef sincof_p1 = lp_build_const_vec(gallivm, bld->type, 8.3321608736E-3); LLVMValueRef sincof_p2 = lp_build_const_vec(gallivm, bld->type, -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, bld->int_vec_type, "y2_i"); LLVMValueRef y_i = LLVMBuildBitCast(b, y_10, bld->int_vec_type, "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, bld->vec_type, "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->gallivm, bld->type, 1.4426950408889634); assert(lp_check_value(bld->type, x)); return lp_build_exp2(bld, lp_build_mul(bld, log2e, x)); } /** * Generate log(x) */ LLVMValueRef lp_build_log(struct lp_build_context *bld, LLVMValueRef x) { /* log(2) */ LLVMValueRef log2 = lp_build_const_vec(bld->gallivm, bld->type, 0.69314718055994529); assert(lp_check_value(bld->type, x)); return lp_build_mul(bld, log2, lp_build_log2(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 even = NULL, odd = NULL; LLVMValueRef x2; 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__); } /* * Calculate odd and even terms seperately to decrease data dependency * Ex: * c[0] + x^2 * c[2] + x^4 * c[4] ... * + x * (c[1] + x^2 * c[3] + x^4 * c[5]) ... */ x2 = lp_build_mul(bld, x, x); for (i = num_coeffs; i--; ) { LLVMValueRef coeff; coeff = lp_build_const_vec(bld->gallivm, type, coeffs[i]); if (i % 2 == 0) { if (even) even = lp_build_add(bld, coeff, lp_build_mul(bld, x2, even)); else even = coeff; } else { if (odd) odd = lp_build_add(bld, coeff, lp_build_mul(bld, x2, odd)); else odd = coeff; } } if (odd) return lp_build_add(bld, lp_build_mul(bld, odd, x), even); else if (even) return even; 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 0.999999925063526176901, 0.693153073200168932794, 0.240153617044375388211, 0.0558263180532956664775, 0.00898934009049466391101, 0.00187757667519147912699 #elif EXP_POLY_DEGREE == 4 1.00000259337069434683, 0.693003834469974940458, 0.24144275689150793076, 0.0520114606103070150235, 0.0135341679161270268764 #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) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, 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(bld->gallivm, type, 129.0)); x = lp_build_max(bld, x, lp_build_const_vec(bld->gallivm, type, -126.99999)); /* ipart = floor(x) */ /* fpart = x - ipart */ lp_build_ifloor_fract(bld, x, &ipart, &fpart); } if(p_exp2_int_part || p_exp2) { /* expipart = (float) (1 << ipart) */ expipart = LLVMBuildAdd(builder, ipart, lp_build_const_int_vec(bld->gallivm, type, 127), ""); expipart = LLVMBuildShl(builder, expipart, lp_build_const_int_vec(bld->gallivm, type, 23), ""); expipart = LLVMBuildBitCast(builder, expipart, vec_type, ""); } if(p_exp2) { expfpart = lp_build_polynomial(bld, fpart, lp_build_exp2_polynomial, Elements(lp_build_exp2_polynomial)); res = LLVMBuildFMul(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; } /** * Extract the exponent of a IEEE-754 floating point value. * * Optionally apply an integer bias. * * Result is an integer value with * * ifloor(log2(x)) + bias */ LLVMValueRef lp_build_extract_exponent(struct lp_build_context *bld, LLVMValueRef x, int bias) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; unsigned mantissa = lp_mantissa(type); LLVMValueRef res; assert(type.floating); assert(lp_check_value(bld->type, x)); x = LLVMBuildBitCast(builder, x, bld->int_vec_type, ""); res = LLVMBuildLShr(builder, x, lp_build_const_int_vec(bld->gallivm, type, mantissa), ""); res = LLVMBuildAnd(builder, res, lp_build_const_int_vec(bld->gallivm, type, 255), ""); res = LLVMBuildSub(builder, res, lp_build_const_int_vec(bld->gallivm, type, 127 - bias), ""); return res; } /** * Extract the mantissa of the a floating. * * Result is a floating point value with * * x / floor(log2(x)) */ LLVMValueRef lp_build_extract_mantissa(struct lp_build_context *bld, LLVMValueRef x) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; unsigned mantissa = lp_mantissa(type); LLVMValueRef mantmask = lp_build_const_int_vec(bld->gallivm, type, (1ULL << mantissa) - 1); LLVMValueRef one = LLVMConstBitCast(bld->one, bld->int_vec_type); LLVMValueRef res; assert(lp_check_value(bld->type, x)); assert(type.floating); x = LLVMBuildBitCast(builder, x, bld->int_vec_type, ""); /* res = x / 2**ipart */ res = LLVMBuildAnd(builder, x, mantmask, ""); res = LLVMBuildOr(builder, res, one, ""); res = LLVMBuildBitCast(builder, res, bld->vec_type, ""); return res; } /** * Minimax polynomial fit of log2((1.0 + sqrt(x))/(1.0 - sqrt(x)))/sqrt(x) ,for x in range of [0, 1/9[ * 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 == 5 2.88539008148777786488L, 0.961796878841293367824L, 0.577058946784739859012L, 0.412914355135828735411L, 0.308591899232910175289L, 0.352376952300281371868L, #elif LOG_POLY_DEGREE == 4 2.88539009343309178325L, 0.961791550404184197881L, 0.577440339438736392009L, 0.403343858251329912514L, 0.406718052498846252698L, #elif LOG_POLY_DEGREE == 3 2.88538959748872753838L, 0.961932915889597772928L, 0.571118517972136195241L, 0.493997535084709500285L, #else #error #endif }; /** * See http://www.devmaster.net/forums/showthread.php?p=43580 * http://en.wikipedia.org/wiki/Logarithm#Calculation * http://www.nezumi.demon.co.uk/consult/logx.htm */ void lp_build_log2_approx(struct lp_build_context *bld, LLVMValueRef x, LLVMValueRef *p_exp, LLVMValueRef *p_floor_log2, LLVMValueRef *p_log2) { LLVMBuilderRef builder = bld->gallivm->builder; const struct lp_type type = bld->type; LLVMTypeRef vec_type = lp_build_vec_type(bld->gallivm, type); LLVMTypeRef int_vec_type = lp_build_int_vec_type(bld->gallivm, type); LLVMValueRef expmask = lp_build_const_int_vec(bld->gallivm, type, 0x7f800000); LLVMValueRef mantmask = lp_build_const_int_vec(bld->gallivm, type, 0x007fffff); LLVMValueRef one = LLVMConstBitCast(bld->one, int_vec_type); LLVMValueRef i = NULL; LLVMValueRef y = NULL; LLVMValueRef z = 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); /* * We don't explicitly handle denormalized numbers. They will yield a * result in the neighbourhood of -127, which appears to be adequate * enough. */ i = LLVMBuildBitCast(builder, x, int_vec_type, ""); /* exp = (float) exponent(x) */ exp = LLVMBuildAnd(builder, i, expmask, ""); } if(p_floor_log2 || p_log2) { logexp = LLVMBuildLShr(builder, exp, lp_build_const_int_vec(bld->gallivm, type, 23), ""); logexp = LLVMBuildSub(builder, logexp, lp_build_const_int_vec(bld->gallivm, type, 127), ""); logexp = LLVMBuildSIToFP(builder, logexp, vec_type, ""); } if(p_log2) { /* mant = 1 + (float) mantissa(x) */ mant = LLVMBuildAnd(builder, i, mantmask, ""); mant = LLVMBuildOr(builder, mant, one, ""); mant = LLVMBuildBitCast(builder, mant, vec_type, ""); /* y = (mant - 1) / (mant + 1) */ y = lp_build_div(bld, lp_build_sub(bld, mant, bld->one), lp_build_add(bld, mant, bld->one) ); /* z = y^2 */ z = lp_build_mul(bld, y, y); /* compute P(z) */ logmant = lp_build_polynomial(bld, z, lp_build_log2_polynomial, Elements(lp_build_log2_polynomial)); /* logmant = y * P(z) */ logmant = lp_build_mul(bld, y, logmant); res = lp_build_add(bld, logmant, logexp); } if(p_exp) { exp = LLVMBuildBitCast(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)) - 1 + x / 2**floor(log2(x)) * * Piece-wise linear approximation, with exact results when x is a * power of two. * * See http://www.flipcode.com/archives/Fast_log_Function.shtml */ LLVMValueRef lp_build_fast_log2(struct lp_build_context *bld, LLVMValueRef x) { LLVMBuilderRef builder = bld->gallivm->builder; LLVMValueRef ipart; LLVMValueRef fpart; assert(lp_check_value(bld->type, x)); assert(bld->type.floating); /* ipart = floor(log2(x)) - 1 */ ipart = lp_build_extract_exponent(bld, x, -1); ipart = LLVMBuildSIToFP(builder, ipart, bld->vec_type, ""); /* fpart = x / 2**ipart */ fpart = lp_build_extract_mantissa(bld, x); /* ipart + fpart */ return LLVMBuildFAdd(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) { LLVMBuilderRef builder = bld->gallivm->builder; LLVMValueRef sqrt2 = lp_build_const_vec(bld->gallivm, bld->type, M_SQRT2); LLVMValueRef ipart; assert(bld->type.floating); assert(lp_check_value(bld->type, x)); /* x * 2^(0.5) i.e., add 0.5 to the log2(x) */ x = LLVMBuildFMul(builder, x, sqrt2, ""); /* ipart = floor(log2(x) + 0.5) */ ipart = lp_build_extract_exponent(bld, x, 0); return ipart; } LLVMValueRef lp_build_mod(struct lp_build_context *bld, LLVMValueRef x, LLVMValueRef y) { LLVMBuilderRef builder = bld->gallivm->builder; LLVMValueRef res; const struct lp_type type = bld->type; assert(lp_check_value(type, x)); assert(lp_check_value(type, y)); if (type.floating) res = LLVMBuildFRem(builder, x, y, ""); else if (type.sign) res = LLVMBuildSRem(builder, x, y, ""); else res = LLVMBuildURem(builder, x, y, ""); return res; }