/** * Generate 1/sqrt(a) */ LLVMValueRef lp_build_rsqrt(struct lp_build_context *bld, LLVMValueRef a) { const struct lp_type type = bld->type; assert(type.floating); if(util_cpu_caps.has_sse && type.width == 32 && type.length == 4) return lp_build_intrinsic_unary(bld->builder, "llvm.x86.sse.rsqrt.ps", lp_build_vec_type(type), a); return lp_build_rcp(bld, lp_build_sqrt(bld, a)); }
/** * Convert linear float values to srgb int values. * Several possibilities how to do this, e.g. * - use table (based on exponent/highest order mantissa bits) and do * linear interpolation (https://gist.github.com/rygorous/2203834) * - Chebyshev polynomial * - Approximation using reciprocals * - using int-to-float and float-to-int tricks for pow() * (http://stackoverflow.com/questions/6475373/optimizations-for-pow-with-const-non-integer-exponent) * * @param src float (vector) value(s) to convert. */ static LLVMValueRef lp_build_linear_to_srgb(struct gallivm_state *gallivm, struct lp_type src_type, LLVMValueRef src) { LLVMBuilderRef builder = gallivm->builder; struct lp_build_context f32_bld; LLVMValueRef lin_thresh, lin, lin_const, is_linear, tmp, pow_final; lp_build_context_init(&f32_bld, gallivm, src_type); src = lp_build_clamp(&f32_bld, src, f32_bld.zero, f32_bld.one); if (0) { /* * using int-to-float and float-to-int trick for pow(). * This is much more accurate than necessary thanks to the correction, * but it most certainly makes no sense without rsqrt available. * Bonus points if you understand how this works... * All in all (including min/max clamp, conversion) 19 instructions. */ float exp_f = 2.0f / 3.0f; /* some compilers can't do exp2f, so this is exp2f(127.0f/exp_f - 127.0f) */ float exp2f_c = 1.30438178253e+19f; float coeff_f = 0.62996f; LLVMValueRef pow_approx, coeff, x2, exponent, pow_1, pow_2; struct lp_type int_type = lp_int_type(src_type); /* * First calculate approx x^8/12 */ exponent = lp_build_const_vec(gallivm, src_type, exp_f); coeff = lp_build_const_vec(gallivm, src_type, exp2f_c * powf(coeff_f, 1.0f / exp_f)); /* premultiply src */ tmp = lp_build_mul(&f32_bld, coeff, src); /* "log2" */ tmp = LLVMBuildBitCast(builder, tmp, lp_build_vec_type(gallivm, int_type), ""); tmp = lp_build_int_to_float(&f32_bld, tmp); /* multiply for pow */ tmp = lp_build_mul(&f32_bld, tmp, exponent); /* "exp2" */ pow_approx = lp_build_itrunc(&f32_bld, tmp); pow_approx = LLVMBuildBitCast(builder, pow_approx, lp_build_vec_type(gallivm, src_type), ""); /* * Since that pow was inaccurate (like 3 bits, though each sqrt step would * give another bit), compensate the error (which is why we chose another * exponent in the first place). */ /* x * x^(8/12) = x^(20/12) */ pow_1 = lp_build_mul(&f32_bld, pow_approx, src); /* x * x * x^(-4/12) = x^(20/12) */ /* Should avoid using rsqrt if it's not available, but * using x * x^(4/12) * x^(4/12) instead will change error weight */ tmp = lp_build_fast_rsqrt(&f32_bld, pow_approx); x2 = lp_build_mul(&f32_bld, src, src); pow_2 = lp_build_mul(&f32_bld, x2, tmp); /* average the values so the errors cancel out, compensate bias, * we also squeeze the 1.055 mul of the srgb conversion plus the 255.0 mul * for conversion to int in here */ tmp = lp_build_add(&f32_bld, pow_1, pow_2); coeff = lp_build_const_vec(gallivm, src_type, 1.0f / (3.0f * coeff_f) * 0.999852f * powf(1.055f * 255.0f, 4.0f)); pow_final = lp_build_mul(&f32_bld, tmp, coeff); /* x^(5/12) = rsqrt(rsqrt(x^20/12)) */ if (lp_build_fast_rsqrt_available(src_type)) { pow_final = lp_build_fast_rsqrt(&f32_bld, lp_build_fast_rsqrt(&f32_bld, pow_final)); } else { pow_final = lp_build_sqrt(&f32_bld, lp_build_sqrt(&f32_bld, pow_final)); } pow_final = lp_build_add(&f32_bld, pow_final, lp_build_const_vec(gallivm, src_type, -0.055f * 255.0f)); } else { /* * using "rational polynomial" approximation here. * Essentially y = a*x^0.375 + b*x^0.5 + c, with also * factoring in the 255.0 mul and the scaling mul. * (a is closer to actual value so has higher weight than b.) * Note: the constants are magic values. They were found empirically, * possibly could be improved but good enough (be VERY careful with * error metric if you'd want to tweak them, they also MUST fit with * the crappy polynomial above for srgb->linear since it is required * that each srgb value maps back to the same value). * This function has an error of max +-0.17 (and we'd only require +-0.6), * for the approximated srgb->linear values the error is naturally larger * (+-0.42) but still accurate enough (required +-0.5 essentially). * All in all (including min/max clamp, conversion) 15 instructions. * FMA would help (minus 2 instructions). */ LLVMValueRef x05, x0375, a_const, b_const, c_const, tmp2; if (lp_build_fast_rsqrt_available(src_type)) { tmp = lp_build_fast_rsqrt(&f32_bld, src); x05 = lp_build_mul(&f32_bld, src, tmp); } else { /* * I don't really expect this to be practical without rsqrt * but there's no reason for triple punishment so at least * save the otherwise resulting division and unnecessary mul... */ x05 = lp_build_sqrt(&f32_bld, src); } tmp = lp_build_mul(&f32_bld, x05, src); if (lp_build_fast_rsqrt_available(src_type)) { x0375 = lp_build_fast_rsqrt(&f32_bld, lp_build_fast_rsqrt(&f32_bld, tmp)); } else { x0375 = lp_build_sqrt(&f32_bld, lp_build_sqrt(&f32_bld, tmp)); } a_const = lp_build_const_vec(gallivm, src_type, 0.675f * 1.0622 * 255.0f); b_const = lp_build_const_vec(gallivm, src_type, 0.325f * 1.0622 * 255.0f); c_const = lp_build_const_vec(gallivm, src_type, -0.0620f * 255.0f); tmp = lp_build_mul(&f32_bld, a_const, x0375); tmp2 = lp_build_mul(&f32_bld, b_const, x05); tmp2 = lp_build_add(&f32_bld, tmp2, c_const); pow_final = lp_build_add(&f32_bld, tmp, tmp2); } /* linear part is easy */ lin_const = lp_build_const_vec(gallivm, src_type, 12.92f * 255.0f); lin = lp_build_mul(&f32_bld, src, lin_const); lin_thresh = lp_build_const_vec(gallivm, src_type, 0.0031308f); is_linear = lp_build_compare(gallivm, src_type, PIPE_FUNC_LEQUAL, src, lin_thresh); tmp = lp_build_select(&f32_bld, is_linear, lin, pow_final); f32_bld.type.sign = 0; return lp_build_iround(&f32_bld, tmp); }