/**
* 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);
}
