mirror of
https://gitlab.freedesktop.org/mesa/mesa.git
synced 2026-05-07 02:48:06 +02:00
glsl, spirv: Improve accuracy of asin() and acos()
The polynomial used for asin_expr() was suboptimal (and its source was
not documented).
A better approximation is found in the _Handbook_of_Mathematical_Functions_
by Abramowitz and Stegun, which is used in Nvidia's Cg toolkit. However,
while this approximation gives a good absolute error bound, its relative
error exceeds the 4096 ulp allowed by the Vulkan spec. Taking a page
from the spirv implementation of asin(), we implement a piecewise
approximation where a Taylor series is used for small values of |x|.
This patch also harmonizes the GLSL and Vulkan implementations by moving
the implementation to common code (nir_builder).
Running tests on asin() with a grid of 64000 samples between 0.0 and +1.0,
the original asin() at 32 bits has:
```
glsl spirv
RMSE: 1.756451e-04 1.609091e-04
worst abs error: 3.904104e-04 at 0.937001 3.904104e-04 at 0.937001
worst ulp error: 11800 at 6.2499e-05 3826 at 0.841331
```
whereas the new implementation has for both:
```
RMSE: 2.528056e-05
worst abs error: 4.962087e-05 at 0.451149
worst ulp error: 2379 at 0.215106
```
Reviewed-by: Marek Olšák <marek.olsak@amd.com>
Reviewed-by: Alyssa Rosenzweig <alyssa.rosenzweig@intel.com>
Acked-by: Mel Henning <mhenning@darkrefraction.com>
Part-of: <https://gitlab.freedesktop.org/mesa/mesa/-/merge_requests/40862>
This commit is contained in:
Eric R. Smith
Marge Bot
parent
fa784fffd0
commit
4ae192a3d9
13 changed files with 121 additions and 131 deletions
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@ -13,7 +13,7 @@ traces:
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checksum: c2264076c2f0ca6b48c3bab152a65a36
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angle/libangle_restricted_traces_candy_crush_soda_saga.so:
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vk-radv-raven:
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checksum: 3370be7bbc95e6d2ec5b1b3ed36c56a0
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checksum: a3e8f7c78583fb0e6c5d13f576dad5d2
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angle/libangle_restricted_traces_free_fire.so:
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vk-radv-raven:
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checksum: 62307dd7a10d656733bca7e0f065ac99
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@ -28,7 +28,7 @@ traces:
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checksum: 47c004fed88bed8d3d387295399f0810
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angle/libangle_restricted_traces_pubg_mobile_battle_royale.so:
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vk-radv-raven:
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checksum: 95092db8df12af91de8de5463e4e4bb6
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checksum: f028e6aeb48690e5a36744be55a56773
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angle/libangle_restricted_traces_temple_run_300.so:
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vk-radv-raven:
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checksum: 4fa6a73dad7d9dd747ba7cbf82aae42e
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@ -1209,8 +1209,6 @@ private:
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ir_swizzle *matrix_elt(ir_variable *var, int col, int row);
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ir_dereference_record *record_ref(ir_variable *var, const char *field);
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ir_expression *asin_expr(ir_variable *x, float p0, float p1);
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/**
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* Call function \param f with parameters specified as the linked
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* list \param params of \c ir_variable objects. \param ret should
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@ -6507,6 +6505,8 @@ builtin_builder::_degrees(builtin_available_predicate avail,
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UNOPA(sin, ir_unop_sin)
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UNOPA(cos, ir_unop_cos)
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UNOPA(asin, ir_unop_asin)
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UNOPA(acos, ir_unop_acos)
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ir_function_signature *
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builtin_builder::_tan(builtin_available_predicate avail,
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@ -6518,20 +6518,6 @@ builtin_builder::_tan(builtin_available_predicate avail,
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return sig;
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}
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ir_expression *
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builtin_builder::asin_expr(ir_variable *x, float p0, float p1)
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{
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return mul(sign(x),
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sub(IMM_FP(x->type, M_PI_2f),
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mul(sqrt(sub(IMM_FP(x->type, 1.0f), abs(x))),
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add(IMM_FP(x->type, M_PI_2f),
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mul(abs(x),
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add(IMM_FP(x->type, (M_PI_4f - 1.0f)),
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mul(abs(x),
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add(IMM_FP(x->type, p0),
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mul(abs(x), IMM_FP(x->type, p1))))))))));
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}
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/**
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* Generate a ir_call to a function with a set of parameters
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*
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@ -6568,30 +6554,6 @@ builtin_builder::call(ir_function *f, ir_variable *ret, ir_exec_list params)
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return new(linalloc) ir_call(sig, deref, &actual_params);
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}
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ir_function_signature *
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builtin_builder::_asin(builtin_available_predicate avail,
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const glsl_type *type)
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{
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ir_variable *x = in_var(type, "x");
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MAKE_SIG(type, avail, 1, x);
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body.emit(ret(asin_expr(x, 0.086566724f, -0.03102955f)));
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return sig;
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}
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ir_function_signature *
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builtin_builder::_acos(builtin_available_predicate avail,
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const glsl_type *type)
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{
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ir_variable *x = in_var(type, "x");
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MAKE_SIG(type, avail, 1, x);
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body.emit(ret(sub(IMM_FP(type, M_PI_2f), asin_expr(x, 0.08132463f, -0.02363318f))));
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return sig;
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}
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ir_function_signature *
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builtin_builder::_sinh(builtin_available_predicate avail,
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const glsl_type *type)
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@ -2358,6 +2358,12 @@ nir_visitor::visit(ir_expression *ir)
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return;
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}
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case ir_unop_asin:
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result = nir_asin(&b, srcs[0]);
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break;
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case ir_unop_acos:
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result = nir_acos(&b, srcs[0]);
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break;
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case ir_unop_atan:
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result = nir_atan(&b, srcs[0]);
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break;
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@ -236,6 +236,8 @@ ir_expression::ir_expression(int op, ir_rvalue *op0)
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case ir_unop_round_even:
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case ir_unop_sin:
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case ir_unop_cos:
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case ir_unop_asin:
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case ir_unop_acos:
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case ir_unop_dFdx:
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case ir_unop_dFdx_coarse:
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case ir_unop_dFdx_fine:
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@ -568,6 +568,8 @@ ir_expression_operation = [
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operation("sin", 1, source_types=(float_type,), c_expression="sinf({src0})"),
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operation("cos", 1, source_types=(float_type,), c_expression="cosf({src0})"),
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operation("atan", 1, source_types=(float_type,), c_expression="atan({src0})"),
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operation("acos", 1, source_types=(float_type,), c_expression="acosf({src0})"),
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operation("asin", 1, source_types=(float_type,), c_expression="asinf({src0})"),
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# Partial derivatives.
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operation("dFdx", 1, source_types=(float_type,), c_expression="0.0f"),
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@ -515,6 +515,8 @@ ir_validate::visit_leave(ir_expression *ir)
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break;
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case ir_unop_sin:
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case ir_unop_cos:
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case ir_unop_asin:
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case ir_unop_acos:
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case ir_unop_dFdx:
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case ir_unop_dFdx_coarse:
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case ir_unop_dFdx_fine:
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@ -28,6 +28,13 @@
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#include "nir_builder.h"
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#include "nir_builtin_builder.h"
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#ifndef M_PIf
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#define M_PIf ((float) M_PI)
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#endif
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#ifndef M_PI_2f
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#define M_PI_2f ((float) M_PI_2)
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#endif
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nir_def *
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nir_cross3(nir_builder *b, nir_def *x, nir_def *y)
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{
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@ -159,6 +166,81 @@ nir_upsample(nir_builder *b, nir_def *hi, nir_def *lo)
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return nir_vec(b, res, lo->num_components);
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}
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/**
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* Approximate asin(x) by formula 4.45 from Abramowitz & Stegun, "Handbook
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* of Mathematical Functions":
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*
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* asin~(x) = (π/2 - sqrt(1 - |x|) * ( a0 + a1 * |x| + a2 * |x|^2 + a3 * |x|^3 )
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*
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* where a0 = 1.5707288 a1 = -0.2121144 a2 = 0.0742610 a3 = -0.0187203
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*
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* This has a very small absolute error, but the relative error can become
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* large when |x| is small. For small |x| the Taylor series makes a good
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* approximation, so when the relative error matters (i.e. for asin rather
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* than acos) we do a piecewise approximation with the Taylor series for
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* |x| < 0.21502245 and formula 4.45 elsewhere. The crossover point is
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* the value in [0.1, 0.7071] where the two approximations are equal.
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*/
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static nir_def *
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build_asin(nir_builder *b, nir_def *x, bool piecewise)
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{
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if (x->bit_size == 16) {
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/* The polynomial approximation may not be precise enough to meet half-float
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* precision requirements. Alternatively, we could implement this using
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* the formula:
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*
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* asin(x) = atan2(x, sqrt(1 - x*x))
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*
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* But that is very expensive, so instead we just do the polynomial
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* approximation in 32-bit math and then we convert the result back to
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* 16-bit.
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*/
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return nir_f2f16(b, build_asin(b, nir_f2f32(b, x), piecewise));
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}
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nir_def *abs_x = nir_fabs(b, x);
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nir_def *p0_plus_xp1 = nir_ffma_imm12(b, abs_x, -0.0187293, 0.0742610);
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nir_def *expr_tail =
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nir_ffma_imm2(b, abs_x,
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nir_ffma_imm2(b, abs_x, p0_plus_xp1, -0.2121144),
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1.5707288);
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nir_def *result0 = nir_fmul(b, nir_fsign(b, x),
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nir_a_minus_bc(b, nir_imm_floatN_t(b, M_PI_2f, x->bit_size),
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nir_fsqrt(b,
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nir_fsub_imm(b, 1.0, abs_x)),
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expr_tail));
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if (piecewise) {
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/* use taylor approximation for |x| < 0.21502245 */
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nir_def *x2 = nir_fmul(b, x, x);
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nir_def *result1 = nir_fmul(b,
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x,
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nir_ffma_imm12(b, x2, (1.0/6.0), 1.0));
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return nir_bcsel(b,
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nir_flt_imm(b, abs_x, 0.21502245),
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result1,
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result0);
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} else {
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return result0;
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}
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}
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nir_def *
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nir_asin(nir_builder *b, nir_def *x)
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{
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/* use piecewise approximation to keep low relative error near 0 */
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return build_asin(b, x, true);
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}
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nir_def *
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nir_acos(nir_builder *b, nir_def *x)
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{
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/* piecewise approximation not needed to keep low relative error */
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return nir_fsub_imm(b, M_PI_2f, build_asin(b, x, false));
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}
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nir_def *
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nir_atan(nir_builder *b, nir_def *y_over_x)
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{
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@ -44,9 +44,12 @@ nir_def *nir_normalize(nir_builder *b, nir_def *vec);
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nir_def *nir_smoothstep(nir_builder *b, nir_def *edge0,
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nir_def *edge1, nir_def *x);
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nir_def *nir_upsample(nir_builder *b, nir_def *hi, nir_def *lo);
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nir_def *nir_acos(nir_builder *b, nir_def *x);
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nir_def *nir_asin(nir_builder *b, nir_def *x);
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nir_def *nir_atan(nir_builder *b, nir_def *y_over_x);
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nir_def *nir_atan2(nir_builder *b, nir_def *y, nir_def *x);
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nir_def *
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nir_build_texture_query(nir_builder *b, nir_tex_instr *tex, nir_texop texop,
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unsigned components, nir_alu_type dest_type,
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@ -120,73 +120,6 @@ matrix_inverse(struct vtn_builder *b, struct vtn_ssa_value *src)
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return val;
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}
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/**
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* Approximate asin(x) by the piecewise formula:
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* for |x| < 0.5, asin~(x) = x * (1 + x²(pS0 + x²(pS1 + x²*pS2)) / (1 + x²*qS1))
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* for |x| ≥ 0.5, asin~(x) = sign(x) * (π/2 - sqrt(1 - |x|) * (π/2 + |x|(π/4 - 1 + |x|(p0 + |x|p1))))
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*
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* The latter is correct to first order at x=0 and x=±1 regardless of the p
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* coefficients but can be made second-order correct at both ends by selecting
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* the fit coefficients appropriately. Different p coefficients can be used
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* in the asin and acos implementation to minimize some relative error metric
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* in each case.
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*/
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static nir_def *
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build_asin(nir_builder *b, nir_def *x, float p0, float p1, bool piecewise)
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{
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if (x->bit_size == 16) {
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/* The polynomial approximation isn't precise enough to meet half-float
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* precision requirements. Alternatively, we could implement this using
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* the formula:
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*
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* asin(x) = atan2(x, sqrt(1 - x*x))
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*
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* But that is very expensive, so instead we just do the polynomial
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* approximation in 32-bit math and then we convert the result back to
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* 16-bit.
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*/
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nir_def *result =
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nir_f2f16(b, build_asin(b, nir_f2f32(b, x), p0, p1, piecewise));
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return result;
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}
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nir_def *one = nir_imm_floatN_t(b, 1.0f, x->bit_size);
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nir_def *half = nir_imm_floatN_t(b, 0.5f, x->bit_size);
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nir_def *abs_x = nir_fabs(b, x);
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nir_def *p0_plus_xp1 = nir_ffma_imm12(b, abs_x, p1, p0);
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nir_def *expr_tail =
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nir_ffma_imm2(b, abs_x,
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nir_ffma_imm2(b, abs_x, p0_plus_xp1, M_PI_4f - 1.0f),
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M_PI_2f);
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nir_def *result0 = nir_fmul(b, nir_fsign(b, x),
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nir_a_minus_bc(b, nir_imm_floatN_t(b, M_PI_2f, x->bit_size),
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nir_fsqrt(b, nir_fsub(b, one, abs_x)),
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expr_tail));
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if (piecewise) {
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/* approximation for |x| < 0.5 */
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const float pS0 = 1.6666586697e-01f;
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const float pS1 = -4.2743422091e-02f;
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const float pS2 = -8.6563630030e-03f;
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const float qS1 = -7.0662963390e-01f;
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nir_def *x2 = nir_fmul(b, x, x);
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nir_def *p = nir_fmul(b,
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x2,
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nir_ffma_imm2(b, x2,
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nir_ffma_imm12(b, x2, pS2, pS1),
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pS0));
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nir_def *q = nir_ffma_imm1(b, x2, qS1, one);
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nir_def *result1 = nir_ffma(b, x, nir_fdiv(b, p, q), x);
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return nir_bcsel(b, nir_flt(b, abs_x, half), result1, result0);
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} else {
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return result0;
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}
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}
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static nir_op
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vtn_nir_alu_op_for_spirv_glsl_opcode(struct vtn_builder *b,
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enum GLSLstd450 opcode,
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@ -567,13 +500,11 @@ handle_glsl450_alu(struct vtn_builder *b, enum GLSLstd450 entrypoint,
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}
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case GLSLstd450Asin:
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dest->def = build_asin(nb, src[0], 0.086566724, -0.03102955, true);
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dest->def = nir_asin(nb, src[0]);
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break;
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case GLSLstd450Acos:
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dest->def =
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nir_fsub_imm(nb, M_PI_2f,
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build_asin(nb, src[0], 0.08132463, -0.02363318, false));
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dest->def = nir_acos(nb, src[0]);
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break;
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case GLSLstd450Atan:
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@ -109,7 +109,7 @@ traces:
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|||
label: [crash]
|
||||
godot/Material Testers.x86_64_2020.04.08_13.38_frame799.rdc:
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||||
gl-virgl:
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||||
checksum: 7ba4f0c52a719d94b805653d31ce22d7
|
||||
checksum: 465410a06d966b377bc8c41e52b21b0f
|
||||
ror/ror-default.trace:
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gl-virgl:
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label: [crash]
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|
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@ -44,17 +44,17 @@ traces:
|
|||
checksum: 58e2d6ea105ca2735b05ce06709691fb
|
||||
text: Clear color for the background can be black or grey
|
||||
zink-radv-gfx1201:
|
||||
checksum: c65527b7db55687e3c2741c0286b70e2
|
||||
checksum: 9c55251c2979a107ba852719d7e41889
|
||||
|
||||
blender/blender-demo-ellie_pose.trace:
|
||||
gl-zink-anv-adl:
|
||||
checksum: ca8df31308386674816c0e801f220565
|
||||
checksum: ddae9bcbff102e46739454eaa09772c0
|
||||
gl-zink-anv-tgl:
|
||||
checksum: ca8df31308386674816c0e801f220565
|
||||
checksum: ddae9bcbff102e46739454eaa09772c0
|
||||
zink-radv-vangogh:
|
||||
checksum: 4670acc17f40e2d20ecf355a64b5612e
|
||||
checksum: c6a14ab73815748450f4feaf50fa9f2e
|
||||
zink-radv-gfx1201:
|
||||
checksum: 4670acc17f40e2d20ecf355a64b5612e
|
||||
checksum: c6a14ab73815748450f4feaf50fa9f2e
|
||||
|
||||
glxgears/glxgears-2-v2.trace:
|
||||
gl-zink-anv-adl:
|
||||
|
|
@ -97,9 +97,9 @@ traces:
|
|||
checksum: dbe1de4e2e812413f173ea6c423117ff
|
||||
text: "'egl_platform.cpp( 227) - Error - Couldn't find a suitable EGL config' -- revisit when we can turn on X11?"
|
||||
zink-radv-vangogh:
|
||||
checksum: 0615d3d7598d0088393bfc8fa24f73c8
|
||||
checksum: 65e86206d1ba3ed8365f8b95dc9e9e71
|
||||
zink-radv-gfx1201:
|
||||
checksum: 07f0e057eeea449544e16c7ff65e965f
|
||||
checksum: f22ee8433dd7b689c46816d576bf3c12
|
||||
|
||||
gputest/pixmark-julia-fp32-v2.trace:
|
||||
gl-zink-anv-adl:
|
||||
|
|
|
|||
|
|
@ -13,7 +13,7 @@ traces:
|
|||
checksum: e038ef82470fff7b94cf958fa869d130
|
||||
angle/libangle_restricted_traces_candy_crush_soda_saga.so:
|
||||
vk-anv-adl:
|
||||
checksum: dcfc2dbc1e383d10b86a9c3a52452aa8
|
||||
checksum: dc5d96a70af6165d88f882b96fb73e73
|
||||
angle/libangle_restricted_traces_free_fire.so:
|
||||
vk-anv-adl:
|
||||
checksum: 1a9f03ed30ee254842afe7ab7792a493
|
||||
|
|
@ -28,7 +28,7 @@ traces:
|
|||
checksum: ae8371870059d87d475da217a453acfc
|
||||
angle/libangle_restricted_traces_pubg_mobile_battle_royale.so:
|
||||
vk-anv-adl:
|
||||
checksum: b1970da0e8d29498078e53d2b6bbff71
|
||||
checksum: 692350e4315d58f2644f5901b954fa15
|
||||
angle/libangle_restricted_traces_temple_run_300.so:
|
||||
vk-anv-adl:
|
||||
checksum: 72610fdadbfb7d99aa5de13d78598ff2
|
||||
|
|
|
|||
|
|
@ -557,7 +557,7 @@ traces:
|
|||
checksum: 85b4f3279fde206dace85ffd727057ea
|
||||
gl-intel-kbl:
|
||||
label: [no-perf]
|
||||
checksum: efab5903f88f7f34e7c948cfcfb54cd9
|
||||
checksum: 46555aa91e3f9b3f12f93a28b4ff069b
|
||||
gl-intel-whl:
|
||||
label: [no-perf]
|
||||
checksum: 6a0e17d98eca33e80810b6158e998aa1
|
||||
|
|
@ -569,19 +569,19 @@ traces:
|
|||
checksum: 85b4f3279fde206dace85ffd727057ea
|
||||
blender/blender-demo-ellie_pose.trace:
|
||||
gl-intel-apl:
|
||||
checksum: 7d0da76cdf72ff785a1ecc6d4e404e0c
|
||||
checksum: 61d144ac9cd8cbba11b19bb1174855bc
|
||||
gl-intel-glx:
|
||||
checksum: 7d0da76cdf72ff785a1ecc6d4e404e0c
|
||||
checksum: 61d144ac9cd8cbba11b19bb1174855bc
|
||||
gl-intel-amly:
|
||||
checksum: 7d0da76cdf72ff785a1ecc6d4e404e0c
|
||||
checksum: 61d144ac9cd8cbba11b19bb1174855bc
|
||||
gl-intel-kbl:
|
||||
checksum: 7d0da76cdf72ff785a1ecc6d4e404e0c
|
||||
checksum: 61d144ac9cd8cbba11b19bb1174855bc
|
||||
gl-intel-whl:
|
||||
checksum: 7d0da76cdf72ff785a1ecc6d4e404e0c
|
||||
checksum: 61d144ac9cd8cbba11b19bb1174855bc
|
||||
gl-intel-cml:
|
||||
checksum: 7d0da76cdf72ff785a1ecc6d4e404e0c
|
||||
checksum: 61d144ac9cd8cbba11b19bb1174855bc
|
||||
gl-intel-adl:
|
||||
checksum: 7d0da76cdf72ff785a1ecc6d4e404e0c
|
||||
checksum: 61d144ac9cd8cbba11b19bb1174855bc
|
||||
unvanquished/unvanquished-lowest.trace:
|
||||
gl-intel-apl:
|
||||
checksum: 884096b6dd40e2f500d0837501287fac
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue