diff options
author | Sergey Sharybin <sergey.vfx@gmail.com> | 2016-06-10 17:13:50 +0300 |
---|---|---|
committer | Sergey Sharybin <sergey.vfx@gmail.com> | 2016-07-07 18:25:48 +0300 |
commit | 17e745426375fe76f5011992d582c01b682d348b (patch) | |
tree | f14a9f2fe707e63396cc2a509b87201976adfdbd /intern/cycles/kernel | |
parent | 1eacbf47e3cdf009b27972e1c617fb1ff56c0aad (diff) |
Cycles: Reduce memory usage by de-duplicating triangle storage
There are several internal changes for this:
First idea is to make __tri_verts to behave similar to __tri_storage,
meaning, __tri_verts array now contains all vertices of all triangles
instead of just mesh vertices. This saves some lookup when reading
triangle coordinates in functions like triangle_normal().
In order to make it efficient needed to store global triangle offset
somewhere. So no __tri_vindex.w contains a global triangle index which
can be used to read triangle vertices.
Additionally, the order of vertices in that array is aligned with
primitives from BVH. This is needed to keep cache as much coherent as
possible for BVH traversal. This causes some extra tricks needed to
fill the array in and deal with True Displacement but those trickery
is fully required to prevent noticeable slowdown.
Next idea was to use this __tri_verts instead of __tri_storage in
intersection code. Unfortunately, this is quite tricky to do without
noticeable speed loss. Mainly this loss is caused by extra lookup
happening to access vertex coordinate.
Fortunately, tricks here and there (i,e, some types changes to avoid
casts which are not really coming for free) reduces those losses to
an acceptable level. So now they are within couple of percent only,
On a positive site we've achieved:
- Few percent of memory save with triangle-only scenes. Actual save
in this case is close to size of all vertices.
On a more fine-subdivided scenes this benefit might become more
obvious.
- Huge memory save of hairy scenes. For example, on koro.blend
there is about 20% memory save. Similar figure for bunny.blend.
This memory save was the main goal of this commit to move forward
with Hair BVH which required more memory per BVH node. So while
this sounds exciting, this memory optimization will become invisible
by upcoming Hair BVH work.
But again on a positive side, we can add an option to NOT use Hair
BVH and then we'll have same-ish render times as we've got currently
but will have this 20% memory benefit on hairy scenes.
Diffstat (limited to 'intern/cycles/kernel')
-rw-r--r-- | intern/cycles/kernel/geom/geom_motion_triangle.h | 32 | ||||
-rw-r--r-- | intern/cycles/kernel/geom/geom_triangle.h | 61 | ||||
-rw-r--r-- | intern/cycles/kernel/geom/geom_triangle_intersect.h | 28 | ||||
-rw-r--r-- | intern/cycles/kernel/kernel_textures.h | 6 |
4 files changed, 63 insertions, 64 deletions
diff --git a/intern/cycles/kernel/geom/geom_motion_triangle.h b/intern/cycles/kernel/geom/geom_motion_triangle.h index ffe55529110..2fb8e219884 100644 --- a/intern/cycles/kernel/geom/geom_motion_triangle.h +++ b/intern/cycles/kernel/geom/geom_motion_triangle.h @@ -47,13 +47,13 @@ ccl_device_inline int find_attribute_motion(KernelGlobals *kg, int object, uint return (attr_map.y == ATTR_ELEMENT_NONE) ? (int)ATTR_STD_NOT_FOUND : (int)attr_map.z; } -ccl_device_inline void motion_triangle_verts_for_step(KernelGlobals *kg, float3 tri_vindex, int offset, int numverts, int numsteps, int step, float3 verts[3]) +ccl_device_inline void motion_triangle_verts_for_step(KernelGlobals *kg, uint4 tri_vindex, int offset, int numverts, int numsteps, int step, float3 verts[3]) { if(step == numsteps) { /* center step: regular vertex location */ - verts[0] = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.x))); - verts[1] = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.y))); - verts[2] = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.z))); + verts[0] = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+0)); + verts[1] = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+1)); + verts[2] = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+2)); } else { /* center step not store in this array */ @@ -62,19 +62,19 @@ ccl_device_inline void motion_triangle_verts_for_step(KernelGlobals *kg, float3 offset += step*numverts; - verts[0] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + __float_as_int(tri_vindex.x))); - verts[1] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + __float_as_int(tri_vindex.y))); - verts[2] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + __float_as_int(tri_vindex.z))); + verts[0] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + tri_vindex.x)); + verts[1] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + tri_vindex.y)); + verts[2] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + tri_vindex.z)); } } -ccl_device_inline void motion_triangle_normals_for_step(KernelGlobals *kg, float3 tri_vindex, int offset, int numverts, int numsteps, int step, float3 normals[3]) +ccl_device_inline void motion_triangle_normals_for_step(KernelGlobals *kg, uint4 tri_vindex, int offset, int numverts, int numsteps, int step, float3 normals[3]) { if(step == numsteps) { /* center step: regular vertex location */ - normals[0] = float4_to_float3(kernel_tex_fetch(__tri_vnormal, __float_as_int(tri_vindex.x))); - normals[1] = float4_to_float3(kernel_tex_fetch(__tri_vnormal, __float_as_int(tri_vindex.y))); - normals[2] = float4_to_float3(kernel_tex_fetch(__tri_vnormal, __float_as_int(tri_vindex.z))); + normals[0] = float4_to_float3(kernel_tex_fetch(__tri_vnormal, tri_vindex.x)); + normals[1] = float4_to_float3(kernel_tex_fetch(__tri_vnormal, tri_vindex.y)); + normals[2] = float4_to_float3(kernel_tex_fetch(__tri_vnormal, tri_vindex.z)); } else { /* center step not stored in this array */ @@ -83,9 +83,9 @@ ccl_device_inline void motion_triangle_normals_for_step(KernelGlobals *kg, float offset += step*numverts; - normals[0] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + __float_as_int(tri_vindex.x))); - normals[1] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + __float_as_int(tri_vindex.y))); - normals[2] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + __float_as_int(tri_vindex.z))); + normals[0] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + tri_vindex.x)); + normals[1] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + tri_vindex.y)); + normals[2] = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + tri_vindex.z)); } } @@ -107,7 +107,7 @@ ccl_device_inline void motion_triangle_vertices(KernelGlobals *kg, int object, i /* fetch vertex coordinates */ float3 next_verts[3]; - float3 tri_vindex = float4_to_float3(kernel_tex_fetch(__tri_vindex, prim)); + uint4 tri_vindex = kernel_tex_fetch(__tri_vindex, prim); motion_triangle_verts_for_step(kg, tri_vindex, offset, numverts, numsteps, step, verts); motion_triangle_verts_for_step(kg, tri_vindex, offset, numverts, numsteps, step+1, next_verts); @@ -259,7 +259,7 @@ ccl_device_noinline void motion_triangle_shader_setup(KernelGlobals *kg, ShaderD /* fetch vertex coordinates */ float3 verts[3], next_verts[3]; - float3 tri_vindex = float4_to_float3(kernel_tex_fetch(__tri_vindex, ccl_fetch(sd, prim))); + uint4 tri_vindex = kernel_tex_fetch(__tri_vindex, ccl_fetch(sd, prim)); motion_triangle_verts_for_step(kg, tri_vindex, offset, numverts, numsteps, step, verts); motion_triangle_verts_for_step(kg, tri_vindex, offset, numverts, numsteps, step+1, next_verts); diff --git a/intern/cycles/kernel/geom/geom_triangle.h b/intern/cycles/kernel/geom/geom_triangle.h index 995dfac5b09..0c2351e1d1b 100644 --- a/intern/cycles/kernel/geom/geom_triangle.h +++ b/intern/cycles/kernel/geom/geom_triangle.h @@ -27,12 +27,11 @@ CCL_NAMESPACE_BEGIN ccl_device_inline float3 triangle_normal(KernelGlobals *kg, ShaderData *sd) { /* load triangle vertices */ - float4 tri_vindex = kernel_tex_fetch(__tri_vindex, ccl_fetch(sd, prim)); + const uint4 tri_vindex = kernel_tex_fetch(__tri_vindex, ccl_fetch(sd, prim)); + const float3 v0 = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+0)); + const float3 v1 = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+1)); + const float3 v2 = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+2)); - float3 v0 = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.x))); - float3 v1 = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.y))); - float3 v2 = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.z))); - /* return normal */ if(ccl_fetch(sd, flag) & SD_NEGATIVE_SCALE_APPLIED) return normalize(cross(v2 - v0, v1 - v0)); @@ -44,11 +43,10 @@ ccl_device_inline float3 triangle_normal(KernelGlobals *kg, ShaderData *sd) ccl_device_inline void triangle_point_normal(KernelGlobals *kg, int object, int prim, float u, float v, float3 *P, float3 *Ng, int *shader) { /* load triangle vertices */ - float4 tri_vindex = kernel_tex_fetch(__tri_vindex, prim); - - float3 v0 = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.x))); - float3 v1 = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.y))); - float3 v2 = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.z))); + const uint4 tri_vindex = kernel_tex_fetch(__tri_vindex, prim); + float3 v0 = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+0)); + float3 v1 = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+1)); + float3 v2 = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+2)); /* compute point */ float t = 1.0f - u - v; @@ -71,11 +69,10 @@ ccl_device_inline void triangle_point_normal(KernelGlobals *kg, int object, int ccl_device_inline void triangle_vertices(KernelGlobals *kg, int prim, float3 P[3]) { - float4 tri_vindex = kernel_tex_fetch(__tri_vindex, prim); - - P[0] = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.x))); - P[1] = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.y))); - P[2] = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.z))); + const uint4 tri_vindex = kernel_tex_fetch(__tri_vindex, prim); + P[0] = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+0)); + P[1] = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+1)); + P[2] = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+2)); } /* Interpolate smooth vertex normal from vertices */ @@ -83,11 +80,10 @@ ccl_device_inline void triangle_vertices(KernelGlobals *kg, int prim, float3 P[3 ccl_device_inline float3 triangle_smooth_normal(KernelGlobals *kg, int prim, float u, float v) { /* load triangle vertices */ - float4 tri_vindex = kernel_tex_fetch(__tri_vindex, prim); - - float3 n0 = float4_to_float3(kernel_tex_fetch(__tri_vnormal, __float_as_int(tri_vindex.x))); - float3 n1 = float4_to_float3(kernel_tex_fetch(__tri_vnormal, __float_as_int(tri_vindex.y))); - float3 n2 = float4_to_float3(kernel_tex_fetch(__tri_vnormal, __float_as_int(tri_vindex.z))); + const uint4 tri_vindex = kernel_tex_fetch(__tri_vindex, prim); + float3 n0 = float4_to_float3(kernel_tex_fetch(__tri_vnormal, tri_vindex.x)); + float3 n1 = float4_to_float3(kernel_tex_fetch(__tri_vnormal, tri_vindex.y)); + float3 n2 = float4_to_float3(kernel_tex_fetch(__tri_vnormal, tri_vindex.z)); return normalize((1.0f - u - v)*n2 + u*n0 + v*n1); } @@ -97,11 +93,10 @@ ccl_device_inline float3 triangle_smooth_normal(KernelGlobals *kg, int prim, flo ccl_device_inline void triangle_dPdudv(KernelGlobals *kg, int prim, ccl_addr_space float3 *dPdu, ccl_addr_space float3 *dPdv) { /* fetch triangle vertex coordinates */ - float4 tri_vindex = kernel_tex_fetch(__tri_vindex, prim); - - float3 p0 = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.x))); - float3 p1 = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.y))); - float3 p2 = float4_to_float3(kernel_tex_fetch(__tri_verts, __float_as_int(tri_vindex.z))); + const uint4 tri_vindex = kernel_tex_fetch(__tri_vindex, prim); + const float3 p0 = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+0)); + const float3 p1 = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+1)); + const float3 p2 = float4_to_float3(kernel_tex_fetch(__prim_tri_verts, tri_vindex.w+2)); /* compute derivatives of P w.r.t. uv */ *dPdu = (p0 - p2); @@ -119,11 +114,11 @@ ccl_device float triangle_attribute_float(KernelGlobals *kg, const ShaderData *s return kernel_tex_fetch(__attributes_float, offset + ccl_fetch(sd, prim)); } else if(elem == ATTR_ELEMENT_VERTEX || elem == ATTR_ELEMENT_VERTEX_MOTION) { - float4 tri_vindex = kernel_tex_fetch(__tri_vindex, ccl_fetch(sd, prim)); + uint4 tri_vindex = kernel_tex_fetch(__tri_vindex, ccl_fetch(sd, prim)); - float f0 = kernel_tex_fetch(__attributes_float, offset + __float_as_int(tri_vindex.x)); - float f1 = kernel_tex_fetch(__attributes_float, offset + __float_as_int(tri_vindex.y)); - float f2 = kernel_tex_fetch(__attributes_float, offset + __float_as_int(tri_vindex.z)); + float f0 = kernel_tex_fetch(__attributes_float, offset + tri_vindex.x); + float f1 = kernel_tex_fetch(__attributes_float, offset + tri_vindex.y); + float f2 = kernel_tex_fetch(__attributes_float, offset + tri_vindex.z); #ifdef __RAY_DIFFERENTIALS__ if(dx) *dx = ccl_fetch(sd, du).dx*f0 + ccl_fetch(sd, dv).dx*f1 - (ccl_fetch(sd, du).dx + ccl_fetch(sd, dv).dx)*f2; @@ -162,11 +157,11 @@ ccl_device float3 triangle_attribute_float3(KernelGlobals *kg, const ShaderData return float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + ccl_fetch(sd, prim))); } else if(elem == ATTR_ELEMENT_VERTEX || elem == ATTR_ELEMENT_VERTEX_MOTION) { - float4 tri_vindex = kernel_tex_fetch(__tri_vindex, ccl_fetch(sd, prim)); + uint4 tri_vindex = kernel_tex_fetch(__tri_vindex, ccl_fetch(sd, prim)); - float3 f0 = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + __float_as_int(tri_vindex.x))); - float3 f1 = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + __float_as_int(tri_vindex.y))); - float3 f2 = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + __float_as_int(tri_vindex.z))); + float3 f0 = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + tri_vindex.x)); + float3 f1 = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + tri_vindex.y)); + float3 f2 = float4_to_float3(kernel_tex_fetch(__attributes_float3, offset + tri_vindex.z)); #ifdef __RAY_DIFFERENTIALS__ if(dx) *dx = ccl_fetch(sd, du).dx*f0 + ccl_fetch(sd, dv).dx*f1 - (ccl_fetch(sd, du).dx + ccl_fetch(sd, dv).dx)*f2; diff --git a/intern/cycles/kernel/geom/geom_triangle_intersect.h b/intern/cycles/kernel/geom/geom_triangle_intersect.h index b6dfc769012..fc081bda525 100644 --- a/intern/cycles/kernel/geom/geom_triangle_intersect.h +++ b/intern/cycles/kernel/geom/geom_triangle_intersect.h @@ -106,9 +106,10 @@ ccl_device_inline bool triangle_intersect(KernelGlobals *kg, const float Sz = isect_precalc->Sz; /* Calculate vertices relative to ray origin. */ - const float4 tri_a = kernel_tex_fetch(__tri_storage, triAddr*TRI_NODE_SIZE+0), - tri_b = kernel_tex_fetch(__tri_storage, triAddr*TRI_NODE_SIZE+1), - tri_c = kernel_tex_fetch(__tri_storage, triAddr*TRI_NODE_SIZE+2); + const uint tri_vindex = kernel_tex_fetch(__prim_tri_index, triAddr); + const float4 tri_a = kernel_tex_fetch(__prim_tri_verts, tri_vindex+0), + tri_b = kernel_tex_fetch(__prim_tri_verts, tri_vindex+1), + tri_c = kernel_tex_fetch(__prim_tri_verts, tri_vindex+2); const float3 A = make_float3(tri_a.x - P.x, tri_a.y - P.y, tri_a.z - P.z); const float3 B = make_float3(tri_b.x - P.x, tri_b.y - P.y, tri_b.z - P.z); const float3 C = make_float3(tri_c.x - P.x, tri_c.y - P.y, tri_c.z - P.z); @@ -202,9 +203,10 @@ ccl_device_inline void triangle_intersect_subsurface( const float Sz = isect_precalc->Sz; /* Calculate vertices relative to ray origin. */ - const float4 tri_a = kernel_tex_fetch(__tri_storage, triAddr*TRI_NODE_SIZE+0), - tri_b = kernel_tex_fetch(__tri_storage, triAddr*TRI_NODE_SIZE+1), - tri_c = kernel_tex_fetch(__tri_storage, triAddr*TRI_NODE_SIZE+2); + const uint tri_vindex = kernel_tex_fetch(__prim_tri_index, triAddr); + const float4 tri_a = kernel_tex_fetch(__prim_tri_verts, tri_vindex+0), + tri_b = kernel_tex_fetch(__prim_tri_verts, tri_vindex+1), + tri_c = kernel_tex_fetch(__prim_tri_verts, tri_vindex+2); const float3 A = make_float3(tri_a.x - P.x, tri_a.y - P.y, tri_a.z - P.z); const float3 B = make_float3(tri_b.x - P.x, tri_b.y - P.y, tri_b.z - P.z); const float3 C = make_float3(tri_c.x - P.x, tri_c.y - P.y, tri_c.z - P.z); @@ -324,9 +326,10 @@ ccl_device_inline float3 triangle_refine(KernelGlobals *kg, P = P + D*t; - const float4 tri_a = kernel_tex_fetch(__tri_storage, isect->prim*TRI_NODE_SIZE+0), - tri_b = kernel_tex_fetch(__tri_storage, isect->prim*TRI_NODE_SIZE+1), - tri_c = kernel_tex_fetch(__tri_storage, isect->prim*TRI_NODE_SIZE+2); + const uint tri_vindex = kernel_tex_fetch(__prim_tri_index, isect->prim); + const float4 tri_a = kernel_tex_fetch(__prim_tri_verts, tri_vindex+0), + tri_b = kernel_tex_fetch(__prim_tri_verts, tri_vindex+1), + tri_c = kernel_tex_fetch(__prim_tri_verts, tri_vindex+2); float3 edge1 = make_float3(tri_a.x - tri_c.x, tri_a.y - tri_c.y, tri_a.z - tri_c.z); float3 edge2 = make_float3(tri_b.x - tri_c.x, tri_b.y - tri_c.y, tri_b.z - tri_c.z); float3 tvec = make_float3(P.x - tri_c.x, P.y - tri_c.y, P.z - tri_c.z); @@ -381,9 +384,10 @@ ccl_device_inline float3 triangle_refine_subsurface(KernelGlobals *kg, P = P + D*t; #ifdef __INTERSECTION_REFINE__ - const float4 tri_a = kernel_tex_fetch(__tri_storage, isect->prim*TRI_NODE_SIZE+0), - tri_b = kernel_tex_fetch(__tri_storage, isect->prim*TRI_NODE_SIZE+1), - tri_c = kernel_tex_fetch(__tri_storage, isect->prim*TRI_NODE_SIZE+2); + const uint tri_vindex = kernel_tex_fetch(__prim_tri_index, isect->prim); + const float4 tri_a = kernel_tex_fetch(__prim_tri_verts, tri_vindex+0), + tri_b = kernel_tex_fetch(__prim_tri_verts, tri_vindex+1), + tri_c = kernel_tex_fetch(__prim_tri_verts, tri_vindex+2); float3 edge1 = make_float3(tri_a.x - tri_c.x, tri_a.y - tri_c.y, tri_a.z - tri_c.z); float3 edge2 = make_float3(tri_b.x - tri_c.x, tri_b.y - tri_c.y, tri_b.z - tri_c.z); float3 tvec = make_float3(P.x - tri_c.x, P.y - tri_c.y, P.z - tri_c.z); diff --git a/intern/cycles/kernel/kernel_textures.h b/intern/cycles/kernel/kernel_textures.h index 245d236ff97..5ba262c1044 100644 --- a/intern/cycles/kernel/kernel_textures.h +++ b/intern/cycles/kernel/kernel_textures.h @@ -25,7 +25,8 @@ /* bvh */ KERNEL_TEX(float4, texture_float4, __bvh_nodes) KERNEL_TEX(float4, texture_float4, __bvh_leaf_nodes) -KERNEL_TEX(float4, texture_float4, __tri_storage) +KERNEL_TEX(float4, texture_float4, __prim_tri_verts) +KERNEL_TEX(uint, texture_uint, __prim_tri_index) KERNEL_TEX(uint, texture_uint, __prim_type) KERNEL_TEX(uint, texture_uint, __prim_visibility) KERNEL_TEX(uint, texture_uint, __prim_index) @@ -39,8 +40,7 @@ KERNEL_TEX(float4, texture_float4, __objects_vector) /* triangles */ KERNEL_TEX(uint, texture_uint, __tri_shader) KERNEL_TEX(float4, texture_float4, __tri_vnormal) -KERNEL_TEX(float4, texture_float4, __tri_vindex) -KERNEL_TEX(float4, texture_float4, __tri_verts) +KERNEL_TEX(uint4, texture_uint4, __tri_vindex) /* curves */ KERNEL_TEX(float4, texture_float4, __curves) |