diff --git a/src/gallium/auxiliary/draw/draw_context.h b/src/gallium/auxiliary/draw/draw_context.h
index 3986d6469e3..44acf011699 100644
--- a/src/gallium/auxiliary/draw/draw_context.h
+++ b/src/gallium/auxiliary/draw/draw_context.h
@@ -39,6 +39,7 @@
 
 
 #include "pipe/p_state.h"
+#include "nir.h"
 
 struct pipe_context;
 struct draw_context;
@@ -130,7 +131,8 @@ boolean
 draw_install_aaline_stage(struct draw_context *draw, struct pipe_context *pipe);
 
 boolean
-draw_install_aapoint_stage(struct draw_context *draw, struct pipe_context *pipe);
+draw_install_aapoint_stage(struct draw_context *draw, struct pipe_context *pipe,
+                           nir_alu_type bool_type);
 
 boolean
 draw_install_pstipple_stage(struct draw_context *draw, struct pipe_context *pipe);
diff --git a/src/gallium/auxiliary/draw/draw_pipe_aapoint.c b/src/gallium/auxiliary/draw/draw_pipe_aapoint.c
index 56fff878885..b1b66f6532f 100644
--- a/src/gallium/auxiliary/draw/draw_pipe_aapoint.c
+++ b/src/gallium/auxiliary/draw/draw_pipe_aapoint.c
@@ -99,6 +99,9 @@ struct aapoint_stage
    /** vertex attrib slot containing position */
    uint pos_slot;
 
+   /** Type of Boolean variables on this hardware. */
+   nir_alu_type bool_type;
+
    /** Currently bound fragment shader */
    struct aapoint_fragment_shader *fs;
 
@@ -418,7 +421,7 @@ generate_aapoint_fs_nir(struct aapoint_stage *aapoint)
    if (!aapoint_fs.ir.nir)
       return FALSE;
 
-   nir_lower_aapoint_fs(aapoint_fs.ir.nir, &aapoint->fs->generic_attrib);
+   nir_lower_aapoint_fs(aapoint_fs.ir.nir, &aapoint->fs->generic_attrib, aapoint->bool_type);
    aapoint->fs->aapoint_fs = aapoint->driver_create_fs_state(pipe, &aapoint_fs);
    if (aapoint->fs->aapoint_fs == NULL)
       goto fail;
@@ -689,7 +692,7 @@ draw_aapoint_prepare_outputs(struct draw_context *draw,
 
 
 static struct aapoint_stage *
-draw_aapoint_stage(struct draw_context *draw)
+draw_aapoint_stage(struct draw_context *draw, nir_alu_type bool_type)
 {
    struct aapoint_stage *aapoint = CALLOC_STRUCT(aapoint_stage);
    if (!aapoint)
@@ -704,6 +707,7 @@ draw_aapoint_stage(struct draw_context *draw)
    aapoint->stage.flush = aapoint_flush;
    aapoint->stage.reset_stipple_counter = aapoint_reset_stipple_counter;
    aapoint->stage.destroy = aapoint_destroy;
+   aapoint->bool_type = bool_type;
 
    if (!draw_alloc_temp_verts(&aapoint->stage, 4))
       goto fail;
@@ -793,7 +797,8 @@ aapoint_delete_fs_state(struct pipe_context *pipe, void *fs)
  */
 boolean
 draw_install_aapoint_stage(struct draw_context *draw,
-                           struct pipe_context *pipe)
+                           struct pipe_context *pipe,
+                           nir_alu_type bool_type)
 {
    struct aapoint_stage *aapoint;
 
@@ -802,7 +807,7 @@ draw_install_aapoint_stage(struct draw_context *draw,
    /*
     * Create / install AA point drawing / prim stage
     */
-   aapoint = draw_aapoint_stage(draw);
+   aapoint = draw_aapoint_stage(draw, bool_type);
    if (!aapoint)
       return FALSE;
 
diff --git a/src/gallium/auxiliary/nir/nir_draw_helpers.c b/src/gallium/auxiliary/nir/nir_draw_helpers.c
index 0ebc1ef0b69..96cd395d44d 100644
--- a/src/gallium/auxiliary/nir/nir_draw_helpers.c
+++ b/src/gallium/auxiliary/nir/nir_draw_helpers.c
@@ -300,8 +300,8 @@ nir_lower_aapoint_block(nir_block *block,
 }
 
 static void
-nir_lower_aapoint_impl(nir_function_impl *impl,
-                      lower_aapoint *state)
+nir_lower_aapoint_impl(nir_function_impl *impl, lower_aapoint *state,
+                       nir_alu_type bool_type)
 {
    nir_builder *b = &state->b;
 
@@ -317,7 +317,21 @@ nir_lower_aapoint_impl(nir_function_impl *impl,
 
    nir_ssa_def *k = nir_channel(b, aainput, 2);
    nir_ssa_def *chan_val_one = nir_channel(b, aainput, 3);
-   nir_ssa_def *comp = nir_flt32(b, chan_val_one, dist);
+   nir_ssa_def *comp;
+
+   switch (bool_type) {
+   case nir_type_bool1:
+      comp = nir_flt(b, chan_val_one, dist);
+      break;
+   case nir_type_bool32:
+      comp = nir_flt32(b, chan_val_one, dist);
+      break;
+   case nir_type_float32:
+      comp = nir_slt(b, chan_val_one, dist);
+      break;
+   default:
+      unreachable("Invalid Boolean type.");
+   }
 
    nir_discard_if(b, comp);
    b->shader->info.fs.uses_discard = true;
@@ -339,7 +353,41 @@ nir_lower_aapoint_impl(nir_function_impl *impl,
     * else
     *    sel = 1.0;
     */
-   nir_ssa_def *sel = nir_b32csel(b, nir_fge32(b, k, dist), coverage, chan_val_one);
+   nir_ssa_def *sel;
+
+   switch (bool_type) {
+   case nir_type_bool1:
+      sel = nir_b32csel(b, nir_fge(b, k, dist), coverage, chan_val_one);
+      break;
+   case nir_type_bool32:
+      sel = nir_b32csel(b, nir_fge32(b, k, dist), coverage, chan_val_one);
+      break;
+   case nir_type_float32: {
+      /* On this path, don't assume that any "fancy" instructions are
+       * supported, but also try to emit something decent.
+       *
+       *    sel = (k >= distance) ? coverage : 1.0;
+       *    sel = (k >= distance) * coverage : (1 - (k >= distance)) * 1.0
+       *    sel = (k >= distance) * coverage : (1 - (k >= distance))
+       *
+       * Since (k >= distance) * coverage is zero when (1 - (k >= distance))
+       * is not zero,
+       *
+       *    sel = (k >= distance) * coverage + (1 - (k >= distance))
+       *
+       * If we assume that coverage == fsat(coverage), this could be further
+       * optimized to fsat(coverage + (1 - (k >= distance))), but I don't feel
+       * like verifying that right now.
+       */
+      nir_ssa_def *cmp_result = nir_sge(b, k, dist);
+      sel = nir_fadd(b,
+                     nir_fmul(b, coverage, cmp_result),
+                     nir_fadd(b, chan_val_one, nir_fneg(b, cmp_result)));
+      break;
+   }
+   default:
+      unreachable("Invalid Boolean type.");
+   }
 
    nir_foreach_block(block, impl) {
      nir_lower_aapoint_block(block, state, sel);
@@ -347,8 +395,12 @@ nir_lower_aapoint_impl(nir_function_impl *impl,
 }
 
 void
-nir_lower_aapoint_fs(struct nir_shader *shader, int *varying)
+nir_lower_aapoint_fs(struct nir_shader *shader, int *varying, const nir_alu_type bool_type)
 {
+   assert(bool_type == nir_type_bool1 ||
+          bool_type == nir_type_bool32 ||
+          bool_type == nir_type_float32);
+
    lower_aapoint state = {
       .shader = shader,
    };
@@ -378,7 +430,7 @@ nir_lower_aapoint_fs(struct nir_shader *shader, int *varying)
 
    nir_foreach_function(function, shader) {
       if (function->impl) {
-         nir_lower_aapoint_impl(function->impl, &state);
+         nir_lower_aapoint_impl(function->impl, &state, bool_type);
       }
    }
 }
diff --git a/src/gallium/auxiliary/nir/nir_draw_helpers.h b/src/gallium/auxiliary/nir/nir_draw_helpers.h
index 114fc8d89b4..ef6ffd79b20 100644
--- a/src/gallium/auxiliary/nir/nir_draw_helpers.h
+++ b/src/gallium/auxiliary/nir/nir_draw_helpers.h
@@ -43,7 +43,8 @@ nir_lower_aaline_fs(struct nir_shader *shader, int *varying,
                     nir_variable *stipple_pattern);
 
 void
-nir_lower_aapoint_fs(struct nir_shader *shader, int *varying);
+nir_lower_aapoint_fs(struct nir_shader *shader, int *varying,
+                     nir_alu_type bool_type);
 
 #ifdef __cplusplus
 }
diff --git a/src/gallium/drivers/i915/ci/i915-g33-fails.txt b/src/gallium/drivers/i915/ci/i915-g33-fails.txt
index caa0ea55084..e450f4d3782 100644
--- a/src/gallium/drivers/i915/ci/i915-g33-fails.txt
+++ b/src/gallium/drivers/i915/ci/i915-g33-fails.txt
@@ -203,8 +203,8 @@ spec@!opengl 1.1@linestipple@Factor 3x,Fail
 spec@!opengl 1.1@linestipple@Line loop,Fail
 spec@!opengl 1.1@linestipple@Line strip,Fail
 
-# "../src/compiler/nir/nir_lower_int_to_float.c:102: lower_alu_instr: Assertion `nir_alu_type_get_base_type(info->output_type) != nir_type_int && nir_alu_type_get_base_type(info->output_type) != nir_type_uint' failed."
-spec@!opengl 1.1@point-line-no-cull,Crash
+# Test no longer crashes on an assertion in NIR, but it still fails.
+spec@!opengl 1.1@point-line-no-cull,Fail
 
 spec@!opengl 1.1@polygon-mode-offset,Fail
 spec@!opengl 1.1@polygon-mode-offset@config 3: Expected white pixel on bottom edge,Fail
@@ -403,9 +403,6 @@ spec@arb_pixel_buffer_object@cubemap npot pbo,Fail
 spec@arb_pixel_buffer_object@fbo-pbo-readpixels-small,Fail
 spec@arb_pixel_buffer_object@pbo-getteximage,Fail
 
-# nir_lower_aapoint_impl() uses b32csel instead of fcsel.
-spec@arb_point_parameters@arb_point_parameters-point-attenuation,Crash
-
 spec@arb_point_parameters@arb_point_parameters-point-attenuation@Aliased combinations,Fail
 spec@arb_provoking_vertex@arb-provoking-vertex-render,Fail
 spec@arb_sampler_objects@gl_ext_texture_srgb_decode,Fail
diff --git a/src/gallium/drivers/i915/i915_context.c b/src/gallium/drivers/i915/i915_context.c
index e283a42f279..dfaa111e725 100644
--- a/src/gallium/drivers/i915/i915_context.c
+++ b/src/gallium/drivers/i915/i915_context.c
@@ -237,7 +237,7 @@ i915_create_context(struct pipe_screen *screen, void *priv, unsigned flags)
    i915->no_log_program_errors = false;
 
    draw_install_aaline_stage(i915->draw, &i915->base);
-   draw_install_aapoint_stage(i915->draw, &i915->base);
+   draw_install_aapoint_stage(i915->draw, &i915->base, nir_type_float32);
    draw_enable_point_sprites(i915->draw, true);
 
    i915->dirty = ~0;
diff --git a/src/gallium/drivers/llvmpipe/lp_context.c b/src/gallium/drivers/llvmpipe/lp_context.c
index 8d9c2ed01ed..343aecc61cc 100644
--- a/src/gallium/drivers/llvmpipe/lp_context.c
+++ b/src/gallium/drivers/llvmpipe/lp_context.c
@@ -303,7 +303,7 @@ llvmpipe_create_context(struct pipe_screen *screen, void *priv,
 
    /* plug in AA line/point stages */
    draw_install_aaline_stage(llvmpipe->draw, &llvmpipe->pipe);
-   draw_install_aapoint_stage(llvmpipe->draw, &llvmpipe->pipe);
+   draw_install_aapoint_stage(llvmpipe->draw, &llvmpipe->pipe, nir_type_bool32);
    draw_install_pstipple_stage(llvmpipe->draw, &llvmpipe->pipe);
 
    /* convert points and lines into triangles:
diff --git a/src/gallium/drivers/softpipe/sp_context.c b/src/gallium/drivers/softpipe/sp_context.c
index ee668330e72..4d98f904c77 100644
--- a/src/gallium/drivers/softpipe/sp_context.c
+++ b/src/gallium/drivers/softpipe/sp_context.c
@@ -54,6 +54,8 @@
 #include "sp_tex_sample.h"
 #include "sp_image.h"
 
+#include "nir.h"
+
 static void
 softpipe_destroy( struct pipe_context *pipe )
 {
@@ -321,7 +323,7 @@ softpipe_create_context(struct pipe_screen *screen,
 
    /* plug in AA line/point stages */
    draw_install_aaline_stage(softpipe->draw, &softpipe->pipe);
-   draw_install_aapoint_stage(softpipe->draw, &softpipe->pipe);
+   draw_install_aapoint_stage(softpipe->draw, &softpipe->pipe, nir_type_bool32);
 
    /* Do polygon stipple w/ texture map + frag prog. */
    draw_install_pstipple_stage(softpipe->draw, &softpipe->pipe);
diff --git a/src/gallium/drivers/svga/svga_swtnl_draw.c b/src/gallium/drivers/svga/svga_swtnl_draw.c
index da2d5f46121..a16d2272201 100644
--- a/src/gallium/drivers/svga/svga_swtnl_draw.c
+++ b/src/gallium/drivers/svga/svga_swtnl_draw.c
@@ -182,6 +182,11 @@ svga_init_swtnl(struct svga_context *svga)
    /* must be done before installing Draw stages */
    util_blitter_cache_all_shaders(svga->blitter);
 
+   const nir_alu_type bool_type =
+      screen->screen.get_shader_param(&screen->screen, PIPE_SHADER_FRAGMENT,
+                                      PIPE_SHADER_CAP_INTEGERS) ?
+      nir_type_bool32 : nir_type_float32;
+
    if (!screen->haveLineSmooth)
       draw_install_aaline_stage(svga->swtnl.draw, &svga->pipe);
 
@@ -189,7 +194,7 @@ svga_init_swtnl(struct svga_context *svga)
    draw_enable_line_stipple(svga->swtnl.draw, !screen->haveLineStipple);
 
    /* always install AA point stage */
-   draw_install_aapoint_stage(svga->swtnl.draw, &svga->pipe);
+   draw_install_aapoint_stage(svga->swtnl.draw, &svga->pipe, bool_type);
 
    /* Set wide line threshold above device limit (so we'll never really use it)
     */