[Mesa-dev] [PATCH 05/10] glsl: Add lowering pass for GLSL ES 3.00 pack/unpack operations

Chad Versace chad.versace at linux.intel.com
Thu Jan 10 00:10:23 PST 2013


Lower them to arithmetic and bit manipulation expressions.

Signed-off-by: Chad Versace <chad.versace at linux.intel.com>
---
 src/glsl/Makefile.sources           |    1 +
 src/glsl/ir_optimization.h          |   18 +
 src/glsl/lower_packing_builtins.cpp | 1566 +++++++++++++++++++++++++++++++++++
 3 files changed, 1585 insertions(+)
 create mode 100644 src/glsl/lower_packing_builtins.cpp

diff --git a/src/glsl/Makefile.sources b/src/glsl/Makefile.sources
index d984c5c..4aecdd7 100644
--- a/src/glsl/Makefile.sources
+++ b/src/glsl/Makefile.sources
@@ -58,6 +58,7 @@ LIBGLSL_FILES = \
 	$(GLSL_SRCDIR)/lower_mat_op_to_vec.cpp \
 	$(GLSL_SRCDIR)/lower_noise.cpp \
 	$(GLSL_SRCDIR)/lower_packed_varyings.cpp \
+	$(GLSL_SRCDIR)/lower_packing_builtins.cpp \
 	$(GLSL_SRCDIR)/lower_texture_projection.cpp \
 	$(GLSL_SRCDIR)/lower_variable_index_to_cond_assign.cpp \
 	$(GLSL_SRCDIR)/lower_vec_index_to_cond_assign.cpp \
diff --git a/src/glsl/ir_optimization.h b/src/glsl/ir_optimization.h
index 6b95191..39d3a74 100644
--- a/src/glsl/ir_optimization.h
+++ b/src/glsl/ir_optimization.h
@@ -37,6 +37,23 @@
 #define MOD_TO_FRACT       0x20
 #define INT_DIV_TO_MUL_RCP 0x40
 
+/**
+ * \see class lower_packing_builtins_visitor
+ */
+enum lower_packing_builtins_op {
+   LOWER_PACK_SNORM_2x16                = 0x0001,
+   LOWER_UNPACK_SNORM_2x16              = 0x0002,
+
+   LOWER_PACK_UNORM_2x16                = 0x0004,
+   LOWER_UNPACK_UNORM_2x16              = 0x0008,
+
+   LOWER_PACK_HALF_2x16                 = 0x0010,
+   LOWER_UNPACK_HALF_2x16               = 0x0020,
+
+   LOWER_PACK_HALF_2x16_TO_SPLIT        = 0x0040,
+   LOWER_UNPACK_HALF_2x16_TO_SPLIT      = 0x0080,
+};
+
 bool do_common_optimization(exec_list *ir, bool linked,
 			    bool uniform_locations_assigned,
 			    unsigned max_unroll_iterations);
@@ -74,6 +91,7 @@ bool lower_variable_index_to_cond_assign(exec_list *instructions,
 bool lower_quadop_vector(exec_list *instructions, bool dont_lower_swz);
 bool lower_clip_distance(gl_shader *shader);
 void lower_output_reads(exec_list *instructions);
+bool lower_packing_builtins(exec_list *instructions, int op_mask);
 void lower_ubo_reference(struct gl_shader *shader, exec_list *instructions);
 void lower_packed_varyings(void *mem_ctx, unsigned location_base,
                            unsigned locations_used, ir_variable_mode mode,
diff --git a/src/glsl/lower_packing_builtins.cpp b/src/glsl/lower_packing_builtins.cpp
new file mode 100644
index 0000000..cd84084
--- /dev/null
+++ b/src/glsl/lower_packing_builtins.cpp
@@ -0,0 +1,1566 @@
+/*
+ * Copyright © 2012 Intel Corporation
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice (including the next
+ * paragraph) shall be included in all copies or substantial portions of the
+ * Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+ * DEALINGS IN THE SOFTWARE.
+ */
+
+#include "ir.h"
+#include "ir_optimization.h"
+#include "ir_rvalue_visitor.h"
+
+namespace {
+
+/**
+ * A visitor that lowers the built-in floating-point packing and unpacking
+ * operations to arithmetic and bit manipulation expressions.
+ */
+class lower_packing_builtins_visitor : public ir_rvalue_visitor {
+public:
+   /**
+    * \param op_mask is a bitmask of `enum lower_packing_builtins_op`
+    */
+   explicit lower_packing_builtins_visitor(int op_mask) :
+      op_mask(op_mask),
+      progress(false),
+      prev_inserted_instruction(NULL)
+   {
+      /* Mutually exclusive options. */
+      assert(!((op_mask & LOWER_PACK_HALF_2x16) &&
+               (op_mask & LOWER_PACK_HALF_2x16_TO_SPLIT)));
+
+      assert(!((op_mask & LOWER_UNPACK_HALF_2x16) &&
+               (op_mask & LOWER_UNPACK_HALF_2x16_TO_SPLIT)));
+
+      return;
+   }
+
+   virtual ~lower_packing_builtins_visitor() {}
+
+   bool get_progress() { return progress; }
+
+   void handle_rvalue(ir_rvalue **rvalue)
+   {
+      if (!*rvalue)
+	 return;
+
+      ir_expression *expr = (*rvalue)->as_expression();
+      if (!expr)
+	 return;
+
+      void *mem_ctx = ralloc_parent(*rvalue);
+      ir_rvalue *op0 = expr->operands[0];
+      reset_instruction_insertion();
+
+      switch (expr->operation) {
+      case ir_unop_pack_snorm_2x16:
+         assert((*rvalue)->type == glsl_type::uint_type);
+         assert(op0->type == glsl_type::vec2_type);
+         if (op_mask & LOWER_PACK_SNORM_2x16) {
+            *rvalue = lower_pack_snorm_2x16(mem_ctx, op0);
+         }
+         break;
+      case ir_unop_pack_unorm_2x16:
+         assert((*rvalue)->type == glsl_type::uint_type);
+         assert(op0->type == glsl_type::vec2_type);
+         if (op_mask & LOWER_PACK_UNORM_2x16) {
+            *rvalue = lower_pack_unorm_2x16(mem_ctx, op0);
+         }
+         break;
+      case ir_unop_pack_half_2x16:
+         assert((*rvalue)->type == glsl_type::uint_type);
+         assert(op0->type == glsl_type::vec2_type);
+         if (op_mask & LOWER_PACK_HALF_2x16) {
+            *rvalue = pack_half_2x16(mem_ctx, op0);
+         } else if (op_mask & LOWER_PACK_HALF_2x16_TO_SPLIT) {
+            *rvalue = split_pack_half_2x16(mem_ctx, op0);
+         }
+         break;
+      case ir_unop_unpack_snorm_2x16:
+         assert((*rvalue)->type == glsl_type::vec2_type);
+         assert(op0->type == glsl_type::uint_type);
+         if (op_mask & LOWER_UNPACK_SNORM_2x16) {
+            *rvalue = lower_unpack_snorm_2x16(mem_ctx, op0);
+         }
+         break;
+      case ir_unop_unpack_unorm_2x16:
+         assert((*rvalue)->type == glsl_type::vec2_type);
+         assert(op0->type == glsl_type::uint_type);
+         if (op_mask & LOWER_UNPACK_UNORM_2x16) {
+            *rvalue = lower_unpack_unorm_2x16(mem_ctx, op0);
+         }
+         break;
+      case ir_unop_unpack_half_2x16:
+         assert((*rvalue)->type == glsl_type::vec2_type);
+         assert(op0->type == glsl_type::uint_type);
+         if (op_mask & LOWER_UNPACK_HALF_2x16) {
+            *rvalue = lower_unpack_half_2x16(mem_ctx, op0);
+         } else if (op_mask & LOWER_UNPACK_HALF_2x16_TO_SPLIT) {
+            *rvalue = split_unpack_half_2x16(mem_ctx, op0);
+         }
+         break;
+      default:
+         return;
+      }
+
+      progress = true;
+   }
+
+private:
+   int op_mask;
+   bool progress;
+   ir_instruction *prev_inserted_instruction;
+
+   void
+   reset_instruction_insertion()
+   {
+      prev_inserted_instruction = NULL;
+   }
+
+   void
+   insert_instruction(ir_instruction *ir)
+   {
+      assert(ir != NULL);
+
+      if (prev_inserted_instruction == NULL) {
+         base_ir->insert_before(ir);
+      } else {
+         prev_inserted_instruction->insert_after(ir);
+      }
+
+      prev_inserted_instruction = ir;
+   }
+
+   /**
+    * \brief Pack two uint16's into a single uint32.
+    *
+    * Interpret the given uvec2 as a uint16 pair. Pack the pair into a uint32
+    * where the least significant bits specify the first element of the pair.
+    * Return the uint32 as a uint rvalue.
+    *
+    * This function generates IR that approximates the following GLSL:
+    *
+    *    uvec2 *u = UVEC2_RVAL;
+    *    return (u.y << 16) | (u.x & 0xffff);
+    */
+   ir_rvalue*
+   pack_uvec2_to_uint(void *mem_ctx, ir_rvalue *uvec2_rval)
+   {
+      assert(uvec2_rval->type == glsl_type::uvec2_type);
+
+      /* uvec2 u = uvec2_rval; */
+      ir_variable *u2 =
+         new(mem_ctx) ir_variable(glsl_type::uvec2_type,
+                                  "tmp_pack_uvec2_to_uint",
+                                  ir_var_temporary);
+      insert_instruction(u2);
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(u2),
+            uvec2_rval));
+
+      /* return (u.y << 16) | (u.x & 0xffff); */
+      return
+         new(mem_ctx) ir_expression(ir_binop_bit_or,
+           new(mem_ctx) ir_expression(ir_binop_lshift,
+             new(mem_ctx) ir_swizzle(
+                new(mem_ctx) ir_dereference_variable(u2),
+                1, 0, 0, 0, 1),
+             new(mem_ctx) ir_constant(16u)),
+           new(mem_ctx) ir_expression(ir_binop_bit_and,
+             new(mem_ctx) ir_swizzle(
+                new(mem_ctx) ir_dereference_variable(u2),
+                0, 0, 0, 0, 1),
+             new(mem_ctx) ir_constant(0xffffu)));
+   }
+
+   /**
+    * \brief Unpack a uint32 to two uint16's.
+    *
+    * Interpret the given uint32 as a uint16 pair where the uint32's least
+    * significant bits specify the pair's first element. Return the uint16
+    * pair as a uvec2 rvalue.
+    *
+    * This function generates IR that approximates the following GLSL:
+    *
+    *    uint u = UINT_RVAL;
+    *    return uvec2(u & 0xffffu, u >> 16u);
+    */
+   ir_rvalue*
+   unpack_uint_to_uvec2(void *mem_ctx, ir_rvalue *uint_rval)
+   {
+      assert(uint_rval->type == glsl_type::uint_type);
+
+      /* uint u; */
+      ir_variable *u =
+         new(mem_ctx) ir_variable(glsl_type::uint_type,
+                                  "tmp_unpack_uint_to_uvec2_u",
+                                  ir_var_temporary);
+      insert_instruction(u);
+
+      /* u = uint_rval; */
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+           new(mem_ctx) ir_dereference_variable(u),
+           uint_rval));
+
+      /* uvec2 u2; */
+      ir_variable *u2 =
+         new(mem_ctx) ir_variable(glsl_type::uvec2_type,
+                                  "tmp_unpack_uint_to_uvec2_u2",
+                                  ir_var_temporary);
+      insert_instruction(u2);
+
+
+      /* u2.x = u & 0xffffu; */
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(u2),
+              new(mem_ctx) ir_expression(
+                ir_binop_bit_and,
+                new(mem_ctx) ir_dereference_variable(u),
+                new(mem_ctx) ir_constant(0xffffu)),
+            NULL /*condition*/,
+            1 /*write mask*/));
+
+      /* u2.y = u >> 16u; */
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(u2),
+              new(mem_ctx) ir_expression(
+                ir_binop_rshift,
+                new(mem_ctx) ir_dereference_variable(u),
+                new(mem_ctx) ir_constant(16u)),
+            NULL /*condition*/,
+            2 /*write mask*/));
+
+      return new(mem_ctx) ir_dereference_variable(u2);
+   }
+
+   /* \brief Lower packSnorm2x16.
+    *
+    * From page 88 (94 of pdf) of the GLSL ES 3.00 spec:
+    *
+    *    hihgp uint packSnorm2x16(vec2 v)
+    *    --------------------------------
+    *    First, converts each component of the normalized floating-point value
+    *    v into 16-bit integer values. Then, the results are packed into the
+    *    returned 32-bit unsigned integer.
+    *
+    *    The conversion for component c of v to fixed point is done as
+    *    follows:
+    *
+    *       packSnorm2x16: round(clamp(c, -1, +1) * 32767.0)
+    *
+    *    The first component of the vector will be written to the least
+    *    significant bits of the output; the last component will be written to
+    *    the most significant bits.
+    *
+    * This function generates IR that approximates the following GLSL:
+    *
+    *     return pack_uvec2_to_uint(
+    *         uvec2(ivec2(
+    *           round(clamp(RVALUE, -1.0f, 1.0f) * 32767.0f))));
+    *
+    * It is necessary to first convert the vec2 to ivec2 rather than directly
+    * converting vec2 to uvec2 because the latter conversion is undefined.
+    * From page 56 (62 of pdf) of the GLSL ES 3.00 spec: "It is undefined to
+    * convert a negative floating point value to an uint".
+    */
+   ir_rvalue*
+   lower_pack_snorm_2x16(void *mem_ctx, ir_rvalue *vec2_rval)
+   {
+      assert(vec2_rval->type == glsl_type::vec2_type);
+
+      ir_rvalue *result =
+         pack_uvec2_to_uint(
+            mem_ctx,
+            new(mem_ctx) ir_expression(ir_unop_i2u,
+               new(mem_ctx) ir_expression(ir_unop_f2i,
+                  new(mem_ctx) ir_expression(ir_unop_round_even,
+                     new(mem_ctx) ir_expression(ir_binop_mul,
+                       new(mem_ctx) ir_expression(ir_binop_min,
+                          new(mem_ctx) ir_expression(ir_binop_max,
+                            vec2_rval,
+                            new(mem_ctx) ir_constant(-1.0f)),
+                          new(mem_ctx) ir_constant(1.0f)),
+                       new(mem_ctx) ir_constant(32767.0f))))));
+
+      assert(result->type == glsl_type::uint_type);
+      return result;
+   }
+
+   /* \brief Lower unpackSnorm2x16.
+    *
+    * From page 88 (94 of pdf) of the GLSL ES 3.00 spec:
+    *
+    *    highp vec2 unpackSnorm2x16 (highp uint p)
+    *    -----------------------------------------
+    *    First, unpacks a single 32-bit unsigned integer p into a pair of
+    *    16-bit unsigned integers. Then, each component is converted to
+    *    a normalized floating-point value to generate the returned
+    *    two-component vector.
+    *
+    *    The conversion for unpacked fixed-point value f to floating point is
+    *    done as follows:
+    *
+    *       unpackSnorm2x16: clamp(f / 32767.0, -1,+1)
+    *
+    *    The first component of the returned vector will be extracted from the
+    *    least significant bits of the input; the last component will be
+    *    extracted from the most significant bits.
+    *
+    * This function generates IR that approximates the following GLSL:
+    *
+    *    return clamp(
+    *       ((ivec2(unpack_uint_to_uvec2(RVALUE)) << 16) >> 16) / 32767.0f,
+    *       -1.0f, 1.0f);
+    *
+    * The above IR may appear unnecessarily complex, but the intermediate
+    * conversion to ivec2 and the bit shifts are necessary to correctly unpack
+    * negative floats.
+    *
+    * To see why, consider packing and then unpacking vec2(-1.0, 0.0).
+    * packSnorm2x16 encodes -1.0 as the int16 0xffff. During unpacking, we
+    * place that int16 into an int32, which results in the *positive* integer
+    * 0x0000ffff.  The int16's sign bit becomes, in the int32, the rather
+    * unimportant bit 16. We must now extend the int16's sign bit into bits
+    * 17-32, which is accomplished by left-shifting then right-shifting.
+    */
+   ir_rvalue*
+   lower_unpack_snorm_2x16(void *mem_ctx, ir_rvalue *uint_rval)
+   {
+      assert(uint_rval->type == glsl_type::uint_type);
+
+      ir_rvalue *result =
+         new(mem_ctx) ir_expression(ir_binop_min,
+            new(mem_ctx) ir_expression(ir_binop_max,
+               new(mem_ctx) ir_expression(ir_binop_div,
+                  new(mem_ctx) ir_expression(ir_unop_i2f,
+                     new(mem_ctx) ir_expression(ir_binop_rshift,
+                        new(mem_ctx) ir_expression(ir_binop_lshift,
+                           new(mem_ctx) ir_expression(ir_unop_u2i,
+                             unpack_uint_to_uvec2(mem_ctx, uint_rval)),
+                           new(mem_ctx) ir_constant(16)),
+                        new(mem_ctx) ir_constant(16))),
+              new(mem_ctx) ir_constant(32767.0f)),
+            new(mem_ctx) ir_constant(-1.0f)),
+          new(mem_ctx) ir_constant(1.0f));
+
+      assert(result->type == glsl_type::vec2_type);
+      return result;
+   }
+
+   /* \brief Lower packUnorm2x16.
+    *
+    * From page 88 (94 of pdf) of the GLSL ES 3.00 spec:
+    *
+    *    highp uint packUnorm2x16 (vec2 v)
+    *    ---------------------------------
+    *    First, converts each component of the normalized floating-point value
+    *    v into 16-bit integer values. Then, the results are packed into the
+    *    returned 32-bit unsigned integer.
+    *
+    *    The conversion for component c of v to fixed point is done as
+    *    follows:
+    *
+    *       packUnorm2x16: round(clamp(c, 0, +1) * 65535.0)
+    *
+    *    The first component of the vector will be written to the least
+    *    significant bits of the output; the last component will be written to
+    *    the most significant bits.
+    *
+    * This function generates IR that approximates the following GLSL:
+    *
+    *     return pack_uvec2_to_uint(uvec2(
+    *                round(clamp(RVALUE, 0.0f, 1.0f) * 65535.0f)));
+    *
+    * Here it is safe to directly convert the vec2 to uvec2 because the the
+    * vec2 has been clamped to a non-negative range.
+    */
+   ir_rvalue*
+   lower_pack_unorm_2x16(void *mem_ctx, ir_rvalue *vec2_rval)
+   {
+      assert(vec2_rval->type == glsl_type::vec2_type);
+
+      ir_rvalue *result =
+         pack_uvec2_to_uint(
+            mem_ctx,
+            new(mem_ctx) ir_expression(ir_unop_f2u,
+               new(mem_ctx) ir_expression(ir_unop_round_even,
+                  new(mem_ctx) ir_expression(ir_binop_mul,
+                    new(mem_ctx) ir_expression(ir_binop_min,
+                       new(mem_ctx) ir_expression(ir_binop_max,
+                         vec2_rval,
+                         new (mem_ctx) ir_constant(0.0f)),
+                       new(mem_ctx) ir_constant(1.0f)),
+                    new(mem_ctx) ir_constant(65535.0f)))));
+
+      assert(result->type == glsl_type::uint_type);
+      return result;
+   }
+
+   /* \brief Lower unpackUnom2x16.
+    *
+    * From page 89 (95 of pdf) of the GLSL ES 3.00 spec:
+    *
+    *    highp vec2 unpackUnorm2x16 (highp uint p)
+    *    -----------------------------------------
+    *    First, unpacks a single 32-bit unsigned integer p into a pair of
+    *    16-bit unsigned integers. Then, each component is converted to
+    *    a normalized floating-point value to generate the returned
+    *    two-component vector.
+    *
+    *    The conversion for unpacked fixed-point value f to floating point is
+    *    done as follows:
+    *
+    *       unpackUnorm2x16: f / 65535.0
+    *
+    *    The first component of the returned vector will be extracted from the
+    *    least significant bits of the input; the last component will be
+    *    extracted from the most significant bits.
+    *
+    * This function generates IR that approximates the following GLSL:
+    *
+    *     return vec2(unpack_uint_to_uvec2(RVALUE)) / 65535.0;
+    */
+   ir_rvalue*
+   lower_unpack_unorm_2x16(void *mem_ctx, ir_rvalue *uint_rval)
+   {
+      assert(uint_rval->type == glsl_type::uint_type);
+
+      ir_rvalue *result =
+         new(mem_ctx) ir_expression(ir_binop_div,
+           new(mem_ctx) ir_expression(ir_unop_u2f,
+              unpack_uint_to_uvec2(mem_ctx, uint_rval)),
+           new(mem_ctx) ir_constant(65535.0f));
+
+      assert(result->type == glsl_type::vec2_type);
+      return result;
+   }
+
+   /* \brief Lower the component-wise calculation of packHalf2x16.
+    *
+    * Given the non-shifted exponent and manstissa bits of a 16-bit float,
+    * this function calculates the corrresponding exponent and mantissa bits
+    * of the corresponding 16-bit float by constructing IR that approximates
+    * the body of the following function:
+    *
+    *    uint
+    *    pack_half_1x16_nosign(uint float32_exponent_bits,
+    *                          uint float32_mantissa_bits)
+    *    {
+    *       uint float16;
+    *
+    *       float16 = float16_exponent_bits(float32_exponent_bits,
+    *                                       float32_mantissa_bits);
+    *       float16 |= float16_mantissa_bits(float32_exponent_bits,
+    *                                        float32_mantissa_bits);
+    *
+    *       return float16;
+    *    }
+    *
+    * What follows is a detailed discussion of the calculation.
+    *
+    * For a float16, the bit layout is:
+    *
+    *   sign:     15
+    *   exponent: 10:14
+    *   mantissa: 0:9
+    *
+    * The sign, exponent, and mantissa of a float16 determine its value thus:
+    *
+    *   if e = 0 and m = 0, then zero:       (-1)^s * 0                           (1)
+    *   if e = 0 and m != 0, then subnormal: (-1)^s * 2^(e - 14) * (m / 2^10)     (2)
+    *   if 0 < e < 31, then normal:          (-1)^s * 2^(e - 15) * (1 + m / 2^10) (3)
+    *   if e = 31 and m = 0, then infinite:  (-1)^s * inf                         (4)
+    *   if e = 31 and m != 0, then NaN                                            (5)
+    *
+    * where 0 <= m < 2^10. The minimum and maximum normal float16 values are
+    *
+    *   min_norm16 = 2^(1 - 15) * (1 + 0 / 2^10) = 2^(-14)                        (6)
+    *   max_norm16 = 2^(30 - 15) * (1 + 1023 / 2^10)                              (7)
+    *
+    * For a float32, the bit layout is:
+    *
+    *   sign: 31
+    *   exponent: 23:30
+    *   mantissa: 0:22
+    *
+    * The sign, exponent, and mantissa of a float32 determine its value thus:
+    *
+    *   if e = 0 and m = 0, then zero:        (-1)^s * 0                             (8)
+    *   if e = 0 and m != 0, then subnormal:  (-1)^s * 2^(e - 126) * (m / 2^23)      (9)
+    *   if 0 < e < 255, then normal:          (-1)^s * 2^(e - 127) * (1 + m / 2^23) (10)
+    *   if e = 255 and m = 0, then infinite:  (-1)^s * inf                          (11)
+    *   if e = 255 and m != 0, then NaN                                             (12)
+    *
+    * where 0 <= m < 2^23.
+    *
+    * Let f32 be a float32. Let s32, e32, and m32 be the value of s, e, and
+    * m in equations 6-10. Let f16 be the float16 which is the conversion of
+    * f32. Likewise, let s16, e16, and m16 be the value of s, e, and m in
+    * equations 1-5. Since this function ignores the sign bit, let
+    * s32 = s16 = 0.
+    *
+    * To calculate e16 and m16, let's consider separately each of the classes
+    * (equations 1-5) to which the resultant f16 may belong.
+    *
+    * # Case 1: f16 is zero
+    *
+    *     This case occurs when f32 is zero or when f32 < min_norm16.
+    *     Calculating the bits in this case is trivial.
+    *
+    *       e16 = 0
+    *       m16 = 0
+    *
+    * # Case 2: f16 is subnormal
+    *
+    *     Below in case 3, we choose to round toward zero any float32 that
+    *     cannot be exactly represented as a float16. We also follow that
+    *     convention here in case 2. As a consequence, we convert f32 to
+    *     a subnormal float16 if and only if
+    *
+    *       f32 < min_norm16                                 (13)
+    *
+    *     (It would valid to choose different rounding method when
+    *     max_subnorm16 < f32 < min_norm16, but that would introduce
+    *     additional complexity into calculations).
+    *
+    *     Calculating the boundary values of e32 and m32 for which
+    *     f32 < min_norm16 gives
+    *
+    *                                    f32 < min_norm16    (14)
+    *       2^(e32 - 127) * (1 + m32 / 2^23) < 2^(-14)       (15)
+    *                          2^(e32 - 127) < 2^(-14)       (16)
+    *                                    e32 < 113           (17)
+    *
+    *     We must now calculate e16 and m16. However, to do so for subnormal
+    *     float16 values requires iterating over the bits of f32's mantissa in
+    *     order to find the position of the most significant enabled bit.
+    *     Considering that packHalf2x16, on supported hardware where it need
+    *     not be lowered, generates only a small number of instructions, to
+    *     generate a loop when lowering packHalf2x16 might produce unexpected,
+    *     and unacceptable, overhead during shader execution.
+    *
+    *     Luckily, the GLSL ES 3.00 and GLSL 4.10 specs allows us to truncate
+    *     subnormal floats to zero. From section 4.5.1 "Range and Precision"
+    *     of the two specs:
+    *
+    *       Any subnormal (denormalized) value input into a shader or
+    *       potentially generated by any operation in a shader can be flushed
+    *       to 0.
+    *
+    *     Therefore we choose
+    *
+    *       e16 = 0
+    *       m16 = 0
+    *
+    * # Case 3: f16 is normal
+    *
+    *     We choose to convert f32 to a normal float16 if and only if
+    *
+    *       min_normal16 <= f32 <= max_normal16                           (18)
+    *
+    *     From similar calculations as those in equations 14-17, the left-hand
+    *     inequality resolves to
+    *
+    *       e32 = 113                                                     (19)
+    *
+    *     Calculating the boundary values of e32 and m32 for the right-hand
+    *     inequality gives
+    *
+    *       f32 <= max_normal15                                                 (20)
+    *       2^(e32 - 127) * (1 + m32 / 2^23) <= 2^15 * (1 + 1023 / 2^ 10)       (21)
+    *
+    *       2^(e32 - 127) < 2^15 or                                             (22)
+    *          (2^(e32 - 127) = 2^15 and 1 + m32 / 2^23 <= 1 + 1023 / 2^ 10)    
+    *
+    *       e32 < 142 or (e32 = 142 and m32 <= 2^13 * 1023)                     (23)
+    *
+    *     Combining equations 19 and 23 gives
+    *
+    *       113 <= e32 < 142 or (e32 = 142 and m32 <= 2^13 * 1023)              (24)
+    *
+    *     Now that we have determined the float32 range that converts to
+    *     a normal float16, we must calculate e16 and m16.
+    *
+    *       2^(e32 - 127) * (1 + m32 / 2^23) = 2^(e16 - 15) * (1 + m16 / 2^10)  (25)
+    *
+    *     Solving equation 25 for e16 and m16 gives
+    *
+    *       e16 = e32 - 112                                               (26)
+    *       m16 = m32 / 2^13                                              (27)
+    *
+    *     However, not all float32 values can be exactly represented as
+    *     a float16. As a consequence, m16 in equation 27 has the potential to
+    *     have a fractional part (consider m32 = 1). We choose to round all
+    *     such float32 values downward to the nearest float16. To accomplish
+    *     this, ignore all but the most 10 significant bits of m32:
+    *
+    *       m16 = (m32 % 2^13) / 2^13                                     (28)
+    *
+    * # Case 4: f16 is infinite
+    *
+    *     The resultant f16 is infinite if and only if f32 exceeds the bounds
+    *     in equation 23. That is, if
+    *
+    *       (e32 = 142 and m32 > 2^13 * 1023) or (e32 > 142)              (29)
+    *
+    *     In this case, the choice for e16 and m16 are trivial:
+    *
+    *       e16 = 31
+    *       m16 = 0
+    *
+    * # Case 5: f16 is NaN
+    *
+    *     The resulting f16 is NaN if and only f32 is NaN, which occurs when
+    *
+    *       e32 = 255
+    *       m32 != 0
+    *
+    *     Any choice of m16 != 0 suffices. We choose m16 where all bits are set:
+    *
+    *       e16 = 31
+    *       m16 = 0x03ff
+    *
+    * We can therefore calculate f32 with the following C:
+    *
+    *   uint32_t f32 = GIVEN;
+    *   uint16_t f16;
+    *
+    *   uint32_t e32 = (f32 >> 23) & 0xff;
+    *   uint32_t m32 = f32 & 0x007fffff;
+    *
+    *   uint16_t e16;
+    *   uint16_t m16;
+    *
+    *   if (e32 == 255 && m32 != 0) {
+    *      // f32 is NaN
+    *      e16 = 31;
+    *      m16 = 0x03ff;
+    *   } else if (e32 < 113) {
+    *      // f32 converts to a zero or subnormal float16.
+    *      // flush subnormal float16's to zero.
+    *      e16 = 0;
+    *      m16 = 0;
+    *   } else if (e32 < 142 || (e32 == 142 && m32 <= (1023 << 13)) {
+    *      // f32 converts to a normal float16
+    *      e16 = e32 + 112;
+    *      m16 = m32 >> 13;
+    *   } else {
+    *      // f32 lies outside of the range of finite float16 values
+    *      e16 = 31;
+    *      m16 = 0;
+    *   }
+    *
+    * However, instruction execution is expensive on the GPU, and this
+    * compiler's quality of optimization is less than ideal. Below is
+    * a C implementation that should execute a near-minimal number of
+    * instructions.
+    *
+    *   uint32_t f32 = GIVEN;
+    *   uint16_t f16;
+    *
+    *   // Get f32's unshifted exponent and mantissa bits.
+    *   uint16_t e = f32 & 0x7f800000;
+    *   uint16_t m = f32 & 0x007fffff;
+    *
+    *   if (e == (255 << 23) && m != 0) {
+    *     // f32 is NaN
+    *     f16 = 0x7fff;
+    *   } else if (e < (113 << 23)) {
+    *     // f32 converts to a zero or subnormal float16.
+    *     // flush subnormal float16's to zero.
+    *     f16 = 0;
+    *   } else if (e < (142 << 23) || (e == (142 << 23) && m <= (1023 << 13)) {
+    *     // f32 converts to a normal float16
+    *     f16 = (m >> 13);
+    *     f16 |= (e - (112 << 23)) >> 13;
+    *   } else {
+    *     // f32 lies outside of the range of finite float16 values
+    *     f16 = (31 << 10);
+    *   }
+    *
+    * The IR constructed by this function is a translation of the above
+    * optimized C, where e and m are provided by the caller.
+    */
+   ir_rvalue*
+   pack_half_1x16_nosign(void *mem_ctx,
+                         ir_rvalue *e_rval,
+                         ir_rvalue *m_rval)
+   {
+       assert(e_rval->type == glsl_type::uint_type);
+       assert(m_rval->type == glsl_type::uint_type);
+
+       /* uint f16; */
+       ir_variable *f16 =
+          new(mem_ctx) ir_variable(glsl_type::uint_type,
+                                   "tmp_pack_half_1x16_f16",
+                                   ir_var_temporary);
+       insert_instruction(f16);
+
+       /* uint e = E_RVAL; */
+       ir_variable *e =
+          new(mem_ctx) ir_variable(glsl_type::uint_type,
+                                   "tmp_pack_half_1x16_e",
+                                   ir_var_temporary);
+       insert_instruction(e);
+       insert_instruction(
+          new(mem_ctx) ir_assignment(
+             new(mem_ctx) ir_dereference_variable(e),
+             e_rval));
+
+       /* uint m = M_RVAL; */
+       ir_variable *m =
+          new(mem_ctx) ir_variable(glsl_type::uint_type,
+                                   "tmp_pack_half_1x16_m",
+                                   ir_var_temporary);
+       insert_instruction(m);
+       insert_instruction(
+          new(mem_ctx) ir_assignment(
+             new(mem_ctx) ir_dereference_variable(m),
+             m_rval));
+
+       /*
+        * if (e == (255 << 23) && m != 0) {
+        *   // f32 is NaN
+        *   f16 = 0x7fff;
+        * }
+        */
+       ir_if *if_nan =
+          new(mem_ctx) ir_if(
+             new(mem_ctx) ir_expression(ir_binop_logic_and,
+                new(mem_ctx) ir_expression(ir_binop_equal,
+                   new(mem_ctx) ir_dereference_variable(e),
+                   new(mem_ctx) ir_constant(255u << 23u)),
+                new(mem_ctx) ir_expression(ir_unop_logic_not,
+                   new(mem_ctx) ir_expression(ir_binop_equal,
+                      new(mem_ctx) ir_dereference_variable(m),
+                      new(mem_ctx) ir_constant(0u)))));
+       insert_instruction(if_nan);
+       if_nan->then_instructions.push_tail(
+          new(mem_ctx) ir_assignment(
+             new(mem_ctx) ir_dereference_variable(f16),
+             new(mem_ctx) ir_constant(0x7fffu)));
+
+       /*
+        * else if (e < (113 << 23)) {
+        *   // f32 converts to a zero or subnormal float16.
+        *   // flush subnormal float16's to zero.
+        *   f16 = 0;
+        * }
+        */
+       ir_if *if_zero =
+          new(mem_ctx) ir_if(
+             new(mem_ctx) ir_expression(ir_binop_less,
+                   new(mem_ctx) ir_dereference_variable(e),
+                   new(mem_ctx) ir_constant(113u << 23u)));
+       if_nan->else_instructions.push_tail(if_zero);
+       if_zero->then_instructions.push_tail(
+          new(mem_ctx) ir_assignment(
+             new(mem_ctx) ir_dereference_variable(f16),
+                new(mem_ctx) ir_constant(0u)));
+
+       /*
+        * else if (e < (142 << 23) || (e == (142 << 23) && m <= (1023 << 13)) {
+        *   // f32 converts to a normal float16
+        *   f16 = (m >> 13);
+        *   f16 |= (e - (112 << 23)) >> 13;
+        * }
+        */
+       ir_if *if_normal =
+          new(mem_ctx) ir_if(
+             new(mem_ctx) ir_expression(ir_binop_logic_or,
+                new(mem_ctx) ir_expression(ir_binop_less,
+                   new(mem_ctx) ir_dereference_variable(e),
+                   new(mem_ctx) ir_constant(142u << 23u)),
+                new(mem_ctx) ir_expression(ir_binop_logic_and,
+                   new(mem_ctx) ir_expression(ir_binop_equal,
+                      new(mem_ctx) ir_dereference_variable(e),
+                      new(mem_ctx) ir_constant(142u << 23u)),
+                   new(mem_ctx) ir_expression(ir_binop_lequal,
+                      new(mem_ctx) ir_dereference_variable(m),
+                      new(mem_ctx) ir_constant(1023u << 13u)))));
+       if_zero->else_instructions.push_tail(if_normal);
+       if_normal->then_instructions.push_tail(
+          new(mem_ctx) ir_assignment(
+             new(mem_ctx) ir_dereference_variable(f16),
+             new(mem_ctx) ir_expression(ir_binop_rshift,
+                new(mem_ctx) ir_dereference_variable(m),
+                new(mem_ctx) ir_constant(13u))));
+       if_normal->then_instructions.push_tail(
+          new(mem_ctx) ir_assignment(
+             new(mem_ctx) ir_dereference_variable(f16),
+             new(mem_ctx) ir_expression(ir_binop_bit_or,
+                new(mem_ctx) ir_dereference_variable(f16),
+                new(mem_ctx) ir_expression(ir_binop_rshift,
+                   new(mem_ctx) ir_expression(ir_binop_sub,
+                      new(mem_ctx) ir_dereference_variable(e),
+                      new(mem_ctx) ir_constant(112u << 23u)),
+                   new(mem_ctx) ir_constant(13u)))));
+
+       /*
+        * else {
+        *   // f32 lies outside of the range of finite float16 values
+        *   f16 = (31 << 10);
+        * }
+        */
+       if_normal->else_instructions.push_tail(
+          new(mem_ctx) ir_assignment(
+             new(mem_ctx) ir_dereference_variable(f16),
+             new(mem_ctx) ir_constant(31u << 10u)));
+
+       /* return f16; */
+       return new(mem_ctx) ir_dereference_variable(f16);
+   }
+
+   /* \brief Lower packHalf2x16.
+    *
+    * From page 89 (95 of pdf) of the GLSL ES 3.00 spec:
+    *
+    *    highp uint packHalf2x16 (mediump vec2 v)
+    *    ----------------------------------------
+    *    Returns an unsigned integer obtained by converting the components of
+    *    a two-component floating-point vector to the 16-bit floating-point
+    *    representation found in the OpenGL ES Specification, and then packing
+    *    these two 16-bit integers into a 32-bit unsigned integer.
+    *
+    *    The first vector component specifies the 16 least- significant bits
+    *    of the result; the second component specifies the 16 most-significant
+    *    bits.
+    *
+    * This function constructs IR that approximates the following GLSL:
+    *
+    *   uvec2 f32 = bitcast_f2u(VEC2_RVALUE);
+    *   uvec2 f16;
+    *
+    *   // Get f32's unshifted exponent and mantissa bits.
+    *   uvec2 e = f32 & 0x7f800000u;
+    *   uvec2 m = f32 & 0x007fffffu;
+    *
+    *   // Set f16's exponent and mantissa bits.
+    *   f16.x = pack_half_1x16_nosign(e.x, m.x);
+    *   f16.y = pack_half_1y16_nosign(e.y, m.y);
+    *
+    *   // Set f16's sign bits.
+    *   f16 |= (f32 & (1u << 31u)) >> 16u;
+    *
+    *   return (f16.y << 16u) | f16.x;
+    */
+   ir_rvalue*
+   pack_half_2x16(void *mem_ctx, ir_rvalue *vec2_rval)
+   {
+      assert(vec2_rval->type == glsl_type::vec2_type);
+
+      /* uvec2 f32 = bitcast_f2u(RVALUE); */
+      ir_variable *f32 =
+         new(mem_ctx) ir_variable(glsl_type::uvec2_type,
+                                  "tmp_pack_half_2x16_f32",
+                                  ir_var_temporary);
+      insert_instruction(f32);
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f32),
+            new(mem_ctx) ir_expression(ir_unop_bitcast_f2u,
+               vec2_rval)));
+
+      /* uvec2 f16; */
+      ir_variable *f16 =
+         new(mem_ctx) ir_variable(glsl_type::uvec2_type,
+                                  "tmp_pack_half_2x16_f16",
+                                  ir_var_temporary);
+      insert_instruction(f16);
+
+      /* Get f32's unshifted exponent bits.
+       *
+       *   uvec2 e = f32 & 0x7f800000u;
+       */
+      ir_variable *e =
+         new(mem_ctx) ir_variable(glsl_type::uvec2_type,
+                                  "tmp_pack_half_2x16_e",
+                                  ir_var_temporary);
+      insert_instruction(e);
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(e),
+            new(mem_ctx) ir_expression(ir_binop_bit_and,
+               new(mem_ctx) ir_dereference_variable(f32),
+               new (mem_ctx) ir_constant(0x7f800000u))));
+
+      /* Get f32's unshifted mantissa bits.
+       *
+       *   uvec2 e = f32 & 0x007fffffu;
+       */
+      ir_variable *m =
+         new(mem_ctx) ir_variable(glsl_type::uvec2_type,
+                                  "tmp_pack_half_2x16_m",
+                                  ir_var_temporary);
+      insert_instruction(m);
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(m),
+            new(mem_ctx) ir_expression(ir_binop_bit_and,
+               new(mem_ctx) ir_dereference_variable(f32),
+               new (mem_ctx) ir_constant(0x007fffffu))));
+
+      /* Set f16's exponent and mantissa bits.
+       *
+       *   f16.x = pack_half_1x16_nosign(e.x, m.x);
+       *   f16.y = pack_half_1y16_nosign(e.y, m.y);
+       */
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f16),
+            pack_half_1x16_nosign(mem_ctx,
+               new(mem_ctx) ir_swizzle(
+                  new(mem_ctx) ir_dereference_variable(e),
+                  0, 0, 0, 0, 1),
+               new(mem_ctx) ir_swizzle(
+                  new(mem_ctx) ir_dereference_variable(m),
+                  0, 0, 0, 0, 1)),
+            NULL /*condition*/,
+            1 /*write mask*/));
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f16),
+            pack_half_1x16_nosign(mem_ctx,
+               new(mem_ctx) ir_swizzle(
+                  new(mem_ctx) ir_dereference_variable(e),
+                  1, 0, 0, 0, 1),
+               new(mem_ctx) ir_swizzle(
+                  new(mem_ctx) ir_dereference_variable(m),
+                  1, 0, 0, 0, 1)),
+            NULL /*condition*/,
+            2 /*write mask*/));
+
+      /* Set f16's sign bits.
+       *
+       *   f16 |= (f32 & (1u << 31u) >> 16u;
+       */
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f16),
+            new(mem_ctx) ir_expression(ir_binop_bit_or,
+               glsl_type::uvec2_type,
+               new(mem_ctx) ir_dereference_variable(f16),
+               new(mem_ctx) ir_expression(ir_binop_rshift,
+                  new(mem_ctx) ir_expression(ir_binop_bit_and,
+                     new(mem_ctx) ir_dereference_variable(f32),
+                     new(mem_ctx) ir_constant(1u << 31u)),
+                  new(mem_ctx) ir_constant(16u)))));
+
+
+      /* return (f16.y << 16u) | f16.x; */
+      ir_rvalue *result =
+         new(mem_ctx) ir_expression(ir_binop_bit_or,
+            new(mem_ctx) ir_expression(ir_binop_lshift,
+               new(mem_ctx) ir_swizzle(
+                  new(mem_ctx) ir_dereference_variable(f16),
+                  1, 0, 0, 0, 1),
+               new(mem_ctx) ir_constant(16u)),
+            new(mem_ctx) ir_swizzle(
+               new(mem_ctx) ir_dereference_variable(f16),
+               0, 0, 0, 0, 1));
+
+      assert(result->type == glsl_type::uint_type);
+      return result;
+   }
+
+   /**
+    * \brief Split packHalf2x16's vec2 operand into two floats.
+    *
+    * Some code generators, such as the i965 fragment shader, require that all
+    * vector expressions be lowered to a sequence of scalar expressions.
+    * However, packHalf2x16 cannot be scalarized by the same method as a true
+    * vector operation because the number of components of its input and
+    * output differ.
+    *
+    * This method scalarizes packHalf2x16 by transforming it from an unary
+    * operation having vector input to a binary operation having scalar input.
+    * That is, it transforms
+    *
+    *    packHalf2x16(VEC2_RVAL);
+    *
+    * into
+    *
+    *    vec2 v = VEC2_RVAL;
+    *    return packHalf2x16_split(v.x, v.y);
+    */
+   ir_rvalue*
+   split_pack_half_2x16(void *mem_ctx, ir_rvalue *vec2_rval)
+   {
+      assert(vec2_rval->type == glsl_type::vec2_type);
+
+      /* vec2 v = vec2_rval; */
+      ir_variable *v =
+         new(mem_ctx) ir_variable(glsl_type::vec2_type,
+                                  "tmp_split_pack_half_2x16_v",
+                                  ir_var_temporary);
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(v),
+            vec2_rval));
+
+      /* return packHalf2x16_split(v.x, v.y); */
+      return
+         new(mem_ctx) ir_expression(ir_binop_pack_half_2x16_split,
+            glsl_type::uint_type,
+            new(mem_ctx) ir_swizzle(
+               new(mem_ctx) ir_dereference_variable(v),
+               0, 0, 0, 0, 1),
+            new(mem_ctx) ir_swizzle(
+               new(mem_ctx) ir_dereference_variable(v),
+               1, 0, 0, 0, 1));
+   }
+
+   /**
+    * \brief Lower the component-wise calculation of unpackHalf2x16.
+    *
+    * Given the non-shifted exponent and mantissa bits of a 16-bit float, this
+    * function calculates the corresponding exponent and mantisssa bits of the
+    * equivalent 32-bit float by constructing IR that approximates the body
+    * following function:
+    *
+    *    uint
+    *    unpack_half_1x16_nosign(uint float16_exponent_bits,
+    *                            uint float16_mantissa_bits)
+    *    {
+    *       uint float32;
+    *
+    *       float32 = float32_exponent_bits(float16_exponent_bits,
+    *                                        float16_mantissa_bits);
+    *       float32 |= float32_mantissa_bits(float16_exponent_bits,
+    *                                        float16_mantissa_bits);
+    *
+    *       return float32;
+    *    }
+    *
+    * What follows is a detailed discussion of the calculation.
+    *
+    * For a float16, the bit layout is:
+    *
+    *   sign:     15
+    *   exponent: 10:14
+    *   mantissa: 0:9
+    *
+    * The sign, exponent, and mantissa of a float16 determine its value thus:
+    *
+    *   if e = 0 and m = 0, then zero:       (-1)^s * 0                           (1)
+    *   if e = 0 and m != 0, then subnormal: (-1)^s * 2^(e - 14) * (m / 2^10)     (2)
+    *   if 0 < e < 31, then normal:          (-1)^s * 2^(e - 15) * (1 + m / 2^10) (3)
+    *   if e = 31 and m = 0, then infinite:  (-1)^s * inf                         (4)
+    *   if e = 31 and m != 0, then NaN                                            (5)
+    *
+    * where 0 <= m < 2^10 .
+    *
+    * For a float32, the bit layout is:
+    *
+    *   sign:     31
+    *   exponent: 23:30
+    *   mantissa: 0:22
+    *
+    * The sign, exponent, and mantissa of a float32 determine its value thus:
+    *
+    *   if e = 0 and m = 0, then zero:        (-1)^s * 0                             (6)
+    *   if e = 0 and m != 0, then subnormal:  (-1)^s * 2^(e - 126) * (m / 2^23)      (7)
+    *   if 0 < e < 255, then normal:          (-1)^s * 2^(e - 127) * (1 + m / 2^23)  (8)
+    *   if e = 255 and m = 0, then infinite:  (-1)^s * inf                           (9)
+    *   if e = 255 and m != 0, then NaN                                             (10)
+    *
+    * where 0 <= m < 2^8 .
+    *
+    * Let f16 and f32 be a float16 and float32 with equal value. Let s16, e16,
+    * and m16 be the value of s, e, and m in equations 1-5. Likewise, let s32,
+    * e32, and m32 be those in equations 6-10.  Since this function ignores
+    * the sign bit, let s16 = s32 = 0.
+    *
+    * To calculate e32 and m32, let's consider separately each of the classes
+    * (equations 1-5) to which f16 may belong.
+    *
+    * # Case 1: f16 is zero
+    *
+    *     Calculating the bits in this case is trivial.
+    *
+    *       e32 := 0
+    *       m32 := 0
+    *
+    * # Case 2: f16 is subnormal
+    *
+    *     To calculate the e32 and m32 in this case requires iterating
+    *     over the bits of the float16's mantissa in order to find the
+    *     position of the most significant enabled bit. Considering that
+    *     unpackHalf2x16, on supported hardware where it need not be lowered,
+    *     generates only a small number of instructions, it would result in
+    *     unexpected overhead during shader execution if we generated a loop
+    *     when lowering unpackHalf2x16.
+    *
+    *     Luckily, the GLSL ES 3.00 and GLSL 4.10 specs allows us to truncate
+    *     subnormal floats to zero. From section 4.5.1 "Range and Precision"
+    *     of the two specs:
+    *
+    *       Any subnormal (denormalized) value input into a shader or
+    *       potentially generated by any operation in a shader can be flushed
+    *       to 0.
+    *
+    *     Therefore we choose
+    *
+    *       e32 = 0
+    *       m32 = 0
+    *
+    * # Case 3: f16 is normal
+    *
+    *     The normal range of float16 is a subset of the normal range of
+    *     float32. Therefore we calculate e32 as
+    *
+    *       2^(e32 - 127) = 2^(e16 - 15)
+    *                 e32 = e16 + 112
+    *
+    *     as m32 as
+    *
+    *       1 + m32 / 2^23 = 1 + m16 / 2^10
+    *                  m32 = 2^13 * m16
+    *
+    * # Case 4: f16 is infinite
+    *
+    *    Calculating the bits in this case is trivial.
+    *
+    *      e32 = 255
+    *      m32 = 0
+    *
+    * # Case 5: f16 is NaN
+    *
+    *    Any choice of m32 != 0 suffices. We choose m32 where all bits are
+    *    set:
+    *
+    *       e32 = 255
+    *       m32 = 0x7fffff (23 bits)
+    *
+    * We can therefore calculate f32 with the following C:
+    *
+    *   uint16_t f16 = GIVEN;
+    *   uint32_t f32;
+    *
+    *   uint32_t e16 = (f16 >> 10) & 0x1f;
+    *   uint32_t m16 = f16 & 0x03ff;
+    *
+    *   uint32_t e32;
+    *   uint32_t m32;
+    *
+    *   if (e16 == 0) {
+    *     // f16 is zero or subnormal.
+    *     // flush subnormal float16's to zero.
+    *     e32 = 0;
+    *     m32 = 0;
+    *   } else if (e16 < 31) {
+    *     // f16 is normal
+    *     e32 = e16 + 112;
+    *     m32 = m16 << 13;
+    *   } else if (e16 == 31 && m16 == 0) {
+    *     // f16 is infinite
+    *     e32 = 255;
+    *     m32 = 0;
+    *   } else {
+    *     // f16 is NaN
+    *     e32 = 255;
+    *     m32 = 0x007fffff;
+    *   }
+    *
+    *   f32 = (e32 << 23) | m32;
+    *   return f32;
+    *
+    * However, instruction execution is expensive on the GPU, and this
+    * compiler's quality of optimization is less than ideal. Below is
+    * a C implementation with that should execute a near-minimal number of
+    * instructions.
+    *
+    *   uint16_t f16 = GIVEN;
+    *   uint32_t f32;
+    *
+    *   // Get f16's unshifted exponent and mantissa bits.
+    *   uint32_t e = f16 & 0x7f00;
+    *   uint32_t m = f16 & 0x03ff;
+    *
+    *   if (e == 0) {
+    *     // f16 is zero or subnormal
+    *     f32 = 0;
+    *   } else if (e < (31 << 10)) {
+    *     // f16 is normal
+    *     f32 = (m << 13);
+    *     f32 |= (e << 13) + (112 << 23);
+    *   } else if (m == 0) {
+    *     // f16 is infinite
+    *     f32 = (255 << 23);
+    *   } else {
+    *     // f16 is NaN
+    *     f32 = 0x7fffffff;
+    *   }
+    *
+    *   return f32;
+    *
+    * The IR constructed by this function is a translation of the above
+    * optimized C, where e and m are provided by the caller.
+    */
+   ir_rvalue*
+   unpack_half_1x16_nosign(void *mem_ctx,
+                           ir_rvalue *e_rval,
+                           ir_rvalue *m_rval)
+   {
+      assert(e_rval->type == glsl_type::uint_type);
+      assert(m_rval->type == glsl_type::uint_type);
+
+      /* uint f32; */
+      ir_variable *f32 =
+         new(mem_ctx) ir_variable(glsl_type::uint_type,
+                                  "tmp_unpack_half_1x16_f32",
+                                  ir_var_temporary);
+      insert_instruction(f32);
+
+      /* uint e = E_RVAL; */
+      ir_variable *e =
+         new(mem_ctx) ir_variable(glsl_type::uint_type,
+                                  "tmp_unpack_half_1x16_e",
+                                  ir_var_temporary);
+      insert_instruction(e);
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(e),
+            e_rval));
+
+      /* uint m = M_RVAL; */
+      ir_variable *m =
+         new(mem_ctx) ir_variable(glsl_type::uint_type,
+                                  "tmp_unpack_half_1x16_m",
+                                  ir_var_temporary);
+      insert_instruction(m);
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(m),
+            m_rval));
+
+      /*
+       * if (e == 0) {
+       *   // f16 is zero or subnormal
+       *   f32 = 0;
+       * }
+       */
+      ir_if *if_zero =
+         new(mem_ctx) ir_if(
+            new(mem_ctx) ir_expression(ir_binop_equal,
+               new(mem_ctx) ir_dereference_variable(e),
+               new(mem_ctx) ir_constant(0u)));
+      insert_instruction(if_zero);
+      if_zero->then_instructions.push_tail(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f32),
+            new(mem_ctx) ir_constant(0u)));
+
+      /*
+       * else if (e < (31 << 10)) {
+       *    // f16 is normal
+       *    f32 = (m << 13);
+       *    f32 |= (e << 13) + (112 << 23);
+       * }
+       */
+      ir_if *if_normal =
+         new(mem_ctx) ir_if(
+            new(mem_ctx) ir_expression(ir_binop_less,
+                  new(mem_ctx) ir_dereference_variable(e),
+                  new(mem_ctx) ir_constant(31u << 10u)));
+      if_zero->else_instructions.push_tail(if_normal);
+      if_normal->then_instructions.push_tail(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f32),
+            new(mem_ctx) ir_expression(ir_binop_lshift,
+               new(mem_ctx) ir_dereference_variable(m),
+               new(mem_ctx) ir_constant(13u))));
+      if_normal->then_instructions.push_tail(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f32),
+            new(mem_ctx) ir_expression(ir_binop_bit_or,
+               new(mem_ctx) ir_dereference_variable(f32),
+               new(mem_ctx) ir_expression(ir_binop_add,
+                  new(mem_ctx) ir_expression(ir_binop_lshift,
+                     new(mem_ctx) ir_dereference_variable(e),
+                     new(mem_ctx) ir_constant(13u)),
+                  new(mem_ctx) ir_constant(112u << 23u)))));
+
+      /*
+       * else if (m == 0) {
+       *    // f16 is infinite
+       *    f32 = (255 << 23);
+       * }
+       */
+      ir_if *if_infinite =
+         new(mem_ctx) ir_if(
+            new(mem_ctx) ir_expression(ir_binop_equal,
+                  new(mem_ctx) ir_dereference_variable(m),
+                  new(mem_ctx) ir_constant(0u)));
+      if_normal->else_instructions.push_tail(if_infinite);
+      if_infinite->then_instructions.push_tail(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f32),
+            new(mem_ctx) ir_constant(255u << 23u)));
+
+      /*
+       * else {
+       *    // f16 is NaN
+       *    f32 = 0x7fffffff;
+       * }
+       */
+      if_infinite->else_instructions.push_tail(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f32),
+            new(mem_ctx) ir_constant(0x7fffffffu)));
+
+      /* return f32; */
+      return new(mem_ctx) ir_dereference_variable(f32);
+   }
+
+   /* From page 89 (95 of pdf) of the GLSL ES 3.00 spec:
+    *
+    *    mediump vec2 unpackHalf2x16 (highp uint v)
+    *    ------------------------------------------
+    *    Returns a two-component floating-point vector with components
+    *    obtained by unpacking a 32-bit unsigned integer into a pair of 16-bit
+    *    values, interpreting those values as 16-bit floating-point numbers
+    *    according to the OpenGL ES Specification, and converting them to
+    *    32-bit floating-point values.
+    *
+    *    The first component of the vector is obtained from the
+    *    16 least-significant bits of v; the second component is obtained from
+    *    the 16 most-significant bits of v.
+    *
+    * This function constructs IR that approximates the following GLSL:
+    *
+    *   uint u = RVALUE;
+    *   uvec2 f16 = uvec2(u & 0xffff, u >> 16);
+    *   uvec2 f32;
+    *
+    *   // Get f16's unshifted exponent and mantissa bits.
+    *   uvec2 e = f16 & 0x7c00u;
+    *   uvec2 m = f16 & 0x03ffu;
+    *
+    *   // Set f32's exponent and mantissa bits.
+    *   f32.x = unpack_half_1x16_nosign(e.x, m.x);
+    *   f32.y = unpack_half_1x16_nosign(e.y, m.y);
+    *
+    *   // Set f32's the sign bit.
+    *   f32 = (f16 & 0x8000u) << 16u;
+    *
+    *   return bitcast_u2f(f32);
+    */
+   ir_rvalue*
+   lower_unpack_half_2x16(void *mem_ctx, ir_rvalue *uint_rval)
+   {
+      assert(uint_rval->type == glsl_type::uint_type);
+
+      /* uint u = RVALUE;
+       * uvec2 f16 = uvec2(u.x & 0xffff, u.y >> 16);
+       */
+      ir_variable *f16 =
+         new(mem_ctx) ir_variable(glsl_type::uvec2_type,
+                                  "tmp_unpack_half_2x16_f16",
+                                  ir_var_temporary);
+      insert_instruction(f16);
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f16),
+            unpack_uint_to_uvec2(mem_ctx, uint_rval)));
+
+      /* uvec2 f32; */
+      ir_variable *f32 =
+         new(mem_ctx) ir_variable(glsl_type::uvec2_type,
+                                  "tmp_unpack_half_2x16_f32",
+                                  ir_var_temporary);
+      insert_instruction(f32);
+
+      /* Get f16's unshifted exponent bits.
+       *
+       *    uvec2 e = f16 & 0x7c00u;
+       */
+      ir_variable *e =
+         new(mem_ctx) ir_variable(glsl_type::uvec2_type,
+                                  "tmp_unpack_half_2x16_e",
+                                  ir_var_temporary);
+      insert_instruction(e);
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(e),
+            new(mem_ctx) ir_expression(ir_binop_bit_and,
+               new(mem_ctx) ir_dereference_variable(f16),
+               new(mem_ctx) ir_constant(0x7c00u))));
+
+      /* Get f16's unshifted mantissa bits.
+       *
+       *    uvec2 m = f16 & 0x03ffu;
+       */
+      ir_variable *m =
+         new(mem_ctx) ir_variable(glsl_type::uvec2_type,
+                                  "tmp_unpack_half_2x16_m",
+                                  ir_var_temporary);
+      insert_instruction(m);
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(m),
+            new(mem_ctx) ir_expression(ir_binop_bit_and,
+               new(mem_ctx) ir_dereference_variable(f16),
+               new(mem_ctx) ir_constant(0x03ffu))));
+
+      /* Set f32's exponent and mantissa bits.
+       *
+       *   f32.x = unpack_half_1x16_nosign(e.x, m.x);
+       *   f32.y = unpack_half_1x16_nosign(e.y, m.y);
+       */
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f32),
+            unpack_half_1x16_nosign(mem_ctx,
+               new(mem_ctx) ir_swizzle(
+                  new (mem_ctx) ir_dereference_variable(e),
+                  0, 0, 0, 0, 1),
+               new(mem_ctx) ir_swizzle(
+                  new(mem_ctx) ir_dereference_variable(m),
+                  0, 0, 0, 0, 1)),
+             NULL /*condition*/,
+             1 /*write mask*/));
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f32),
+            unpack_half_1x16_nosign(mem_ctx,
+               new(mem_ctx) ir_swizzle(
+                  new (mem_ctx) ir_dereference_variable(e),
+                  1, 0, 0, 0, 1),
+               new(mem_ctx) ir_swizzle(
+                  new(mem_ctx) ir_dereference_variable(m),
+                  1, 0, 0, 0, 1)),
+             NULL /*condition*/,
+             2 /*write mask*/));
+
+      /* Set f32's sign bit.
+       *
+       *    f32 |= (f16 & 0x8000u) << 16u;
+       */
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(f32),
+            new(mem_ctx) ir_expression(ir_binop_bit_or,
+               glsl_type::uvec2_type,
+               new(mem_ctx) ir_dereference_variable(f32),
+               new(mem_ctx) ir_expression(ir_binop_lshift,
+                  new(mem_ctx) ir_expression(ir_binop_bit_and,
+                     new(mem_ctx) ir_dereference_variable(f16),
+                     new(mem_ctx) ir_constant(0x8000u)),
+                  new(mem_ctx) ir_constant(16u)))));
+
+      ir_rvalue *result =
+         new(mem_ctx) ir_expression(ir_unop_bitcast_u2f,
+            new(mem_ctx) ir_dereference_variable(f32));
+
+      assert(result->type == glsl_type::vec2_type);
+      return result;
+   }
+
+   /**
+    * \brief Split unpackHalf2x16 into two operations.
+    *
+    * Some code generators, such as the i965 fragment shader, require that all
+    * vector expressions be lowered to a sequence of scalar expressions.
+    * However, unpackHalf2x16 cannot be scalarized by the same method as
+    * a true vector operation because the number of components of its input
+    * and output differ.
+    *
+    * This method scalarizes unpackHalf2x16 by transforming it from a single
+    * operation having vec2 output to a pair of operations each having float
+    * output. That is, it transforms
+    *
+    *   unpackHalf2x16(UINT_RVAL)
+    *
+    * into
+    *
+    *   uint u = UINT_RVAL;
+    *   vec2 v;
+    *
+    *   v.x = unpackHalf2x16_split_x(u);
+    *   v.y = unpackHalf2x16_split_y(u);
+    *
+    *   return v;
+    */
+   ir_rvalue*
+   split_unpack_half_2x16(void *mem_ctx, ir_rvalue *uint_rval)
+   {
+      assert(uint_rval->type == glsl_type::uint_type);
+
+      /* uint u = uint_rval; */
+      ir_variable *u =
+         new(mem_ctx) ir_variable(glsl_type::uint_type,
+                                  "tmp_split_unpack_half_2x16_u",
+                                  ir_var_temporary);
+      insert_instruction(u);
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(u),
+            uint_rval));
+
+      /* vec2 v; */
+      ir_variable *v =
+         new(mem_ctx) ir_variable(glsl_type::vec2_type,
+                                  "tmp_split_unpack_half_2x16_v",
+                                  ir_var_temporary);
+      insert_instruction(v);
+
+      /* v.x = unpack_half_2x16_split_x(u); */
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(v),
+            new(mem_ctx) ir_expression(ir_unop_unpack_half_2x16_split_x,
+               glsl_type::float_type,
+               new(mem_ctx) ir_dereference_variable(u)),
+            NULL /*condition*/,
+            1 /*write mask*/));
+
+      /* v.y = unpack_half_2x16_split_y(u); */
+      insert_instruction(
+         new(mem_ctx) ir_assignment(
+            new(mem_ctx) ir_dereference_variable(v),
+            new(mem_ctx) ir_expression(ir_unop_unpack_half_2x16_split_y,
+               glsl_type::float_type,
+               new(mem_ctx) ir_dereference_variable(u)),
+            NULL /*condition*/,
+            2 /*write mask*/));
+
+      /* return v; */
+      return new(mem_ctx) ir_dereference_variable(v);
+   }
+};
+
+} // namespace anonymous
+
+/**
+ * \brief Lower the builtin packing functions.
+ *
+ * \param op_mask is a bitmask of `enum lower_packing_builtins_op`.
+ */
+bool
+lower_packing_builtins(exec_list *instructions, int op_mask)
+{
+   lower_packing_builtins_visitor v(op_mask);
+   visit_list_elements(&v, instructions, true);
+   return v.get_progress();
+}
-- 
1.8.1



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