[AArch64] Emit square root using the Newton series

2016-06-13  Evandro Menezes  <e.menezes@samsung.com>
            Wilco Dijkstra  <wilco.dijkstra@arm.com>

gcc/
	* config/aarch64/aarch64-protos.h
	(aarch64_emit_approx_rsqrt): Replace with new function
	"aarch64_emit_approx_sqrt".
	(cpu_approx_modes): New member "sqrt".
	* config/aarch64/aarch64.c
	(generic_approx_modes): New member "sqrt".
	(exynosm1_approx_modes): Likewise.
	(xgene1_approx_modes): Likewise.
	(aarch64_emit_approx_rsqrt): Replace with new function
	"aarch64_emit_approx_sqrt".
	(aarch64_override_options_after_change_1): Handle new option.
	* config/aarch64/aarch64-simd.md
	(rsqrt<mode>2): Use new function instead.
	(sqrt<mode>2): New expansion and insn definitions.
	* config/aarch64/aarch64.md: Likewise.
	* config/aarch64/aarch64.opt
	(mlow-precision-sqrt): Add new option description.
	* doc/invoke.texi (mlow-precision-sqrt): Likewise.

From-SVN: r237396

gcc/config/aarch64/aarch64-protos.h

@@ -192,7 +192,8 @@ struct cpu_branch_cost
 /* Allowed modes for approximations.  */
 struct cpu_approx_modes
 {
-  const unsigned int recip_sqrt; /* Reciprocal square root.  */
+  const unsigned int sqrt;		/* Square root.  */
+  const unsigned int recip_sqrt;	/* Reciprocal square root.  */
 };
 
 struct tune_params
@@ -302,6 +303,7 @@ int aarch64_branch_cost (bool, bool);
 enum aarch64_symbol_type aarch64_classify_symbolic_expression (rtx);
 bool aarch64_const_vec_all_same_int_p (rtx, HOST_WIDE_INT);
 bool aarch64_constant_address_p (rtx);
+bool aarch64_emit_approx_sqrt (rtx, rtx, bool);
 bool aarch64_expand_movmem (rtx *);
 bool aarch64_float_const_zero_rtx_p (rtx);
 bool aarch64_function_arg_regno_p (unsigned);
@@ -383,7 +385,6 @@ void aarch64_register_pragmas (void);
 void aarch64_relayout_simd_types (void);
 void aarch64_reset_previous_fndecl (void);
 void aarch64_save_restore_target_globals (tree);
-void aarch64_emit_approx_rsqrt (rtx, rtx);
 
 /* Initialize builtins for SIMD intrinsics.  */
 void init_aarch64_simd_builtins (void);

gcc/config/aarch64/aarch64-simd.md

@@ -405,7 +405,7 @@
 		     UNSPEC_RSQRT))]
   "TARGET_SIMD"
 {
-  aarch64_emit_approx_rsqrt (operands[0], operands[1]);
+  aarch64_emit_approx_sqrt (operands[0], operands[1], true);
   DONE;
 })
 
@@ -4298,7 +4298,16 @@
 
 ;; sqrt
 
-(define_insn "sqrt<mode>2"
+(define_expand "sqrt<mode>2"
+  [(set (match_operand:VDQF 0 "register_operand")
+	(sqrt:VDQF (match_operand:VDQF 1 "register_operand")))]
+  "TARGET_SIMD"
+{
+  if (aarch64_emit_approx_sqrt (operands[0], operands[1], false))
+    DONE;
+})
+
+(define_insn "*sqrt<mode>2"
   [(set (match_operand:VDQF 0 "register_operand" "=w")
         (sqrt:VDQF (match_operand:VDQF 1 "register_operand" "w")))]
   "TARGET_SIMD"

gcc/config/aarch64/aarch64.c

@@ -396,18 +396,21 @@ static const struct cpu_branch_cost cortexa57_branch_cost =
 /* Generic approximation modes.  */
 static const cpu_approx_modes generic_approx_modes =
 {
+  AARCH64_APPROX_NONE,	/* sqrt  */
   AARCH64_APPROX_NONE	/* recip_sqrt  */
 };
 
 /* Approximation modes for Exynos M1.  */
 static const cpu_approx_modes exynosm1_approx_modes =
 {
+  AARCH64_APPROX_ALL,	/* sqrt  */
   AARCH64_APPROX_ALL	/* recip_sqrt  */
 };
 
 /* Approximation modes for X-Gene 1.  */
 static const cpu_approx_modes xgene1_approx_modes =
 {
+  AARCH64_APPROX_NONE,	/* sqrt  */
   AARCH64_APPROX_ALL	/* recip_sqrt  */
 };
 
@@ -7370,10 +7373,10 @@ aarch64_builtin_reciprocal (tree fndecl)
 
 typedef rtx (*rsqrte_type) (rtx, rtx);
 
-/* Select reciprocal square root initial estimate
-   insn depending on machine mode.  */
+/* Select reciprocal square root initial estimate insn depending on machine
+   mode.  */
 
-rsqrte_type
+static rsqrte_type
 get_rsqrte_type (machine_mode mode)
 {
   switch (mode)
@@ -7389,10 +7392,9 @@ get_rsqrte_type (machine_mode mode)
 
 typedef rtx (*rsqrts_type) (rtx, rtx, rtx);
 
-/* Select reciprocal square root Newton-Raphson step
-   insn depending on machine mode.  */
+/* Select reciprocal square root series step insn depending on machine mode.  */
 
-rsqrts_type
+static rsqrts_type
 get_rsqrts_type (machine_mode mode)
 {
   switch (mode)
@@ -7406,46 +7408,84 @@ get_rsqrts_type (machine_mode mode)
   }
 }
 
-/* Emit instruction sequence to compute the reciprocal square root using the
-   Newton-Raphson series.  Iterate over the series twice for SF
-   and thrice for DF.  */
+/* Emit instruction sequence to compute either the approximate square root
+   or its approximate reciprocal, depending on the flag RECP, and return
+   whether the sequence was emitted or not.  */
 
-void
-aarch64_emit_approx_rsqrt (rtx dst, rtx src)
+bool
+aarch64_emit_approx_sqrt (rtx dst, rtx src, bool recp)
 {
-  machine_mode mode = GET_MODE (src);
-  gcc_assert (
-    mode == SFmode || mode == V2SFmode || mode == V4SFmode
-	|| mode == DFmode || mode == V2DFmode);
-
-  rtx xsrc = gen_reg_rtx (mode);
-  emit_move_insn (xsrc, src);
-  rtx x0 = gen_reg_rtx (mode);
+  machine_mode mode = GET_MODE (dst);
+  machine_mode mmsk = mode_for_vector
+		        (int_mode_for_mode (GET_MODE_INNER (mode)),
+			 GET_MODE_NUNITS (mode));
+  bool use_approx_sqrt_p = (!recp
+			    && (flag_mlow_precision_sqrt
+			        || (aarch64_tune_params.approx_modes->sqrt
+				    & AARCH64_APPROX_MODE (mode))));
+  bool use_approx_rsqrt_p = (recp
+			     && (flag_mrecip_low_precision_sqrt
+				 || (aarch64_tune_params.approx_modes->recip_sqrt
+				     & AARCH64_APPROX_MODE (mode))));
+
+  if (!flag_finite_math_only
+      || flag_trapping_math
+      || !flag_unsafe_math_optimizations
+      || !(use_approx_sqrt_p || use_approx_rsqrt_p)
+      || optimize_function_for_size_p (cfun))
+    return false;
 
-  emit_insn ((*get_rsqrte_type (mode)) (x0, xsrc));
+  rtx xmsk = gen_reg_rtx (mmsk);
+  if (!recp)
+    /* When calculating the approximate square root, compare the argument with
+       0.0 and create a mask.  */
+    emit_insn (gen_rtx_SET (xmsk, gen_rtx_NEG (mmsk, gen_rtx_EQ (mmsk, src,
+							  CONST0_RTX (mode)))));
 
-  bool double_mode = (mode == DFmode || mode == V2DFmode);
+  /* Estimate the approximate reciprocal square root.  */
+  rtx xdst = gen_reg_rtx (mode);
+  emit_insn ((*get_rsqrte_type (mode)) (xdst, src));
 
-  int iterations = double_mode ? 3 : 2;
+  /* Iterate over the series twice for SF and thrice for DF.  */
+  int iterations = (GET_MODE_INNER (mode) == DFmode) ? 3 : 2;
 
-  /* Optionally iterate over the series one less time than otherwise.  */
-  if (flag_mrecip_low_precision_sqrt)
+  /* Optionally iterate over the series once less for faster performance
+     while sacrificing the accuracy.  */
+  if ((recp && flag_mrecip_low_precision_sqrt)
+      || (!recp && flag_mlow_precision_sqrt))
     iterations--;
 
-  for (int i = 0; i < iterations; ++i)
+  /* Iterate over the series to calculate the approximate reciprocal square
+     root.  */
+  rtx x1 = gen_reg_rtx (mode);
+  while (iterations--)
     {
-      rtx x1 = gen_reg_rtx (mode);
       rtx x2 = gen_reg_rtx (mode);
-      rtx x3 = gen_reg_rtx (mode);
-      emit_set_insn (x2, gen_rtx_MULT (mode, x0, x0));
+      emit_set_insn (x2, gen_rtx_MULT (mode, xdst, xdst));
+
+      emit_insn ((*get_rsqrts_type (mode)) (x1, src, x2));
 
-      emit_insn ((*get_rsqrts_type (mode)) (x3, xsrc, x2));
+      if (iterations > 0)
+	emit_set_insn (xdst, gen_rtx_MULT (mode, xdst, x1));
+    }
+
+  if (!recp)
+    {
+      /* Qualify the approximate reciprocal square root when the argument is
+	 0.0 by squashing the intermediary result to 0.0.  */
+      rtx xtmp = gen_reg_rtx (mmsk);
+      emit_set_insn (xtmp, gen_rtx_AND (mmsk, gen_rtx_NOT (mmsk, xmsk),
+					      gen_rtx_SUBREG (mmsk, xdst, 0)));
+      emit_move_insn (xdst, gen_rtx_SUBREG (mode, xtmp, 0));
 
-      emit_set_insn (x1, gen_rtx_MULT (mode, x0, x3));
-      x0 = x1;
+      /* Calculate the approximate square root.  */
+      emit_set_insn (xdst, gen_rtx_MULT (mode, xdst, src));
     }
 
-  emit_move_insn (dst, x0);
+  /* Finalize the approximation.  */
+  emit_set_insn (dst, gen_rtx_MULT (mode, xdst, x1));
+
+  return true;
 }
 
 /* Return the number of instructions that can be issued per cycle.  */
@@ -7975,6 +8015,12 @@ aarch64_override_options_after_change_1 (struct gcc_options *opts)
       && (aarch64_cmodel == AARCH64_CMODEL_TINY
 	  || aarch64_cmodel == AARCH64_CMODEL_TINY_PIC))
     aarch64_nopcrelative_literal_loads = false;
+
+  /* When enabling the lower precision Newton series for the square root, also
+     enable it for the reciprocal square root, since the latter is an
+     intermediary step for the former.  */
+  if (flag_mlow_precision_sqrt)
+    flag_mrecip_low_precision_sqrt = true;
 }
 
 /* 'Unpack' up the internal tuning structs and update the options

gcc/config/aarch64/aarch64.md

@@ -4733,7 +4733,16 @@
   [(set_attr "type" "ffarith<s>")]
 )
 
-(define_insn "sqrt<mode>2"
+(define_expand "sqrt<mode>2"
+  [(set (match_operand:GPF 0 "register_operand")
+        (sqrt:GPF (match_operand:GPF 1 "register_operand")))]
+  "TARGET_FLOAT"
+{
+  if (aarch64_emit_approx_sqrt (operands[0], operands[1], false))
+    DONE;
+})
+
+(define_insn "*sqrt<mode>2"
   [(set (match_operand:GPF 0 "register_operand" "=w")
         (sqrt:GPF (match_operand:GPF 1 "register_operand" "w")))]
   "TARGET_FLOAT"

gcc/config/aarch64/aarch64.opt

@@ -151,5 +151,13 @@ PC relative literal loads.
 
 mlow-precision-recip-sqrt
 Common Var(flag_mrecip_low_precision_sqrt) Optimization
-When calculating the reciprocal square root approximation,
-uses one less step than otherwise, thus reducing latency and precision.
+Enable the reciprocal square root approximation.  Enabling this reduces
+precision of reciprocal square root results to about 16 bits for
+single precision and to 32 bits for double precision.
+
+mlow-precision-sqrt
+Common Var(flag_mlow_precision_sqrt) Optimization
+Enable the square root approximation.  Enabling this reduces
+precision of square root results to about 16 bits for
+single precision and to 32 bits for double precision.
+If enabled, it implies -mlow-precision-recip-sqrt.

gcc/doc/invoke.texi

@@ -576,6 +576,7 @@ Objective-C and Objective-C++ Dialects}.
 -mfix-cortex-a53-835769  -mno-fix-cortex-a53-835769 @gol
 -mfix-cortex-a53-843419  -mno-fix-cortex-a53-843419 @gol
 -mlow-precision-recip-sqrt -mno-low-precision-recip-sqrt@gol
+-mlow-precision-sqrt -mno-low-precision-sqrt@gol
 -march=@var{name}  -mcpu=@var{name}  -mtune=@var{name}}
 
 @emph{Adapteva Epiphany Options}
@@ -13028,6 +13029,17 @@ This option only has an effect if @option{-ffast-math} or
 precision of reciprocal square root results to about 16 bits for
 single precision and to 32 bits for double precision.
 
+@item -mlow-precision-sqrt
+@item -mno-low-precision-sqrt
+@opindex -mlow-precision-sqrt
+@opindex -mno-low-precision-sqrt
+Enable or disable the square root approximation.
+This option only has an effect if @option{-ffast-math} or
+@option{-funsafe-math-optimizations} is used as well.  Enabling this reduces
+precision of square root results to about 16 bits for
+single precision and to 32 bits for double precision.
+If enabled, it implies @option{-mlow-precision-recip-sqrt}.
+
 @item -march=@var{name}
 @opindex march
 Specify the name of the target architecture and, optionally, one or