[AArch64] Compute the Newton series for reciprocals natively

Implement the Newton series for square root, its reciprocal and reciprocal
natively using the specialized instructions in AArch64 to perform each
series iteration.

Differential revision: https://reviews.llvm.org/D26518

llvm-svn: 286907
diff --git a/llvm/test/CodeGen/AArch64/recp-fastmath.ll b/llvm/test/CodeGen/AArch64/recp-fastmath.ll
index 280ef75..38e0fb3 100644
--- a/llvm/test/CodeGen/AArch64/recp-fastmath.ll
+++ b/llvm/test/CodeGen/AArch64/recp-fastmath.ll
@@ -16,8 +16,8 @@
 
 ; CHECK-LABEL: frecp1:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: frecpe
-; CHECK-NEXT: fmov
+; CHECK-NEXT: frecpe [[R:s[0-7]]]
+; CHECK-NEXT: frecps {{s[0-7](, s[0-7])?}}, [[R]]
 }
 
 define <2 x float> @f2recp0(<2 x float> %x) #0 {
@@ -36,8 +36,8 @@
 
 ; CHECK-LABEL: f2recp1:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frecpe
+; CHECK-NEXT: frecpe [[R:v[0-7]\.2s]]
+; CHECK-NEXT: frecps {{v[0-7]\.2s(, v[0-7].2s)?}}, [[R]]
 }
 
 define <4 x float> @f4recp0(<4 x float> %x) #0 {
@@ -56,8 +56,8 @@
 
 ; CHECK-LABEL: f4recp1:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frecpe
+; CHECK-NEXT: frecpe [[R:v[0-7]\.4s]]
+; CHECK-NEXT: frecps {{v[0-7]\.4s(, v[0-7].4s)?}}, [[R]]
 }
 
 define <8 x float> @f8recp0(<8 x float> %x) #0 {
@@ -77,9 +77,10 @@
 
 ; CHECK-LABEL: f8recp1:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frecpe
-; CHECK: frecpe
+; CHECK-NEXT: frecpe [[RA:v[0-7]\.4s]]
+; CHECK-NEXT: frecpe [[RB:v[0-7]\.4s]]
+; CHECK-NEXT: frecps {{v[0-7]\.4s(, v[0-7].4s)?}}, [[RA]]
+; CHECK: frecps {{v[0-7]\.4s(, v[0-7].4s)?}}, [[RB]]
 }
 
 define double @drecp0(double %x) #0 {
@@ -98,8 +99,8 @@
 
 ; CHECK-LABEL: drecp1:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: frecpe
-; CHECK-NEXT: fmov
+; CHECK-NEXT: frecpe [[R:d[0-7]]]
+; CHECK-NEXT: frecps {{d[0-7](, d[0-7])?}}, [[R]]
 }
 
 define <2 x double> @d2recp0(<2 x double> %x) #0 {
@@ -118,8 +119,8 @@
 
 ; CHECK-LABEL: d2recp1:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frecpe
+; CHECK-NEXT: frecpe [[R:v[0-7]\.2d]]
+; CHECK-NEXT: frecps {{v[0-7]\.2d(, v[0-7].2d)?}}, [[R]]
 }
 
 define <4 x double> @d4recp0(<4 x double> %x) #0 {
@@ -139,9 +140,10 @@
 
 ; CHECK-LABEL: d4recp1:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frecpe
-; CHECK: frecpe
+; CHECK-NEXT: frecpe [[RA:v[0-7]\.2d]]
+; CHECK-NEXT: frecpe [[RB:v[0-7]\.2d]]
+; CHECK-NEXT: frecps {{v[0-7]\.2d(, v[0-7].2d)?}}, [[RA]]
+; CHECK: frecps {{v[0-7]\.2d(, v[0-7].2d)?}}, [[RB]]
 }
 
 attributes #0 = { nounwind "unsafe-fp-math"="true" }
diff --git a/llvm/test/CodeGen/AArch64/sqrt-fastmath.ll b/llvm/test/CodeGen/AArch64/sqrt-fastmath.ll
index cd8200b..079562c 100644
--- a/llvm/test/CodeGen/AArch64/sqrt-fastmath.ll
+++ b/llvm/test/CodeGen/AArch64/sqrt-fastmath.ll
@@ -19,8 +19,10 @@
 
 ; CHECK-LABEL: fsqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frsqrte
+; CHECK-NEXT: frsqrte [[RA:s[0-7]]]
+; CHECK-NEXT: fmul [[RB:s[0-7]]], [[RA]], [[RA]]
+; CHECK-NEXT: frsqrts {{s[0-7](, s[0-7])?}}, [[RB]]
+; CHECK: fcmp s0, #0
 }
 
 define <2 x float> @f2sqrt(<2 x float> %a) #0 {
@@ -33,9 +35,10 @@
 
 ; CHECK-LABEL: f2sqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: mov
-; CHECK-NEXT: frsqrte
+; CHECK-NEXT: frsqrte [[RA:v[0-7]\.2s]]
+; CHECK-NEXT: fmul [[RB:v[0-7]\.2s]], [[RA]], [[RA]]
+; CHECK-NEXT: frsqrts {{v[0-7]\.2s(, v[0-7]\.2s)?}}, [[RB]]
+; CHECK: fcmeq {{v[0-7]\.2s, v0\.2s}}, #0
 }
 
 define <4 x float> @f4sqrt(<4 x float> %a) #0 {
@@ -48,9 +51,10 @@
 
 ; CHECK-LABEL: f4sqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: mov
-; CHECK-NEXT: frsqrte
+; CHECK-NEXT: frsqrte [[RA:v[0-7]\.4s]]
+; CHECK-NEXT: fmul [[RB:v[0-7]\.4s]], [[RA]], [[RA]]
+; CHECK-NEXT: frsqrts {{v[0-7]\.4s(, v[0-7]\.4s)?}}, [[RB]]
+; CHECK: fcmeq {{v[0-7]\.4s, v0\.4s}}, #0
 }
 
 define <8 x float> @f8sqrt(<8 x float> %a) #0 {
@@ -64,10 +68,10 @@
 
 ; CHECK-LABEL: f8sqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: mov
-; CHECK-NEXT: frsqrte
-; CHECK: frsqrte
+; CHECK-NEXT: frsqrte [[RA:v[0-7]\.4s]]
+; CHECK: fmul [[RB:v[0-7]\.4s]], [[RA]], [[RA]]
+; CHECK: frsqrts {{v[0-7]\.4s(, v[0-7]\.4s)?}}, [[RB]]
+; CHECK: fcmeq {{v[0-7]\.4s, v[0-1]\.4s}}, #0
 }
 
 define double @dsqrt(double %a) #0 {
@@ -80,8 +84,10 @@
 
 ; CHECK-LABEL: dsqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frsqrte
+; CHECK-NEXT: frsqrte [[RA:d[0-7]]]
+; CHECK-NEXT: fmul [[RB:d[0-7]]], [[RA]], [[RA]]
+; CHECK-NEXT: frsqrts {{d[0-7](, d[0-7])?}}, [[RB]]
+; CHECK: fcmp d0, #0
 }
 
 define <2 x double> @d2sqrt(<2 x double> %a) #0 {
@@ -94,9 +100,10 @@
 
 ; CHECK-LABEL: d2sqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: mov
-; CHECK-NEXT: frsqrte
+; CHECK-NEXT: frsqrte [[RA:v[0-7]\.2d]]
+; CHECK-NEXT: fmul [[RB:v[0-7]\.2d]], [[RA]], [[RA]]
+; CHECK-NEXT: frsqrts {{v[0-7]\.2d(, v[0-7]\.2d)?}}, [[RB]]
+; CHECK: fcmeq {{v[0-7]\.2d, v0\.2d}}, #0
 }
 
 define <4 x double> @d4sqrt(<4 x double> %a) #0 {
@@ -110,10 +117,10 @@
 
 ; CHECK-LABEL: d4sqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: mov
-; CHECK-NEXT: frsqrte
-; CHECK: frsqrte
+; CHECK-NEXT: frsqrte [[RA:v[0-7]\.2d]]
+; CHECK: fmul [[RB:v[0-7]\.2d]], [[RA]], [[RA]]
+; CHECK: frsqrts {{v[0-7]\.2d(, v[0-7]\.2d)?}}, [[RB]]
+; CHECK: fcmeq {{v[0-7]\.2d, v[0-1]\.2d}}, #0
 }
 
 define float @frsqrt(float %a) #0 {
@@ -127,8 +134,10 @@
 
 ; CHECK-LABEL: frsqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frsqrte
+; CHECK-NEXT: frsqrte [[RA:s[0-7]]]
+; CHECK-NEXT: fmul [[RB:s[0-7]]], [[RA]], [[RA]]
+; CHECK-NEXT: frsqrts {{s[0-7](, s[0-7])?}}, [[RB]]
+; CHECK-NOT: fcmp {{s[0-7]}}, #0
 }
 
 define <2 x float> @f2rsqrt(<2 x float> %a) #0 {
@@ -142,8 +151,10 @@
 
 ; CHECK-LABEL: f2rsqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frsqrte
+; CHECK-NEXT: frsqrte [[RA:v[0-7]\.2s]]
+; CHECK-NEXT: fmul [[RB:v[0-7]\.2s]], [[RA]], [[RA]]
+; CHECK-NEXT: frsqrts {{v[0-7]\.2s(, v[0-7]\.2s)?}}, [[RB]]
+; CHECK-NOT: fcmeq {{v[0-7]\.2s, v0\.2s}}, #0
 }
 
 define <4 x float> @f4rsqrt(<4 x float> %a) #0 {
@@ -157,8 +168,10 @@
 
 ; CHECK-LABEL: f4rsqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frsqrte
+; CHECK-NEXT: frsqrte [[RA:v[0-7]\.4s]]
+; CHECK-NEXT: fmul [[RB:v[0-7]\.4s]], [[RA]], [[RA]]
+; CHECK-NEXT: frsqrts {{v[0-7]\.4s(, v[0-7]\.4s)?}}, [[RB]]
+; CHECK-NOT: fcmeq {{v[0-7]\.4s, v0\.4s}}, #0
 }
 
 define <8 x float> @f8rsqrt(<8 x float> %a) #0 {
@@ -173,9 +186,10 @@
 
 ; CHECK-LABEL: f8rsqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frsqrte
-; CHECK: frsqrte
+; CHECK-NEXT: frsqrte [[RA:v[0-7]\.4s]]
+; CHECK: fmul [[RB:v[0-7]\.4s]], [[RA]], [[RA]]
+; CHECK: frsqrts {{v[0-7]\.4s(, v[0-7]\.4s)?}}, [[RB]]
+; CHECK-NOT: fcmeq {{v[0-7]\.4s, v0\.4s}}, #0
 }
 
 define double @drsqrt(double %a) #0 {
@@ -189,8 +203,10 @@
 
 ; CHECK-LABEL: drsqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frsqrte
+; CHECK-NEXT: frsqrte [[RA:d[0-7]]]
+; CHECK-NEXT: fmul [[RB:d[0-7]]], [[RA]], [[RA]]
+; CHECK-NEXT: frsqrts {{d[0-7](, d[0-7])?}}, [[RB]]
+; CHECK-NOT: fcmp d0, #0
 }
 
 define <2 x double> @d2rsqrt(<2 x double> %a) #0 {
@@ -204,8 +220,10 @@
 
 ; CHECK-LABEL: d2rsqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frsqrte
+; CHECK-NEXT: frsqrte [[RA:v[0-7]\.2d]]
+; CHECK-NEXT: fmul [[RB:v[0-7]\.2d]], [[RA]], [[RA]]
+; CHECK-NEXT: frsqrts {{v[0-7]\.2d(, v[0-7]\.2d)?}}, [[RB]]
+; CHECK-NOT: fcmeq {{v[0-7]\.2d, v0\.2d}}, #0
 }
 
 define <4 x double> @d4rsqrt(<4 x double> %a) #0 {
@@ -220,9 +238,10 @@
 
 ; CHECK-LABEL: d4rsqrt:
 ; CHECK-NEXT: BB#0
-; CHECK-NEXT: fmov
-; CHECK-NEXT: frsqrte
-; CHECK: frsqrte
+; CHECK-NEXT: frsqrte [[RA:v[0-7]\.2d]]
+; CHECK: fmul [[RB:v[0-7]\.2d]], [[RA]], [[RA]]
+; CHECK: frsqrts {{v[0-7]\.2d(, v[0-7]\.2d)?}}, [[RB]]
+; CHECK-NOT: fcmeq {{v[0-7]\.2d, v0\.2d}}, #0
 }
 
 attributes #0 = { nounwind "unsafe-fp-math"="true" }