From 74e28e6938c1fecb1a5efa15db41b83216bce5f6 Mon Sep 17 00:00:00 2001
From: Simon Byrne <simonbyrne@gmail.com>
Date: Thu, 22 Jan 2015 12:11:41 +0000
Subject: [PATCH 1/3] use muladd in horner macro

---
 base/math.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/base/math.jl b/base/math.jl
index 5e984d71282ae..f7f2ed40edf34 100644
--- a/base/math.jl
+++ b/base/math.jl
@@ -45,7 +45,7 @@ clamp{T}(x::AbstractArray{T}, lo, hi) =
 macro horner(x, p...)
     ex = esc(p[end])
     for i = length(p)-1:-1:1
-        ex = :($(esc(p[i])) + t * $ex)
+        ex = :(muladd(t, $ex, $(esc(p[i]))))
     end
     Expr(:block, :(t = $(esc(x))), ex)
 end

From 45a27dad02019fbf544b2f91688d99adcbf5e08d Mon Sep 17 00:00:00 2001
From: Simon Byrne <simonbyrne@gmail.com>
Date: Thu, 22 Jan 2015 14:10:46 +0000
Subject: [PATCH 2/3] muladd fallback

---
 base/promotion.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/base/promotion.jl b/base/promotion.jl
index 657eb39fa9aaf..0603b578db4e8 100644
--- a/base/promotion.jl
+++ b/base/promotion.jl
@@ -196,7 +196,7 @@ no_op_err(name, T) = error(name," not defined for ",T)
 
 fma{T<:Number}(x::T, y::T, z::T) = no_op_err("fma", T)
 fma(x::Integer, y::Integer, z::Integer) = x*y+z
-muladd{T<:Number}(x::T, y::T, z::T) = no_op_err("muladd", T)
+muladd{T<:Number}(x::T, y::T, z::T) = x*y+z
 
 (&){T<:Integer}(x::T, y::T) = no_op_err("&", T)
 (|){T<:Integer}(x::T, y::T) = no_op_err("|", T)

From 1df19b8d165dc637e43c57ba7471ea2732c63cea Mon Sep 17 00:00:00 2001
From: Simon Byrne <simonbyrne@gmail.com>
Date: Thu, 22 Jan 2015 15:47:53 +0000
Subject: [PATCH 3/3] muladd in evalpoly macro

---
 base/math.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/base/math.jl b/base/math.jl
index f7f2ed40edf34..89b1b08966a0e 100644
--- a/base/math.jl
+++ b/base/math.jl
@@ -61,8 +61,8 @@ macro evalpoly(z, p...)
     for i = length(p)-2:-1:1
         ai = symbol("a", i)
         push!(as, :($ai = $a))
-        a = :($b + r*$ai)
-        b = :($(esc(p[i])) - s * $ai)
+        a = :(muladd(r, $ai, $b))
+        b = :(muladd(-s, $ai, $(esc(p[i]))))
     end
     ai = :a0
     push!(as, :($ai = $a))
@@ -72,7 +72,7 @@ macro evalpoly(z, p...)
              :(r = x + x),
              :(s = x*x + y*y),
              as...,
-             :($ai * tt + $b))
+             :(muladd($ai, tt, $b)))
     R = Expr(:macrocall, symbol("@horner"), :tt, p...)
     :(let tt = $(esc(z))
           isa(tt, Complex) ? $C : $R