From 950cea6f6d6a21649a137fec6324b32934b76177 Mon Sep 17 00:00:00 2001
From: Michael Abbott <32575566+mcabbott@users.noreply.github.com>
Date: Thu, 12 May 2022 20:15:13 -0400
Subject: [PATCH] generic frexp

---
 src/math/prearith/prearith.jl | 18 +++++++++++++++---
 test/prearith.jl              | 18 ++++++++++++++----
 2 files changed, 29 insertions(+), 7 deletions(-)

diff --git a/src/math/prearith/prearith.jl b/src/math/prearith/prearith.jl
index 52911790..207f7fbd 100644
--- a/src/math/prearith/prearith.jl
+++ b/src/math/prearith/prearith.jl
@@ -41,21 +41,33 @@ end
 flipsign(x::DoubleFloat{T}, y::U) where {T<:IEEEFloat, U<:Unsigned} = +x
 copysign(x::DoubleFloat{T}, y::U) where {T<:IEEEFloat, U<:Unsigned} = +x
 
-function Base.Math.frexp(x::DoubleFloat{T}) where {T<:IEEEFloat}
+"""
+    frexps(x::DoubleFloat)
+
+Applies `Base.frexp` to both `hi` and `lo` parts, and returns a tuple of tuples.
+See also `DoubleFloats.ldexps` for the inverse, and `DoubleFloats.signs` similar tuple.
+"""
+function frexps(x::DoubleFloat{T}) where {T<:IEEEFloat}
     frhi, exphi = frexp(HI(x))
     frlo, explo = frexp(LO(x))
     return (frhi, exphi), (frlo, explo)
 end
 
+function Base.Math.frexp(x::DoubleFloat{T}) where {T<:IEEEFloat}
+    frhi, exphi = frexp(HI(x))
+    frlo, explo = frexp(LO(x))
+    return DoubleFloat{T}(frhi, ldexp(frlo, explo - exphi)), exphi
+end
+
 function Base.Math.ldexp(x::DoubleFloat{T}, exponent::I) where {T<:IEEEFloat, I<:Integer}
     return DoubleFloat{T}(ldexp(HI(x), exponent), ldexp(LO(x), exponent))
 end
 
-function Base.Math.ldexp(dhi::Tuple{T,I}, dlo::Tuple{T,I}) where {T<:IEEEFloat, I<:Integer}
+function ldexps(dhi::Tuple{T,I}, dlo::Tuple{T,I}) where {T<:IEEEFloat, I<:Integer}
     return DoubleFloat(ldexp(dhi[1], dhi[2]), ldexp(dlo[1], dlo[2]))
 end
 
-function Base.Math.ldexp(dhilo::Tuple{Tuple{T,I}, Tuple{T,I}}) where {T<:IEEEFloat, I<:Integer}
+function ldexps(dhilo::Tuple{Tuple{T,I}, Tuple{T,I}}) where {T<:IEEEFloat, I<:Integer}
     return ldexp(dhilo[1], dhilo[2])
 end
 
diff --git a/test/prearith.jl b/test/prearith.jl
index f678d113..7cdaa76e 100644
--- a/test/prearith.jl
+++ b/test/prearith.jl
@@ -10,12 +10,22 @@
     @test flipsign(negval, 1) == negval
     @test copysign(val, -1) == negval
     @test copysign(negval, 1) == val
-    
+
     @test ldexp(frexp(val)...,) == val
-   # @test ldexp(significand(val), exponent(val)) == val
-  
-    @test signs(val) == (sign(HI(val)), sign(LO(val)))
+    fr, ex = frexp(val)
+    @test fr * T(2)^ex == val
+
+    @test fr ≈ frexp(Float64(val))[1]
+    @test ex == frexp(Float64(val))[2]
 
+    @test isnan(frexp(T(NaN))[1])
+    @test isinf(frexp(T(Inf))[1])
+    @test iszero(frexp(T(0))[1])
+
+    @test DoubleFloats.ldexps(DoubleFloats.frexps(val)...,) == val
+    # @test ldexp(significand(val), exponent(val)) == val
+
+    @test signs(val) == (sign(HI(val)), sign(LO(val)))
 end
 
 @testset "trunc $T" for T in (Double16, Double32, Double64)