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# The example numbers in these specs are ported from the C++
# "double-conversions" library. The following is their license:
# Copyright 2012 the V8 project authors. All rights reserved.
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
#
# * Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above
# copyright notice, this list of conditions and the following
# disclaimer in the documentation and/or other materials provided
# with the distribution.
# * Neither the name of Google Inc. nor the names of its
# contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
# A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
# OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
require "spec"
private def gen_bound(v : UInt64)
f = v.unsafe_as(Float64)
gen_bound(f)
end
private def gen_bound(v : UInt32)
f = v.unsafe_as(Float32)
gen_bound(f)
end
private def gen_bound(v : Float64 | Float32)
fp = Float::Printer::DiyFP.from_f_normalized(v)
b = Float::Printer::IEEE.normalized_boundaries(v)
b[:minus].exp.should eq fp.exp
b[:plus].exp.should eq fp.exp
return fp.frac, b[:minus].frac, b[:plus].frac
end
describe "Float64 boundaries" do
it "boundaries 1.5" do
fp, mi, pl = gen_bound(1.5)
# 1.5 does not have a significand of the form 2^p (for some p).
# Therefore its boundaries are at the same distance.
(pl - fp).should eq(fp - mi)
(fp - mi).should eq(1 << 10)
end
it "boundaries 1.0" do
fp, mi, pl = gen_bound(1.0)
# 1.0 does have a significand of the form 2^p (for some p).
# Therefore its lower boundary is twice as close as the upper boundary.
(pl - fp).should be > fp - mi
(fp - mi).should eq 1 << 9
(pl - fp).should eq 1 << 10
end
it "boundaries min float64" do
fp, mi, pl = gen_bound(0x0000000000000001_u64)
# min-value does not have a significand of the form 2^p (for some p).
# Therefore its boundaries are at the same distance.
(pl - fp).should eq fp - mi
(fp - mi).should eq 1_u64 << 62
end
it "boundaries min normal f64" do
fp, mi, pl = gen_bound(0x0010000000000000_u64)
# Even though the significand is of the form 2^p (for some p), its boundaries
# are at the same distance. (This is the only exception).
(fp - mi).should eq(pl - fp)
(fp - mi).should eq(1 << 10)
end
it "boundaries max denormal f64" do
fp, mi, pl = gen_bound(0x000FFFFFFFFFFFFF_u64)
(fp - mi).should eq(pl - fp)
(fp - mi).should eq(1 << 11)
end
it "boundaries max f64" do
fp, mi, pl = gen_bound(0x7fEFFFFFFFFFFFFF_u64)
# max-value does not have a significand of the form 2^p (for some p).
# Therefore its boundaries are at the same distance.
(fp - mi).should eq(pl - fp)
(fp - mi).should eq(1 << 10)
end
end
describe "Float32 boundaries" do
it "boundaries 1.5" do
fp, mi, pl = gen_bound(1.5_f32)
# 1.5 does not have a significand of the form 2^p (for some p).
# Therefore its boundaries are at the same distance.
(pl - fp).should eq(fp - mi)
# Normalization shifts the significand by 8 bits. Add 32 bits for the bigger
# data-type, and remove 1 because boundaries are at half a ULP.
(fp - mi).should eq(1_u64 << 39)
end
it "boundaries 1.0" do
fp, mi, pl = gen_bound(1.0_f32)
# 1.0 does have a significand of the form 2^p (for some p).
# Therefore its lower boundary is twice as close as the upper boundary.
(pl - fp).should be > fp - mi
(fp - mi).should eq(1_u64 << 38)
(pl - fp).should eq(1_u64 << 39)
end
it "min Float32" do
fp, mi, pl = gen_bound(0x00000001_u32)
# min-value does not have a significand of the form 2^p (for some p).
# Therefore its boundaries are at the same distance.
(pl - fp).should eq(fp - mi)
# Denormals have their boundaries much closer.
(fp - mi).should eq(1_u64 << 62)
end
it "smallest normal 32" do
fp, mi, pl = gen_bound(0x00800000_u32)
# Even though the significand is of the form 2^p (for some p), its boundaries
# are at the same distance. (This is the only exception).
(pl - fp).should eq(fp - mi)
(fp - mi).should eq(1_u64 << 39)
end
it "largest denormal 32" do
fp, mi, pl = gen_bound(0x007FFFFF_u32)
(pl - fp).should eq(fp - mi)
(fp - mi).should eq(1_u64 << 40)
end
it "max Float32" do
fp, mi, pl = gen_bound(0x7F7FFFFF_u32)
# max-value does not have a significand of the form 2^p (for some p).
# Therefore its boundaries are at the same distance.
(pl - fp).should eq(fp - mi)
(fp - mi).should eq(1_u64 << 39)
end
end
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