diff --git a/QCBOR.xcodeproj/project.pbxproj b/QCBOR.xcodeproj/project.pbxproj
index b259a6c..d1b3881 100644
--- a/QCBOR.xcodeproj/project.pbxproj
+++ b/QCBOR.xcodeproj/project.pbxproj
@@ -8,6 +8,7 @@
 
 /* Begin PBXBuildFile section */
 		E73B574E215713FA0080D658 /* half_precision_test.c in Sources */ = {isa = PBXBuildFile; fileRef = E73B574D215713FA0080D658 /* half_precision_test.c */; };
+		E73B575121589DB20080D658 /* half_to_double_from_rfc7049.c in Sources */ = {isa = PBXBuildFile; fileRef = E73B575021589DB20080D658 /* half_to_double_from_rfc7049.c */; };
 		E776E08F214AE07500E67947 /* qcbor_encode.c in Sources */ = {isa = PBXBuildFile; fileRef = E776E08C214AE07400E67947 /* qcbor_encode.c */; };
 		E776E090214AE07500E67947 /* UsefulBuf.c in Sources */ = {isa = PBXBuildFile; fileRef = E776E08D214AE07500E67947 /* UsefulBuf.c */; };
 		E776E091214AE07500E67947 /* qcbor_decode.c in Sources */ = {isa = PBXBuildFile; fileRef = E776E08E214AE07500E67947 /* qcbor_decode.c */; };
@@ -31,6 +32,8 @@
 /* Begin PBXFileReference section */
 		E73B574C215713FA0080D658 /* half_precision_test.h */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.h; name = half_precision_test.h; path = test/half_precision_test.h; sourceTree = "<group>"; };
 		E73B574D215713FA0080D658 /* half_precision_test.c */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.c; name = half_precision_test.c; path = test/half_precision_test.c; sourceTree = "<group>"; };
+		E73B574F21589DB20080D658 /* half_to_double_from_rfc7049.h */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.h; name = half_to_double_from_rfc7049.h; path = test/half_to_double_from_rfc7049.h; sourceTree = "<group>"; };
+		E73B575021589DB20080D658 /* half_to_double_from_rfc7049.c */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.c.c; name = half_to_double_from_rfc7049.c; path = test/half_to_double_from_rfc7049.c; sourceTree = "<group>"; };
 		E776E07C214ADF7F00E67947 /* QCBOR */ = {isa = PBXFileReference; explicitFileType = "compiled.mach-o.executable"; includeInIndex = 0; path = QCBOR; sourceTree = BUILT_PRODUCTS_DIR; };
 		E776E08C214AE07400E67947 /* qcbor_encode.c */ = {isa = PBXFileReference; fileEncoding = 4; indentWidth = 3; lastKnownFileType = sourcecode.c.c; name = qcbor_encode.c; path = src/qcbor_encode.c; sourceTree = "<group>"; tabWidth = 3; };
 		E776E08D214AE07500E67947 /* UsefulBuf.c */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.c.c; name = UsefulBuf.c; path = src/UsefulBuf.c; sourceTree = "<group>"; };
@@ -102,6 +105,8 @@
 				E73B574C215713FA0080D658 /* half_precision_test.h */,
 				E776E09C214AEEEA00E67947 /* basic_test.c */,
 				E776E09B214AEEEA00E67947 /* basic_test.h */,
+				E73B574F21589DB20080D658 /* half_to_double_from_rfc7049.h */,
+				E73B575021589DB20080D658 /* half_to_double_from_rfc7049.c */,
 			);
 			name = test;
 			sourceTree = "<group>";
@@ -168,6 +173,7 @@
 				E776E164214F81EC00E67947 /* ieee754.c in Sources */,
 				E776E090214AE07500E67947 /* UsefulBuf.c in Sources */,
 				E776E097214AE0C700E67947 /* cmd_line_main.c in Sources */,
+				E73B575121589DB20080D658 /* half_to_double_from_rfc7049.c in Sources */,
 				E776E09D214AEEEA00E67947 /* basic_test.c in Sources */,
 			);
 			runOnlyForDeploymentPostprocessing = 0;
diff --git a/src/ieee754.c b/src/ieee754.c
index bcad14d..12877bd 100644
--- a/src/ieee754.c
+++ b/src/ieee754.c
@@ -459,7 +459,7 @@
     const uint64_t uDroppedSingleBits = DOUBLE_SIGNIFICAND_MASK >> SINGLE_NUM_SIGNIFICAND_BITS;
         
     // The various cases
-    if(uDouble == 0) {
+    if(d == 0.0) { // Take care of positive and negative zero
         // Value is 0.0000, not a a subnormal
         result.uTag = IEEE754_UNION_IS_HALF;
         result.u16  = IEEE754_DoubleToHalf(d);
diff --git a/src/qcbor_encode.c b/src/qcbor_encode.c
index 9683b27..f70037c 100644
--- a/src/qcbor_encode.c
+++ b/src/qcbor_encode.c
@@ -259,7 +259,7 @@
    // always generated internally, not by the caller, b) this is for CBOR
    // _generation_, not parsing c) a mistake will result in bad CBOR generation,
    // not a security vulnerability.
-   uMajorType <<= 5;
+   uMajorType <<= 5; // TODO: make this a constant
    
    if(uNumber > 0xffffffff || uMinLen >= 8) {
       UsefulOutBuf_InsertByte(&(me->OutBuf), uMajorType + LEN_IS_EIGHT_BYTES, uPos);
diff --git a/test/basic_test.c b/test/basic_test.c
index 89d4623..3e85d00 100644
--- a/test/basic_test.c
+++ b/test/basic_test.c
@@ -128,7 +128,10 @@
     TEST_ENTRY(basic_test_one),
     //TEST_ENTRY(fail_test),
     TEST_ENTRY(half_precision_encode_basic),
-    TEST_ENTRY(half_precision_decode_basic)
+    TEST_ENTRY(half_precision_decode_basic),
+    TEST_ENTRY(half_precision_to_float_transitive_test),
+    TEST_ENTRY(double_as_smallest_encode_basic),
+    TEST_ENTRY(half_precision_to_float_vs_rfc_test),
 };
 
 
diff --git a/test/half_precision_test.c b/test/half_precision_test.c
index 91bcebd..4038cd6 100644
--- a/test/half_precision_test.c
+++ b/test/half_precision_test.c
@@ -33,8 +33,8 @@
 
 #include "half_precision_test.h"
 #include "qcbor.h"
-
-#include <math.h> // For INFINITY and NaN
+#include "half_to_double_from_rfc7049.h"
+#include <math.h> // For INFINITY and NAN and isnan()
 
 static const uint8_t ExpectedHalf[] = {
     0xAD,
@@ -97,7 +97,7 @@
     // Float 65536.0F is 0x47800000 in hex. It has an exponent of 16, which is larger than 15, the largest half-precision exponent
     QCBOREncode_AddFloatAsHalfToMap(&EC, "too-large half-precision", 65536.0F);
     // Should convert to smallest possible half precision which is encodded as 0x00 0x01 or 5.960464477539063e-8
-    QCBOREncode_AddFloatAsHalfToMap(&EC, "smallest subnormal", 0.0000000596046448);
+    QCBOREncode_AddFloatAsHalfToMap(&EC, "smallest subnormal", 0.0000000596046448F);
     QCBOREncode_AddFloatAsHalfToMap(&EC, "smallest normal",    0.0000610351526F); // in hex single is 0x387fffff, exponent -15, significand 7fffff
     QCBOREncode_AddFloatAsHalfToMap(&EC, "biggest subnormal",  0.0000610351563F); // in hex single is 0x38800000, exponent -14, significand 0
     QCBOREncode_AddFloatAsHalfToMap(&EC, "subnormal single", 4e-40F); 
@@ -105,9 +105,7 @@
     QCBOREncode_CloseMap(&EC);
     
     EncodedCBOR EncodedHalfs;
-    
     int nReturn = QCBOREncode_Finish2(&EC, &EncodedHalfs);
-    
     if(nReturn) {
         return -1;
     }
@@ -205,3 +203,236 @@
     
     return 0;
 }
+
+
+int half_precision_to_float_transitive_test()
+{
+    for(uint32_t uHalfP = 0; uHalfP < 0xffff; uHalfP += 1) {
+        // Contruct the CBOR for the half-precision float by hand
+        UsefulBuf_MakeStackUB(EncodedCBORMem, 3);
+        UsefulOutBuf UOB;
+        UsefulOutBuf_Init(&UOB, EncodedCBORMem);
+        
+        const uint8_t uHalfPrecInitialByte = HALF_PREC_FLOAT + (CBOR_MAJOR_TYPE_SIMPLE << 5); // 0xf9
+        UsefulOutBuf_AppendByte(&UOB, uHalfPrecInitialByte); // The initial byte for a half-precision float
+        UsefulOutBuf_AppendUint16(&UOB, (uint16_t)uHalfP);
+        
+        
+        // Now parse the hand-constructed CBOR. This will invoke the conversion to a float
+        QCBORDecodeContext DC;
+        QCBORDecode_Init(&DC, UsefulOutBuf_OutUBuf(&UOB), 0);
+        
+        QCBORItem Item;
+        QCBORDecode_GetNext(&DC, &Item);
+        if(Item.uDataType != QCBOR_TYPE_FLOAT) {
+            return -1;
+        }
+        
+        //printf("%04x  QCBOR:%15.15f  \n", uHalfP,Item.val.fnum);
+
+        
+        // Now generate CBOR with the half-precision value. This will invoke the conversion from float to half
+        UsefulBuf_MakeStackUB(OtherEncodedCBORMem, 5);
+        QCBOREncodeContext EC;
+        QCBOREncode_Init(&EC, OtherEncodedCBORMem);
+        QCBOREncode_AddFloatAsHalf(&EC, Item.val.fnum);
+        EncodedCBOR EnCBOR;
+        QCBOREncode_Finish2(&EC, &EnCBOR); // todo check return code
+        
+        
+        // Finally parse the CBOR by hand to get at half-precision that was actually encoded.
+        UsefulInputBuf UIB;
+        UsefulInputBuf_Init(&UIB, EnCBOR.Bytes);
+        if(UsefulInputBuf_GetByte(&UIB) != uHalfPrecInitialByte) {
+            return -2;
+        }
+        if(UsefulInputBuf_GetUint16(&UIB) != uHalfP) { // the moment of truth did we get back what we started with?
+            return -3;
+        }
+    }
+    
+    return 0;
+}
+
+
+int half_precision_to_float_vs_rfc_test()
+{
+    for(uint32_t uHalfP = 0; uHalfP < 0x1fff; uHalfP += 10) {
+        unsigned char x[2];
+        x[1] = uHalfP & 0xff;
+        x[0] = uHalfP >> 8;
+        double d = decode_half(x);
+        
+        // Contruct the CBOR for the half-precision float by hand
+        UsefulBuf_MakeStackUB(__xx, 3);
+        UsefulOutBuf UOB;
+        UsefulOutBuf_Init(&UOB, __xx);
+        
+        const uint8_t uHalfPrecInitialByte = HALF_PREC_FLOAT + (CBOR_MAJOR_TYPE_SIMPLE << 5); // 0xf9
+        UsefulOutBuf_AppendByte(&UOB, uHalfPrecInitialByte); // The initial byte for a half-precision float
+        UsefulOutBuf_AppendUint16(&UOB, (uint16_t)uHalfP);
+
+        // Now parse the hand-constructed CBOR. This will invoke the conversion to a float
+        QCBORDecodeContext DC;
+        QCBORDecode_Init(&DC, UsefulOutBuf_OutUBuf(&UOB), 0);
+        
+        QCBORItem Item;
+        
+        QCBORDecode_GetNext(&DC, &Item);
+        if(Item.uDataType != QCBOR_TYPE_FLOAT) {
+            return -1;
+        }
+        
+        //printf("%04x  QCBOR:%15.15f  RFC: %15.15f\n", uHalfP,Item.val.fnum, d );
+        
+        if(Item.val.fnum != d) {
+            return -2;
+        }
+    }
+    return 0;
+}
+
+
+/*
+ {"zero": 0.0, "negative zero": -0.0, "infinitity": Infinity, "negative infinitity": -Infinity, "NaN": NaN, "one": 1.0, "one third": 0.333251953125, "largest half-precision": 65504.0, "largest half-precision point one": 65504.1, "too-large half-precision": 65536.0, "smallest subnormal": 5.96046448e-8, "smallest normal": 0.00006103515261202119, "biggest subnormal": 0.00006103515625, "subnormal single": 4.00000646641519e-40, 3: -2.0, "large single exp": 2.5521177519070385e+38, "too-large single exp": 5.104235503814077e+38, "biggest single with prec": 16777216.0, "first single with prec loss": 16777217.0, 1: "fin"}
+ 
+ */
+static const uint8_t sExpectedSmallest[] = {
+    0xB4, 0x64, 0x7A, 0x65, 0x72, 0x6F, 0xF9, 0x00, 0x00, 0x6D, 0x6E, 0x65, 0x67, 0x61, 0x74, 0x69, 0x76, 0x65, 0x20, 0x7A, 0x65, 0x72, 0x6F, 0xF9, 0x80, 0x00, 0x6A, 0x69, 0x6E, 0x66, 0x69, 0x6E, 0x69, 0x74, 0x69, 0x74, 0x79, 0xF9, 0x7C, 0x00, 0x73, 0x6E, 0x65, 0x67, 0x61, 0x74, 0x69, 0x76, 0x65, 0x20, 0x69, 0x6E, 0x66, 0x69, 0x6E, 0x69, 0x74, 0x69, 0x74, 0x79, 0xF9, 0xFC, 0x00, 0x63, 0x4E, 0x61, 0x4E, 0xF9, 0x7E, 0x00, 0x63, 0x6F, 0x6E, 0x65, 0xF9, 0x3C, 0x00, 0x69, 0x6F, 0x6E, 0x65, 0x20, 0x74, 0x68, 0x69, 0x72, 0x64, 0xF9, 0x35, 0x55, 0x76, 0x6C, 0x61, 0x72, 0x67, 0x65, 0x73, 0x74, 0x20, 0x68, 0x61, 0x6C, 0x66, 0x2D, 0x70, 0x72, 0x65, 0x63, 0x69, 0x73, 0x69, 0x6F, 0x6E, 0xF9, 0x7B, 0xFF, 0x78, 0x20, 0x6C, 0x61, 0x72, 0x67, 0x65, 0x73, 0x74, 0x20, 0x68, 0x61, 0x6C, 0x66, 0x2D, 0x70, 0x72, 0x65, 0x63, 0x69, 0x73, 0x69, 0x6F, 0x6E, 0x20, 0x70, 0x6F, 0x69, 0x6E, 0x74, 0x20, 0x6F, 0x6E, 0x65, 0xFB, 0x40, 0xEF, 0xFC, 0x03, 0x33, 0x33, 0x33, 0x33, 0x78, 0x18, 0x74, 0x6F, 0x6F, 0x2D, 0x6C, 0x61, 0x72, 0x67, 0x65, 0x20, 0x68, 0x61, 0x6C, 0x66, 0x2D, 0x70, 0x72, 0x65, 0x63, 0x69, 0x73, 0x69, 0x6F, 0x6E, 0xFA, 0x47, 0x80, 0x00, 0x00, 0x72, 0x73, 0x6D, 0x61, 0x6C, 0x6C, 0x65, 0x73, 0x74, 0x20, 0x73, 0x75, 0x62, 0x6E, 0x6F, 0x72, 0x6D, 0x61, 0x6C, 0xFB, 0x3E, 0x70, 0x00, 0x00, 0x00, 0x1C, 0x5F, 0x68, 0x6F, 0x73, 0x6D, 0x61, 0x6C, 0x6C, 0x65, 0x73, 0x74, 0x20, 0x6E, 0x6F, 0x72, 0x6D, 0x61, 0x6C, 0xFA, 0x38, 0x7F, 0xFF, 0xFF, 0x71, 0x62, 0x69, 0x67, 0x67, 0x65, 0x73, 0x74, 0x20, 0x73, 0x75, 0x62, 0x6E, 0x6F, 0x72, 0x6D, 0x61, 0x6C, 0xF9, 0x04, 0x00, 0x70, 0x73, 0x75, 0x62, 0x6E, 0x6F, 0x72, 0x6D, 0x61, 0x6C, 0x20, 0x73, 0x69, 0x6E, 0x67, 0x6C, 0x65, 0xFB, 0x37, 0xC1, 0x6C, 0x28, 0x00, 0x00, 0x00, 0x00, 0x03, 0xF9, 0xC0, 0x00, 0x70, 0x6C, 0x61, 0x72, 0x67, 0x65, 0x20, 0x73, 0x69, 0x6E, 0x67, 0x6C, 0x65, 0x20, 0x65, 0x78, 0x70, 0xFA, 0x7F, 0x40, 0x00, 0x00, 0x74, 0x74, 0x6F, 0x6F, 0x2D, 0x6C, 0x61, 0x72, 0x67, 0x65, 0x20, 0x73, 0x69, 0x6E, 0x67, 0x6C, 0x65, 0x20, 0x65, 0x78, 0x70, 0xFB, 0x47, 0xF8, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x78, 0x18, 0x62, 0x69, 0x67, 0x67, 0x65, 0x73, 0x74, 0x20, 0x73, 0x69, 0x6E, 0x67, 0x6C, 0x65, 0x20, 0x77, 0x69, 0x74, 0x68, 0x20, 0x70, 0x72, 0x65, 0x63, 0xFA, 0x4B, 0x80, 0x00, 0x00, 0x78, 0x1B, 0x66, 0x69, 0x72, 0x73, 0x74, 0x20, 0x73, 0x69, 0x6E, 0x67, 0x6C, 0x65, 0x20, 0x77, 0x69, 0x74, 0x68, 0x20, 0x70, 0x72, 0x65, 0x63, 0x20, 0x6C, 0x6F, 0x73, 0x73, 0xFB, 0x41, 0x70, 0x00, 0x00, 0x10, 0x00, 0x00, 0x00, 0x01, 0x63, 0x66, 0x69, 0x6E
+};
+
+
+int double_as_smallest_encode_basic()
+{
+    UsefulBuf_MakeStackUB(EncodedHalfsMem, 420);
+    
+    QCBOREncodeContext EC;
+    QCBOREncode_Init(&EC, EncodedHalfsMem);
+    // These are mostly from https://en.wikipedia.org/wiki/Half-precision_floating-point_format
+    QCBOREncode_OpenMap(&EC);
+    // 64                                   # text(4)
+    //    7A65726F                          # "zero"
+    // F9 0000                              # primitive(0)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "zero", 0.00);
+
+    // 64                                   # text(4)
+    //    7A65726F                          # "negative zero"
+    // F9 8000                              # primitive(0)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "negative zero", -0.00);
+    
+    // 6A                                   # text(10)
+    //    696E66696E6974697479              # "infinitity"
+    // F9 7C00                              # primitive(31744)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "infinitity", INFINITY);
+    
+    // 73                                   # text(19)
+    //    6E6567617469766520696E66696E6974697479 # "negative infinitity"
+    // F9 FC00                              # primitive(64512)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "negative infinitity", -INFINITY);
+    
+    // 63                                   # text(3)
+    //    4E614E                            # "NaN"
+    // F9 7E00                              # primitive(32256)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "NaN", NAN);
+    
+    // TODO: test a few NaN variants
+    
+    // 63                                   # text(3)
+    //    6F6E65                            # "one"
+    // F9 3C00                              # primitive(15360)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "one", 1.0);
+    
+    // 69                                   # text(9)
+    //    6F6E65207468697264                # "one third"
+    // F9 3555                              # primitive(13653)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "one third", 0.333251953125);
+    
+    // 76                                   # text(22)
+    //    6C6172676573742068616C662D707265636973696F6E # "largest half-precision"
+    // F9 7BFF                              # primitive(31743)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "largest half-precision",65504.0);
+
+    // 76                                   # text(22)
+    //    6C6172676573742068616C662D707265636973696F6E # "largest half-precision"
+    // F9 7BFF                              # primitive(31743)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "largest half-precision point one",65504.1);
+    
+    // Float 65536.0F is 0x47800000 in hex. It has an exponent of 16, which is larger than 15, the largest half-precision exponent
+    // 78 18                                # text(24)
+    //    746F6F2D6C617267652068616C662D707265636973696F6E # "too-large half-precision"
+    // FA 47800000                          # primitive(31743)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "too-large half-precision", 65536.0);
+    
+    // The smallest possible half-precision subnormal, but digitis are lost converting
+    // to half, so this turns into a double
+    // 72                                   # text(18)
+    //    736D616C6C657374207375626E6F726D616C # "smallest subnormal"
+    // FB 3E700000001C5F68                  # primitive(4499096027744984936)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "smallest subnormal", 0.0000000596046448);
+    
+    // The smallest possible half-precision snormal, but digitis are lost converting
+    // to half, so this turns into a single TODO: confirm this is right
+    // 6F                                   # text(15)
+    //    736D616C6C657374206E6F726D616C    # "smallest normal"
+    // FA 387FFFFF                          # primitive(947912703)
+    // in hex single is 0x387fffff, exponent -15, significand 7fffff
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "smallest normal",    0.0000610351526F);
+    
+    // 71                                   # text(17)
+    //    62696767657374207375626E6F726D616C # "biggest subnormal"
+    // F9 0400                              # primitive(1024)
+    // in hex single is 0x38800000, exponent -14, significand 0
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "biggest subnormal",  0.0000610351563F);
+    
+    // 70                                   # text(16)
+    //    7375626E6F726D616C2073696E676C65  # "subnormal single"
+    // FB 37C16C2800000000                  # primitive(4017611261645684736)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "subnormal single", 4e-40F);
+    
+    // 03                                   # unsigned(3)
+    // F9 C000                              # primitive(49152)
+    QCBOREncode_AddDoubleAsSmallestToMapN(&EC, 3, -2.0);
+    
+    // 70                                   # text(16)
+    //    6C617267652073696E676C6520657870  # "large single exp"
+    // FA 7F400000                          # primitive(2134900736)
+    // (0x01LL << (DOUBLE_NUM_SIGNIFICAND_BITS-1)) | ((127LL + DOUBLE_EXPONENT_BIAS) << DOUBLE_EXPONENT_SHIFT);
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "large single exp", 2.5521177519070385E+38); // Exponent fits  single
+
+    // 74                                   # text(20)
+    //    746F6F2D6C617267652073696E676C6520657870 # "too-large single exp"
+    // FB 47F8000000000000                  # primitive(5185894970917126144)
+    // (0x01LL << (DOUBLE_NUM_SIGNIFICAND_BITS-1)) | ((128LL + DOUBLE_EXPONENT_BIAS) << DOUBLE_EXPONENT_SHIFT);
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "too-large single exp", 5.104235503814077E+38); // Exponent too large for single
+
+    // 66                                   # text(6)
+    //    646664666465                      # "dfdfde"
+    // FA 4B800000                          # primitive(1266679808)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "biggest single with prec",16777216); // Single with no precision loss
+    
+    // 78 18                                # text(24)
+    //    626967676573742073696E676C6520776974682070726563 # "biggest single with prec"
+    // FA 4B800000                          # primitive(1266679808)
+    QCBOREncode_AddDoubleAsSmallestToMap(&EC, "first single with prec loss",16777217); // Double becuase of precision loss
+    
+    // Just a convenient marker when cutting and pasting encoded CBOR
+    QCBOREncode_AddSZStringToMapN(&EC, 1, "fin");
+
+    QCBOREncode_CloseMap(&EC);
+    
+    EncodedCBOR EncodedHalfs;
+    int nReturn = QCBOREncode_Finish2(&EC, &EncodedHalfs);
+    if(nReturn) {
+        return -1;
+    }
+    
+    if(UsefulBuf_Compare(EncodedHalfs.Bytes, UsefulBuf_FromByteArrayLiteral(sExpectedSmallest))) {
+        return -3;
+    }
+    
+    return 0;
+}
+
+
+
+
diff --git a/test/half_precision_test.h b/test/half_precision_test.h
index d663f54..a980d35 100644
--- a/test/half_precision_test.h
+++ b/test/half_precision_test.h
@@ -22,7 +22,8 @@
  SOFTWARE.
  
  (This is the MIT license)
- ==============================================================================*///
+ ==============================================================================*/
+//
 //  half_precision_test.h
 //  QCBOR
 //
@@ -37,5 +38,11 @@
 
 int half_precision_decode_basic(void);
 
+int half_precision_to_float_transitive_test(void);
+
+int double_as_smallest_encode_basic(void);
+
+int half_precision_to_float_vs_rfc_test(void);
+
 
 #endif /* half_precision_test_h */
diff --git a/test/half_to_double_from_rfc7049.c b/test/half_to_double_from_rfc7049.c
new file mode 100644
index 0000000..68d03cb
--- /dev/null
+++ b/test/half_to_double_from_rfc7049.c
@@ -0,0 +1,45 @@
+/*
+ 
+ Copyright (c) 2013 IETF Trust and the persons identified as the
+ document authors.  All rights reserved.
+ 
+ This document is subject to BCP 78 and the IETF Trust's Legal
+ Provisions Relating to IETF Documents
+ (http://trustee.ietf.org/license-info) in effect on the date of
+ publication of this document.  Please review these documents
+ carefully, as they describe your rights and restrictions with respect
+ to this document.  Code Components extracted from this document must
+ include Simplified BSD License text as described in Section 4.e of
+ the Trust Legal Provisions and are provided without warranty as
+ described in the Simplified BSD License.
+ 
+ */
+
+/*
+ This code is from RFC 7049. It is not used in the main implementation
+ because:
+   a) it adds a dependency on <math.h> and ldexp().
+   b) the license may be an issue
+ 
+ QCBOR does support half-precision, but rather than using
+ floating point math like this, it does it with bit shifting
+ and masking.
+ 
+ This code is here to test that code.
+ 
+ */
+
+#include "half_to_double_from_rfc7049.h"
+
+#include <math.h>
+
+double decode_half(unsigned char *halfp) {
+    int half = (halfp[0] << 8) + halfp[1];
+    int exp = (half >> 10) & 0x1f;
+    int mant = half & 0x3ff;
+    double val;
+    if (exp == 0) val = ldexp(mant, -24);
+    else if (exp != 31) val = ldexp(mant + 1024, exp - 25);
+    else val = mant == 0 ? INFINITY : NAN;
+    return half & 0x8000 ? -val : val;
+}
diff --git a/test/half_to_double_from_rfc7049.h b/test/half_to_double_from_rfc7049.h
new file mode 100644
index 0000000..6b5f0e0
--- /dev/null
+++ b/test/half_to_double_from_rfc7049.h
@@ -0,0 +1,40 @@
+/*==============================================================================
+ Copyright 2018 Laurence Lundblade
+ 
+ Permission is hereby granted, free of charge, to any person obtaining
+ a copy of this software and associated documentation files (the
+ "Software"), to deal in the Software without restriction, including
+ without limitation the rights to use, copy, modify, merge, publish,
+ distribute, sublicense, and/or sell copies of the Software, and to
+ permit persons to whom the Software is furnished to do so, subject to
+ the following conditions:
+ 
+ The above copyright notice and this permission notice shall be included
+ in all copies or substantial portions of the Software.
+ 
+ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ SOFTWARE.
+ 
+ (This is the MIT license)
+ ==============================================================================*/
+
+//
+//  half_to_double_from_rfc7049.h
+//  QCBOR
+//
+//  Created by Laurence Lundblade on 9/23/18.
+//  Copyright © 2018 Laurence Lundblade. All rights reserved.
+//
+
+#ifndef half_to_double_from_rfc7049_h
+#define half_to_double_from_rfc7049_h
+
+double decode_half(unsigned char *halfp);
+
+#endif /* half_to_double_from_rfc7049_h */