SR-3131: Adjust choice of decimal vs. exponential format

For each floating-point type, there is a range of integers which
can be exactly represented in that type.  Adjust the formatting
logic so that we use decimal format for integers within this
range, exponential format for numbers outside of this range.

For example, Double has a 53-bit significand so can exactly
represent every integer from `-(2^53)...(2^53)`.  With this
change, we now use decimal format for these integers and
exponential format for values outside of this range.  This is
a relatively small change from the previous logic -- we've
basically just moved the cutoff from 10^15 to 2^53 (about 10^17).

The decision for using exponential format for small numbers is
not changed.

Author: tbkka

stdlib/public/runtime/SwiftDtoa.cpp

@@ -1063,7 +1063,9 @@ size_t swift_format_float(float d, char *dest, size_t length)
     int8_t digits[9];
     int digitCount =
         swift_decompose_float(d, digits, sizeof(digits), &decimalExponent);
-    if (decimalExponent < -3 || decimalExponent > 6) {
+    // People use float to model integers <= 2^24, so we use that
+    // as a cutoff for decimal vs. exponential format.
+    if (decimalExponent < -3 || fabsf(d) > (float)(1 << 24)) {
         return swift_format_exponential(dest, length, signbit(d),
                  digits, digitCount, decimalExponent);
     } else {
@@ -1117,7 +1119,9 @@ size_t swift_format_double(double d, char *dest, size_t length)
     int8_t digits[17];
     int digitCount =
         swift_decompose_double(d, digits, sizeof(digits), &decimalExponent);
-    if (decimalExponent < -3 || decimalExponent > 15) {
+    // People use double to model integers <= 2^53, so we use that
+    // as a cutoff for decimal vs. exponential format.
+    if (decimalExponent < -3 || fabs(d) > (double)((uint64_t)1 << 53)) {
         return swift_format_exponential(dest, length, signbit(d),
                  digits, digitCount, decimalExponent);
     } else {
@@ -1166,13 +1170,16 @@ size_t swift_format_float80(long double d, char *dest, size_t length)
         }
     }
 
-    // Decimal numeric formatting
     // Decimal numeric formatting
     int decimalExponent;
     int8_t digits[21];
     int digitCount =
         swift_decompose_float80(d, digits, sizeof(digits), &decimalExponent);
-    if (decimalExponent < -3 || decimalExponent > 18) {
+    // People use long double to model integers <= 2^64, so we use that
+    // as a cutoff for decimal vs. exponential format.
+    // The constant is written out in full here since it can't be
+    // expressed as a 64-bit integer.
+    if (decimalExponent < -3 || fabsl(d) > 18446744073709551616.0L) {
         return swift_format_exponential(dest, length, signbit(d),
                  digits, digitCount, decimalExponent);
     } else {

test/stdlib/PrintFloat.swift.gyb

@@ -544,7 +544,7 @@ PrintTests.test("Printable_Float") {
   // Every power of 10 should print with only a single digit '1'
   for power in -45 ... 38 {
     let s: String
-    if power < -4 || power > 5 { // Exponential form
+    if power < -4 || power > 7 { // Exponential form
       s = exponentialPowerOfTen(power)
     } else if power < 0 { // Fractional decimal form
       s = "0." + String(repeating: "0", count: -power - 1) + "1"
@@ -562,8 +562,14 @@ PrintTests.test("Printable_Float") {
     expectAccurateDescription(f.nextUp)
   }
 
-  // Check that the formatter chooses exponential
-  // format when it should:
+  // Float can represent all integers -(2^24)...(2^24)
+  let maxDecimalForm = Float(1 << 24)
+  expectDescription("16777216.0", maxDecimalForm)
+  expectDescription("-16777216.0", -maxDecimalForm)
+  // Outside of that range, use exponential form
+  expectDescription("1.6777218e+07", maxDecimalForm.nextUp)
+  expectDescription("-1.6777218e+07", -maxDecimalForm.nextUp)
+
   expectDescription("1.00001", asFloat32(1.00001))
   expectDescription("1.25e+17", asFloat32(125000000000000000.0))
   expectDescription("1.25e+16", asFloat32(12500000000000000.0))
@@ -575,8 +581,8 @@ PrintTests.test("Printable_Float") {
   expectDescription("1.25e+10", asFloat32(12500000000.0))
   expectDescription("1.25e+09", asFloat32(1250000000.0))
   expectDescription("1.25e+08", asFloat32(125000000.0))
-  expectDescription("1.25e+07", asFloat32(12500000.0))
-  expectDescription("1.25e+06", asFloat32(1250000.0))
+  expectDescription("12500000.0", asFloat32(12500000.0))
+  expectDescription("1250000.0", asFloat32(1250000.0))
   expectDescription("125000.0", asFloat32(125000.0))
   expectDescription("12500.0",  asFloat32(12500.0))
   expectDescription("1250.0",   asFloat32(1250.0))
@@ -660,7 +666,7 @@ PrintTests.test("Printable_Double") {
   // We know how every power of 10 should print
   for power in -323 ... 308 {
     let s: String
-    if power < -4 || power > 14 { // Exponential form
+    if power < -4 || power > 15 { // Exponential form
       s = exponentialPowerOfTen(power)
     } else if power < 0 { // Fractional decimal form
       s = "0." + String(repeating: "0", count: -power - 1) + "1"
@@ -687,12 +693,18 @@ PrintTests.test("Printable_Double") {
     }
   }
 
-  // Check that the formatter chooses exponential
-  // format when it should:
+  // Double can represent all integers -(2^53)...(2^53)
+  let maxDecimalForm = Double(1 << 53)
+  expectDescription("9007199254740992.0", maxDecimalForm)
+  expectDescription("-9007199254740992.0", -maxDecimalForm)
+  // Outside of that range, we use exponential form:
+  expectDescription("9.007199254740994e+15", maxDecimalForm.nextUp)
+  expectDescription("-9.007199254740994e+15", -maxDecimalForm.nextUp)
+
   expectDescription("1.00000000000001", asFloat64(1.00000000000001))
   expectDescription("1.25e+17", asFloat64(125000000000000000.0))
   expectDescription("1.25e+16", asFloat64(12500000000000000.0))
-  expectDescription("1.25e+15", asFloat64(1250000000000000.0))
+  expectDescription("1250000000000000.0", asFloat64(1250000000000000.0))
   expectDescription("125000000000000.0", asFloat64(125000000000000.0))
   expectDescription("12500000000000.0", asFloat64(12500000000000.0))
   expectDescription("1250000000000.0", asFloat64(1250000000000.0))
@@ -769,7 +781,7 @@ PrintTests.test("Printable_Float80") {
   // We know how every power of 10 should print
   for power in -4950 ... 4932 {
     let s: String
-    if power < -4 || power > 17 { // Exponential form
+    if power < -4 || power > 19 { // Exponential form
       s = exponentialPowerOfTen(power)
     } else if power < 0 { // Fractional decimal form
       s = "0." + String(repeating: "0", count: -power - 1) + "1"
@@ -794,11 +806,19 @@ PrintTests.test("Printable_Float80") {
     }
   }
 
-  // Check that the formatter chooses exponential
-  // format when it should:
+  // Float80 can represent all integers -(2^64)...(2^64):
+  let maxDecimalForm = Float80(UInt64.max) + 1.0
+  expectDescription("18446744073709551616.0", maxDecimalForm)
+  expectDescription("-18446744073709551616.0", -maxDecimalForm)
+  // Outside of that range, use exponential form
+  expectDescription("1.8446744073709551618e+19", maxDecimalForm.nextUp)
+  expectDescription("-1.8446744073709551618e+19", -maxDecimalForm.nextUp)
+
   expectDescription("1.00000000000000001", asFloat80(1.00000000000000001))
-  expectDescription("1.25e+19", asFloat80(12500000000000000000.0))
-  expectDescription("1.25e+18", asFloat80(1250000000000000000.0))
+  expectDescription("1.25e+21", asFloat80(1250000000000000000000.0))
+  expectDescription("1.25e+20", asFloat80(125000000000000000000.0))
+  expectDescription("12500000000000000000.0", asFloat80(12500000000000000000.0))
+  expectDescription("1250000000000000000.0", asFloat80(1250000000000000000.0))
   expectDescription("125000000000000000.0", asFloat80(125000000000000000.0))
   expectDescription("12500000000000000.0", asFloat80(12500000000000000.0))
   expectDescription("1250000000000000.0", asFloat80(1250000000000000.0))