math/big: add Int.Float64 conversion

This operation converts a big.Int to float64,
reporting the accuracy of the result, with
a fast path in hardware.

Fixes golang#56984

Change-Id: I86d0fb0e105a06a4009986f2f5fd87a4d446f6f9
Reviewed-on: https://go-review.googlesource.com/c/go/+/453115
Reviewed-by: Robert Griesemer <gri@google.com>
TryBot-Result: Gopher Robot <gobot@golang.org>
Run-TryBot: Alan Donovan <adonovan@google.com>

api/next/56984.txt

@@ -0,0 +1 @@
+pkg math/big, method (*Int) ToFloat64() (float64, Accuracy) #56984

src/math/big/int.go

@@ -442,6 +442,26 @@ func (x *Int) IsUint64() bool {
 	return !x.neg && len(x.abs) <= 64/_W
 }
 
+// ToFloat64 returns the float64 value nearest x,
+// and an indication of any rounding that occurred.
+func (x *Int) ToFloat64() (float64, Accuracy) {
+	n := x.abs.bitLen() // NB: still uses slow crypto impl!
+	if n == 0 {
+		return 0.0, Exact
+	}
+
+	// Fast path: no more than 53 significant bits.
+	if n <= 53 || n < 64 && n-int(x.abs.trailingZeroBits()) <= 53 {
+		f := float64(low64(x.abs))
+		if x.neg {
+			f = -f
+		}
+		return f, Exact
+	}
+
+	return new(Float).SetInt(x).Float64()
+}
+
 // SetString sets z to the value of s, interpreted in the given base,
 // and returns z and a boolean indicating success. The entire string
 // (not just a prefix) must be valid for success. If SetString fails,

src/math/big/int_test.go

@@ -1955,3 +1955,52 @@ func TestNewIntAllocs(t *testing.T) {
 		}
 	}
 }
+
+func TestToFloat64(t *testing.T) {
+	for _, test := range []struct {
+		istr string
+		f    float64
+		acc  Accuracy
+	}{
+		{"-1000000000000000000000000000000000000000000000000000000", -1000000000000000078291540404596243842305360299886116864.000000, Below},
+		{"-9223372036854775809", math.MinInt64, Above},
+		{"-9223372036854775808", -9223372036854775808, Exact}, // -2^63
+		{"-9223372036854775807", -9223372036854775807, Below},
+		{"-18014398509481985", -18014398509481984.000000, Above},
+		{"-18014398509481984", -18014398509481984.000000, Exact}, // -2^54
+		{"-18014398509481983", -18014398509481984.000000, Below},
+		{"-9007199254740993", -9007199254740992.000000, Above},
+		{"-9007199254740992", -9007199254740992.000000, Exact}, // -2^53
+		{"-9007199254740991", -9007199254740991.000000, Exact},
+		{"-4503599627370497", -4503599627370497.000000, Exact},
+		{"-4503599627370496", -4503599627370496.000000, Exact}, // -2^52
+		{"-4503599627370495", -4503599627370495.000000, Exact},
+		{"-12345", -12345, Exact},
+		{"-1", -1, Exact},
+		{"0", 0, Exact},
+		{"1", 1, Exact},
+		{"12345", 12345, Exact},
+		{"0x1010000000000000", 0x1010000000000000, Exact}, // >2^53 but exact nonetheless
+		{"9223372036854775807", 9223372036854775808, Above},
+		{"9223372036854775808", 9223372036854775808, Exact}, // +2^63
+		{"1000000000000000000000000000000000000000000000000000000", 1000000000000000078291540404596243842305360299886116864.000000, Above},
+	} {
+		i, ok := new(Int).SetString(test.istr, 0)
+		if !ok {
+			t.Errorf("SetString(%s) failed", test.istr)
+			continue
+		}
+
+		// Test against expectation.
+		f, acc := i.ToFloat64()
+		if f != test.f || acc != test.acc {
+			t.Errorf("%s: got %f (%s); want %f (%s)", test.istr, f, acc, test.f, test.acc)
+		}
+
+		// Cross-check the fast path against the big.Float implementation.
+		f2, acc2 := new(Float).SetInt(i).Float64()
+		if f != f2 || acc != acc2 {
+			t.Errorf("%s: got %f (%s); Float.Float64 gives %f (%s)", test.istr, f, acc, f2, acc2)
+		}
+	}
+}