zig

float_from_int.zig (4111B) - Raw

---

 const std = @import("std");
 const Int = std.meta.Int;
 const math = std.math;
 
 pub fn floatFromInt(comptime T: type, x: anytype) T {
     if (x == 0) return 0;
 
     // Various constants whose values follow from the type parameters.
     // Any reasonable optimizer will fold and propagate all of these.
     const Z = Int(.unsigned, @bitSizeOf(@TypeOf(x)));
     const uT = Int(.unsigned, @bitSizeOf(T));
     const inf = math.inf(T);
     const float_bits = @bitSizeOf(T);
     const int_bits = @bitSizeOf(@TypeOf(x));
     const exp_bits = math.floatExponentBits(T);
     const fractional_bits = math.floatFractionalBits(T);
     const exp_bias = math.maxInt(Int(.unsigned, exp_bits - 1));
     const implicit_bit = if (T != f80) @as(uT, 1) << fractional_bits else 0;
     const max_exp = exp_bias;
 
     // Sign
     const abs_val = @abs(x);
     const sign_bit = if (x < 0) @as(uT, 1) << (float_bits - 1) else 0;
     var result: uT = sign_bit;
 
     // Compute significand
     const exp = int_bits - @clz(abs_val) - 1;
     if (int_bits <= fractional_bits or exp <= fractional_bits) {
         const shift_amt = fractional_bits - @as(math.Log2Int(uT), @intCast(exp));
 
         // Shift up result to line up with the significand - no rounding required
         result = @as(uT, @intCast(abs_val)) << shift_amt;
         result ^= implicit_bit; // Remove implicit integer bit
     } else {
         const shift_amt: math.Log2Int(Z) = @intCast(exp - fractional_bits);
         const exact_tie: bool = @ctz(abs_val) == shift_amt - 1;
 
         // Shift down result and remove implicit integer bit
         result = @as(uT, @intCast((abs_val >> (shift_amt - 1)))) ^ (implicit_bit << 1);
 
         // Round result, including round-to-even for exact ties
         result = ((result + 1) >> 1) & ~@as(uT, @intFromBool(exact_tie));
     }
 
     // Compute exponent
     if ((int_bits > max_exp) and (exp > max_exp)) // If exponent too large, overflow to infinity
         return @bitCast(sign_bit | @as(uT, @bitCast(inf)));
 
     result += (@as(uT, exp) + exp_bias) << math.floatMantissaBits(T);
 
     // If the result included a carry, we need to restore the explicit integer bit
     if (T == f80) result |= 1 << fractional_bits;
 
     return @bitCast(sign_bit | result);
 }
 
 const endian = @import("builtin").cpu.arch.endian();
 inline fn limb(limbs: []const u32, index: usize) u32 {
     return switch (endian) {
         .little => limbs[index],
         .big => limbs[limbs.len - 1 - index],
     };
 }
 
 pub inline fn floatFromBigInt(comptime T: type, comptime signedness: std.builtin.Signedness, x: []const u32) T {
     switch (x.len) {
         0 => return 0,
         inline 1...4 => |limbs_len| return @floatFromInt(@as(
             @Type(.{ .int = .{ .signedness = signedness, .bits = 32 * limbs_len } }),
             @bitCast(x[0..limbs_len].*),
         )),
         else => {},
     }
 
     // sign implicit fraction round sticky
     const I = comptime @Type(.{ .int = .{
         .signedness = signedness,
         .bits = @as(u16, @intFromBool(signedness == .signed)) + 1 + math.floatFractionalBits(T) + 1 + 1,
     } });
 
     const clrsb = clrsb: {
         var clsb: usize = 0;
         const sign_bits: u32 = switch (signedness) {
             .signed => @bitCast(@as(i32, @bitCast(limb(x, x.len - 1))) >> 31),
             .unsigned => 0,
         };
         for (0..x.len) |limb_index| {
             const l = limb(x, x.len - 1 - limb_index) ^ sign_bits;
             clsb += @clz(l);
             if (l != 0) break;
         }
         break :clrsb clsb - @intFromBool(signedness == .signed);
     };
     const active_bits = 32 * x.len - clrsb;
     const exponent = active_bits -| @bitSizeOf(I);
     const exponent_limb = exponent / 32;
     const sticky = for (0..exponent_limb) |limb_index| {
         if (limb(x, limb_index) != 0) break true;
     } else limb(x, exponent_limb) & ((@as(u32, 1) << @truncate(exponent)) - 1) != 0;
     return math.ldexp(@as(T, @floatFromInt(
         std.mem.readPackedIntNative(I, std.mem.sliceAsBytes(x), exponent) | @intFromBool(sticky),
     )), @intCast(exponent));
 }
 
 test {
     _ = @import("float_from_int_test.zig");
 }