// // === NaN Packing Strategy === // // Format of a double, in Zig least-to-most significant field order: // // { fraction: u52, exponent: u11, sign: u1 } // // When the exponent bits are all set, it's either a NaN or an Infinity. // // For value packing, almost all remaining 53 bits are available, giving us // about 2^53 values, except for the four following bit patterns: // // *** FORBIDDEN VALUES *** // // 1. Negative cqNaN = { sign = 1, exponent = max, fraction = 2^51 } // // 2. Negative Infinity = { sign = 1, exponent = max, fraction = 0 } // // 3. Positive cqNaN = { sign = 0, exponent = max, fraction = 2^51 } // // 4. Positive Infinity = { sign = 0, exponent = max, fraction = 0 } // // The abbreviation "cqNaN" stands for canonical quiet NaN. // // Note that 2^51 means the MSb of the 52 fraction bits being set, and the rest // being zero. The fraction MSb is also called the is_quiet flag, because it // demarcates quiet NaNs. The rest being zero makes it the canonical qNaN. // // The positive and negative cqNaN are the *only* NaN values that can actually // be returned by any FP operations, which is why we don't use them to pack // values; we want to be able to represent NaN in Zisp as a double. // // Beyond those four bit patterns, all values with a maximum exponent (all bits // set) are fair game for representing other values, so 2^53 - 4 possibilities. // // We split those 2^53 - 4 available values into four groups, each allowing for // 2^51 - 1 different values to be encoded in them: // // sign = 1, quiet = 1 :: Negative Fixnum from -1 to -2^51+1 // // sign = 1, quiet = 0 :: Positive Fixnum from 0 to 2^51-2 // // sign = 0, quiet = 1 :: Pointers // // sign = 0, quiet = 0 :: Others // // // === Fixnums === // // Negative fixnums actually represent themselves without needing to go through // any transformation. Only the smallest 52-bit signed negative, -2^51, cannot // be represented, as it would step on forbidden value 1, Negative cqNaN. // // Positive fixnums go through bitsiwe NOT (implemented via an XOR mask here to // make it one operation together with the NaN masking) to avoid the all-zero // payload value, which would step on forbidden value 2, Negative Infinity. // // // === Pointers === // // Pointers are further subdivided as follows based on the remaining 51 bits, // with the first three bits used as a sort of tag: // // 000 :: Pointer to Zisp heap object (string, vector, etc.) // // 001 :: Weak pointer to Zisp heap object // // 01. :: Undefined (may be used by GC to flag pointers for some reason?) // // 1.. :: Foreign pointer (basically, a 50-bit fixnum of another type) // // This means pointers to the Zisp heap are 48 bits. Of those, we only really // need 45, since 64-bit platforms are in practice limited to 48-bit addresses, // and allocations happen at 8-byte boundaries, meaning the least significant 3 // bits are always unset. Thus, we are able to store yet another 3-bit tag in // those 48-bit pointers alongside the actual, multiple-of-8, 48-bit address. // // The forbidden value 3, Positive cqNaN, is avoided thanks to the fact that a // regular Zisp heap pointer can never be null. Weak pointers, which can be // null, avoid stepping on that forbidden value thanks to bit 49 being set. // // Foreign pointers allow storing arbitrary pointers, or integers basically, of // up to 50 bits, without any further definition in Zisp of what they mean. // // // === Other values === // // This 51-bit range is divided as follows, based on the high bits: // // 000 :: Runes // // 001 :: Short string // // 010 :: Unicode code point // // 011 :: Singleton values // // 1.. :: Undefined // // Runes are symbols of 1 to 6 ASCII letters, used to implement reader syntax; // both built-in and extensions. // // Zisp strings are immutable. Any string fitting into 6 bytes or less will be // stored as an immediate value, not requiring any heap allocation or interning. // It's implicitly interned, so to speak. This includes the empty string. // // The null byte serves as a terminator and cannot appear in these strings; a // string that short but actually containing a null byte will need to be heap // allocated like other strings. // // There may also be uninterned strings on the heap that are also as short but // ended up on the heap due to being uninterned. Calling intern on them will // return the equivalent short string as an immediate. // // Unicode code points need a maximum of 21 bits, yet we have 48 available. // This may be exploited for a future extension. // // Similarly, it's extremely unlikely that we will ever need more than a few // dozen singleton values (false, true, null, and so on). As such, this range // of bit patterns may be subdivided in the future. Right now, only the lowest // 8 bits are allowed to be set, with the other 40 being reserved, so there's a // limit of 256 singleton values that can be defined. // // And on top of all that we still have a 50-bit range left! // // The forbidden value 4, Positive Infinity, would be the "empty string rune" // but that isn't allowed anyway, so all is fine. // // Here's the original article explaining the strategy: // // https://tkammer.de/zisp/notes/nan.html // // More about runes: // // https://tkammer.de/zisp/notes/symbols.html // // Note: Packed structs are least-to-most significant, so the order of fields // must be reversed relative to a typical big-endian illustration of the bit // patterns of IEEE 754 double-precision floating point numbers. const std = @import("std"); pub const double = @import("value/double.zig"); pub const fixnum = @import("value/fixnum.zig"); pub const ptr = @import("value/ptr.zig"); pub const rune = @import("value/rune.zig"); pub const sstr = @import("value/sstr.zig"); pub const char = @import("value/char.zig"); pub const boole = @import("value/boole.zig"); pub const nil = @import("value/nil.zig"); pub const eof = @import("value/eof.zig"); pub const pair = @import("value/pair.zig"); // To fill up the u11 exponent part of a NaN. const FILL = 0x7ff; /// Represents a Zisp value/object. pub const Value = packed union { /// To get the value as a regular double. double: f64, /// To get an agnostic value for direct comparison with == i.e. eq?. bits: u64, // Some of the structs below are just for inspection, whereas others are to // initialize a new value of that category as well as read it that way. /// Inspection through the lens of the general IEEE 754 double layout. ieee: packed struct { rest: u51, quiet: bool, exp: u11, sign: bool, }, /// For initializing and reading fixnums. fixnum: packed struct { code: u51, negative: bool, _: u11 = FILL, _is_fixnum: bool = true, }, /// Inspection through the lens of the ptr category. ptr: packed struct { _value: u48, is_weak: bool, _unused: bool, is_foreign: bool, _is_ptr: bool, _: u11, _is_fixnum: bool, }, /// For initializing and reading foreign pointers. fptr: packed struct { value: u50, _is_foreign: bool = true, _is_ptr: bool = true, _: u11 = FILL, _is_fixnum: bool = false, }, /// For initializing and reading Zisp heap pointers. zptr: packed struct { tagged_value: u48, is_weak: bool = false, _unused: bool = false, _is_foreign: bool = false, _is_ptr: bool = true, _: u11 = FILL, _is_fixnum: bool = false, }, /// Inspection as an other (non-fixnum, non-pointer) packed value. other: packed struct { _value: u48, tag: OtherTag, _is_ptr: bool, _: u11, _is_ifxnum: bool, }, /// For initializing and reading runes. rune: packed struct { // actually [6]u8 but packed struct cannot contain arrays name: u48, _tag: OtherTag = .rune, _is_ptr: bool = false, _: u11 = FILL, _is_fixnum: bool = false, }, /// For initializing and reading short strings. sstr: packed struct { // actually [6]u8 but packed struct cannot contain arrays string: u48, _tag: OtherTag = .sstr, _is_ptr: bool = false, _: u11 = FILL, _is_fixnum: bool = false, }, /// For initializing and reading characters. char: packed struct { char: u21, _reserved: u27 = 0, _tag: OtherTag = .char, _is_ptr: bool = false, _: u11 = FILL, _is_fixnum: bool = false, }, /// For initializing and reading misc values aka singletons. misc: packed struct { value: u8, _reserved: u40 = 0, _tag: OtherTag = .misc, _is_ptr: bool = false, _: u11 = FILL, _is_fixnum: bool = false, }, const OtherTag = enum(u3) { rune, sstr, char, misc }; const Self = @This(); /// Hexdumps the value. pub fn dump(self: Self) void { std.debug.dumpHex(std.mem.asBytes(&self)); } // The following aren't type predicates per se, but rather determine which // general category the value is in. The exceptions are fixnum and double, // since those aren't sub-categorized into further types. /// Checks for a Zisp double, including: +nan.0, -nan.0, +inf.0, -inf.0 pub fn isDouble(self: Self) bool { return self.ieee.exp != FILL or self.ieee.rest == 0; } /// Checks for a non-double Zisp value packed into a NaN. pub fn isPacked(self: Self) bool { return !self.isDouble(); } /// Checks for a fixnum. pub fn isFixnum(self: Self) bool { return self.isPacked() and self.ieee.sign; } /// Checks for any kind of pointer. pub fn isPtr(self: Self) bool { return self.isPacked() and !self.ieee.sign and self.ieee.quiet; } /// Checks for a non-double, non-fixnum, non-pointer Zisp value. fn _isOther(self: Self) bool { return self.isPacked() and !self.ieee.sign and !self.ieee.quiet; } /// Checks for any "other" type of value. pub fn isOther(self: Self, tag: OtherTag) bool { return self._isOther() and self.other.tag == tag; } };