zig

divdf3.zig (9366B) - Raw

---

 //! Ported from:
 //!
 //! https://github.com/llvm/llvm-project/commit/d674d96bc56c0f377879d01c9d8dfdaaa7859cdb/compiler-rt/lib/builtins/divdf3.c
 
 const std = @import("std");
 const builtin = @import("builtin");
 const arch = builtin.cpu.arch;
 const common = @import("common.zig");
 
 const normalize = common.normalize;
 const wideMultiply = common.wideMultiply;
 
 pub const panic = common.panic;
 
 comptime {
     if (common.want_aeabi) {
         @export(&__aeabi_ddiv, .{ .name = "__aeabi_ddiv", .linkage = common.linkage, .visibility = common.visibility });
     } else {
         @export(&__divdf3, .{ .name = "__divdf3", .linkage = common.linkage, .visibility = common.visibility });
     }
 }
 
 pub fn __divdf3(a: f64, b: f64) callconv(.c) f64 {
     return div(a, b);
 }
 
 fn __aeabi_ddiv(a: f64, b: f64) callconv(.{ .arm_aapcs = .{} }) f64 {
     return div(a, b);
 }
 
 inline fn div(a: f64, b: f64) f64 {
     const Z = std.meta.Int(.unsigned, 64);
     const SignedZ = std.meta.Int(.signed, 64);
 
     const significandBits = std.math.floatMantissaBits(f64);
     const exponentBits = std.math.floatExponentBits(f64);
 
     const signBit = (@as(Z, 1) << (significandBits + exponentBits));
     const maxExponent = ((1 << exponentBits) - 1);
     const exponentBias = (maxExponent >> 1);
 
     const implicitBit = (@as(Z, 1) << significandBits);
     const quietBit = implicitBit >> 1;
     const significandMask = implicitBit - 1;
 
     const absMask = signBit - 1;
     const exponentMask = absMask ^ significandMask;
     const qnanRep = exponentMask | quietBit;
     const infRep = @as(Z, @bitCast(std.math.inf(f64)));
 
     const aExponent: u32 = @truncate((@as(Z, @bitCast(a)) >> significandBits) & maxExponent);
     const bExponent: u32 = @truncate((@as(Z, @bitCast(b)) >> significandBits) & maxExponent);
     const quotientSign: Z = (@as(Z, @bitCast(a)) ^ @as(Z, @bitCast(b))) & signBit;
 
     var aSignificand: Z = @as(Z, @bitCast(a)) & significandMask;
     var bSignificand: Z = @as(Z, @bitCast(b)) & significandMask;
     var scale: i32 = 0;
 
     // Detect if a or b is zero, denormal, infinity, or NaN.
     if (aExponent -% 1 >= maxExponent - 1 or bExponent -% 1 >= maxExponent - 1) {
         const aAbs: Z = @as(Z, @bitCast(a)) & absMask;
         const bAbs: Z = @as(Z, @bitCast(b)) & absMask;
 
         // NaN / anything = qNaN
         if (aAbs > infRep) return @bitCast(@as(Z, @bitCast(a)) | quietBit);
         // anything / NaN = qNaN
         if (bAbs > infRep) return @bitCast(@as(Z, @bitCast(b)) | quietBit);
 
         if (aAbs == infRep) {
             // infinity / infinity = NaN
             if (bAbs == infRep) {
                 return @bitCast(qnanRep);
             }
             // infinity / anything else = +/- infinity
             else {
                 return @bitCast(aAbs | quotientSign);
             }
         }
 
         // anything else / infinity = +/- 0
         if (bAbs == infRep) return @bitCast(quotientSign);
 
         if (aAbs == 0) {
             // zero / zero = NaN
             if (bAbs == 0) {
                 return @bitCast(qnanRep);
             }
             // zero / anything else = +/- zero
             else {
                 return @bitCast(quotientSign);
             }
         }
         // anything else / zero = +/- infinity
         if (bAbs == 0) return @bitCast(infRep | quotientSign);
 
         // one or both of a or b is denormal, the other (if applicable) is a
         // normal number.  Renormalize one or both of a and b, and set scale to
         // include the necessary exponent adjustment.
         if (aAbs < implicitBit) scale +%= normalize(f64, &aSignificand);
         if (bAbs < implicitBit) scale -%= normalize(f64, &bSignificand);
     }
 
     // Or in the implicit significand bit.  (If we fell through from the
     // denormal path it was already set by normalize( ), but setting it twice
     // won't hurt anything.)
     aSignificand |= implicitBit;
     bSignificand |= implicitBit;
     var quotientExponent: i32 = @as(i32, @bitCast(aExponent -% bExponent)) +% scale;
 
     // Align the significand of b as a Q31 fixed-point number in the range
     // [1, 2.0) and get a Q32 approximate reciprocal using a small minimax
     // polynomial approximation: reciprocal = 3/4 + 1/sqrt(2) - b/2.  This
     // is accurate to about 3.5 binary digits.
     const q31b: u32 = @truncate(bSignificand >> 21);
     var recip32 = @as(u32, 0x7504f333) -% q31b;
 
     // Now refine the reciprocal estimate using a Newton-Raphson iteration:
     //
     //     x1 = x0 * (2 - x0 * b)
     //
     // This doubles the number of correct binary digits in the approximation
     // with each iteration, so after three iterations, we have about 28 binary
     // digits of accuracy.
     var correction32: u32 = undefined;
     correction32 = @truncate(~(@as(u64, recip32) *% q31b >> 32) +% 1);
     recip32 = @truncate(@as(u64, recip32) *% correction32 >> 31);
     correction32 = @truncate(~(@as(u64, recip32) *% q31b >> 32) +% 1);
     recip32 = @truncate(@as(u64, recip32) *% correction32 >> 31);
     correction32 = @truncate(~(@as(u64, recip32) *% q31b >> 32) +% 1);
     recip32 = @truncate(@as(u64, recip32) *% correction32 >> 31);
 
     // recip32 might have overflowed to exactly zero in the preceding
     // computation if the high word of b is exactly 1.0.  This would sabotage
     // the full-width final stage of the computation that follows, so we adjust
     // recip32 downward by one bit.
     recip32 -%= 1;
 
     // We need to perform one more iteration to get us to 56 binary digits;
     // The last iteration needs to happen with extra precision.
     const q63blo: u32 = @truncate(bSignificand << 11);
     var correction: u64 = undefined;
     var reciprocal: u64 = undefined;
     correction = ~(@as(u64, recip32) *% q31b +% (@as(u64, recip32) *% q63blo >> 32)) +% 1;
     const cHi: u32 = @truncate(correction >> 32);
     const cLo: u32 = @truncate(correction);
     reciprocal = @as(u64, recip32) *% cHi +% (@as(u64, recip32) *% cLo >> 32);
 
     // We already adjusted the 32-bit estimate, now we need to adjust the final
     // 64-bit reciprocal estimate downward to ensure that it is strictly smaller
     // than the infinitely precise exact reciprocal.  Because the computation
     // of the Newton-Raphson step is truncating at every step, this adjustment
     // is small; most of the work is already done.
     reciprocal -%= 2;
 
     // The numerical reciprocal is accurate to within 2^-56, lies in the
     // interval [0.5, 1.0), and is strictly smaller than the true reciprocal
     // of b.  Multiplying a by this reciprocal thus gives a numerical q = a/b
     // in Q53 with the following properties:
     //
     //    1. q < a/b
     //    2. q is in the interval [0.5, 2.0)
     //    3. the error in q is bounded away from 2^-53 (actually, we have a
     //       couple of bits to spare, but this is all we need).
 
     // We need a 64 x 64 multiply high to compute q, which isn't a basic
     // operation in C, so we need to be a little bit fussy.
     var quotient: Z = undefined;
     var quotientLo: Z = undefined;
     wideMultiply(Z, aSignificand << 2, reciprocal, &quotient, &quotientLo);
 
     // Two cases: quotient is in [0.5, 1.0) or quotient is in [1.0, 2.0).
     // In either case, we are going to compute a residual of the form
     //
     //     r = a - q*b
     //
     // We know from the construction of q that r satisfies:
     //
     //     0 <= r < ulp(q)*b
     //
     // if r is greater than 1/2 ulp(q)*b, then q rounds up.  Otherwise, we
     // already have the correct result.  The exact halfway case cannot occur.
     // We also take this time to right shift quotient if it falls in the [1,2)
     // range and adjust the exponent accordingly.
     var residual: Z = undefined;
     if (quotient < (implicitBit << 1)) {
         residual = (aSignificand << 53) -% quotient *% bSignificand;
         quotientExponent -%= 1;
     } else {
         quotient >>= 1;
         residual = (aSignificand << 52) -% quotient *% bSignificand;
     }
 
     const writtenExponent = quotientExponent +% exponentBias;
 
     if (writtenExponent >= maxExponent) {
         // If we have overflowed the exponent, return infinity.
         return @bitCast(infRep | quotientSign);
     } else if (writtenExponent < 1) {
         if (writtenExponent == 0) {
             // Check whether the rounded result is normal.
             const round = @intFromBool((residual << 1) > bSignificand);
             // Clear the implicit bit.
             var absResult = quotient & significandMask;
             // Round.
             absResult += round;
             if ((absResult & ~significandMask) != 0) {
                 // The rounded result is normal; return it.
                 return @bitCast(absResult | quotientSign);
             }
         }
         // Flush denormals to zero.  In the future, it would be nice to add
         // code to round them correctly.
         return @bitCast(quotientSign);
     } else {
         const round = @intFromBool((residual << 1) > bSignificand);
         // Clear the implicit bit
         var absResult = quotient & significandMask;
         // Insert the exponent
         absResult |= @as(Z, @bitCast(@as(SignedZ, writtenExponent))) << significandBits;
         // Round
         absResult +%= round;
         // Insert the sign and return
         return @bitCast(absResult | quotientSign);
     }
 }
 
 test {
     _ = @import("divdf3_test.zig");
 }