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+// Ported from:
+//
+// https://github.com/llvm/llvm-project/commit/d674d96bc56c0f377879d01c9d8dfdaaa7859cdb/compiler-rt/lib/builtins/divdf3.c
+
+const std = @import("std");
+const builtin = @import("builtin");
+
+pub extern fn __divdf3(a: f64, b: f64) f64 {
+ @setRuntimeSafety(builtin.is_test);
+ const Z = @IntType(false, f64.bit_count);
+ const SignedZ = @IntType(true, f64.bit_count);
+
+ const typeWidth = f64.bit_count;
+ const significandBits = std.math.floatMantissaBits(f64);
+ const exponentBits = std.math.floatExponentBits(f64);
+
+ const signBit = (Z(1) << (significandBits + exponentBits));
+ const maxExponent = ((1 << exponentBits) - 1);
+ const exponentBias = (maxExponent >> 1);
+
+ const implicitBit = (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 = @bitCast(Z, std.math.inf(f64));
+
+ const aExponent = @truncate(u32, (@bitCast(Z, a) >> significandBits) & maxExponent);
+ const bExponent = @truncate(u32, (@bitCast(Z, b) >> significandBits) & maxExponent);
+ const quotientSign: Z = (@bitCast(Z, a) ^ @bitCast(Z, b)) & signBit;
+
+ var aSignificand: Z = @bitCast(Z, a) & significandMask;
+ var bSignificand: Z = @bitCast(Z, 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 = @bitCast(Z, a) & absMask;
+ const bAbs: Z = @bitCast(Z, b) & absMask;
+
+ // NaN / anything = qNaN
+ if (aAbs > infRep) return @bitCast(f64, @bitCast(Z, a) | quietBit);
+ // anything / NaN = qNaN
+ if (bAbs > infRep) return @bitCast(f64, @bitCast(Z, b) | quietBit);
+
+ if (aAbs == infRep) {
+ // infinity / infinity = NaN
+ if (bAbs == infRep) {
+ return @bitCast(f64, qnanRep);
+ }
+ // infinity / anything else = +/- infinity
+ else {
+ return @bitCast(f64, aAbs | quotientSign);
+ }
+ }
+
+ // anything else / infinity = +/- 0
+ if (bAbs == infRep) return @bitCast(f64, quotientSign);
+
+ if (aAbs == 0) {
+ // zero / zero = NaN
+ if (bAbs == 0) {
+ return @bitCast(f64, qnanRep);
+ }
+ // zero / anything else = +/- zero
+ else {
+ return @bitCast(f64, quotientSign);
+ }
+ }
+ // anything else / zero = +/- infinity
+ if (bAbs == 0) return @bitCast(f64, 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 = @bitCast(i32, 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(u32, bSignificand >> 21);
+ var recip32 = 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(u32, ~(u64(recip32) *% q31b >> 32) +% 1);
+ recip32 = @truncate(u32, u64(recip32) *% correction32 >> 31);
+ correction32 = @truncate(u32, ~(u64(recip32) *% q31b >> 32) +% 1);
+ recip32 = @truncate(u32, u64(recip32) *% correction32 >> 31);
+ correction32 = @truncate(u32, ~(u64(recip32) *% q31b >> 32) +% 1);
+ recip32 = @truncate(u32, 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(u32, bSignificand << 11);
+ var correction: u64 = undefined;
+ var reciprocal: u64 = undefined;
+ correction = ~(u64(recip32) *% q31b +% (u64(recip32) *% q63blo >> 32)) +% 1;
+ const cHi = @truncate(u32, correction >> 32);
+ const cLo = @truncate(u32, correction);
+ reciprocal = u64(recip32) *% cHi +% (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(f64, infRep | quotientSign);
+ } else if (writtenExponent < 1) {
+ if (writtenExponent == 0) {
+ // Check whether the rounded result is normal.
+ const round = @boolToInt((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(f64, absResult | quotientSign);
+ }
+ }
+ // Flush denormals to zero. In the future, it would be nice to add
+ // code to round them correctly.
+ return @bitCast(f64, quotientSign);
+ } else {
+ const round = @boolToInt((residual << 1) > bSignificand);
+ // Clear the implicit bit
+ var absResult = quotient & significandMask;
+ // Insert the exponent
+ absResult |= @bitCast(Z, SignedZ(writtenExponent)) << significandBits;
+ // Round
+ absResult +%= round;
+ // Insert the sign and return
+ return @bitCast(f64, absResult | quotientSign);
+ }
+}
+
+fn wideMultiply(comptime Z: type, a: Z, b: Z, hi: *Z, lo: *Z) void {
+ @setRuntimeSafety(builtin.is_test);
+ switch (Z) {
+ u32 => {
+ // 32x32 --> 64 bit multiply
+ const product = u64(a) * u64(b);
+ hi.* = @truncate(u32, product >> 32);
+ lo.* = @truncate(u32, product);
+ },
+ u64 => {
+ const S = struct {
+ fn loWord(x: u64) u64 {
+ return @truncate(u32, x);
+ }
+ fn hiWord(x: u64) u64 {
+ return @truncate(u32, x >> 32);
+ }
+ };
+ // 64x64 -> 128 wide multiply for platforms that don't have such an operation;
+ // many 64-bit platforms have this operation, but they tend to have hardware
+ // floating-point, so we don't bother with a special case for them here.
+ // Each of the component 32x32 -> 64 products
+ const plolo: u64 = S.loWord(a) * S.loWord(b);
+ const plohi: u64 = S.loWord(a) * S.hiWord(b);
+ const philo: u64 = S.hiWord(a) * S.loWord(b);
+ const phihi: u64 = S.hiWord(a) * S.hiWord(b);
+ // Sum terms that contribute to lo in a way that allows us to get the carry
+ const r0: u64 = S.loWord(plolo);
+ const r1: u64 = S.hiWord(plolo) +% S.loWord(plohi) +% S.loWord(philo);
+ lo.* = r0 +% (r1 << 32);
+ // Sum terms contributing to hi with the carry from lo
+ hi.* = S.hiWord(plohi) +% S.hiWord(philo) +% S.hiWord(r1) +% phihi;
+ },
+ u128 => {
+ const Word_LoMask = u64(0x00000000ffffffff);
+ const Word_HiMask = u64(0xffffffff00000000);
+ const Word_FullMask = u64(0xffffffffffffffff);
+ const S = struct {
+ fn Word_1(x: u128) u64 {
+ return @truncate(u32, x >> 96);
+ }
+ fn Word_2(x: u128) u64 {
+ return @truncate(u32, x >> 64);
+ }
+ fn Word_3(x: u128) u64 {
+ return @truncate(u32, x >> 32);
+ }
+ fn Word_4(x: u128) u64 {
+ return @truncate(u32, x);
+ }
+ };
+ // 128x128 -> 256 wide multiply for platforms that don't have such an operation;
+ // many 64-bit platforms have this operation, but they tend to have hardware
+ // floating-point, so we don't bother with a special case for them here.
+
+ const product11: u64 = S.Word_1(a) * S.Word_1(b);
+ const product12: u64 = S.Word_1(a) * S.Word_2(b);
+ const product13: u64 = S.Word_1(a) * S.Word_3(b);
+ const product14: u64 = S.Word_1(a) * S.Word_4(b);
+ const product21: u64 = S.Word_2(a) * S.Word_1(b);
+ const product22: u64 = S.Word_2(a) * S.Word_2(b);
+ const product23: u64 = S.Word_2(a) * S.Word_3(b);
+ const product24: u64 = S.Word_2(a) * S.Word_4(b);
+ const product31: u64 = S.Word_3(a) * S.Word_1(b);
+ const product32: u64 = S.Word_3(a) * S.Word_2(b);
+ const product33: u64 = S.Word_3(a) * S.Word_3(b);
+ const product34: u64 = S.Word_3(a) * S.Word_4(b);
+ const product41: u64 = S.Word_4(a) * S.Word_1(b);
+ const product42: u64 = S.Word_4(a) * S.Word_2(b);
+ const product43: u64 = S.Word_4(a) * S.Word_3(b);
+ const product44: u64 = S.Word_4(a) * S.Word_4(b);
+
+ const sum0: u128 = u128(product44);
+ const sum1: u128 = u128(product34) +%
+ u128(product43);
+ const sum2: u128 = u128(product24) +%
+ u128(product33) +%
+ u128(product42);
+ const sum3: u128 = u128(product14) +%
+ u128(product23) +%
+ u128(product32) +%
+ u128(product41);
+ const sum4: u128 = u128(product13) +%
+ u128(product22) +%
+ u128(product31);
+ const sum5: u128 = u128(product12) +%
+ u128(product21);
+ const sum6: u128 = u128(product11);
+
+ const r0: u128 = (sum0 & Word_FullMask) +%
+ ((sum1 & Word_LoMask) << 32);
+ const r1: u128 = (sum0 >> 64) +%
+ ((sum1 >> 32) & Word_FullMask) +%
+ (sum2 & Word_FullMask) +%
+ ((sum3 << 32) & Word_HiMask);
+
+ lo.* = r0 +% (r1 << 64);
+ hi.* = (r1 >> 64) +%
+ (sum1 >> 96) +%
+ (sum2 >> 64) +%
+ (sum3 >> 32) +%
+ sum4 +%
+ (sum5 << 32) +%
+ (sum6 << 64);
+ },
+ else => @compileError("unsupported"),
+ }
+}
+
+fn normalize(comptime T: type, significand: *@IntType(false, T.bit_count)) i32 {
+ @setRuntimeSafety(builtin.is_test);
+ const Z = @IntType(false, T.bit_count);
+ const significandBits = std.math.floatMantissaBits(T);
+ const implicitBit = Z(1) << significandBits;
+
+ const shift = @clz(Z, significand.*) - @clz(Z, implicitBit);
+ significand.* <<= @intCast(std.math.Log2Int(Z), shift);
+ return 1 - shift;
+}
+
+test "import divdf3" {
+ _ = @import("divdf3_test.zig");
+}
generated by cgit v1.2.3 (git 2.39.1) at 2025-12-27 22:04:07 +0000