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justinbalexanderandrewrk
justinbalexander
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andrewrk
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Add divdf3 to compiler_rt
Also adds __aeabi_ddiv for arm32 targets
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‎CMakeLists.txt

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Original file line numberDiff line numberDiff line change
@@ -633,6 +633,7 @@ set(ZIG_STD_FILES
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"special/compiler_rt/aullrem.zig"
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"special/compiler_rt/comparetf2.zig"
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"special/compiler_rt/divsf3.zig"
636+
"special/compiler_rt/divdf3.zig"
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"special/compiler_rt/divti3.zig"
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"special/compiler_rt/extendXfYf2.zig"
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"special/compiler_rt/fixdfdi.zig"

‎std/special/compiler_rt.zig

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@@ -33,6 +33,7 @@ comptime {
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@export("__multf3", @import("compiler_rt/mulXf3.zig").__multf3, linkage);
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@export("__divsf3", @import("compiler_rt/divsf3.zig").__divsf3, linkage);
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@export("__divdf3", @import("compiler_rt/divdf3.zig").__divdf3, linkage);
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@export("__floattitf", @import("compiler_rt/floattitf.zig").__floattitf, linkage);
3839
@export("__floattidf", @import("compiler_rt/floattidf.zig").__floattidf, linkage);
@@ -142,6 +143,7 @@ comptime {
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@export("__aeabi_d2iz", @import("compiler_rt/fixdfsi.zig").__fixdfsi, linkage);
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@export("__aeabi_fdiv", @import("compiler_rt/divsf3.zig").__divsf3, linkage);
146+
@export("__aeabi_ddiv", @import("compiler_rt/divdf3.zig").__divdf3, linkage);
145147
}
146148
if (builtin.os == builtin.Os.windows) {
147149
switch (builtin.arch) {

‎std/special/compiler_rt/divdf3.zig

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// Ported from:
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//
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// https://github.com/llvm/llvm-project/commit/d674d96bc56c0f377879d01c9d8dfdaaa7859cdb/compiler-rt/lib/builtins/divdf3.c
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const std = @import("std");
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const builtin = @import("builtin");
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pub extern fn __divdf3(a: f64, b: f64) f64 {
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@setRuntimeSafety(builtin.is_test);
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const Z = @IntType(false, f64.bit_count);
11+
const SignedZ = @IntType(true, f64.bit_count);
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const typeWidth = f64.bit_count;
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const significandBits = std.math.floatMantissaBits(f64);
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const exponentBits = std.math.floatExponentBits(f64);
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const signBit = (Z(1) << (significandBits + exponentBits));
18+
const maxExponent = ((1 << exponentBits) - 1);
19+
const exponentBias = (maxExponent >> 1);
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const implicitBit = (Z(1) << significandBits);
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const quietBit = implicitBit >> 1;
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const significandMask = implicitBit - 1;
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const absMask = signBit - 1;
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const exponentMask = absMask ^ significandMask;
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const qnanRep = exponentMask | quietBit;
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const infRep = @bitCast(Z, std.math.inf(f64));
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const aExponent = @truncate(u32, (@bitCast(Z, a) >> significandBits) & maxExponent);
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const bExponent = @truncate(u32, (@bitCast(Z, b) >> significandBits) & maxExponent);
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const quotientSign: Z = (@bitCast(Z, a) ^ @bitCast(Z, b)) & signBit;
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var aSignificand: Z = @bitCast(Z, a) & significandMask;
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var bSignificand: Z = @bitCast(Z, b) & significandMask;
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var scale: i32 = 0;
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// Detect if a or b is zero, denormal, infinity, or NaN.
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if (aExponent -% 1 >= maxExponent -% 1 or bExponent -% 1 >= maxExponent -% 1) {
40+
const aAbs: Z = @bitCast(Z, a) & absMask;
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const bAbs: Z = @bitCast(Z, b) & absMask;
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// NaN / anything = qNaN
44+
if (aAbs > infRep) return @bitCast(f64, @bitCast(Z, a) | quietBit);
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// anything / NaN = qNaN
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if (bAbs > infRep) return @bitCast(f64, @bitCast(Z, b) | quietBit);
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if (aAbs == infRep) {
49+
// infinity / infinity = NaN
50+
if (bAbs == infRep) {
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return @bitCast(f64, qnanRep);
52+
}
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// infinity / anything else = +/- infinity
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else {
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return @bitCast(f64, aAbs | quotientSign);
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}
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}
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// anything else / infinity = +/- 0
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if (bAbs == infRep) return @bitCast(f64, quotientSign);
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if (aAbs == 0) {
63+
// zero / zero = NaN
64+
if (bAbs == 0) {
65+
return @bitCast(f64, qnanRep);
66+
}
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// zero / anything else = +/- zero
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else {
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return @bitCast(f64, quotientSign);
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}
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}
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// anything else / zero = +/- infinity
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if (bAbs == 0) return @bitCast(f64, infRep | quotientSign);
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// one or both of a or b is denormal, the other (if applicable) is a
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// normal number. Renormalize one or both of a and b, and set scale to
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// include the necessary exponent adjustment.
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if (aAbs < implicitBit) scale +%= normalize(f64, &aSignificand);
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if (bAbs < implicitBit) scale -%= normalize(f64, &bSignificand);
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}
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// Or in the implicit significand bit. (If we fell through from the
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// denormal path it was already set by normalize( ), but setting it twice
84+
// won't hurt anything.)
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aSignificand |= implicitBit;
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bSignificand |= implicitBit;
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var quotientExponent: i32 = @bitCast(i32, aExponent -% bExponent) +% scale;
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// Align the significand of b as a Q31 fixed-point number in the range
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// [1, 2.0) and get a Q32 approximate reciprocal using a small minimax
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// polynomial approximation: reciprocal = 3/4 + 1/sqrt(2) - b/2. This
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// is accurate to about 3.5 binary digits.
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const q31b: u32 = @truncate(u32, bSignificand >> 21);
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var recip32 = u32(0x7504f333) -% q31b;
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// Now refine the reciprocal estimate using a Newton-Raphson iteration:
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//
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// x1 = x0 * (2 - x0 * b)
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//
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// This doubles the number of correct binary digits in the approximation
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// with each iteration, so after three iterations, we have about 28 binary
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// digits of accuracy.
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var correction32: u32 = undefined;
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correction32 = @truncate(u32, ~(u64(recip32) *% q31b >> 32) +% 1);
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recip32 = @truncate(u32, u64(recip32) *% correction32 >> 31);
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correction32 = @truncate(u32, ~(u64(recip32) *% q31b >> 32) +% 1);
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recip32 = @truncate(u32, u64(recip32) *% correction32 >> 31);
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correction32 = @truncate(u32, ~(u64(recip32) *% q31b >> 32) +% 1);
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recip32 = @truncate(u32, u64(recip32) *% correction32 >> 31);
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// recip32 might have overflowed to exactly zero in the preceding
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// computation if the high word of b is exactly 1.0. This would sabotage
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// the full-width final stage of the computation that follows, so we adjust
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// recip32 downward by one bit.
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recip32 -%= 1;
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// We need to perform one more iteration to get us to 56 binary digits;
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// The last iteration needs to happen with extra precision.
119+
const q63blo: u32 = @truncate(u32, bSignificand << 11);
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var correction: u64 = undefined;
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var reciprocal: u64 = undefined;
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correction = ~(u64(recip32) *% q31b +% (u64(recip32) *% q63blo >> 32)) +% 1;
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const cHi = @truncate(u32, correction >> 32);
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const cLo = @truncate(u32, correction);
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reciprocal = u64(recip32) *% cHi +% (u64(recip32) *% cLo >> 32);
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// We already adjusted the 32-bit estimate, now we need to adjust the final
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// 64-bit reciprocal estimate downward to ensure that it is strictly smaller
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// than the infinitely precise exact reciprocal. Because the computation
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// of the Newton-Raphson step is truncating at every step, this adjustment
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// is small; most of the work is already done.
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reciprocal -%= 2;
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// The numerical reciprocal is accurate to within 2^-56, lies in the
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// interval [0.5, 1.0), and is strictly smaller than the true reciprocal
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// of b. Multiplying a by this reciprocal thus gives a numerical q = a/b
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// in Q53 with the following properties:
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//
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// 1. q < a/b
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// 2. q is in the interval [0.5, 2.0)
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// 3. the error in q is bounded away from 2^-53 (actually, we have a
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// couple of bits to spare, but this is all we need).
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// We need a 64 x 64 multiply high to compute q, which isn't a basic
145+
// operation in C, so we need to be a little bit fussy.
146+
var quotient: Z = undefined;
147+
var quotientLo: Z = undefined;
148+
wideMultiply(Z, aSignificand << 2, reciprocal, &quotient, &quotientLo);
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// Two cases: quotient is in [0.5, 1.0) or quotient is in [1.0, 2.0).
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// In either case, we are going to compute a residual of the form
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//
153+
// r = a - q*b
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//
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// We know from the construction of q that r satisfies:
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//
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// 0 <= r < ulp(q)*b
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//
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// if r is greater than 1/2 ulp(q)*b, then q rounds up. Otherwise, we
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// already have the correct result. The exact halfway case cannot occur.
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// We also take this time to right shift quotient if it falls in the [1,2)
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// range and adjust the exponent accordingly.
163+
var residual: Z = undefined;
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if (quotient < (implicitBit << 1)) {
165+
residual = (aSignificand << 53) -% quotient *% bSignificand;
166+
quotientExponent -%= 1;
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} else {
168+
quotient >>= 1;
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residual = (aSignificand << 52) -% quotient *% bSignificand;
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}
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172+
const writtenExponent = quotientExponent +% exponentBias;
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174+
if (writtenExponent >= maxExponent) {
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// If we have overflowed the exponent, return infinity.
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return @bitCast(f64, infRep | quotientSign);
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} else if (writtenExponent < 1) {
178+
if (writtenExponent == 0) {
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// Check whether the rounded result is normal.
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const round = @boolToInt((residual << 1) > bSignificand);
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// Clear the implicit bit.
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var absResult = quotient & significandMask;
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// Round.
184+
absResult += round;
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if ((absResult & ~significandMask) != 0) {
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// The rounded result is normal; return it.
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return @bitCast(f64, absResult | quotientSign);
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}
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}
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// Flush denormals to zero. In the future, it would be nice to add
191+
// code to round them correctly.
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return @bitCast(f64, quotientSign);
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} else {
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const round = @boolToInt((residual << 1) > bSignificand);
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// Clear the implicit bit
196+
var absResult = quotient & significandMask;
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// Insert the exponent
198+
absResult |= @bitCast(Z, SignedZ(writtenExponent)) << significandBits;
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// Round
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absResult +%= round;
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// Insert the sign and return
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return @bitCast(f64, absResult | quotientSign);
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}
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}
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fn wideMultiply(comptime Z: type, a: Z, b: Z, hi: *Z, lo: *Z) void {
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@setRuntimeSafety(builtin.is_test);
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switch (Z) {
209+
u32 => {
210+
// 32x32 --> 64 bit multiply
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const product = u64(a) * u64(b);
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hi.* = @truncate(u32, product >> 32);
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lo.* = @truncate(u32, product);
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},
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u64 => {
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const S = struct {
217+
fn loWord(x: u64) u64 {
218+
return @truncate(u32, x);
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}
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fn hiWord(x: u64) u64 {
221+
return @truncate(u32, x >> 32);
222+
}
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};
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// 64x64 -> 128 wide multiply for platforms that don't have such an operation;
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// many 64-bit platforms have this operation, but they tend to have hardware
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// floating-point, so we don't bother with a special case for them here.
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// Each of the component 32x32 -> 64 products
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const plolo: u64 = S.loWord(a) * S.loWord(b);
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const plohi: u64 = S.loWord(a) * S.hiWord(b);
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const philo: u64 = S.hiWord(a) * S.loWord(b);
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const phihi: u64 = S.hiWord(a) * S.hiWord(b);
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// Sum terms that contribute to lo in a way that allows us to get the carry
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const r0: u64 = S.loWord(plolo);
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const r1: u64 = S.hiWord(plolo) +% S.loWord(plohi) +% S.loWord(philo);
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lo.* = r0 +% (r1 << 32);
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// Sum terms contributing to hi with the carry from lo
237+
hi.* = S.hiWord(plohi) +% S.hiWord(philo) +% S.hiWord(r1) +% phihi;
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},
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u128 => {
240+
const Word_LoMask = u64(0x00000000ffffffff);
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const Word_HiMask = u64(0xffffffff00000000);
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const Word_FullMask = u64(0xffffffffffffffff);
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const S = struct {
244+
fn Word_1(x: u128) u64 {
245+
return @truncate(u32, x >> 96);
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}
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fn Word_2(x: u128) u64 {
248+
return @truncate(u32, x >> 64);
249+
}
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fn Word_3(x: u128) u64 {
251+
return @truncate(u32, x >> 32);
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}
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fn Word_4(x: u128) u64 {
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return @truncate(u32, x);
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}
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};
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// 128x128 -> 256 wide multiply for platforms that don't have such an operation;
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// many 64-bit platforms have this operation, but they tend to have hardware
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// floating-point, so we don't bother with a special case for them here.
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const product11: u64 = S.Word_1(a) * S.Word_1(b);
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const product12: u64 = S.Word_1(a) * S.Word_2(b);
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const product13: u64 = S.Word_1(a) * S.Word_3(b);
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const product14: u64 = S.Word_1(a) * S.Word_4(b);
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const product21: u64 = S.Word_2(a) * S.Word_1(b);
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const product22: u64 = S.Word_2(a) * S.Word_2(b);
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const product23: u64 = S.Word_2(a) * S.Word_3(b);
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const product24: u64 = S.Word_2(a) * S.Word_4(b);
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const product31: u64 = S.Word_3(a) * S.Word_1(b);
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const product32: u64 = S.Word_3(a) * S.Word_2(b);
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const product33: u64 = S.Word_3(a) * S.Word_3(b);
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const product34: u64 = S.Word_3(a) * S.Word_4(b);
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const product41: u64 = S.Word_4(a) * S.Word_1(b);
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const product42: u64 = S.Word_4(a) * S.Word_2(b);
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const product43: u64 = S.Word_4(a) * S.Word_3(b);
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const product44: u64 = S.Word_4(a) * S.Word_4(b);
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const sum0: u128 = u128(product44);
279+
const sum1: u128 = u128(product34) +%
280+
u128(product43);
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const sum2: u128 = u128(product24) +%
282+
u128(product33) +%
283+
u128(product42);
284+
const sum3: u128 = u128(product14) +%
285+
u128(product23) +%
286+
u128(product32) +%
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u128(product41);
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const sum4: u128 = u128(product13) +%
289+
u128(product22) +%
290+
u128(product31);
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const sum5: u128 = u128(product12) +%
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u128(product21);
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const sum6: u128 = u128(product11);
294+
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const r0: u128 = (sum0 & Word_FullMask) +%
296+
((sum1 & Word_LoMask) << 32);
297+
const r1: u128 = (sum0 >> 64) +%
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((sum1 >> 32) & Word_FullMask) +%
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(sum2 & Word_FullMask) +%
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((sum3 << 32) & Word_HiMask);
301+
302+
lo.* = r0 +% (r1 << 64);
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hi.* = (r1 >> 64) +%
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(sum1 >> 96) +%
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(sum2 >> 64) +%
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(sum3 >> 32) +%
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sum4 +%
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(sum5 << 32) +%
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(sum6 << 64);
310+
},
311+
else => @compileError("unsupported"),
312+
}
313+
}
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315+
fn normalize(comptime T: type, significand: *@IntType(false, T.bit_count)) i32 {
316+
@setRuntimeSafety(builtin.is_test);
317+
const Z = @IntType(false, T.bit_count);
318+
const significandBits = std.math.floatMantissaBits(T);
319+
const implicitBit = Z(1) << significandBits;
320+
321+
const shift = @clz(significand.*) - @clz(implicitBit);
322+
significand.* <<= @intCast(std.math.Log2Int(Z), shift);
323+
return 1 - shift;
324+
}
325+
326+
test "import divdf3" {
327+
_ = @import("divdf3_test.zig");
328+
}

‎std/special/compiler_rt/divdf3_test.zig

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// Ported from:
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//
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// https://github.com/llvm/llvm-project/commit/d674d96bc56c0f377879d01c9d8dfdaaa7859cdb/compiler-rt/test/builtins/Unit/divdf3_test.c
4+
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const __divdf3 = @import("divdf3.zig").__divdf3;
6+
const testing = @import("std").testing;
7+
8+
fn compareResultD(result: f64, expected: u64) bool {
9+
const rep = @bitCast(u64, result);
10+
11+
if (rep == expected) {
12+
return true;
13+
}
14+
// test other possible NaN representation(signal NaN)
15+
else if (expected == 0x7ff8000000000000) {
16+
if ((rep & 0x7ff0000000000000) == 0x7ff0000000000000 and
17+
(rep & 0xfffffffffffff) > 0)
18+
{
19+
return true;
20+
}
21+
}
22+
return false;
23+
}
24+
25+
fn test__divdf3(a: f64, b: f64, expected: u64) void {
26+
const x = __divdf3(a, b);
27+
const ret = compareResultD(x, expected);
28+
testing.expect(ret == true);
29+
}
30+
31+
test "divdf3" {
32+
test__divdf3(1.0, 3.0, 0x3fd5555555555555);
33+
test__divdf3(4.450147717014403e-308, 2.0, 0x10000000000000);
34+
}

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