add mulXf3 to compiler-rt

this adds the following functions to compiler-rt:

 * `__mulsf3`
 * `__muldf3`
 * `__multf3`

See #1290

Author: andrewrk

CMakeLists.txt

@@ -662,6 +662,7 @@ set(ZIG_STD_FILES
     "special/compiler_rt/floatuntisf.zig"
     "special/compiler_rt/floatuntitf.zig"
     "special/compiler_rt/muloti4.zig"
+    "special/compiler_rt/mulXf3.zig"
     "special/compiler_rt/multi3.zig"
     "special/compiler_rt/popcountdi2.zig"
     "special/compiler_rt/truncXfYf2.zig"

std/math.zig

@@ -593,7 +593,16 @@ fn testRem() void {
 
 /// Returns the absolute value of the integer parameter.
 /// Result is an unsigned integer.
-pub fn absCast(x: var) @IntType(false, @typeOf(x).bit_count) {
+pub fn absCast(x: var) t: {
+    if (@typeOf(x) == comptime_int) {
+        break :t comptime_int;
+    } else {
+        break :t @IntType(false, @typeOf(x).bit_count);
+    }
+} {
+    if (@typeOf(x) == comptime_int) {
+        return if (x < 0) -x else x;
+    }
     const uint = @IntType(false, @typeOf(x).bit_count);
     if (x >= 0) return @intCast(uint, x);
 
@@ -609,6 +618,8 @@ test "math.absCast" {
 
     testing.expect(absCast(i32(minInt(i32))) == -minInt(i32));
     testing.expect(@typeOf(absCast(i32(minInt(i32)))) == u32);
+
+    testing.expect(absCast(-999) == 999);
 }
 
 /// Returns the negation of the integer parameter.

std/special/compiler_rt.zig

@@ -24,6 +24,10 @@ comptime {
     @export("__addtf3", @import("compiler_rt/addXf3.zig").__addtf3, linkage);
     @export("__subtf3", @import("compiler_rt/addXf3.zig").__subtf3, linkage);
 
+    @export("__mulsf3", @import("compiler_rt/mulXf3.zig").__mulsf3, linkage);
+    @export("__muldf3", @import("compiler_rt/mulXf3.zig").__muldf3, linkage);
+    @export("__multf3", @import("compiler_rt/mulXf3.zig").__multf3, linkage);
+
     @export("__floattitf", @import("compiler_rt/floattitf.zig").__floattitf, linkage);
     @export("__floattidf", @import("compiler_rt/floattidf.zig").__floattidf, linkage);
     @export("__floattisf", @import("compiler_rt/floattisf.zig").__floattisf, linkage);

std/special/compiler_rt/mulXf3.zig

@@ -0,0 +1,285 @@
+// Ported from:
+//
+// https://github.com/llvm/llvm-project/blob/2ffb1b0413efa9a24eb3c49e710e36f92e2cb50b/compiler-rt/lib/builtins/fp_mul_impl.inc
+
+const std = @import("std");
+const builtin = @import("builtin");
+const compiler_rt = @import("../compiler_rt.zig");
+
+pub extern fn __multf3(a: f128, b: f128) f128 {
+    return mulXf3(f128, a, b);
+}
+pub extern fn __muldf3(a: f64, b: f64) f64 {
+    return mulXf3(f64, a, b);
+}
+pub extern fn __mulsf3(a: f32, b: f32) f32 {
+    return mulXf3(f32, a, b);
+}
+
+fn mulXf3(comptime T: type, a: T, b: T) T {
+    const Z = @IntType(false, T.bit_count);
+
+    const typeWidth = T.bit_count;
+    const significandBits = std.math.floatMantissaBits(T);
+    const exponentBits = std.math.floatExponentBits(T);
+
+    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(T));
+
+    const aExponent = @truncate(u32, (@bitCast(Z, a) >> significandBits) & maxExponent);
+    const bExponent = @truncate(u32, (@bitCast(Z, b) >> significandBits) & maxExponent);
+    const productSign: 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(T, @bitCast(Z, a) | quietBit);
+        // anything * NaN = qNaN
+        if (bAbs > infRep) return @bitCast(T, @bitCast(Z, b) | quietBit);
+
+        if (aAbs == infRep) {
+            // infinity * non-zero = +/- infinity
+            if (bAbs != 0) {
+                return @bitCast(T, aAbs | productSign);
+            } else {
+                // infinity * zero = NaN
+                return @bitCast(T, qnanRep);
+            }
+        }
+
+        if (bAbs == infRep) {
+            //? non-zero * infinity = +/- infinity
+            if (aAbs != 0) {
+                return @bitCast(T, bAbs | productSign);
+            } else {
+                // zero * infinity = NaN
+                return @bitCast(T, qnanRep);
+            }
+        }
+
+        // zero * anything = +/- zero
+        if (aAbs == 0) return @bitCast(T, productSign);
+        // anything * zero = +/- zero
+        if (bAbs == 0) return @bitCast(T, productSign);
+
+        // 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(T, &aSignificand);
+        if (bAbs < implicitBit) scale +%= normalize(T, &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;
+
+    // Get the significand of a*b.  Before multiplying the significands, shift
+    // one of them left to left-align it in the field.  Thus, the product will
+    // have (exponentBits + 2) integral digits, all but two of which must be
+    // zero.  Normalizing this result is just a conditional left-shift by one
+    // and bumping the exponent accordingly.
+    var productHi: Z = undefined;
+    var productLo: Z = undefined;
+    wideMultiply(Z, aSignificand, bSignificand << exponentBits, &productHi, &productLo);
+
+    var productExponent: i32 = @bitCast(i32, aExponent +% bExponent) -% exponentBias +% scale;
+
+    // Normalize the significand, adjust exponent if needed.
+    if ((productHi & implicitBit) != 0) {
+        productExponent +%= 1;
+    } else {
+        productHi = (productHi << 1) | (productLo >> (typeWidth - 1));
+        productLo = productLo << 1;
+    }
+
+    // If we have overflowed the type, return +/- infinity.
+    if (productExponent >= maxExponent) return @bitCast(T, infRep | productSign);
+
+    if (productExponent <= 0) {
+        // Result is denormal before rounding
+        //
+        // If the result is so small that it just underflows to zero, return
+        // a zero of the appropriate sign.  Mathematically there is no need to
+        // handle this case separately, but we make it a special case to
+        // simplify the shift logic.
+        const shift: u32 = @truncate(u32, Z(1) -% @bitCast(u32, productExponent));
+        if (shift >= typeWidth) return @bitCast(T, productSign);
+
+        // Otherwise, shift the significand of the result so that the round
+        // bit is the high bit of productLo.
+        wideRightShiftWithSticky(Z, &productHi, &productLo, shift);
+    } else {
+        // Result is normal before rounding; insert the exponent.
+        productHi &= significandMask;
+        productHi |= Z(@bitCast(u32, productExponent)) << significandBits;
+    }
+
+    // Insert the sign of the result:
+    productHi |= productSign;
+
+    // Final rounding.  The final result may overflow to infinity, or underflow
+    // to zero, but those are the correct results in those cases.  We use the
+    // default IEEE-754 round-to-nearest, ties-to-even rounding mode.
+    if (productLo > signBit) productHi +%= 1;
+    if (productLo == signBit) productHi +%= productHi & 1;
+    return @bitCast(T, productHi);
+}
+
+fn wideMultiply(comptime Z: type, a: Z, b: Z, hi: *Z, lo: *Z) void {
+    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 {
+    const Z = @IntType(false, T.bit_count);
+    const significandBits = std.math.floatMantissaBits(T);
+    const implicitBit = Z(1) << significandBits;
+
+    const shift = @clz(significand.*) - @clz(implicitBit);
+    significand.* <<= @intCast(std.math.Log2Int(Z), shift);
+    return 1 - shift;
+}
+
+fn wideRightShiftWithSticky(comptime Z: type, hi: *Z, lo: *Z, count: u32) void {
+    const typeWidth = Z.bit_count;
+    const S = std.math.Log2Int(Z);
+    if (count < typeWidth) {
+        const sticky = @truncate(u8, lo.* << @intCast(S, typeWidth -% count));
+        lo.* = (hi.* << @intCast(S, typeWidth -% count)) | (lo.* >> @intCast(S, count)) | sticky;
+        hi.* = hi.* >> @intCast(S, count);
+    } else if (count < 2 * typeWidth) {
+        const sticky = @truncate(u8, hi.* << @intCast(S, 2 * typeWidth -% count) | lo.*);
+        lo.* = hi.* >> @intCast(S, count -% typeWidth) | sticky;
+        hi.* = 0;
+    } else {
+        const sticky = @truncate(u8, hi.* | lo.*);
+        lo.* = sticky;
+        hi.* = 0;
+    }
+}
+
+test "import mulXf3" {
+    _ = @import("mulXf3_test.zig");
+}