zig/lib/compiler_rt/divdf3.zig
Andrew Kelley 0556a2ba53 compiler-rt: finish cleanups
Finishes cleanups that I started in other commits in this branch.

 * Use common.linkage for all exports instead of redoing the logic in
   each file.
 * Remove pointless `@setRuntimeSafety` calls.
 * Avoid redundantly exporting multiple versions of functions. For
   example, if PPC wants `ceilf128` then don't also export `ceilq`;
   similarly if ARM wants `__aeabi_ddiv` then don't also export
   `__divdf3`.
 * Use `inline` for helper functions instead of making inline calls at
   callsites.
2022-06-17 18:10:00 -07:00

231 lines
9.1 KiB
Zig

//! 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 is_test = builtin.is_test;
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 });
} else {
@export(__divdf3, .{ .name = "__divdf3", .linkage = common.linkage });
}
}
pub fn __divdf3(a: f64, b: f64) callconv(.C) f64 {
return div(a, b);
}
fn __aeabi_ddiv(a: f64, b: f64) callconv(.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 = @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 = @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(u32, ~(@as(u64, recip32) *% q31b >> 32) +% 1);
recip32 = @truncate(u32, @as(u64, recip32) *% correction32 >> 31);
correction32 = @truncate(u32, ~(@as(u64, recip32) *% q31b >> 32) +% 1);
recip32 = @truncate(u32, @as(u64, recip32) *% correction32 >> 31);
correction32 = @truncate(u32, ~(@as(u64, recip32) *% q31b >> 32) +% 1);
recip32 = @truncate(u32, @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(u32, bSignificand << 11);
var correction: u64 = undefined;
var reciprocal: u64 = undefined;
correction = ~(@as(u64, recip32) *% q31b +% (@as(u64, recip32) *% q63blo >> 32)) +% 1;
const cHi = @truncate(u32, correction >> 32);
const cLo = @truncate(u32, 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(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, @as(SignedZ, writtenExponent)) << significandBits;
// Round
absResult +%= round;
// Insert the sign and return
return @bitCast(f64, absResult | quotientSign);
}
}
test {
_ = @import("divdf3_test.zig");
}