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+// Ported from:
+//
+// https://github.com/llvm/llvm-project/commit/d674d96bc56c0f377879d01c9d8dfdaaa7859cdb/compiler-rt/lib/builtins/divsf3.c
+
+const std = @import("std");
+const builtin = @import("builtin");
+
+pub extern fn __divsf3(a: f32, b: f32) f32 {
+ @setRuntimeSafety(builtin.is_test);
+ const Z = @IntType(false, f32.bit_count);
+
+ const typeWidth = f32.bit_count;
+ const significandBits = std.math.floatMantissaBits(f32);
+ const exponentBits = std.math.floatExponentBits(f32);
+
+ 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(f32));
+
+ 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(f32, @bitCast(Z, a) | quietBit);
+ // anything / NaN = qNaN
+ if (bAbs > infRep) return @bitCast(f32, @bitCast(Z, b) | quietBit);
+
+ if (aAbs == infRep) {
+ // infinity / infinity = NaN
+ if (bAbs == infRep) {
+ return @bitCast(f32, qnanRep);
+ }
+ // infinity / anything else = +/- infinity
+ else {
+ return @bitCast(f32, aAbs | quotientSign);
+ }
+ }
+
+ // anything else / infinity = +/- 0
+ if (bAbs == infRep) return @bitCast(f32, quotientSign);
+
+ if (aAbs == 0) {
+ // zero / zero = NaN
+ if (bAbs == 0) {
+ return @bitCast(f32, qnanRep);
+ }
+ // zero / anything else = +/- zero
+ else {
+ return @bitCast(f32, quotientSign);
+ }
+ }
+ // anything else / zero = +/- infinity
+ if (bAbs == 0) return @bitCast(f32, 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(f32, &aSignificand);
+ if (bAbs < implicitBit) scale -%= normalize(f32, &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 = bSignificand << 8;
+ var reciprocal = 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 correction: u32 = undefined;
+ correction = @truncate(u32, ~(u64(reciprocal) *% q31b >> 32) +% 1);
+ reciprocal = @truncate(u32, u64(reciprocal) *% correction >> 31);
+ correction = @truncate(u32, ~(u64(reciprocal) *% q31b >> 32) +% 1);
+ reciprocal = @truncate(u32, u64(reciprocal) *% correction >> 31);
+ correction = @truncate(u32, ~(u64(reciprocal) *% q31b >> 32) +% 1);
+ reciprocal = @truncate(u32, u64(reciprocal) *% correction >> 31);
+
+ // Exhaustive testing shows that the error in reciprocal after three steps
+ // is in the interval [-0x1.f58108p-31, 0x1.d0e48cp-29], in line with our
+ // expectations. We bump the reciprocal by a tiny value to force the error
+ // to be strictly positive (in the range [0x1.4fdfp-37,0x1.287246p-29], to
+ // be specific). This also causes 1/1 to give a sensible approximation
+ // instead of zero (due to overflow).
+ reciprocal -%= 2;
+
+ // The numerical reciprocal is accurate to within 2^-28, lies in the
+ // interval [0x1.000000eep-1, 0x1.fffffffcp-1], and is strictly smaller
+ // than the true reciprocal of b. Multiplying a by this reciprocal thus
+ // gives a numerical q = a/b in Q24 with the following properties:
+ //
+ // 1. q < a/b
+ // 2. q is in the interval [0x1.000000eep-1, 0x1.fffffffcp0)
+ // 3. the error in q is at most 2^-24 + 2^-27 -- the 2^24 term comes
+ // from the fact that we truncate the product, and the 2^27 term
+ // is the error in the reciprocal of b scaled by the maximum
+ // possible value of a. As a consequence of this error bound,
+ // either q or nextafter(q) is the correctly rounded
+ var quotient: Z = @truncate(u32, u64(reciprocal) *% (aSignificand << 1) >> 32);
+
+ // 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 << 24) -% quotient *% bSignificand;
+ quotientExponent -%= 1;
+ } else {
+ quotient >>= 1;
+ residual = (aSignificand << 23) -% quotient *% bSignificand;
+ }
+
+ const writtenExponent = quotientExponent +% exponentBias;
+
+ if (writtenExponent >= maxExponent) {
+ // If we have overflowed the exponent, return infinity.
+ return @bitCast(f32, 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(f32, absResult | quotientSign);
+ }
+ }
+ // Flush denormals to zero. In the future, it would be nice to add
+ // code to round them correctly.
+ return @bitCast(f32, quotientSign);
+ } else {
+ const round = @boolToInt((residual << 1) > bSignificand);
+ // Clear the implicit bit
+ var absResult = quotient & significandMask;
+ // Insert the exponent
+ absResult |= @bitCast(Z, writtenExponent) << significandBits;
+ // Round
+ absResult +%= round;
+ // Insert the sign and return
+ return @bitCast(f32, absResult | quotientSign);
+ }
+}
+
+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 divsf3" {
+ _ = @import("divsf3_test.zig");
+}