diff options
Diffstat (limited to 'lib/std/special/compiler_rt/divsf3.zig')
| -rw-r--r-- | lib/std/special/compiler_rt/divsf3.zig | 201 |
1 files changed, 201 insertions, 0 deletions
diff --git a/lib/std/special/compiler_rt/divsf3.zig b/lib/std/special/compiler_rt/divsf3.zig new file mode 100644 index 0000000000..447653fbe1 --- /dev/null +++ b/lib/std/special/compiler_rt/divsf3.zig @@ -0,0 +1,201 @@ +// 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"); +} |
