Move original compiler-rt functions (libgcc replacement) to lib/builtins directory

git-svn-id: https://llvm.org/svn/llvm-project/compiler-rt/trunk@201393 91177308-0d34-0410-b5e6-96231b3b80d8

1 files changed, 168 insertions, 0 deletions

diff --git a/lib/builtins/divsf3.c b/lib/builtins/divsf3.c
new file mode 100644
index 000000000..c91c648fa
--- /dev/null
+++ b/lib/builtins/divsf3.c
@@ -0,0 +1,168 @@
+//===-- lib/divsf3.c - Single-precision division ------------------*- C -*-===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is dual licensed under the MIT and the University of Illinois Open
+// Source Licenses. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// This file implements single-precision soft-float division
+// with the IEEE-754 default rounding (to nearest, ties to even).
+//
+// For simplicity, this implementation currently flushes denormals to zero.
+// It should be a fairly straightforward exercise to implement gradual
+// underflow with correct rounding.
+//
+//===----------------------------------------------------------------------===//
+
+#define SINGLE_PRECISION
+#include "fp_lib.h"
+
+ARM_EABI_FNALIAS(fdiv, divsf3)
+
+fp_t __divsf3(fp_t a, fp_t b) {
+    
+    const unsigned int aExponent = toRep(a) >> significandBits & maxExponent;
+    const unsigned int bExponent = toRep(b) >> significandBits & maxExponent;
+    const rep_t quotientSign = (toRep(a) ^ toRep(b)) & signBit;
+    
+    rep_t aSignificand = toRep(a) & significandMask;
+    rep_t bSignificand = toRep(b) & significandMask;
+    int scale = 0;
+    
+    // Detect if a or b is zero, denormal, infinity, or NaN.
+    if (aExponent-1U >= maxExponent-1U || bExponent-1U >= maxExponent-1U) {
+        
+        const rep_t aAbs = toRep(a) & absMask;
+        const rep_t bAbs = toRep(b) & absMask;
+        
+        // NaN / anything = qNaN
+        if (aAbs > infRep) return fromRep(toRep(a) | quietBit);
+        // anything / NaN = qNaN
+        if (bAbs > infRep) return fromRep(toRep(b) | quietBit);
+        
+        if (aAbs == infRep) {
+            // infinity / infinity = NaN
+            if (bAbs == infRep) return fromRep(qnanRep);
+            // infinity / anything else = +/- infinity
+            else return fromRep(aAbs | quotientSign);
+        }
+        
+        // anything else / infinity = +/- 0
+        if (bAbs == infRep) return fromRep(quotientSign);
+        
+        if (!aAbs) {
+            // zero / zero = NaN
+            if (!bAbs) return fromRep(qnanRep);
+            // zero / anything else = +/- zero
+            else return fromRep(quotientSign);
+        }
+        // anything else / zero = +/- infinity
+        if (!bAbs) return fromRep(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(&aSignificand);
+        if (bAbs < implicitBit) scale -= normalize(&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;
+    int quotientExponent = 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.
+    uint32_t q31b = bSignificand << 8;
+    uint32_t reciprocal = UINT32_C(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.
+    uint32_t correction;
+    correction = -((uint64_t)reciprocal * q31b >> 32);
+    reciprocal = (uint64_t)reciprocal * correction >> 31;
+    correction = -((uint64_t)reciprocal * q31b >> 32);
+    reciprocal = (uint64_t)reciprocal * correction >> 31;
+    correction = -((uint64_t)reciprocal * q31b >> 32);
+    reciprocal = (uint64_t)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 
+    rep_t quotient = (uint64_t)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.
+    rep_t residual;
+    if (quotient < (implicitBit << 1)) {
+        residual = (aSignificand << 24) - quotient * bSignificand;
+        quotientExponent--;
+    } else {
+        quotient >>= 1;
+        residual = (aSignificand << 23) - quotient * bSignificand;
+    }
+
+    const int writtenExponent = quotientExponent + exponentBias;
+    
+    if (writtenExponent >= maxExponent) {
+        // If we have overflowed the exponent, return infinity.
+        return fromRep(infRep | quotientSign);
+    }
+    
+    else if (writtenExponent < 1) {
+        // Flush denormals to zero.  In the future, it would be nice to add
+        // code to round them correctly.
+        return fromRep(quotientSign);
+    }
+    
+    else {
+        const bool round = (residual << 1) > bSignificand;
+        // Clear the implicit bit
+        rep_t absResult = quotient & significandMask;
+        // Insert the exponent
+        absResult |= (rep_t)writtenExponent << significandBits;
+        // Round
+        absResult += round;
+        // Insert the sign and return
+        return fromRep(absResult | quotientSign);
+    }
+}