softfloat: Implement fused multiply-add

Implement fused multiply-add as a softfloat primitive. This implements
"a+b*c" as a single step without any intermediate rounding; it is
specified in IEEE 754-2008 and implemented in a number of CPUs.

Signed-off-by: Peter Maydell <peter.maydell@linaro.org>

1 files changed, 427 insertions, 0 deletions

diff --git a/fpu/softfloat.c b/fpu/softfloat.c
index 3aafa81d58..81a7d1ae09 100644
--- a/fpu/softfloat.c
+++ b/fpu/softfloat.c
@@ -2118,6 +2118,213 @@ float32 float32_rem( float32 a, float32 b STATUS_PARAM )
 }
 
 /*----------------------------------------------------------------------------
+| Returns the result of multiplying the single-precision floating-point values
+| `a' and `b' then adding 'c', with no intermediate rounding step after the
+| multiplication.  The operation is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic 754-2008.
+| The flags argument allows the caller to select negation of the
+| addend, the intermediate product, or the final result. (The difference
+| between this and having the caller do a separate negation is that negating
+| externally will flip the sign bit on NaNs.)
+*----------------------------------------------------------------------------*/
+
+float32 float32_muladd(float32 a, float32 b, float32 c, int flags STATUS_PARAM)
+{
+    flag aSign, bSign, cSign, zSign;
+    int aExp, bExp, cExp, pExp, zExp, expDiff;
+    uint32_t aSig, bSig, cSig;
+    flag pInf, pZero, pSign;
+    uint64_t pSig64, cSig64, zSig64;
+    uint32_t pSig;
+    int shiftcount;
+    flag signflip, infzero;
+
+    a = float32_squash_input_denormal(a STATUS_VAR);
+    b = float32_squash_input_denormal(b STATUS_VAR);
+    c = float32_squash_input_denormal(c STATUS_VAR);
+    aSig = extractFloat32Frac(a);
+    aExp = extractFloat32Exp(a);
+    aSign = extractFloat32Sign(a);
+    bSig = extractFloat32Frac(b);
+    bExp = extractFloat32Exp(b);
+    bSign = extractFloat32Sign(b);
+    cSig = extractFloat32Frac(c);
+    cExp = extractFloat32Exp(c);
+    cSign = extractFloat32Sign(c);
+
+    infzero = ((aExp == 0 && aSig == 0 && bExp == 0xff && bSig == 0) ||
+               (aExp == 0xff && aSig == 0 && bExp == 0 && bSig == 0));
+
+    /* It is implementation-defined whether the cases of (0,inf,qnan)
+     * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN
+     * they return if they do), so we have to hand this information
+     * off to the target-specific pick-a-NaN routine.
+     */
+    if (((aExp == 0xff) && aSig) ||
+        ((bExp == 0xff) && bSig) ||
+        ((cExp == 0xff) && cSig)) {
+        return propagateFloat32MulAddNaN(a, b, c, infzero STATUS_VAR);
+    }
+
+    if (infzero) {
+        float_raise(float_flag_invalid STATUS_VAR);
+        return float32_default_nan;
+    }
+
+    if (flags & float_muladd_negate_c) {
+        cSign ^= 1;
+    }
+
+    signflip = (flags & float_muladd_negate_result) ? 1 : 0;
+
+    /* Work out the sign and type of the product */
+    pSign = aSign ^ bSign;
+    if (flags & float_muladd_negate_product) {
+        pSign ^= 1;
+    }
+    pInf = (aExp == 0xff) || (bExp == 0xff);
+    pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0);
+
+    if (cExp == 0xff) {
+        if (pInf && (pSign ^ cSign)) {
+            /* addition of opposite-signed infinities => InvalidOperation */
+            float_raise(float_flag_invalid STATUS_VAR);
+            return float32_default_nan;
+        }
+        /* Otherwise generate an infinity of the same sign */
+        return packFloat32(cSign ^ signflip, 0xff, 0);
+    }
+
+    if (pInf) {
+        return packFloat32(pSign ^ signflip, 0xff, 0);
+    }
+
+    if (pZero) {
+        if (cExp == 0) {
+            if (cSig == 0) {
+                /* Adding two exact zeroes */
+                if (pSign == cSign) {
+                    zSign = pSign;
+                } else if (STATUS(float_rounding_mode) == float_round_down) {
+                    zSign = 1;
+                } else {
+                    zSign = 0;
+                }
+                return packFloat32(zSign ^ signflip, 0, 0);
+            }
+            /* Exact zero plus a denorm */
+            if (STATUS(flush_to_zero)) {
+                float_raise(float_flag_output_denormal STATUS_VAR);
+                return packFloat32(cSign ^ signflip, 0, 0);
+            }
+        }
+        /* Zero plus something non-zero : just return the something */
+        return c ^ (signflip << 31);
+    }
+
+    if (aExp == 0) {
+        normalizeFloat32Subnormal(aSig, &aExp, &aSig);
+    }
+    if (bExp == 0) {
+        normalizeFloat32Subnormal(bSig, &bExp, &bSig);
+    }
+
+    /* Calculate the actual result a * b + c */
+
+    /* Multiply first; this is easy. */
+    /* NB: we subtract 0x7e where float32_mul() subtracts 0x7f
+     * because we want the true exponent, not the "one-less-than"
+     * flavour that roundAndPackFloat32() takes.
+     */
+    pExp = aExp + bExp - 0x7e;
+    aSig = (aSig | 0x00800000) << 7;
+    bSig = (bSig | 0x00800000) << 8;
+    pSig64 = (uint64_t)aSig * bSig;
+    if ((int64_t)(pSig64 << 1) >= 0) {
+        pSig64 <<= 1;
+        pExp--;
+    }
+
+    zSign = pSign ^ signflip;
+
+    /* Now pSig64 is the significand of the multiply, with the explicit bit in
+     * position 62.
+     */
+    if (cExp == 0) {
+        if (!cSig) {
+            /* Throw out the special case of c being an exact zero now */
+            shift64RightJamming(pSig64, 32, &pSig64);
+            pSig = pSig64;
+            return roundAndPackFloat32(zSign, pExp - 1,
+                                       pSig STATUS_VAR);
+        }
+        normalizeFloat32Subnormal(cSig, &cExp, &cSig);
+    }
+
+    cSig64 = (uint64_t)cSig << (62 - 23);
+    cSig64 |= LIT64(0x4000000000000000);
+    expDiff = pExp - cExp;
+
+    if (pSign == cSign) {
+        /* Addition */
+        if (expDiff > 0) {
+            /* scale c to match p */
+            shift64RightJamming(cSig64, expDiff, &cSig64);
+            zExp = pExp;
+        } else if (expDiff < 0) {
+            /* scale p to match c */
+            shift64RightJamming(pSig64, -expDiff, &pSig64);
+            zExp = cExp;
+        } else {
+            /* no scaling needed */
+            zExp = cExp;
+        }
+        /* Add significands and make sure explicit bit ends up in posn 62 */
+        zSig64 = pSig64 + cSig64;
+        if ((int64_t)zSig64 < 0) {
+            shift64RightJamming(zSig64, 1, &zSig64);
+        } else {
+            zExp--;
+        }
+    } else {
+        /* Subtraction */
+        if (expDiff > 0) {
+            shift64RightJamming(cSig64, expDiff, &cSig64);
+            zSig64 = pSig64 - cSig64;
+            zExp = pExp;
+        } else if (expDiff < 0) {
+            shift64RightJamming(pSig64, -expDiff, &pSig64);
+            zSig64 = cSig64 - pSig64;
+            zExp = cExp;
+            zSign ^= 1;
+        } else {
+            zExp = pExp;
+            if (cSig64 < pSig64) {
+                zSig64 = pSig64 - cSig64;
+            } else if (pSig64 < cSig64) {
+                zSig64 = cSig64 - pSig64;
+                zSign ^= 1;
+            } else {
+                /* Exact zero */
+                zSign = signflip;
+                if (STATUS(float_rounding_mode) == float_round_down) {
+                    zSign ^= 1;
+                }
+                return packFloat32(zSign, 0, 0);
+            }
+        }
+        --zExp;
+        /* Normalize to put the explicit bit back into bit 62. */
+        shiftcount = countLeadingZeros64(zSig64) - 1;
+        zSig64 <<= shiftcount;
+        zExp -= shiftcount;
+    }
+    shift64RightJamming(zSig64, 32, &zSig64);
+    return roundAndPackFloat32(zSign, zExp, zSig64 STATUS_VAR);
+}
+
+
+/*----------------------------------------------------------------------------
 | Returns the square root of the single-precision floating-point value `a'.
 | The operation is performed according to the IEC/IEEE Standard for Binary
 | Floating-Point Arithmetic.
@@ -3465,6 +3672,226 @@ float64 float64_rem( float64 a, float64 b STATUS_PARAM )
 }
 
 /*----------------------------------------------------------------------------
+| Returns the result of multiplying the double-precision floating-point values
+| `a' and `b' then adding 'c', with no intermediate rounding step after the
+| multiplication.  The operation is performed according to the IEC/IEEE
+| Standard for Binary Floating-Point Arithmetic 754-2008.
+| The flags argument allows the caller to select negation of the
+| addend, the intermediate product, or the final result. (The difference
+| between this and having the caller do a separate negation is that negating
+| externally will flip the sign bit on NaNs.)
+*----------------------------------------------------------------------------*/
+
+float64 float64_muladd(float64 a, float64 b, float64 c, int flags STATUS_PARAM)
+{
+    flag aSign, bSign, cSign, zSign;
+    int aExp, bExp, cExp, pExp, zExp, expDiff;
+    uint64_t aSig, bSig, cSig;
+    flag pInf, pZero, pSign;
+    uint64_t pSig0, pSig1, cSig0, cSig1, zSig0, zSig1;
+    int shiftcount;
+    flag signflip, infzero;
+
+    a = float64_squash_input_denormal(a STATUS_VAR);
+    b = float64_squash_input_denormal(b STATUS_VAR);
+    c = float64_squash_input_denormal(c STATUS_VAR);
+    aSig = extractFloat64Frac(a);
+    aExp = extractFloat64Exp(a);
+    aSign = extractFloat64Sign(a);
+    bSig = extractFloat64Frac(b);
+    bExp = extractFloat64Exp(b);
+    bSign = extractFloat64Sign(b);
+    cSig = extractFloat64Frac(c);
+    cExp = extractFloat64Exp(c);
+    cSign = extractFloat64Sign(c);
+
+    infzero = ((aExp == 0 && aSig == 0 && bExp == 0x7ff && bSig == 0) ||
+               (aExp == 0x7ff && aSig == 0 && bExp == 0 && bSig == 0));
+
+    /* It is implementation-defined whether the cases of (0,inf,qnan)
+     * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN
+     * they return if they do), so we have to hand this information
+     * off to the target-specific pick-a-NaN routine.
+     */
+    if (((aExp == 0x7ff) && aSig) ||
+        ((bExp == 0x7ff) && bSig) ||
+        ((cExp == 0x7ff) && cSig)) {
+        return propagateFloat64MulAddNaN(a, b, c, infzero STATUS_VAR);
+    }
+
+    if (infzero) {
+        float_raise(float_flag_invalid STATUS_VAR);
+        return float64_default_nan;
+    }
+
+    if (flags & float_muladd_negate_c) {
+        cSign ^= 1;
+    }
+
+    signflip = (flags & float_muladd_negate_result) ? 1 : 0;
+
+    /* Work out the sign and type of the product */
+    pSign = aSign ^ bSign;
+    if (flags & float_muladd_negate_product) {
+        pSign ^= 1;
+    }
+    pInf = (aExp == 0x7ff) || (bExp == 0x7ff);
+    pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0);
+
+    if (cExp == 0x7ff) {
+        if (pInf && (pSign ^ cSign)) {
+            /* addition of opposite-signed infinities => InvalidOperation */
+            float_raise(float_flag_invalid STATUS_VAR);
+            return float64_default_nan;
+        }
+        /* Otherwise generate an infinity of the same sign */
+        return packFloat64(cSign ^ signflip, 0x7ff, 0);
+    }
+
+    if (pInf) {
+        return packFloat64(pSign ^ signflip, 0x7ff, 0);
+    }
+
+    if (pZero) {
+        if (cExp == 0) {
+            if (cSig == 0) {
+                /* Adding two exact zeroes */
+                if (pSign == cSign) {
+                    zSign = pSign;
+                } else if (STATUS(float_rounding_mode) == float_round_down) {
+                    zSign = 1;
+                } else {
+                    zSign = 0;
+                }
+                return packFloat64(zSign ^ signflip, 0, 0);
+            }
+            /* Exact zero plus a denorm */
+            if (STATUS(flush_to_zero)) {
+                float_raise(float_flag_output_denormal STATUS_VAR);
+                return packFloat64(cSign ^ signflip, 0, 0);
+            }
+        }
+        /* Zero plus something non-zero : just return the something */
+        return c ^ ((uint64_t)signflip << 63);
+    }
+
+    if (aExp == 0) {
+        normalizeFloat64Subnormal(aSig, &aExp, &aSig);
+    }
+    if (bExp == 0) {
+        normalizeFloat64Subnormal(bSig, &bExp, &bSig);
+    }
+
+    /* Calculate the actual result a * b + c */
+
+    /* Multiply first; this is easy. */
+    /* NB: we subtract 0x3fe where float64_mul() subtracts 0x3ff
+     * because we want the true exponent, not the "one-less-than"
+     * flavour that roundAndPackFloat64() takes.
+     */
+    pExp = aExp + bExp - 0x3fe;
+    aSig = (aSig | LIT64(0x0010000000000000))<<10;
+    bSig = (bSig | LIT64(0x0010000000000000))<<11;
+    mul64To128(aSig, bSig, &pSig0, &pSig1);
+    if ((int64_t)(pSig0 << 1) >= 0) {
+        shortShift128Left(pSig0, pSig1, 1, &pSig0, &pSig1);
+        pExp--;
+    }
+
+    zSign = pSign ^ signflip;
+
+    /* Now [pSig0:pSig1] is the significand of the multiply, with the explicit
+     * bit in position 126.
+     */
+    if (cExp == 0) {
+        if (!cSig) {
+            /* Throw out the special case of c being an exact zero now */
+            shift128RightJamming(pSig0, pSig1, 64, &pSig0, &pSig1);
+            return roundAndPackFloat64(zSign, pExp - 1,
+                                       pSig1 STATUS_VAR);
+        }
+        normalizeFloat64Subnormal(cSig, &cExp, &cSig);
+    }
+
+    /* Shift cSig and add the explicit bit so [cSig0:cSig1] is the
+     * significand of the addend, with the explicit bit in position 126.
+     */
+    cSig0 = cSig << (126 - 64 - 52);
+    cSig1 = 0;
+    cSig0 |= LIT64(0x4000000000000000);
+    expDiff = pExp - cExp;
+
+    if (pSign == cSign) {
+        /* Addition */
+        if (expDiff > 0) {
+            /* scale c to match p */
+            shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1);
+            zExp = pExp;
+        } else if (expDiff < 0) {
+            /* scale p to match c */
+            shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1);
+            zExp = cExp;
+        } else {
+            /* no scaling needed */
+            zExp = cExp;
+        }
+        /* Add significands and make sure explicit bit ends up in posn 126 */
+        add128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1);
+        if ((int64_t)zSig0 < 0) {
+            shift128RightJamming(zSig0, zSig1, 1, &zSig0, &zSig1);
+        } else {
+            zExp--;
+        }
+        shift128RightJamming(zSig0, zSig1, 64, &zSig0, &zSig1);
+        return roundAndPackFloat64(zSign, zExp, zSig1 STATUS_VAR);
+    } else {
+        /* Subtraction */
+        if (expDiff > 0) {
+            shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1);
+            sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1);
+            zExp = pExp;
+        } else if (expDiff < 0) {
+            shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1);
+            sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1);
+            zExp = cExp;
+            zSign ^= 1;
+        } else {
+            zExp = pExp;
+            if (lt128(cSig0, cSig1, pSig0, pSig1)) {
+                sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1);
+            } else if (lt128(pSig0, pSig1, cSig0, cSig1)) {
+                sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1);
+                zSign ^= 1;
+            } else {
+                /* Exact zero */
+                zSign = signflip;
+                if (STATUS(float_rounding_mode) == float_round_down) {
+                    zSign ^= 1;
+                }
+                return packFloat64(zSign, 0, 0);
+            }
+        }
+        --zExp;
+        /* Do the equivalent of normalizeRoundAndPackFloat64() but
+         * starting with the significand in a pair of uint64_t.
+         */
+        if (zSig0) {
+            shiftcount = countLeadingZeros64(zSig0) - 1;
+            shortShift128Left(zSig0, zSig1, shiftcount, &zSig0, &zSig1);
+            if (zSig1) {
+                zSig0 |= 1;
+            }
+            zExp -= shiftcount;
+        } else {
+            shiftcount = countLeadingZeros64(zSig1) - 1;
+            zSig0 = zSig1 << shiftcount;
+            zExp -= (shiftcount + 64);
+        }
+        return roundAndPackFloat64(zSign, zExp, zSig0 STATUS_VAR);
+    }
+}
+
+/*----------------------------------------------------------------------------
 | Returns the square root of the double-precision floating-point value `a'.
 | The operation is performed according to the IEC/IEEE Standard for Binary
 | Floating-Point Arithmetic.