diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/s_fma.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/s_fma.c | 103 |
1 files changed, 88 insertions, 15 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_fma.c b/sysdeps/ieee754/dbl-64/s_fma.c index ca7300c11e..911682eceb 100644 --- a/sysdeps/ieee754/dbl-64/s_fma.c +++ b/sysdeps/ieee754/dbl-64/s_fma.c @@ -39,15 +39,20 @@ __fma (double x, double y, double z) >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG, 0) || __builtin_expect (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) || __builtin_expect (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) - || __builtin_expect (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0)) + || __builtin_expect (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent + v.ieee.exponent + <= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG, 0)) { - /* If x or y or z is Inf/NaN or if fma will certainly overflow, + /* If x or y or z is Inf/NaN, or if fma will certainly overflow, + or if x * y is less than half of DBL_DENORM_MIN, compute as x * y + z. */ if (u.ieee.exponent == 0x7ff || v.ieee.exponent == 0x7ff || w.ieee.exponent == 0x7ff || u.ieee.exponent + v.ieee.exponent - > 0x7ff + IEEE754_DOUBLE_BIAS) + > 0x7ff + IEEE754_DOUBLE_BIAS + || u.ieee.exponent + v.ieee.exponent + < IEEE754_DOUBLE_BIAS - DBL_MANT_DIG - 2) return x * y + z; if (u.ieee.exponent + v.ieee.exponent >= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG) @@ -87,7 +92,7 @@ __fma (double x, double y, double z) else v.d *= 0x1p53; } - else + else if (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG) { v.ieee.exponent -= DBL_MANT_DIG; if (u.ieee.exponent) @@ -95,6 +100,24 @@ __fma (double x, double y, double z) else u.d *= 0x1p53; } + else /* if (u.ieee.exponent + v.ieee.exponent + <= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG) */ + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * DBL_MANT_DIG; + else + v.ieee.exponent += 2 * DBL_MANT_DIG; + if (w.ieee.exponent <= 4 * DBL_MANT_DIG + 4) + { + if (w.ieee.exponent) + w.ieee.exponent += 2 * DBL_MANT_DIG; + else + w.d *= 0x1p106; + adjust = -1; + } + /* Otherwise x * y should just affect inexact + and nothing else. */ + } x = u.d; y = v.d; z = w.d; @@ -123,18 +146,68 @@ __fma (double x, double y, double z) fesetround (FE_TOWARDZERO); /* Perform m2 + a2 addition with round to odd. */ u.d = a2 + m2; - if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) - u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; - feupdateenv (&env); - - /* Add that to a1. */ - a1 = a1 + u.d; - /* And adjust exponent if needed. */ - if (__builtin_expect (adjust, 0)) - a1 *= 0x1p53; - - return a1; + if (__builtin_expect (adjust == 0, 1)) + { + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) + u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Result is a1 + u.d. */ + return a1 + u.d; + } + else if (__builtin_expect (adjust > 0, 1)) + { + if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff) + u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Result is a1 + u.d, scaled up. */ + return (a1 + u.d) * 0x1p53; + } + else + { + v.d = a1 + u.d; + int j = fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); + /* Ensure the following computations are performed in default rounding + mode instead of just reusing the round to zero computation. */ + asm volatile ("" : "=m" (u) : "m" (u)); + /* If a1 + u.d is exact, the only rounding happens during + scaling down. */ + if (j == 0) + return v.d * 0x1p-106; + /* If result rounded to zero is not subnormal, no double + rounding will occur. */ + if (v.ieee.exponent > 106) + return (a1 + u.d) * 0x1p-106; + /* If v.d * 0x1p-106 with round to zero is a subnormal above + or equal to DBL_MIN / 2, then v.d * 0x1p-106 shifts mantissa + down just by 1 bit, which means v.ieee.mantissa1 |= j would + change the round bit, not sticky or guard bit. + v.d * 0x1p-106 never normalizes by shifting up, + so round bit plus sticky bit should be already enough + for proper rounding. */ + if (v.ieee.exponent == 106) + { + /* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding, + v.ieee.mantissa1 & 1 is the round bit and j is our sticky + bit. In round-to-nearest 001 rounds down like 00, + 011 rounds up, even though 01 rounds down (thus we need + to adjust), 101 rounds down like 10 and 111 rounds up + like 11. */ + if ((v.ieee.mantissa1 & 3) == 1) + { + v.d *= 0x1p-106; + if (v.ieee.negative) + return v.d - 0x1p-1074 /* __DBL_DENORM_MIN__ */; + else + return v.d + 0x1p-1074 /* __DBL_DENORM_MIN__ */; + } + else + return v.d * 0x1p-106; + } + v.ieee.mantissa1 |= j; + return v.d * 0x1p-106; + } } #ifndef __fma weak_alias (__fma, fma) |