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Diffstat (limited to 'libquadmath/math/fmaq.c')
| -rw-r--r-- | libquadmath/math/fmaq.c | 241 |
1 files changed, 241 insertions, 0 deletions
diff --git a/libquadmath/math/fmaq.c b/libquadmath/math/fmaq.c new file mode 100644 index 000000000..126b0a2d2 --- /dev/null +++ b/libquadmath/math/fmaq.c @@ -0,0 +1,241 @@ +/* Compute x * y + z as ternary operation. + Copyright (C) 2010 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, write to the Free + Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA + 02111-1307 USA. */ + +#include "quadmath-imp.h" +#include <math.h> +#include <float.h> +#ifdef HAVE_FENV_H +# include <fenv.h> +# if defined HAVE_FEHOLDEXCEPT && defined HAVE_FESETROUND \ + && defined HAVE_FEUPDATEENV && defined HAVE_FETESTEXCEPT \ + && defined FE_TOWARDZERO && defined FE_INEXACT +# define USE_FENV_H +# endif +#endif + +/* This implementation uses rounding to odd to avoid problems with + double rounding. See a paper by Boldo and Melquiond: + http://www.lri.fr/~melquion/doc/08-tc.pdf */ + +__float128 +fmaq (__float128 x, __float128 y, __float128 z) +{ + ieee854_float128 u, v, w; + int adjust = 0; + u.value = x; + v.value = y; + w.value = z; + if (__builtin_expect (u.ieee.exponent + v.ieee.exponent + >= 0x7fff + IEEE854_FLOAT128_BIAS + - FLT128_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0) + || __builtin_expect (v.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0) + || __builtin_expect (w.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0) + || __builtin_expect (u.ieee.exponent + v.ieee.exponent + <= IEEE854_FLOAT128_BIAS + FLT128_MANT_DIG, 0)) + { + /* If z is Inf, but x and y are finite, the result should be + z rather than NaN. */ + if (w.ieee.exponent == 0x7fff + && u.ieee.exponent != 0x7fff + && v.ieee.exponent != 0x7fff) + return (z + x) + y; + /* If x or y or z is Inf/NaN, or if fma will certainly overflow, + or if x * y is less than half of FLT128_DENORM_MIN, + compute as x * y + z. */ + if (u.ieee.exponent == 0x7fff + || v.ieee.exponent == 0x7fff + || w.ieee.exponent == 0x7fff + || u.ieee.exponent + v.ieee.exponent + > 0x7fff + IEEE854_FLOAT128_BIAS + || u.ieee.exponent + v.ieee.exponent + < IEEE854_FLOAT128_BIAS - FLT128_MANT_DIG - 2) + return x * y + z; + if (u.ieee.exponent + v.ieee.exponent + >= 0x7fff + IEEE854_FLOAT128_BIAS - FLT128_MANT_DIG) + { + /* Compute 1p-113 times smaller result and multiply + at the end. */ + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent -= FLT128_MANT_DIG; + else + v.ieee.exponent -= FLT128_MANT_DIG; + /* If x + y exponent is very large and z exponent is very small, + it doesn't matter if we don't adjust it. */ + if (w.ieee.exponent > FLT128_MANT_DIG) + w.ieee.exponent -= FLT128_MANT_DIG; + adjust = 1; + } + else if (w.ieee.exponent >= 0x7fff - FLT128_MANT_DIG) + { + /* Similarly. + If z exponent is very large and x and y exponents are + very small, it doesn't matter if we don't adjust it. */ + if (u.ieee.exponent > v.ieee.exponent) + { + if (u.ieee.exponent > FLT128_MANT_DIG) + u.ieee.exponent -= FLT128_MANT_DIG; + } + else if (v.ieee.exponent > FLT128_MANT_DIG) + v.ieee.exponent -= FLT128_MANT_DIG; + w.ieee.exponent -= FLT128_MANT_DIG; + adjust = 1; + } + else if (u.ieee.exponent >= 0x7fff - FLT128_MANT_DIG) + { + u.ieee.exponent -= FLT128_MANT_DIG; + if (v.ieee.exponent) + v.ieee.exponent += FLT128_MANT_DIG; + else + v.value *= 0x1p113Q; + } + else if (v.ieee.exponent >= 0x7fff - FLT128_MANT_DIG) + { + v.ieee.exponent -= FLT128_MANT_DIG; + if (u.ieee.exponent) + u.ieee.exponent += FLT128_MANT_DIG; + else + u.value *= 0x1p113Q; + } + else /* if (u.ieee.exponent + v.ieee.exponent + <= IEEE854_FLOAT128_BIAS + FLT128_MANT_DIG) */ + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * FLT128_MANT_DIG; + else + v.ieee.exponent += 2 * FLT128_MANT_DIG; + if (w.ieee.exponent <= 4 * FLT128_MANT_DIG + 4) + { + if (w.ieee.exponent) + w.ieee.exponent += 2 * FLT128_MANT_DIG; + else + w.value *= 0x1p226Q; + adjust = -1; + } + /* Otherwise x * y should just affect inexact + and nothing else. */ + } + x = u.value; + y = v.value; + z = w.value; + } + /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ +#define C ((1LL << (FLT128_MANT_DIG + 1) / 2) + 1) + __float128 x1 = x * C; + __float128 y1 = y * C; + __float128 m1 = x * y; + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + __float128 x2 = x - x1; + __float128 y2 = y - y1; + __float128 m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; + + /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ + __float128 a1 = z + m1; + __float128 t1 = a1 - z; + __float128 t2 = a1 - t1; + t1 = m1 - t1; + t2 = z - t2; + __float128 a2 = t1 + t2; + +#ifdef USE_FENV_H + fenv_t env; + feholdexcept (&env); + fesetround (FE_TOWARDZERO); +#endif + /* Perform m2 + a2 addition with round to odd. */ + u.value = a2 + m2; + + if (__builtin_expect (adjust == 0, 1)) + { +#ifdef USE_FENV_H + if ((u.ieee.mant_low & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); +#endif + /* Result is a1 + u.value. */ + return a1 + u.value; + } + else if (__builtin_expect (adjust > 0, 1)) + { +#ifdef USE_FENV_H + if ((u.ieee.mant_low & 1) == 0 && u.ieee.exponent != 0x7fff) + u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); +#endif + /* Result is a1 + u.value, scaled up. */ + return (a1 + u.value) * 0x1p113Q; + } + else + { +#ifdef USE_FENV_H + if ((u.ieee.mant_low & 1) == 0) + u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0; +#endif + v.value = a1 + u.value; + /* Ensure the addition is not scheduled after fetestexcept call. */ + asm volatile ("" : : "m" (v)); +#ifdef USE_FENV_H + int j = fetestexcept (FE_INEXACT) != 0; + feupdateenv (&env); +#else + int j = 0; +#endif + /* 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.value is exact, the only rounding happens during + scaling down. */ + if (j == 0) + return v.value * 0x1p-226Q; + /* If result rounded to zero is not subnormal, no double + rounding will occur. */ + if (v.ieee.exponent > 226) + return (a1 + u.value) * 0x1p-226Q; + /* If v.value * 0x1p-226Q with round to zero is a subnormal above + or equal to FLT128_MIN / 2, then v.value * 0x1p-226Q shifts mantissa + down just by 1 bit, which means v.ieee.mant_low |= j would + change the round bit, not sticky or guard bit. + v.value * 0x1p-226Q never normalizes by shifting up, + so round bit plus sticky bit should be already enough + for proper rounding. */ + if (v.ieee.exponent == 226) + { + /* v.ieee.mant_low & 2 is LSB bit of the result before rounding, + v.ieee.mant_low & 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.mant_low & 3) == 1) + { + v.value *= 0x1p-226Q; + if (v.ieee.negative) + return v.value - 0x1p-16494Q /* __FLT128_DENORM_MIN__ */; + else + return v.value + 0x1p-16494Q /* __FLT128_DENORM_MIN__ */; + } + else + return v.value * 0x1p-226Q; + } + v.ieee.mant_low |= j; + return v.value * 0x1p-226Q; + } +} |