# fma.m4 serial 2 dnl Copyright (C) 2011-2015 Free Software Foundation, Inc. dnl This file is free software; the Free Software Foundation dnl gives unlimited permission to copy and/or distribute it, dnl with or without modifications, as long as this notice is preserved. AC_DEFUN([gl_FUNC_FMA], [ AC_REQUIRE([gl_MATH_H_DEFAULTS]) dnl Determine FMA_LIBM. gl_MATHFUNC([fma], [double], [(double, double, double)], [extern #ifdef __cplusplus "C" #endif double fma (double, double, double); ]) if test $gl_cv_func_fma_no_libm = yes \ || test $gl_cv_func_fma_in_libm = yes; then dnl Also check whether it's declared. dnl IRIX 6.5 has fma() in libm but doesn't declare it in , dnl and the function is buggy. AC_CHECK_DECL([fma], , [REPLACE_FMA=1], [[#include ]]) if test $REPLACE_FMA = 0; then gl_FUNC_FMA_WORKS case "$gl_cv_func_fma_works" in *no) REPLACE_FMA=1 ;; esac fi else HAVE_FMA=0 fi if test $HAVE_FMA = 0 || test $REPLACE_FMA = 1; then dnl Find libraries needed to link lib/fmal.c. AC_REQUIRE([gl_FUNC_FREXP]) AC_REQUIRE([gl_FUNC_LDEXP]) AC_REQUIRE([gl_FUNC_FEGETROUND]) FMA_LIBM= dnl Append $FREXP_LIBM to FMA_LIBM, avoiding gratuitous duplicates. case " $FMA_LIBM " in *" $FREXP_LIBM "*) ;; *) FMA_LIBM="$FMA_LIBM $FREXP_LIBM" ;; esac dnl Append $LDEXP_LIBM to FMA_LIBM, avoiding gratuitous duplicates. case " $FMA_LIBM " in *" $LDEXP_LIBM "*) ;; *) FMA_LIBM="$FMA_LIBM $LDEXP_LIBM" ;; esac dnl Append $FEGETROUND_LIBM to FMA_LIBM, avoiding gratuitous duplicates. case " $FMA_LIBM " in *" $FEGETROUND_LIBM "*) ;; *) FMA_LIBM="$FMA_LIBM $FEGETROUND_LIBM" ;; esac fi AC_SUBST([FMA_LIBM]) ]) dnl Test whether fma() has any of the 7 known bugs of glibc 2.11.3 on x86_64. AC_DEFUN([gl_FUNC_FMA_WORKS], [ AC_REQUIRE([AC_PROG_CC]) AC_REQUIRE([AC_CANONICAL_HOST]) dnl for cross-compiles AC_REQUIRE([gl_FUNC_LDEXP]) save_LIBS="$LIBS" LIBS="$LIBS $FMA_LIBM $LDEXP_LIBM" AC_CACHE_CHECK([whether fma works], [gl_cv_func_fma_works], [ AC_RUN_IFELSE( [AC_LANG_SOURCE([[ #include #include double p0 = 0.0; int main() { int failed_tests = 0; /* These tests fail with glibc 2.11.3 on x86_64. */ { volatile double x = 1.5; /* 3 * 2^-1 */ volatile double y = x; volatile double z = ldexp (1.0, DBL_MANT_DIG + 1); /* 2^54 */ /* x * y + z with infinite precision: 2^54 + 9 * 2^-2. Lies between (2^52 + 0) * 2^2 and (2^52 + 1) * 2^2 and is closer to (2^52 + 1) * 2^2, therefore the rounding must round up and produce (2^52 + 1) * 2^2. */ volatile double expected = z + 4.0; volatile double result = fma (x, y, z); if (result != expected) failed_tests |= 1; } { volatile double x = 1.25; /* 2^0 + 2^-2 */ volatile double y = - x; volatile double z = ldexp (1.0, DBL_MANT_DIG + 1); /* 2^54 */ /* x * y + z with infinite precision: 2^54 - 2^0 - 2^-1 - 2^-4. Lies between (2^53 - 1) * 2^1 and 2^53 * 2^1 and is closer to (2^53 - 1) * 2^1, therefore the rounding must round down and produce (2^53 - 1) * 2^1. */ volatile double expected = (ldexp (1.0, DBL_MANT_DIG) - 1.0) * 2.0; volatile double result = fma (x, y, z); if (result != expected) failed_tests |= 2; } { volatile double x = 1.0 + ldexp (1.0, 1 - DBL_MANT_DIG); /* 2^0 + 2^-52 */ volatile double y = x; volatile double z = 4.0; /* 2^2 */ /* x * y + z with infinite precision: 2^2 + 2^0 + 2^-51 + 2^-104. Lies between (2^52 + 2^50) * 2^-50 and (2^52 + 2^50 + 1) * 2^-50 and is closer to (2^52 + 2^50 + 1) * 2^-50, therefore the rounding must round up and produce (2^52 + 2^50 + 1) * 2^-50. */ volatile double expected = 4.0 + 1.0 + ldexp (1.0, 3 - DBL_MANT_DIG); volatile double result = fma (x, y, z); if (result != expected) failed_tests |= 4; } { volatile double x = 1.0 + ldexp (1.0, 1 - DBL_MANT_DIG); /* 2^0 + 2^-52 */ volatile double y = - x; volatile double z = 8.0; /* 2^3 */ /* x * y + z with infinite precision: 2^2 + 2^1 + 2^0 - 2^-51 - 2^-104. Lies between (2^52 + 2^51 + 2^50 - 1) * 2^-50 and (2^52 + 2^51 + 2^50) * 2^-50 and is closer to (2^52 + 2^51 + 2^50 - 1) * 2^-50, therefore the rounding must round down and produce (2^52 + 2^51 + 2^50 - 1) * 2^-50. */ volatile double expected = 7.0 - ldexp (1.0, 3 - DBL_MANT_DIG); volatile double result = fma (x, y, z); if (result != expected) failed_tests |= 8; } { volatile double x = 1.25; /* 2^0 + 2^-2 */ volatile double y = - 0.75; /* - 2^0 + 2^-2 */ volatile double z = ldexp (1.0, DBL_MANT_DIG); /* 2^53 */ /* x * y + z with infinite precision: 2^53 - 2^0 + 2^-4. Lies between (2^53 - 2^0) and 2^53 and is closer to (2^53 - 2^0), therefore the rounding must round down and produce (2^53 - 2^0). */ volatile double expected = ldexp (1.0, DBL_MANT_DIG) - 1.0; volatile double result = fma (x, y, z); if (result != expected) failed_tests |= 16; } if ((DBL_MANT_DIG % 2) == 1) { volatile double x = 1.0 + ldexp (1.0, - (DBL_MANT_DIG + 1) / 2); /* 2^0 + 2^-27 */ volatile double y = 1.0 - ldexp (1.0, - (DBL_MANT_DIG + 1) / 2); /* 2^0 - 2^-27 */ volatile double z = - ldexp (1.0, DBL_MIN_EXP - DBL_MANT_DIG); /* - 2^-1074 */ /* x * y + z with infinite precision: 2^0 - 2^-54 - 2^-1074. Lies between (2^53 - 1) * 2^-53 and 2^53 * 2^-53 and is closer to (2^53 - 1) * 2^-53, therefore the rounding must round down and produce (2^53 - 1) * 2^-53. */ volatile double expected = 1.0 - ldexp (1.0, - DBL_MANT_DIG); volatile double result = fma (x, y, z); if (result != expected) failed_tests |= 32; } { double minus_inf = -1.0 / p0; volatile double x = ldexp (1.0, DBL_MAX_EXP - 1); volatile double y = ldexp (1.0, DBL_MAX_EXP - 1); volatile double z = minus_inf; volatile double result = fma (x, y, z); if (!(result == minus_inf)) failed_tests |= 64; } return failed_tests; }]])], [gl_cv_func_fma_works=yes], [gl_cv_func_fma_works=no], [dnl Guess no, even on glibc systems. gl_cv_func_fma_works="guessing no" ]) ]) LIBS="$save_LIBS" ]) # Prerequisites of lib/fma.c. AC_DEFUN([gl_PREREQ_FMA], [:])