| # fmal.m4 serial 7 |
| dnl Copyright (C) 2011-2020 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_FMAL], |
| [ |
| AC_REQUIRE([gl_MATH_H_DEFAULTS]) |
| AC_REQUIRE([gl_LONG_DOUBLE_VS_DOUBLE]) |
| |
| dnl Persuade glibc <math.h> to declare fmal(). |
| AC_REQUIRE([gl_USE_SYSTEM_EXTENSIONS]) |
| |
| dnl Determine FMAL_LIBM. |
| gl_MATHFUNC([fmal], [long double], [(long double, long double, long double)], |
| [extern |
| #ifdef __cplusplus |
| "C" |
| #endif |
| long double fmal (long double, long double, long double); |
| ]) |
| if test $gl_cv_func_fmal_no_libm = yes \ |
| || test $gl_cv_func_fmal_in_libm = yes; then |
| dnl Also check whether it's declared. |
| dnl IRIX 6.5 has fmal() in libm but doesn't declare it in <math.h>, |
| dnl and the function is buggy. |
| AC_CHECK_DECL([fmal], , [REPLACE_FMAL=1], [[#include <math.h>]]) |
| if test $REPLACE_FMAL = 0; then |
| gl_FUNC_FMAL_WORKS |
| case "$gl_cv_func_fmal_works" in |
| *no) REPLACE_FMAL=1 ;; |
| esac |
| fi |
| else |
| HAVE_FMAL=0 |
| fi |
| if test $HAVE_FMAL = 0 || test $REPLACE_FMAL = 1; then |
| dnl Find libraries needed to link lib/fmal.c. |
| if test $HAVE_SAME_LONG_DOUBLE_AS_DOUBLE = 1; then |
| AC_REQUIRE([gl_FUNC_FMA]) |
| FMAL_LIBM="$FMA_LIBM" |
| else |
| AC_REQUIRE([gl_FUNC_FREXPL]) |
| AC_REQUIRE([gl_FUNC_LDEXPL]) |
| AC_REQUIRE([gl_FUNC_FEGETROUND]) |
| FMAL_LIBM= |
| dnl Append $FREXPL_LIBM to FMAL_LIBM, avoiding gratuitous duplicates. |
| case " $FMAL_LIBM " in |
| *" $FREXPL_LIBM "*) ;; |
| *) FMAL_LIBM="$FMAL_LIBM $FREXPL_LIBM" ;; |
| esac |
| dnl Append $LDEXPL_LIBM to FMAL_LIBM, avoiding gratuitous duplicates. |
| case " $FMAL_LIBM " in |
| *" $LDEXPL_LIBM "*) ;; |
| *) FMAL_LIBM="$FMAL_LIBM $LDEXPL_LIBM" ;; |
| esac |
| dnl Append $FEGETROUND_LIBM to FMAL_LIBM, avoiding gratuitous duplicates. |
| case " $FMAL_LIBM " in |
| *" $FEGETROUND_LIBM "*) ;; |
| *) FMAL_LIBM="$FMAL_LIBM $FEGETROUND_LIBM" ;; |
| esac |
| fi |
| fi |
| AC_SUBST([FMAL_LIBM]) |
| ]) |
| |
| dnl Test whether fmal() has any of the 15 known bugs of glibc 2.11.3 on x86_64. |
| AC_DEFUN([gl_FUNC_FMAL_WORKS], |
| [ |
| AC_REQUIRE([AC_PROG_CC]) |
| AC_REQUIRE([AC_CANONICAL_HOST]) dnl for cross-compiles |
| AC_REQUIRE([gl_FUNC_LDEXPL]) |
| save_LIBS="$LIBS" |
| LIBS="$LIBS $FMAL_LIBM $LDEXPL_LIBM" |
| AC_CACHE_CHECK([whether fmal works], [gl_cv_func_fmal_works], |
| [ |
| AC_RUN_IFELSE( |
| [AC_LANG_SOURCE([[ |
| #include <float.h> |
| #include <math.h> |
| /* Override the values of <float.h>, like done in float.in.h. */ |
| #if defined __i386__ && (defined __BEOS__ || defined __OpenBSD__) |
| # undef LDBL_MANT_DIG |
| # define LDBL_MANT_DIG 64 |
| # undef LDBL_MIN_EXP |
| # define LDBL_MIN_EXP (-16381) |
| # undef LDBL_MAX_EXP |
| # define LDBL_MAX_EXP 16384 |
| #endif |
| #if defined __i386__ && (defined __FreeBSD__ || defined __DragonFly__) |
| # undef LDBL_MANT_DIG |
| # define LDBL_MANT_DIG 64 |
| # undef LDBL_MIN_EXP |
| # define LDBL_MIN_EXP (-16381) |
| # undef LDBL_MAX_EXP |
| # define LDBL_MAX_EXP 16384 |
| #endif |
| #if (defined _ARCH_PPC || defined _POWER) && defined _AIX && (LDBL_MANT_DIG == 106) && defined __GNUC__ |
| # undef LDBL_MIN_EXP |
| # define LDBL_MIN_EXP DBL_MIN_EXP |
| #endif |
| #if defined __sgi && (LDBL_MANT_DIG >= 106) |
| # undef LDBL_MANT_DIG |
| # define LDBL_MANT_DIG 106 |
| # if defined __GNUC__ |
| # undef LDBL_MIN_EXP |
| # define LDBL_MIN_EXP DBL_MIN_EXP |
| # endif |
| #endif |
| long double p0 = 0.0L; |
| int main() |
| { |
| int failed_tests = 0; |
| /* This test fails on glibc 2.11 powerpc. */ |
| { |
| volatile long double x = 1.5L; /* 3 * 2^-1 */ |
| volatile long double y = x; |
| volatile long double z = ldexpl (1.0L, LDBL_MANT_DIG + 1); /* 2^65 */ |
| /* x * y + z with infinite precision: 2^65 + 9 * 2^-2. |
| Lies between (2^63 + 0) * 2^2 and (2^63 + 1) * 2^2 |
| and is closer to (2^63 + 1) * 2^2, therefore the rounding |
| must round up and produce (2^63 + 1) * 2^2. */ |
| volatile long double expected = z + 4.0L; |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 1; |
| } |
| /* This test fails on glibc 2.11 powerpc. */ |
| { |
| volatile long double x = 1.25L; /* 2^0 + 2^-2 */ |
| volatile long double y = - x; |
| volatile long double z = ldexpl (1.0L, LDBL_MANT_DIG + 1); /* 2^65 */ |
| /* x * y + z with infinite precision: 2^65 - 2^0 - 2^-1 - 2^-4. |
| Lies between (2^64 - 1) * 2^1 and 2^64 * 2^1 |
| and is closer to (2^64 - 1) * 2^1, therefore the rounding |
| must round down and produce (2^64 - 1) * 2^1. */ |
| volatile long double expected = (ldexpl (1.0L, LDBL_MANT_DIG) - 1.0L) * 2.0L; |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 1; |
| } |
| /* This test fails on glibc 2.11 x86,x86_64,powerpc, glibc 2.7 hppa,sparc, |
| OSF/1 5.1, mingw. */ |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, 1 - LDBL_MANT_DIG); /* 2^0 + 2^-63 */ |
| volatile long double y = x; |
| volatile long double z = 4.0L; /* 2^2 */ |
| /* x * y + z with infinite precision: 2^2 + 2^0 + 2^-62 + 2^-126. |
| Lies between (2^63 + 2^61) * 2^-61 and (2^63 + 2^61 + 1) * 2^-61 |
| and is closer to (2^63 + 2^61 + 1) * 2^-61, therefore the rounding |
| must round up and produce (2^63 + 2^61 + 1) * 2^-61. */ |
| volatile long double expected = 4.0L + 1.0L + ldexpl (1.0L, 3 - LDBL_MANT_DIG); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 2; |
| } |
| /* This test fails on glibc 2.11 x86,x86_64,powerpc glibc 2.7 hppa,sparc, |
| OSF/1 5.1, mingw. */ |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, 1 - LDBL_MANT_DIG); /* 2^0 + 2^-63 */ |
| volatile long double y = - x; |
| volatile long double z = 8.0L; /* 2^3 */ |
| /* x * y + z with infinite precision: 2^2 + 2^1 + 2^0 - 2^-62 - 2^-126. |
| Lies between (2^63 + 2^62 + 2^61 - 1) * 2^-61 and |
| (2^63 + 2^62 + 2^61) * 2^-61 and is closer to |
| (2^63 + 2^62 + 2^61 - 1) * 2^-61, therefore the rounding |
| must round down and produce (2^63 + 2^62 + 2^61 - 1) * 2^-61. */ |
| volatile long double expected = 7.0L - ldexpl (1.0L, 3 - LDBL_MANT_DIG); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 2; |
| } |
| /* This test fails on glibc 2.11 powerpc. */ |
| { |
| volatile long double x = 1.25L; /* 2^0 + 2^-2 */ |
| volatile long double y = - 0.75L; /* - 2^0 + 2^-2 */ |
| volatile long double z = ldexpl (1.0L, LDBL_MANT_DIG); /* 2^64 */ |
| /* x * y + z with infinite precision: 2^64 - 2^0 + 2^-4. |
| Lies between (2^64 - 2^0) and 2^64 and is closer to (2^64 - 2^0), |
| therefore the rounding must round down and produce (2^64 - 2^0). */ |
| volatile long double expected = ldexpl (1.0L, LDBL_MANT_DIG) - 1.0L; |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 1; |
| } |
| if ((LDBL_MANT_DIG % 2) == 1) |
| { |
| /* These tests fail on glibc 2.7 hppa,sparc, OSF/1 5.1. */ |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - (LDBL_MANT_DIG + 1) / 2); /* 2^0 + 2^-27 */ |
| volatile long double y = 1.0L - ldexpl (1.0L, - (LDBL_MANT_DIG + 1) / 2); /* 2^0 - 2^-27 */ |
| volatile long double z = - ldexpl (1.0L, LDBL_MIN_EXP - LDBL_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 long double expected = 1.0L - ldexpl (1.0L, - LDBL_MANT_DIG); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 4; |
| } |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - (LDBL_MANT_DIG + 1) / 2); /* 2^0 + 2^-57 */ |
| volatile long double y = x; |
| volatile long double z = ldexpl (1.0L, - LDBL_MANT_DIG); /* 2^-113 */ |
| /* x * y + z with infinite precision: 2^0 + 2^-56 + 2^-113 + 2^-114. |
| Lies between (2^112 + 2^56) * 2^-112 and (2^112 + 2^56 + 1) * 2^-112 |
| and is closer to (2^112 + 2^56 + 1) * 2^-112, therefore the rounding |
| must round up and produce (2^112 + 2^56 + 1) * 2^-112. */ |
| volatile long double expected = |
| 1.0L + ldexpl (1.0L, - (LDBL_MANT_DIG - 1) / 2) + ldexpl (1.0L, 1 - LDBL_MANT_DIG); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 4; |
| } |
| } |
| else |
| { |
| /* These tests fail on glibc 2.11 x86,x86_64,powerpc, mingw. */ |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */ |
| volatile long double y = x; |
| volatile long double z = ldexpl (1.0L, LDBL_MIN_EXP - LDBL_MANT_DIG); /* 2^-16445 */ |
| /* x * y + z with infinite precision: 2^0 + 2^-31 + 2^-64 + 2^-16445. |
| Lies between (2^63 + 2^32 + 0) * 2^-63 and (2^63 + 2^32 + 1) * 2^-63 |
| and is closer to (2^63 + 2^32 + 1) * 2^-63, therefore the rounding |
| must round up and produce (2^63 + 2^32 + 1) * 2^-63. */ |
| volatile long double expected = |
| 1.0L + ldexpl (1.0L, 1 - LDBL_MANT_DIG / 2) + ldexpl (1.0L, 1 - LDBL_MANT_DIG); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 8; |
| } |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */ |
| volatile long double y = x; |
| volatile long double z = ldexpl (1.0L, - LDBL_MANT_DIG); /* 2^-64 */ |
| /* x * y + z with infinite precision: 2^0 + 2^-31 + 2^-63. |
| Rounding must return this value unchanged. */ |
| volatile long double expected = 1.0L + ldexpl (1.0L, 1 - LDBL_MANT_DIG / 2) + ldexpl (1.0L, 1 - LDBL_MANT_DIG); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 8; |
| } |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */ |
| volatile long double y = x; |
| volatile long double z = ldexpl (1.0L, 1 - LDBL_MANT_DIG); /* 2^-63 */ |
| /* x * y + z with infinite precision: 2^0 + 2^-31 + 2^-63 + 2^-64. |
| Lies between (2^63 + 2^32 + 1) * 2^-63 and (2^63 + 2^32 + 2) * 2^-63 |
| and is at the same distance from each. According to the round-to-even |
| rule, the rounding must round up and produce (2^63 + 2^32 + 2) * 2^-63. */ |
| volatile long double expected = 1.0L + ldexpl (1.0L, -31) + ldexpl (1.0L, -62); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 8; |
| } |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */ |
| volatile long double y = x; |
| volatile long double z = ldexpl (1.0L, LDBL_MANT_DIG / 2 + 1); /* 2^33 */ |
| /* x * y + z with infinite precision: 2^33 + 2^0 + 2^-31 + 2^-64. |
| Lies between (2^63 + 2^30) * 2^-30 and (2^63 + 2^30 + 1) * 2^-30 |
| and is closer to (2^63 + 2^30 + 1) * 2^-30, therefore the rounding |
| must round up and produce (2^63 + 2^30 + 1) * 2^-30. */ |
| volatile long double expected = z + 1.0L + ldexp (1.0L, 2 - LDBL_MANT_DIG / 2); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 8; |
| } |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */ |
| volatile long double y = x; |
| volatile long double z = - ldexpl (1.0, 1 - LDBL_MANT_DIG); /* - 2^-63 */ |
| /* x * y + z with infinite precision: 2^0 + 2^-31 - 2^-64. |
| Lies between (2^63 + 2^32 - 1) * 2^-63 and (2^63 + 2^32) * 2^-63 |
| and is at the same distance from each. According to the round-to-even |
| rule, the rounding must round up and produce (2^63 + 2^32) * 2^-63. */ |
| volatile long double expected = 1.0L + ldexpl (1.0L, 1 - LDBL_MANT_DIG / 2); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 8; |
| } |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */ |
| volatile long double y = x; |
| volatile long double z = - 1.0L; /* - 2^0 */ |
| /* x * y + z with infinite precision: 2^-31 + 2^-64. |
| Rounding must return this value unchanged. */ |
| volatile long double expected = ldexpl (1.0L, 1 - LDBL_MANT_DIG / 2) + ldexpl (1.0L, - LDBL_MANT_DIG); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 8; |
| } |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */ |
| volatile long double y = - x; |
| volatile long double z = 2.0L; /* 2^1 */ |
| /* x * y + z with infinite precision: 2^0 - 2^31 - 2^-64. |
| Rounding must return this value unchanged. */ |
| volatile long double expected = 1.0L - ldexpl (1.0L, 1 - LDBL_MANT_DIG / 2) - ldexpl (1.0L, - LDBL_MANT_DIG); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 8; |
| } |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */ |
| volatile long double y = - x; |
| volatile long double z = ldexpl (1.0L, LDBL_MANT_DIG / 2 + 2); /* 2^34 */ |
| /* x * y + z with infinite precision: 2^34 - (2^0 + 2^-31 + 2^-64). |
| Lies between (2^64 - 2^30 - 1) * 2^-30 and (2^64 - 2^30) * 2^-30 |
| and is closer to (2^64 - 2^30 - 1) * 2^-30, therefore the rounding |
| must round down and produce (2^64 - 2^30 - 1) * 2^-30. */ |
| volatile long double expected = z - 1.0L - ldexpl (1.0L, 2 - LDBL_MANT_DIG / 2); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 8; |
| } |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2 - 1); /* 2^0 + 2^-33 */ |
| volatile long double y = 1.0L - ldexpl (1.0L, - LDBL_MANT_DIG / 2 - 1); /* 2^0 - 2^-33 */ |
| volatile long double z = - ldexpl (1.0L, - LDBL_MANT_DIG - 1); /* 2^-65 */ |
| /* x * y + z with infinite precision: 2^0 - 2^-65 - 2^-66. |
| Lies between (2^64 - 1) * 2^-64 and 2^64 * 2^-64 and is closer to |
| (2^64 - 1) * 2^-64, therefore the rounding must round down and |
| produce (2^64 - 1) * 2^-64. */ |
| volatile long double expected = 1.0L - ldexpl (1.0L, - LDBL_MANT_DIG); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 8; |
| } |
| { |
| volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2 - 1); /* 2^0 + 2^-33 */ |
| volatile long double y = 1.0L - ldexpl (1.0L, - LDBL_MANT_DIG / 2 - 1); /* 2^0 - 2^-33 */ |
| volatile long double z = - 1.0L; /* 2^0 */ |
| /* x * y + z with infinite precision: - 2^-66. |
| Rounding must return this value unchanged. */ |
| volatile long double expected = - ldexpl (1.0L, - LDBL_MANT_DIG - 2); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 8; |
| } |
| } |
| /* This test fails on glibc 2.11 x86,x86_64,powerpc, glibc 2.7 hppa,sparc, |
| FreeBSD 6.4 x86, mingw. */ |
| { |
| long double minus_inf = -1.0L / p0; |
| volatile long double x = ldexpl (1.0L, LDBL_MAX_EXP - 1); |
| volatile long double y = ldexpl (1.0L, LDBL_MAX_EXP - 1); |
| volatile long double z = minus_inf; |
| volatile long double result = fmal (x, y, z); |
| if (!(result == minus_inf)) |
| failed_tests |= 16; |
| } |
| /* This test fails on glibc 2.11 x86,x86_64,powerpc glibc 2.7 hppa,sparc, |
| Mac OS X 10.5, FreeBSD 6.4 x86, OSF/1 5.1, mingw. */ |
| { |
| volatile long double x = ldexpl (1.0L, LDBL_MAX_EXP - 1); |
| volatile long double y = 2.0L; |
| volatile long double z = |
| - ldexpl (ldexpl (1.0L, LDBL_MAX_EXP - 1) - ldexpl (1.0L, LDBL_MAX_EXP - LDBL_MANT_DIG - 1), 1); |
| volatile long double expected = ldexpl (1.0L, LDBL_MAX_EXP - LDBL_MANT_DIG); |
| volatile long double result = fmal (x, y, z); |
| if (result != expected) |
| failed_tests |= 32; |
| } |
| return failed_tests; |
| }]])], |
| [gl_cv_func_fmal_works=yes], |
| [gl_cv_func_fmal_works=no], |
| [dnl Guess yes on native Windows with MSVC. |
| dnl Otherwise guess no, even on glibc systems. |
| gl_cv_func_fmal_works="$gl_cross_guess_normal" |
| case "$host_os" in |
| mingw*) |
| AC_EGREP_CPP([Known], [ |
| #ifdef _MSC_VER |
| Known |
| #endif |
| ], [gl_cv_func_fmal_works="guessing yes"]) |
| ;; |
| esac |
| ]) |
| ]) |
| LIBS="$save_LIBS" |
| ]) |
| |
| # Prerequisites of lib/fmal.c. |
| AC_DEFUN([gl_PREREQ_FMAL], [:]) |