Merge "Fix our <complex.h> support."
This commit is contained in:
Elliott Hughes
Gerrit Code Review
commit
39ba30354a
@ -18,6 +18,8 @@ libm_common_src_files += \
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upstream-freebsd/lib/msun/bsdsrc/b_exp.c \
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upstream-freebsd/lib/msun/bsdsrc/b_exp.c \
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upstream-freebsd/lib/msun/bsdsrc/b_log.c \
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upstream-freebsd/lib/msun/bsdsrc/b_log.c \
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upstream-freebsd/lib/msun/bsdsrc/b_tgamma.c \
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upstream-freebsd/lib/msun/bsdsrc/b_tgamma.c \
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upstream-freebsd/lib/msun/src/catrig.c \
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upstream-freebsd/lib/msun/src/catrigf.c \
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upstream-freebsd/lib/msun/src/e_acos.c \
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upstream-freebsd/lib/msun/src/e_acos.c \
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upstream-freebsd/lib/msun/src/e_acosf.c \
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upstream-freebsd/lib/msun/src/e_acosf.c \
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upstream-freebsd/lib/msun/src/e_acosh.c \
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upstream-freebsd/lib/msun/src/e_acosh.c \
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@ -84,6 +86,7 @@ libm_common_src_files += \
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upstream-freebsd/lib/msun/src/s_atanf.c \
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upstream-freebsd/lib/msun/src/s_atanf.c \
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upstream-freebsd/lib/msun/src/s_carg.c \
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upstream-freebsd/lib/msun/src/s_carg.c \
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upstream-freebsd/lib/msun/src/s_cargf.c \
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upstream-freebsd/lib/msun/src/s_cargf.c \
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upstream-freebsd/lib/msun/src/s_cargl.c \
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upstream-freebsd/lib/msun/src/s_cbrt.c \
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upstream-freebsd/lib/msun/src/s_cbrt.c \
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upstream-freebsd/lib/msun/src/s_cbrtf.c \
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upstream-freebsd/lib/msun/src/s_cbrtf.c \
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upstream-freebsd/lib/msun/src/s_ccosh.c \
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upstream-freebsd/lib/msun/src/s_ccosh.c \
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@ -94,20 +97,25 @@ libm_common_src_files += \
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upstream-freebsd/lib/msun/src/s_cexpf.c \
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upstream-freebsd/lib/msun/src/s_cexpf.c \
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upstream-freebsd/lib/msun/src/s_cimag.c \
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upstream-freebsd/lib/msun/src/s_cimag.c \
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upstream-freebsd/lib/msun/src/s_cimagf.c \
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upstream-freebsd/lib/msun/src/s_cimagf.c \
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upstream-freebsd/lib/msun/src/s_cimagl.c \
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upstream-freebsd/lib/msun/src/s_conj.c \
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upstream-freebsd/lib/msun/src/s_conj.c \
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upstream-freebsd/lib/msun/src/s_conjf.c \
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upstream-freebsd/lib/msun/src/s_conjf.c \
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upstream-freebsd/lib/msun/src/s_conjl.c \
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upstream-freebsd/lib/msun/src/s_copysign.c \
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upstream-freebsd/lib/msun/src/s_copysign.c \
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upstream-freebsd/lib/msun/src/s_copysignf.c \
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upstream-freebsd/lib/msun/src/s_copysignf.c \
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upstream-freebsd/lib/msun/src/s_cos.c \
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upstream-freebsd/lib/msun/src/s_cos.c \
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upstream-freebsd/lib/msun/src/s_cosf.c \
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upstream-freebsd/lib/msun/src/s_cosf.c \
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upstream-freebsd/lib/msun/src/s_cproj.c \
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upstream-freebsd/lib/msun/src/s_cproj.c \
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upstream-freebsd/lib/msun/src/s_cprojf.c \
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upstream-freebsd/lib/msun/src/s_cprojf.c \
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upstream-freebsd/lib/msun/src/s_cprojl.c \
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upstream-freebsd/lib/msun/src/s_creal.c \
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upstream-freebsd/lib/msun/src/s_creal.c \
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upstream-freebsd/lib/msun/src/s_crealf.c \
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upstream-freebsd/lib/msun/src/s_crealf.c \
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upstream-freebsd/lib/msun/src/s_creall.c \
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upstream-freebsd/lib/msun/src/s_csinh.c \
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upstream-freebsd/lib/msun/src/s_csinh.c \
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upstream-freebsd/lib/msun/src/s_csinhf.c \
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upstream-freebsd/lib/msun/src/s_csinhf.c \
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upstream-freebsd/lib/msun/src/s_csqrt.c \
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upstream-freebsd/lib/msun/src/s_csqrt.c \
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upstream-freebsd/lib/msun/src/s_csqrtf.c \
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upstream-freebsd/lib/msun/src/s_csqrtf.c \
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upstream-freebsd/lib/msun/src/s_csqrtl.c \
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upstream-freebsd/lib/msun/src/s_ctanh.c \
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upstream-freebsd/lib/msun/src/s_ctanh.c \
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upstream-freebsd/lib/msun/src/s_ctanhf.c \
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upstream-freebsd/lib/msun/src/s_ctanhf.c \
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upstream-freebsd/lib/msun/src/s_erf.c \
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upstream-freebsd/lib/msun/src/s_erf.c \
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@ -174,6 +182,7 @@ libm_common_src_files += \
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upstream-freebsd/lib/msun/src/s_truncf.c \
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upstream-freebsd/lib/msun/src/s_truncf.c \
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upstream-freebsd/lib/msun/src/w_cabs.c \
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upstream-freebsd/lib/msun/src/w_cabs.c \
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upstream-freebsd/lib/msun/src/w_cabsf.c \
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upstream-freebsd/lib/msun/src/w_cabsf.c \
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upstream-freebsd/lib/msun/src/w_cabsl.c \
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upstream-freebsd/lib/msun/src/w_drem.c \
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upstream-freebsd/lib/msun/src/w_drem.c \
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upstream-freebsd/lib/msun/src/w_dremf.c \
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upstream-freebsd/lib/msun/src/w_dremf.c \
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@ -181,7 +190,7 @@ libm_common_src_files += \
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fake_long_double.c \
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fake_long_double.c \
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signbit.c \
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signbit.c \
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libm_ld_src_files = \
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libm_ld128_src_files = \
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upstream-freebsd/lib/msun/src/e_acosl.c \
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upstream-freebsd/lib/msun/src/e_acosl.c \
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upstream-freebsd/lib/msun/src/e_acoshl.c \
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upstream-freebsd/lib/msun/src/e_acoshl.c \
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upstream-freebsd/lib/msun/src/e_asinl.c \
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upstream-freebsd/lib/msun/src/e_asinl.c \
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@ -225,7 +234,7 @@ libm_ld_src_files = \
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upstream-freebsd/lib/msun/src/s_tanl.c \
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upstream-freebsd/lib/msun/src/s_tanl.c \
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upstream-freebsd/lib/msun/src/s_truncl.c \
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upstream-freebsd/lib/msun/src/s_truncl.c \
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libm_ld_src_files += \
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libm_ld128_src_files += \
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upstream-freebsd/lib/msun/ld128/invtrig.c \
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upstream-freebsd/lib/msun/ld128/invtrig.c \
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upstream-freebsd/lib/msun/ld128/e_lgammal_r.c \
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upstream-freebsd/lib/msun/ld128/e_lgammal_r.c \
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upstream-freebsd/lib/msun/ld128/k_cosl.c \
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upstream-freebsd/lib/msun/ld128/k_cosl.c \
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@ -282,18 +291,18 @@ LOCAL_C_INCLUDES_arm := $(LOCAL_PATH)/arm
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LOCAL_SRC_FILES_arm := arm/fenv.c
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LOCAL_SRC_FILES_arm := arm/fenv.c
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LOCAL_C_INCLUDES_arm64 := $(libm_ld_includes)
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LOCAL_C_INCLUDES_arm64 := $(libm_ld_includes)
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LOCAL_SRC_FILES_arm64 := arm64/fenv.c $(libm_ld_src_files)
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LOCAL_SRC_FILES_arm64 := arm64/fenv.c $(libm_ld128_src_files)
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LOCAL_C_INCLUDES_x86 := $(LOCAL_PATH)/i387
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LOCAL_C_INCLUDES_x86 := $(LOCAL_PATH)/i387
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LOCAL_SRC_FILES_x86 := i387/fenv.c
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LOCAL_SRC_FILES_x86 := i387/fenv.c
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LOCAL_C_INCLUDES_x86_64 := $(libm_ld_includes)
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LOCAL_C_INCLUDES_x86_64 := $(libm_ld_includes)
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LOCAL_SRC_FILES_x86_64 := amd64/fenv.c $(libm_ld_src_files)
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LOCAL_SRC_FILES_x86_64 := amd64/fenv.c $(libm_ld128_src_files)
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LOCAL_SRC_FILES_mips := mips/fenv.c
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LOCAL_SRC_FILES_mips := mips/fenv.c
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LOCAL_C_INCLUDES_mips64 := $(libm_ld_includes)
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LOCAL_C_INCLUDES_mips64 := $(libm_ld_includes)
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LOCAL_SRC_FILES_mips64 := mips/fenv.c $(libm_ld_src_files)
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LOCAL_SRC_FILES_mips64 := mips/fenv.c $(libm_ld128_src_files)
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LOCAL_CXX_STL := none
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LOCAL_CXX_STL := none
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include $(BUILD_STATIC_LIBRARY)
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include $(BUILD_STATIC_LIBRARY)
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@ -46,14 +46,39 @@ _Static_assert(__generic(_Complex_I, float _Complex, 1, 0),
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#define complex _Complex
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#define complex _Complex
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#define I _Complex_I
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#define I _Complex_I
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#if __ISO_C_VISIBLE >= 2011
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#ifdef __clang__
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#define CMPLX(x, y) ((double complex){ x, y })
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#define CMPLXF(x, y) ((float complex){ x, y })
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#define CMPLXL(x, y) ((long double complex){ x, y })
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#elif __GNUC_PREREQ__(4, 7)
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#define CMPLX(x, y) __builtin_complex((double)(x), (double)(y))
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#define CMPLXF(x, y) __builtin_complex((float)(x), (float)(y))
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#define CMPLXL(x, y) __builtin_complex((long double)(x), (long double)(y))
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#endif
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#endif /* __ISO_C_VISIBLE >= 2011 */
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__BEGIN_DECLS
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__BEGIN_DECLS
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#pragma GCC visibility push(default)
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double cabs(double complex);
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double cabs(double complex);
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float cabsf(float complex);
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float cabsf(float complex);
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long double cabsl(long double complex);
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long double cabsl(long double complex);
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double complex cacos(double complex);
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float complex cacosf(float complex);
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double complex cacosh(double complex);
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float complex cacoshf(float complex);
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double carg(double complex);
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double carg(double complex);
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float cargf(float complex);
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float cargf(float complex);
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long double cargl(long double complex);
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long double cargl(long double complex);
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double complex casin(double complex);
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float complex casinf(float complex);
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double complex casinh(double complex);
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float complex casinhf(float complex);
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double complex catan(double complex);
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float complex catanf(float complex);
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double complex catanh(double complex);
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float complex catanhf(float complex);
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double complex ccos(double complex);
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double complex ccos(double complex);
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float complex ccosf(float complex);
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float complex ccosf(float complex);
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double complex ccosh(double complex);
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double complex ccosh(double complex);
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@ -87,6 +112,7 @@ float complex ctanf(float complex);
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double complex ctanh(double complex);
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double complex ctanh(double complex);
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float complex ctanhf(float complex);
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float complex ctanhf(float complex);
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#pragma GCC visibility pop
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__END_DECLS
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__END_DECLS
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#endif /* _COMPLEX_H */
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#endif /* _COMPLEX_H */
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639
libm/upstream-freebsd/lib/msun/src/catrig.c
Normal file
639
libm/upstream-freebsd/lib/msun/src/catrig.c
Normal file
@ -0,0 +1,639 @@
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/*-
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* Copyright (c) 2012 Stephen Montgomery-Smith <stephen@FreeBSD.ORG>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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|
* modification, are permitted provided that the following conditions
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* are met:
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|
* 1. Redistributions of source code must retain the above copyright
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|
* notice, this list of conditions and the following disclaimer.
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||||||
|
* 2. Redistributions in binary form must reproduce the above copyright
|
||||||
|
* notice, this list of conditions and the following disclaimer in the
|
||||||
|
* documentation and/or other materials provided with the distribution.
|
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|
*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
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|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||||
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
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|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
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|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||||
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||||
|
* SUCH DAMAGE.
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||||||
|
*/
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|
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#include <complex.h>
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#include <float.h>
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#include "math.h"
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|
#include "math_private.h"
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|
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#undef isinf
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#define isinf(x) (fabs(x) == INFINITY)
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|
#undef isnan
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#define isnan(x) ((x) != (x))
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#define raise_inexact() do { volatile float junk = 1 + tiny; } while(0)
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#undef signbit
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#define signbit(x) (__builtin_signbit(x))
|
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|
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/* We need that DBL_EPSILON^2/128 is larger than FOUR_SQRT_MIN. */
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static const double
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|
A_crossover = 10, /* Hull et al suggest 1.5, but 10 works better */
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|
B_crossover = 0.6417, /* suggested by Hull et al */
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FOUR_SQRT_MIN = 0x1p-509, /* >= 4 * sqrt(DBL_MIN) */
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QUARTER_SQRT_MAX = 0x1p509, /* <= sqrt(DBL_MAX) / 4 */
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m_e = 2.7182818284590452e0, /* 0x15bf0a8b145769.0p-51 */
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|
m_ln2 = 6.9314718055994531e-1, /* 0x162e42fefa39ef.0p-53 */
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pio2_hi = 1.5707963267948966e0, /* 0x1921fb54442d18.0p-52 */
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|
RECIP_EPSILON = 1 / DBL_EPSILON,
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|
SQRT_3_EPSILON = 2.5809568279517849e-8, /* 0x1bb67ae8584caa.0p-78 */
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|
SQRT_6_EPSILON = 3.6500241499888571e-8, /* 0x13988e1409212e.0p-77 */
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|
SQRT_MIN = 0x1p-511; /* >= sqrt(DBL_MIN) */
|
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|
|
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|
static const volatile double
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|
pio2_lo = 6.1232339957367659e-17; /* 0x11a62633145c07.0p-106 */
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|
static const volatile float
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|
tiny = 0x1p-100;
|
||||||
|
|
||||||
|
static double complex clog_for_large_values(double complex z);
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|
||||||
|
/*
|
||||||
|
* Testing indicates that all these functions are accurate up to 4 ULP.
|
||||||
|
* The functions casin(h) and cacos(h) are about 2.5 times slower than asinh.
|
||||||
|
* The functions catan(h) are a little under 2 times slower than atanh.
|
||||||
|
*
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||||||
|
* The code for casinh, casin, cacos, and cacosh comes first. The code is
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|
* rather complicated, and the four functions are highly interdependent.
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|
*
|
||||||
|
* The code for catanh and catan comes at the end. It is much simpler than
|
||||||
|
* the other functions, and the code for these can be disconnected from the
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||||||
|
* rest of the code.
|
||||||
|
*/
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|
|
||||||
|
/*
|
||||||
|
* ================================
|
||||||
|
* | casinh, casin, cacos, cacosh |
|
||||||
|
* ================================
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
* The algorithm is very close to that in "Implementing the complex arcsine
|
||||||
|
* and arccosine functions using exception handling" by T. E. Hull, Thomas F.
|
||||||
|
* Fairgrieve, and Ping Tak Peter Tang, published in ACM Transactions on
|
||||||
|
* Mathematical Software, Volume 23 Issue 3, 1997, Pages 299-335,
|
||||||
|
* http://dl.acm.org/citation.cfm?id=275324.
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||||||
|
*
|
||||||
|
* Throughout we use the convention z = x + I*y.
|
||||||
|
*
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||||||
|
* casinh(z) = sign(x)*log(A+sqrt(A*A-1)) + I*asin(B)
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||||||
|
* where
|
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|
* A = (|z+I| + |z-I|) / 2
|
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|
* B = (|z+I| - |z-I|) / 2 = y/A
|
||||||
|
*
|
||||||
|
* These formulas become numerically unstable:
|
||||||
|
* (a) for Re(casinh(z)) when z is close to the line segment [-I, I] (that
|
||||||
|
* is, Re(casinh(z)) is close to 0);
|
||||||
|
* (b) for Im(casinh(z)) when z is close to either of the intervals
|
||||||
|
* [I, I*infinity) or (-I*infinity, -I] (that is, |Im(casinh(z))| is
|
||||||
|
* close to PI/2).
|
||||||
|
*
|
||||||
|
* These numerical problems are overcome by defining
|
||||||
|
* f(a, b) = (hypot(a, b) - b) / 2 = a*a / (hypot(a, b) + b) / 2
|
||||||
|
* Then if A < A_crossover, we use
|
||||||
|
* log(A + sqrt(A*A-1)) = log1p((A-1) + sqrt((A-1)*(A+1)))
|
||||||
|
* A-1 = f(x, 1+y) + f(x, 1-y)
|
||||||
|
* and if B > B_crossover, we use
|
||||||
|
* asin(B) = atan2(y, sqrt(A*A - y*y)) = atan2(y, sqrt((A+y)*(A-y)))
|
||||||
|
* A-y = f(x, y+1) + f(x, y-1)
|
||||||
|
* where without loss of generality we have assumed that x and y are
|
||||||
|
* non-negative.
|
||||||
|
*
|
||||||
|
* Much of the difficulty comes because the intermediate computations may
|
||||||
|
* produce overflows or underflows. This is dealt with in the paper by Hull
|
||||||
|
* et al by using exception handling. We do this by detecting when
|
||||||
|
* computations risk underflow or overflow. The hardest part is handling the
|
||||||
|
* underflows when computing f(a, b).
|
||||||
|
*
|
||||||
|
* Note that the function f(a, b) does not appear explicitly in the paper by
|
||||||
|
* Hull et al, but the idea may be found on pages 308 and 309. Introducing the
|
||||||
|
* function f(a, b) allows us to concentrate many of the clever tricks in this
|
||||||
|
* paper into one function.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
* Function f(a, b, hypot_a_b) = (hypot(a, b) - b) / 2.
|
||||||
|
* Pass hypot(a, b) as the third argument.
|
||||||
|
*/
|
||||||
|
static inline double
|
||||||
|
f(double a, double b, double hypot_a_b)
|
||||||
|
{
|
||||||
|
if (b < 0)
|
||||||
|
return ((hypot_a_b - b) / 2);
|
||||||
|
if (b == 0)
|
||||||
|
return (a / 2);
|
||||||
|
return (a * a / (hypot_a_b + b) / 2);
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* All the hard work is contained in this function.
|
||||||
|
* x and y are assumed positive or zero, and less than RECIP_EPSILON.
|
||||||
|
* Upon return:
|
||||||
|
* rx = Re(casinh(z)) = -Im(cacos(y + I*x)).
|
||||||
|
* B_is_usable is set to 1 if the value of B is usable.
|
||||||
|
* If B_is_usable is set to 0, sqrt_A2my2 = sqrt(A*A - y*y), and new_y = y.
|
||||||
|
* If returning sqrt_A2my2 has potential to result in an underflow, it is
|
||||||
|
* rescaled, and new_y is similarly rescaled.
|
||||||
|
*/
|
||||||
|
static inline void
|
||||||
|
do_hard_work(double x, double y, double *rx, int *B_is_usable, double *B,
|
||||||
|
double *sqrt_A2my2, double *new_y)
|
||||||
|
{
|
||||||
|
double R, S, A; /* A, B, R, and S are as in Hull et al. */
|
||||||
|
double Am1, Amy; /* A-1, A-y. */
|
||||||
|
|
||||||
|
R = hypot(x, y + 1); /* |z+I| */
|
||||||
|
S = hypot(x, y - 1); /* |z-I| */
|
||||||
|
|
||||||
|
/* A = (|z+I| + |z-I|) / 2 */
|
||||||
|
A = (R + S) / 2;
|
||||||
|
/*
|
||||||
|
* Mathematically A >= 1. There is a small chance that this will not
|
||||||
|
* be so because of rounding errors. So we will make certain it is
|
||||||
|
* so.
|
||||||
|
*/
|
||||||
|
if (A < 1)
|
||||||
|
A = 1;
|
||||||
|
|
||||||
|
if (A < A_crossover) {
|
||||||
|
/*
|
||||||
|
* Am1 = fp + fm, where fp = f(x, 1+y), and fm = f(x, 1-y).
|
||||||
|
* rx = log1p(Am1 + sqrt(Am1*(A+1)))
|
||||||
|
*/
|
||||||
|
if (y == 1 && x < DBL_EPSILON * DBL_EPSILON / 128) {
|
||||||
|
/*
|
||||||
|
* fp is of order x^2, and fm = x/2.
|
||||||
|
* A = 1 (inexactly).
|
||||||
|
*/
|
||||||
|
*rx = sqrt(x);
|
||||||
|
} else if (x >= DBL_EPSILON * fabs(y - 1)) {
|
||||||
|
/*
|
||||||
|
* Underflow will not occur because
|
||||||
|
* x >= DBL_EPSILON^2/128 >= FOUR_SQRT_MIN
|
||||||
|
*/
|
||||||
|
Am1 = f(x, 1 + y, R) + f(x, 1 - y, S);
|
||||||
|
*rx = log1p(Am1 + sqrt(Am1 * (A + 1)));
|
||||||
|
} else if (y < 1) {
|
||||||
|
/*
|
||||||
|
* fp = x*x/(1+y)/4, fm = x*x/(1-y)/4, and
|
||||||
|
* A = 1 (inexactly).
|
||||||
|
*/
|
||||||
|
*rx = x / sqrt((1 - y) * (1 + y));
|
||||||
|
} else { /* if (y > 1) */
|
||||||
|
/*
|
||||||
|
* A-1 = y-1 (inexactly).
|
||||||
|
*/
|
||||||
|
*rx = log1p((y - 1) + sqrt((y - 1) * (y + 1)));
|
||||||
|
}
|
||||||
|
} else {
|
||||||
|
*rx = log(A + sqrt(A * A - 1));
|
||||||
|
}
|
||||||
|
|
||||||
|
*new_y = y;
|
||||||
|
|
||||||
|
if (y < FOUR_SQRT_MIN) {
|
||||||
|
/*
|
||||||
|
* Avoid a possible underflow caused by y/A. For casinh this
|
||||||
|
* would be legitimate, but will be picked up by invoking atan2
|
||||||
|
* later on. For cacos this would not be legitimate.
|
||||||
|
*/
|
||||||
|
*B_is_usable = 0;
|
||||||
|
*sqrt_A2my2 = A * (2 / DBL_EPSILON);
|
||||||
|
*new_y = y * (2 / DBL_EPSILON);
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* B = (|z+I| - |z-I|) / 2 = y/A */
|
||||||
|
*B = y / A;
|
||||||
|
*B_is_usable = 1;
|
||||||
|
|
||||||
|
if (*B > B_crossover) {
|
||||||
|
*B_is_usable = 0;
|
||||||
|
/*
|
||||||
|
* Amy = fp + fm, where fp = f(x, y+1), and fm = f(x, y-1).
|
||||||
|
* sqrt_A2my2 = sqrt(Amy*(A+y))
|
||||||
|
*/
|
||||||
|
if (y == 1 && x < DBL_EPSILON / 128) {
|
||||||
|
/*
|
||||||
|
* fp is of order x^2, and fm = x/2.
|
||||||
|
* A = 1 (inexactly).
|
||||||
|
*/
|
||||||
|
*sqrt_A2my2 = sqrt(x) * sqrt((A + y) / 2);
|
||||||
|
} else if (x >= DBL_EPSILON * fabs(y - 1)) {
|
||||||
|
/*
|
||||||
|
* Underflow will not occur because
|
||||||
|
* x >= DBL_EPSILON/128 >= FOUR_SQRT_MIN
|
||||||
|
* and
|
||||||
|
* x >= DBL_EPSILON^2 >= FOUR_SQRT_MIN
|
||||||
|
*/
|
||||||
|
Amy = f(x, y + 1, R) + f(x, y - 1, S);
|
||||||
|
*sqrt_A2my2 = sqrt(Amy * (A + y));
|
||||||
|
} else if (y > 1) {
|
||||||
|
/*
|
||||||
|
* fp = x*x/(y+1)/4, fm = x*x/(y-1)/4, and
|
||||||
|
* A = y (inexactly).
|
||||||
|
*
|
||||||
|
* y < RECIP_EPSILON. So the following
|
||||||
|
* scaling should avoid any underflow problems.
|
||||||
|
*/
|
||||||
|
*sqrt_A2my2 = x * (4 / DBL_EPSILON / DBL_EPSILON) * y /
|
||||||
|
sqrt((y + 1) * (y - 1));
|
||||||
|
*new_y = y * (4 / DBL_EPSILON / DBL_EPSILON);
|
||||||
|
} else { /* if (y < 1) */
|
||||||
|
/*
|
||||||
|
* fm = 1-y >= DBL_EPSILON, fp is of order x^2, and
|
||||||
|
* A = 1 (inexactly).
|
||||||
|
*/
|
||||||
|
*sqrt_A2my2 = sqrt((1 - y) * (1 + y));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* casinh(z) = z + O(z^3) as z -> 0
|
||||||
|
*
|
||||||
|
* casinh(z) = sign(x)*clog(sign(x)*z) + O(1/z^2) as z -> infinity
|
||||||
|
* The above formula works for the imaginary part as well, because
|
||||||
|
* Im(casinh(z)) = sign(x)*atan2(sign(x)*y, fabs(x)) + O(y/z^3)
|
||||||
|
* as z -> infinity, uniformly in y
|
||||||
|
*/
|
||||||
|
double complex
|
||||||
|
casinh(double complex z)
|
||||||
|
{
|
||||||
|
double x, y, ax, ay, rx, ry, B, sqrt_A2my2, new_y;
|
||||||
|
int B_is_usable;
|
||||||
|
double complex w;
|
||||||
|
|
||||||
|
x = creal(z);
|
||||||
|
y = cimag(z);
|
||||||
|
ax = fabs(x);
|
||||||
|
ay = fabs(y);
|
||||||
|
|
||||||
|
if (isnan(x) || isnan(y)) {
|
||||||
|
/* casinh(+-Inf + I*NaN) = +-Inf + I*NaN */
|
||||||
|
if (isinf(x))
|
||||||
|
return (cpack(x, y + y));
|
||||||
|
/* casinh(NaN + I*+-Inf) = opt(+-)Inf + I*NaN */
|
||||||
|
if (isinf(y))
|
||||||
|
return (cpack(y, x + x));
|
||||||
|
/* casinh(NaN + I*0) = NaN + I*0 */
|
||||||
|
if (y == 0)
|
||||||
|
return (cpack(x + x, y));
|
||||||
|
/*
|
||||||
|
* All other cases involving NaN return NaN + I*NaN.
|
||||||
|
* C99 leaves it optional whether to raise invalid if one of
|
||||||
|
* the arguments is not NaN, so we opt not to raise it.
|
||||||
|
*/
|
||||||
|
return (cpack(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
|
||||||
|
}
|
||||||
|
|
||||||
|
if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
|
||||||
|
/* clog...() will raise inexact unless x or y is infinite. */
|
||||||
|
if (signbit(x) == 0)
|
||||||
|
w = clog_for_large_values(z) + m_ln2;
|
||||||
|
else
|
||||||
|
w = clog_for_large_values(-z) + m_ln2;
|
||||||
|
return (cpack(copysign(creal(w), x), copysign(cimag(w), y)));
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Avoid spuriously raising inexact for z = 0. */
|
||||||
|
if (x == 0 && y == 0)
|
||||||
|
return (z);
|
||||||
|
|
||||||
|
/* All remaining cases are inexact. */
|
||||||
|
raise_inexact();
|
||||||
|
|
||||||
|
if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
|
||||||
|
return (z);
|
||||||
|
|
||||||
|
do_hard_work(ax, ay, &rx, &B_is_usable, &B, &sqrt_A2my2, &new_y);
|
||||||
|
if (B_is_usable)
|
||||||
|
ry = asin(B);
|
||||||
|
else
|
||||||
|
ry = atan2(new_y, sqrt_A2my2);
|
||||||
|
return (cpack(copysign(rx, x), copysign(ry, y)));
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* casin(z) = reverse(casinh(reverse(z)))
|
||||||
|
* where reverse(x + I*y) = y + I*x = I*conj(z).
|
||||||
|
*/
|
||||||
|
double complex
|
||||||
|
casin(double complex z)
|
||||||
|
{
|
||||||
|
double complex w = casinh(cpack(cimag(z), creal(z)));
|
||||||
|
|
||||||
|
return (cpack(cimag(w), creal(w)));
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* cacos(z) = PI/2 - casin(z)
|
||||||
|
* but do the computation carefully so cacos(z) is accurate when z is
|
||||||
|
* close to 1.
|
||||||
|
*
|
||||||
|
* cacos(z) = PI/2 - z + O(z^3) as z -> 0
|
||||||
|
*
|
||||||
|
* cacos(z) = -sign(y)*I*clog(z) + O(1/z^2) as z -> infinity
|
||||||
|
* The above formula works for the real part as well, because
|
||||||
|
* Re(cacos(z)) = atan2(fabs(y), x) + O(y/z^3)
|
||||||
|
* as z -> infinity, uniformly in y
|
||||||
|
*/
|
||||||
|
double complex
|
||||||
|
cacos(double complex z)
|
||||||
|
{
|
||||||
|
double x, y, ax, ay, rx, ry, B, sqrt_A2mx2, new_x;
|
||||||
|
int sx, sy;
|
||||||
|
int B_is_usable;
|
||||||
|
double complex w;
|
||||||
|
|
||||||
|
x = creal(z);
|
||||||
|
y = cimag(z);
|
||||||
|
sx = signbit(x);
|
||||||
|
sy = signbit(y);
|
||||||
|
ax = fabs(x);
|
||||||
|
ay = fabs(y);
|
||||||
|
|
||||||
|
if (isnan(x) || isnan(y)) {
|
||||||
|
/* cacos(+-Inf + I*NaN) = NaN + I*opt(-)Inf */
|
||||||
|
if (isinf(x))
|
||||||
|
return (cpack(y + y, -INFINITY));
|
||||||
|
/* cacos(NaN + I*+-Inf) = NaN + I*-+Inf */
|
||||||
|
if (isinf(y))
|
||||||
|
return (cpack(x + x, -y));
|
||||||
|
/* cacos(0 + I*NaN) = PI/2 + I*NaN with inexact */
|
||||||
|
if (x == 0)
|
||||||
|
return (cpack(pio2_hi + pio2_lo, y + y));
|
||||||
|
/*
|
||||||
|
* All other cases involving NaN return NaN + I*NaN.
|
||||||
|
* C99 leaves it optional whether to raise invalid if one of
|
||||||
|
* the arguments is not NaN, so we opt not to raise it.
|
||||||
|
*/
|
||||||
|
return (cpack(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
|
||||||
|
}
|
||||||
|
|
||||||
|
if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
|
||||||
|
/* clog...() will raise inexact unless x or y is infinite. */
|
||||||
|
w = clog_for_large_values(z);
|
||||||
|
rx = fabs(cimag(w));
|
||||||
|
ry = creal(w) + m_ln2;
|
||||||
|
if (sy == 0)
|
||||||
|
ry = -ry;
|
||||||
|
return (cpack(rx, ry));
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Avoid spuriously raising inexact for z = 1. */
|
||||||
|
if (x == 1 && y == 0)
|
||||||
|
return (cpack(0, -y));
|
||||||
|
|
||||||
|
/* All remaining cases are inexact. */
|
||||||
|
raise_inexact();
|
||||||
|
|
||||||
|
if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
|
||||||
|
return (cpack(pio2_hi - (x - pio2_lo), -y));
|
||||||
|
|
||||||
|
do_hard_work(ay, ax, &ry, &B_is_usable, &B, &sqrt_A2mx2, &new_x);
|
||||||
|
if (B_is_usable) {
|
||||||
|
if (sx == 0)
|
||||||
|
rx = acos(B);
|
||||||
|
else
|
||||||
|
rx = acos(-B);
|
||||||
|
} else {
|
||||||
|
if (sx == 0)
|
||||||
|
rx = atan2(sqrt_A2mx2, new_x);
|
||||||
|
else
|
||||||
|
rx = atan2(sqrt_A2mx2, -new_x);
|
||||||
|
}
|
||||||
|
if (sy == 0)
|
||||||
|
ry = -ry;
|
||||||
|
return (cpack(rx, ry));
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* cacosh(z) = I*cacos(z) or -I*cacos(z)
|
||||||
|
* where the sign is chosen so Re(cacosh(z)) >= 0.
|
||||||
|
*/
|
||||||
|
double complex
|
||||||
|
cacosh(double complex z)
|
||||||
|
{
|
||||||
|
double complex w;
|
||||||
|
double rx, ry;
|
||||||
|
|
||||||
|
w = cacos(z);
|
||||||
|
rx = creal(w);
|
||||||
|
ry = cimag(w);
|
||||||
|
/* cacosh(NaN + I*NaN) = NaN + I*NaN */
|
||||||
|
if (isnan(rx) && isnan(ry))
|
||||||
|
return (cpack(ry, rx));
|
||||||
|
/* cacosh(NaN + I*+-Inf) = +Inf + I*NaN */
|
||||||
|
/* cacosh(+-Inf + I*NaN) = +Inf + I*NaN */
|
||||||
|
if (isnan(rx))
|
||||||
|
return (cpack(fabs(ry), rx));
|
||||||
|
/* cacosh(0 + I*NaN) = NaN + I*NaN */
|
||||||
|
if (isnan(ry))
|
||||||
|
return (cpack(ry, ry));
|
||||||
|
return (cpack(fabs(ry), copysign(rx, cimag(z))));
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* Optimized version of clog() for |z| finite and larger than ~RECIP_EPSILON.
|
||||||
|
*/
|
||||||
|
static double complex
|
||||||
|
clog_for_large_values(double complex z)
|
||||||
|
{
|
||||||
|
double x, y;
|
||||||
|
double ax, ay, t;
|
||||||
|
|
||||||
|
x = creal(z);
|
||||||
|
y = cimag(z);
|
||||||
|
ax = fabs(x);
|
||||||
|
ay = fabs(y);
|
||||||
|
if (ax < ay) {
|
||||||
|
t = ax;
|
||||||
|
ax = ay;
|
||||||
|
ay = t;
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* Avoid overflow in hypot() when x and y are both very large.
|
||||||
|
* Divide x and y by E, and then add 1 to the logarithm. This depends
|
||||||
|
* on E being larger than sqrt(2).
|
||||||
|
* Dividing by E causes an insignificant loss of accuracy; however
|
||||||
|
* this method is still poor since it is uneccessarily slow.
|
||||||
|
*/
|
||||||
|
if (ax > DBL_MAX / 2)
|
||||||
|
return (cpack(log(hypot(x / m_e, y / m_e)) + 1, atan2(y, x)));
|
||||||
|
|
||||||
|
/*
|
||||||
|
* Avoid overflow when x or y is large. Avoid underflow when x or
|
||||||
|
* y is small.
|
||||||
|
*/
|
||||||
|
if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN)
|
||||||
|
return (cpack(log(hypot(x, y)), atan2(y, x)));
|
||||||
|
|
||||||
|
return (cpack(log(ax * ax + ay * ay) / 2, atan2(y, x)));
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* =================
|
||||||
|
* | catanh, catan |
|
||||||
|
* =================
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
* sum_squares(x,y) = x*x + y*y (or just x*x if y*y would underflow).
|
||||||
|
* Assumes x*x and y*y will not overflow.
|
||||||
|
* Assumes x and y are finite.
|
||||||
|
* Assumes y is non-negative.
|
||||||
|
* Assumes fabs(x) >= DBL_EPSILON.
|
||||||
|
*/
|
||||||
|
static inline double
|
||||||
|
sum_squares(double x, double y)
|
||||||
|
{
|
||||||
|
|
||||||
|
/* Avoid underflow when y is small. */
|
||||||
|
if (y < SQRT_MIN)
|
||||||
|
return (x * x);
|
||||||
|
|
||||||
|
return (x * x + y * y);
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* real_part_reciprocal(x, y) = Re(1/(x+I*y)) = x/(x*x + y*y).
|
||||||
|
* Assumes x and y are not NaN, and one of x and y is larger than
|
||||||
|
* RECIP_EPSILON. We avoid unwarranted underflow. It is important to not use
|
||||||
|
* the code creal(1/z), because the imaginary part may produce an unwanted
|
||||||
|
* underflow.
|
||||||
|
* This is only called in a context where inexact is always raised before
|
||||||
|
* the call, so no effort is made to avoid or force inexact.
|
||||||
|
*/
|
||||||
|
static inline double
|
||||||
|
real_part_reciprocal(double x, double y)
|
||||||
|
{
|
||||||
|
double scale;
|
||||||
|
uint32_t hx, hy;
|
||||||
|
int32_t ix, iy;
|
||||||
|
|
||||||
|
/*
|
||||||
|
* This code is inspired by the C99 document n1124.pdf, Section G.5.1,
|
||||||
|
* example 2.
|
||||||
|
*/
|
||||||
|
GET_HIGH_WORD(hx, x);
|
||||||
|
ix = hx & 0x7ff00000;
|
||||||
|
GET_HIGH_WORD(hy, y);
|
||||||
|
iy = hy & 0x7ff00000;
|
||||||
|
#define BIAS (DBL_MAX_EXP - 1)
|
||||||
|
/* XXX more guard digits are useful iff there is extra precision. */
|
||||||
|
#define CUTOFF (DBL_MANT_DIG / 2 + 1) /* just half or 1 guard digit */
|
||||||
|
if (ix - iy >= CUTOFF << 20 || isinf(x))
|
||||||
|
return (1 / x); /* +-Inf -> +-0 is special */
|
||||||
|
if (iy - ix >= CUTOFF << 20)
|
||||||
|
return (x / y / y); /* should avoid double div, but hard */
|
||||||
|
if (ix <= (BIAS + DBL_MAX_EXP / 2 - CUTOFF) << 20)
|
||||||
|
return (x / (x * x + y * y));
|
||||||
|
scale = 1;
|
||||||
|
SET_HIGH_WORD(scale, 0x7ff00000 - ix); /* 2**(1-ilogb(x)) */
|
||||||
|
x *= scale;
|
||||||
|
y *= scale;
|
||||||
|
return (x / (x * x + y * y) * scale);
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* catanh(z) = log((1+z)/(1-z)) / 2
|
||||||
|
* = log1p(4*x / |z-1|^2) / 4
|
||||||
|
* + I * atan2(2*y, (1-x)*(1+x)-y*y) / 2
|
||||||
|
*
|
||||||
|
* catanh(z) = z + O(z^3) as z -> 0
|
||||||
|
*
|
||||||
|
* catanh(z) = 1/z + sign(y)*I*PI/2 + O(1/z^3) as z -> infinity
|
||||||
|
* The above formula works for the real part as well, because
|
||||||
|
* Re(catanh(z)) = x/|z|^2 + O(x/z^4)
|
||||||
|
* as z -> infinity, uniformly in x
|
||||||
|
*/
|
||||||
|
double complex
|
||||||
|
catanh(double complex z)
|
||||||
|
{
|
||||||
|
double x, y, ax, ay, rx, ry;
|
||||||
|
|
||||||
|
x = creal(z);
|
||||||
|
y = cimag(z);
|
||||||
|
ax = fabs(x);
|
||||||
|
ay = fabs(y);
|
||||||
|
|
||||||
|
/* This helps handle many cases. */
|
||||||
|
if (y == 0 && ax <= 1)
|
||||||
|
return (cpack(atanh(x), y));
|
||||||
|
|
||||||
|
/* To ensure the same accuracy as atan(), and to filter out z = 0. */
|
||||||
|
if (x == 0)
|
||||||
|
return (cpack(x, atan(y)));
|
||||||
|
|
||||||
|
if (isnan(x) || isnan(y)) {
|
||||||
|
/* catanh(+-Inf + I*NaN) = +-0 + I*NaN */
|
||||||
|
if (isinf(x))
|
||||||
|
return (cpack(copysign(0, x), y + y));
|
||||||
|
/* catanh(NaN + I*+-Inf) = sign(NaN)0 + I*+-PI/2 */
|
||||||
|
if (isinf(y))
|
||||||
|
return (cpack(copysign(0, x),
|
||||||
|
copysign(pio2_hi + pio2_lo, y)));
|
||||||
|
/*
|
||||||
|
* All other cases involving NaN return NaN + I*NaN.
|
||||||
|
* C99 leaves it optional whether to raise invalid if one of
|
||||||
|
* the arguments is not NaN, so we opt not to raise it.
|
||||||
|
*/
|
||||||
|
return (cpack(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
|
||||||
|
}
|
||||||
|
|
||||||
|
if (ax > RECIP_EPSILON || ay > RECIP_EPSILON)
|
||||||
|
return (cpack(real_part_reciprocal(x, y),
|
||||||
|
copysign(pio2_hi + pio2_lo, y)));
|
||||||
|
|
||||||
|
if (ax < SQRT_3_EPSILON / 2 && ay < SQRT_3_EPSILON / 2) {
|
||||||
|
/*
|
||||||
|
* z = 0 was filtered out above. All other cases must raise
|
||||||
|
* inexact, but this is the only only that needs to do it
|
||||||
|
* explicitly.
|
||||||
|
*/
|
||||||
|
raise_inexact();
|
||||||
|
return (z);
|
||||||
|
}
|
||||||
|
|
||||||
|
if (ax == 1 && ay < DBL_EPSILON)
|
||||||
|
rx = (m_ln2 - log(ay)) / 2;
|
||||||
|
else
|
||||||
|
rx = log1p(4 * ax / sum_squares(ax - 1, ay)) / 4;
|
||||||
|
|
||||||
|
if (ax == 1)
|
||||||
|
ry = atan2(2, -ay) / 2;
|
||||||
|
else if (ay < DBL_EPSILON)
|
||||||
|
ry = atan2(2 * ay, (1 - ax) * (1 + ax)) / 2;
|
||||||
|
else
|
||||||
|
ry = atan2(2 * ay, (1 - ax) * (1 + ax) - ay * ay) / 2;
|
||||||
|
|
||||||
|
return (cpack(copysign(rx, x), copysign(ry, y)));
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* catan(z) = reverse(catanh(reverse(z)))
|
||||||
|
* where reverse(x + I*y) = y + I*x = I*conj(z).
|
||||||
|
*/
|
||||||
|
double complex
|
||||||
|
catan(double complex z)
|
||||||
|
{
|
||||||
|
double complex w = catanh(cpack(cimag(z), creal(z)));
|
||||||
|
|
||||||
|
return (cpack(cimag(w), creal(w)));
|
||||||
|
}
|
||||||
393
libm/upstream-freebsd/lib/msun/src/catrigf.c
Normal file
393
libm/upstream-freebsd/lib/msun/src/catrigf.c
Normal file
@ -0,0 +1,393 @@
|
|||||||
|
/*-
|
||||||
|
* Copyright (c) 2012 Stephen Montgomery-Smith <stephen@FreeBSD.ORG>
|
||||||
|
* All rights reserved.
|
||||||
|
*
|
||||||
|
* Redistribution and use in source and binary forms, with or without
|
||||||
|
* modification, are permitted provided that the following conditions
|
||||||
|
* are met:
|
||||||
|
* 1. Redistributions of source code must retain the above copyright
|
||||||
|
* notice, this list of conditions and the following disclaimer.
|
||||||
|
* 2. Redistributions in binary form must reproduce the above copyright
|
||||||
|
* notice, this list of conditions and the following disclaimer in the
|
||||||
|
* documentation and/or other materials provided with the distribution.
|
||||||
|
*
|
||||||
|
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
|
||||||
|
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||||
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||||
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
|
||||||
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||||
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||||
|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||||
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||||
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||||
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||||
|
* SUCH DAMAGE.
|
||||||
|
*/
|
||||||
|
|
||||||
|
/*
|
||||||
|
* The algorithm is very close to that in "Implementing the complex arcsine
|
||||||
|
* and arccosine functions using exception handling" by T. E. Hull, Thomas F.
|
||||||
|
* Fairgrieve, and Ping Tak Peter Tang, published in ACM Transactions on
|
||||||
|
* Mathematical Software, Volume 23 Issue 3, 1997, Pages 299-335,
|
||||||
|
* http://dl.acm.org/citation.cfm?id=275324.
|
||||||
|
*
|
||||||
|
* See catrig.c for complete comments.
|
||||||
|
*
|
||||||
|
* XXX comments were removed automatically, and even short ones on the right
|
||||||
|
* of statements were removed (all of them), contrary to normal style. Only
|
||||||
|
* a few comments on the right of declarations remain.
|
||||||
|
*/
|
||||||
|
|
||||||
|
#include <sys/cdefs.h>
|
||||||
|
__FBSDID("$FreeBSD$");
|
||||||
|
|
||||||
|
#include <complex.h>
|
||||||
|
#include <float.h>
|
||||||
|
|
||||||
|
#include "math.h"
|
||||||
|
#include "math_private.h"
|
||||||
|
|
||||||
|
#undef isinf
|
||||||
|
#define isinf(x) (fabsf(x) == INFINITY)
|
||||||
|
#undef isnan
|
||||||
|
#define isnan(x) ((x) != (x))
|
||||||
|
#define raise_inexact() do { volatile float junk = 1 + tiny; } while(0)
|
||||||
|
#undef signbit
|
||||||
|
#define signbit(x) (__builtin_signbitf(x))
|
||||||
|
|
||||||
|
static const float
|
||||||
|
A_crossover = 10,
|
||||||
|
B_crossover = 0.6417,
|
||||||
|
FOUR_SQRT_MIN = 0x1p-61,
|
||||||
|
QUARTER_SQRT_MAX = 0x1p61,
|
||||||
|
m_e = 2.7182818285e0, /* 0xadf854.0p-22 */
|
||||||
|
m_ln2 = 6.9314718056e-1, /* 0xb17218.0p-24 */
|
||||||
|
pio2_hi = 1.5707962513e0, /* 0xc90fda.0p-23 */
|
||||||
|
RECIP_EPSILON = 1 / FLT_EPSILON,
|
||||||
|
SQRT_3_EPSILON = 5.9801995673e-4, /* 0x9cc471.0p-34 */
|
||||||
|
SQRT_6_EPSILON = 8.4572793338e-4, /* 0xddb3d7.0p-34 */
|
||||||
|
SQRT_MIN = 0x1p-63;
|
||||||
|
|
||||||
|
static const volatile float
|
||||||
|
pio2_lo = 7.5497899549e-8, /* 0xa22169.0p-47 */
|
||||||
|
tiny = 0x1p-100;
|
||||||
|
|
||||||
|
static float complex clog_for_large_values(float complex z);
|
||||||
|
|
||||||
|
static inline float
|
||||||
|
f(float a, float b, float hypot_a_b)
|
||||||
|
{
|
||||||
|
if (b < 0)
|
||||||
|
return ((hypot_a_b - b) / 2);
|
||||||
|
if (b == 0)
|
||||||
|
return (a / 2);
|
||||||
|
return (a * a / (hypot_a_b + b) / 2);
|
||||||
|
}
|
||||||
|
|
||||||
|
static inline void
|
||||||
|
do_hard_work(float x, float y, float *rx, int *B_is_usable, float *B,
|
||||||
|
float *sqrt_A2my2, float *new_y)
|
||||||
|
{
|
||||||
|
float R, S, A;
|
||||||
|
float Am1, Amy;
|
||||||
|
|
||||||
|
R = hypotf(x, y + 1);
|
||||||
|
S = hypotf(x, y - 1);
|
||||||
|
|
||||||
|
A = (R + S) / 2;
|
||||||
|
if (A < 1)
|
||||||
|
A = 1;
|
||||||
|
|
||||||
|
if (A < A_crossover) {
|
||||||
|
if (y == 1 && x < FLT_EPSILON * FLT_EPSILON / 128) {
|
||||||
|
*rx = sqrtf(x);
|
||||||
|
} else if (x >= FLT_EPSILON * fabsf(y - 1)) {
|
||||||
|
Am1 = f(x, 1 + y, R) + f(x, 1 - y, S);
|
||||||
|
*rx = log1pf(Am1 + sqrtf(Am1 * (A + 1)));
|
||||||
|
} else if (y < 1) {
|
||||||
|
*rx = x / sqrtf((1 - y) * (1 + y));
|
||||||
|
} else {
|
||||||
|
*rx = log1pf((y - 1) + sqrtf((y - 1) * (y + 1)));
|
||||||
|
}
|
||||||
|
} else {
|
||||||
|
*rx = logf(A + sqrtf(A * A - 1));
|
||||||
|
}
|
||||||
|
|
||||||
|
*new_y = y;
|
||||||
|
|
||||||
|
if (y < FOUR_SQRT_MIN) {
|
||||||
|
*B_is_usable = 0;
|
||||||
|
*sqrt_A2my2 = A * (2 / FLT_EPSILON);
|
||||||
|
*new_y = y * (2 / FLT_EPSILON);
|
||||||
|
return;
|
||||||
|
}
|
||||||
|
|
||||||
|
*B = y / A;
|
||||||
|
*B_is_usable = 1;
|
||||||
|
|
||||||
|
if (*B > B_crossover) {
|
||||||
|
*B_is_usable = 0;
|
||||||
|
if (y == 1 && x < FLT_EPSILON / 128) {
|
||||||
|
*sqrt_A2my2 = sqrtf(x) * sqrtf((A + y) / 2);
|
||||||
|
} else if (x >= FLT_EPSILON * fabsf(y - 1)) {
|
||||||
|
Amy = f(x, y + 1, R) + f(x, y - 1, S);
|
||||||
|
*sqrt_A2my2 = sqrtf(Amy * (A + y));
|
||||||
|
} else if (y > 1) {
|
||||||
|
*sqrt_A2my2 = x * (4 / FLT_EPSILON / FLT_EPSILON) * y /
|
||||||
|
sqrtf((y + 1) * (y - 1));
|
||||||
|
*new_y = y * (4 / FLT_EPSILON / FLT_EPSILON);
|
||||||
|
} else {
|
||||||
|
*sqrt_A2my2 = sqrtf((1 - y) * (1 + y));
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
float complex
|
||||||
|
casinhf(float complex z)
|
||||||
|
{
|
||||||
|
float x, y, ax, ay, rx, ry, B, sqrt_A2my2, new_y;
|
||||||
|
int B_is_usable;
|
||||||
|
float complex w;
|
||||||
|
|
||||||
|
x = crealf(z);
|
||||||
|
y = cimagf(z);
|
||||||
|
ax = fabsf(x);
|
||||||
|
ay = fabsf(y);
|
||||||
|
|
||||||
|
if (isnan(x) || isnan(y)) {
|
||||||
|
if (isinf(x))
|
||||||
|
return (cpackf(x, y + y));
|
||||||
|
if (isinf(y))
|
||||||
|
return (cpackf(y, x + x));
|
||||||
|
if (y == 0)
|
||||||
|
return (cpackf(x + x, y));
|
||||||
|
return (cpackf(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
|
||||||
|
}
|
||||||
|
|
||||||
|
if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
|
||||||
|
if (signbit(x) == 0)
|
||||||
|
w = clog_for_large_values(z) + m_ln2;
|
||||||
|
else
|
||||||
|
w = clog_for_large_values(-z) + m_ln2;
|
||||||
|
return (cpackf(copysignf(crealf(w), x),
|
||||||
|
copysignf(cimagf(w), y)));
|
||||||
|
}
|
||||||
|
|
||||||
|
if (x == 0 && y == 0)
|
||||||
|
return (z);
|
||||||
|
|
||||||
|
raise_inexact();
|
||||||
|
|
||||||
|
if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
|
||||||
|
return (z);
|
||||||
|
|
||||||
|
do_hard_work(ax, ay, &rx, &B_is_usable, &B, &sqrt_A2my2, &new_y);
|
||||||
|
if (B_is_usable)
|
||||||
|
ry = asinf(B);
|
||||||
|
else
|
||||||
|
ry = atan2f(new_y, sqrt_A2my2);
|
||||||
|
return (cpackf(copysignf(rx, x), copysignf(ry, y)));
|
||||||
|
}
|
||||||
|
|
||||||
|
float complex
|
||||||
|
casinf(float complex z)
|
||||||
|
{
|
||||||
|
float complex w = casinhf(cpackf(cimagf(z), crealf(z)));
|
||||||
|
|
||||||
|
return (cpackf(cimagf(w), crealf(w)));
|
||||||
|
}
|
||||||
|
|
||||||
|
float complex
|
||||||
|
cacosf(float complex z)
|
||||||
|
{
|
||||||
|
float x, y, ax, ay, rx, ry, B, sqrt_A2mx2, new_x;
|
||||||
|
int sx, sy;
|
||||||
|
int B_is_usable;
|
||||||
|
float complex w;
|
||||||
|
|
||||||
|
x = crealf(z);
|
||||||
|
y = cimagf(z);
|
||||||
|
sx = signbit(x);
|
||||||
|
sy = signbit(y);
|
||||||
|
ax = fabsf(x);
|
||||||
|
ay = fabsf(y);
|
||||||
|
|
||||||
|
if (isnan(x) || isnan(y)) {
|
||||||
|
if (isinf(x))
|
||||||
|
return (cpackf(y + y, -INFINITY));
|
||||||
|
if (isinf(y))
|
||||||
|
return (cpackf(x + x, -y));
|
||||||
|
if (x == 0)
|
||||||
|
return (cpackf(pio2_hi + pio2_lo, y + y));
|
||||||
|
return (cpackf(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
|
||||||
|
}
|
||||||
|
|
||||||
|
if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
|
||||||
|
w = clog_for_large_values(z);
|
||||||
|
rx = fabsf(cimagf(w));
|
||||||
|
ry = crealf(w) + m_ln2;
|
||||||
|
if (sy == 0)
|
||||||
|
ry = -ry;
|
||||||
|
return (cpackf(rx, ry));
|
||||||
|
}
|
||||||
|
|
||||||
|
if (x == 1 && y == 0)
|
||||||
|
return (cpackf(0, -y));
|
||||||
|
|
||||||
|
raise_inexact();
|
||||||
|
|
||||||
|
if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
|
||||||
|
return (cpackf(pio2_hi - (x - pio2_lo), -y));
|
||||||
|
|
||||||
|
do_hard_work(ay, ax, &ry, &B_is_usable, &B, &sqrt_A2mx2, &new_x);
|
||||||
|
if (B_is_usable) {
|
||||||
|
if (sx == 0)
|
||||||
|
rx = acosf(B);
|
||||||
|
else
|
||||||
|
rx = acosf(-B);
|
||||||
|
} else {
|
||||||
|
if (sx == 0)
|
||||||
|
rx = atan2f(sqrt_A2mx2, new_x);
|
||||||
|
else
|
||||||
|
rx = atan2f(sqrt_A2mx2, -new_x);
|
||||||
|
}
|
||||||
|
if (sy == 0)
|
||||||
|
ry = -ry;
|
||||||
|
return (cpackf(rx, ry));
|
||||||
|
}
|
||||||
|
|
||||||
|
float complex
|
||||||
|
cacoshf(float complex z)
|
||||||
|
{
|
||||||
|
float complex w;
|
||||||
|
float rx, ry;
|
||||||
|
|
||||||
|
w = cacosf(z);
|
||||||
|
rx = crealf(w);
|
||||||
|
ry = cimagf(w);
|
||||||
|
if (isnan(rx) && isnan(ry))
|
||||||
|
return (cpackf(ry, rx));
|
||||||
|
if (isnan(rx))
|
||||||
|
return (cpackf(fabsf(ry), rx));
|
||||||
|
if (isnan(ry))
|
||||||
|
return (cpackf(ry, ry));
|
||||||
|
return (cpackf(fabsf(ry), copysignf(rx, cimagf(z))));
|
||||||
|
}
|
||||||
|
|
||||||
|
static float complex
|
||||||
|
clog_for_large_values(float complex z)
|
||||||
|
{
|
||||||
|
float x, y;
|
||||||
|
float ax, ay, t;
|
||||||
|
|
||||||
|
x = crealf(z);
|
||||||
|
y = cimagf(z);
|
||||||
|
ax = fabsf(x);
|
||||||
|
ay = fabsf(y);
|
||||||
|
if (ax < ay) {
|
||||||
|
t = ax;
|
||||||
|
ax = ay;
|
||||||
|
ay = t;
|
||||||
|
}
|
||||||
|
|
||||||
|
if (ax > FLT_MAX / 2)
|
||||||
|
return (cpackf(logf(hypotf(x / m_e, y / m_e)) + 1,
|
||||||
|
atan2f(y, x)));
|
||||||
|
|
||||||
|
if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN)
|
||||||
|
return (cpackf(logf(hypotf(x, y)), atan2f(y, x)));
|
||||||
|
|
||||||
|
return (cpackf(logf(ax * ax + ay * ay) / 2, atan2f(y, x)));
|
||||||
|
}
|
||||||
|
|
||||||
|
static inline float
|
||||||
|
sum_squares(float x, float y)
|
||||||
|
{
|
||||||
|
|
||||||
|
if (y < SQRT_MIN)
|
||||||
|
return (x * x);
|
||||||
|
|
||||||
|
return (x * x + y * y);
|
||||||
|
}
|
||||||
|
|
||||||
|
static inline float
|
||||||
|
real_part_reciprocal(float x, float y)
|
||||||
|
{
|
||||||
|
float scale;
|
||||||
|
uint32_t hx, hy;
|
||||||
|
int32_t ix, iy;
|
||||||
|
|
||||||
|
GET_FLOAT_WORD(hx, x);
|
||||||
|
ix = hx & 0x7f800000;
|
||||||
|
GET_FLOAT_WORD(hy, y);
|
||||||
|
iy = hy & 0x7f800000;
|
||||||
|
#define BIAS (FLT_MAX_EXP - 1)
|
||||||
|
#define CUTOFF (FLT_MANT_DIG / 2 + 1)
|
||||||
|
if (ix - iy >= CUTOFF << 23 || isinf(x))
|
||||||
|
return (1 / x);
|
||||||
|
if (iy - ix >= CUTOFF << 23)
|
||||||
|
return (x / y / y);
|
||||||
|
if (ix <= (BIAS + FLT_MAX_EXP / 2 - CUTOFF) << 23)
|
||||||
|
return (x / (x * x + y * y));
|
||||||
|
SET_FLOAT_WORD(scale, 0x7f800000 - ix);
|
||||||
|
x *= scale;
|
||||||
|
y *= scale;
|
||||||
|
return (x / (x * x + y * y) * scale);
|
||||||
|
}
|
||||||
|
|
||||||
|
float complex
|
||||||
|
catanhf(float complex z)
|
||||||
|
{
|
||||||
|
float x, y, ax, ay, rx, ry;
|
||||||
|
|
||||||
|
x = crealf(z);
|
||||||
|
y = cimagf(z);
|
||||||
|
ax = fabsf(x);
|
||||||
|
ay = fabsf(y);
|
||||||
|
|
||||||
|
if (y == 0 && ax <= 1)
|
||||||
|
return (cpackf(atanhf(x), y));
|
||||||
|
|
||||||
|
if (x == 0)
|
||||||
|
return (cpackf(x, atanf(y)));
|
||||||
|
|
||||||
|
if (isnan(x) || isnan(y)) {
|
||||||
|
if (isinf(x))
|
||||||
|
return (cpackf(copysignf(0, x), y + y));
|
||||||
|
if (isinf(y))
|
||||||
|
return (cpackf(copysignf(0, x),
|
||||||
|
copysignf(pio2_hi + pio2_lo, y)));
|
||||||
|
return (cpackf(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
|
||||||
|
}
|
||||||
|
|
||||||
|
if (ax > RECIP_EPSILON || ay > RECIP_EPSILON)
|
||||||
|
return (cpackf(real_part_reciprocal(x, y),
|
||||||
|
copysignf(pio2_hi + pio2_lo, y)));
|
||||||
|
|
||||||
|
if (ax < SQRT_3_EPSILON / 2 && ay < SQRT_3_EPSILON / 2) {
|
||||||
|
raise_inexact();
|
||||||
|
return (z);
|
||||||
|
}
|
||||||
|
|
||||||
|
if (ax == 1 && ay < FLT_EPSILON)
|
||||||
|
rx = (m_ln2 - logf(ay)) / 2;
|
||||||
|
else
|
||||||
|
rx = log1pf(4 * ax / sum_squares(ax - 1, ay)) / 4;
|
||||||
|
|
||||||
|
if (ax == 1)
|
||||||
|
ry = atan2f(2, -ay) / 2;
|
||||||
|
else if (ay < FLT_EPSILON)
|
||||||
|
ry = atan2f(2 * ay, (1 - ax) * (1 + ax)) / 2;
|
||||||
|
else
|
||||||
|
ry = atan2f(2 * ay, (1 - ax) * (1 + ax) - ay * ay) / 2;
|
||||||
|
|
||||||
|
return (cpackf(copysignf(rx, x), copysignf(ry, y)));
|
||||||
|
}
|
||||||
|
|
||||||
|
float complex
|
||||||
|
catanf(float complex z)
|
||||||
|
{
|
||||||
|
float complex w = catanhf(cpackf(cimagf(z), crealf(z)));
|
||||||
|
|
||||||
|
return (cpackf(cimagf(w), crealf(w)));
|
||||||
|
}
|
||||||
@ -54,6 +54,7 @@ test_cppflags = \
|
|||||||
libBionicStandardTests_src_files := \
|
libBionicStandardTests_src_files := \
|
||||||
arpa_inet_test.cpp \
|
arpa_inet_test.cpp \
|
||||||
buffer_tests.cpp \
|
buffer_tests.cpp \
|
||||||
|
complex_test.cpp \
|
||||||
ctype_test.cpp \
|
ctype_test.cpp \
|
||||||
dirent_test.cpp \
|
dirent_test.cpp \
|
||||||
eventfd_test.cpp \
|
eventfd_test.cpp \
|
||||||
|
|||||||
260
tests/complex_test.cpp
Normal file
260
tests/complex_test.cpp
Normal file
@ -0,0 +1,260 @@
|
|||||||
|
/*
|
||||||
|
* Copyright (C) 2014 The Android Open Source Project
|
||||||
|
*
|
||||||
|
* Licensed under the Apache License, Version 2.0 (the "License");
|
||||||
|
* you may not use this file except in compliance with the License.
|
||||||
|
* You may obtain a copy of the License at
|
||||||
|
*
|
||||||
|
* http://www.apache.org/licenses/LICENSE-2.0
|
||||||
|
*
|
||||||
|
* Unless required by applicable law or agreed to in writing, software
|
||||||
|
* distributed under the License is distributed on an "AS IS" BASIS,
|
||||||
|
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
||||||
|
* See the License for the specific language governing permissions and
|
||||||
|
* limitations under the License.
|
||||||
|
*/
|
||||||
|
|
||||||
|
#include <gtest/gtest.h>
|
||||||
|
|
||||||
|
// libc++ actively gets in the way of including <complex.h> from C++, so we
|
||||||
|
// have to declare the complex math functions ourselves.
|
||||||
|
// (libc++ also seems to have really bad implementations of its own that ignore
|
||||||
|
// the intricacies of floating point math.)
|
||||||
|
// http://llvm.org/bugs/show_bug.cgi?id=21504
|
||||||
|
|
||||||
|
#include <math.h> // For M_PI.
|
||||||
|
|
||||||
|
extern "C" double cabs(double _Complex);
|
||||||
|
TEST(complex, cabs) {
|
||||||
|
ASSERT_EQ(0.0, cabs(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float cabsf(float _Complex);
|
||||||
|
TEST(complex, cabsf) {
|
||||||
|
ASSERT_EQ(0.0, cabsf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" long double cabsl(long double _Complex);
|
||||||
|
TEST(complex, cabsl) {
|
||||||
|
ASSERT_EQ(0.0, cabsl(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex cacos(double _Complex);
|
||||||
|
TEST(complex, cacos) {
|
||||||
|
ASSERT_EQ(M_PI/2.0, cacos(0.0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex cacosf(float _Complex);
|
||||||
|
TEST(complex, cacosf) {
|
||||||
|
ASSERT_EQ(static_cast<float>(M_PI)/2.0f, cacosf(0.0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex cacosh(double _Complex);
|
||||||
|
TEST(complex, cacosh) {
|
||||||
|
ASSERT_EQ(0.0, cacosh(1.0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex cacoshf(float _Complex);
|
||||||
|
TEST(complex, cacoshf) {
|
||||||
|
ASSERT_EQ(0.0, cacoshf(1.0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double carg(double _Complex);
|
||||||
|
TEST(complex, carg) {
|
||||||
|
ASSERT_EQ(0.0, carg(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float cargf(float _Complex);
|
||||||
|
TEST(complex, cargf) {
|
||||||
|
ASSERT_EQ(0.0, cargf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" long double cargl(long double _Complex);
|
||||||
|
TEST(complex, cargl) {
|
||||||
|
ASSERT_EQ(0.0, cargl(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex casin(double _Complex);
|
||||||
|
TEST(complex, casin) {
|
||||||
|
ASSERT_EQ(0.0, casin(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex casinf(float _Complex);
|
||||||
|
TEST(complex, casinf) {
|
||||||
|
ASSERT_EQ(0.0, casinf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex casinh(double _Complex);
|
||||||
|
TEST(complex, casinh) {
|
||||||
|
ASSERT_EQ(0.0, casinh(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex casinhf(float _Complex);
|
||||||
|
TEST(complex, casinhf) {
|
||||||
|
ASSERT_EQ(0.0, casinhf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex catan(double _Complex);
|
||||||
|
TEST(complex, catan) {
|
||||||
|
ASSERT_EQ(0.0, catan(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex catanf(float _Complex);
|
||||||
|
TEST(complex, catanf) {
|
||||||
|
ASSERT_EQ(0.0, catanf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex catanh(double _Complex);
|
||||||
|
TEST(complex, catanh) {
|
||||||
|
ASSERT_EQ(0.0, catanh(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex catanhf(float _Complex);
|
||||||
|
TEST(complex, catanhf) {
|
||||||
|
ASSERT_EQ(0.0, catanhf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex ccos(double _Complex);
|
||||||
|
TEST(complex, ccos) {
|
||||||
|
ASSERT_EQ(1.0, ccos(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex ccosf(float _Complex);
|
||||||
|
TEST(complex, ccosf) {
|
||||||
|
ASSERT_EQ(1.0, ccosf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex ccosh(double _Complex);
|
||||||
|
TEST(complex, ccosh) {
|
||||||
|
ASSERT_EQ(1.0, ccosh(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex ccoshf(float _Complex);
|
||||||
|
TEST(complex, ccoshf) {
|
||||||
|
ASSERT_EQ(1.0, ccoshf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex cexp(double _Complex);
|
||||||
|
TEST(complex, cexp) {
|
||||||
|
ASSERT_EQ(1.0, cexp(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex cexpf(float _Complex);
|
||||||
|
TEST(complex, cexpf) {
|
||||||
|
ASSERT_EQ(1.0, cexpf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double cimag(double _Complex);
|
||||||
|
TEST(complex, cimag) {
|
||||||
|
ASSERT_EQ(0.0, cimag(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float cimagf(float _Complex);
|
||||||
|
TEST(complex, cimagf) {
|
||||||
|
ASSERT_EQ(0.0f, cimagf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" long double cimagl(long double _Complex);
|
||||||
|
TEST(complex, cimagl) {
|
||||||
|
ASSERT_EQ(0.0, cimagl(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex conj(double _Complex);
|
||||||
|
TEST(complex, conj) {
|
||||||
|
ASSERT_EQ(0.0, conj(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex conjf(float _Complex);
|
||||||
|
TEST(complex, conjf) {
|
||||||
|
ASSERT_EQ(0.0f, conjf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" long double _Complex conjl(long double _Complex);
|
||||||
|
TEST(complex, conjl) {
|
||||||
|
ASSERT_EQ(0.0, conjl(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex cproj(double _Complex);
|
||||||
|
TEST(complex, cproj) {
|
||||||
|
ASSERT_EQ(0.0, cproj(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex cprojf(float _Complex);
|
||||||
|
TEST(complex, cprojf) {
|
||||||
|
ASSERT_EQ(0.0f, cprojf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" long double _Complex cprojl(long double _Complex);
|
||||||
|
TEST(complex, cprojl) {
|
||||||
|
ASSERT_EQ(0.0, cprojl(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double creal(double _Complex);
|
||||||
|
TEST(complex, creal) {
|
||||||
|
ASSERT_EQ(0.0, creal(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float crealf(float _Complex);
|
||||||
|
TEST(complex, crealf) {
|
||||||
|
ASSERT_EQ(0.0f, crealf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" long double creall(long double _Complex);
|
||||||
|
TEST(complex, creall) {
|
||||||
|
ASSERT_EQ(0.0, creall(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex csin(double _Complex);
|
||||||
|
TEST(complex, csin) {
|
||||||
|
ASSERT_EQ(0.0, csin(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex csinf(float _Complex);
|
||||||
|
TEST(complex, csinf) {
|
||||||
|
ASSERT_EQ(0.0, csinf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex csinh(double _Complex);
|
||||||
|
TEST(complex, csinh) {
|
||||||
|
ASSERT_EQ(0.0, csinh(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex csinhf(float _Complex);
|
||||||
|
TEST(complex, csinhf) {
|
||||||
|
ASSERT_EQ(0.0, csinhf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex csqrt(double _Complex);
|
||||||
|
TEST(complex, csqrt) {
|
||||||
|
ASSERT_EQ(0.0, csqrt(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex csqrtf(float _Complex);
|
||||||
|
TEST(complex, csqrtf) {
|
||||||
|
ASSERT_EQ(0.0f, csqrt(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" long double _Complex csqrtl(long double _Complex);
|
||||||
|
TEST(complex, csqrtl) {
|
||||||
|
ASSERT_EQ(0.0, csqrtl(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex ctan(double _Complex);
|
||||||
|
TEST(complex, ctan) {
|
||||||
|
ASSERT_EQ(0.0, ctan(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex ctanf(float _Complex);
|
||||||
|
TEST(complex, ctanf) {
|
||||||
|
ASSERT_EQ(0.0, ctanf(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" double _Complex ctanh(double _Complex);
|
||||||
|
TEST(complex, ctanh) {
|
||||||
|
ASSERT_EQ(0.0, ctanh(0));
|
||||||
|
}
|
||||||
|
|
||||||
|
extern "C" float _Complex ctanhf(float _Complex);
|
||||||
|
TEST(complex, ctanhf) {
|
||||||
|
ASSERT_EQ(0.0, ctanhf(0));
|
||||||
|
}
|
||||||
Loading…
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Reference in New Issue
Block a user