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catrig.c
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catrigf.c
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catrigl.c
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e_acos.c
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e_acosf.c
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e_acosh.c
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e_acoshf.c
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e_acoshl.c
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e_acosl.c
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e_asin.c
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e_asinf.c
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e_asinl.c
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e_atan2.c
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e_atan2f.c
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e_atan2l.c
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e_atanh.c
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e_atanhf.c
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e_atanhl.c
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e_cosh.c
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e_coshf.c
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e_coshl.c
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e_exp.c
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e_expf.c
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e_fmod.c
(3.34 KB)
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e_fmodf.c
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e_fmodl.c
(3.77 KB)
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e_gamma.c
(725 B)
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e_gamma_r.c
(801 B)
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e_gammaf.c
(814 B)
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e_gammaf_r.c
(890 B)
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e_hypot.c
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e_hypotf.c
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e_hypotl.c
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e_j0.c
(14.39 KB)
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e_j0f.c
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e_j1.c
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e_j1f.c
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e_jn.c
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e_jnf.c
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e_lgamma.c
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e_lgamma_r.c
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e_lgammaf.c
(820 B)
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e_lgammaf_r.c
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e_lgammal.c
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e_log.c
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e_log10.c
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e_log10f.c
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e_log2.c
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e_log2f.c
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e_logf.c
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e_pow.c
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e_powf.c
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e_rem_pio2.c
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e_rem_pio2f.c
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e_remainder.c
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e_remainderf.c
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e_remainderl.c
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e_scalb.c
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e_scalbf.c
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e_sinh.c
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e_sinhf.c
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e_sinhl.c
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e_sqrt.c
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e_sqrtf.c
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e_sqrtl.c
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fenv-softfloat.h
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imprecise.c
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k_cos.c
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k_cosf.c
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k_exp.c
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k_expf.c
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k_log.h
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k_logf.h
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k_rem_pio2.c
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k_sin.c
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k_sincos.h
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k_sincosf.h
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k_sincosl.h
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k_sinf.c
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k_tan.c
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k_tanf.c
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math.h
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math_private.h
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s_asinh.c
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s_asinhf.c
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s_asinhl.c
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s_atan.c
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s_atanf.c
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s_atanl.c
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s_carg.c
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s_cargf.c
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s_cargl.c
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s_cbrt.c
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s_cbrtf.c
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s_cbrtl.c
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s_ccosh.c
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s_ccoshf.c
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s_ceil.c
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s_ceilf.c
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s_ceill.c
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s_cexp.c
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s_cexpf.c
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s_cimag.c
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s_cimagf.c
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s_cimagl.c
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s_clog.c
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s_clogf.c
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s_clogl.c
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s_conj.c
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s_conjf.c
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s_conjl.c
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s_copysign.c
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s_copysignf.c
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s_copysignl.c
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s_cos.c
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s_cosf.c
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s_cosl.c
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s_cpow.c
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s_cpowf.c
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s_cpowl.c
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s_cproj.c
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s_cprojf.c
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s_cprojl.c
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s_creal.c
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s_crealf.c
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s_creall.c
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s_csinh.c
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s_csinhf.c
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s_csqrt.c
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s_csqrtf.c
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s_csqrtl.c
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s_ctanh.c
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s_ctanhf.c
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s_erf.c
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s_erff.c
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s_exp2.c
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s_exp2f.c
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s_expm1.c
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s_expm1f.c
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s_fabs.c
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s_fabsf.c
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s_fabsl.c
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s_fdim.c
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s_finite.c
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s_finitef.c
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s_floor.c
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s_floorf.c
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s_floorl.c
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s_fma.c
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s_fmaf.c
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s_fmal.c
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s_fmax.c
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s_fmaxf.c
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s_fmaxl.c
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s_fmin.c
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s_fminf.c
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s_fminl.c
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s_frexp.c
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s_frexpf.c
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s_frexpl.c
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s_ilogb.c
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s_ilogbf.c
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s_ilogbl.c
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s_isfinite.c
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s_isnan.c
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s_isnormal.c
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s_llrint.c
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s_llrintf.c
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s_llrintl.c
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s_llround.c
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s_llroundf.c
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s_llroundl.c
(222 B)
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s_log1p.c
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s_log1pf.c
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s_logb.c
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s_logbf.c
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s_logbl.c
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s_lrint.c
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s_lrintf.c
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s_lrintl.c
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s_lround.c
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s_lroundf.c
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s_lroundl.c
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s_modf.c
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s_modff.c
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s_modfl.c
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s_nan.c
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s_nearbyint.c
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s_nextafter.c
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s_nextafterf.c
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s_nextafterl.c
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s_nexttoward.c
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s_nexttowardf.c
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s_remquo.c
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s_remquof.c
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s_remquol.c
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s_rint.c
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s_rintf.c
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s_rintl.c
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s_round.c
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s_roundf.c
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s_roundl.c
(1.84 KB)
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s_scalbln.c
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s_scalbn.c
(1.9 KB)
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s_scalbnf.c
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s_scalbnl.c
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s_signbit.c
(1.7 KB)
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s_signgam.c
(61 B)
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s_significand.c
(727 B)
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s_significandf.c
(691 B)
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s_sin.c
(2.18 KB)
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s_sincos.c
(1.6 KB)
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s_sincosf.c
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s_sincosl.c
(2.67 KB)
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s_sinf.c
(2.18 KB)
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s_sinl.c
(2.49 KB)
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s_tan.c
(2.02 KB)
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s_tanf.c
(1.97 KB)
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s_tanh.c
(2.02 KB)
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s_tanhf.c
(1.39 KB)
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s_tanhl.c
(5.09 KB)
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s_tanl.c
(2.6 KB)
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s_tgammaf.c
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s_trunc.c
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s_truncf.c
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s_truncl.c
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w_cabs.c
(365 B)
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w_cabsf.c
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w_cabsl.c
(357 B)
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w_drem.c
(211 B)
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w_dremf.c
(254 B)
Editing: k_tan.c
/* @(#)k_tan.c 1.5 04/04/22 SMI */ /* * ==================================================== * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. * * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* INDENT OFF */ #include <sys/cdefs.h> __FBSDID("$FreeBSD$"); /* __kernel_tan( x, y, k ) * kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 * Input x is assumed to be bounded by ~pi/4 in magnitude. * Input y is the tail of x. * Input k indicates whether tan (if k = 1) or -1/tan (if k = -1) is returned. * * Algorithm * 1. Since tan(-x) = -tan(x), we need only to consider positive x. * 2. Callers must return tan(-0) = -0 without calling here since our * odd polynomial is not evaluated in a way that preserves -0. * Callers may do the optimization tan(x) ~ x for tiny x. * 3. tan(x) is approximated by a odd polynomial of degree 27 on * [0,0.67434] * 3 27 * tan(x) ~ x + T1*x + ... + T13*x * where * * |tan(x) 2 4 26 | -59.2 * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 * | x | * * Note: tan(x+y) = tan(x) + tan'(x)*y * ~ tan(x) + (1+x*x)*y * Therefore, for better accuracy in computing tan(x+y), let * 3 2 2 2 2 * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) * then * 3 2 * tan(x+y) = x + (T1*x + (x *(r+y)+y)) * * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) */ #include "math.h" #include "math_private.h" static const double xxx[] = { 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */ 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */ 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */ 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */ 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */ -1.85586374855275456654e-05, /* BEF375CB, DB605373 */ 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */ /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ /* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ /* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */ }; #define one xxx[13] #define pio4 xxx[14] #define pio4lo xxx[15] #define T xxx /* INDENT ON */ double __kernel_tan(double x, double y, int iy) { double z, r, v, w, s; int32_t ix, hx; GET_HIGH_WORD(hx,x); ix = hx & 0x7fffffff; /* high word of |x| */ if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */ if (hx < 0) { x = -x; y = -y; } z = pio4 - x; w = pio4lo - y; x = z + w; y = 0.0; } z = x * x; w = z * z; /* * Break x^5*(T[1]+x^2*T[2]+...) into * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) */ r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + w * T[11])))); v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + w * T[12]))))); s = z * x; r = y + z * (s * (r + v) + y); r += T[0] * s; w = x + r; if (ix >= 0x3FE59428) { v = (double) iy; return (double) (1 - ((hx >> 30) & 2)) * (v - 2.0 * (x - (w * w / (w + v) - r))); } if (iy == 1) return w; else { /* * if allow error up to 2 ulp, simply return * -1.0 / (x+r) here */ /* compute -1.0 / (x+r) accurately */ double a, t; z = w; SET_LOW_WORD(z,0); v = r - (z - x); /* z+v = r+x */ t = a = -1.0 / w; /* a = -1.0/w */ SET_LOW_WORD(t,0); s = 1.0 + t * z; return t + a * (s + t * v); } }
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