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catrig.c
(18.56 KB)
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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
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e_fmodf.c
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e_fmodl.c
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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
(3.16 KB)
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e_j0.c
(14.39 KB)
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e_j0f.c
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e_j1.c
(14.12 KB)
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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
(2.37 KB)
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e_logf.c
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e_pow.c
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e_powf.c
(7.34 KB)
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e_rem_pio2.c
(4.7 KB)
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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
(992 B)
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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
(13.92 KB)
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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
(808 B)
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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
(2.45 KB)
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s_erf.c
(11 KB)
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s_erff.c
(5.11 KB)
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s_exp2.c
(14.03 KB)
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s_exp2f.c
(4.14 KB)
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s_expm1.c
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s_expm1f.c
(3.41 KB)
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s_fabs.c
(677 B)
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s_fabsf.c
(765 B)
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s_fabsl.c
(1.68 KB)
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s_fdim.c
(1.7 KB)
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s_finite.c
(700 B)
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s_finitef.c
(796 B)
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s_floor.c
(1.74 KB)
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s_floorf.c
(1.41 KB)
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s_floorl.c
(2.38 KB)
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s_fma.c
(7.92 KB)
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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
(1.98 KB)
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s_fmin.c
(2.01 KB)
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s_fminf.c
(1.88 KB)
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s_fminl.c
(1.98 KB)
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s_frexp.c
(1.31 KB)
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s_frexpf.c
(1.02 KB)
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s_frexpl.c
(2 KB)
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s_ilogb.c
(1.14 KB)
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s_ilogbf.c
(976 B)
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s_ilogbl.c
(1.21 KB)
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s_isfinite.c
(1.72 KB)
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s_isnan.c
(2.1 KB)
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s_isnormal.c
(1.78 KB)
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s_llrint.c
(156 B)
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s_llrintf.c
(157 B)
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s_llrintl.c
(163 B)
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s_llround.c
(215 B)
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s_llroundf.c
(216 B)
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s_llroundl.c
(222 B)
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s_log1p.c
(5.6 KB)
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s_log1pf.c
(3.14 KB)
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s_logb.c
(1.13 KB)
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s_logbf.c
(1023 B)
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s_logbl.c
(1.24 KB)
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s_lrint.c
(2.1 KB)
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s_lrintf.c
(151 B)
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s_lrintl.c
(157 B)
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s_lround.c
(2.45 KB)
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s_lroundf.c
(208 B)
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s_lroundl.c
(214 B)
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s_modf.c
(1.88 KB)
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s_modff.c
(1.39 KB)
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s_modfl.c
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s_nan.c
(3.32 KB)
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s_nearbyint.c
(2.29 KB)
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s_nextafter.c
(2.03 KB)
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s_nextafterf.c
(1.61 KB)
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s_nextafterl.c
(2.02 KB)
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s_nexttoward.c
(1.75 KB)
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s_nexttowardf.c
(1.42 KB)
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s_remquo.c
(3.86 KB)
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s_remquof.c
(3.02 KB)
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s_remquol.c
(4.42 KB)
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s_rint.c
(2.33 KB)
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s_rintf.c
(1.22 KB)
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s_rintl.c
(2.77 KB)
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s_round.c
(1.83 KB)
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s_roundf.c
(1.74 KB)
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s_roundl.c
(1.84 KB)
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s_scalbln.c
(1.82 KB)
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s_scalbn.c
(1.9 KB)
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s_scalbnf.c
(1.67 KB)
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s_scalbnl.c
(1.9 KB)
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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
(2.57 KB)
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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
(1.75 KB)
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s_trunc.c
(1.5 KB)
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s_truncf.c
(1.21 KB)
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s_truncl.c
(1.61 KB)
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w_cabs.c
(365 B)
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w_cabsf.c
(350 B)
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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: s_exp2.c
/*- * SPDX-License-Identifier: BSD-2-Clause-FreeBSD * * Copyright (c) 2005 David Schultz <das@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. */ #include <sys/cdefs.h> __FBSDID("$FreeBSD$"); #include <float.h> #include "math.h" #include "math_private.h" #define TBLBITS 8 #define TBLSIZE (1 << TBLBITS) static const double redux = 0x1.8p52 / TBLSIZE, P1 = 0x1.62e42fefa39efp-1, P2 = 0x1.ebfbdff82c575p-3, P3 = 0x1.c6b08d704a0a6p-5, P4 = 0x1.3b2ab88f70400p-7, P5 = 0x1.5d88003875c74p-10; static volatile double huge = 0x1p1000, twom1000 = 0x1p-1000; static const double tbl[TBLSIZE * 2] = { /* exp2(z + eps) eps */ 0x1.6a09e667f3d5dp-1, 0x1.9880p-44, 0x1.6b052fa751744p-1, 0x1.8000p-50, 0x1.6c012750bd9fep-1, -0x1.8780p-45, 0x1.6cfdcddd476bfp-1, 0x1.ec00p-46, 0x1.6dfb23c651a29p-1, -0x1.8000p-50, 0x1.6ef9298593ae3p-1, -0x1.c000p-52, 0x1.6ff7df9519386p-1, -0x1.fd80p-45, 0x1.70f7466f42da3p-1, -0x1.c880p-45, 0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46, 0x1.72f8286eacf05p-1, -0x1.8300p-44, 0x1.73f9a48a58152p-1, -0x1.0c00p-47, 0x1.74fbd35d7ccfcp-1, 0x1.f880p-45, 0x1.75feb564267f1p-1, 0x1.3e00p-47, 0x1.77024b1ab6d48p-1, -0x1.7d00p-45, 0x1.780694fde5d38p-1, -0x1.d000p-50, 0x1.790b938ac1d00p-1, 0x1.3000p-49, 0x1.7a11473eb0178p-1, -0x1.d000p-49, 0x1.7b17b0976d060p-1, 0x1.0400p-45, 0x1.7c1ed0130c133p-1, 0x1.0000p-53, 0x1.7d26a62ff8636p-1, -0x1.6900p-45, 0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47, 0x1.7f3878491c3e8p-1, -0x1.4580p-45, 0x1.80427543e1b4ep-1, 0x1.3000p-44, 0x1.814d2add1071ap-1, 0x1.f000p-47, 0x1.82589994ccd7ep-1, -0x1.1c00p-45, 0x1.8364c1eb942d0p-1, 0x1.9d00p-45, 0x1.8471a4623cab5p-1, 0x1.7100p-43, 0x1.857f4179f5bbcp-1, 0x1.2600p-45, 0x1.868d99b4491afp-1, -0x1.2c40p-44, 0x1.879cad931a395p-1, -0x1.3000p-45, 0x1.88ac7d98a65b8p-1, -0x1.a800p-45, 0x1.89bd0a4785800p-1, -0x1.d000p-49, 0x1.8ace5422aa223p-1, 0x1.3280p-44, 0x1.8be05bad619fap-1, 0x1.2b40p-43, 0x1.8cf3216b54383p-1, -0x1.ed00p-45, 0x1.8e06a5e08664cp-1, -0x1.0500p-45, 0x1.8f1ae99157807p-1, 0x1.8280p-45, 0x1.902fed0282c0ep-1, -0x1.cb00p-46, 0x1.9145b0b91ff96p-1, -0x1.5e00p-47, 0x1.925c353aa2ff9p-1, 0x1.5400p-48, 0x1.93737b0cdc64ap-1, 0x1.7200p-46, 0x1.948b82b5f98aep-1, -0x1.9000p-47, 0x1.95a44cbc852cbp-1, 0x1.5680p-45, 0x1.96bdd9a766f21p-1, -0x1.6d00p-44, 0x1.97d829fde4e2ap-1, -0x1.1000p-47, 0x1.98f33e47a23a3p-1, 0x1.d000p-45, 0x1.9a0f170ca0604p-1, -0x1.8a40p-44, 0x1.9b2bb4d53ff89p-1, 0x1.55c0p-44, 0x1.9c49182a3f15bp-1, 0x1.6b80p-45, 0x1.9d674194bb8c5p-1, -0x1.c000p-49, 0x1.9e86319e3238ep-1, 0x1.7d00p-46, 0x1.9fa5e8d07f302p-1, 0x1.6400p-46, 0x1.a0c667b5de54dp-1, -0x1.5000p-48, 0x1.a1e7aed8eb8f6p-1, 0x1.9e00p-47, 0x1.a309bec4a2e27p-1, 0x1.ad80p-45, 0x1.a42c980460a5dp-1, -0x1.af00p-46, 0x1.a5503b23e259bp-1, 0x1.b600p-47, 0x1.a674a8af46213p-1, 0x1.8880p-44, 0x1.a799e1330b3a7p-1, 0x1.1200p-46, 0x1.a8bfe53c12e8dp-1, 0x1.6c00p-47, 0x1.a9e6b5579fcd2p-1, -0x1.9b80p-45, 0x1.ab0e521356fb8p-1, 0x1.b700p-45, 0x1.ac36bbfd3f381p-1, 0x1.9000p-50, 0x1.ad5ff3a3c2780p-1, 0x1.4000p-49, 0x1.ae89f995ad2a3p-1, -0x1.c900p-45, 0x1.afb4ce622f367p-1, 0x1.6500p-46, 0x1.b0e07298db790p-1, 0x1.fd40p-45, 0x1.b20ce6c9a89a9p-1, 0x1.2700p-46, 0x1.b33a2b84f1a4bp-1, 0x1.d470p-43, 0x1.b468415b747e7p-1, -0x1.8380p-44, 0x1.b59728de5593ap-1, 0x1.8000p-54, 0x1.b6c6e29f1c56ap-1, 0x1.ad00p-47, 0x1.b7f76f2fb5e50p-1, 0x1.e800p-50, 0x1.b928cf22749b2p-1, -0x1.4c00p-47, 0x1.ba5b030a10603p-1, -0x1.d700p-47, 0x1.bb8e0b79a6f66p-1, 0x1.d900p-47, 0x1.bcc1e904bc1ffp-1, 0x1.2a00p-47, 0x1.bdf69c3f3a16fp-1, -0x1.f780p-46, 0x1.bf2c25bd71db8p-1, -0x1.0a00p-46, 0x1.c06286141b2e9p-1, -0x1.1400p-46, 0x1.c199bdd8552e0p-1, 0x1.be00p-47, 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0x1.5d84590998e3fp+0, 0x1.69a0p-43, 0x1.5e76f15ad20e1p+0, -0x1.b400p-46, 0x1.5f6a320dcebcap+0, 0x1.7700p-46, 0x1.605e1b976dcb8p+0, 0x1.6f80p-45, 0x1.6152ae6cdf715p+0, 0x1.1000p-47, 0x1.6247eb03a5531p+0, -0x1.5d00p-46, 0x1.633dd1d1929b5p+0, -0x1.2d00p-46, 0x1.6434634ccc313p+0, -0x1.a800p-49, 0x1.652b9febc8efap+0, -0x1.8600p-45, 0x1.6623882553397p+0, 0x1.1fe0p-40, 0x1.671c1c708328ep+0, -0x1.7200p-44, 0x1.68155d44ca97ep+0, 0x1.6800p-49, 0x1.690f4b19e9471p+0, -0x1.9780p-45, }; /* * exp2(x): compute the base 2 exponential of x * * Accuracy: Peak error < 0.503 ulp for normalized results. * * Method: (accurate tables) * * Reduce x: * x = 2**k + y, for integer k and |y| <= 1/2. * Thus we have exp2(x) = 2**k * exp2(y). * * Reduce y: * y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE. * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]), * with |z - eps[i]| <= 2**-9 + 2**-39 for the table used. * * We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via * a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61. * The values in exp2t[] and eps[] are chosen such that * exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such * that exp2t[i] is accurate to 2**-64. * * Note that the range of i is +-TBLSIZE/2, so we actually index the tables * by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are * virtual tables, interleaved in the real table tbl[]. * * This method is due to Gal, with many details due to Gal and Bachelis: * * Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library * for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991). */ double exp2(double x) { double r, t, twopk, twopkp1000, z; uint32_t hx, ix, lx, i0; int k; /* Filter out exceptional cases. */ GET_HIGH_WORD(hx,x); ix = hx & 0x7fffffff; /* high word of |x| */ if(ix >= 0x40900000) { /* |x| >= 1024 */ if(ix >= 0x7ff00000) { GET_LOW_WORD(lx,x); if(((ix & 0xfffff) | lx) != 0 || (hx & 0x80000000) == 0) return (x + x); /* x is NaN or +Inf */ else return (0.0); /* x is -Inf */ } if(x >= 0x1.0p10) return (huge * huge); /* overflow */ if(x <= -0x1.0ccp10) return (twom1000 * twom1000); /* underflow */ } else if (ix < 0x3c900000) { /* |x| < 0x1p-54 */ return (1.0 + x); } /* Reduce x, computing z, i0, and k. */ STRICT_ASSIGN(double, t, x + redux); GET_LOW_WORD(i0, t); i0 += TBLSIZE / 2; k = (i0 >> TBLBITS) << 20; i0 = (i0 & (TBLSIZE - 1)) << 1; t -= redux; z = x - t; /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */ t = tbl[i0]; /* exp2t[i0] */ z -= tbl[i0 + 1]; /* eps[i0] */ if (k >= -(1021 << 20)) INSERT_WORDS(twopk, 0x3ff00000 + k, 0); else INSERT_WORDS(twopkp1000, 0x3ff00000 + k + (1000 << 20), 0); r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5)))); /* Scale by 2**(k>>20). */ if(k >= -(1021 << 20)) { if (k == 1024 << 20) return (r * 2.0 * 0x1p1023); return (r * twopk); } else { return (r * twopkp1000 * twom1000); } } #if (LDBL_MANT_DIG == 53) __weak_reference(exp2, exp2l); #endif
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