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cosmopolitan/libc/math.h
Justine Tunney 957c61cbbf
Release Cosmopolitan v3.3 
This change upgrades to GCC 12.3 and GNU binutils 2.42. The GNU linker
appears to have changed things so that only a single de-duplicated str
table is present in the binary, and it gets placed wherever the linker
wants, regardless of what the linker script says. To cope with that we
need to stop using .ident to embed licenses. As such, this change does
significant work to revamp how third party licenses are defined in the
codebase, using `.section .notice,"aR",@progbits`.

This new GCC 12.3 toolchain has support for GNU indirect functions. It
lets us support __target_clones__ for the first time. This is used for
optimizing the performance of libc string functions such as strlen and
friends so far on x86, by ensuring AVX systems favor a second codepath
that uses VEX encoding. It shaves some latency off certain operations.
It's a useful feature to have for scientific computing for the reasons
explained by the test/libcxx/openmp_test.cc example which compiles for
fifteen different microarchitectures. Thanks to the upgrades, it's now
also possible to use newer instruction sets, such as AVX512FP16, VNNI.

Cosmo now uses the %gs register on x86 by default for TLS. Doing it is
helpful for any program that links `cosmo_dlopen()`. Such programs had
to recompile their binaries at startup to change the TLS instructions.
That's not great, since it means every page in the executable needs to
be faulted. The work of rewriting TLS-related x86 opcodes, is moved to
fixupobj.com instead. This is great news for MacOS x86 users, since we
previously needed to morph the binary every time for that platform but
now that's no longer necessary. The only platforms where we need fixup
of TLS x86 opcodes at runtime are now Windows, OpenBSD, and NetBSD. On
Windows we morph TLS to point deeper into the TIB, based on a TlsAlloc
assignment, and on OpenBSD/NetBSD we morph %gs back into %fs since the
kernels do not allow us to specify a value for the %gs register.

OpenBSD users are now required to use APE Loader to run Cosmo binaries
and assimilation is no longer possible. OpenBSD kernel needs to change
to allow programs to specify a value for the %gs register, or it needs
to stop marking executable pages loaded by the kernel as mimmutable().

This release fixes __constructor__, .ctor, .init_array, and lastly the
.preinit_array so they behave the exact same way as glibc.

We no longer use hex constants to define math.h symbols like M_PI.
2024-02-20 13:27:59 -08:00

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#ifndef COSMOPOLITAN_LIBC_MATH_H_
#define COSMOPOLITAN_LIBC_MATH_H_
/*─────────────────────────────────────────────────────────────────────────────╗
│ cosmopolitan § mathematics │
╚─────────────────────────────────────────────────────────────────────────────*/
#define M_E 2.7182818284590452354 /* 𝑒 */
#define M_LOG2E 1.4426950408889634074 /* log₂𝑒 */
#define M_LOG10E 0.43429448190325182765 /* log₁₀𝑒 */
#define M_LN2 0.69314718055994530942 /* logₑ2 */
#define M_LN10 2.30258509299404568402 /* logₑ10 */
#define M_PI 3.14159265358979323846 /* pi */
#define M_PI_2 1.57079632679489661923 /* pi/2 */
#define M_PI_4 0.78539816339744830962 /* pi/4 */
#define M_1_PI 0.31830988618379067154 /* 1/pi */
#define M_2_PI 0.63661977236758134308 /* 2/pi */
#define M_2_SQRTPI 1.12837916709551257390 /* 2/sqrt(pi) */
#define M_SQRT2 1.41421356237309504880 /* sqrt(2) */
#define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
#define DBL_DECIMAL_DIG __DBL_DECIMAL_DIG__
#define DBL_DIG __DBL_DIG__
#define DBL_EPSILON __DBL_EPSILON__
#define DBL_HAS_SUBNORM __DBL_HAS_DENORM__
#define DBL_IS_IEC_60559 __DBL_IS_IEC_60559__
#define DBL_MANT_DIG __DBL_MANT_DIG__
#define DBL_MANT_DIG __DBL_MANT_DIG__
#define DBL_MAX __DBL_MAX__
#define DBL_MAX_10_EXP __DBL_MAX_10_EXP__
#define DBL_MAX_EXP __DBL_MAX_EXP__
#define DBL_MIN __DBL_MIN__ /* 2.23e–308 ↔ 1.79e308 */
#define DBL_MIN_10_EXP __DBL_MIN_10_EXP__
#define DBL_MIN_EXP __DBL_MIN_EXP__
#define DBL_NORM_MAX __DBL_NORM_MAX__
#define DBL_TRUE_MIN __DBL_DENORM_MIN__
#define DECIMAL_DIG __LDBL_DECIMAL_DIG__
#define FLT_DECIMAL_DIG __FLT_DECIMAL_DIG__
#define FLT_DIG __FLT_DIG__
#define FLT_EPSILON __FLT_EPSILON__
#define FLT_HAS_SUBNORM __FLT_HAS_DENORM__
#define FLT_IS_IEC_60559 __FLT_IS_IEC_60559__
#define FLT_MANT_DIG __FLT_MANT_DIG__
#define FLT_MANT_DIG __FLT_MANT_DIG__
#define FLT_MAX __FLT_MAX__
#define FLT_MAX_10_EXP __FLT_MAX_10_EXP__
#define FLT_MAX_EXP __FLT_MAX_EXP__
#define FLT_MIN __FLT_MIN__ /* 1.18e–38 ↔ 3.40e38 */
#define FLT_MIN_10_EXP __FLT_MIN_10_EXP__
#define FLT_MIN_EXP __FLT_MIN_EXP__
#define FLT_NORM_MAX __FLT_NORM_MAX__
#define FLT_RADIX __FLT_RADIX__
#define FLT_TRUE_MIN __FLT_DENORM_MIN__
#define HLF_MAX 6.50e4f
#define HLF_MIN 3.10e-5f
#define LDBL_DECIMAL_DIG __LDBL_DECIMAL_DIG__
#define LDBL_DIG __LDBL_DIG__
#define LDBL_EPSILON __LDBL_EPSILON__
#define LDBL_HAS_SUBNORM __LDBL_HAS_DENORM__
#define LDBL_IS_IEC_60559 __LDBL_IS_IEC_60559__
#define LDBL_MANT_DIG __LDBL_MANT_DIG__
#define LDBL_MANT_DIG __LDBL_MANT_DIG__
#define LDBL_MAX __LDBL_MAX__
#define LDBL_MAX_10_EXP __LDBL_MAX_10_EXP__
#define LDBL_MAX_EXP __LDBL_MAX_EXP__
#define LDBL_MIN __LDBL_MIN__ /* 3.37e–4932 ↔ 1.18e4932 */
#define LDBL_MIN_10_EXP __LDBL_MIN_10_EXP__
#define LDBL_MIN_EXP __LDBL_MIN_EXP__
#define LDBL_NORM_MAX __LDBL_NORM_MAX__
#define LDBL_TRUE_MIN __LDBL_DENORM_MIN__
#define FP_NAN 0
#define FP_INFINITE 1
#define FP_ZERO 2
#define FP_SUBNORMAL 3
#define FP_NORMAL 4
#define FP_ILOGB0 (-2147483647 - 1)
#define FP_ILOGBNAN (-2147483647 - 1)
COSMOPOLITAN_C_START_
#define NAN __builtin_nanf("")
#define INFINITY __builtin_inff()
#define HUGE_VAL __builtin_inf()
#define HUGE_VALF __builtin_inff()
#define HUGE_VALL __builtin_infl()
#if __FLT_EVAL_METHOD__ + 0 == 2
typedef long double float_t;
typedef long double double_t;
#else
typedef float float_t;
typedef double double_t;
#endif
#define isinf(x) __builtin_isinf(x)
#define isnan(x) __builtin_isnan(x)
#define isfinite(x) __builtin_isfinite(x)
#define isnormal(x) __builtin_isnormal(x)
#define isgreater(x, y) __builtin_isgreater(x, y)
#define isgreaterequal(x, y) __builtin_isgreaterequal(x, y)
#define isless(x, y) __builtin_isless(x, y)
#define islessequal(x, y) __builtin_islessequal(x, y)
#define islessgreater(x, y) __builtin_islessgreater(x, y)
#define isunordered(x, y) __builtin_isunordered(x, y)
#define fpclassify(x) \
__builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
#define signbit(x) \
(sizeof(x) == sizeof(double) ? __builtin_signbit(x) \
: sizeof(x) == sizeof(float) ? __builtin_signbitf(x) \
: __builtin_signbitl(x))
extern int signgam;
double acos(double) libcesque;
double acosh(double) libcesque;
double asin(double) libcesque;
double asinh(double) libcesque;
double atan(double) libcesque;
double atan2(double, double) libcesque;
double atanh(double) libcesque;
double cbrt(double) libcesque;
double ceil(double) libcesque;
double copysign(double, double) libcesque;
double cos(double) libcesque;
double cosh(double) libcesque;
double drem(double, double) libcesque;
double erf(double) libcesque;
double erfc(double) libcesque;
double exp(double) libcesque;
double exp10(double) libcesque;
double exp2(double) libcesque;
double expm1(double) libcesque;
double fabs(double) libcesque;
double fdim(double, double) libcesque;
double floor(double) libcesque;
double fma(double, double, double) libcesque;
double fmax(double, double) libcesque;
double fmin(double, double) libcesque;
double fmod(double, double) libcesque;
double hypot(double, double) libcesque;
double ldexp(double, int) libcesque;
double log(double) libcesque;
double log10(double) libcesque;
double log1p(double) libcesque;
double log2(double) libcesque;
double logb(double) libcesque;
double nearbyint(double) libcesque;
double nextafter(double, double) libcesque;
double nexttoward(double, long double) libcesque;
double pow(double, double) libcesque;
double pow10(double) libcesque;
double powi(double, int) libcesque;
double remainder(double, double) libcesque;
double rint(double) libcesque;
double round(double) libcesque;
double scalb(double, double) libcesque;
double scalbln(double, long int) libcesque;
double scalbn(double, int) libcesque;
double significand(double) libcesque;
double sin(double) libcesque;
double sinh(double) libcesque;
double sqrt(double) libcesque;
double tan(double) libcesque;
double tanh(double) libcesque;
double trunc(double) libcesque;
double tgamma(double) libcesque;
double lgamma(double) libcesque;
double lgamma_r(double, int *) libcesque;
int finite(double) libcesque;
float acosf(float) libcesque;
float acoshf(float) libcesque;
float asinf(float) libcesque;
float asinhf(float) libcesque;
float atan2f(float, float) libcesque;
float atanf(float) libcesque;
float atanhf(float) libcesque;
float cbrtf(float) libcesque;
float ceilf(float) libcesque;
float copysignf(float, float) libcesque;
float cosf(float) libcesque;
float coshf(float) libcesque;
float dremf(float, float) libcesque;
float erfcf(float) libcesque;
float erff(float) libcesque;
float exp10f(float) libcesque;
float exp2f(float) libcesque;
float expf(float) libcesque;
float expm1f(float) libcesque;
float fabsf(float) libcesque;
float fdimf(float, float) libcesque;
float floorf(float) libcesque;
float fmaf(float, float, float) libcesque;
float fmaxf(float, float) libcesque;
float fminf(float, float) libcesque;
float fmodf(float, float) libcesque;
float hypotf(float, float) libcesque;
float ldexpf(float, int) libcesque;
float lgammaf(float) libcesque;
float lgammaf_r(float, int *) libcesque;
float log10f(float) libcesque;
float log1pf(float) libcesque;
float log2f(float) libcesque;
float logbf(float) libcesque;
float logf(float) libcesque;
float nearbyintf(float) libcesque;
float nextafterf(float, float) libcesque;
float nexttowardf(float, long double) libcesque;
float pow10f(float) libcesque;
float powf(float, float) libcesque;
float powif(float, int) libcesque;
float remainderf(float, float) libcesque;
float rintf(float) libcesque;
float roundf(float) libcesque;
float scalbf(float, float) libcesque;
float scalblnf(float, long int) libcesque;
float scalbnf(float, int) libcesque;
float significandf(float) libcesque;
float sinf(float) libcesque;
float sinhf(float) libcesque;
float sqrtf(float) libcesque;
float tanf(float) libcesque;
float tanhf(float) libcesque;
float tgammaf(float) libcesque;
float truncf(float) libcesque;
int finitef(float) libcesque;
int finitel(long double) libcesque;
long double acoshl(long double) libcesque;
long double acosl(long double) libcesque;
long double asinhl(long double) libcesque;
long double asinl(long double) libcesque;
long double atan2l(long double, long double) libcesque;
long double atanhl(long double) libcesque;
long double atanl(long double) libcesque;
long double cbrtl(long double) libcesque;
long double ceill(long double) libcesque;
long double copysignl(long double, long double) libcesque;
long double coshl(long double) libcesque;
long double cosl(long double) libcesque;
long double dreml(long double, long double) libcesque;
long double erfcl(long double) libcesque;
long double erfl(long double) libcesque;
long double exp10l(long double) libcesque;
long double exp2l(long double) libcesque;
long double expl(long double) libcesque;
long double expm1l(long double) libcesque;
long double fabsl(long double) libcesque;
long double fdiml(long double, long double) libcesque;
long double floorl(long double) libcesque;
long double fmal(long double, long double, long double) libcesque;
long double fmaxl(long double, long double) libcesque;
long double fminl(long double, long double) libcesque;
long double fmodl(long double, long double) libcesque;
long double hypotl(long double, long double) libcesque;
long double ldexpl(long double, int) libcesque;
long double lgammal(long double) libcesque;
long double lgammal_r(long double, int *) libcesque;
long double log10l(long double) libcesque;
long double log1pl(long double) libcesque;
long double log2l(long double) libcesque;
long double logbl(long double) libcesque;
long double logl(long double) libcesque;
long double nearbyintl(long double) libcesque;
long double nextafterl(long double, long double) libcesque;
long double nexttowardl(long double, long double) libcesque;
long double pow10l(long double) libcesque;
long double powl(long double, long double) libcesque;
long double remainderl(long double, long double) libcesque;
long double rintl(long double) libcesque;
long double roundl(long double) libcesque;
long double scalbl(long double, long double) libcesque;
long double scalblnl(long double, long int) libcesque;
long double scalbnl(long double, int) libcesque;
long double significandl(long double) libcesque;
long double sinhl(long double) libcesque;
long double sinl(long double) libcesque;
long double sqrtl(long double) libcesque;
long double tanhl(long double) libcesque;
long double tanl(long double) libcesque;
long double tgammal(long double) libcesque;
long double truncl(long double) libcesque;
long lrint(double) libcesque;
long lrintf(float) libcesque;
long lrintl(long double) libcesque;
long lround(double) libcesque;
long lroundf(float) libcesque;
long lroundl(long double) libcesque;
int ilogbf(float) libcesque;
int ilogb(double) libcesque;
int ilogbl(long double) libcesque;
long long llrint(double) libcesque;
long long llrintf(float) libcesque;
long long llrintl(long double) libcesque;
long long llround(double) libcesque;
long long llroundf(float) libcesque;
long long llroundl(long double) libcesque;
double frexp(double, int *) libcesque;
double modf(double, double *) libcesque;
double nan(const char *) libcesque;
double remquo(double, double, int *) libcesque;
float frexpf(float, int *) libcesque;
float modff(float, float *) libcesque;
float nanf(const char *) libcesque;
float remquof(float, float, int *) libcesque;
long double frexpl(long double, int *) libcesque;
long double modfl(long double, long double *) libcesque;
long double nanl(const char *) libcesque;
long double remquol(long double, long double, int *) libcesque;
void sincos(double, double *, double *) libcesque;
void sincosf(float, float *, float *) libcesque;
void sincosl(long double, long double *, long double *) libcesque;
double fsumf(const float *, size_t) libcesque;
double fsum(const double *, size_t) libcesque;
double j0(double) libcesque;
double j1(double) libcesque;
double jn(int, double) libcesque;
float j0f(float) libcesque;
float j1f(float) libcesque;
float jnf(int, float) libcesque;
double y0(double) libcesque;
double y1(double) libcesque;
double yn(int, double) libcesque;
float y0f(float) libcesque;
float y1f(float) libcesque;
float ynf(int, float) libcesque;
COSMOPOLITAN_C_END_
#endif /* COSMOPOLITAN_LIBC_MATH_H_ */
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