cosmopolitan/libc/tinymath/tanhf.c

/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-│
│vi: set et ft=c ts=8 tw=8 fenc=utf-8                                       :vi│
╚──────────────────────────────────────────────────────────────────────────────╝
│                                                                              │
│  Musl Libc                                                                   │
│  Copyright © 2005-2014 Rich Felker, et al.                                   │
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╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"

asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off

/**
 * Returns hyperbolic tangent of 𝑥.
 * 
 * @define `tanhf(x)=(expf(x)-expf(-x))/(expf(x)+expf(-x))`
 * @define `tanhf(x)=(expf(2.f*x)-1.f)/(expf(2.f*x)-1.f+2.f)`
 */
float tanhf(float x)
{
	union {float f; uint32_t i;} u = {.f = x};
	uint32_t w;
	int sign;
	float t;

	/* x = |x| */
	sign = u.i >> 31;
	u.i &= 0x7fffffff;
	x = u.f;
	w = u.i;

	if (w > 0x3f0c9f54) {
		/* |x| > log(3)/2 ~= 0.5493 or nan */
		if (w > 0x41200000) {
			/* |x| > 10 */
			t = 1 + 0/x;
		} else {
			t = expm1f(2*x);
			t = 1 - 2/(t+2);
		}
	} else if (w > 0x3e82c578) {
		/* |x| > log(5/3)/2 ~= 0.2554 */
		t = expm1f(2*x);
		t = t/(t+2);
	} else if (w >= 0x00800000) {
		/* |x| >= 0x1p-126 */
		t = expm1f(-2*x);
		t = -t/(t+2);
	} else {
		/* |x| is subnormal */
		FORCE_EVAL(x*x);
		t = x;
	}
	return sign ? -t : t;
}