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      1 /*-
      2  * Copyright (c) 2017,2023 Steven G. Kargl
      3  * All rights reserved.
      4  *
      5  * Redistribution and use in source and binary forms, with or without
      6  * modification, are permitted provided that the following conditions
      7  * are met:
      8  * 1. Redistributions of source code must retain the above copyright
      9  *    notice unmodified, this list of conditions, and the following
     10  *    disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  *
     15  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
     16  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
     17  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
     18  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
     19  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
     20  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
     21  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
     22  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
     23  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
     24  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
     25  */
     26 
     27 #include <sys/cdefs.h>
     28 
     29 /*
     30  * See ../src/s_tanpi.c for implementation details.
     31  */
     32 
     33 #include "namespace.h"
     34 __weak_alias(tanpif, _tanpif)
     35 #define INLINE_KERNEL_TANDF
     36 
     37 #include "math.h"
     38 #include "math_private.h"
     39 #include "k_tandf.c"
     40 
     41 static const float
     42 pi_hi =  3.14160156e+00F,	/* 0x40491000 */
     43 pi_lo = -8.90890988e-06F;	/* 0xb715777a */
     44 
     45 static inline float
     46 __kernel_tanpif(float x)
     47 {
     48 	float t;
     49 
     50 	if (x < 0.25F)
     51 		t = __kernel_tandf(M_PI * x, 1);
     52 	else if (x > 0.25F)
     53 		t = -__kernel_tandf(M_PI * (0.5 - x), -1);
     54 	else
     55 		t = 1;
     56 
     57 	return (t);
     58 }
     59 
     60 static volatile const float vzero = 0;
     61 
     62 float
     63 tanpif(float x)
     64 {
     65 	float ax, hi, lo, odd, t;
     66 	uint32_t hx, ix, jj0;
     67 
     68 	GET_FLOAT_WORD(hx, x);
     69 	ix = hx & 0x7fffffff;
     70 	SET_FLOAT_WORD(ax, ix);
     71 
     72 	if (ix < 0x3f800000) {			/* |x| < 1 */
     73 		if (ix < 0x3f000000) {		/* |x| < 0.5 */
     74 			if (ix < 0x38800000) {	/* |x| < 0x1p-14 */
     75 				if (ix == 0)
     76 					return (x);
     77 				SET_FLOAT_WORD(hi, hx & 0xffff0000);
     78 				hi *= 0x1p23F;
     79 				lo = x * 0x1p23F - hi;
     80 				t = (pi_lo + pi_hi) * lo + pi_lo * hi +
     81 				    pi_hi * hi;
     82 				return (t * 0x1p-23F);
     83 			}
     84 			t = __kernel_tanpif(ax);
     85 		} else if (ix == 0x3f000000)
     86 			t = 1 / vzero;
     87 		else
     88 			t = - __kernel_tanpif(1 - ax);
     89 		return ((hx & 0x80000000) ? -t : t);
     90 	}
     91 
     92 	if (ix < 0x4b000000) {		/* 1 <= |x| < 0x1p23 */
     93 		FFLOORF(x, jj0, ix);	/* Integer part of ax. */
     94 		odd = (uint32_t)x & 1 ? -1 : 1;
     95 		ax -= x;
     96 		GET_FLOAT_WORD(ix, ax);
     97 
     98 		if (ix < 0x3f000000)		/* |x| < 0.5 */
     99 			t = ix == 0 ? copysignf(0, odd) : __kernel_tanpif(ax);
    100 		else if (ix == 0x3f000000)
    101 			t = odd / vzero;
    102 		else
    103 			t = - __kernel_tanpif(1 - ax);
    104 		return ((hx & 0x80000000) ? -t : t);
    105 	}
    106 
    107 	/* x = +-inf or nan. */
    108 	if (ix >= 0x7f800000)
    109 		return (vzero / vzero);
    110 
    111 	/*
    112 	 * For 0x1p23 <= |x| < 0x1p24 need to determine if x is an even
    113 	 * or odd integer to set t = +0 or -0.
    114 	 * For |x| >= 0x1p24, it is always an even integer, so t = 0.
    115 	 */
    116 	t = ix >= 0x4b800000 ? 0 : (copysignf(0, (ix & 1) ? -1 : 1));
    117 	return ((hx & 0x80000000) ? -t : t);
    118 }
    119