cosmopolitan/libc/tinymath/rempio2.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.                                   │
│                                                                              │
│  Permission is hereby granted, free of charge, to any person obtaining       │
│  a copy of this software and associated documentation files (the             │
│  "Software"), to deal in the Software without restriction, including         │
│  without limitation the rights to use, copy, modify, merge, publish,         │
│  distribute, sublicense, and/or sell copies of the Software, and to          │
│  permit persons to whom the Software is furnished to do so, subject to       │
│  the following conditions:                                                   │
│                                                                              │
│  The above copyright notice and this permission notice shall be              │
│  included in all copies or substantial portions of the Software.             │
│                                                                              │
│  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,             │
│  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF          │
│  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.      │
│  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY        │
│  CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,        │
│  TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE           │
│  SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                      │
│                                                                              │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/runtime/fenv.h"
#include "libc/tinymath/kernel.internal.h"

asm(".ident\t\"\\n\\n\
fdlibm (fdlibm license)\\n\
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\"");
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 */

/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 *
 * Optimized by Bruce D. Evans.
 */
/* __rem_pio2(x,y)
 *
 * return the remainder of x rem pi/2 in y[0]+y[1]
 * use __rem_pio2_large() for large x
 */

#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
#define EPS DBL_EPSILON
#elif FLT_EVAL_METHOD==2
#define EPS LDBL_EPSILON
#endif

/*
 * invpio2:  53 bits of 2/pi
 * pio2_1:   first  33 bit of pi/2
 * pio2_1t:  pi/2 - pio2_1
 * pio2_2:   second 33 bit of pi/2
 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
 * pio2_3:   third  33 bit of pi/2
 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
 */
#define toint (1.5/EPS)
#define pio4 0x1.921fb54442d18p-1
#define invpio2 6.36619772367581382433e-01
#define pio2_1 1.57079632673412561417e+00
#define pio2_1t 6.07710050650619224932e-11
#define pio2_2 6.07710050630396597660e-11
#define pio2_2t 2.02226624879595063154e-21
#define pio2_3 2.02226624871116645580e-21
#define pio2_3t 8.47842766036889956997e-32

/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
int __rem_pio2(double x, double *y)
{
	union {double f; uint64_t i;} u = {x};
	double_t z,w,t,r,fn;
	double tx[3],ty[2];
	uint32_t ix;
	int sign, n, ex, ey, i;
	sign = u.i>>63;
	ix = u.i>>32 & 0x7fffffff;
	if (ix <= 0x400f6a7a) {  /* |x| ~<= 5pi/4 */
		if ((ix & 0xfffff) == 0x921fb)  /* |x| ~= pi/2 or 2pi/2 */
			goto medium;  /* cancellation -- use medium case */
		if (ix <= 0x4002d97c) {  /* |x| ~<= 3pi/4 */
			if (!sign) {
				z = x - pio2_1;  /* one round good to 85 bits */
				y[0] = z - pio2_1t;
				y[1] = (z-y[0]) - pio2_1t;
				return 1;
			} else {
				z = x + pio2_1;
				y[0] = z + pio2_1t;
				y[1] = (z-y[0]) + pio2_1t;
				return -1;
			}
		} else {
			if (!sign) {
				z = x - 2*pio2_1;
				y[0] = z - 2*pio2_1t;
				y[1] = (z-y[0]) - 2*pio2_1t;
				return 2;
			} else {
				z = x + 2*pio2_1;
				y[0] = z + 2*pio2_1t;
				y[1] = (z-y[0]) + 2*pio2_1t;
				return -2;
			}
		}
	}
	if (ix <= 0x401c463b) {  /* |x| ~<= 9pi/4 */
		if (ix <= 0x4015fdbc) {  /* |x| ~<= 7pi/4 */
			if (ix == 0x4012d97c)  /* |x| ~= 3pi/2 */
				goto medium;
			if (!sign) {
				z = x - 3*pio2_1;
				y[0] = z - 3*pio2_1t;
				y[1] = (z-y[0]) - 3*pio2_1t;
				return 3;
			} else {
				z = x + 3*pio2_1;
				y[0] = z + 3*pio2_1t;
				y[1] = (z-y[0]) + 3*pio2_1t;
				return -3;
			}
		} else {
			if (ix == 0x401921fb)  /* |x| ~= 4pi/2 */
				goto medium;
			if (!sign) {
				z = x - 4*pio2_1;
				y[0] = z - 4*pio2_1t;
				y[1] = (z-y[0]) - 4*pio2_1t;
				return 4;
			} else {
				z = x + 4*pio2_1;
				y[0] = z + 4*pio2_1t;
				y[1] = (z-y[0]) + 4*pio2_1t;
				return -4;
			}
		}
	}
	if (ix < 0x413921fb) {  /* |x| ~< 2^20*(pi/2), medium size */
medium:
		/* rint(x/(pi/2)) */
		fn = (double_t)x*invpio2 + toint - toint;
		n = (int32_t)fn;
		r = x - fn*pio2_1;
		w = fn*pio2_1t;  /* 1st round, good to 85 bits */
		/* Matters with directed rounding. */
		if (UNLIKELY(r - w < -pio4)) {
			n--;
			fn--;
			r = x - fn*pio2_1;
			w = fn*pio2_1t;
		} else if (UNLIKELY(r - w > pio4)) {
			n++;
			fn++;
			r = x - fn*pio2_1;
			w = fn*pio2_1t;
		}
		y[0] = r - w;
		u.f = y[0];
		ey = u.i>>52 & 0x7ff;
		ex = ix>>20;
		if (ex - ey > 16) { /* 2nd round, good to 118 bits */
			t = r;
			w = fn*pio2_2;
			r = t - w;
			w = fn*pio2_2t - ((t-r)-w);
			y[0] = r - w;
			u.f = y[0];
			ey = u.i>>52 & 0x7ff;
			if (ex - ey > 49) {  /* 3rd round, good to 151 bits, covers all cases */
				t = r;
				w = fn*pio2_3;
				r = t - w;
				w = fn*pio2_3t - ((t-r)-w);
				y[0] = r - w;
			}
		}
		y[1] = (r - y[0]) - w;
		return n;
	}
	/*
	 * all other (large) arguments
	 */
	if (ix >= 0x7ff00000) {  /* x is inf or NaN */
		y[0] = y[1] = x - x;
		return 0;
	}
	/* set z = scalbn(|x|,-ilogb(x)+23) */
	u.f = x;
	u.i &= (uint64_t)-1>>12;
	u.i |= (uint64_t)(0x3ff + 23)<<52;
	z = u.f;
	for (i=0; i < 2; i++) {
		tx[i] = (double)(int32_t)z;
		z     = (z-tx[i])*0x1p24;
	}
	tx[i] = z;
	/* skip zero terms, first term is non-zero */
	while (tx[i] == 0.0)
		i--;
	n = __rem_pio2_large(tx,ty,(int)(ix>>20)-(0x3ff+23),i+1,1);
	if (sign) {
		y[0] = -ty[0];
		y[1] = -ty[1];
		return -n;
	}
	y[0] = ty[0];
	y[1] = ty[1];
	return n;
}