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alexbevi
GitHub Repository: alexbevi/BizHawk
 Path: blob/master/waterbox/libc/functions/math/__rem_pio2l.c
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/* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */

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/*

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 * ====================================================

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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

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 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.

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 *

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 * Developed at SunSoft, a Sun Microsystems, Inc. business.

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 * Permission to use, copy, modify, and distribute this

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 * software is freely granted, provided that this notice

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 * is preserved.

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 * ====================================================

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 *

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 * Optimized by Bruce D. Evans.

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 */

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#include "libm.h"

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#if (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384

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/* ld80 and ld128 version of __rem_pio2(x,y)

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 *

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 * return the remainder of x rem pi/2 in y[0]+y[1]

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 * use __rem_pio2_large() for large x

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 */

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static const long double toint = 1.5/LDBL_EPSILON;

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#if LDBL_MANT_DIG == 64

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/* u ~< 0x1p25*pi/2 */

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#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.m>>48) < ((0x3fff + 25)<<16 | 0x921f>>1 | 0x8000))

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#define QUOBITS(x) ((uint32_t)(int32_t)x & 0x7fffffff)

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#define ROUND1 22

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#define ROUND2 61

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#define NX 3

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#define NY 2

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/*

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 * invpio2:  64 bits of 2/pi

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 * pio2_1:   first  39 bits of pi/2

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 * pio2_1t:  pi/2 - pio2_1

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 * pio2_2:   second 39 bits of pi/2

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 * pio2_2t:  pi/2 - (pio2_1+pio2_2)

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 * pio2_3:   third  39 bits of pi/2

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 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)

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 */

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static const double

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pio2_1 =  1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */

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pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */

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pio2_3 =  6.36831716351370313614e-25; /*  0x18a2e037074000.0p-133 */

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static const long double

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invpio2 =  6.36619772367581343076e-01L, /*  0xa2f9836e4e44152a.0p-64 */

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pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */

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pio2_2t =  6.36831716351095013979e-25L, /*  0xc51701b839a25205.0p-144 */

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pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */

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#elif LDBL_MANT_DIG == 113

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/* u ~< 0x1p45*pi/2 */

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#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.top) < ((0x3fff + 45)<<16 | 0x921f))

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#define QUOBITS(x) ((uint32_t)(int64_t)x & 0x7fffffff)

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#define ROUND1 51

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#define ROUND2 119

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#define NX 5

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#define NY 3

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static const long double

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invpio2 =  6.3661977236758134307553505349005747e-01L,	/*  0x145f306dc9c882a53f84eafa3ea6a.0p-113 */

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pio2_1  =  1.5707963267948966192292994253909555e+00L,	/*  0x1921fb54442d18469800000000000.0p-112 */

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pio2_1t =  2.0222662487959507323996846200947577e-21L,	/*  0x13198a2e03707344a4093822299f3.0p-181 */

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pio2_2  =  2.0222662487959507323994779168837751e-21L,	/*  0x13198a2e03707344a400000000000.0p-181 */

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pio2_2t =  2.0670321098263988236496903051604844e-43L,	/*  0x127044533e63a0105df531d89cd91.0p-254 */

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pio2_3  =  2.0670321098263988236499468110329591e-43L,	/*  0x127044533e63a0105e00000000000.0p-254 */

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pio2_3t = -2.5650587247459238361625433492959285e-65L;	/* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327 */

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#endif

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int __rem_pio2l(long double x, long double *y)

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{

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	union ldshape u,uz;

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	long double z,w,t,r,fn;

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	double tx[NX],ty[NY];

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	int ex,ey,n,i;

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	u.f = x;

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	ex = u.i.se & 0x7fff;

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	if (SMALL(u)) {

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		/* rint(x/(pi/2)), Assume round-to-nearest. */

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		fn = x*invpio2 + toint - toint;

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		n = QUOBITS(fn);

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		r = x-fn*pio2_1;

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		w = fn*pio2_1t;  /* 1st round good to 102/180 bits (ld80/ld128) */

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		y[0] = r-w;

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		u.f = y[0];

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		ey = u.i.se & 0x7fff;

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		if (ex - ey > ROUND1) {  /* 2nd iteration needed, good to 141/248 (ld80/ld128) */

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			t = r;

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			w = fn*pio2_2;

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			r = t-w;

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			w = fn*pio2_2t-((t-r)-w);

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			y[0] = r-w;

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			u.f = y[0];

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			ey = u.i.se & 0x7fff;

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			if (ex - ey > ROUND2) {  /* 3rd iteration, good to 180/316 bits */

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				t = r; /* will cover all possible cases (not verified for ld128) */

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				w = fn*pio2_3;

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				r = t-w;

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				w = fn*pio2_3t-((t-r)-w);

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				y[0] = r-w;

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			}

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		}

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		y[1] = (r - y[0]) - w;

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		return n;

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	}

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	/*

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	 * all other (large) arguments

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	 */

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	if (ex == 0x7fff) {                /* x is inf or NaN */

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		y[0] = y[1] = x - x;

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		return 0;

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	}

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	/* set z = scalbn(|x|,-ilogb(x)+23) */

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	uz.f = x;

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	uz.i.se = 0x3fff + 23;

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	z = uz.f;

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	for (i=0; i < NX - 1; i++) {

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		tx[i] = (double)(int32_t)z;

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		z     = (z-tx[i])*0x1p24;

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	}

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	tx[i] = z;

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	while (tx[i] == 0)

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		i--;

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	n = __rem_pio2_large(tx, ty, ex-0x3fff-23, i+1, NY);

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	w = ty[1];

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	if (NY == 3)

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		w += ty[2];

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	r = ty[0] + w;

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	/* TODO: for ld128 this does not follow the recommendation of the

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	comments of __rem_pio2_large which seem wrong if |ty[0]| > |ty[1]+ty[2]| */

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	w -= r - ty[0];

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	if (u.i.se >> 15) {

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		y[0] = -r;

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		y[1] = -w;

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		return -n;

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	}

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	y[0] = r;

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	y[1] = w;

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	return n;

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}

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#endif

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