src/libm/e_rem_pio2.c
author Sam Lantinga <slouken@libsdl.org>
Thu, 04 Jun 2020 12:30:25 -0700
changeset 13898 aa9d7c43a982
parent 12084 f0092ea3a038
permissions -rw-r--r--
Fixed exception if getManifestEnvironmentVariables() is called without a current SDL activity
     1 /*
     2  * ====================================================
     3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     4  *
     5  * Developed at SunPro, a Sun Microsystems, Inc. business.
     6  * Permission to use, copy, modify, and distribute this
     7  * software is freely granted, provided that this notice
     8  * is preserved.
     9  * ====================================================
    10  */
    11 
    12 /* __ieee754_rem_pio2(x,y)
    13  *
    14  * return the remainder of x rem pi/2 in y[0]+y[1]
    15  * use __kernel_rem_pio2()
    16  */
    17 
    18 #include "math_libm.h"
    19 #include "math_private.h"
    20 
    21 /*
    22  * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
    23  */
    24 static const int32_t two_over_pi[] = {
    25 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
    26 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
    27 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
    28 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
    29 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
    30 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
    31 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
    32 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
    33 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
    34 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
    35 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
    36 };
    37 
    38 static const int32_t npio2_hw[] = {
    39 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
    40 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
    41 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
    42 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
    43 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
    44 0x404858EB, 0x404921FB,
    45 };
    46 
    47 /*
    48  * invpio2:  53 bits of 2/pi
    49  * pio2_1:   first  33 bit of pi/2
    50  * pio2_1t:  pi/2 - pio2_1
    51  * pio2_2:   second 33 bit of pi/2
    52  * pio2_2t:  pi/2 - (pio2_1+pio2_2)
    53  * pio2_3:   third  33 bit of pi/2
    54  * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
    55  */
    56 
    57 static const double
    58 zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
    59 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
    60 two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
    61 invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
    62 pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
    63 pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
    64 pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
    65 pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
    66 pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
    67 pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
    68 
    69 int32_t attribute_hidden __ieee754_rem_pio2(double x, double *y)
    70 {
    71 	double z=0.0,w,t,r,fn;
    72 	double tx[3];
    73 	int32_t e0,i,j,nx,n,ix,hx;
    74 	u_int32_t low;
    75 
    76 	GET_HIGH_WORD(hx,x);		/* high word of x */
    77 	ix = hx&0x7fffffff;
    78 	if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
    79 	    {y[0] = x; y[1] = 0; return 0;}
    80 	if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
    81 	    if(hx>0) {
    82 		z = x - pio2_1;
    83 		if(ix!=0x3ff921fb) { 	/* 33+53 bit pi is good enough */
    84 		    y[0] = z - pio2_1t;
    85 		    y[1] = (z-y[0])-pio2_1t;
    86 		} else {		/* near pi/2, use 33+33+53 bit pi */
    87 		    z -= pio2_2;
    88 		    y[0] = z - pio2_2t;
    89 		    y[1] = (z-y[0])-pio2_2t;
    90 		}
    91 		return 1;
    92 	    } else {	/* negative x */
    93 		z = x + pio2_1;
    94 		if(ix!=0x3ff921fb) { 	/* 33+53 bit pi is good enough */
    95 		    y[0] = z + pio2_1t;
    96 		    y[1] = (z-y[0])+pio2_1t;
    97 		} else {		/* near pi/2, use 33+33+53 bit pi */
    98 		    z += pio2_2;
    99 		    y[0] = z + pio2_2t;
   100 		    y[1] = (z-y[0])+pio2_2t;
   101 		}
   102 		return -1;
   103 	    }
   104 	}
   105 	if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
   106 	    t  = fabs(x);
   107 	    n  = (int32_t) (t*invpio2+half);
   108 	    fn = (double)n;
   109 	    r  = t-fn*pio2_1;
   110 	    w  = fn*pio2_1t;	/* 1st round good to 85 bit */
   111 	    if(n<32&&ix!=npio2_hw[n-1]) {
   112 		y[0] = r-w;	/* quick check no cancellation */
   113 	    } else {
   114 	        u_int32_t high;
   115 	        j  = ix>>20;
   116 	        y[0] = r-w;
   117 		GET_HIGH_WORD(high,y[0]);
   118 	        i = j-((high>>20)&0x7ff);
   119 	        if(i>16) {  /* 2nd iteration needed, good to 118 */
   120 		    t  = r;
   121 		    w  = fn*pio2_2;
   122 		    r  = t-w;
   123 		    w  = fn*pio2_2t-((t-r)-w);
   124 		    y[0] = r-w;
   125 		    GET_HIGH_WORD(high,y[0]);
   126 		    i = j-((high>>20)&0x7ff);
   127 		    if(i>49)  {	/* 3rd iteration need, 151 bits acc */
   128 		    	t  = r;	/* will cover all possible cases */
   129 		    	w  = fn*pio2_3;
   130 		    	r  = t-w;
   131 		    	w  = fn*pio2_3t-((t-r)-w);
   132 		    	y[0] = r-w;
   133 		    }
   134 		}
   135 	    }
   136 	    y[1] = (r-y[0])-w;
   137 	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
   138 	    else	 return n;
   139 	}
   140     /*
   141      * all other (large) arguments
   142      */
   143 	if(ix>=0x7ff00000) {		/* x is inf or NaN */
   144 	    y[0]=y[1]=x-x; return 0;
   145 	}
   146     /* set z = scalbn(|x|,ilogb(x)-23) */
   147 	GET_LOW_WORD(low,x);
   148 	SET_LOW_WORD(z,low);
   149 	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
   150 	SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
   151 	for(i=0;i<2;i++) {
   152 		tx[i] = (double)((int32_t)(z));
   153 		z     = (z-tx[i])*two24;
   154 	}
   155 	tx[2] = z;
   156 	nx = 3;
   157 	while((nx > 0) && tx[nx-1]==zero) nx--;	/* skip zero term */
   158 	n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
   159 	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
   160 	return n;
   161 }