1 /* e_rem_pio2f.c -- float version of e_rem_pio2.c 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 */ 4 5 /* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16 /* __ieee754_rem_pio2f(x,y) 17 * 18 * return the remainder of x rem pi/2 in y[0]+y[1] 19 * use __kernel_rem_pio2f() 20 */ 21 22 #include "math.h" 23 #include "math_private.h" 24 25 /* 26 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 27 */ 28 static const int32_t two_over_pi[] = { 29 0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, 30 0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, 31 0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63, 32 0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, 33 0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, 34 0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, 35 0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44, 36 0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, 37 0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, 38 0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, 39 0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11, 40 0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, 41 0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, 42 0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, 43 0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92, 44 0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, 45 0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, 46 0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, 47 0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85, 48 0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, 49 0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, 50 0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, 51 }; 52 53 /* This array is like the one in e_rem_pio2.c, but the numbers are 54 single precision and the last 8 bits are forced to 0. */ 55 static const int32_t npio2_hw[] = { 56 0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, 57 0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, 58 0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, 59 0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, 60 0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, 61 0x4242c700, 0x42490f00 62 }; 63 64 /* 65 * invpio2: 24 bits of 2/pi 66 * pio2_1: first 17 bit of pi/2 67 * pio2_1t: pi/2 - pio2_1 68 * pio2_2: second 17 bit of pi/2 69 * pio2_2t: pi/2 - (pio2_1+pio2_2) 70 * pio2_3: third 17 bit of pi/2 71 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 72 */ 73 74 static const float 75 zero = 0.0000000000e+00, /* 0x00000000 */ 76 half = 5.0000000000e-01, /* 0x3f000000 */ 77 two8 = 2.5600000000e+02, /* 0x43800000 */ 78 invpio2 = 6.3661980629e-01, /* 0x3f22f984 */ 79 pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */ 80 pio2_1t = 1.0804334124e-05, /* 0x37354443 */ 81 pio2_2 = 1.0804273188e-05, /* 0x37354400 */ 82 pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */ 83 pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */ 84 pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ 85 86 int32_t 87 __ieee754_rem_pio2f(float x, float *y) 88 { 89 float z,w,t,r,fn; 90 float tx[3]; 91 int32_t e0,i,j,nx,n,ix,hx; 92 93 GET_FLOAT_WORD(hx,x); 94 ix = hx&0x7fffffff; 95 if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ 96 {y[0] = x; y[1] = 0; return 0;} 97 if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ 98 if(hx>0) { 99 z = x - pio2_1; 100 if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ 101 y[0] = z - pio2_1t; 102 y[1] = (z-y[0])-pio2_1t; 103 } else { /* near pi/2, use 24+24+24 bit pi */ 104 z -= pio2_2; 105 y[0] = z - pio2_2t; 106 y[1] = (z-y[0])-pio2_2t; 107 } 108 return 1; 109 } else { /* negative x */ 110 z = x + pio2_1; 111 if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ 112 y[0] = z + pio2_1t; 113 y[1] = (z-y[0])+pio2_1t; 114 } else { /* near pi/2, use 24+24+24 bit pi */ 115 z += pio2_2; 116 y[0] = z + pio2_2t; 117 y[1] = (z-y[0])+pio2_2t; 118 } 119 return -1; 120 } 121 } 122 if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ 123 t = fabsf(x); 124 n = (int32_t) (t*invpio2+half); 125 fn = (float)n; 126 r = t-fn*pio2_1; 127 w = fn*pio2_1t; /* 1st round good to 40 bit */ 128 if(n<32&&(ix&0xffffff00)!=(u_int32_t)npio2_hw[n-1]) { 129 y[0] = r-w; /* quick check no cancellation */ 130 } else { 131 u_int32_t high; 132 j = ix>>23; 133 y[0] = r-w; 134 GET_FLOAT_WORD(high,y[0]); 135 i = j-((high>>23)&0xff); 136 if(i>8) { /* 2nd iteration needed, good to 57 */ 137 t = r; 138 w = fn*pio2_2; 139 r = t-w; 140 w = fn*pio2_2t-((t-r)-w); 141 y[0] = r-w; 142 GET_FLOAT_WORD(high,y[0]); 143 i = j-((high>>23)&0xff); 144 if(i>25) { /* 3rd iteration need, 74 bits acc */ 145 t = r; /* will cover all possible cases */ 146 w = fn*pio2_3; 147 r = t-w; 148 w = fn*pio2_3t-((t-r)-w); 149 y[0] = r-w; 150 } 151 } 152 } 153 y[1] = (r-y[0])-w; 154 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 155 else return n; 156 } 157 /* 158 * all other (large) arguments 159 */ 160 if(ix>=0x7f800000) { /* x is inf or NaN */ 161 y[0]=y[1]=x-x; return 0; 162 } 163 /* set z = scalbn(|x|,ilogb(x)-7) */ 164 e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */ 165 SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23))); 166 for(i=0;i<2;i++) { 167 tx[i] = (float)((int32_t)(z)); 168 z = (z-tx[i])*two8; 169 } 170 tx[2] = z; 171 nx = 3; 172 while(tx[nx-1]==zero) nx--; /* skip zero term */ 173 n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi); 174 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 175 return n; 176 } 177