1 /* 2 * This file is part of the MicroPython project, http://micropython.org/ 3 * 4 * These math functions are taken from newlib-nano-2, the newlib/libm/math 5 * directory, available from https://github.com/32bitmicro/newlib-nano-2. 6 * 7 * Appropriate copyright headers are reproduced below. 8 */ 9 10 /* kf_rem_pio2.c -- float version of k_rem_pio2.c 11 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 12 */ 13 14 /* 15 * ==================================================== 16 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 17 * 18 * Developed at SunPro, a Sun Microsystems, Inc. business. 19 * Permission to use, copy, modify, and distribute this 20 * software is freely granted, provided that this notice 21 * is preserved. 22 * ==================================================== 23 */ 24 25 #include "fdlibm.h" 26 27 /* In the float version, the input parameter x contains 8 bit 28 integers, not 24 bit integers. 113 bit precision is not supported. */ 29 30 #ifdef __STDC__ 31 static const int init_jk[] = {4,7,9}; /* initial value for jk */ 32 #else 33 static int init_jk[] = {4,7,9}; 34 #endif 35 36 #ifdef __STDC__ 37 static const float PIo2[] = { 38 #else 39 static float PIo2[] = { 40 #endif 41 1.5703125000e+00f, /* 0x3fc90000 */ 42 4.5776367188e-04f, /* 0x39f00000 */ 43 2.5987625122e-05f, /* 0x37da0000 */ 44 7.5437128544e-08f, /* 0x33a20000 */ 45 6.0026650317e-11f, /* 0x2e840000 */ 46 7.3896444519e-13f, /* 0x2b500000 */ 47 5.3845816694e-15f, /* 0x27c20000 */ 48 5.6378512969e-18f, /* 0x22d00000 */ 49 8.3009228831e-20f, /* 0x1fc40000 */ 50 3.2756352257e-22f, /* 0x1bc60000 */ 51 6.3331015649e-25f, /* 0x17440000 */ 52 }; 53 54 #ifdef __STDC__ 55 static const float 56 #else 57 static float 58 #endif 59 zero = 0.0f, 60 one = 1.0f, 61 two8 = 2.5600000000e+02f, /* 0x43800000 */ 62 twon8 = 3.9062500000e-03f; /* 0x3b800000 */ 63 64 #ifdef __STDC__ __kernel_rem_pio2f(float * x,float * y,int e0,int nx,int prec,const __uint8_t * ipio2)65 int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __uint8_t *ipio2) 66 #else 67 int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2) 68 float x[], y[]; int e0,nx,prec; __uint8_t ipio2[]; 69 #endif 70 { 71 __int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 72 float z,fw,f[20],fq[20],q[20]; 73 74 /* initialize jk*/ 75 jk = init_jk[prec]; 76 jp = jk; 77 78 /* determine jx,jv,q0, note that 3>q0 */ 79 jx = nx-1; 80 jv = (e0-3)/8; if(jv<0) jv=0; 81 q0 = e0-8*(jv+1); 82 83 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 84 j = jv-jx; m = jx+jk; 85 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; 86 87 /* compute q[0],q[1],...q[jk] */ 88 for (i=0;i<=jk;i++) { 89 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 90 q[i] = fw; 91 } 92 93 jz = jk; 94 recompute: 95 /* distill q[] into iq[] reversingly */ 96 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 97 fw = (float)((__int32_t)(twon8* z)); 98 iq[i] = (__int32_t)(z-two8*fw); 99 z = q[j-1]+fw; 100 } 101 102 /* compute n */ 103 z = scalbnf(z,(int)q0); /* actual value of z */ 104 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ 105 n = (__int32_t) z; 106 z -= (float)n; 107 ih = 0; 108 if(q0>0) { /* need iq[jz-1] to determine n */ 109 i = (iq[jz-1]>>(8-q0)); n += i; 110 iq[jz-1] -= i<<(8-q0); 111 ih = iq[jz-1]>>(7-q0); 112 } 113 else if(q0==0) ih = iq[jz-1]>>8; 114 else if(z>=(float)0.5) ih=2; 115 116 if(ih>0) { /* q > 0.5 */ 117 n += 1; carry = 0; 118 for(i=0;i<jz ;i++) { /* compute 1-q */ 119 j = iq[i]; 120 if(carry==0) { 121 if(j!=0) { 122 carry = 1; iq[i] = 0x100- j; 123 } 124 } else iq[i] = 0xff - j; 125 } 126 if(q0>0) { /* rare case: chance is 1 in 12 */ 127 switch(q0) { 128 case 1: 129 iq[jz-1] &= 0x7f; break; 130 case 2: 131 iq[jz-1] &= 0x3f; break; 132 } 133 } 134 if(ih==2) { 135 z = one - z; 136 if(carry!=0) z -= scalbnf(one,(int)q0); 137 } 138 } 139 140 /* check if recomputation is needed */ 141 if(z==zero) { 142 j = 0; 143 for (i=jz-1;i>=jk;i--) j |= iq[i]; 144 if(j==0) { /* need recomputation */ 145 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 146 147 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 148 f[jx+i] = (float) ipio2[jv+i]; 149 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 150 q[i] = fw; 151 } 152 jz += k; 153 goto recompute; 154 } 155 } 156 157 /* chop off zero terms */ 158 if(z==(float)0.0) { 159 jz -= 1; q0 -= 8; 160 while(iq[jz]==0) { jz--; q0-=8;} 161 } else { /* break z into 8-bit if necessary */ 162 z = scalbnf(z,-(int)q0); 163 if(z>=two8) { 164 fw = (float)((__int32_t)(twon8*z)); 165 iq[jz] = (__int32_t)(z-two8*fw); 166 jz += 1; q0 += 8; 167 iq[jz] = (__int32_t) fw; 168 } else iq[jz] = (__int32_t) z ; 169 } 170 171 /* convert integer "bit" chunk to floating-point value */ 172 fw = scalbnf(one,(int)q0); 173 for(i=jz;i>=0;i--) { 174 q[i] = fw*(float)iq[i]; fw*=twon8; 175 } 176 177 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 178 for(i=jz;i>=0;i--) { 179 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 180 fq[jz-i] = fw; 181 } 182 183 /* compress fq[] into y[] */ 184 switch(prec) { 185 case 0: 186 fw = 0.0; 187 for (i=jz;i>=0;i--) fw += fq[i]; 188 y[0] = (ih==0)? fw: -fw; 189 break; 190 case 1: 191 case 2: 192 fw = 0.0; 193 for (i=jz;i>=0;i--) fw += fq[i]; 194 y[0] = (ih==0)? fw: -fw; 195 fw = fq[0]-fw; 196 for (i=1;i<=jz;i++) fw += fq[i]; 197 y[1] = (ih==0)? fw: -fw; 198 break; 199 case 3: /* painful */ 200 for (i=jz;i>0;i--) { 201 fw = fq[i-1]+fq[i]; 202 fq[i] += fq[i-1]-fw; 203 fq[i-1] = fw; 204 } 205 for (i=jz;i>1;i--) { 206 fw = fq[i-1]+fq[i]; 207 fq[i] += fq[i-1]-fw; 208 fq[i-1] = fw; 209 } 210 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 211 if(ih==0) { 212 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 213 } else { 214 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 215 } 216 } 217 return n&7; 218 } 219