#include "math_private.h" #include "wcclibm.h" /* e_rem_pio2f.c -- float version of e_rem_pio2.c * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #if defined(LIBM_SCCS) && !defined(lint) static char rcsid[] = "$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $"; #endif /* __ieee754_rem_pio2f(x,y) * * return the remainder of x rem pi/2 in y[0]+y[1] * use __kernel_rem_pio2f() */ /* This array is like the one in e_rem_pio2.c, but the numbers are single precision and the last 8 bits are forced to 0. */ static const int32_t susan_npio2_hw[] = { 0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, 0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, 0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, 0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, 0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, 0x4242c700, 0x42490f00 }; /* * invpio2: 24 bits of 2/pi * pio2_1: first 17 bit of pi/2 * pio2_1t: pi/2 - pio2_1 * pio2_2: second 17 bit of pi/2 * pio2_2t: pi/2 - (pio2_1+pio2_2) * pio2_3: third 17 bit of pi/2 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) */ static const float /* zero = 0.0000000000e+00f, /\* 0x00000000 *\/ */ /* half = 5.0000000000e-01f, /\* 0x3f000000 *\/ */ /* two8 = 2.5600000000e+02f, /\* 0x43800000 *\/ */ susan_invpio2 = 6.3661980629e-01f, /* 0x3f22f984 */ susan_pio2_1 = 1.5707855225e+00f, /* 0x3fc90f80 */ susan_pio2_1t = 1.0804334124e-05f, /* 0x37354443 */ susan_pio2_2 = 1.0804273188e-05f, /* 0x37354400 */ susan_pio2_2t = 6.0770999344e-11f, /* 0x2e85a308 */ susan_pio2_3 = 6.0770943833e-11f, /* 0x2e85a300 */ susan_pio2_3t = 6.1232342629e-17f; /* 0x248d3132 */ int32_t susan___ieee754_rem_pio2f(float x, float *y) { float z,w,t,r,fn; int32_t i,j,n,ix,hx; GET_FLOAT_WORD(hx,x); ix = hx&0x7fffffff; if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ {y[0] = x; y[1] = 0; return 0;} if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ if(hx>0) { z = x - susan_pio2_1; if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ y[0] = z - susan_pio2_1t; y[1] = (z-y[0])-susan_pio2_1t; } else { /* near pi/2, use 24+24+24 bit pi */ z -= susan_pio2_2; y[0] = z - susan_pio2_2t; y[1] = (z-y[0])-susan_pio2_2t; } return 1; } else { /* negative x */ z = x + susan_pio2_1; if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ y[0] = z + susan_pio2_1t; y[1] = (z-y[0])+susan_pio2_1t; } else { /* near pi/2, use 24+24+24 bit pi */ z += susan_pio2_2; y[0] = z + susan_pio2_2t; y[1] = (z-y[0])+susan_pio2_2t; } return -1; } } if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ t = fabsf(x); n = (int32_t) (t*susan_invpio2+susan_half); fn = (float)n; r = t-fn*susan_pio2_1; w = fn*susan_pio2_1t; /* 1st round good to 40 bit */ if(n<32&&(int32_t)(ix&0xffffff00)!=susan_npio2_hw[n-1]) { y[0] = r-w; /* quick check no cancellation */ } else { u_int32_t high; j = ix>>23; y[0] = r-w; GET_FLOAT_WORD(high,y[0]); i = j-((high>>23)&0xff); if(i>8) { /* 2nd iteration needed, good to 57 */ t = r; w = fn*susan_pio2_2; r = t-w; w = fn*susan_pio2_2t-((t-r)-w); y[0] = r-w; GET_FLOAT_WORD(high,y[0]); i = j-((high>>23)&0xff); if(i>25) { /* 3rd iteration need, 74 bits acc */ t = r; /* will cover all possible cases */ w = fn*susan_pio2_3; r = t-w; w = fn*susan_pio2_3t-((t-r)-w); y[0] = r-w; } } } y[1] = (r-y[0])-w; if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} else return n; } /* * all other (large) arguments */ if(ix>=0x7f800000) { /* x is inf or NaN */ y[0]=y[1]=x-x; return 0; } y[0]=y[1]=x-x; return 0; /* dummy initialisation */ return 0; /* doesn't happen for our input */ } /* k_cosf.c -- float version of k_cos.c * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #if defined(LIBM_SCCS) && !defined(lint) static char rcsid[] = "$NetBSD: k_cosf.c,v 1.4 1995/05/10 20:46:23 jtc Exp $"; #endif static const float /* one = 1.0000000000e+00, /\* 0x3f800000 *\/ */ susan_C1 = 4.1666667908e-02f, /* 0x3d2aaaab */ susan_C2 = -1.3888889225e-03f, /* 0xbab60b61 */ susan_C3 = 2.4801587642e-05f, /* 0x37d00d01 */ susan_C4 = -2.7557314297e-07f, /* 0xb493f27c */ susan_C5 = 2.0875723372e-09f, /* 0x310f74f6 */ susan_C6 = -1.1359647598e-11f; /* 0xad47d74e */ float susan___kernel_cosf(float x, float y) { float a,hz,z,r,qx; int32_t ix; GET_FLOAT_WORD(ix,x); ix &= 0x7fffffff; /* ix = |x|'s high word*/ if(ix<0x32000000) { /* if x < 2**27 */ if(((int)x)==0) return susan_one; /* generate inexact */ } z = x*x; r = z*(susan_C1+z*(susan_C2+z*(susan_C3+z*(susan_C4+z*(susan_C5+z*susan_C6))))); if(ix < 0x3e99999a) /* if |x| < 0.3 */ return susan_one - ((float)0.5f*z - (z*r - x*y)); else { if(ix > 0x3f480000) { /* x > 0.78125 */ qx = (float)0.28125f; } else { SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */ } hz = (float)0.5f*z-qx; a = susan_one-qx; return a - (hz - (z*r-x*y)); } } /* k_sinf.c -- float version of k_sin.c * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #if defined(LIBM_SCCS) && !defined(lint) static char rcsid[] = "$NetBSD: k_sinf.c,v 1.4 1995/05/10 20:46:33 jtc Exp $"; #endif static const float /* half = 5.0000000000e-01f,/\* 0x3f000000 *\/ */ susan_S1 = -1.6666667163e-01f, /* 0xbe2aaaab */ susan_S2 = 8.3333337680e-03f, /* 0x3c088889 */ susan_S3 = -1.9841270114e-04f, /* 0xb9500d01 */ susan_S4 = 2.7557314297e-06f, /* 0x3638ef1b */ susan_S5 = -2.5050759689e-08f, /* 0xb2d72f34 */ susan_S6 = 1.5896910177e-10f; /* 0x2f2ec9d3 */ float susan___kernel_sinf(float x, float y, int iy) { float z,r,v; int32_t ix; GET_FLOAT_WORD(ix,x); ix &= 0x7fffffff; /* high word of x */ if(ix<0x32000000) /* |x| < 2**-27 */ {if((int)x==0) return x;} /* generate inexact */ z = x*x; v = z*x; r = susan_S2+z*(susan_S3+z*(susan_S4+z*(susan_S5+z*susan_S6))); if(iy==0) return x+v*(susan_S1+z*r); else return x-((z*(susan_half*y-v*r)-y)-v*susan_S1); } /* s_atanf.c -- float version of s_atan.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #if defined(LIBM_SCCS) && !defined(lint) static char rcsid[] = "$NetBSD: s_atanf.c,v 1.4 1995/05/10 20:46:47 jtc Exp $"; #endif static const float susan_atanhi[] = { 4.6364760399e-01f, /* atan(0.5)hi 0x3eed6338 */ 7.8539812565e-01f, /* atan(1.0)hi 0x3f490fda */ 9.8279368877e-01f, /* atan(1.5)hi 0x3f7b985e */ 1.5707962513e+00f, /* atan(inf)hi 0x3fc90fda */ }; static const float susan_atanlo[] = { 5.0121582440e-09f, /* atan(0.5)lo 0x31ac3769 */ 3.7748947079e-08f, /* atan(1.0)lo 0x33222168 */ 3.4473217170e-08f, /* atan(1.5)lo 0x33140fb4 */ 7.5497894159e-08f, /* atan(inf)lo 0x33a22168 */ }; static const float susan_aT[] = { 3.3333334327e-01f, /* 0x3eaaaaaa */ -2.0000000298e-01f, /* 0xbe4ccccd */ 1.4285714924e-01f, /* 0x3e124925 */ -1.1111110449e-01f, /* 0xbde38e38 */ 9.0908870101e-02f, /* 0x3dba2e6e */ -7.6918758452e-02f, /* 0xbd9d8795 */ 6.6610731184e-02f, /* 0x3d886b35 */ -5.8335702866e-02f, /* 0xbd6ef16b */ 4.9768779427e-02f, /* 0x3d4bda59 */ -3.6531571299e-02f, /* 0xbd15a221 */ 1.6285819933e-02f, /* 0x3c8569d7 */ }; float susan___atanf(float x) { float w,s1,s2,z; int32_t ix,hx,id; GET_FLOAT_WORD(hx,x); ix = hx&0x7fffffff; if(ix>=0x50800000) { /* if |x| >= 2^34 */ if(ix>0x7f800000) return x+x; /* NaN */ if(hx>0) return susan_atanhi[3]+susan_atanlo[3]; else return -susan_atanhi[3]-susan_atanlo[3]; } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ if (ix < 0x31000000) { /* |x| < 2^-29 */ if(susan_huge+x>susan_one) return x; /* raise inexact */ } id = -1; } else { x = fabsf(x); if (ix < 0x3f980000) { /* |x| < 1.1875 */ if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ id = 0; x = ((float)2.0f*x-susan_one)/((float)2.0f+x); } else { /* 11/16<=|x|< 19/16 */ id = 1; x = (x-susan_one)/(x+susan_one); } } else { if (ix < 0x401c0000) { /* |x| < 2.4375 */ id = 2; x = (x-(float)1.5f)/(susan_one+(float)1.5f*x); } else { /* 2.4375 <= |x| < 2^66 */ id = 3; x = -(float)1.0f/x; } }} /* end of argument reduction */ z = x*x; w = z*z; /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ s1 = z*(susan_aT[0]+w*(susan_aT[2]+w*(susan_aT[4]+w*(susan_aT[6]+w*(susan_aT[8]+w*susan_aT[10]))))); s2 = w*(susan_aT[1]+w*(susan_aT[3]+w*(susan_aT[5]+w*(susan_aT[7]+w*susan_aT[9])))); if (id<0) return x - x*(s1+s2); else { z = susan_atanhi[id] - ((x*(s1+s2) - susan_atanlo[id]) - x); return (hx<0)? -z:z; } } /* s_cosf.c -- float version of s_cos.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ float susan___cosf(float x) { float y[2],z=0.0f; int32_t n,ix; GET_FLOAT_WORD(ix,x); /* |x| ~< pi/4 */ ix &= 0x7fffffff; if(ix <= 0x3f490fd8) return susan___kernel_cosf(x,z); /* cos(Inf or NaN) is NaN */ else if (ix>=0x7f800000) return x-x; /* argument reduction needed */ else { n = susan___ieee754_rem_pio2f(x,y); switch(n&3) { case 0: return susan___kernel_cosf(y[0],y[1]); case 1: return -susan___kernel_sinf(y[0],y[1],1); case 2: return -susan___kernel_cosf(y[0],y[1]); default: return susan___kernel_sinf(y[0],y[1],1); } } } /* s_sinf.c -- float version of s_sin.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ float susan___sinf(float x) { float y[2],z=0.0; int32_t n, ix; GET_FLOAT_WORD(ix,x); /* |x| ~< pi/4 */ ix &= 0x7fffffff; if(ix <= 0x3f490fd8) return susan___kernel_sinf(x,z,0); /* sin(Inf or NaN) is NaN */ else if (ix>=0x7f800000) return x-x; /* argument reduction needed */ else { n = susan___ieee754_rem_pio2f(x,y); switch(n&3) { case 0: return susan___kernel_sinf(y[0],y[1],1); case 1: return susan___kernel_cosf(y[0],y[1]); case 2: return -susan___kernel_sinf(y[0],y[1],1); default: return -susan___kernel_cosf(y[0],y[1]); } } } /* s_fabsf.c -- float version of s_fabs.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* * fabsf(x) returns the absolute value of x. */ float susan___fabsf(float x) { u_int32_t ix; GET_FLOAT_WORD(ix,x); SET_FLOAT_WORD(x,ix&0x7fffffff); return x; }