src/libm/s_atan.c
 author Ryan C. Gordon Mon, 23 Jan 2017 12:06:10 -0500 changeset 10837 c2f241c2f6ad parent 8056 abd9434c5d3e child 11683 48bcba563d9c permissions -rw-r--r--
audio: Fix same bug as last commit, but for _mm_bslli_si128 vs _mm_slli_si128.
 slouken@4873 1 /* slouken@4873 2 * ==================================================== slouken@4873 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. slouken@4873 4 * slouken@4873 5 * Developed at SunPro, a Sun Microsystems, Inc. business. slouken@4873 6 * Permission to use, copy, modify, and distribute this slouken@4873 7 * software is freely granted, provided that this notice slouken@4873 8 * is preserved. slouken@4873 9 * ==================================================== slouken@4873 10 */ slouken@4873 11 slouken@4873 12 /* atan(x) slouken@4873 13 * Method slouken@4873 14 * 1. Reduce x to positive by atan(x) = -atan(-x). slouken@4873 15 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument slouken@4873 16 * is further reduced to one of the following intervals and the slouken@4873 17 * arctangent of t is evaluated by the corresponding formula: slouken@4873 18 * slouken@4873 19 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) slouken@4873 20 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) slouken@4873 21 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) slouken@4873 22 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) slouken@4873 23 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) slouken@4873 24 * slouken@4873 25 * Constants: slouken@4873 26 * The hexadecimal values are the intended ones for the following slouken@4873 27 * constants. The decimal values may be used, provided that the slouken@4873 28 * compiler will convert from decimal to binary accurately enough slouken@4873 29 * to produce the hexadecimal values shown. slouken@4873 30 */ slouken@4873 31 slouken@6044 32 #include "math_libm.h" slouken@4873 33 #include "math_private.h" slouken@4873 34 slouken@4873 35 static const double atanhi[] = { slouken@4873 36 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ slouken@4873 37 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ slouken@4873 38 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ slouken@4873 39 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ slouken@4873 40 }; slouken@4873 41 slouken@4873 42 static const double atanlo[] = { slouken@4873 43 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ slouken@4873 44 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ slouken@4873 45 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ slouken@4873 46 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ slouken@4873 47 }; slouken@4873 48 slouken@4873 49 static const double aT[] = { slouken@4873 50 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ slouken@4873 51 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ slouken@4873 52 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ slouken@4873 53 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ slouken@4873 54 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ slouken@4873 55 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ slouken@4873 56 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ slouken@4873 57 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ slouken@4873 58 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ slouken@4873 59 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ slouken@4873 60 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ slouken@4873 61 }; slouken@4873 62 slouken@4873 63 static const double slouken@4873 64 one = 1.0, slouken@4873 65 huge = 1.0e300; slouken@4873 66 slouken@4873 67 double atan(double x) slouken@4873 68 { slouken@4873 69 double w,s1,s2,z; slouken@4873 70 int32_t ix,hx,id; slouken@4873 71 slouken@4873 72 GET_HIGH_WORD(hx,x); slouken@4873 73 ix = hx&0x7fffffff; slouken@4873 74 if(ix>=0x44100000) { /* if |x| >= 2^66 */ slouken@4873 75 u_int32_t low; slouken@4873 76 GET_LOW_WORD(low,x); slouken@4873 77 if(ix>0x7ff00000|| slouken@4873 78 (ix==0x7ff00000&&(low!=0))) slouken@4873 79 return x+x; /* NaN */ slouken@4873 80 if(hx>0) return atanhi[3]+atanlo[3]; slouken@4873 81 else return -atanhi[3]-atanlo[3]; slouken@4873 82 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ slouken@4873 83 if (ix < 0x3e200000) { /* |x| < 2^-29 */ slouken@4873 84 if(huge+x>one) return x; /* raise inexact */ slouken@4873 85 } slouken@4873 86 id = -1; slouken@4873 87 } else { slouken@4873 88 x = fabs(x); slouken@4873 89 if (ix < 0x3ff30000) { /* |x| < 1.1875 */ slouken@4873 90 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ slouken@4873 91 id = 0; x = (2.0*x-one)/(2.0+x); slouken@4873 92 } else { /* 11/16<=|x|< 19/16 */ slouken@4873 93 id = 1; x = (x-one)/(x+one); slouken@4873 94 } slouken@4873 95 } else { slouken@4873 96 if (ix < 0x40038000) { /* |x| < 2.4375 */ slouken@4873 97 id = 2; x = (x-1.5)/(one+1.5*x); slouken@4873 98 } else { /* 2.4375 <= |x| < 2^66 */ slouken@4873 99 id = 3; x = -1.0/x; slouken@4873 100 } slouken@4873 101 }} slouken@4873 102 /* end of argument reduction */ slouken@4873 103 z = x*x; slouken@4873 104 w = z*z; slouken@4873 105 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ slouken@4873 106 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); slouken@4873 107 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); slouken@4873 108 if (id<0) return x - x*(s1+s2); slouken@4873 109 else { slouken@4873 110 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); slouken@4873 111 return (hx<0)? -z:z; slouken@4873 112 } slouken@4873 113 } slouken@4873 114 libm_hidden_def(atan) slouken@8004 115