| 1 | /* ef_rem_pio2.c -- float version of e_rem_pio2.c |
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| 2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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| 3 | */ |
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| 4 | |
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| 5 | /* |
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| 6 | * ==================================================== |
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| 7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 8 | * |
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| 9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 10 | * Permission to use, copy, modify, and distribute this |
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| 11 | * software is freely granted, provided that this notice |
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| 12 | * is preserved. |
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| 13 | * ==================================================== |
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| 14 | * |
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| 15 | */ |
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| 16 | |
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| 17 | /* __ieee754_rem_pio2f(x,y) |
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| 18 | * |
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| 19 | * return the remainder of x rem pi/2 in y[0]+y[1] |
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| 20 | * use __kernel_rem_pio2f() |
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| 21 | */ |
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| 22 | |
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| 23 | #include "fdlibm.h" |
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| 24 | |
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| 25 | /* |
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| 26 | * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
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| 27 | */ |
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| 28 | #ifdef __STDC__ |
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| 29 | static const __int32_t two_over_pi[] = { |
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| 30 | #else |
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| 31 | static __int32_t two_over_pi[] = { |
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| 32 | #endif |
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| 33 | 0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, |
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| 34 | 0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, |
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| 35 | 0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63, |
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| 36 | 0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, |
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| 37 | 0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, |
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| 38 | 0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, |
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| 39 | 0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44, |
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| 40 | 0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, |
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| 41 | 0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, |
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| 42 | 0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, |
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| 43 | 0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11, |
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| 44 | 0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, |
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| 45 | 0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, |
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| 46 | 0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, |
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| 47 | 0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92, |
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| 48 | 0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, |
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| 49 | 0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, |
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| 50 | 0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, |
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| 51 | 0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85, |
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| 52 | 0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, |
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| 53 | 0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, |
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| 54 | 0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, |
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| 55 | }; |
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| 56 | |
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| 57 | /* This array is like the one in e_rem_pio2.c, but the numbers are |
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| 58 | single precision and the last 8 bits are forced to 0. */ |
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| 59 | #ifdef __STDC__ |
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| 60 | static const __int32_t npio2_hw[] = { |
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| 61 | #else |
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| 62 | static __int32_t npio2_hw[] = { |
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| 63 | #endif |
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| 64 | 0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, |
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| 65 | 0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, |
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| 66 | 0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, |
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| 67 | 0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, |
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| 68 | 0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, |
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| 69 | 0x4242c700, 0x42490f00 |
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| 70 | }; |
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| 71 | |
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| 72 | /* |
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| 73 | * invpio2: 24 bits of 2/pi |
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| 74 | * pio2_1: first 17 bit of pi/2 |
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| 75 | * pio2_1t: pi/2 - pio2_1 |
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| 76 | * pio2_2: second 17 bit of pi/2 |
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| 77 | * pio2_2t: pi/2 - (pio2_1+pio2_2) |
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| 78 | * pio2_3: third 17 bit of pi/2 |
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| 79 | * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
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| 80 | */ |
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| 81 | |
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| 82 | #ifdef __STDC__ |
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| 83 | static const float |
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| 84 | #else |
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| 85 | static float |
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| 86 | #endif |
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| 87 | zero = 0.0000000000e+00, /* 0x00000000 */ |
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| 88 | half = 5.0000000000e-01, /* 0x3f000000 */ |
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| 89 | two8 = 2.5600000000e+02, /* 0x43800000 */ |
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| 90 | invpio2 = 6.3661980629e-01, /* 0x3f22f984 */ |
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| 91 | pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */ |
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| 92 | pio2_1t = 1.0804334124e-05, /* 0x37354443 */ |
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| 93 | pio2_2 = 1.0804273188e-05, /* 0x37354400 */ |
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| 94 | pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */ |
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| 95 | pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */ |
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| 96 | pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ |
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| 97 | |
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| 98 | #ifdef __STDC__ |
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| 99 | __int32_t __ieee754_rem_pio2f(float x, float *y) |
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| 100 | #else |
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| 101 | __int32_t __ieee754_rem_pio2f(x,y) |
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| 102 | float x,y[]; |
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| 103 | #endif |
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| 104 | { |
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| 105 | float z,w,t,r,fn; |
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| 106 | float tx[3]; |
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| 107 | __int32_t i,j,n,ix,hx; |
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| 108 | int e0,nx; |
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| 109 | |
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| 110 | GET_FLOAT_WORD(hx,x); |
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| 111 | ix = hx&0x7fffffff; |
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| 112 | if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ |
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| 113 | {y[0] = x; y[1] = 0; return 0;} |
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| 114 | if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ |
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| 115 | if(hx>0) { |
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| 116 | z = x - pio2_1; |
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| 117 | if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ |
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| 118 | y[0] = z - pio2_1t; |
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| 119 | y[1] = (z-y[0])-pio2_1t; |
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| 120 | } else { /* near pi/2, use 24+24+24 bit pi */ |
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| 121 | z -= pio2_2; |
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| 122 | y[0] = z - pio2_2t; |
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| 123 | y[1] = (z-y[0])-pio2_2t; |
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| 124 | } |
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| 125 | return 1; |
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| 126 | } else { /* negative x */ |
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| 127 | z = x + pio2_1; |
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| 128 | if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ |
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| 129 | y[0] = z + pio2_1t; |
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| 130 | y[1] = (z-y[0])+pio2_1t; |
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| 131 | } else { /* near pi/2, use 24+24+24 bit pi */ |
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| 132 | z += pio2_2; |
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| 133 | y[0] = z + pio2_2t; |
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| 134 | y[1] = (z-y[0])+pio2_2t; |
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| 135 | } |
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| 136 | return -1; |
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| 137 | } |
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| 138 | } |
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| 139 | if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ |
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| 140 | t = fabsf(x); |
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| 141 | n = (__int32_t) (t*invpio2+half); |
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| 142 | fn = (float)n; |
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| 143 | r = t-fn*pio2_1; |
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| 144 | w = fn*pio2_1t; /* 1st round good to 40 bit */ |
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| 145 | if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) { |
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| 146 | y[0] = r-w; /* quick check no cancellation */ |
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| 147 | } else { |
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| 148 | __uint32_t high; |
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| 149 | j = ix>>23; |
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| 150 | y[0] = r-w; |
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| 151 | GET_FLOAT_WORD(high,y[0]); |
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| 152 | i = j-((high>>23)&0xff); |
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| 153 | if(i>8) { /* 2nd iteration needed, good to 57 */ |
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| 154 | t = r; |
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| 155 | w = fn*pio2_2; |
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| 156 | r = t-w; |
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| 157 | w = fn*pio2_2t-((t-r)-w); |
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| 158 | y[0] = r-w; |
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| 159 | GET_FLOAT_WORD(high,y[0]); |
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| 160 | i = j-((high>>23)&0xff); |
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| 161 | if(i>25) { /* 3rd iteration need, 74 bits acc */ |
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| 162 | t = r; /* will cover all possible cases */ |
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| 163 | w = fn*pio2_3; |
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| 164 | r = t-w; |
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| 165 | w = fn*pio2_3t-((t-r)-w); |
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| 166 | y[0] = r-w; |
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| 167 | } |
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| 168 | } |
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| 169 | } |
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| 170 | y[1] = (r-y[0])-w; |
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| 171 | if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
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| 172 | else return n; |
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| 173 | } |
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| 174 | /* |
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| 175 | * all other (large) arguments |
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| 176 | */ |
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| 177 | if(!FLT_UWORD_IS_FINITE(ix)) { |
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| 178 | y[0]=y[1]=x-x; return 0; |
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| 179 | } |
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| 180 | /* set z = scalbn(|x|,ilogb(x)-7) */ |
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| 181 | e0 = (int)((ix>>23)-134); /* e0 = ilogb(z)-7; */ |
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| 182 | SET_FLOAT_WORD(z, ix - ((__int32_t)e0<<23)); |
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| 183 | for(i=0;i<2;i++) { |
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| 184 | tx[i] = (float)((__int32_t)(z)); |
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| 185 | z = (z-tx[i])*two8; |
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| 186 | } |
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| 187 | tx[2] = z; |
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| 188 | nx = 3; |
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| 189 | while(tx[nx-1]==zero) nx--; /* skip zero term */ |
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| 190 | n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi); |
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| 191 | if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
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| 192 | return n; |
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| 193 | } |
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