1 /*---------------------------------------------------------------------------+ 2 | poly_2xm1.c | 3 | | 4 | Function to compute 2^x-1 by a polynomial approximation. | 5 | | 6 | Copyright (C) 1992,1993,1994,1997 | 7 | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia | 8 | E-mail billm@suburbia.net | 9 | | 10 | | 11 +---------------------------------------------------------------------------*/ 12 13 #include "exception.h" 14 #include "reg_constant.h" 15 #include "fpu_emu.h" 16 #include "fpu_system.h" 17 #include "control_w.h" 18 #include "poly.h" 19 20 21 #define HIPOWER 11 22 static const unsigned long long lterms[HIPOWER] = 23 { 24 0x0000000000000000LL, /* This term done separately as 12 bytes */ 25 0xf5fdeffc162c7543LL, 26 0x1c6b08d704a0bfa6LL, 27 0x0276556df749cc21LL, 28 0x002bb0ffcf14f6b8LL, 29 0x0002861225ef751cLL, 30 0x00001ffcbfcd5422LL, 31 0x00000162c005d5f1LL, 32 0x0000000da96ccb1bLL, 33 0x0000000078d1b897LL, 34 0x000000000422b029LL 35 }; 36 37 static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194); 38 39 /* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0, 40 These numbers are 2^(1/4), 2^(1/2), and 2^(3/4) 41 */ 42 static const Xsig shiftterm0 = MK_XSIG(0, 0, 0); 43 static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318); 44 static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3); 45 static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9); 46 47 static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1, 48 &shiftterm2, &shiftterm3 }; 49 50 51 /*--- poly_2xm1() -----------------------------------------------------------+ 52 | Requires st(0) which is TAG_Valid and < 1. | 53 +---------------------------------------------------------------------------*/ 54 int poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result) 55 { 56 long int exponent, shift; 57 unsigned long long Xll; 58 Xsig accumulator, Denom, argSignif; 59 u_char tag; 60 61 exponent = exponent16(arg); 62 63 #ifdef PARANOID 64 if ( exponent >= 0 ) /* Don't want a |number| >= 1.0 */ 65 { 66 /* Number negative, too large, or not Valid. */ 67 EXCEPTION(EX_INTERNAL|0x127); 68 return 1; 69 } 70 #endif /* PARANOID */ 71 72 argSignif.lsw = 0; 73 XSIG_LL(argSignif) = Xll = significand(arg); 74 75 if ( exponent == -1 ) 76 { 77 shift = (argSignif.msw & 0x40000000) ? 3 : 2; 78 /* subtract 0.5 or 0.75 */ 79 exponent -= 2; 80 XSIG_LL(argSignif) <<= 2; 81 Xll <<= 2; 82 } 83 else if ( exponent == -2 ) 84 { 85 shift = 1; 86 /* subtract 0.25 */ 87 exponent--; 88 XSIG_LL(argSignif) <<= 1; 89 Xll <<= 1; 90 } 91 else 92 shift = 0; 93 94 if ( exponent < -2 ) 95 { 96 /* Shift the argument right by the required places. */ 97 if ( FPU_shrx(&Xll, -2-exponent) >= 0x80000000U ) 98 Xll++; /* round up */ 99 } 100 101 accumulator.lsw = accumulator.midw = accumulator.msw = 0; 102 polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER-1); 103 mul_Xsig_Xsig(&accumulator, &argSignif); 104 shr_Xsig(&accumulator, 3); 105 106 mul_Xsig_Xsig(&argSignif, &hiterm); /* The leading term */ 107 add_two_Xsig(&accumulator, &argSignif, &exponent); 108 109 if ( shift ) 110 { 111 /* The argument is large, use the identity: 112 f(x+a) = f(a) * (f(x) + 1) - 1; 113 */ 114 shr_Xsig(&accumulator, - exponent); 115 accumulator.msw |= 0x80000000; /* add 1.0 */ 116 mul_Xsig_Xsig(&accumulator, shiftterm[shift]); 117 accumulator.msw &= 0x3fffffff; /* subtract 1.0 */ 118 exponent = 1; 119 } 120 121 if ( sign != SIGN_POS ) 122 { 123 /* The argument is negative, use the identity: 124 f(-x) = -f(x) / (1 + f(x)) 125 */ 126 Denom.lsw = accumulator.lsw; 127 XSIG_LL(Denom) = XSIG_LL(accumulator); 128 if ( exponent < 0 ) 129 shr_Xsig(&Denom, - exponent); 130 else if ( exponent > 0 ) 131 { 132 /* exponent must be 1 here */ 133 XSIG_LL(Denom) <<= 1; 134 if ( Denom.lsw & 0x80000000 ) 135 XSIG_LL(Denom) |= 1; 136 (Denom.lsw) <<= 1; 137 } 138 Denom.msw |= 0x80000000; /* add 1.0 */ 139 div_Xsig(&accumulator, &Denom, &accumulator); 140 } 141 142 /* Convert to 64 bit signed-compatible */ 143 exponent += round_Xsig(&accumulator); 144 145 result = &st(0); 146 significand(result) = XSIG_LL(accumulator); 147 setexponent16(result, exponent); 148 149 tag = FPU_round(result, 1, 0, FULL_PRECISION, sign); 150 151 setsign(result, sign); 152 FPU_settag0(tag); 153 154 return 0; 155 156 } 157