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