static DEC_TYPE IEEE_FUNCTION_NAME (DEC_TYPE x) { decContext context; decNumber dn_result; DEC_TYPE result, one, temp; decNumber dn_x, dn_temp, dn_one; /* int comp;*/ one=DFP_CONSTANT(1.0); FUNC_CONVERT_TO_DN (&one, &dn_one); FUNC_CONVERT_TO_DN (&x, &dn_x); /* Handle NaN and early exit for x==0 */ if (decNumberIsNaN (&dn_x) || decNumberIsZero (&dn_x)) return x + x; decContextDefault (&context, DEFAULT_CONTEXT); decNumberAbs (&dn_temp, &dn_x, &context); FUNC_CONVERT_FROM_DN (&dn_temp, &temp, &context); if(temp==one) { /* |x| == 1 -> Pole Error */ DFP_EXCEPT (FE_DIVBYZERO); return decNumberIsNegative(&dn_x) ? -DFP_HUGE_VAL:DFP_HUGE_VAL; } else if (temp>one) { /* |x| > 1 -> Domain Error (this handles +-Inf too) */ DFP_EXCEPT (FE_INVALID); return DFP_NAN; } // comp = decCompare (&dn_temp, &dn_one); // switch (comp) // { // case 0: /* |x| == 1 -> Pole Error */ // DFP_EXCEPT (FE_DIVBYZERO); // return decNumberIsNegative(&dn_x) ? -DFP_HUGE_VAL:DFP_HUGE_VAL; // case 1: /* |x| > 1 -> Domain Error (this handles +-Inf too) */ // DFP_EXCEPT (FE_INVALID); // return DFP_NAN; // } /* Using trig identity: atanh(x) = 1/2 * log((1+x)/(1-x)) */ decNumberAdd (&dn_result, &dn_one, &dn_x, &context); decNumberSubtract (&dn_temp, &dn_one, &dn_x, &context); decNumberDivide (&dn_result, &dn_result, &dn_temp, &context); decNumberLn (&dn_result, &dn_result, &context); decNumberAdd (&dn_temp, &dn_one, &dn_one, &context); /* 2 */ decNumberDivide (&dn_result, &dn_result, &dn_temp, &context); FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); return result; }
_RETURN_TYPE INTERNAL_FUNCTION_NAME (DEC_TYPE x) { DEC_TYPE result; decContext context; decNumber dn_result; decNumber dn_x; decNumber dn_absx; decNumber dn_logx; decNumber dn_one; decNumber dn_cmp; enum rounding round; FUNC_CONVERT_TO_DN (&x, &dn_x); if (decNumberIsZero (&dn_x)) { DFP_EXCEPT (FE_INVALID); DFP_ERRNO (EDOM); return _FBLOG0; } if (decNumberIsInfinite (&dn_x)) { DFP_EXCEPT (FE_INVALID); DFP_ERRNO (EDOM); return decNumberIsNegative (&dn_x) ? _MIN_VALUE : _MAX_VALUE; } if (decNumberIsNaN (&dn_x)) { DFP_EXCEPT (FE_INVALID); DFP_ERRNO (EDOM); return _FBLOGNAN; } decContextDefault (&context, DEFAULT_CONTEXT); decNumberAbs (&dn_absx, &dn_x, &context); /* For DFP, we use radix 10 instead of whatever FLT_RADIX happens to be */ decNumberLog10 (&dn_logx, &dn_absx, &context); /* Capture the case where truncation will return the wrong result, by rounding up if -1.0 < x < 1.0 */ round = DEC_ROUND_DOWN; decNumberFromInt32 (&dn_one, 1); decNumberCompare (&dn_cmp, &dn_x, &dn_one, &context); if (-decNumberIsNegative(&dn_cmp)) { decNumberFromInt32 (&dn_one, -1); decNumberCompare (&dn_cmp, &dn_x, &dn_one, &context); if (!decNumberIsNegative(&dn_cmp) && !decNumberIsZero(&dn_cmp)) round = DEC_ROUND_UP; } context.round = round; decNumberToIntegralValue (&dn_result, &dn_logx, &context); FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); /* Use _Decimal* to int casting. */ return (_RETURN_TYPE) result; }
DEC_TYPE PREFIXED_FUNCTION_NAME (DEC_TYPE x, DEC_TYPE y) { DEC_TYPE result; decNumber dn_x, dn_y, dn_result; decContext context; decContextDefault(&context, DEFAULT_CONTEXT); FUNC_CONVERT_TO_DN(&x, &dn_x); FUNC_CONVERT_TO_DN(&y, &dn_y); decNumberSubtract(&dn_result, &dn_x, &dn_y, &context); if (context.status != 0) { int ieee_flags = 0; if (context.status & DEC_IEEE_854_Division_by_zero) ieee_flags |= FE_DIVBYZERO; if (context.status & DEC_IEEE_854_Inexact) ieee_flags |= FE_INEXACT; if (context.status & DEC_IEEE_854_Invalid_operation) ieee_flags |= FE_INVALID; if (context.status & DEC_IEEE_854_Overflow) ieee_flags |= FE_OVERFLOW; if (context.status & DEC_IEEE_854_Underflow) ieee_flags |= FE_UNDERFLOW; if (ieee_flags != 0) feraiseexcept (ieee_flags); } FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); return result; }
static DEC_TYPE IEEE_FUNCTION_NAME (DEC_TYPE x) { decContext context; decNumber dn_result; DEC_TYPE result; decNumber dn_x; FUNC_CONVERT_TO_DN(&x, &dn_x); if (decNumberIsNaN (&dn_x)) return x+x; if (decNumberIsZero (&dn_x)) /* If x == 0: Pole Error */ { DFP_EXCEPT (FE_DIVBYZERO); return -DFP_HUGE_VAL; } if (decNumberIsNegative (&dn_x)) /* If x < 0,: Domain Error */ { DFP_EXCEPT (FE_INVALID); return DFP_NAN; } if (decNumberIsInfinite (&dn_x)) return x; decContextDefault (&context, DEFAULT_CONTEXT); decNumberLn(&dn_result, &dn_x, &context); FUNC_CONVERT_FROM_DN(&dn_result, &result, &context); return result; }
_Decimal128 __quantumd128 (_Decimal128 x) { decNumber dn_x; decNumber dn_result; decContext context; _Decimal128 result; FUNC_CONVERT_TO_DN (&x, &dn_x); if (decNumberIsNaN (&dn_x) || decNumberIsZero (&dn_x)) return x; if (decNumberIsInfinite (&dn_x)) return DEC_INFINITY; /* The quantum of a finite number is defined as 1 x 10^exponent, so first get input absolute value and then sets its coefficient to 1. */ decContextDefault (&context, DEFAULT_CONTEXT); decNumberAbs (&dn_result, &dn_x, &context); dn_result.digits = 1; dn_result.lsu[0] = 1; FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); return result; }
static DEC_TYPE IEEE_FUNCTION_NAME (DEC_TYPE x) { decContext context; decNumber dn_result; DEC_TYPE result; decNumber dn_x; decNumber dn_one; decNumber dn_exponent; DEC_TYPE one = DFP_CONSTANT(1.0); FUNC_CONVERT_TO_DN(&x, &dn_x); FUNC_CONVERT_TO_DN(&one, &dn_one); if (decNumberIsNaN (&dn_x)) return x+x; if (decNumberIsInfinite (&dn_x)) return decNumberIsNegative (&dn_x) ? DFP_CONSTANT(-1.0) : x; decContextDefault(&context, DEFAULT_CONTEXT); decNumberExp(&dn_exponent, &dn_x, &context); decNumberSubtract(&dn_result, &dn_exponent, &dn_one, &context); FUNC_CONVERT_FROM_DN(&dn_result, &result, &context); if (context.status & DEC_Overflow) DFP_EXCEPT (FE_OVERFLOW); return result; }
static DEC_TYPE IEEE_FUNCTION_NAME (DEC_TYPE x) { decContext context; decNumber dn_result; DEC_TYPE result; decNumber dn_x; decNumber dn_two; DEC_TYPE two = DFP_CONSTANT(2.0); FUNC_CONVERT_TO_DN (&two, &dn_two); FUNC_CONVERT_TO_DN (&x, &dn_x); if (decNumberIsNaN (&dn_x)) return x+x; if (decNumberIsInfinite (&dn_x) ) return decNumberIsNegative (&dn_x) ? DFP_CONSTANT(0.0) : x; decContextDefault (&context, DEFAULT_CONTEXT); /* decNumberPow (&dn_result, &dn_two, &dn_x, &context); */ decNumberPower (&dn_result, &dn_two, &dn_x, &context); FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); if(context.status & DEC_Overflow) DFP_EXCEPT (FE_OVERFLOW); return result; }
static __ROUND_RETURN_TYPE IEEE_FUNCTION_NAME (DEC_TYPE x) { DEC_TYPE result; decContext context; decNumber dn_result; decNumber dn_x; FUNC_CONVERT_TO_DN (&x, &dn_x); if (decNumberIsNaN (&dn_x) || decNumberIsInfinite (&dn_x) || x > __MAX_VALUE || x < __MIN_VALUE) { DFP_EXCEPT (FE_INVALID); return (__ROUND_RETURN_TYPE) x; } decContextDefault (&context, DEFAULT_CONTEXT); context.round = __ROUND_MODE; decNumberToIntegralValue (&dn_result,&dn_x,&context); FUNC_CONVERT_FROM_DN(&dn_result, &result, &context); /* Use _Decimal* to __ROUND_RETURN_TYPE casting. */ return (__ROUND_RETURN_TYPE)result; /* return (__ROUND_RETURN_TYPE)decNumberToInteger (&dn_result); */ }
DEC_TYPE INTERNAL_FUNCTION_NAME (DEC_TYPE x) { decContext context; decNumber dn_result; DEC_TYPE result; decNumber dn_x; FUNC_CONVERT_TO_DN (&x, &dn_x); decContextDefault (&context, DEFAULT_CONTEXT); if (decNumberIsInfinite (&dn_x)) { if (decNumberIsNegative (&dn_x)) result = -M_PI_2dl; else result = M_PI_2dl; } else { decNumberAtan (&dn_result, &dn_x, &context); FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); } return result; }
DEC_TYPE INTERNAL_FUNCTION_NAME (DEC_TYPE x) { decContext context; decNumber dn_result; DEC_TYPE result, one; decNumber dn_x, dn_one; one = DFP_CONSTANT(1.0); FUNC_CONVERT_TO_DN (&one, &dn_one); FUNC_CONVERT_TO_DN (&x, &dn_x); if (decNumberIsNaN (&dn_x) || decNumberIsZero (&dn_x) || decNumberIsInfinite (&dn_x)) { return x + x; } decContextDefault (&context, DEFAULT_CONTEXT); /* using trig identity: acosh(x) = log(x+sqrt(x*x-1)) */ decNumberMultiply (&dn_result, &dn_x, &dn_x, &context); decNumberAdd (&dn_result, &dn_result, &dn_one, &context); decNumberSquareRoot (&dn_result, &dn_result, &context); decNumberAdd (&dn_result, &dn_result, &dn_x, &context); decNumberLn (&dn_result, &dn_result, &context); FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); return result; }
DEC_TYPE INTERNAL_FUNCTION_NAME (DEC_TYPE x) { decContext context; decNumber dn_result; DEC_TYPE result; decNumber dn_x; decNumber dn_tmp; decNumber dn_log10; decNumber dn_one; decNumber dn_cmp; enum rounding round; FUNC_CONVERT_TO_DN (&x, &dn_x); if (decNumberIsNaN (&dn_x)) return x+x; if (decNumberIsInfinite (&dn_x)) /* +-Inf: Inf */ return DEC_INFINITY; if (decNumberIsZero (&dn_x)) /* Pole Error if x==0 */ { DFP_ERRNO (ERANGE); DFP_EXCEPT (FE_DIVBYZERO); return -DFP_HUGE_VAL; } if (decNumberIsInfinite (&dn_x) && decNumberIsNegative (&dn_x)) return -x; decContextDefault (&context, DEFAULT_CONTEXT); decNumberAbs (&dn_tmp, &dn_x, &context); /* For DFP, we use radix 10 instead of whatever FLT_RADIX happens to be */ decNumberLog10 (&dn_log10, &dn_tmp, &context); /* Capture the case where truncation will return the wrong result, by rounding up if -1.0 < x < 1.0 */ round = DEC_ROUND_DOWN; decNumberFromInt32 (&dn_one, 1); decNumberCompare (&dn_cmp, &dn_x, &dn_one, &context); if (-decNumberIsNegative(&dn_cmp)) { decNumberFromInt32 (&dn_one, -1); decNumberCompare (&dn_cmp, &dn_x, &dn_one, &context); if (!decNumberIsNegative(&dn_cmp) && !decNumberIsZero(&dn_cmp)) round = DEC_ROUND_UP; } context.round = round; decNumberToIntegralValue (&dn_result, &dn_log10, &context); FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); return result; }
static DEC_TYPE IEEE_FUNCTION_NAME (DEC_TYPE x, int y) { DEC_TYPE result; long newexp; #if NUMDIGITS_SUPPORT==1 newexp = FUNC_D (getexp) (x) + y + 1; if (newexp > PASTE(DECIMAL,PASTE(_DECIMAL_SIZE,_Emax))) { result = DFP_HUGE_VAL; DFP_EXCEPT (FE_OVERFLOW); } else if (newexp < PASTE(DECIMAL,PASTE(_DECIMAL_SIZE,_Emin))) { result = -DFP_HUGE_VAL; DFP_EXCEPT (FE_OVERFLOW); } else result = FUNC_D(setexp) (x, newexp); #else decContext context; decNumber dn_x; FUNC_CONVERT_TO_DN (&x, &dn_x); if (___decNumberIsNaN (&dn_x) || ___decNumberIsZero (&dn_x) || ___decNumberIsInfinite (&dn_x)) return x+x; if (y == 0) return x; /* ldexp(x,y) is just x*10**y, which is equivalent to increasing the exponent * by y + 1. */ newexp = dn_x.exponent + y + 1; if(newexp > INT_MAX) newexp = INT_MAX; if(newexp < -INT_MAX) newexp = -INT_MAX; dn_x.exponent = newexp; decContextDefault (&context, DEFAULT_CONTEXT); FUNC_CONVERT_FROM_DN (&dn_x, &result, &context); if (context.status & DEC_Overflow) DFP_EXCEPT (FE_OVERFLOW); #endif return result; }
static DEC_TYPE IEEE_FUNCTION_NAME (DEC_TYPE x, DEC_TYPE y) { decContext context; decNumber dn_result; DEC_TYPE result; decNumber dn_x; decNumber dn_y; decNumber dn_diff; DEC_TYPE temp_diff; DEC_TYPE temp_result; FUNC_CONVERT_TO_DN (&x, &dn_x); FUNC_CONVERT_TO_DN (&y, &dn_y); if(decNumberIsNaN (&dn_x) || decNumberIsNaN (&dn_y)) return x; decContextDefault (&context, DEFAULT_CONTEXT); decNumberSubtract (&dn_diff, &dn_x, &dn_y, &context); decNumberSubtract (&dn_result, &dn_x, &dn_x, &context); FUNC_CONVERT_FROM_DN (&dn_diff, &temp_diff, &context); FUNC_CONVERT_FROM_DN (&dn_result, &temp_result, &context); if(temp_diff>temp_result) decNumberAdd (&dn_result,&dn_result,&dn_diff,&context); /* if(decCompare (&dn_diff,&dn_result) == 1) decNumberAdd (&dn_result,&dn_result,&dn_diff,&context); */ FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); if (context.status & DEC_Overflow) DFP_EXCEPT (FE_OVERFLOW); return result; }
DEC_TYPE INTERNAL_FUNCTION_NAME (DEC_TYPE x) { decContext context; decNumber dn_result; DEC_TYPE result; decNumber dn_x; FUNC_CONVERT_TO_DN(&x, &dn_x); decContextDefault(&context, DEFAULT_CONTEXT); context.round = DEC_ROUND_DOWN; decNumberToIntegralValue(&dn_result, &dn_x, &context); FUNC_CONVERT_FROM_DN(&dn_result, &result, &context); return result; }
DEC_TYPE INTERNAL_FUNCTION_NAME (DEC_TYPE x, DEC_TYPE y) { decContext context; decNumber dn_result; DEC_TYPE result; decNumber dn_x; decNumber dn_y; FUNC_CONVERT_TO_DN(&x, &dn_x); FUNC_CONVERT_TO_DN(&y, &dn_y); decContextDefault(&context, DEFAULT_CONTEXT); decNumberMax(&dn_result, &dn_x, &dn_y, &context); FUNC_CONVERT_FROM_DN(&dn_result, &result, &context); return result; }
DEC_TYPE FUNC_NAME (_Decimal128 hi, _Decimal128 mid, _Decimal128 low) { DEC_TYPE result; /* hi = m_hi * 10^34 * mid = m_mid * 10^17 * low = m_low * 10^0 * * Note, m_hi is only at most 5 digits for int128. */ decNumber dn_hi, dn_mid, dn_low, dn_result; decNumber dn_hi_s, dn_mid_s, dn_result_s; decNumber dn_17, dn_34; decContext context; decContextDefault (&context, DEC_INIT_DECIMAL128); /* Hack, we're using 39 digits here. */ context.digits = 39; decNumberFromInt32(&dn_17, 17); decNumberFromInt32(&dn_34, 34); __DECIMAL_TO_DECNUMBER (&hi, &dn_hi, 128); __DECIMAL_TO_DECNUMBER (&mid, &dn_mid, 128); __DECIMAL_TO_DECNUMBER (&low, &dn_low, 128); /* Rotate addends into proper position. */ decNumberShift(&dn_hi_s,&dn_hi,&dn_34,&context); decNumberShift(&dn_mid_s,&dn_mid,&dn_17,&context); /* Sum the three components. */ decNumberAdd(&dn_result_s, &dn_hi_s, &dn_mid_s, &context); decNumberAdd(&dn_result, &dn_result_s, &dn_low, &context); /* Convert to the destination format. */ FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); /* Don't care about exceptions here... I don't think. */ return result; }
static DEC_TYPE IEEE_FUNCTION_NAME (DEC_TYPE x) { decContext context; decNumber dn_result; DEC_TYPE result; decNumber dn_x; decNumber dn_sum; decNumber dn_one; DEC_TYPE one = DFP_CONSTANT(1.0); FUNC_CONVERT_TO_DN (&x, &dn_x); FUNC_CONVERT_TO_DN (&one, &dn_one); /* For NaN, 0, or +Inf, just return x */ if (decNumberIsNaN (&dn_x) || decNumberIsZero (&dn_x) || (decNumberIsInfinite (&dn_x) && !decNumberIsNegative (&dn_x))) return x+x; decContextDefault(&context, DEFAULT_CONTEXT); decNumberAdd(&dn_sum, &dn_x, &dn_one, &context); if (decNumberIsZero(&dn_sum)) /* Pole Error if x was -1 */ { DFP_EXCEPT (FE_DIVBYZERO); return -DFP_HUGE_VAL; } if (decNumberIsNegative(&dn_sum)) /* Domain Error if x < -1 */ { DFP_EXCEPT (FE_INVALID); return DFP_NAN; } decNumberLn(&dn_result, &dn_sum, &context); FUNC_CONVERT_FROM_DN(&dn_result, &result, &context); return result; }
DEC_TYPE INTERNAL_FUNCTION_NAME (DEC_TYPE x) { decContext context; decNumber dn_result; DEC_TYPE result; decNumber dn_x; FUNC_CONVERT_TO_DN (&x, &dn_x); if (decNumberIsNaN (&dn_x) || decNumberIsInfinite (&dn_x) || decNumberIsZero (&dn_x)) return x+x; decContextDefault (&context, DEFAULT_CONTEXT); context.round = __ROUND_MODE; decNumberToIntegralValue (&dn_result, &dn_x, &context); FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); if (context.status & DEC_Overflow) DFP_EXCEPT (FE_OVERFLOW); return result; }
static DEC_TYPE IEEE_FUNCTION_NAME (DEC_TYPE x, DEC_TYPE y) { decContext context; decNumber dn_result; DEC_TYPE result; DEC_TYPE absx; decNumber dn_x; decNumber dn_absx; decNumber dn_y; decNumber dn_one; decNumber dn_two; decNumber dn_temp; decNumber dn_temp2; decNumber dn_temp3; int y_is_int; int y_is_oddint=0; int abs_x_vs_1; DEC_TYPE one = DFP_CONSTANT(1.0); DEC_TYPE two = DFP_CONSTANT(2.0); FUNC_CONVERT_TO_DN (&x, &dn_x); FUNC_CONVERT_TO_DN (&y, &dn_y); FUNC_CONVERT_TO_DN (&one, &dn_one); decContextDefault (&context, DEFAULT_CONTEXT); if (decNumberIsZero (&dn_y)) return one; if (decNumberIsNaN (&dn_x)) return x+x; decNumberAbs (&dn_absx, &dn_x, &context); FUNC_CONVERT_FROM_DN (&dn_absx, &absx, &context); if(absx<one) abs_x_vs_1 = -1; else if (absx==one) abs_x_vs_1 = 0; else abs_x_vs_1 = 1; /* abs_x_vs_1 = decCompare(&dn_absx, &dn_one); */ if(abs_x_vs_1 == 0 && !decNumberIsNegative (&dn_x)) /* If x == +1 */ return one; if (decNumberIsNaN (&dn_y)) return y+y; /* Detect if y is odd/an integer */ decNumberToIntegralValue (&dn_temp, &dn_y, &context); decNumberSubtract (&dn_temp2, &dn_temp, &dn_y, &context); y_is_int = decNumberIsZero (&dn_temp2); if (y_is_int) { FUNC_CONVERT_TO_DN (&two, &dn_two); decNumberDivide (&dn_temp, &dn_y, &dn_two, &context); decNumberToIntegralValue (&dn_temp2, &dn_temp, &context); decNumberSubtract (&dn_temp3, &dn_temp2, &dn_temp, &context); y_is_oddint = !decNumberIsZero (&dn_temp3); } /* Handle all special cases for which x = +-0 */ if (decNumberIsZero (&dn_x)) { if(decNumberIsNegative (&dn_y)) { if (decNumberIsInfinite (&dn_y)) /* +-0^-Inf = +Inf */ return -y; /* Pole Error for x = +-0, y < 0 */ DFP_EXCEPT (FE_DIVBYZERO); return decNumberIsNegative(&dn_x) && y_is_oddint ? -DFP_HUGE_VAL : DFP_HUGE_VAL; } return decNumberIsNegative(&dn_x) && y_is_oddint ? -DFP_CONSTANT(0.0) : DFP_CONSTANT(0.0); } /* Handle remaining special cases for x = +-Inf or y = +-Inf */ if (decNumberIsInfinite (&dn_x) || decNumberIsInfinite (&dn_y)) { if (abs_x_vs_1 == 0) /* If (-1)^(+-Inf) */ return one; if (abs_x_vs_1 < 0) /* x^(+-Inf), where 0<x<1 */ return decNumberIsNegative (&dn_y) ? DFP_HUGE_VAL : DFP_CONSTANT(0.0); if (decNumberIsNegative (&dn_y)) result = DFP_CONSTANT(0.0); else result = (DEC_TYPE)DEC_INFINITY; if (y_is_oddint && decNumberIsNegative(&dn_x)) result = -result; return result; } /* Domain Error: x < 0 && y is a finite non-int */ if (decNumberIsNegative (&dn_x) && !y_is_int) { DFP_EXCEPT (FE_INVALID); return DFP_NAN; } decNumberPower (&dn_result, &dn_x, &dn_y, &context); FUNC_CONVERT_FROM_DN (&dn_result, &result, &context); if (context.status & DEC_Overflow) DFP_EXCEPT (FE_OVERFLOW); if (context.status & DEC_Underflow) DFP_EXCEPT (FE_UNDERFLOW); return result; }