| |
| /* @(#)z_logarithm.c 1.0 98/08/13 */ |
| /****************************************************************** |
| * The following routines are coded directly from the algorithms |
| * and coefficients given in "Software Manual for the Elementary |
| * Functions" by William J. Cody, Jr. and William Waite, Prentice |
| * Hall, 1980. |
| ******************************************************************/ |
| |
| /* |
| FUNCTION |
| <<log>>, <<logf>>, <<log10>>, <<log10f>>, <<logarithm>>, <<logarithmf>>---natural or base 10 logarithms |
| |
| INDEX |
| log |
| INDEX |
| logf |
| INDEX |
| log10 |
| INDEX |
| log10f |
| |
| ANSI_SYNOPSIS |
| #include <math.h> |
| double log(double <[x]>); |
| float logf(float <[x]>); |
| double log10(double <[x]>); |
| float log10f(float <[x]>); |
| |
| TRAD_SYNOPSIS |
| #include <math.h> |
| double log(<[x]>); |
| double <[x]>; |
| |
| float logf(<[x]>); |
| float <[x]>; |
| |
| double log10(<[x]>); |
| double <[x]>; |
| |
| float log10f(<[x]>); |
| float <[x]>; |
| |
| DESCRIPTION |
| Return the natural or base 10 logarithm of <[x]>, that is, its logarithm base e |
| (where e is the base of the natural system of logarithms, 2.71828@dots{}) or |
| base 10. |
| <<log>> and <<logf>> are identical save for the return and argument types. |
| <<log10>> and <<log10f>> are identical save for the return and argument types. |
| |
| RETURNS |
| Normally, returns the calculated value. When <[x]> is zero, the |
| returned value is <<-HUGE_VAL>> and <<errno>> is set to <<ERANGE>>. |
| When <[x]> is negative, the returned value is <<-HUGE_VAL>> and |
| <<errno>> is set to <<EDOM>>. You can control the error behavior via |
| <<matherr>>. |
| |
| PORTABILITY |
| <<log>> is ANSI. <<logf>> is an extension. |
| |
| <<log10>> is ANSI. <<log10f>> is an extension. |
| */ |
| |
| |
| /****************************************************************** |
| * Logarithm |
| * |
| * Input: |
| * x - floating point value |
| * ten - indicates base ten numbers |
| * |
| * Output: |
| * logarithm of x |
| * |
| * Description: |
| * This routine calculates logarithms. |
| * |
| *****************************************************************/ |
| |
| #include "fdlibm.h" |
| #include "zmath.h" |
| |
| #ifndef _DOUBLE_IS_32BITS |
| |
| static const double a[] = { -0.64124943423745581147e+02, |
| 0.16383943563021534222e+02, |
| -0.78956112887481257267 }; |
| static const double b[] = { -0.76949932108494879777e+03, |
| 0.31203222091924532844e+03, |
| -0.35667977739034646171e+02 }; |
| static const double C1 = 22713.0 / 32768.0; |
| static const double C2 = 1.428606820309417232e-06; |
| static const double C3 = 0.43429448190325182765; |
| |
| double |
| _DEFUN (logarithm, (double, int), |
| double x _AND |
| int ten) |
| { |
| int N; |
| double f, w, z; |
| |
| /* Check for range and domain errors here. */ |
| if (x == 0.0) |
| { |
| errno = ERANGE; |
| return (-z_infinity.d); |
| } |
| else if (x < 0.0) |
| { |
| errno = EDOM; |
| return (z_notanum.d); |
| } |
| else if (!isfinite(x)) |
| { |
| if (isnan(x)) |
| return (z_notanum.d); |
| else |
| return (z_infinity.d); |
| } |
| |
| /* Get the exponent and mantissa where x = f * 2^N. */ |
| f = frexp (x, &N); |
| |
| z = f - 0.5; |
| |
| if (f > __SQRT_HALF) |
| z = (z - 0.5) / (f * 0.5 + 0.5); |
| else |
| { |
| N--; |
| z /= (z * 0.5 + 0.5); |
| } |
| w = z * z; |
| |
| /* Use Newton's method with 4 terms. */ |
| z += z * w * ((a[2] * w + a[1]) * w + a[0]) / (((w + b[2]) * w + b[1]) * w + b[0]); |
| |
| if (N != 0) |
| z = (N * C2 + z) + N * C1; |
| |
| if (ten) |
| z *= C3; |
| |
| return (z); |
| } |
| |
| #endif /* _DOUBLE_IS_32BITS */ |