From 6475f68ff6d1755375df03317a74f0eed8a3b25d Mon Sep 17 00:00:00 2001From: Jeff Johnston Date: Tue, 3 Feb 2004 00:42:19 +0000Subject: 2004-02-02 Jeff Johnston * COPYING.NEWLIB: Updated with 1.12 version. * README: Ditto. * docs_html: Updated to point to new libc/libm docs. * libc_html: Updated to 1.12. * libm_html: Ditto. * news_html: Ditto.--- libm_html | 762 ++++++++++++++++++++++++++++++++++++++++++++------------------ 1 file changed, 545 insertions(+), 217 deletions(-)(limited to 'libm_html')diff --git a/libm_html b/libm_htmlindex 79f09db..b3e0d8f 100644--- a/libm_html+++ b/libm_html@@ -1,6 +1,6 @@ -+ @@ -119,7 +128,7 @@ machines--are available when you include `fastmath.h' instead of 1.16 frexp, frexpf---split floating-point number  Split floating-point number 1.17 gamma, gammaf, lgamma, lgammaf, gamma_r,  Logarithmic gamma function 1.18 hypot, hypotf---distance from origin  Distance from origin-1.33 ilogb, ilogbf---get exponent of floating point number  Get exponent+1.33 ilogb, ilogbf---get exponent of floating-point number  Get exponent 1.34 infinity, infinityf---representation of infinity  Floating infinity 1.19 isnan,isnanf,isinf,isinff,finite,finitef---test for exceptional numbers  Check type of number 1.20 ldexp, ldexpf---load exponent  Load exponent@@ -128,11 +137,11 @@ machines--are available when you include `fastmath.h' instead of 1.35 log1p, log1pf---log of 1 + x  Log of 1 + X 1.36 matherr---modifiable math error handler  Modifiable math error handler 1.37 modf, modff---split fractional and integer parts  Split fractional and integer parts-1.38 nan, nanf---representation of infinity  Floating Not a Number+1.38 nan, nanf---representation of "Not a Number"  Floating Not a Number 1.39 nextafter, nextafterf---get next number  Get next representable number 1.23 pow, powf---x to the power y  X to the power Y 1.24 remainder, remainderf---round and remainder  remainder of X divided by Y-1.40 scalbn, scalbnf---scale by integer  scalbn+1.40 scalbn, scalbnf---scale by power of two  scalbn 1.26 sin, sinf, cos, cosf---sine or cosine  Sine or cosine (sin, cos) 1.27 sinh, sinhf---hyperbolic sine  Hyperbolic sine 1.25 sqrt, sqrtf---positive square root  Positive square root@@ -149,9 +158,9 @@ machines--are available when you include `fastmath.h' instead of [ > ]   [ << ] [ Up ]-[ >> ]-         [Top]-[Contents]+[ >> ]+         [Top]+[Contents] [Index] [ ? ] @@ -184,7 +193,7 @@ called, but warning message are not printed.

In SVID mode, functions which overflow return 3.40282346638528860e+38,-the maximum single precision floating point value, rather than infinity.+the maximum single-precision floating-point value, rather than infinity. Also, errno is set correctly, matherr is called, and, if matherr returns 0, warning messages are printed for some errors. For example, by default `log(-1.0)' writes this message on standard@@ -203,11 +212,11 @@ The library is set to X/Open mode by default. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -231,6 +240,7 @@ its calculations on floats.
Returns
+acos and acosf return values in radians, in the range of 0 to pi.

If x is not between -1 and 1, the returned value is NaN@@ -250,11 +260,11 @@ You can modify error handling for these functions using matherr. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -268,7 +278,8 @@ float acoshf(float x); Description
acosh calculates the inverse hyperbolic cosine of x. acosh is defined as-

+
 
 log(x + sqrt(x*x-1))+

x must be a number greater than or equal to 1.

@@ -301,11 +312,11 @@ for portable programs. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -332,6 +343,7 @@ You can modify error handling for these routines using matherr.
Returns
+asin returns values in radians, in the range of -pi/2 to pi/2.

If x is not in the range -1 to 1, asin and asinf@@ -351,11 +363,11 @@ You can change this error treatment using matherr. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -369,7 +381,8 @@ float asinhf(float x); Description
asinh calculates the inverse hyperbolic sine of x. asinh is defined as-

+
 
 sgn(x) * log(abs(x) + sqrt(1+x*x))+

asinhf is identical, other than taking and returning floats.

@@ -393,11 +406,11 @@ Neither asinh nor asinhf are ANSI C. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -419,6 +432,7 @@ float atanf(float x);
Returns
+atan returns a value in radians, in the range of -pi/2 to pi/2.


@@ -435,11 +449,11 @@ float atanf(float x); -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -455,6 +469,7 @@ float atan2f(float y,float x); atan2 computes the inverse tangent (arc tangent) of y/x. atan2 produces the correct result even for angles near+pi/2 or -pi/2 (that is, when x is near 0).

@@ -465,6 +480,7 @@ float atan2f(float y,float x);
Returns
atan2 and atan2f return a value in radians, in the range of+-pi to pi.

If both x and y are 0.0, atan2 causes a DOMAIN error.@@ -487,11 +503,11 @@ You can modify error handling for these functions using matherr. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -516,12 +532,14 @@ float atanhf(float x);

If-is greater than 1, the global errno is set to EDOM and+
 
x|+
is greater than 1, the global errno is set to EDOM and the result is a NaN. A DOMAIN error is reported.

If-is 1, the global errno is set to EDOM; and the result is+
 
x|+
is 1, the global errno is set to EDOM; and the result is infinity with the same sign as x. A SING error is reported.

@@ -545,9 +563,9 @@ Neither atanh nor atanhf are ANSI C. [ > ]   [ << ] [ Up ]-[ >> ]-         [Top]-[Contents]+[ >> ]+         [Top]+[Contents] [Index] [ ? ] @@ -571,7 +589,9 @@ float ynf(int n, float x); Description
The Bessel functions are a family of functions that solve the differential equation-These functions have many applications in engineering and physics.+
 
 2 2 2+ x y'' + xy' + (x - p )y = 0+
These functions have many applications in engineering and physics.

jn calculates the Bessel function of the first kind of order@@ -607,11 +627,11 @@ None of the Bessel functions are in ANSI C. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -627,7 +647,8 @@ float coshf(float x) cosh computes the hyperbolic cosine of the argument x. cosh(x) is defined as-

+
 
 (exp(x) + exp(-x))/2+

Angles are specified in radians. coshf is identical, save that it takes and returns float.@@ -659,11 +680,11 @@ function matherr. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -712,11 +733,11 @@ None of the variants of erf are ANSI C. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -729,6 +750,7 @@ float expf(float x); Description
exp and expf calculate the exponential of x, that is,+e raised to the power x (where e is the base of the natural system of logarithms, approximately 2.71828).

@@ -758,11 +780,11 @@ either case, errno is set to ERANGE. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -799,11 +821,11 @@ The calculated value is returned. No errors are detected. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -844,11 +866,11 @@ the nearest integer greater than or equal to x. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -867,6 +889,7 @@ remainder of x/y (x modulo y).
Returns
The fmod function returns the value+x-i*y, for the largest integer i such that, if y is nonzero, the result has the same sign as x and magnitude less than the magnitude of y.@@ -892,11 +915,11 @@ You can modify error treatment for these functions using matherr. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -908,7 +931,7 @@ double frexp(double val, int *exp); float frexpf(float val, int *exp); Description
-All non zero, normal numbers can be described as m * 2**p.+All nonzero, normal numbers can be described as m * 2**p. frexp represents the double val as a mantissa m and a power of two p. The resulting mantissa will always be greater than or equal to 0.5, and less than 1.0 (as@@ -916,6 +939,10 @@ long as val is nonzero). The power of two will be stored in *exp.

+m and p are calculated so that+val is m times 2 to the power p.+

+ frexpf is identical, other than taking and returning floats rather than doubles.

@@ -941,11 +968,11 @@ or Nan, frexp will set *exp to 0 [ < ] [ > ]-   [ << ]+   [ << ] [ Up ]-[ >> ]-         [Top]-[Contents]+[ >> ]+         [Top]+[Contents] [Index] [ ? ] @@ -967,8 +994,11 @@ float lgammaf_r(float x, int *signgamp); the natural logarithm of the gamma function of x. The gamma function (exp(gamma(x))) is a generalization of factorial, and retains the property that+exp(gamma(N)) is equivalent to N*exp(gamma(N-1)). Accordingly, the results of the gamma function itself grow very quickly. gamma is defined as+the natural log of the gamma function, rather than the gamma function+itself, to extend the useful range of results representable.

@@ -1021,11 +1051,11 @@ Neither gamma nor gammaf is ANSI C. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1038,6 +1068,7 @@ float hypotf(float x, float y); Description
hypot calculates the Euclidean distance+sqrt(x*x + y*y) between the origin (0,0) and a point represented by the Cartesian coordinates (x,y). hypotf differs only in the type of its arguments and result.@@ -1065,11 +1096,11 @@ You can change the error treatment with matherr. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1085,7 +1116,7 @@ int isinff(float arg); int finitef(float arg); Description
-These functions provide information on the floating point+These functions provide information on the floating-point argument supplied.

@@ -1095,13 +1126,13 @@ There are five major number formats -

zero
a number which contains all zero bits.
subnormal-
Is used to represent number with a zero exponent, but a non zero fraction.+
Is used to represent number with a zero exponent, but a nonzero fraction.
normal
A number with an exponent, and a fraction
infinity
A number with an all 1's exponent and a zero fraction.
NAN-
A number with an all 1's exponent and a non zero fraction.+
A number with an all 1's exponent and a nonzero fraction.

@@ -1112,7 +1143,7 @@ returns 1 if the argument is infinity. finite returns 1 if the argument is zero, subnormal or normal. The isnanf, isinff and finitef perform the same operations as their isnan, isinf and finite-counterparts, but on single precision floating point numbers.+counterparts, but on single-precision floating-point numbers.


@@ -1124,11 +1155,11 @@ counterparts, but on single precision floating point numbers. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1141,6 +1172,7 @@ float ldexpf(float val, int exp); Description
ldexp calculates the value+val times 2 to the power exp. ldexpf is identical, save that it takes and returns float rather than double values.

@@ -1169,11 +1201,11 @@ On overflow, ldexp returns plus or minus HUGE_VAL. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1217,11 +1249,11 @@ When x is negative, the returned value is -HUGE_VAL and -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1262,11 +1294,11 @@ See the description of log for information on errors. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1278,7 +1310,7 @@ double pow(double x, double y); float pow(float x, float y); Description
-pow and powf calculate x raised to the exp1.0nt y.+pow and powf calculate x raised to the exponent y.


@@ -1309,11 +1341,11 @@ You can modify error handling for these functions using matherr. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1349,11 +1381,11 @@ float remainderf(float x, float y); -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1391,11 +1423,11 @@ negative, the global value errno is set to EDOM (domai -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1437,11 +1469,11 @@ The sine or cosine of x is returned. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1455,7 +1487,8 @@ float sinhf(float x); Description
sinh computes the hyperbolic sine of the argument x. Angles are specified in radians. sinh(x) is defined as-

+
 
 (exp(x) - exp(-x))/2+

sinhf is identical, save that it takes and returns float values.

@@ -1489,11 +1522,11 @@ You can modify error handling for these functions with matherr. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1531,11 +1564,11 @@ The tangent of x is returned. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1575,11 +1608,11 @@ The hyperbolic tangent of x is returned. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1611,11 +1644,11 @@ The cube root is returned. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1657,11 +1690,11 @@ Definition (Issue 2). -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1675,6 +1708,7 @@ float expm1f(float x); Description
expm1 and expm1f calculate the exponential of x and subtract 1, that is,+e raised to the power x minus 1 (where e is the base of the natural system of logarithms, approximately 2.71828). The result is accurate even for small values of x, where using exp(x)-1 would lose many@@ -1699,15 +1733,15 @@ the System V Interface Definition (Issue 2). -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
-

1.33 ilogb, ilogbf---get exponent of floating point number

+

1.33 ilogb, ilogbf---get exponent of floating-point number

Synopsis
 
#include <math.h>@@ -1717,7 +1751,7 @@ int ilogbf(float val);
Description

-All non zero, normal numbers can be described as m *+All nonzero, normal numbers can be described as m * 2**p. ilogb and ilogbf examine the argument val, and return p. The functions frexp and frexpf are similar to ilogb and ilogbf, but also@@ -1729,7 +1763,7 @@ return m.

ilogb and ilogbf return the power of two used to form the-floating point argument. If val is 0, they return -+floating-point argument. If val is 0, they return - INT_MAX (INT_MAX is defined in limits.h). If val is infinite, or NaN, they return INT_MAX.

@@ -1745,11 +1779,11 @@ the System V Interface Definition (Issue 2). -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1762,8 +1796,8 @@ float infinityf(void); Description
infinity and infinityf return the special number IEEE-infinity in double and single precision arithmetic-respectivly.+infinity in double- and single-precision arithmetic+respectively.


@@ -1773,11 +1807,11 @@ respectivly. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1818,11 +1852,11 @@ Interface Definition (Issue 2). -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1940,11 +1974,11 @@ an error message. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -1985,24 +2019,25 @@ sign as the supplied argument val. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
-

1.38 nan, nanf---representation of infinity

+

1.38 nan, nanf---representation of "Not a Number"

Synopsis
 
#include <math.h>-double nan(void);-float nanf(void);+double nan(const char *);+float nanf(const char *);
Description
nan and nanf return an IEEE NaN (Not a Number) in-double and single precision arithmetic respectivly.+double- and single-precision arithmetic respectively. The+argument is currently disregarded.


@@ -2012,11 +2047,11 @@ double and single precision arithmetic respectivly. -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
@@ -2028,7 +2063,7 @@ double nextafter(double val, double dir); float nextafterf(float val, float dir); Description
-nextafter returns the double) precision floating point number+nextafter returns the double-precision floating-point number closest to val in the direction toward dir. nextafterf performs the same operation in single precision. For example, nextafter(0.0,1.0) returns the smallest positive number which is@@ -2054,15 +2089,15 @@ or by the System V Interface Definition (Issue 2). -+---+++
[ < ] [ > ]   [ << ]   [ << ] [ Up ][ >> ]         [Top][Contents][ >> ]         [Top][Contents] [Index] [ ? ]
-

1.40 scalbn, scalbnf---scale by integer

+

1.40 scalbn, scalbnf---scale by power of two

Synopsis -+--++
 
#include <math.h>@@ -2097,10 +2132,10 @@ Interface Definition (Issue 2).
[ < ] [ > ]   [ << ][ Up ][ Up ] [ >> ]         [Top][Contents]         [Top][Contents] [Index] [ ? ]
@@ -2137,10 +2172,10 @@ calls; in that situation, the math functions behave reentrantly. [ < ] [ > ]   [ << ]-[ Up ]+[ Up ] [ >> ]-         [Top]-[Contents]+         [Top]+[Contents] [Index] [ ? ] @@ -2243,8 +2278,8 @@ calls; in that situation, the math functions behave reentrantly. hypotf1.18 hypot, hypotf---distance from origin
I-ilogb1.33 ilogb, ilogbf---get exponent of floating point number-ilogbf1.33 ilogb, ilogbf---get exponent of floating point number+ilogb1.33 ilogb, ilogbf---get exponent of floating-point number+ilogbf1.33 ilogb, ilogbf---get exponent of floating-point number infinity1.34 infinity, infinityf---representation of infinity infinityf1.34 infinity, infinityf---representation of infinity isinf1.19 isnan,isnanf,isinf,isinff,finite,finitef---test for exceptional numbers@@ -2281,8 +2316,8 @@ calls; in that situation, the math functions behave reentrantly. modff1.37 modf, modff---split fractional and integer parts
N-nan1.38 nan, nanf---representation of infinity-nanf1.38 nan, nanf---representation of infinity+nan1.38 nan, nanf---representation of "Not a Number"+nanf1.38 nan, nanf---representation of "Not a Number" nextafter1.39 nextafter, nextafterf---get next number nextafterf1.39 nextafter, nextafterf---get next number
@@ -2299,8 +2334,8 @@ calls; in that situation, the math functions behave reentrantly. remainderf1.24 remainder, remainderf---round and remainder
S-scalbn1.40 scalbn, scalbnf---scale by integer-scalbnf1.40 scalbn, scalbnf---scale by integer+scalbn1.40 scalbn, scalbnf---scale by power of two+scalbnf1.40 scalbn, scalbnf---scale by power of two sin1.26 sin, sinf, cos, cosf---sine or cosine sinf1.26 sin, sinf, cos, cosf---sine or cosine sinh1.27 sinh, sinhf---hyperbolic sine@@ -2362,3 +2397,296 @@ calls; in that situation, the math functions behave reentrantly.

+++++++
[Top][Contents][Index][ ? ]
+

Table of Contents

++
+++++++
[Top][Contents][Index][ ? ]
+

Short Table of Contents

+
+1. Mathematical Functions (`math.h')+
+2. Reentrancy Properties of libm+
+Index+
++
+
+++++++
[Top][Contents][Index][ ? ]
+

About this document

+This document was generated by Jeff Johnston on January, 30 2004+using texi2html+

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