diff --git a/man3/acos.3 b/man3/acos.3 index 40ebe7797..877fc35c2 100644 --- a/man3/acos.3 +++ b/man3/acos.3 @@ -63,9 +63,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR acos () -function calculates the arc cosine of +These functions calculate the arc cosine of .IR x ; that is the value whose cosine is diff --git a/man3/acosh.3 b/man3/acosh.3 index 7a0c40e75..679810e41 100644 --- a/man3/acosh.3 +++ b/man3/acosh.3 @@ -75,9 +75,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR acosh () -function calculates the inverse hyperbolic cosine of +These functions calculate the inverse hyperbolic cosine of .IR x ; that is the value whose hyperbolic cosine is .IR x . diff --git a/man3/asin.3 b/man3/asin.3 index 9605bd208..890456de2 100644 --- a/man3/asin.3 +++ b/man3/asin.3 @@ -65,9 +65,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR asin () -function calculates the principal value of the arc sine of +These functions calculate the principal value of the arc sine of .IR x ; that is the value whose sine is .IR x . diff --git a/man3/asinh.3 b/man3/asinh.3 index 20012e429..932d21c3e 100644 --- a/man3/asinh.3 +++ b/man3/asinh.3 @@ -75,9 +75,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR asinh () -function calculates the inverse hyperbolic sine of +These functions calculate the inverse hyperbolic sine of .IR x ; that is the value whose hyperbolic sine is .IR x . diff --git a/man3/atan.3 b/man3/atan.3 index ef2bdc4e8..8ba043901 100644 --- a/man3/atan.3 +++ b/man3/atan.3 @@ -65,9 +65,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR atan () -function calculates the principal value of the arc tangent of +These functions calculate the principal value of the arc tangent of .IR x ; that is the value whose tangent is .IR x . diff --git a/man3/atan2.3 b/man3/atan2.3 index 38cc49f15..8ecd5f656 100644 --- a/man3/atan2.3 +++ b/man3/atan2.3 @@ -63,9 +63,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR atan2 () -function calculates the principal value of the arc tangent of +These functions calculate the principal value of the arc tangent of .IR y/x , using the signs of the two arguments to determine the quadrant of the result. diff --git a/man3/atanh.3 b/man3/atanh.3 index a7bc3cec5..673f012a3 100644 --- a/man3/atanh.3 +++ b/man3/atanh.3 @@ -75,9 +75,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR atanh () -function calculates the inverse hyperbolic tangent of +These functions calculate the inverse hyperbolic tangent of .IR x ; that is the value whose hyperbolic tangent is .IR x . diff --git a/man3/cabs.3 b/man3/cabs.3 index 699b5eb0c..44cf31af3 100644 --- a/man3/cabs.3 +++ b/man3/cabs.3 @@ -18,9 +18,7 @@ cabs, cabsf, cabsl \- absolute value of a complex number .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR cabs () -function returns the absolute value of the complex number +These functions return the absolute value of the complex number .IR z . The result is a real number. .SH VERSIONS diff --git a/man3/cacos.3 b/man3/cacos.3 index 94277e21d..6c7b0e2dd 100644 --- a/man3/cacos.3 +++ b/man3/cacos.3 @@ -19,9 +19,7 @@ cacos, cacosf, cacosl \- complex arc cosine .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR cacos () -function calculates the complex arc cosine of +These functions calculate the complex arc cosine of .IR z . If \fIy\ =\ cacos(z)\fP, then \fIz\ =\ ccos(y)\fP. The real part of diff --git a/man3/cacosh.3 b/man3/cacosh.3 index fa677e5b2..f27364ce6 100644 --- a/man3/cacosh.3 +++ b/man3/cacosh.3 @@ -19,9 +19,7 @@ cacosh, cacoshf, cacoshl \- complex arc hyperbolic cosine .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR cacosh () -function calculates the complex arc hyperbolic cosine of +These functions calculate the complex arc hyperbolic cosine of .IR z . If \fIy\ =\ cacosh(z)\fP, then \fIz\ =\ ccosh(y)\fP. The imaginary part of diff --git a/man3/casin.3 b/man3/casin.3 index 4c4473b79..294a874f0 100644 --- a/man3/casin.3 +++ b/man3/casin.3 @@ -18,9 +18,7 @@ casin, casinf, casinl \- complex arc sine .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR casin () -function calculates the complex arc sine of +These functions calculate the complex arc sine of .IR z . If \fIy\ =\ casin(z)\fP, then \fIz\ =\ csin(y)\fP. The real part of diff --git a/man3/casinh.3 b/man3/casinh.3 index e33201214..70b4441bc 100644 --- a/man3/casinh.3 +++ b/man3/casinh.3 @@ -18,9 +18,7 @@ casinh, casinhf, casinhl \- complex arc sine hyperbolic .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR casinh () -function calculates the complex arc hyperbolic sine of +These functions calculate the complex arc hyperbolic sine of .IR z . If \fIy\ =\ casinh(z)\fP, then \fIz\ =\ csinh(y)\fP. The imaginary part of diff --git a/man3/catan.3 b/man3/catan.3 index d7d3c59d3..4725ab5f7 100644 --- a/man3/catan.3 +++ b/man3/catan.3 @@ -19,9 +19,7 @@ catan, catanf, catanl \- complex arc tangents .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR catan () -function calculates the complex arc tangent of +These functions calculate the complex arc tangent of .IR z . If \fIy\ =\ catan(z)\fP, then \fIz\ =\ ctan(y)\fP. The real part of y is chosen in the interval [\-pi/2,pi/2]. diff --git a/man3/catanh.3 b/man3/catanh.3 index ca0ee431a..c5417c057 100644 --- a/man3/catanh.3 +++ b/man3/catanh.3 @@ -19,9 +19,7 @@ catanh, catanhf, catanhl \- complex arc tangents hyperbolic .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR catanh () -function calculates the complex arc hyperbolic tangent of +These functions calculate the complex arc hyperbolic tangent of .IR z . If \fIy\ =\ catanh(z)\fP, then \fIz\ =\ ctanh(y)\fP. The imaginary part of diff --git a/man3/cbrt.3 b/man3/cbrt.3 index 9a18660d1..76aa87248 100644 --- a/man3/cbrt.3 +++ b/man3/cbrt.3 @@ -70,9 +70,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR cbrt () -function returns the (real) cube root of +These functions return the (real) cube root of .IR x . This function cannot fail; every representable real value has a representable real cube root. diff --git a/man3/cexp.3 b/man3/cexp.3 index 4e7597bf2..ce26da96d 100644 --- a/man3/cexp.3 +++ b/man3/cexp.3 @@ -18,7 +18,7 @@ cexp, cexpf, cexpl \- complex exponential function .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The function calculates e (2.71828..., the base of natural logarithms) +These functions calculate e (2.71828..., the base of natural logarithms) raised to the power of .IR z . .LP diff --git a/man3/cimag.3 b/man3/cimag.3 index 2b58d965e..e0d4f26e0 100644 --- a/man3/cimag.3 +++ b/man3/cimag.3 @@ -18,9 +18,7 @@ cimag, cimagf, cimagl \- get imaginary part of a complex number .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR cimag () -function returns the imaginary part of the complex number +These functions return the imaginary part of the complex number .IR z . .LP One has: diff --git a/man3/conj.3 b/man3/conj.3 index 07c368334..4d4ad81ef 100644 --- a/man3/conj.3 +++ b/man3/conj.3 @@ -18,9 +18,7 @@ conj, conjf, conjl \- calculate the complex conjugate .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR conj () -function returns the complex conjugate value of +These functions return the complex conjugate value of .IR z . That is the value obtained by changing the sign of the imaginary part. .LP diff --git a/man3/copysign.3 b/man3/copysign.3 index 5456c198f..ce400b989 100644 --- a/man3/copysign.3 +++ b/man3/copysign.3 @@ -62,13 +62,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR copysign (), -.BR copysignf (), -and -.BR copysignl () -functions return a value whose absolute value matches -that of +These functions return a value whose absolute value matches that of .IR x , but whose sign bit matches that of .IR y . diff --git a/man3/cos.3 b/man3/cos.3 index f0c0a3939..65f41dda9 100644 --- a/man3/cos.3 +++ b/man3/cos.3 @@ -64,9 +64,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR cos () -function returns the cosine of +These functions return the cosine of .IR x , where .I x diff --git a/man3/cosh.3 b/man3/cosh.3 index 2cf4c8933..b5800e149 100644 --- a/man3/cosh.3 +++ b/man3/cosh.3 @@ -66,12 +66,9 @@ or .RE .ad .SH DESCRIPTION -The -.BR cosh () -function returns the hyperbolic cosine of +These functions return the hyperbolic cosine of .IR x , -which -is defined mathematically as: +which is defined mathematically as: .nf cosh(x) = (exp(x) + exp(\-x)) / 2 diff --git a/man3/cpow.3 b/man3/cpow.3 index b9aa88d92..e84c3017c 100644 --- a/man3/cpow.3 +++ b/man3/cpow.3 @@ -21,11 +21,11 @@ cpow, cpowf, cpowl \- complex power function Link with \fI\-lm\fP. .fi .SH DESCRIPTION -The function calculates +These functions calculate .I x raised to the power -.IR z . -(With a branch cut for +.IR z +(with a branch cut for .I x along the negative real axis.) .SH VERSIONS diff --git a/man3/creal.3 b/man3/creal.3 index 2fe5f561e..8681a708b 100644 --- a/man3/creal.3 +++ b/man3/creal.3 @@ -18,9 +18,7 @@ creal, crealf, creall \- get real part of a complex number .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR creal () -function returns the real part of the complex number +These functions return the real part of the complex number .IR z . .LP One has: diff --git a/man3/erf.3 b/man3/erf.3 index 862ab4d13..d573bb0cf 100644 --- a/man3/erf.3 +++ b/man3/erf.3 @@ -72,12 +72,9 @@ or .RE .ad b .SH DESCRIPTION -The -.BR erf () -function returns the error function of +These functions return the error function of .IR x , -defined -as +defined as .TP erf(x) = 2/sqrt(pi)* integral from 0 to x of exp(\-t*t) dt .SH RETURN VALUE diff --git a/man3/erfc.3 b/man3/erfc.3 index 08810c2b1..a3382f9fc 100644 --- a/man3/erfc.3 +++ b/man3/erfc.3 @@ -63,9 +63,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR erfc () -function returns the complementary error function of +These functions return the complementary error function of .IR x , that is, 1.0 \- erf(x). .SH RETURN VALUE diff --git a/man3/exp.3 b/man3/exp.3 index ad6c356f6..ca6defb28 100644 --- a/man3/exp.3 +++ b/man3/exp.3 @@ -66,9 +66,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR exp () -function returns the value of e (the base of natural +These functions return the value of e (the base of natural logarithms) raised to the power of .IR x . .SH RETURN VALUE diff --git a/man3/exp10.3 b/man3/exp10.3 index a48ed3e38..63aa22905 100644 --- a/man3/exp10.3 +++ b/man3/exp10.3 @@ -50,9 +50,7 @@ exp10, exp10f, exp10l \- base-10 exponential function .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR exp10 () -function returns the value of 10 +These functions return the value of 10 raised to the power of .IR x . .SH RETURN VALUE diff --git a/man3/exp2.3 b/man3/exp2.3 index cf9546f7a..9f912b3a8 100644 --- a/man3/exp2.3 +++ b/man3/exp2.3 @@ -66,10 +66,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR exp2 () -function returns the value of 2 -raised to the power of +These functions return the value of 2 raised to the power of .IR x . .SH RETURN VALUE On success, these functions return the base-2 exponential value of diff --git a/man3/expm1.3 b/man3/expm1.3 index 2319c88d2..1bc68aabf 100644 --- a/man3/expm1.3 +++ b/man3/expm1.3 @@ -70,15 +70,13 @@ or .RE .ad b .SH DESCRIPTION -.I expm1(x) -returns a value equivalent to +These functions return a value equivalent to .nf exp(x) \- 1 .fi -It is -computed in a way that is accurate even if the value of +The result is computed in a way that is accurate even if the value of .I x is near zero\(ema case where diff --git a/man3/fma.3 b/man3/fma.3 index 23c0c89f3..3bd00299c 100644 --- a/man3/fma.3 +++ b/man3/fma.3 @@ -43,9 +43,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR fma () -function computes +These functions compute .IR x " * " y " + " z . The result is rounded as one ternary operation according to the current rounding mode (see diff --git a/man3/fmod.3 b/man3/fmod.3 index c70675245..700a1eedf 100644 --- a/man3/fmod.3 +++ b/man3/fmod.3 @@ -65,9 +65,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR fmod () -function computes the floating-point remainder of dividing +These functions compute the floating-point remainder of dividing .I x by .IR y . diff --git a/man3/frexp.3 b/man3/frexp.3 index 559e968b7..d126d8532 100644 --- a/man3/frexp.3 +++ b/man3/frexp.3 @@ -64,17 +64,13 @@ or .RE .ad .SH DESCRIPTION -The -.BR frexp () -function is used to split the number +These functions are used to split the number .I x into a normalized fraction and an exponent which is stored in .IR exp . .SH RETURN VALUE -The -.BR frexp () -function returns the normalized fraction. +These functions return the normalized fraction. If the argument .I x is not zero, diff --git a/man3/hypot.3 b/man3/hypot.3 index 1392f4adb..1e5221a9e 100644 --- a/man3/hypot.3 +++ b/man3/hypot.3 @@ -72,9 +72,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR hypot () -function returns +These functions return .RI sqrt( x * x + y * y ). This is the length of the hypotenuse of a right-angled triangle with sides of length diff --git a/man3/ldexp.3 b/man3/ldexp.3 index 3926b59f6..1e22fec79 100644 --- a/man3/ldexp.3 +++ b/man3/ldexp.3 @@ -64,9 +64,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR ldexp () -function returns the result of multiplying the floating-point number +These functions return the result of multiplying the floating-point number .I x by 2 raised to the power .IR exp . diff --git a/man3/lgamma.3 b/man3/lgamma.3 index 667f00fab..af2925f30 100644 --- a/man3/lgamma.3 +++ b/man3/lgamma.3 @@ -73,8 +73,11 @@ For the definition of the Gamma function, see .BR tgamma (3). .PP The -.BR lgamma () -function returns the natural logarithm of +.BR lgamma (), +.BR lgammaf (), +and +.BR lgammal () +functions return the natural logarithm of the absolute value of the Gamma function. The sign of the Gamma function is returned in the external integer diff --git a/man3/log.3 b/man3/log.3 index c2761aabd..6ae17d263 100644 --- a/man3/log.3 +++ b/man3/log.3 @@ -66,9 +66,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR log () -function returns the natural logarithm of +These functions return the natural logarithm of .IR x . .SH RETURN VALUE On success, these functions return the natural logarithm of diff --git a/man3/log10.3 b/man3/log10.3 index abf48e58c..c096a9f04 100644 --- a/man3/log10.3 +++ b/man3/log10.3 @@ -66,9 +66,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR log10 () -function returns the base 10 logarithm of +These functions return the base 10 logarithm of .IR x . .SH RETURN VALUE On success, these functions return the base 10 logarithm of diff --git a/man3/log1p.3 b/man3/log1p.3 index 0a93d17ff..0889e5746 100644 --- a/man3/log1p.3 +++ b/man3/log1p.3 @@ -69,14 +69,13 @@ or .RE .ad b .SH DESCRIPTION -.I log1p(x) -returns a value equivalent to +These functions return a value equivalent to .nf log (1 + \fIx\fP) .fi -It is computed in a way +The result is computed in a way that is accurate even if the value of .I x is near zero. diff --git a/man3/log2.3 b/man3/log2.3 index c2d574622..e0f9f8a7f 100644 --- a/man3/log2.3 +++ b/man3/log2.3 @@ -66,9 +66,7 @@ or .RE .ad b .SH DESCRIPTION -The -.BR log2 () -function returns the base 2 logarithm of +These functions return the base 2 logarithm of .IR x . .SH RETURN VALUE On success, these functions return the base 2 logarithm of diff --git a/man3/modf.3 b/man3/modf.3 index a8e8c9973..62155e77d 100644 --- a/man3/modf.3 +++ b/man3/modf.3 @@ -64,9 +64,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR modf () -function breaks the argument +These functions break the argument .I x into an integral part and a fractional part, each of which has the same sign as @@ -74,9 +72,7 @@ part and a fractional part, each of which has the same sign as The integral part is stored in the location pointed to by .IR iptr . .SH RETURN VALUE -The -.BR modf () -function returns the fractional part of +These functions return the fractional part of .IR x . If diff --git a/man3/pow.3 b/man3/pow.3 index 1e5ba5d5d..3fc8ccf12 100644 --- a/man3/pow.3 +++ b/man3/pow.3 @@ -65,9 +65,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR pow () -function returns the value of +These functions return the value of .I x raised to the power of diff --git a/man3/pow10.3 b/man3/pow10.3 index d0c3e704f..355b77e34 100644 --- a/man3/pow10.3 +++ b/man3/pow10.3 @@ -39,10 +39,7 @@ pow10, pow10f, pow10l \- base-10 power functions .sp Link with \fI\-lm\fP. .SH DESCRIPTION -The -.BR pow10 () -function returns the value of 10 raised to the -power +These functions return the value of 10 raised to the power .IR x . .SH VERSIONS These functions first appeared in glibc in version 2.1. diff --git a/man3/remainder.3 b/man3/remainder.3 index f46851afa..49c4214ec 100644 --- a/man3/remainder.3 +++ b/man3/remainder.3 @@ -90,9 +90,8 @@ _SVID_SOURCE || _BSD_SOURCE .RE .ad b .SH DESCRIPTION -The -.BR remainder () -function computes the remainder of dividing +These +functions compute the remainder of dividing .I x by .IR y . diff --git a/man3/significand.3 b/man3/significand.3 index 2f6aa882f..ae7ab03cb 100644 --- a/man3/significand.3 +++ b/man3/significand.3 @@ -35,12 +35,10 @@ _SVID_SOURCE || _BSD_SOURCE .RE .ad b .SH DESCRIPTION -The -.BR significand () -function returns the mantissa of +These functions return the mantissa of .I x scaled to the range [1,2). -It is equivalent to +They are equivalent to .sp .in +4n scalb(x, (double) \-ilogb(x)) diff --git a/man3/sin.3 b/man3/sin.3 index b44879497..cff26e9c7 100644 --- a/man3/sin.3 +++ b/man3/sin.3 @@ -65,9 +65,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR sin () -function returns the sine of +These functions return the sine of .IR x , where .I x diff --git a/man3/sinh.3 b/man3/sinh.3 index 346c09d08..3648c4bd8 100644 --- a/man3/sinh.3 +++ b/man3/sinh.3 @@ -66,9 +66,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR sinh () -function returns the hyperbolic sine of +These functions return the hyperbolic sine of .IR x , which is defined mathematically as: diff --git a/man3/sqrt.3 b/man3/sqrt.3 index 96697b6aa..40fee56cb 100644 --- a/man3/sqrt.3 +++ b/man3/sqrt.3 @@ -64,9 +64,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR sqrt () -function returns the nonnegative square root of +These functions return the nonnegative square root of .IR x . .SH RETURN VALUE On success, these functions return the square root of diff --git a/man3/tan.3 b/man3/tan.3 index 1ccd0413c..ad44cf4ec 100644 --- a/man3/tan.3 +++ b/man3/tan.3 @@ -65,9 +65,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR tan () -function returns the tangent of +These functions return the tangent of .IR x , where .I x diff --git a/man3/tanh.3 b/man3/tanh.3 index 982af39cb..f86de0232 100644 --- a/man3/tanh.3 +++ b/man3/tanh.3 @@ -65,9 +65,7 @@ or .RE .ad .SH DESCRIPTION -The -.BR tanh () -function returns the hyperbolic tangent of +These functions return the hyperbolic tangent of .IR x , which is defined mathematically as: diff --git a/man3/tgamma.3 b/man3/tgamma.3 index 233f62d72..1bd04e7ae 100644 --- a/man3/tgamma.3 +++ b/man3/tgamma.3 @@ -42,6 +42,9 @@ or .RE .ad .SH DESCRIPTION +These functions calculate the Gamma function of +.IR x . + The Gamma function is defined by .sp Gamma(x) = integral from 0 to infinity of t^(x\-1) e^\-t dt