diff options
| -rw-r--r-- | lib/libm/man/j0.3 | 4 | ||||
| -rw-r--r-- | lib/libm/man/math.3 | 42 |
2 files changed, 25 insertions, 21 deletions
diff --git a/lib/libm/man/j0.3 b/lib/libm/man/j0.3 index 269a2a759e0..93efe10e16a 100644 --- a/lib/libm/man/j0.3 +++ b/lib/libm/man/j0.3 @@ -1,4 +1,4 @@ -.\" $OpenBSD: j0.3,v 1.9 2003/02/27 01:45:03 jason Exp $ +.\" $OpenBSD: j0.3,v 1.10 2003/03/28 09:51:33 jmc Exp $ .\" Copyright (c) 1985, 1991 Regents of the University of California. .\" All rights reserved. .\" @@ -48,7 +48,7 @@ .Nm y1f , .Nm yn , .Nm ynf -.Nd bessel functions of first and second kind +.Nd Bessel functions of first and second kind .Sh SYNOPSIS .Fd #include <math.h> .Ft double diff --git a/lib/libm/man/math.3 b/lib/libm/man/math.3 index 77b498a93a3..55fc0411d54 100644 --- a/lib/libm/man/math.3 +++ b/lib/libm/man/math.3 @@ -1,4 +1,4 @@ -.\" $OpenBSD: math.3,v 1.13 2003/03/01 21:10:53 millert Exp $ +.\" $OpenBSD: math.3,v 1.14 2003/03/28 09:51:33 jmc Exp $ .\" Copyright (c) 1985 Regents of the University of California. .\" All rights reserved. .\" @@ -75,9 +75,9 @@ Declarations for these functions may be obtained from the include file .It ilogb Ta ieee(3) Ta "exponent extraction" Ta 0 .It isinf Ta isinf(3) Ta "check exceptions" .It isnan Ta isnan(3) Ta "check exceptions" -.It j0 Ta j0(3) Ta "bessel function" Ta ??? -.It j1 Ta j0(3) Ta "bessel function" Ta ??? -.It jn Ta j0(3) Ta "bessel function" Ta ??? +.It j0 Ta j0(3) Ta "Bessel function" Ta ??? +.It j1 Ta j0(3) Ta "Bessel function" Ta ??? +.It jn Ta j0(3) Ta "Bessel function" Ta ??? .It lgamma Ta lgamma(3) Ta "log gamma function" Ta ??? .It log Ta exp(3) Ta "natural logarithm" Ta 1 .It log10 Ta exp(3) Ta "logarithm to base 10" Ta 3 @@ -91,9 +91,9 @@ Declarations for these functions may be obtained from the include file .It sqrt Ta sqrt(3) Ta "square root" Ta 1 .It tan Ta tan(3) Ta "trigonometric function" Ta 3 .It tanh Ta tanh(3) Ta "hyperbolic function" Ta 3 -.It y0 Ta j0(3) Ta "bessel function" Ta ??? -.It y1 Ta j0(3) Ta "bessel function" Ta ??? -.It yn Ta j0(3) Ta "bessel function" Ta ??? +.It y0 Ta j0(3) Ta "Bessel function" Ta ??? +.It y1 Ta j0(3) Ta "Bessel function" Ta ??? +.It yn Ta j0(3) Ta "Bessel function" Ta ??? .El .Sh NOTES In @@ -150,10 +150,10 @@ double-precision format. The earlier .Tn DEC MicroVAXs have no D format, only G double-precision. -(Why? Why not?) +(Why? Why not?) .Pp Properties of D_floating-point: -.Bl -tag -width "Precision:" -offset indent -compact +.Bl -tag -width "Precision:" -offset indent -compact .It Wordsize: 64 bits, 8 bytes. .It Radix: @@ -169,7 +169,7 @@ Overflow threshold = 2.0**127 = 1.7e38. .br Underflow threshold = 0.5**128 = 2.9e-39. .br -NOTE: THIS RANGE IS COMPARATIVELY NARROW. +NOTE: THIS RANGE IS COMPARATIVELY NARROW. .br Overflow customarily stops computation. .br @@ -187,7 +187,7 @@ the hardware, only the obvious representation is ever produced. There is no -0 on a VAX. .It \*(If is not part of the VAX architecture. .It Reserved operands: -of the 2**55 that the hardware +Of the 2**55 that the hardware recognizes, only one of them is ever produced. Any floating-point operation upon a reserved operand, even a MOVF or MOVD, customarily stops @@ -198,7 +198,7 @@ overflow are invalid operations that customarily stop computation or, in earlier machines, produce reserved operands that will stop computation. .It Rounding: -Every rational operation (+, -, \(**, /) on a +Every rational operation (+, -, \(**, /) on a VAX (but not necessarily on a PDP-11), if not an over/underflow nor division by zero, is rounded to within half a \fIulp\fR, and when the rounding error is @@ -272,7 +272,7 @@ This is the most widely adopted standard for computer arithmetic. VLSI chips that conform to some version of that standard have been produced by a host of manufacturers, among them: .Bl -column -offset indent -compact "Intel i8070, i80287" "Western Electric (AT&T) WE32106" -.It "Intel i8087, i80287" Ta "National Semiconductor 32081" +.It "Intel i8087, i80287" Ta "National Semiconductor 32081" .It "Motorola 68881" Ta "Weitek WTL-1032, ... , -1165" .It "Zilog Z8070" Ta "Western Electric (AT&T) WE32106" .El @@ -364,7 +364,8 @@ rounding to the nearest integer multiple of 0.5**1074 = 4.9e-324. Its sign transforms correctly through multiplication or division, and is preserved by addition of zeros with like signs; but x-x yields +0 for every -finite x. The only operations that reveal zero's +finite x. +The only operations that reveal zero's sign are division by zero and copysign(x,\*(Pm0). In particular, comparison (x > y, x \*(Ge y, etc.) cannot be affected by the sign of zero; but if @@ -432,10 +433,12 @@ listed below in declining order of probable importance. .It "Underflow" Ta "Gradual Underflow" .It "Inexact" Ta "Rounded value" .El -NOTE: An Exception is not an Error unless handled -badly. What makes a class of exceptions exceptional +NOTE: An Exception is not an Error unless handled +badly. +What makes a class of exceptions exceptional is that no single default response can be satisfactory -in every instance. On the other hand, if a default +in every instance. +On the other hand, if a default response will serve most instances satisfactorily, the unsatisfactory instances cannot justify aborting computation every time the exception occurs. @@ -462,12 +465,13 @@ since the program last reset its flag. .It 3) Test a result to see whether it is a value that only an exception could have produced. -.Bd -filled +.Bd -filled CAUTION: The only reliable ways to discover whether Underflow has occurred are to test whether products or quotients lie closer to zero than the underflow threshold, or to test the Underflow -flag. (Sums and differences cannot underflow in +flag. +(Sums and differences cannot underflow in .St -ieee754 ; if x \*(Ne y then x-y is correct to full precision and certainly nonzero regardless of |