Flonums are a subset of the inexact real numbers provided by a Scheme implementation. In most Schemes, the flonums and the inexact reals are the same.
The procedures in this package don't have hard-coded prefixes. The intent is that they be placed in a module. Users can then import this module with their own prefix such as fl, or ƒ if their Scheme implementation supports that character, or with no prefix at all if the intent is to override the normal Scheme arithmetic routines.
(flonum? obj)
Returns #t if obj is a flonum, #f otherwise.
(real->flonum x)
Returns the best flonum representation of x.
The following core Scheme procedures have flonum equivalents:
= < <= > >= integer? zero? positive? negative? odd? even? finite? infinite? nan? + - * / abs numerator denominator floor ceiling truncate round exp log sin cos tan asin acos atan sqrt exptTODO: need to see about integer division procedures
The following constants are defined in terms of the constants of the <math.h> header of ISO/IEC 9899:1999 (C language).
|
Scheme name |
C name |
Comments |
|
e |
M_E |
Value of e |
|
log2-e |
M_LOG2E |
Value of log2e |
|
log10-e |
M_LOG10E |
Value of log10e |
|
ln-2 |
M_LN2 |
Value of loge2 |
|
ln-10 |
M_LN10 |
Value of loge10 |
|
pi |
M_PI |
Value of pi |
|
pi/2 |
M_PI_2 |
Value of pi/2 |
|
pi/4 |
M_PI_4 |
Value of pi/4 |
|
one-over-pi |
M_1_PI |
Value of 1/pi |
|
two-over-pi |
M_2_PI |
Value of 2/pi |
|
two-over-sqrt-pi |
M_2_SQRTPI |
Value of 2/sqrt(pi) |
|
sqrt-2 |
M_SQRT2 |
Value of sqrt(2) |
|
one-over-sqrt-2 |
M_SQRT1_2 |
Value of 1/sqrt(2) |
|
maximum-flonum |
HUGE_VAL |
+inf.0 or else the largest finite flonum |
|
fast-multiply-add |
FP_FAST_FMA, or 0 if not defined |
multiply-add is fast |
|
integer-exponent-zero |
FP_ILOGB0 |
what (integer-binary-log 0) returns |
|
integer-exponent-nan |
FP_ILOGBNAN |
what (integer-binary-log +0.nan) returns |
The following procedures are defined in terms of the functions of the <math.h> header of ISO/IEC 9899:1999 (C language). In the C signatures, the types "double" and "int" are mapped to Scheme flonums and (suitably bounded) Scheme exact integers respectively.
|
Scheme name |
C signature |
Comments |
|
acosh |
double acosh(double) |
hyperbolic arc cosine |
|
asinh |
double asinh(double) |
hyperbolic arc sine |
|
atanh |
double atanh(double) |
hyperbolic arc tangent |
|
cbrt |
double cbrt(double); |
cube root |
|
complementary-error-function |
double erfc(double) |
- |
|
copy-sign |
double copysign(double x, double y) |
result has magnitude of x and sign of y |
|
cosh |
double cosh(double) |
hyperbolic cosine |
||make-flonum||double ldexp(double x, int n)||x*2^n
|
error-function |
double erf(double) |
- |
|
exp-binary |
double exp2(double) |
base-2 exponential |
|
exp-minus-1 |
double expm1(double) |
exp(x)-1 |
|
exponent |
double logb(double x) |
the exponent of x, which is the integral part of log_r(|x|), as a signed floating-point value, for non-zero x, where r is the radix of the machine's floating-point arithmetic |
|
first-bessel-order-0 |
double j0(double) |
bessel function of the first kind, order 0 |
|
first-bessel-order-1 |
double j1(double) |
bessel function of the first kind, order 1 |
|
first-bessel |
double jn(int n, double) |
bessel function of the first kind, order n |
|
fraction-exponent |
double modf(double, double *) |
returns two values, fraction and int exponent |
|
gamma |
double tgamma(double) |
- |
|
hypotenuse |
double hypot(double, double) |
sqrt(x2+y2) |
|
integer-exponent |
int ilogb(double) |
binary log as int |
|
log-binary |
double log2(double) |
log base 2 |
|
log-decimal |
double log10(double) |
log base 10 |
|
log-gamma |
double lgamma(double) |
returns two values, log(|gamma(x)|) and sgn(gamma(x)) |
|
log-one-plus |
double log1p(double x) |
log (1+x) |
|
multiply-add |
double fma(double a, double b, double c) |
a*b+c |
|
next-after |
double nextafter(double, double) |
next flonum following x in the direction of y |
|
normalized-fraction-exponent |
double frexp(double, int *) |
returns two values, fraction in range [1/2,1) and int exponent |
|
positive-difference |
double fdim(double, double) |
- |
||remquo||double remquo(double, double, int *)||returns two values, rounded remainder and low-order n bits of the quotient (n is implementation-defined)
|
scalbn |
double scalbn(double x, int y) |
x*r^y, where r is the machine float radix |
|
second-bessel-order-0 |
double y0(double) |
bessel function of the second kind, order 0 |
|
second-bessel-order-1 |
double y1(double) |
bessel function of the second kind, order 1 |
|
second-bessel |
double yn(int n, double) |
bessel function of the second kind, order n |
|
sinh |
double cosh(double) |
hyperbolic sine |
|
tanh |
double cosh(double) |
hyperbolic tangent |
In the event that these operations do not yield a real result for the given arguments, the result may be +nan.0, or may be some unspecified flonum.
Implementations that use IEEE binary floating-point arithmetic should follow the relevant standards for these procedures.
A compnum is a complex number encoded rectangularly as a pair of flonums. The following procedures should be in a different module from the flonum procedures, since they will only be relevant to Schemes that support general complex numbers, and since there are conflicting names.
|
Scheme name |
C signature |
Comments |
|
abs |
double cabs(double complex) |
same as magnitude |
|
acos |
double complex cacos(double complex) |
- |
|
acosh |
double complex cacosh(double complex) |
- |
|
angle |
double carg(double complex) |
- |
|
asin |
double complex casin(double complex) |
- |
|
asinh |
double complex casinh(double complex) |
- |
|
`atan |
double complex catan(double complex)` |
- |
|
atanh |
double complex catanh(double complex) |
- |
|
conjugate |
double complex conj(double complex) |
complex conjugate |
|
cos |
double complex ccos(double complex) |
- |
|
cosh |
double complex ccosh(double complex) |
- |
|
exp |
double complex cexp(double complex) |
- |
|
expt |
double complex cpow(double complex, double complex) |
- |
|
imag-part |
double cimag(double complex) |
- |
|
log |
double complex clog(double complex) |
- |
|
magnitude |
double cabs(double complex) |
same as abs |
||projection||double complex cproj(double complex)||projects to Riemann sphere
|
real-part |
double creal(double complex) |
- |
|
sin |
double complex csin(double complex) |
- |
|
sinh |
double complex csinh(double complex) |
- |
|
sqrt |
double complex csqrt(double complex) |
- |
|
ctan |
double complex ctan(double complex) |
- |
|
ctanh |
double complex ctanh(double complex) |
- |