Documentation
¶
Overview ¶
Package math provides transcendental and advanced mathematical primitives.
Transcendental Functions (R7RS 6.2.6) ¶
- sin, cos, tan, asin, acos, atan
- exp, log
- sqrt, expt
Rounding ¶
- floor, ceiling, truncate, round
Numeric Conversion ¶
- numerator, denominator
- rationalize
- exact-integer-sqrt
Use Extension or AddToRegistry to register all primitives.
Index ¶
- Variables
- func PrimAngle(mc machine.CallContext) error
- func PrimAtan(mc machine.CallContext) error
- func PrimComplexInexactWithAccuracy(mc machine.CallContext) error
- func PrimDenominator(mc machine.CallContext) error
- func PrimExactIntegerSqrt(mc machine.CallContext) error
- func PrimExp(mc machine.CallContext) error
- func PrimExpt(mc machine.CallContext) error
- func PrimFiniteQ(mc machine.CallContext) error
- func PrimFloorDiv(mc machine.CallContext) error
- func PrimFloorQuotient(mc machine.CallContext) error
- func PrimFloorRemainder(mc machine.CallContext) error
- func PrimImagPart(mc machine.CallContext) error
- func PrimInexactAccuracy(mc machine.CallContext) error
- func PrimInexactLosslessQ(mc machine.CallContext) error
- func PrimInexactWithAccuracy(mc machine.CallContext) error
- func PrimInfiniteQ(mc machine.CallContext) error
- func PrimLog(mc machine.CallContext) error
- func PrimMagnitude(mc machine.CallContext) error
- func PrimMakePolar(mc machine.CallContext) error
- func PrimMakeRectangular(mc machine.CallContext) error
- func PrimNanQ(mc machine.CallContext) error
- func PrimNumberToString(mc machine.CallContext) error
- func PrimNumerator(mc machine.CallContext) error
- func PrimRationalize(mc machine.CallContext) error
- func PrimRealPart(mc machine.CallContext) error
- func PrimSqrt(mc machine.CallContext) error
- func PrimStringToNumber(mc machine.CallContext) error
- func PrimTruncateDiv(mc machine.CallContext) error
- func PrimTruncateQuotient(mc machine.CallContext) error
- func PrimTruncateRemainder(mc machine.CallContext) error
Constants ¶
This section is empty.
Variables ¶
var ( PrimSin = makeComplexPrimitive("sin", cmplx.Sin, values.BigSin, values.BigComplexSin) PrimCos = makeComplexPrimitive("cos", cmplx.Cos, values.BigCos, values.BigComplexCos) PrimTan = makeComplexPrimitive("tan", cmplx.Tan, values.BigTan, values.BigComplexTan) PrimAsin = makeComplexPrimitive("asin", cmplx.Asin, values.BigAsin, values.BigComplexAsin) PrimAcos = makeComplexPrimitive("acos", cmplx.Acos, values.BigAcos, values.BigComplexAcos) )
Unary transcendental primitives (R7RS §6.2.6). Big-real kernels are wired in as they land. exp is custom (below) for the bounded-real overflow rescue.
var AddToRegistry = Builder.AddToRegistry
AddToRegistry registers all math primitives.
var Builder = registry.NewRegistryBuilder(addPrimitives)
Builder aggregates all math registration functions.
var Extension = registry.NewDescribedExtension("math", "Extended math: trigonometry, logarithms, bitwise operations.", AddToRegistry)
Extension is the math extension.
var PrimCeiling = makeRealNumberPrimitive(realNumberOp{ name: "ceiling", mode: roundCeiling, floatOp: math.Ceil, })
var PrimFloor = makeRealNumberPrimitive(realNumberOp{ name: "floor", mode: roundFloor, floatOp: math.Floor, })
var PrimRound = makeRealNumberPrimitive(realNumberOp{ name: "round", mode: roundNearestEven, floatOp: math.RoundToEven, })
var PrimTruncate = makeRealNumberPrimitive(realNumberOp{ name: "truncate", mode: roundTruncate, floatOp: math.Trunc, })
Functions ¶
func PrimAngle ¶
func PrimAngle(mc machine.CallContext) error
PrimAngle implements R7RS §6.2.6 angle.
The five real kinds used to be hand-unrolled here, one arm each, and every arm carried the same three bugs -- which is what a hand-unrolled dispatch buys you: the same mistake, five times, fixed one at a time forever. They ask ONE question, so they get one answer: angleOfReal.
func PrimAtan ¶
func PrimAtan(mc machine.CallContext) error
PrimAtan implements the (atan z) and (atan y x) primitives.
func PrimComplexInexactWithAccuracy ¶ added in v1.16.0
func PrimComplexInexactWithAccuracy(mc machine.CallContext) error
PrimComplexInexactWithAccuracy implements (complex-inexact-with-accuracy n) — the uniform 3-value variant.
Always returns (values inexact-c real-acc-sym imag-acc-sym), regardless of whether the input is real or complex. For real input N, the imaginary accuracy is trivially 'exact. Useful when callers want a single arity regardless of input domain.
func PrimDenominator ¶
func PrimDenominator(mc machine.CallContext) error
PrimDenominator implements the (denominator) primitive.
func PrimExactIntegerSqrt ¶
func PrimExactIntegerSqrt(mc machine.CallContext) error
PrimExactIntegerSqrt implements the (exact-integer-sqrt) primitive.
R7RS §6.2.6: Returns two non-negative exact integers s and r where n = s² + r and n < (s+1)².
func PrimExp ¶
func PrimExp(mc machine.CallContext) error
PrimExp implements (exp z). Unlike the other unary transcendentals, exp overflows float64 at ~709 — inside the bounded range — so besides the big-precision path for unbounded-tier operands it also rescues a bounded real operand whose exp over/underflows float64 to a finite BigFloat (e^1000 ≈ 1.97e434 is representable as a bignum even though math.Exp returns +Inf).
func PrimExpt ¶
func PrimExpt(mc machine.CallContext) error
PrimExpt implements the (expt) primitive.
func PrimFiniteQ ¶
func PrimFiniteQ(mc machine.CallContext) error
PrimFiniteQ implements the (finite?) primitive.
func PrimFloorDiv ¶
func PrimFloorDiv(mc machine.CallContext) error
PrimFloorDiv implements the (floor/) primitive.
R7RS §6.2.6: Returns two values: floor quotient and floor remainder.
func PrimFloorQuotient ¶
func PrimFloorQuotient(mc machine.CallContext) error
PrimFloorQuotient implements the (floor-quotient) primitive.
R7RS §6.2.6: Returns the floor quotient for any real numbers.
func PrimFloorRemainder ¶
func PrimFloorRemainder(mc machine.CallContext) error
PrimFloorRemainder implements the (floor-remainder) primitive.
R7RS §6.2.6: Returns the floor remainder for any real numbers.
func PrimImagPart ¶
func PrimImagPart(mc machine.CallContext) error
PrimImagPart implements the (imag-part) primitive.
func PrimInexactAccuracy ¶ added in v1.16.0
func PrimInexactAccuracy(mc machine.CallContext) error
PrimInexactAccuracy implements (inexact-accuracy n).
Polymorphic return shape: real input → one symbol; complex input → two symbols via mc.SetValues. R7RS-style multi-value protocol.
func PrimInexactLosslessQ ¶ added in v1.16.0
func PrimInexactLosslessQ(mc machine.CallContext) error
PrimInexactLosslessQ implements (inexact-lossless? n).
Returns #t iff (exact->inexact n) would lose no information. For real input, this means the float64 conversion is big.Exact. For complex input, BOTH real and imaginary components must be big.Exact. (For real-only inputs the imaginary accuracy is trivially big.Exact, so the complex predicate collapses to the real-part check — hence the unified ToComplex128WithAccuracy path.)
func PrimInexactWithAccuracy ¶ added in v1.16.0
func PrimInexactWithAccuracy(mc machine.CallContext) error
PrimInexactWithAccuracy implements (inexact-with-accuracy n).
Polymorphic return: real input → (values inexact-n acc-sym); complex input → (values inexact-c real-acc-sym imag-acc-sym). The inexact value is the actual float64 / complex128 produced by the conversion; the accuracy symbols indicate the rounding direction.
func PrimInfiniteQ ¶
func PrimInfiniteQ(mc machine.CallContext) error
PrimInfiniteQ implements the (infinite?) primitive.
func PrimLog ¶
func PrimLog(mc machine.CallContext) error
PrimLog implements the (log z) and (log z1 z2) primitives. A positive, unbounded-tier real argument takes the big-precision log (so a value beyond the float64 range no longer overflows its input to +Inf); non-positive or complex arguments keep the branch-correct complex path.
func PrimMagnitude ¶
func PrimMagnitude(mc machine.CallContext) error
PrimMagnitude implements the (magnitude) primitive.
func PrimMakePolar ¶
func PrimMakePolar(mc machine.CallContext) error
PrimMakePolar implements the (make-polar) primitive.
func PrimMakeRectangular ¶
func PrimMakeRectangular(mc machine.CallContext) error
PrimMakeRectangular implements make-rectangular. R7RS §6.2.6: If both arguments are exact, the result is exact.
func PrimNumberToString ¶
func PrimNumberToString(mc machine.CallContext) error
PrimNumberToString implements the number->string primitive.
Every result is a MUTABLE string. R7RS §3.4's storage model makes a newly allocated object's locations mutable unless a procedure's own description says otherwise, and number->string has no such clause — unlike command-line and the get-environment-variable family (§6.14, "it is an error to mutate any of these strings"), which correctly refuse.
values.NewString defaults to immutable, so mutability is not the absence of a flag here: an allocator that wants it must call NewMutableString explicitly. That polarity is why every one of these arms was wrong the same way.
func PrimNumerator ¶
func PrimNumerator(mc machine.CallContext) error
PrimNumerator implements the numerator primitive.
func PrimRationalize ¶
func PrimRationalize(mc machine.CallContext) error
PrimRationalize implements the (rationalize) primitive.
func PrimRealPart ¶
func PrimRealPart(mc machine.CallContext) error
PrimRealPart implements the (real-part) primitive.
func PrimSqrt ¶
func PrimSqrt(mc machine.CallContext) error
PrimSqrt implements the (sqrt) primitive.
R7RS §6.2.6: The branch cut for sqrt lies along the negative real axis, continuous with quadrant II. This means for values on the negative real axis (including those with -0.0 imaginary part), sqrt returns positive imaginary.
func PrimStringToNumber ¶
func PrimStringToNumber(mc machine.CallContext) error
PrimStringToNumber implements the string->number primitive.
R7RS §6.2.7: string->number returns a number of the maximally precise representation expressed by the given string. It is an error if radix is not 2, 8, 10, or 16.
R7RS §7.1.1: The string may contain prefix directives #b, #o, #d, #x (radix) and #e, #i (exactness), in either order, up to one of each. A radix prefix in the string overrides the radix argument.
func PrimTruncateDiv ¶
func PrimTruncateDiv(mc machine.CallContext) error
PrimTruncateDiv implements the truncate/ primitive.
R7RS §6.2.6: Returns two values: truncate quotient and truncate remainder.
func PrimTruncateQuotient ¶
func PrimTruncateQuotient(mc machine.CallContext) error
PrimTruncateQuotient implements the truncate-quotient primitive.
R7RS §6.2.6: Returns the truncate quotient for any real numbers.
func PrimTruncateRemainder ¶
func PrimTruncateRemainder(mc machine.CallContext) error
PrimTruncateRemainder implements the truncate-remainder primitive.
R7RS §6.2.6: Returns the truncate remainder for any real numbers.
Types ¶
This section is empty.
Source Files