simpsons-rule's Introduction

simpsons-rule

This system is for numeric integration of functions of one variable. See an example:

CL-USER> ;; Integrate sin(500x)/x from -5 to 5
; No value
CL-USER> (simpsons-rule:integrate
 (serapeum:hook
  (serapeum:flip #'/)
  (alexandria:compose
   #'sin
   (alexandria:curry #'* 500)))
 -5d0 5d0)
3.1409850016443404d0

All numeric arguments to SIMPSONS-RULE:INTEGRATE must be of the same floating point type T and the function must be of the type T -> T.

The compiler produces specialized code when types of arguments are known at compile time and when optimizing for speed:

CL-USER> (defun integrate-in-unit-range (fn)
  (declare (optimize speed))
  (simpsons-rule:integrate fn 0d0 1d0))
INTEGRATE-IN-UNIT-RANGE
CL-USER> (disassemble 'integrate-in-unit-range)
; disassembly for INTEGRATE-IN-UNIT-RANGE
; Size: 46 bytes. Origin: #x224A91BD                          ; INTEGRATE-IN-UNIT-RANGE
; BD:       488B3DC4FFFFFF   MOV RDI, [RIP-60]                ; 0.0d0
; C4:       488B35B5FFFFFF   MOV RSI, [RIP-75]                ; 1.0d0
; CB:       488B05A6FFFFFF   MOV RAX, [RIP-90]                ; 1.0d-6
; D2:       488945F0         MOV [RBP-16], RAX
; D6:       488B5DF0         MOV RBX, [RBP-16]
; DA:       B908000000       MOV ECX, 8
; DF:       FF7508           PUSH QWORD PTR [RBP+8]
; E2:       B882B74520       MOV EAX, #x2045B782              ; #<FDEFN SIMPSONS-RULE:INTEGRATE/DOUBLE-FLOAT>
; E7:       FFE0             JMP RAX
; E9:       CC10             INT3 16                          ; Invalid argument count trap
NIL
CL-USER>

SIMPSONS-RULE:INTEGRATE expands to one of specialized versions: either SIMPSONS-RULE:INTEGRATE/SINGLE-FLOAT or SIMPSONS-RULE:INTEGRATE/DOUBLE-FLOAT when possible.

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