diff options
Diffstat (limited to 'libgo/go/math/trig_reduce.go')
| -rw-r--r-- | libgo/go/math/trig_reduce.go | 16 |
1 files changed, 11 insertions, 5 deletions
diff --git a/libgo/go/math/trig_reduce.go b/libgo/go/math/trig_reduce.go index 6f8eaba..5cdf4fa 100644 --- a/libgo/go/math/trig_reduce.go +++ b/libgo/go/math/trig_reduce.go @@ -8,13 +8,19 @@ import ( "math/bits" ) -// reduceThreshold is the maximum value where the reduction using Pi/4 -// in 3 float64 parts still gives accurate results. Above this -// threshold Payne-Hanek range reduction must be used. -const reduceThreshold = (1 << 52) / (4 / Pi) +// reduceThreshold is the maximum value of x where the reduction using Pi/4 +// in 3 float64 parts still gives accurate results. This threshold +// is set by y*C being representable as a float64 without error +// where y is given by y = floor(x * (4 / Pi)) and C is the leading partial +// terms of 4/Pi. Since the leading terms (PI4A and PI4B in sin.go) have 30 +// and 32 trailing zero bits, y should have less than 30 significant bits. +// y < 1<<30 -> floor(x*4/Pi) < 1<<30 -> x < (1<<30 - 1) * Pi/4 +// So, conservatively we can take x < 1<<29. +// Above this threshold Payne-Hanek range reduction must be used. +const reduceThreshold = 1 << 29 // trigReduce implements Payne-Hanek range reduction by Pi/4 -// for x > 0. It returns the integer part mod 8 (j) and +// for x > 0. It returns the integer part mod 8 (j) and // the fractional part (z) of x / (Pi/4). // The implementation is based on: // "ARGUMENT REDUCTION FOR HUGE ARGUMENTS: Good to the Last Bit" |