| // Copyright ©2015 The gonum Authors. All rights reserved. |
| // Use of this source code is governed by a BSD-style |
| // license that can be found in the LICENSE file. |
| |
| package gonum |
| |
| import "math" |
| |
| // Dlasq6 computes one dqd transform in ping-pong form with protection against |
| // overflow and underflow. z has length at least 4*(n0+1) and holds the qd array. |
| // i0 is the zero-based first index. |
| // n0 is the zero-based last index. |
| // |
| // Dlasq6 is an internal routine. It is exported for testing purposes. |
| func (impl Implementation) Dlasq6(i0, n0 int, z []float64, pp int) (dmin, dmin1, dmin2, dn, dnm1, dnm2 float64) { |
| if len(z) < 4*(n0+1) { |
| panic(badZ) |
| } |
| if n0-i0-1 <= 0 { |
| return dmin, dmin1, dmin2, dn, dnm1, dnm2 |
| } |
| safmin := dlamchS |
| j4 := 4*(i0+1) + pp - 4 // -4 rather than -3 for zero indexing |
| emin := z[j4+4] |
| d := z[j4] |
| dmin = d |
| if pp == 0 { |
| for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 { |
| j4 := j4loop - 1 // Translate back to zero-indexed. |
| z[j4-2] = d + z[j4-1] |
| if z[j4-2] == 0 { |
| z[j4] = 0 |
| d = z[j4+1] |
| dmin = d |
| emin = 0 |
| } else if safmin*z[j4+1] < z[j4-2] && safmin*z[j4-2] < z[j4+1] { |
| tmp := z[j4+1] / z[j4-2] |
| z[j4] = z[j4-1] * tmp |
| d *= tmp |
| } else { |
| z[j4] = z[j4+1] * (z[j4-1] / z[j4-2]) |
| d = z[j4+1] * (d / z[j4-2]) |
| } |
| dmin = math.Min(dmin, d) |
| emin = math.Min(emin, z[j4]) |
| } |
| } else { |
| for j4loop := 4 * (i0 + 1); j4loop <= 4*((n0+1)-3); j4loop += 4 { |
| j4 := j4loop - 1 |
| z[j4-3] = d + z[j4] |
| if z[j4-3] == 0 { |
| z[j4-1] = 0 |
| d = z[j4+2] |
| dmin = d |
| emin = 0 |
| } else if safmin*z[j4+2] < z[j4-3] && safmin*z[j4-3] < z[j4+2] { |
| tmp := z[j4+2] / z[j4-3] |
| z[j4-1] = z[j4] * tmp |
| d *= tmp |
| } else { |
| z[j4-1] = z[j4+2] * (z[j4] / z[j4-3]) |
| d = z[j4+2] * (d / z[j4-3]) |
| } |
| dmin = math.Min(dmin, d) |
| emin = math.Min(emin, z[j4-1]) |
| } |
| } |
| // Unroll last two steps. |
| dnm2 = d |
| dmin2 = dmin |
| j4 = 4*(n0-1) - pp - 1 |
| j4p2 := j4 + 2*pp - 1 |
| z[j4-2] = dnm2 + z[j4p2] |
| if z[j4-2] == 0 { |
| z[j4] = 0 |
| dnm1 = z[j4p2+2] |
| dmin = dnm1 |
| emin = 0 |
| } else if safmin*z[j4p2+2] < z[j4-2] && safmin*z[j4-2] < z[j4p2+2] { |
| tmp := z[j4p2+2] / z[j4-2] |
| z[j4] = z[j4p2] * tmp |
| dnm1 = dnm2 * tmp |
| } else { |
| z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2]) |
| dnm1 = z[j4p2+2] * (dnm2 / z[j4-2]) |
| } |
| dmin = math.Min(dmin, dnm1) |
| dmin1 = dmin |
| j4 += 4 |
| j4p2 = j4 + 2*pp - 1 |
| z[j4-2] = dnm1 + z[j4p2] |
| if z[j4-2] == 0 { |
| z[j4] = 0 |
| dn = z[j4p2+2] |
| dmin = dn |
| emin = 0 |
| } else if safmin*z[j4p2+2] < z[j4-2] && safmin*z[j4-2] < z[j4p2+2] { |
| tmp := z[j4p2+2] / z[j4-2] |
| z[j4] = z[j4p2] * tmp |
| dn = dnm1 * tmp |
| } else { |
| z[j4] = z[j4p2+2] * (z[j4p2] / z[j4-2]) |
| dn = z[j4p2+2] * (dnm1 / z[j4-2]) |
| } |
| dmin = math.Min(dmin, dn) |
| z[j4+2] = dn |
| z[4*(n0+1)-pp-1] = emin |
| return dmin, dmin1, dmin2, dn, dnm1, dnm2 |
| } |
