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// Copyright 2010 The Go Authors.  All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// Software IEEE754 64-bit floating point.
// Only referred to (and thus linked in) by arm port
// and by gotest in this directory.

package runtime

const (
        mantbits64 uint = 52
        expbits64  uint = 11
        bias64          = -1<<(expbits64-1) + 1

        nan64 uint64 = (1<<expbits64-1)<<mantbits64 + 1
        inf64 uint64 = (1<<expbits64 - 1) << mantbits64
        neg64 uint64 = 1 << (expbits64 + mantbits64)

        mantbits32 uint = 23
        expbits32  uint = 8
        bias32          = -1<<(expbits32-1) + 1

        nan32 uint32 = (1<<expbits32-1)<<mantbits32 + 1
        inf32 uint32 = (1<<expbits32 - 1) << mantbits32
        neg32 uint32 = 1 << (expbits32 + mantbits32)
)

func funpack64(f uint64) (sign, mant uint64, exp int, inf, nan bool) {
        sign = f & (1 << (mantbits64 + expbits64))
        mant = f & (1<<mantbits64 - 1)
        exp = int(f>>mantbits64) & (1<<expbits64 - 1)

        switch exp {
        case 1<<expbits64 - 1:
                if mant != 0 {
                        nan = true
                        return
                }
                inf = true
                return

        case 0:
                // denormalized
                if mant != 0 {
                        exp += bias64 + 1
                        for mant < 1<<mantbits64 {
                                mant <<= 1
                                exp--
                        }
                }

        default:
                // add implicit top bit
                mant |= 1 << mantbits64
                exp += bias64
        }
        return
}

func funpack32(f uint32) (sign, mant uint32, exp int, inf, nan bool) {
        sign = f & (1 << (mantbits32 + expbits32))
        mant = f & (1<<mantbits32 - 1)
        exp = int(f>>mantbits32) & (1<<expbits32 - 1)

        switch exp {
        case 1<<expbits32 - 1:
                if mant != 0 {
                        nan = true
                        return
                }
                inf = true
                return

        case 0:
                // denormalized
                if mant != 0 {
                        exp += bias32 + 1
                        for mant < 1<<mantbits32 {
                                mant <<= 1
                                exp--
                        }
                }

        default:
                // add implicit top bit
                mant |= 1 << mantbits32
                exp += bias32
        }
        return
}

func fpack64(sign, mant uint64, exp int, trunc uint64) uint64 {
        mant0, exp0, trunc0 := mant, exp, trunc
        if mant == 0 {
                return sign
        }
        for mant < 1<<mantbits64 {
                mant <<= 1
                exp--
        }
        for mant >= 4<<mantbits64 {
                trunc |= mant & 1
                mant >>= 1
                exp++
        }
        if mant >= 2<<mantbits64 {
                if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
                        mant++
                        if mant >= 4<<mantbits64 {
                                mant >>= 1
                                exp++
                        }
                }
                mant >>= 1
                exp++
        }
        if exp >= 1<<expbits64-1+bias64 {
                return sign ^ inf64
        }
        if exp < bias64+1 {
                if exp < bias64-int(mantbits64) {
                        return sign | 0
                }
                // repeat expecting denormal
                mant, exp, trunc = mant0, exp0, trunc0
                for exp < bias64 {
                        trunc |= mant & 1
                        mant >>= 1
                        exp++
                }
                if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
                        mant++
                }
                mant >>= 1
                exp++
                if mant < 1<<mantbits64 {
                        return sign | mant
                }
        }
        return sign | uint64(exp-bias64)<<mantbits64 | mant&(1<<mantbits64-1)
}

func fpack32(sign, mant uint32, exp int, trunc uint32) uint32 {
        mant0, exp0, trunc0 := mant, exp, trunc
        if mant == 0 {
                return sign
        }
        for mant < 1<<mantbits32 {
                mant <<= 1
                exp--
        }
        for mant >= 4<<mantbits32 {
                trunc |= mant & 1
                mant >>= 1
                exp++
        }
        if mant >= 2<<mantbits32 {
                if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
                        mant++
                        if mant >= 4<<mantbits32 {
                                mant >>= 1
                                exp++
                        }
                }
                mant >>= 1
                exp++
        }
        if exp >= 1<<expbits32-1+bias32 {
                return sign ^ inf32
        }
        if exp < bias32+1 {
                if exp < bias32-int(mantbits32) {
                        return sign | 0
                }
                // repeat expecting denormal
                mant, exp, trunc = mant0, exp0, trunc0
                for exp < bias32 {
                        trunc |= mant & 1
                        mant >>= 1
                        exp++
                }
                if mant&1 != 0 && (trunc != 0 || mant&2 != 0) {
                        mant++
                }
                mant >>= 1
                exp++
                if mant < 1<<mantbits32 {
                        return sign | mant
                }
        }
        return sign | uint32(exp-bias32)<<mantbits32 | mant&(1<<mantbits32-1)
}

func fadd64(f, g uint64) uint64 {
        fs, fm, fe, fi, fn := funpack64(f)
        gs, gm, ge, gi, gn := funpack64(g)

        // Special cases.
        switch {
        case fn || gn: // NaN + x or x + NaN = NaN
                return nan64

        case fi && gi && fs != gs: // +Inf + -Inf or -Inf + +Inf = NaN
                return nan64

        case fi: // ±Inf + g = ±Inf
                return f

        case gi: // f + ±Inf = ±Inf
                return g

        case fm == 0 && gm == 0 && fs != 0 && gs != 0: // -0 + -0 = -0
                return f

        case fm == 0: // 0 + g = g but 0 + -0 = +0
                if gm == 0 {
                        g ^= gs
                }
                return g

        case gm == 0: // f + 0 = f
                return f

        }

        if fe < ge || fe == ge && fm < gm {
                f, g, fs, fm, fe, gs, gm, ge = g, f, gs, gm, ge, fs, fm, fe
        }

        shift := uint(fe - ge)
        fm <<= 2
        gm <<= 2
        trunc := gm & (1<<shift - 1)
        gm >>= shift
        if fs == gs {
                fm += gm
        } else {
                fm -= gm
                if trunc != 0 {
                        fm--
                }
        }
        if fm == 0 {
                fs = 0
        }
        return fpack64(fs, fm, fe-2, trunc)
}

func fsub64(f, g uint64) uint64 {
        return fadd64(f, fneg64(g))
}

func fneg64(f uint64) uint64 {
        return f ^ (1 << (mantbits64 + expbits64))
}

func fmul64(f, g uint64) uint64 {
        fs, fm, fe, fi, fn := funpack64(f)
        gs, gm, ge, gi, gn := funpack64(g)

        // Special cases.
        switch {
        case fn || gn: // NaN * g or f * NaN = NaN
                return nan64

        case fi && gi: // Inf * Inf = Inf (with sign adjusted)
                return f ^ gs

        case fi && gm == 0, fm == 0 && gi: // 0 * Inf = Inf * 0 = NaN
                return nan64

        case fm == 0: // 0 * x = 0 (with sign adjusted)
                return f ^ gs

        case gm == 0: // x * 0 = 0 (with sign adjusted)
                return g ^ fs
        }

        // 53-bit * 53-bit = 107- or 108-bit
        lo, hi := mullu(fm, gm)
        shift := mantbits64 - 1
        trunc := lo & (1<<shift - 1)
        mant := hi<<(64-shift) | lo>>shift
        return fpack64(fs^gs, mant, fe+ge-1, trunc)
}

func fdiv64(f, g uint64) uint64 {
        fs, fm, fe, fi, fn := funpack64(f)
        gs, gm, ge, gi, gn := funpack64(g)

        // Special cases.
        switch {
        case fn || gn: // NaN / g = f / NaN = NaN
                return nan64

        case fi && gi: // ±Inf / ±Inf = NaN
                return nan64

        case !fi && !gi && fm == 0 && gm == 0: // 0 / 0 = NaN
                return nan64

        case fi, !gi && gm == 0: // Inf / g = f / 0 = Inf
                return fs ^ gs ^ inf64

        case gi, fm == 0: // f / Inf = 0 / g = Inf
                return fs ^ gs ^ 0
        }
        _, _, _, _ = fi, fn, gi, gn

        // 53-bit<<54 / 53-bit = 53- or 54-bit.
        shift := mantbits64 + 2
        q, r := divlu(fm>>(64-shift), fm<<shift, gm)
        return fpack64(fs^gs, q, fe-ge-2, r)
}

func f64to32(f uint64) uint32 {
        fs, fm, fe, fi, fn := funpack64(f)
        if fn {
                return nan32
        }
        fs32 := uint32(fs >> 32)
        if fi {
                return fs32 ^ inf32
        }
        const d = mantbits64 - mantbits32 - 1
        return fpack32(fs32, uint32(fm>>d), fe-1, uint32(fm&(1<<d-1)))
}

func f32to64(f uint32) uint64 {
        const d = mantbits64 - mantbits32
        fs, fm, fe, fi, fn := funpack32(f)
        if fn {
                return nan64
        }
        fs64 := uint64(fs) << 32
        if fi {
                return fs64 ^ inf64
        }
        return fpack64(fs64, uint64(fm)<<d, fe, 0)
}

func fcmp64(f, g uint64) (cmp int, isnan bool) {
        fs, fm, _, fi, fn := funpack64(f)
        gs, gm, _, gi, gn := funpack64(g)

        switch {
        case fn, gn: // flag NaN
                return 0, true

        case !fi && !gi && fm == 0 && gm == 0: // ±0 == ±0
                return 0, false

        case fs > gs: // f < 0, g > 0
                return -1, false

        case fs < gs: // f > 0, g < 0
                return +1, false

        // Same sign, not NaN.
        // Can compare encodings directly now.
        // Reverse for sign.
        case fs == 0 && f < g, fs != 0 && f > g:
                return -1, false

        case fs == 0 && f > g, fs != 0 && f < g:
                return +1, false
        }

        // f == g
        return 0, false
}

func f64toint(f uint64) (val int64, ok bool) {
        fs, fm, fe, fi, fn := funpack64(f)

        switch {
        case fi, fn: // NaN
                return 0, false

        case fe < -1: // f < 0.5
                return 0, false

        case fe > 63: // f >= 2^63
                if fs != 0 && fm == 0 { // f == -2^63
                        return -1 << 63, true
                }
                if fs != 0 {
                        return 0, false
                }
                return 0, false
        }

        for fe > int(mantbits64) {
                fe--
                fm <<= 1
        }
        for fe < int(mantbits64) {
                fe++
                fm >>= 1
        }
        val = int64(fm)
        if fs != 0 {
                val = -val
        }
        return val, true
}

func fintto64(val int64) (f uint64) {
        fs := uint64(val) & (1 << 63)
        mant := uint64(val)
        if fs != 0 {
                mant = -mant
        }
        return fpack64(fs, mant, int(mantbits64), 0)
}

// 64x64 -> 128 multiply.
// adapted from hacker's delight.
func mullu(u, v uint64) (lo, hi uint64) {
        const (
                s    = 32
                mask = 1<<s - 1
        )
        u0 := u & mask
        u1 := u >> s
        v0 := v & mask
        v1 := v >> s
        w0 := u0 * v0
        t := u1*v0 + w0>>s
        w1 := t & mask
        w2 := t >> s
        w1 += u0 * v1
        return u * v, u1*v1 + w2 + w1>>s
}

// 128/64 -> 64 quotient, 64 remainder.
// adapted from hacker's delight
func divlu(u1, u0, v uint64) (q, r uint64) {
        const b = 1 << 32

        if u1 >= v {
                return 1<<64 - 1, 1<<64 - 1
        }

        // s = nlz(v); v <<= s
        s := uint(0)
        for v&(1<<63) == 0 {
                s++
                v <<= 1
        }

        vn1 := v >> 32
        vn0 := v & (1<<32 - 1)
        un32 := u1<<s | u0>>(64-s)
        un10 := u0 << s
        un1 := un10 >> 32
        un0 := un10 & (1<<32 - 1)
        q1 := un32 / vn1
        rhat := un32 - q1*vn1

again1:
        if q1 >= b || q1*vn0 > b*rhat+un1 {
                q1--
                rhat += vn1
                if rhat < b {
                        goto again1
                }
        }

        un21 := un32*b + un1 - q1*v
        q0 := un21 / vn1
        rhat = un21 - q0*vn1

again2:
        if q0 >= b || q0*vn0 > b*rhat+un0 {
                q0--
                rhat += vn1
                if rhat < b {
                        goto again2
                }
        }

        return q1*b + q0, (un21*b + un0 - q0*v) >> s
}

// callable from C

func fadd64c(f, g uint64, ret *uint64)            { *ret = fadd64(f, g) }
func fsub64c(f, g uint64, ret *uint64)            { *ret = fsub64(f, g) }
func fmul64c(f, g uint64, ret *uint64)            { *ret = fmul64(f, g) }
func fdiv64c(f, g uint64, ret *uint64)            { *ret = fdiv64(f, g) }
func fneg64c(f uint64, ret *uint64)               { *ret = fneg64(f) }
func f32to64c(f uint32, ret *uint64)              { *ret = f32to64(f) }
func f64to32c(f uint64, ret *uint32)              { *ret = f64to32(f) }
func fcmp64c(f, g uint64, ret *int, retnan *bool) { *ret, *retnan = fcmp64(f, g) }
func fintto64c(val int64, ret *uint64)            { *ret = fintto64(val) }
func f64tointc(f uint64, ret *int64, retok *bool) { *ret, *retok = f64toint(f) }