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📄 abs.go(366 B)
📄 acos_s390x.s(3.73 KB)
📄 acosh.go(1.71 KB)
📄 acosh_s390x.s(4.32 KB)
📄 all_test.go(86.77 KB)
📄 arith_s390x.go(3.73 KB)
📄 arith_s390x_test.go(10.78 KB)
📄 asin.go(1.09 KB)
📄 asin_s390x.s(4.16 KB)
📄 asinh.go(1.92 KB)
📄 asinh_s390x.s(5.74 KB)
📄 atan.go(3.03 KB)
📄 atan2.go(1.52 KB)
📄 atan2_s390x.s(6.93 KB)
📄 atan_s390x.s(3.69 KB)
📄 atanh.go(1.99 KB)
📄 atanh_s390x.s(5.06 KB)
📁 big
📁 bits
📄 bits.go(1.87 KB)
📄 cbrt.go(2.31 KB)
📄 cbrt_s390x.s(4.89 KB)
📁 cmplx
📄 const.go(2.76 KB)
📄 const_test.go(1.29 KB)
📄 copysign.go(396 B)
📄 cosh_s390x.s(5.59 KB)
📄 dim.go(1.87 KB)
📄 dim_amd64.s(1.92 KB)
📄 dim_arm64.s(963 B)
📄 dim_asm.go(344 B)
📄 dim_noasm.go(410 B)
📄 dim_riscv64.s(1.16 KB)
📄 dim_s390x.s(1.97 KB)
📄 erf.go(11.51 KB)
📄 erf_s390x.s(8.5 KB)
📄 erfc_s390x.s(14.4 KB)
📄 erfinv.go(3.37 KB)
📄 example_test.go(3.75 KB)
📄 exp.go(5.38 KB)
📄 exp2_asm.go(252 B)
📄 exp2_noasm.go(284 B)
📄 exp_amd64.go(261 B)
📄 exp_amd64.s(4.24 KB)
📄 exp_arm64.s(5.36 KB)
📄 exp_asm.go(268 B)
📄 exp_noasm.go(302 B)
📄 exp_s390x.s(4.65 KB)
📄 expm1.go(7.91 KB)
📄 expm1_s390x.s(5.29 KB)
📄 export_s390x_test.go(732 B)
📄 export_test.go(357 B)
📄 floor.go(3.29 KB)
📄 floor_386.s(1.47 KB)
📄 floor_amd64.s(2 KB)
📄 floor_arm64.s(573 B)
📄 floor_asm.go(431 B)
📄 floor_noasm.go(531 B)
📄 floor_ppc64x.s(499 B)
📄 floor_s390x.s(579 B)
📄 floor_wasm.s(459 B)
📄 fma.go(4.61 KB)
📄 frexp.go(929 B)
📄 gamma.go(5.53 KB)
📄 huge_test.go(2.91 KB)
📄 hypot.go(850 B)
📄 hypot_386.s(1.81 KB)
📄 hypot_amd64.s(1.05 KB)
📄 hypot_asm.go(264 B)
📄 hypot_noasm.go(297 B)
📄 j0.go(13.6 KB)
📄 j1.go(13.3 KB)
📄 jn.go(7.18 KB)
📄 ldexp.go(1.05 KB)
📄 lgamma.go(11.03 KB)
📄 log.go(3.86 KB)
📄 log10.go(873 B)
📄 log10_s390x.s(4.73 KB)
📄 log1p.go(6.34 KB)
📄 log1p_s390x.s(5.15 KB)
📄 log_amd64.s(3.66 KB)
📄 log_asm.go(259 B)
📄 log_s390x.s(4.31 KB)
📄 log_stub.go(292 B)
📄 logb.go(1021 B)
📄 mod.go(903 B)
📄 modf.go(913 B)
📄 modf_arm64.s(447 B)
📄 modf_asm.go(292 B)
📄 modf_noasm.go(326 B)
📄 modf_ppc64x.s(416 B)
📄 nextafter.go(1.21 KB)
📄 pow.go(3.65 KB)
📄 pow10.go(1.24 KB)
📄 pow_s390x.s(16.27 KB)
📁 rand
📄 remainder.go(2.04 KB)
📄 signbit.go(302 B)
📄 sin.go(6.35 KB)
📄 sin_s390x.s(8.57 KB)
📄 sincos.go(1.76 KB)
📄 sinh.go(1.69 KB)
📄 sinh_s390x.s(5.98 KB)
📄 sqrt.go(4.75 KB)
📄 stubs.go(2.57 KB)
📄 stubs_s390x.s(12.38 KB)
📄 tan.go(3.68 KB)
📄 tan_s390x.s(2.72 KB)
📄 tanh.go(2.66 KB)
📄 tanh_s390x.s(4.57 KB)
📄 trig_reduce.go(3.34 KB)
📄 unsafe.go(1.27 KB)

Editing: fma.go

// Copyright 2019 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.

package math

import "math/bits"

func zero(x uint64) uint64 {
	if x == 0 {
		return 1
	}
	return 0
	// branchless:
	// return ((x>>1 | x&1) - 1) >> 63
}

func nonzero(x uint64) uint64 {
	if x != 0 {
		return 1
	}
	return 0
	// branchless:
	// return 1 - ((x>>1|x&1)-1)>>63
}

func shl(u1, u2 uint64, n uint) (r1, r2 uint64) {
	r1 = u1<<n | u2>>(64-n) | u2<<(n-64)
	r2 = u2 << n
	return
}

func shr(u1, u2 uint64, n uint) (r1, r2 uint64) {
	r2 = u2>>n | u1<<(64-n) | u1>>(n-64)
	r1 = u1 >> n
	return
}

// shrcompress compresses the bottom n+1 bits of the two-word
// value into a single bit. the result is equal to the value
// shifted to the right by n, except the result's 0th bit is
// set to the bitwise OR of the bottom n+1 bits.
func shrcompress(u1, u2 uint64, n uint) (r1, r2 uint64) {
	// TODO: Performance here is really sensitive to the
	// order/placement of these branches. n == 0 is common
	// enough to be in the fast path. Perhaps more measurement
	// needs to be done to find the optimal order/placement?
	switch {
	case n == 0:
		return u1, u2
	case n == 64:
		return 0, u1 | nonzero(u2)
	case n >= 128:
		return 0, nonzero(u1 | u2)
	case n < 64:
		r1, r2 = shr(u1, u2, n)
		r2 |= nonzero(u2 & (1<<n - 1))
	case n < 128:
		r1, r2 = shr(u1, u2, n)
		r2 |= nonzero(u1&(1<<(n-64)-1) | u2)
	}
	return
}

func lz(u1, u2 uint64) (l int32) {
	l = int32(bits.LeadingZeros64(u1))
	if l == 64 {
		l += int32(bits.LeadingZeros64(u2))
	}
	return l
}

// split splits b into sign, biased exponent, and mantissa.
// It adds the implicit 1 bit to the mantissa for normal values,
// and normalizes subnormal values.
func split(b uint64) (sign uint32, exp int32, mantissa uint64) {
	sign = uint32(b >> 63)
	exp = int32(b>>52) & mask
	mantissa = b & fracMask

if exp == 0 {
		// Normalize value if subnormal.
		shift := uint(bits.LeadingZeros64(mantissa) - 11)
		mantissa <<= shift
		exp = 1 - int32(shift)
	} else {
		// Add implicit 1 bit
		mantissa |= 1 << 52
	}
	return
}

// FMA returns x * y + z, computed with only one rounding.
// (That is, FMA returns the fused multiply-add of x, y, and z.)
func FMA(x, y, z float64) float64 {
	bx, by, bz := Float64bits(x), Float64bits(y), Float64bits(z)

// Inf or NaN or zero involved. At most one rounding will occur.
	if x == 0.0 || y == 0.0 || z == 0.0 || bx&uvinf == uvinf || by&uvinf == uvinf {
		return x*y + z
	}
	// Handle non-finite z separately. Evaluating x*y+z where
	// x and y are finite, but z is infinite, should always result in z.
	if bz&uvinf == uvinf {
		return z
	}

// Inputs are (sub)normal.
	// Split x, y, z into sign, exponent, mantissa.
	xs, xe, xm := split(bx)
	ys, ye, ym := split(by)
	zs, ze, zm := split(bz)

// Compute product p = x*y as sign, exponent, two-word mantissa.
	// Start with exponent. "is normal" bit isn't subtracted yet.
	pe := xe + ye - bias + 1

// pm1:pm2 is the double-word mantissa for the product p.
	// Shift left to leave top bit in product. Effectively
	// shifts the 106-bit product to the left by 21.
	pm1, pm2 := bits.Mul64(xm<<10, ym<<11)
	zm1, zm2 := zm<<10, uint64(0)
	ps := xs ^ ys // product sign

// normalize to 62nd bit
	is62zero := uint((^pm1 >> 62) & 1)
	pm1, pm2 = shl(pm1, pm2, is62zero)
	pe -= int32(is62zero)

// Swap addition operands so |p| >= |z|
	if pe < ze || pe == ze && pm1 < zm1 {
		ps, pe, pm1, pm2, zs, ze, zm1, zm2 = zs, ze, zm1, zm2, ps, pe, pm1, pm2
	}

// Special case: if p == -z the result is always +0 since neither operand is zero.
	if ps != zs && pe == ze && pm1 == zm1 && pm2 == zm2 {
		return 0
	}

// Align significands
	zm1, zm2 = shrcompress(zm1, zm2, uint(pe-ze))

// Compute resulting significands, normalizing if necessary.
	var m, c uint64
	if ps == zs {
		// Adding (pm1:pm2) + (zm1:zm2)
		pm2, c = bits.Add64(pm2, zm2, 0)
		pm1, _ = bits.Add64(pm1, zm1, c)
		pe -= int32(^pm1 >> 63)
		pm1, m = shrcompress(pm1, pm2, uint(64+pm1>>63))
	} else {
		// Subtracting (pm1:pm2) - (zm1:zm2)
		// TODO: should we special-case cancellation?
		pm2, c = bits.Sub64(pm2, zm2, 0)
		pm1, _ = bits.Sub64(pm1, zm1, c)
		nz := lz(pm1, pm2)
		pe -= nz
		m, pm2 = shl(pm1, pm2, uint(nz-1))
		m |= nonzero(pm2)
	}

// Round and break ties to even
	if pe > 1022+bias || pe == 1022+bias && (m+1<<9)>>63 == 1 {
		// rounded value overflows exponent range
		return Float64frombits(uint64(ps)<<63 | uvinf)
	}
	if pe < 0 {
		n := uint(-pe)
		m = m>>n | nonzero(m&(1<<n-1))
		pe = 0
	}
	m = ((m + 1<<9) >> 10) & ^zero((m&(1<<10-1))^1<<9)
	pe &= -int32(nonzero(m))
	return Float64frombits(uint64(ps)<<63 + uint64(pe)<<52 + m)
}

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Editing: fma.go

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